The stellar mass distribution in early-type disk galaxies surface photometry and bulge-disk

科普知识英语作文八百字The Enigmatic World of Black Holes: Exploring the Cosmic Colossi.In the vast and uncharted expanses of our universe reside enigmatic celestial entities that captivate the imaginations of astrophysicists and laypeople alike: black holes. These enigmatic cosmic giants, characterized bytheir immense gravitational pull and enigmatic nature, have long been a subject of scientific fascination and speculation.Birth and Formation.The genesis of a black hole is a cataclysmic event the gravitational collapse of a massive star. When a star exhausts its nuclear fuel, its core undergoes a gravitational implosion, resulting in an immense explosion known as a supernova. If the star's mass surpasses acritical threshold, known as the Chandrasekhar limit, thesupernova remnants collapse further under their own gravity, forming a singularity a point of infinite density and zero volume. This singularity is encased within an invisible boundary called an event horizon, beyond which light itself cannot escape the gravitational pull.Size and Mass.Black holes vary greatly in size and mass. Stellar-mass black holes, formed from the collapse of individual stars, typically possess masses ranging from several to tens of solar masses. Supermassive black holes, on the other hand, are colossal entities residing at the heart of most galaxies, with masses that can exceed billions of solar masses.Gravitational Pull.The most defining characteristic of black holes istheir immense gravitational pull. The gravitational field within the event horizon is so intense that nothing, not even light, can escape its clutches. Matter and energy thatventure too close are inexorably drawn into the singularity, where they are crushed and compressed to unthinkable densities.Singularity and Hawking Radiation.At the center of a black hole lies the singularity, a region of infinite density and zero volume. It represents the ultimate point of gravitational collapse, and its properties defy our current understanding of physics. In 1974, renowned physicist Stephen Hawking proposed the concept of Hawking radiation, suggesting that quantumeffects allow black holes to emit faint radiation due tothe gravitational interactions at their event horizons.Event Horizon.The event horizon, a boundary around the black hole, marks the point of no return. Once matter crosses the event horizon, it is irrevocably trapped within the black hole's gravitational grasp, forever lost to the outside universe. The event horizon itself is a theoretical surface that isinvisible to observers, but its presence can be inferred from gravitational effects on surrounding matter.Accretion Disks and Jet Streams.As matter falls towards a black hole, it forms a swirling disk of gas and dust called an accretion disk. This disk emits intense radiation as the infalling matter is heated and compressed. Some black holes also exhibit powerful jets of matter that are expelled from their poles at near-light speeds. These jets are thought to be generated by the magnetic fields that permeate the black hole's environment.Role in Galaxies.Supermassive black holes are believed to play a crucial role in the formation and evolution of galaxies. Their gravitational influence shapes the distribution of stars and gas within galaxies, and they may act as engines for the activity observed in galactic nuclei. By studying the properties and behavior of black holes in galaxies,astrophysicists can gain insights into the fundamental processes that govern the universe.Observing Black Holes.Directly observing black holes is impossible due to their inherent darkness and the inability of light to escape their event horizons. However, scientists can study them indirectly by observing their effects on surrounding matter. By analyzing the motion of stars and gas near black holes, astronomers can infer their presence and estimate their masses. The first direct image of a black hole, known as M87, was captured in 2019 by the Event Horizon Telescope (EHT), an international collaboration of radio telescopes.Conclusion.Black holes remain enigmatic cosmic entities that continue to captivate and intrigue scientists and laypeople alike. Their immense gravitational pull, enigmatic nature, and potential role in shaping the universe make them fascinating subjects of ongoing research. As ourunderstanding of black holes deepens, we may unlock further insights into the fundamental laws that govern our universe and the enigmatic nature of space and time.。

近邻恒星形成星系的主序关系李力;郝彩娜;郭蕊【摘要】为了验证现有孔径改正方法的有效性,基于一个具有星系总体Hα、Hβ发射线流量和紫外(UV)、远红外(FIR)多波段数据的近邻(＜150 Mpc)星系样本,研究不受孔径效应影响的Hα作为恒星形成率指示剂的恒星形成主序关系,并对Hα和远紫外(FUV)分别作为恒星形成率探针时的主序关系进行对比.结果表明:不受孔径效应影响的Hα作为恒星形成率指示剂的主序关系与已有的利用孔径改正所得主序关系一致,表明通常采用的孔径改正方法可以还原星系整体Hα流量.此外,利用总红外(TIR)与FUV之比以及FUV-NUV颜色对FUV流量进行尘埃消光改正所得FUV 作为恒星形成率示踪物的主序关系一致,表明FUV-NUV颜色对FUV流量进行消光改正没有引入更大的误差.【期刊名称】《天津师范大学学报（自然科学版）》【年(卷),期】2018(038)003【总页数】7页(P14-20)【关键词】近邻恒星形成星系;恒星形成率;孔径效应【作者】李力;郝彩娜;郭蕊【作者单位】天津师范大学天体物理中心,天津300387;天津师范大学天体物理中心,天津300387;天津师范大学天体物理中心,天津300387【正文语种】中文【中图分类】P157通过对各类深度多波段巡天项目所释放的观测数据进行大样本统计分析可知，星系的颜色和形态等参数均呈现出双峰分布[1-2]，据此可以把星系分为恒星形成星系和宁静星系两大类.相比于宁静星系，恒星形成星系是一类富含气体、正在进行恒星形成且包含大量年轻恒星的星系.恒星形成星系的恒星形成率SFR（star formation rate）与恒星质量M*（stellar mass）具有紧密的相关关系，称为恒星形成星系的主序关系（main sequence）[3].这一恒星形成的主序关系从近邻宇宙[4-6]一直到z～7的高红移宇宙[7-15]都存在，因此主序关系已作为一项基本关系应用于星系形成与演化的模型检验中[9，16]，对理解星系形成与演化的物理过程具有极为重要的意义.主序关系在对数空间下表示为具有一定弥散的线性关系lgSFR=algM*+b.描述主序关系的参数主要有斜率、截距和弥散，这些参数反映了星系形成与演化的物理[17-19]，并有随红移演化的趋势.主序关系斜率表示不同恒星质量的星系具有不同的比恒星形成率（specific SFR=SFR/mass）.截距是主序关系在纵轴上的截距，反映了宇宙整体恒星形成活动的强度.在红移0～2范围内，主序关系的截距增加了近30倍[5]表明z=2时的宇宙恒星形成活动更剧烈，此结论与标准宇宙学模型描述的宇宙恒星形成历史相吻合.除了观测及测量方法造成的系统误差外，主序关系的本征弥散（σMS）与星系的气体质量分数[20-21]、星系所处环境[22-23]、星系间的相互作用和并合过程[24-25]以及星系形态[26-27]等有关，其值一般为±0.3 dex，且随红移的变化不明显.主序关系参数的确定受到样本选择效应、SFR 探针的选取以及尘埃消光改正方法等因素的影响，因此不同研究可能得出不同的主序关系参数[28].由于近邻宇宙观测数据具有易获得性，近十几年来有关近邻星系恒星形成主序的研究取得了一定进展.2004年，Brinchmann等[5]对斯隆数字巡天（Sloan digitalsky survey，SDSS）观测的数十万近邻星系进行研究，试图给出星系各参数间的关系，其中包括星系SFR与M*的关系.Noeske等[3]研究了AEGIS（all wavelength extended groth strip international survey）中红移范围为0.2～0.7的2 905个恒星形成的星系，用Hα、紫外（UV）和红外（IR）数据联合探测星系的SFR，利用星系光谱能量分布（SED）拟合光学/红外光谱得到星系恒星质量 M*，给出 SFR 和 M*的关系为 lgSFR=（0.67±0.08）lgM*-（6.19±0.78），并第1次将其称为主序关系.同年的Elbaz等[4]使用SDSS第4次释放的数据（SDSS DR4），以多波段测光数据进行SED拟合，计算星系M*，并以Hα作为SFR探针，得到红移范围为0.015～0.100的近邻主序关系，其斜率为0.77.Salim 等[6]以GALEX的UV测光数据示踪GALEX和SDSS DR4中红移范围为0.005～0.200的105个近邻恒星形成星系的SFR，所得主序关系斜率为0.65，弥散为0.3 dex.Whitaker等[29]以UV+IR示踪SFR得到斜率为0.67、弥散为0.34 dex 的z=0的主序关系.Guo等[30]选择SDSS DR7的152 137个恒星形成星系，分别用Hα发射线和SED拟合的方法获得星系的SFR和M*，拟合所得主序关系斜率为1.02，弥散为0.3 dex.以上研究均采用UV或Hα发射线作为SFR探针.2种探针在示踪恒星形成率方面各有利弊[31]，Hα比UV连续谱示踪的恒星形成时标更短，更能体现正在进行的恒星形成活动强度，但获取整个星系的Hα和用于消光改正的Hβ流量会耗费大量望远镜时间.目前已有的基于Hα进行的主序关系研究主要利用2"～3"的小孔径光谱观测数据，然后通过孔径改正得到总流量.孔径改正主要基于r波段宽波段轮廓与Hα发射线轮廓近似一致的假设[32]，但这一假设对有些星系可能并不成立.此外，对UV和Hα进行尘埃消光改正的方法也不相同.这些均可能造成由UV和Hα得到的主序关系不同.本研究为了解决这些问题，选取同时具有Hα、Hβ发射线和UV连续谱数据的星系样本，用以比较这2种SFR探针对主序关系参数造成的影响，同时为了避免引入孔径改正误差，星系样本来自积分光谱巡天.本研究SFR和M*的计算采用Kroupa初始质量函数（initial mass function，IMF），宇宙学参数为H0=70km·s-1·Mpc-1、Ωm=0.3和ΩΛ=0.7.1 样本选择和数据处理1.1 样本选择1.1.1 Hα样本本研究样本选自文献[33]中的近邻星系样本.文献[33]对417个近邻（＜150 Mpc）星系进行了积分光谱测光巡天，光谱波长为360～390 nm.该巡天使用文献[34]中的drift-scanning技术，用一个2.5"×200"的长缝在星系所在的矩形区域来回移动，移动范围最暗达到星系面亮度为B25mag/arcsec2处.图1为样本星系NGC1084在g波段的光学图像，其中的矩形孔径就是drift-scanning扫描的星系范围，由文献[33]中给出的扫描参数确定.通过这项技术所得星系积分光谱包含星系发射线流量的80%，甚至100%，避免了孔径改正带来的误差.文献[33]同时还提供了这些星系的25、60和100 μm流量.图1 样本星系NGC1084在g波段的光学图像Fig.1 The g band image ofNGC1084本研究选取文献[33]中近邻星系样本中的276个恒星形成星系作为样本，研究近邻恒星形成星系的主序关系.筛选恒星形成星系的条件包括能探测到Hα发射线和红外波段流量，且Hβ发射线信噪比大于15（S/N＞15）[35].由于计算星系恒星形成率的Hα流量来自矩形孔径内部，为了保证用于计算星系恒星质量的g和r波段流量也来自同一区域，使用SDSS DR12观测的星系图像对星系做矩形孔径测光，用以计算星系恒星质量.SDSS是一个覆盖全天1/4的大型巡天项目，其上搭载的2.5 m光学望远镜可以获取天体u、g、r、i和z共5个波段的光学图像.首先，将这276个星系的赤经和赤纬与SDSS DR12测光表交叉，得到219个星系，下载它们的g波段和r波段图像，再根据文献[33]中给出的drift scanning参数计算drift scanning扫描所得星系矩形孔径4个顶点在图像上的坐标.计算发现有些星系的孔径坐标超出图像范围，表明星系不能完整显示在SDSS图像上，把这些星系从样本中剔除，则g波段和r波段均对星系有完整覆盖的样本数为187个.此外，本研究限制了星系的恒星质量在108.5M⊙以上，最终得到星系样本数为155.这155个星系包含Hα、Hβ发射线流量及25、60和100 μm红外单色光流量信息.1.1.2 UV样本Hao等[36]利用文献[33]中的星系样本与GALEX空间望远镜第4次释放数据GR4（GALEX Data Release 4）交叉得到97个星系的远紫外（FUV，中心波长152.8 nm）和近紫外（NUV，中心波长227.1 nm）流量，将这97个星系与本研究的Hα样本交叉，得到包含FUV和NUV流量的55个星系的子样本.1.2 数据处理1.2.1 光学波段图像孔径测光使用天文数据处理软件IRAF（image reduction and analysis facility）中的polyphot命令对155个星系进行矩形孔径测光.SDSS DR12提供的星系图像已经减过天光背景，因此可以直接对目标源进行测光.通过孔径测光得到这些星系在g 波段和r波段的流量Fν，并把流量转换成AB星等系统下的视星等根据文献[33]给出的星系光度距离D，将视星等转换成绝对星等计算出视星等和绝对星等后，对其进行银河系消光改正，消光值来自SDSS DR12.1.2.2 星系的恒星质量目前应用最广泛的获取星系恒星质量的方法是根据对SED的拟合模型得到星系恒星质量[37].但这一方法要求星系具有多波段测光数据.Bell等[38]指出，拟合 6个（SDSS的 u、g、r、i、z波段和 2MASS的 K 波段）波段数据所得星系恒星质量与只用SDSS的g、r两波段所得星系恒星质量具有高度一致性，所以可用两波段光学颜色计算星系的M*.本研究采用文献[38]中由g-r颜色定标的计算星系M*的公式式（3）中：M*/M⊙为以太阳质量为单位的星系的恒星质量；Mr，AB为 AB 星等系统下 r波段的绝对星等；（g-r）AB为AB星等系统下星系g波段和r波段的视星等之差，即g-r颜色；ar和br的取值分别为-0.306和1.097；-0.15代表恒星质量的计算采用Kroupa IMF.1.2.3 星系的恒星形成率以Hα发射线流量作为恒星形成率探针，首先用巴尔末减缩原理对Hα观测流量做消光改正.定义由尘埃红化引起的色余[39]式（4）中：（fHα/fHβ）obs为观测到的巴尔末线强比；（fHα /fHβ）int为本征巴尔末线强比；kλ≡Aλ/E（B-V）为消光曲线；kHα和kHβ分别为kλ在656.3 nm和486.1 nm处的值，采用文献[40]给出的消光曲线，kHα=2.519，kHβ=3.663.对于HII区，可近似合理假设case B（光学厚）情况，在温度T=104K和电子密度为Ne=104cm-3物理条件下，（fHα/fHβ）int=2.86[41]. Hα处的尘埃消光值为改正后的真实流量和光度分别为再由Kroupa IMF下恒星形成率与Hα光度的关系，计算得到星系的SFR[35]对于UV子样本，除去用Hα流量计算的SFR外，采用FUV流量计算其SFR.在计算SFR前，要对观测所得FUV光度进行尘埃消光改正.Hao等[36]给出了2种估计尘埃消光的方法：一种基于能量守恒原理，利用TIR（total infrared）与FUV 的光度之比；另一种则利用FUV-NUV颜色，即FUV和NUV波段的星等差.本研究分别利用这2种方法对FUV光度进行消光改正，并对结果进行比较.总红外光度（total infrared luminosity，LTIR）改正FUV光度的经验公式为式（9）中：LTIR可根据文献[42]由 25、60 和100 μm 的红外单色光流量估计得出，式（10）中：[ζ1，ζ2，ζ3]=[2.403，-0.2454，1.6381]，ν和Lν分别为相应的单色红外光的频率和光度.文献[36]中还给出了用FUV-NUV颜色计算尘埃消光的经验关系再由式（6）和式（7）计算改正后的真实流量及光度.根据文献[36]中给出的用FUV光度计算所得SFR的系数，可知2 结果与讨论2.1 Hα作为恒星形成率探针的主序关系（MSHα）以用巴尔末减缩法做尘埃消光改正后的星系总Hα流量示踪SFR，bisector方法拟合得到图2为本研究与其他近邻恒星形成星系研究工作测量所得MSHα的比较图，其中黑色点为本研究Hα样本星系在主序关系图中的位置，黑色实线是用bisector拟合的MSHα，虚线为本研究1σ弥散，红色实线为文献[30]拟合所得恒星形成星系MSHα，蓝色实线为文献[43]所得MSHα研究结果.文献[30]和文献[43]的研究结果均已转换至与本研究相同的IMF和宇宙学参数下.本研究拟合主序关系的样本数为155，主序关系斜率为1.130，与文献[30]给出的1.020±0.001和文献[43]的0.935 ±0.001一致.本研究的主序关系在3σ clipping后的1σ弥散为0.36dex，如图2中虚线所示，高于其他研究结果（～0.3 dex），这可能是本研究星系样本小造成的.图2 近邻恒星形成星系MSHα测量结果比较Fig.2 Comparison of works of nearby star-forming galaxies MSHα值得注意的是，文献[30]采用文献[32]的孔径改正方法改正Hα光度，而文献[43]是把文献[44]通过CALIFA观测的165个近邻星系积分光谱所得孔径改正经验关系应用于SDSS Hα的孔径改正.由图2可以看出，此二项研究所得主序关系在本研究MSHα的1σ之内，表明现有的孔径改正方法可以较好地还原星系总Hα光度.2.2 FUV作为恒星形成率探针的主序关系（MSFUV）本研究分别用LTIR和FUV-NUV改正子样本的FUV光度，拟合得到式（14）中：IRX为TIR与观测所得FUV光度之比[36].图3为MSFUV,IRX和MSFUV,FUV-NUV的拟合图.图3 MSFUV，IRX 和 MSFUV，FUV-NUV 的比较Fig.3 Comparison between MSFUV，IRXand MSFUV，FUV-NUV根据文献[36]的研究结果可知，用FUV-NUV颜色改正UV光度会受到恒星形成历史等星系性质的影响，尘埃消光改正的不确定性比红外改正的大2.5倍.整体来说，用FUV-NUV颜色改正UV消光不是理想的尘埃消光改正方法.但由图3可知，MSFUV,FUV-NUV与MSFUV,IRX斜率差别小于1σ，两者弥散基本相同，截距差别略大于1σ，并未体现出FUV-NUV在尘埃消光改正方面的明显不足.由于用FUV-NUV改正UV光度不需要红外数据，因此缺乏红外数据的高红移主序关系研究可以采用FUV-NUV颜色改正尘埃消光.值得注意的是UV样本星系的样本数更少，但主序关系的弥散却比Hα样本略小.为了研究不同SFR探针对主序关系的影响，对UV子样本采用Hα示踪的SFR拟合主序关系UV子样本的MSHα拟合图如图4所示.图4中斜率和截距与相同UV子样本的MSFUV,IRX结果一致，弥散介于MSFUV,IRX和总样本MSHα之间.图4 UV子样本的MSHαFig.4 MSHαof UV subsample在高红移（1.37＜z＜2.61）主序关系研究中，Shivaei等[45]对比了1 000个恒星形成星系的MSHα和MSUV，给出MSHα和MSUV的本征弥散分别为0.36 dex和0.30 dex.对于相同星系样本，这2种SFR探针示踪不同的恒星形成时标，因此基于UV和Hα得到的SFR或MS具有不同的弥散.星系形成模拟结果认为，对于具有典型并合历史的大质量星系（z=0，Mhalo～1012M⊙），长恒星形成时标（100 Myr）下的SFR弥散比短恒星形成时标（10 Myr）下的小 0.03～0.10 dex[46-47].本研究中，相同样本的MSUV弥散比MSHα小0.02 dex，示踪不同恒星形成时标的2种SFR探针对主序关系弥散的影响不明显.图5为本研究MSFUV,IRX与其他近邻恒星形成星系研究工作测量所得MSUV的比较图，图中黑色点为本研究UV样本星系在主序关系图中的位置，实线为用bisector方法拟合的MSHα，虚线为本研究的1σ弥散，红线和蓝线分别为文献[6]和文献[29]用y vs.x方法拟合的恒星形成星系MSHα，研究结果均已转换至与本研究相同的IMF和宇宙学参数下.图5 近邻恒星形成星系MSUV测量结果比较Fig.5 Comparison of works of nearby star-forming galaxies MSUV本研究主序关系斜率为1.07，高于文献[6]的0.65和文献[29]的0.7.主序关系1σ弥散为0.32 dex，与文献[6]的0.3 dex和文献[29]的0.34 dex一致.本研究的MSUV斜率明显高于文献[6]和文献[29]，这主要是由于主序关系拟合方法不同造成的[45].值得注意的是，本研究的MSUV与MSHα结果一致，而文献[45]对红移1.37～2.61的恒星形成星系的研究也发现MSUV与MSHα基本一致.3 结论本研究将文献[33]中的276个近邻恒星形成星系与SDSSDR12交叉，限制星系的恒星质量在108.5M⊙以上，得到155个近邻恒星形成星系.用文献[33]提供的星系总Hα和Hβ流量计算消光改正后的星系恒星形成率，用SDSS DR12观测的星系在g、r波段的图像做孔径测光计算星系恒星质量，得到主序关系lgSFRHα=（1.13±0.036）lg（M*/M⊙）-（11.14±0.358），与文献[30]和文献[43]的研究结果相符，弥散为0.36 dex，略大于典型主序关系弥散（～0.3 dex）.此外，本研究将Hα星系样本与文献[36]中的97个星系交叉，得到55个既有Hα总流量又有紫外观测数据的星系子样本，由GALEX DR4观测的星系FUV和NUV 波段数据以及IRAS红外波段数据计算星系恒星形成率，得到以下结果：（1）对样本数为55的紫外子样本，分别用IRX和FUV-NUV对星系SFR作尘埃消光改正，得到主序关系 lgSFRFUV,IRX=（1.07±0.07）lg（M*/M⊙）-（10.47±0.66）和 lgSFRFUV,FUV-NUV=（0.99±0.06）lg（M*/M⊙）-（9.66±0.60），弥散分别为0.32和0.31 dex.FUV-NUV作尘埃消光所得主序关系未见明显不足.因此，对于缺乏红外数据的高红移主序关系研究，使用FUV-NUV颜色改正尘埃消光可能不会引入更大弥散.（2）对紫外子样本以Hα作为SFR探针的主序关系lgSFRHα =（1.08±0.07）lg（M*/M⊙）－（10.59±0.74），弥散为0.34 dex，与UV子样本的MSFUV,IRX 一致.【相关文献】[1]STRATEVA I，KNAPP G R，NARAYANAN V K，et al.Color separation of galaxy types in the Sloan digital sky survey imaging data[J].Astronomical Journal，2001，122（4）：1861-1874.[2]BALDRY I K，GLAZEBROOK K，BRINKMANN J，et al.Quantifying the bimodal color-magnitude distribution of galaxies[J].Astrophysical Journal，2004，600（2）：681-694. 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a r X i v :a s t r o -p h /9907364v 1 26 J u l 1999FORMATION OF LOW MASS STARS IN ELLIPTICAL GALAXYCOOLING FLOWSWilliam G.Mathews 2and Fabrizio Brighenti 2,32University of California Observatories/Lick Observatory,Board of Studies in Astronomy and Astrophysics,University of California,Santa Cruz,CA95064mathews@3Dipartimento di Astronomia,Universit`a di Bologna,viaZamboni 33,Bologna 40126,Italy brighenti@astbo3.bo.astro.itAbstractThermal X-ray emission from cooling flows in ellip-tical galaxies indicates that ∼1M ⊙of hot (T ∼107K)interstellar gas cools each year,accumulating ∼1010M ⊙over a Hubble time.Paradoxically,optical and radio frequency emission from the cooled gas is lacking,indicating that less than ∼10−3of the cooled gas remains.Many have speculated that the cooled gas has formed into relatively invisible low mass stars,particularly in the context of massive cooling flows in galaxy clusters.We focus here on cooling flows in el-liptical galaxies like NGC 4472where the cooled gas is made visible in emission lines from HII regions ionized and heated (T HII ∼104K)by stellar ultraviolet ra-diation.The low filling factor of HII gas requires that the hot gas cools at ∼106cooling sites within several kpc of the galactic center.HII mass slowly increases at each site at ∼10−6M ⊙yr −1until a neutral core develops.Neutral cores are heated (T HI ∼15K)and ionized (x ∼10−6)by thermal X-rays from the entire interstellar cooling flow.We show that the maximum mass of spherical HI cores that become gravitation-ally unstable is only ∼2M ⊙.No star can exceed this mass and fragmentation of collapsing cores produces stars of even lower mass.By this means we establish with some confidence that the hypothesis of low mass star formation is indeed correct –the IMF is bottom heavy,but may be optically luminous.Slightly more massive stars <∼4.5M ⊙can form near the effective ra-dius (r =8.57kpc in NGC 4472)if sufficient masses of interstellar gas cool there,producing a luminous pop-ulation of intermediate mass stars perhaps with radial orbits that may contribute to the stellar H βindex.The degree of ionization in gravitationally collapsing cores is sufficiently low to allow magnetic fields to dis-connect by ambipolar diffusion.Low mass star forma-tion is very efficient,involving ∼106M ⊙of galactic cold gas at any time,in agreement with observed up-per limits on cold gas mass.We discuss the cooling region surrounding a typical cooling site and show that the total X-ray absorption in cold and cooling gas is much less that that indicated by recent X-ray ing a mass dropout scheme consis-tent with X-ray observations and dynamical mass to light ratios,we plot the global H βsurface brightness profile in NGC 4472and compare it with the smaller contribution from HII gas recently ejected from red giant stars.The lifetime of cooled gas at each cooling site,∼105yrs,is too short to permit dust formation and perhaps also gas phase formation of molecules.Subject headings:galaxies:elliptical and lenticular –stars:formation –galaxies:cooling flows –galaxies:interstellar medium –X-rays:galaxies1.INTRODUCTION AND OVER VIEWStrong X-ray emission from luminous elliptical galaxies is clear evidence that the hot interstellar gas they contain is losing energy.Throughout most of the galactic volume,this loss of energy does not result in lower temperatures since the gas is continuously re-heated by compression in the galactic gravitational potential as it slowly moves inward.In this sense the galactic “cooling flow”is a misnomer.Ultimately,however,in the central regions of the flow the gas density becomes large enough for radiative losses to overwhelm dynamical compression and the gas cools catastrophically.For a typical galactic cooling rate,∼1M ⊙per year,the total amount of gas that cools in a massive elliptical over a Hubble time is large,several 1010M ⊙,a few percent of the total stellar mass.Remarkably,the amount of cold gas observed in el-lipticals,either in atomic or molecular form,is many orders of magnitude less than 1010M ⊙(Bregman,Hogg &Roberts 1992).The mass of central black holes in bright ellipticals is also relatively small,typi-cally less than a few 109M ⊙(Magorrian et al.1998),so the cooled gas cannot be in the holes.Soft X-ray absorption has been observed in some galactic cool-ing flows,indicating masses of cold gas comparable to the predicted value,but the quantitative significance or reality of this absorption is unclear at present.In addition to cold gas deposited by cooling flows,it is possible that additional cold,dusty gas is oc-casionally delivered to the centers of ellipticals as aresult of merging with gas-rich companion galaxies. While this is plausible for some gas-rich ellipticals having dusty clouds or lanes,if merging were an im-portant source of cold gas for all massive ellipticals, the merging rate would need to be carefully regulated in order to maintain the small amount of cold gas observed in normal ellipticals.For many years the standard theoretical explana-tion for this shortage of cooled gas is that it has been consumed in forming low mass stars(e.g.Fabian, Nulsen&Canizares1982;Thomas1986;Cowie& Binney1988;Ferland,Fabian,&Johnstone1994). Such young stars must have low masses since neither luminous OB stars nor Type II supernovae have been observed in normal ellipticals.Explaining the disap-pearance of cooled gas by invoking the poorly under-stood physics of star formation may seem contrived and the low stellar mass hypothesis has led to some ridicule.The fate of cooled gas in coolingflows associated with clusters of galaxies has received most of the ob-servational and theoretical attention because of the spectacularly large inferred mass deposition rates,˙M>∼100M⊙yr−1(Fabian1994).In addition to low mass stars,the apparent soft X-ray intrinsic ab-sorption of N∼1021cm−2indicates that∼1010M⊙of cold gas lies within∼100kpc of the cluster cores. Although enormous,this amount of gas would still be only a few percent of the total cooled gas based on the estimated˙M,so low mass stars are still the preferred endstate for most of the cooled cluster gas (Allen&Fabian1997).However,as with elliptical galaxies,this amount of cold gas should in general be detectable in HI or CO emission but has not(O’Dea et al.1994;Ferland,Fabian&Johnstone1994;Vogt &Donahue1995;Puy,Grenacher,&Jetzer1999), amounting to a colossal discrepancy between expec-tation and reality.In the discussion that follows we revisit the prob-lem of cooled gas from the perspective of the galactic coolingflow in NGC4472,a large,well-observed el-liptical galaxy.For relatively nearby ellipticals the threshold for radio detection is much lower and the ratio of observed to predicted cold gas masses is sim-ilar to that of more distant cluster coolingflows;e.g. H2and HI are undetected in NGC4472with an up-per limit107M⊙(Bregman,Roberts&Giovanelli 1988;Braine,Henkel&Wiklind1988),far below the ∼1010M⊙expected.Nevertheless,the intrinsic soft X-ray absorbing column in NGC4472,3×1021cm−2,and its relatively large covering factor indicates cool gas masses far in excess of the radio upper limit.The coolingflow in NGC4472clearly suffers from a minia-ture version of the same coolingflow problems of dis-tant clusterflows.But because of its proximity,there is a large available body of additional observational information for NGC4472that make it a more appro-priate venue to resolve or constrain theoretical possi-bilities for the fate of cooled gas.But the main advantage afforded by large,rela-tively nearby ellipticals emphasized here is that the cooled gas is heated,ionized and therefore illuminated by ultraviolet radiation from highly evolved galactic stars.We argue that the diffuse optical line emission from HII gas at T∼104K distributed across the cen-tral regions of most or all bright ellipticals is a direct tracer of cooled gas deposited by the hot interstellar gas.A simple analysis of this HII gas leads to the con-clusion that hot phase gas is not cooling into a single large cloud of neutral gas,but is cooling at a large number(∼106)of cooling sites located throughout the central regions of NGC4472.The HII gas pro-vides direct observational support for a distributed mass dropout that has been assumed by many authors in the past based on their interpretation of X-ray sur-face brightness profiles(e.g.Thomas1986;Sarazin &Ashe1989).As the mass of HII increases at each cooling site,a neutral core of very low temperature (T≈10−20K)eventually develops.We show that these neutral cores are very weakly ionized and can undergo gravitational collapse even in the presence of maximum strength magneticfields.Evidently this collapse results in local star formation.Another important conclusion from our study of the ionized gas in NGC4472is that only a very small amount,∼1M⊙,of neutral(or molecular)gas can accumulate at each cooling site before it undergoes gravitational collapse.The small mass of collaps-ing neutral cores is an essential requirement for low mass star formation.Previous studies(e.g.Ferland, Fabian&Johnstone1994)have shown that the gas temperature and Jeans mass are small deep within HI or H2gas irradiated by X-rays in cluster coolingflows, but this does not guarantee that massive stars can-not form.For example,the Jeans mass is often very low in Galactic molecular clouds but these clouds are also the birthsites for massive OB stars.The limited mass of cold gas at each cooling site in NGC4472and other similar ellipticals naturally prohibits stars more massive than about1M⊙from forming.The low mass star formation process we propose is also very efficient:the total mass of cold gas at all cooling sites in NGC4472at any time is very small, consistent with observed upper limit of cold gas(< 107M⊙).NGC4472is an excellent galaxy for study-ing this unique star formation process since very lit-tle alien gas or stars have been recently accreted into NGC4472by a merging process.Dusty,and there-fore accreted,gas is confined to within r<∼0.05r e (van Dokkum&Franx1995;Ferrari et al.1999) Afinal advantage of studying cooled gas in ellipti-cals like NGC4472is that the neutral gas formed in the cores of HII regions with temperatures T∼10K, only lasts for a time,<∼105years,that is too short for dust(and possibly many molecules)to form.Al-though dust and molecules are not required for low mass star formation to proceed,these components have complicated previous discussions of coolingflows in clusters of galaxies where,we assume,the cooling process resembles that in NGC4472.One shortcoming of our presentation–as with those of previous authors–is that we cannot reconcile the observed soft X-ray absorption in NGC4472with the small amount of cold gas indicated by null obser-vations of HI and CO emission.We assume,without much justification,that these contradictory observa-tions will be resolved in favor of the radio observations and that the soft X-ray absorption can be interpreted in another way.HII gas in elliptical galaxies can also arise from stellar mass loss which is ionized by hot central stars (planetary nebulae)and galactic UV radiation.We begin our discussion below with an argument that coolingflow dropout,not stellar mass loss,is likely to be the main contributor to internally-produced HII gas mass observed in nearby ellipticals.Then we dis-cuss an elementary model for the HII gas at a typi-cal interstellar cooling site and infer from this a low globalfilling factor for HII gas within the central re-gion of NGC4472.Next we model the cooling of hot gas from∼107to∼104K with a subsonicflow in pressure equilibrium–thisflow is useful in esti-mating the possible contribution of cooling gas to the X-ray absorption.This is followed by a discussion of the temperature,ionization level and gravitational instability of neutral cores at the centers of HII cool-ing site clouds.This part of our presentation fol-lows rather closely several previous discussions,but serves to illustrate that the more spatially concen-trated radiative transfer in spherical geometry still allows low temperatures and low mass star formation within these cores.We then show from observational considerations that magneticfields play little or no role in inhibiting the compression of interstellar gas as it cools from107to104K and from theoretical con-siderations that even the strongest observationally al-lowed magneticfields are unlikely to inhibit thefinal collapse of neutral cores to stellar densities.At the end of our presentation we discuss the effects of galac-tic gravitational forces and stellar collisions on cooling site clouds.Finally,to stimulate further observations of optical emission lines,we present a surface bright-ness map of NGC4472showing all the major com-ponents:stars,X-ray emitting gas,and HII gas from interstellar dropout and stellar ejecta.2.NGC4472:A PROTOTYPICAL ELLIP-TICAL GALAXYFor quantitative estimates in the following discus-sion,we use a specific galaxy,NGC4472,a massive E2 galaxy associated with the Virgo cluster.NGC4472 has been extensively observed at X-ray frequencies with Einstein HRI(Trinchieri,Fabbiano,&Canizares 1986)and with ROSAT HRI and PSPC(Irwin& Sarazin1996).The radial variations of hot gas density and temperature based on these X-ray data are illus-trated in Brighenti&Mathews(1997a).Although the outer region of the X-ray image of NGC4472is distorted,possibly by ram pressure interaction with ambient Virgo gas,the azimuthally averaged radial variation of electron density in NGC4472is typical of other bright ellipticals(Mathews&Brighenti1998).The most likely region for low mass star forma-tion in NGC4472is the volume within∼0.1r e where r e=8.57kpc is the effective or half-light radius at a distance of17Mpc.The gas that cools in NGC4472 cannot all collect at the origin,nor is it likely that most of the cooling occurs at very large galactic radii where the radiative cooling rate(∝n2)is inefficient. Brighenti&Mathews(1999a)have shown that if all the cooled gas accumulates at or near the very cen-ter of the galaxy,r<∼100pc,the remaining uncooled hot gas there is locally compressed and becomes very hot,but this is not observed.Alternatively,if most of the cooling and low mass star formation occurs in 0.1<∼r/r e<∼1,then the extremely close agreement between the total mass inferred from X-ray data and the known stellar mass in this region would be up-set(Brighenti&Mathews1997a).Finally,there isgood evidence from observed gas abundance and tem-perature gradients that hot interstellar gas isflowing inward within∼3r e through the optically bright re-gions of NGC4472(Brighenti&Mathews1999a),so it is unlikely that a significant number of low mass stars could form at r>∼3r e.It is most interesting therefore that HII optical line emission in Hα+[NII] lines is observed just in the region of NGC4472where low mass star formation is most expected,r<∼0.24r e (Macchetto et al.1996).3.SEVERAL SOURCES OF HII GASIn addition to interstellar gas cooling from the hot phase,cold gas is continuously expelled from stars throughout the galaxy as a result of normal stel-lar evolution.The total rate that mass is supplied by a population of old stars in NGC4472is˙M=α∗(t n)M∗t≈1M⊙yr−1where M∗t=7.26×1011 M⊙is the stellar mass in NGC4472andα∗(t n)≈1.7×10−12yr−1is the specific mass loss rate froma single burst of star formation after t n=13Gyrs (Mathews1989).The supply of gas from stars is com-parable to the rate that gas is observed to cool from the hot phase:˙M=(2µm p/5kT)L x,bol≈2.5M⊙yr−1,where m p is the proton mass and L x≈7.2×1041 ergs s−1is the bolometric X-ray luminosity of NGC 4472at a distance of17Mpc.Several lines of evidence suggest that most of the gas lost from stars in ellipticals is dissipatively and conductively heated and rapidly merges with the gen-eral hot interstellar coolingflow.Gas lost from orbit-ing stars inherits stellar velocities which,when dis-sipated in shocks or by thermal conductivity,equili-brates to the virial temperature of the stellar system, T∼1keV.However,the stellar virial temperature is about30percent lower than that of the more exten-sive dark halo.As coolingflow gas slowlyflows in-ward from the halo into the stellar region,it is cooled by∼0.3keV as it mixes with slightly cooler virial-ized gas ejected from local stars(Brighenti&Math-ews1999a).This produces the positive temperature gradients observed within a few r e.In addition,the iron,silicon and other elements supplied by the stars increases the metal abundance in the hot interstellar gas as it slowlyflows toward the galactic center within ∼r e,producing negative abundance gradients(Mat-sushita1997).These observations indicate that most or all of the gas ejected by stars merges with the hot gas phase.For simplicity,in the following discussion we ignore the HII contribution from stellar mass loss, but return to this question in§11.This is contrary to the hypothesis of Thomas(1986)that gas ejected from stars remains largely neutral and collapses into (very)low mass stars without joining the hot phase.The assimilation of stellar ejecta into the hot in-terstellar gas is greatly accelerated by dynamical and thermal processes resulting from the orbital motion of mass-losing stars through the coolingflow(Mathews 1990).Rayleigh-Taylor and other instabilities shred the ejected gas into many tiny cloudlets,greatly in-creasing the surface area presented to the hot cool-ingflow gas and their rapid dissipation by conductive heating.In addition,neutral clumps of gas expelled from stars always have ionized outer layers which are easily ablated and reformed;this results in a rapid and complete disruptive heating of the clump.In con-trast,cold gas produced as gas cools directly from the hot interstellar phase is necessarily formed in the local rest frame of the coolingflow gas so the violent dy-namical instabilities that accompany stellar mass loss are not expected.After∼106years,however,the denser cooling region may begin to fall in the galac-tic gravitationalfield(see§10),possibly leading to some disruption at the cloud boundary(Malagoli et al.1990;Hattori&Habe1990).Assuming that ra-diative cooling from the hot interstellar phase occurs, as gas cools through HII temperatures it is thermally protected by surrounding gas at intermediate tem-peratures(104<T<107K)where the thermal con-ductivity is very low.The global kinematics of the two HII gas components of internal origin are quite different.HII regions produced by stellar ejecta will initially tend to mimic local random and systematic stellar motions while HII gas arising from cooling gas will initially share the velocity of local hot gas.A third source of HII gas in ellipticals are the ion-ized parts of gas acquired in recent merging events such as the small dusty clouds within∼0.05r e of the center of NGC4472(van Dokkum&Franx1995). This gas is spatially disorganized and is dynamically unrelaxed.Dust is another clue of its external ori-gin since gas formed by cooling from the hot phase should be nearly dust-free due to sputtering(Draine &Salpeter1979;Tsai&Mathews1995;1996)and may not have time to grow dust in the gas phase(§7).Our interest here is with the HII component pro-duced as gas cools from the hot phase and we assume that this component dominates the optical line emis-sion in NGC4472.4.THE INVERSE HII REGIONA small cloud of HII gas that has cooled from the hot interstellar medium is photoionized by stellar UV radiation arriving at its outer boundary;this is the inverse geometry of normal HII regions ionized by a central star.We suppose that the HII cloud is spheri-cal and that the electron density n e and temperature T=104K are uniform throughout the HII gas.The spatial uniformity of the HII density is essentially un-affected by small local gravitationalfields due to inter-nal stars,the neutral core in the cloud if one exists, or the HII gas itself.The mass of these HII clouds located at the centers of local cooling sites slowly in-creases with time.Thefirst step in understanding the evolution of HII clouds is to determine the maximum size and mass that can be ionized by stellar UV in the central regions of NGC4472.This size depends on the HII electron density and the mean intensity of galactic UV starlight J uv(r).The intensity of ionizing radiation can be deter-mined by an appropriate integral over the galactic stellar distribution.For this we assume a de Vau-couleurs stellar distribution similar to that in NGC 4472,with an effective radius of r e=8.57kpc and an outer maximum stellar radius of25r e.The stellar density and mass are given to a good approximation byρ∗=ρo(b4r/r e)−0.855exp[−(b4r/r e)1/4]andM(r)=M oγ(8.58,[b4r/r e]1/4)where b=7.66925andγ(a,z)is the incomplete gamma function(Mellier&Mathez1987).If the de Vaucouleurs distribution extends to in-finity,the total mass would be M t=M oΓ(8.58)= 1.6582×104M o where M o=16πρo(r e/b4)3.It is nat-ural to normalize the density coefficientρo tofit the de Vaucouleurs distribution for NGC4472in the re-gion0.1<∼r/r e<∼1where the X-ray and stellar mass determinations agree,i.e.ρo=3.80×10−18gm/cm3. When the stellar distribution is truncated at25r e the total mass6.97×107M⊙is only about1percent less than an infinite stellar distribution having the same ρo.At every radiusx=r/r ein the de Vaucouleurs distribution the mean stellar column density˜J can be found by integrating over solid angle,˜J=1n2αB.The density of HII gas isρ=nMfρwhere fρ= 5µ/(2+µ)=1.20,assumingµ=0.61for the molec-ular weight.The total mass of the Stromgren sphereism s=4n5α3Bwhere m p is the proton mass.Some imprecision is ex-pected since we have ignored those ionizing photons that pass through the HII cloud unabsorbed.How-ever,calculations of the transfer of ionizing radiation in the inverse HII region indicate that Equation(1) is accurate to<∼5percent.Figure2illustrates the radial variation of electron density n e=(ρ/m p)(2+µ)/5µin HII gas(solid line) with galactic radius in NGC4472and the correspond-ing local inverse Stromgren radius r s(long dashed line).Within the radius where Hαis observed in NGC4472,x=r/r e<∼0.24wefind r s≈0.3−0.8 pc,n e≈20−90cm−3,and the mass of a typical Stromgren cloud is m s≈2M⊙.The radial col-umn density in an HII Stromgren cloud is typically N s=n e r s≈1.2×1020cm−2.Hot gas is assumed to be cooling at numerous sites throughout this central region of NGC4472and the cooling is made visible by optical line emission from the HII regions.The mass of any particular HII cloud increases slowly with time,supplied by local cool-ing from the hot gas phase or by dissipative merging of clouds.Presumably,new HII clouds are contin-uously forming from the cooling interstellar gas at newly-formed cooling sites and old sites and associ-ated clouds are disappearing.But we suppose that the mean age of cooling sites is long compared to the time required for typical HII clouds to reach the Stromgren mass;in this case the average cloud can be approximated with Stromgren parameters.Notice also that r s≪r so that even the largest HII clouds are very small compared to their distance to the cen-ter of the galaxy.5.GEOMETRY OF HII AND COLD GASWe propose that most of the extended Balmer line emission in ellipticals arises from a multitude of HII clouds at or near their Stromgren radii.If so,the to-tal volume within clouds occupies only a tiny fraction f F of the galactic volume within the Hα-emitting re-gion of NGC4472,r<∼2kpc.Thefilling factor f F can be estimated by comparing the total volume of HII required to produce the observed Balmer line lu-minosity to the apparent volume from which optical line emission is observed.In most optical observations,such as those of Mac-chetto et al(1996),Hα(6562˚A)is blended with two nearby[NII]lines at6584and6548˚A.The totalflux observed by Macchetto et al.(1996)in all three lines is F lines=17.30×10−14ergs cm−2 s−1.Observations at higher resolution reveal that the F([NII]6584)/F(Hα)≈1.38and F(6584)/F(6548)=bining all these ratios,and adopting CaseB conditions F Hα/F Hβ=2.86,the Hβflux from NGC4472is F Hβ=2.13×10−14ergs cm−2s−1 and the total luminosity from all HII emission is L Hβ=4πD2F Hβ=7.34×1038erg s−1,assuming a distance of D=17Mpc to Virgo.How many dust-free Stromgren clouds are required to produce this total luminosity?The Hβluminosity of a single Stromgren cloud isℓβ,s=n2eǫβ(4π/3)r3s=1.5×1031n2e r3spc ergs s−1 whereǫβ=1.0×10−25erg cm3s−1is the Hβemis-sivity at T=104K.For typical values of n e and r spc(in parsecs)in the central galaxy x<∼0.25,ℓβ≈3−7.5×1033ergs s−1.Therefore,about N cl= 105−106Stromgren clouds are required to account for the Balmer line luminosity observed.The HIIfill-ing factor is found by comparing the volume of all HII gas V cl=L Hβ/ n e 2ǫHβ=2.5×1060cm3(assuming n e =50cm−3)with the total volume of the Hβ-emitting region,V tot=(4/3)π(0.24r e)3=1.1×1066 cm−3.Thefilling factor of HII gas f F=2×10−6is very small,consistent with our proposition that HII emission arises from many small clouds and with ear-lier estimates of f F(Baum1992).If∼1M⊙of hot gas cools each year in NGC4472,then the mass of each cloud will grow quite slowly,∼10−6−10−5M⊙yr−1,requiring t s∼2×105−2×106years to form a typical Stromgren cloud.The total mass of all the HII emitting gas in NGC4472is M II= n Mf F V cl≈1.2×105M⊙,similar to values in the literature but here evaluated using a consistent physical model.A smallfilling factor also implies that each HII cloud is exposed to the unabsorbed stellar UV emis-sion from the entire galaxy,provided the cloud sys-tem is approximately spherical.The“optical depth”for intersecting a Stromgren cloud across the opti-cal line-emitting region within r t=0.24r e isτ=πr2s r t N cl/V tot≈0.006−0.06.Sinceτ≪1the clouds do not shadow each other.In realityτcould be larger (i)if the typical cloud crossection is much less than πr2s(τ∝r−1s)or(ii)if the cloud system were not spherical;a disk-like configuration could result from galactic rotation.In any case,the assumption thateach HII cloud is exposed to the full,unabsorbed stel-lar UV emission is likely to be a reasonably good ap-proximation.Combining previous results,the average column depth that HII gas presents to X-radiation through-out the galactic core,N∼N sτ∼1018−1019cm−2,is much less than the value N∼3×1021cm−2that best fits the observed X-ray continuum(Buote1999).The size that an HII cloud presents to absorbing X-rays is larger than r s since we have ignored the extended cooling region around each cloud with temperatures between106and104K in which X-rays can still be absorbed.This assumption will be justified below.The total mass of HI or H2gas observed in the cen-tral regions of NGC4472,M cold<107M⊙,is another potential source of X-ray absorption.If this mass of cold gas were arranged in a disk of thickness of the X-ray absorbing column N=3×1021cm−2,located in the galactic core and oriented with its symmetry axis along the line of sight,it would have a radius<370 pc,somewhat larger than the faint patch of dust ob-served by van Dokkum&Franx(1996).However a cloud of size370pc obscures only∼0.007of the total X-ray luminosity of NGC4472and would therefore produce negligible X-ray absorption.The true X-ray absorption is very probably much less than3×1021 cm−2.The observation of NGC4472by Buote us-ing the∼4’beam of ASCA also included the nearby gas-rich dwarf irregular galaxy UGC7636(Irwin& Sarazin1996;Irwin,Frayer&Sarazin1997)which may be the source of the X-ray absorbing column at-tributed to NGC4472if its covering factor is suffi-ciently large.Although it seems likely that interstellar magnetic fields are important in the centers of ellipticals(Math-ews&Brighenti1997;Godon,Soker&White1998), it is remarkable that the observed optical line emis-sion does not indicate strongfields in the HII gas. Typical HII densities in bright ellipticals determined from[SII]6716/6731line ratios are∼100−200cm−3 (Heckman et al.1989;Donahue&Voit1997),similar to(or even a bit larger than)the values found here for NGC4472(Figure2).(Unfortunately,we have been unable tofind a determination of the HII density spe-cific to NGC4472.)This suggests that the HII gas density is not being diluted by magnetic support,i.e. B2/8π<2nkT or B<70µG in the HII gas.HII densities of∼100are also supported by comparing the ionization parameter U=n iph/n e for pressure equilibrium HII gas in NGC4472(short dashed line in Figure2)with values that characterize the entire observed line spectrum.Within∼r e in NGC4472log U≈−3.3,very similar to values of U required to reproduce LINER type spectrum typically observed in ellipticals(e.g.Johnstone&Fabian1988);thisprovides an independent check on our HII gas density and J near the center of NGC4472.The apparent absence of magnetic support in the HII gas is interesting since the hot phase gas is re-quired to havefields of at least severalµG at largegalactic radii to explain Faraday depolarization of ra-dio sources and distant quasars(Garrington&Con-way1991).Interstellarfields>∼1µG can be generated in a natural way by stellar seedfields and turbulent dynamo action in the hot gas(Mathews&Brighenti1997).As the gas density increases by∼1000when it cools from the hot phase to HII temperatures,a field of1µG would grow to100µG ifflux is con-served,B∝ρ2/3.The initialfield in the hot gas in r<∼0.24r e would need to be surprisingly small, <∼0.7µG,to evolve into the rather smallfields allowed in HII clouds,B<∼70µG,implied by typical electron densities.Small HIIfields can be understood if localcooling sites form in interstellar regions having lower than averagefields;in pressure balance,lowerfields require higher hot gas densities which cool preferen-tially.Alternatively,it is possible thatfield reconnec-tion has been very efficient during cooling,implying a disorganizedfield and considerable stirring motion during the cooling process.6.COOLING SITE GAS DYNAMICSCooling sites in the hot interstellar gas are initiated in regions of low entropy(i.e.low temperature,high density)which cool preferentially by radiative losses. Entropyfluctuations can be generated by a variety of complex events:stellar mass loss,occasional Type Ia supernovae,sporadic mergers with other nearby (dwarf)galaxies,and differential SNII heating events and outflows that occurred in pregalactic condensa-tions.Due to the complicated nature of these inter-actions,it is difficult to predict the amplitudes and mass scales of the entropy inhomogeneities so the de-tailed nature of the initial cooling process remains unclear.However,once cooling commences,the gas flow toward the cooling site may evolve toward a sim-ple profile provided entropyfluctuations in the hot gas are not too severe over theflow region.We now describe such a model for cooling site。

a r X i v :a s t r o -p h /9906218v 1 12 J u n 1999The IMF and its EvolutionBruce ElmegreenIBM T.J.Watson Research Center,P.O.Box 218,Yorktown Hts.,NY 10598,USAABSTRACTObservations of the stellar initial mass function are reviewed.The IMF is flat,or possibly declining,below several tenths of a Solar mass,and declining above this mass in a power law with a slope of about −1.35on a log-log plot.The flattening at low mass is evidence for a characteristic mass in star formation,which,according to recent theory,may be either the minimum stellar mass for the onset of deuterium burning,or the thermal Jeans mass.The first of these masses should not vary with environment as much as the second,so any observed variations in the mass of the flattened part are important for understanding star formation.Starburst galaxies may be an example where the characteristic mass is larger than it is locally,but this old observation has been challenged lately.A steeper high-mass slope in the extreme field studied by Massey et al.may be the result of cloud destruction and the termination of star formation by ionization,with a normal IMF in each separate cluster.The lack of a density dependence in cluster IMFs suggests that star and protostar interactions play little role in star formation or the IMF.This is unlike the case for binaries and disks,which do show an environmental influence,and all are consistent with the observed stellar density in clusters,which is high enough to promote interactions between binaries and disks,but not individual stars.These considerations,along with indirect observations of the IMF in the early Universe,suggest that the IMF does not vary much in its basic form over position and time,but that shifts in the characteristic mass might occur in regions with extremely high or low star formation activity,or perhaps light-to-mass ratio,with the characteristic mass,star formation efficiency,and gas consumption rate all following the light-to-mass ratio.to appear in The evolution of Galaxies on Cosmological Timescales,ed.J.E.Beckman and T.J.Mahoney,ASP Conference Series,San Francisco,1999,in press.1.IntroductionObservations of clusters and associations suggest an average stellar initial mass function (IMF)that is approximately a power law like the Salpeter (1955)function,with a slope of x ∼1.35on a log n −log M plot,and a flattening below ∼0.35M ⊙.This IMF appears in clusters and whole galaxies,for all galactic populations,and even in the intergalactic medium (Sect.2.1,2.3,2.4).However,there are still fluctuations in the slope of the power-law by ±0.5from cluster to cluster (Scalo 1998),and there are other curious variations too,like a steeper slope in the field (Sect.2.2),the mass of the most massive star increasing with cloud mass (Sect.3),the formation of massive stars relatively late and near the centers of clusters (Sect.3),and the greater proportion of massive stars in starburst galaxies (Sect.2.5).Considering the robust nature of the IMF,any theory for its origin should be able to reproduce both the average shape and the variations around it with a minimum of free parameters and a minimal dependence on the physical properties of the star-forming clouds.Another important mass function for star formation is the distribution of cloud and clump masses. This differs from the stellar function in both slope(x∼0.5−0.8for clouds)and range(M cloud∼10−4−107 M⊙;Heithausen et al.1998;Dickey&Garwood1989),leading one to wonder why stars form with a steeper mass distribution than their clumps.There must be a preferential selection of lower clump masses for stars, and a cutoffat some minimum star mass.There are tantalizing indications that we may be able to understand the IMF without fully understanding the origin of either the cloud structure or the processes involved with individual stars.Given the observed structures of clouds,we can imagine how star formation processes might select pieces of this structure in a certain order and end up with the observed IMF and all of its variations.If such clump selection is the correct explanation for the IMF,then it presumably works because most of the star mass is determined by the gas mass immediately available to it during the protostar phase,and because the IMF is an average over many different processes,with each losing its unique contribution when the mass distribution is averaged over a cluster.Numerical simulations of such sampling demonstrate this point by reproducing essentially all of the observations of the IMF and its systematic and stochastic variations without any free parameters or physical input other than a single characteristic mass for the minimum clump that can make a star.These models obtain(Elmegreen1997,1999a):(1)the correct power-law slope and turnover shape of the IMF,with the correct turnover mass,(2)the tendency for the most massive star in a cluster to increase with cloud mass, (3)the shift in the peak or turnover mass for starburst regions without a change in the power-law slope,(4) the delayed formation of massive stars in a cluster,(5)thefluctuations in the slope of the power-law part from cluster to cluster(which result from sampling statistics),and(6)the tendency for the most massive stars in a cluster to concentrate toward the cluster center.The only input to the model is the hierarchical (and fractal)distribution of cloud structure,and the only assumption is that pieces of this hierarchy make stars at a rate that scales with the square root of the local density,which is the rate at which essentially all of the physical processes involved with the onset of star formation operate,including self-gravity,magnetic diffusion,clump collisions,and turbulence dissipation,given the molecular cloud scaling laws.The hypotheses that IMF theories may be simplified by the gross averaging of star formation processes during the build up of a cluster,and by the intimate connection between its power-law slope and cloud structure,also help to explain why its power-law slope is so similar from region to region,even in different environments and at different times.The point is that the cloud and star formation details may not matter much for the IMF,and that power-law cloud structures are more-or-less universal,perhaps as a result of pervasive turbulence.In the next section we review the observations of the IMF and some of the implications of these observations in an attempt to sort out what is physically significant and compelling for a theory.Other reviews can be found in the conference proceedings The Stellar Initial Mass Function,edited by Gilmore, Parry&Ryan for ASP Press in1998.A review that compares various theories with the constraints from observations is in Elmegreen(1999b).2.Observations of the IMF and Implications for the Theory2.1.The Salpeter Slope in Clusters and GalaxiesThe IMF at intermediate to high mass can be written n(M)d log M∝M−x d log M for slope x on a log−log plot.For most clusters,x is in the range1–1.5.Salpeter(1955)suggested x∼1.35,which is about the average of the values observed today.The most dependable values come from a mixture of photometry and spectroscopy of star clusters.IMFs based on photometry alone are generally steeper than x∼1.35 because of an ambiguity in mass for high mass stars(see discussion in Massey1998).Table1summarizes the recent observations that obtain x∼1−1.5in various regions.This“Salpeter”slope is found by star counts in local clusters,integrated light from whole galaxies,elemental abundances, and galaxy evolution models.Steeper values of x∼1.5−2are found in samples of localfield stars or in the low density parts of some clusters(Table2).Shallower values are found at low mass,where the IMF flattens to nearly zero slope on a log−log plot(Table3).Shifts either in the peak or in the slope,favoring higher masses,have been found in starburst galaxies(Table4).The observations in these tables suggest that the IMF varies a lot,but in fact most of the functions that deviate from the turned-over Salpeter slope are based on indirect measurements that contain questionable assumptions.For example,the slope determined for the localfield tends to get steep only at high mass, and the increased value depends on an assumed recent star formation history and an assumed scale height variation with mass and age.The localfield is also more populated by low mass stars than high mass stars because low mass stars live longer and drift further from their sites of star formation than high mass stars.The low density regions of clusters show a steeper IMF too because of an excess of low mass stars, but this is probably related to the greater concentration of high mass stars in cluster cores,as discussed more in Section3;the overall cluster can still have aflattened-Salpeter IMF.The Hipparcos results quoted by Brown(1998)were based on photometry,rather than spectra,and are typically steep for photometry. Massey et al.(1995)has shown how such IMF values become shallower,like the Salpeter function,when spectra are considered for the determination of stellar mass.2.2.A Steep IMF Slope in The Extreme FieldThe most extreme deviation for an IMF measurement is in the remotefield regions of the LMC and Milky Way(Table2).These are regions defined by Massey et al.(1995)to be further than30pc from the boundaries of catalogued OB associations.Here the slope at high mass has been measured to be around x∼4.Evidently something very unusual is happening.There are several ways to explain this,if it turns out to be true.One way has a normal(x∼1.35)IMF in every individual region of star formation,and a steeper IMF in the composite of many regions.This difference between cluster and intergrated IMFs illustrates an important point about cloud destruction,so we discuss it in some detail here(see also Elmegreen1999a).In a large region there will in general be many separate clouds that form stars,and these clouds willdM c forγ∼1.5−2.If intermediate and high mass stars destroy have some mass function n(M c)dM c∝M−γctheir clouds because of ionization,and as a result,halt the star formation processes inside them,then more massive clouds will require more massive stars before star formation ends.This leads to a situation where a lot of low mass clouds make primarily low mass stars,with a normal IMF,and where a few high mass clouds make both low mass and high mass stars,also with a normal IMF.But,since there are more low mass clouds,the composite region will have a lot more low mass stars in proportion to high mass stars than is given by each cluster IMF.It follows that even if the IMF inside each region of star formation is theTable1:Observations of a Salpeter IMF with x=1−1.5Localfield stars Miller&Scalo1979;Garmany,Conti,&Chiosi1982;Humphreys&McElroy1984Blaha&Humphreys1989;Basu&Rana1992Kroupa,Tout,&Gilmore1993;Scalo1986(x=1.5−2for high mass stars)Local OB associations(review of Hipparcos results:Brown1998) LMC clusters in regions J.K.Hill et al.1994;R.S.Hill et al.1995low young-star densityUnclustered embedded Ali&DePoy1995stars in OrionExtremefield stars Massey et al.1995in the LMC(x∼4)same,a Salpeter IMF for example,the composite IMF from many clouds will be steeper than this.Consider a specific example.Suppose the IMF in each region of star formation has a certain slope x,and the largest mass of a star,M L,required to destroy a cloud scales with cloud mass M c as M L∝Mαcforα>0.Then the composite IMF from all of the clouds combined will have a slope x comp=(γ−1)/α,which is independent of the IMF slope in each individual cluster.To evaluate this composite slope,we takeγ=2for a hierarchical cloud system(Fleck1996;Elmegreen&Falgarone1996),andα=5/16for cluster destruction with a largest stellar mass M L.This value ofαcomes from the mass-luminosity relation of ionizing radiation,which scales as L∝M4for luminosity L andstellar mass M(Vacca,Garmany,&Shull1996).A whole cluster’s ionizing luminosity can be evaluatedfrom the expression M L0L(M)n(M)dM for maximum mass M L and IMF n(M)dM=xM x L M−1−x dM. This cluster luminosity scales with M4L too.The constant term in the IMF,xM x L,gives one star at amaximum mass M L from the expression ∞M L n(M)dM=1.The luminosity required to destroy a cloud is the binding energy divided by the cloud crossing time,which is GM2c/R GM c/R3 1/2∝M5/4c,using the Larson(1981)scaling laws for molecular clouds.Setting the luminosity of a cluster,∝M4L,equal to thepower required to destroy a cloud,∝M5/4c,then givesα=5/16in the expression M L∝Mαc.Withγ=2andα=5/16,the slope of the composite IMF is x comp=(γ−1)/α=16/5∼3.2.Thevalue observed by Massey et al.(1995)is∼4,which is pretty close to this theoretical result,given theuncertainties in the M−L relation and other assumptions,and with the observations.It is important to note that the extremefield IMF found by Massey et al.(1995)is not representativeof galaxies in general.Integrated light and elemental abundances give an average IMF for whole galaxiesthat has the same slope at intermediate and high mass as individual clusters,namely,the Salpeter value ofx∼1.35.This simple fact implies that massive stars cannot generally halt star formation in their clouds.Ifthey did,then the composite IMF for a whole galaxy would be significantly steeper than the individual IMFin each cluster.Massive stars may destroy their clouds,in the sense that they push the gas around,butthey cannot generally halt star formation in them except possibly in the extremefield.The extremefieldcould differ from the environment in OB associations because of a much lower pressure in the extremefield.A low pressure could conceivably lead to more efficient cloud ionization and the cessation of star formationin even the dense clumps.The requirement that the composite IMF be equal to the cluster IMF also means thatα=1/x in theabove analysis(withγ=2,as required for a hierarchical gas distribution).This is just what is expected forrandom star formation,where the largest stellar mass increases with cloud mass simply because of randomsampling from the IMF.That is,the largest stellar mass satisfies ∞M L n(M)dM=1,as discussed above, and this gives a constant of proportionality n0=xM x L in the expression n(M)=n0M−1−x.Thus the total number of stars scales with M x L.If the efficiency is about constant with cloud mass(and the smallest mass star is much less massive than M L),then this total number scales about with the cloud mass,giving M x L∝M c,orα=1/x.There are other explanations for the steep IMF in the extremefield.Star forming regions are typicallymuch larger than30pc,often extending in a coherent fashion up to several hundred parsecs(Efremov1995),so the30pc limit in the definition of the extremefield may allow some normal cluster,association,or star-complex members to be included.In that case,the steep slope in the outer regions of a cluster mayoccur for the same reasons as the shallow slope in the inner region,i.e.,segregation of the most massivestars towards the center.In summary,the general form of the IMF is probably invariant among clouds of different masses,giving a maximum stellar mass that increases with cloud mass as the power1/x=1/1.35as a result of random sampling(i.e.,more massive clouds sample further out into the high mass tail of the IMF).This explains the similarity between the composite IMF of whole galaxies and the IMFs of individual clusters.However, in the extremefield,where conditions like ambient pressure are very different than in OB associations, star-forming clouds could be more quickly and easily destroyed by ionization from stars,and in this case, the maximum stellar mass could increase much more slowly with cloud mass,as the power1/4instead of 1/1.35.As a result,the composite IMF can be much steeper than the individual IMFs in each cluster. Alternatively,the extremefield IMF could be sampling only the low mass members of an extended cluster whose other members are more centrally located.2.3.An IMF that is Independent of Cluster DensityOne of the most startling aspects of the observed IMF is that it is virtually invariant from cluster to cluster,aside from likely statisticalfluctuations(Elmegreen1999a),and this relative invariance spans a range of a factor of200in cluster density(Hunter et al.1997;Massey&Hunter1998)and a factor of10in metal abundance(Freedman1985;Massey,Johnson&DeGioia-Eastwood1995).The density independence means that the IMF is probably not the result of protostar,star,or clump interactions.If it were,then dense regions,which should have more of these interactions,would differ from low density regions,where there are few or no interactions.The IMF is also not likely to result from accretion of cloud material during stellar orbital motion.Stars in denser regions orbit in a shorter time and have more gas to accrete.Neither is the IMF or any part of it from the coalescence of stars(i.e.,massive stars are not formed from the coalescence of low mass stars or protostars).This lack of a density dependence for individual stars in the IMF contrasts with the situation for binary stars and disks.The binary fraction is smaller in denser regions,and protostellar disks are smaller too(see review in Elmegreen et al.1999).The protostellar binary fraction is lower in both the Trapezium cluster(Petr et al.1998)and the Pleiades cluster(Bouvier et al.1997)than it is in the Tau-Aur region, by a factor of∼3.Also,the peak in the separation distribution for binaries is smaller(90AU)in the part of the Sco-Cen association that contains early type stars than it is(215AU)in the part of the Sco-Cen association that contains no early type stars(Brandner&K¨o hler1998).The cluster environment also apparently affects disks.Mundy et al.(1995)suggested that massive disks are relatively rare in the Trapezium cluster,and N¨u rnberger et al.(1997)found that protostellar disk mass decreases with stellar age in the Lupus young cluster,but not in the Tau-Aur region,which is less dense.When massive stars are present,as in the Trapezium cluster,uv radiation can photoionize the neighboring disks(Johnstone et al.1998).These observations make sense in terms of the relative interaction rates for stars,binaries,and disks (Elmegreen et al.1999).The size of a typical embedded cluster is∼0.1pc,and the number of stars is several hundred.This makes the stellar density on the order of103−104stars pc−3.For example,in the Trapezium cluster,the stellar density is∼5000stars pc−3(Prosser et al.1994)or higher(McCaughrean &Stauffer1994),and in Mon R2it is∼9000stars pc−3(Carpenter et al.1997).A stellar density of 103M⊙pc−3corresponds to an H2density of∼104cm−3.Molecular cores with densities of105cm−3or higher(e.g.,Lada1992)can easily make clusters this dense,because star formation efficiencies are typically 10%-40%(e.g.,see Greene&Young1992;Megeath et al.1996;Tapia et al.1996).The density of n star=103stars pc−3in a cloud core of size R core∼0.2pc implies that objects with thisdensity will collide with each other in one crossing time if their cross section isσ∼(n star R core)−1∼0.005 pc2,which corresponds to a physical size of∼6500 R core[pc]n star/103 −1/2AU.This is the size of protostellar disks and long-period binary stars.Thus disks and binaries should be affected by interactionsin the cluster environment,but not individual stars or the IMF.2.4.The Flattening at Low Mass:a Characteristic Mass for StarsThe IMFflattens on a log−log plot at stellar masses of around and below0.3M⊙.Table3summarizesthe observations.The mass at which thisflattening occurs is observed to vary a bit from region to region,particularly in clusters(i.e.,the mass at the peak in NGC6231is2.5M⊙,much higher than normal;Sung,Bessell,&Lee1998),but such variations could be the result of mass segregation in the sense that highmass stars are often concentrated towards cluster cores(see Sect.3).There is even evidence for a turnoverin the IMF at masses less than0.3M⊙for several regions,but this is uncertain because the stars at the lowmass end are usually close to the limit of detection.The importance of the IMFflattening is that this is the only characteristic scale known for the starformation process.Molecular clouds and their pieces have a power law mass distribution from sub-stellarmasses to the masses of clouds as big as the galactic scale height.There is essentially no characteristicscale for clouds.The mass distributions for open clusters and perhaps even primordial globular clustersare power laws too,with about the same slope as for clouds(Elmegreen&Efremov1997;see review inElmegreen et al.1999).The rest of the IMF is a power law too.But the IMF does have a characteristicscale at the low mass end,where itflattens at about0.3M⊙.The existence of such a characteristic mass is an important clue to the mechanism of star formation.For example,we know now that the characteristic mass is not the Jeans mass at an optical depth of unity,asformerly suggested,because this mass is too small,∼10−3M⊙(e.g.,Rees1976).The two most promisingsuggestions for the origin of the characteristic mass are:(1)self-limitation of accretion by protostellar windstriggered at the deuterium-burning mass(Nakano,Hasegawa,&Norman1995;Adams&Fatuzzo1996),and(2)the inability of a cloud piece smaller than the thermal Jeans mass to become self-gravitating andcollapse to a star,given the temperature and pressure of a molecular cloud core(Larson1992;Elmegreen1997).Thefirst of these limits would seem to be relatively independent of environment,while the secondshould scale with T2/P1/2for cloud temperature T and cloud-core pressure P.Both values are about thesame locally,where T∼10K and P∼106k B cm−3,and since T2and P1/2tend to vary together withgalactocentric radius and star formation activity(Elmegreen1997,1999b),the two masses should remainthe same in most normal regions.To check the theoretical predictions,we should look for places where T2/P1/2deviates a lot from itslocal value.If the mass at the peak of the IMF,or where the IMFflattens,varies from region to regionalong with the quantity T2/P1/2,then the second model would be preferred;if the peak mass does not,then thefirst model is better.For example,Larson(1998)suggested that the peak in the IMF was shiftedtowards higher masses in the early Universe,in order to account for the G dwarf problem,the large heavyelement abundance and high temperature in galactic cluster gas,and the high luminosities of distantgalaxies.Variations like this would be more easily explained by an IMF model that depends on the thermalJeans mass.Table3:Observations at Low MassThe thermal Jeans mass,which contains the combination of parameters T2/P1/2,is approximately constant in normal regions of star formation.This is because the numerator in this expression is approximately proportional to the cooling rate per unit mass in molecular clouds(which scales about as T2−T3–see Neufeld,Lepp,&Melnick1995),and the denominator is approximately proportional to the heating rate per unit mass from starlight and cosmic rays in typically active disks.The starlight and cosmic ray intensities scale with the background column density of stars,and the pressure in the midplane of the disk scales with the square of this column density.Thus the square root of pressure goes with the column density of background stars.As long as heating equals cooling and the mass-to-light ratio in a galactic disk is about constant,and as long as the factor by which star-forming clouds have a higher pressure than the ambient pressure is about constant,the thermal Jeans mass is about the same in all dense cloud regions.If the mass-to-light ratio goes down,then the thermal Jeans mass can go up.Perhaps this occurs in starburst regions.Conversely,if the mass-to-light ratio is abnormally high,then the thermal Jeans mass can go down.An example of the latter situation might arise in the inner regions of M31.There the molecular cloud heating rate is low and the cloud temperature is close to3K,instead of the usual10K(Allen et al.1995; Loinard&Allen1998).These clouds also exist in the part of the disk where the stellar column density is high in old stars,so the interstellar pressure is not particularly low.As a result,the thermal Jeans mass can be lower in ultracold clouds than in normal clouds,possibly as low as0.01M⊙instead of0.3M⊙(Elmegreen1999c).For this reason,a significant population of Brown Dwarf stars might be present in ultracold molecular clouds.If they are found,then the model based on the thermal Jeans mass would be preferred over the model based on the deuterium burning limit.The thermal Jeans model is preferred also if a reasonably high fraction,say>10%,of all the material in a collapsing cloud piece gets into a star.This leaves a lot of mass for wind expulsion and disk erosion, but it also implies that the star mass depends somewhat on the mass of the cloud piece in which it forms. In that case,wind-limitations to the stellar mass would not be very important,causing only a factor of2–10 variation in the ratio of star mass to cloud mass.Most of the mass variation along the IMF,which spans a factor of∼103in mass,would then have to come from something else,and the mass of the pre-stellar cloud piece is a likely place.Another observation that could help distinguish between possible origins for the characteristic stellar mass is the discovery of powerful pre-main sequence winds from extremely low-mass Brown Dwarfs,i.e., stars too small to ignite even deuterium.If pre-main sequence contraction energy alone is enough to start a wind,then deuterium burning would not be relevant to the limitation of stellar mass.There is some evidence already that the mass function for dense cloud cores containing about a solar mass is similar to the IMF(Motte,Andr´e,&Neri1998;Testi&Sargent1998).This is the type of observation that could clarify the origin of the characteristic mass for star formation.2.5.Top-Heavy IMFs in Starburst RegionsThere has been considerable discussion about a shift in the IMF towards proportionally more high mass stars in starburst regions,although many of the initial reports are now being questioned.The original motivation for this idea was the observation that the luminosity of the starburst was so high,given the total mass from the rotation curve,that there could not be a normal proportion of high and low mass stars but only an excess of high mass stars.Now,more detailed modeling,and in the case of M82,a lower extinction correction(Devereux1989,Satyapal et al.1997),makes the stellar luminosity seem about right for themass.A summary of these observations is in Table4.In addition,a top-heavy IMF would produce too much oxygen in proportion to other elements(Wang&Silk1993),and the aging population of stars would be too red(Charlot et al.1993).Considering the basic form of the IMF,which is a power law with a lower cutofforflattening at some characteristic mass,one can easily envision variations that lead to top-heavy IMFs as a result of an upward shift in the characteristic mass.A predicted downward shift leading to an excess of Brown Dwarfs was mentioned in a previous section.The upward shift would come in the same way,but from an increase rather than a decrease in the value of T2/P1/2.It is more difficult to envision a top heavy IMF that results from a decrease in the slope of the power law part,because the very existence of a power law suggests a scale-free process,which means that it is essentially free of dependence on physical parameters.Power law mass distributions often result from geometric(e.g.,fractal)or self-regulatory(e.g.,equilibrium coalescence) effects instead.The IMF model in Elmegreen(1997),in which the power law part comes from a weighted selection of clump pieces in a hierarchically structured cloud and the low mass cutoffcomes from the thermal Jeans mass,gets a simple shift in the whole IMF towards higher mass,with a constant slope in the power-law part,as T2/P−1/2increases.A computer simulation showing this result was in that paper.An amazing thing about the IMF is that the characteristic mass at the low end,where theflattening occurs,appears to be nearly constant from region to region.As discussed above,this may simply reflect equilibrium thermal conditions with varying T and P but constant T2/P1/2,or it may reflect a constant wind-limited mass at the threshold of deuterium burning.The upward shift for starbursts,if real,provides a good test for the models.It is easier to increase T2/P1/2in warm regions at slightly elevated pressures than to affect the deuterium burning limit,which would seem to be independent of environment.Thus the exact form of the IMF in starburst conditions is extremely important for the models.In this respect,the reported slight upward shift in the characteristic mass for the30Dor cluster in the LMC(Nota et al.1998) is noteworthy.This is the closest starburst-like region,and therefore the most promising for providing a firm observation of the IMF from direct star counting.Unfortunately,this cluster could suffer from mass segregation effects as in other clusters,in which case the upward shift would appear only in the nuclear region.The discussion about starburst IMFs begs the question of whether there is an upper limit to the mass of a star that can form.No such upper limit has been found yet.That is,the upper limit in any particular region just keeps increasing as the total stellar mass increases,as expected for random star formation(see theory in Elmegreen1983,1997,and observations in Massey&Hunter1998).Yet there would seem to come a time where this stellar mass increase would have to stop.After all,if we scale the1/x power law Table4:Key IMF Observations in Starburst Galaxies。

宇宙银河系科普英文作文Title: Exploring the Wonders of the Milky Way Galaxy。

The Milky Way galaxy, our celestial home, is a vast and mysterious expanse that has captured the imaginations of humans for centuries. Stretching across approximately100,000 light-years, it is a swirling mass of stars, planets, nebulae, and other cosmic wonders. Let's embark on a journey to explore the fascinating features of our galaxy.First and foremost, the Milky Way is a barred spiral galaxy, characterized by a central bar-shaped structure surrounded by spiral arms. These arms are comprised of stars, gas, and dust, swirling in a majestic dance through space. Our solar system is situated within one of these spiral arms, known as the Orion Arm or Local Spur.At the heart of the Milky Way lies a supermassive black hole called Sagittarius A. This gravitational behemoth hasa mass equivalent to millions of suns and exerts a powerfulinfluence on the surrounding stars and matter. While it may seem ominous, Sagittarius A plays a crucial role in shaping the dynamics of our galaxy.Throughout the Milky Way, stellar nurseries known as nebulae dot the cosmic landscape. These clouds of gas and dust are where new stars are born, emerging from the swirling mists of creation. One of the most famous examples is the Orion Nebula, a stellar nursery located in the Orion Arm near our solar system.Among the myriad stars that populate the Milky Way, our own sun holds a special place. Classified as a yellow dwarf star, the sun is a relatively average-sized star in terms of mass and luminosity. Yet, it is the source of light and warmth that sustains life on Earth, making it indispensable to our existence.As we journey further into the Milky Way, we encounter a diverse array of star systems and exoplanets. Some of these worlds may harbor conditions conducive to life, sparking the imaginations of scientists and dreamers alike.While the search for extraterrestrial life remains ongoing, each discovery brings us closer to unraveling the mysteries of the cosmos.In addition to stars and planets, the Milky Way is home to various types of celestial phenomena, including supernovae, pulsars, and black holes. These cosmic events shape the evolution of galaxies and contribute to the rich tapestry of the universe. Studying them allows us to gain insight into the fundamental processes that govern the cosmos.One of the most awe-inspiring aspects of the Milky Way is its sheer scale and beauty. From the majestic spiral arms to the glittering star clusters, every corner of our galaxy is a testament to the wonders of the universe. Through telescopes and space probes, we continue to explore and uncover its secrets, expanding our understanding of the cosmos.In conclusion, the Milky Way galaxy is a captivating tapestry of stars, planets, and cosmic phenomena. From itscentral bulge to its spiral arms, it offers a glimpse into the vastness and complexity of the universe. As we continue to explore and study our celestial home, we deepen our appreciation for the beauty and grandeur of the cosmos.。

a r X i v :a s t r o -p h /0606682v 1 28 J u n 2006Mon.Not.R.Astron.Soc.000,1–17(2006)Printed 5February 2008(MN L A T E X style file v2.2)Mass Accretion onto T Tauri StarsS.G.Gregory 1⋆,M.Jardine 1,I.Simpson 1and J.-F.Donati 21School of Physics and Astronomy,University of St Andrews,North Haugh,St Andrews,Fife,KY169SS,U.K.2Laboratoired’Astrophysique,Observatoire Midi-Pyr´e n´e es,14Av.E.Belin,F-31400Toulouse,FranceABSTRACTIt is now accepted that accretion onto classical T Tauri stars is controlled by thestellar magnetosphere,yet to date most accretion models have assumed that their magnetic fields are dipolar.By considering a simple steady state accretion model with both dipolar and complex magnetic fields we find a correlation between massaccretion rate and stellar mass of the form ˙M ∝M α∗,with our results consistentwithin observed scatter.For any particular stellar mass there can be several orders of magnitude difference in the mass accretion rate,with accretion filling factors of a few percent.We demonstrate that the field geometry has a significant effect in controlling the location and distribution of hot spots,formed on the stellar surface from the high velocity impact of accreting material.We find that hot spots are often at mid to low latitudes,in contrast to what is expected for accretion to dipolar fields,and that particularly for higher mass stars,the accretion flow is predominantly carried by open field lines.Key words:Stars:pre-main sequence –Stars:magnetic fields –Stars:spots –Stars:formation –Stars:coronae –Stars:low mass,brown dwarfs1INTRODUCTIONClassical T Tauri stars (CTTSs)are young,low mass,pre-main sequence stars that are actively accreting from a sur-rounding disc which is the eventual birth-place of planets.Uchida &Shibata (1984)suggested that the magnetic field of a CTTS disrupts the inner disc.In the early 1990s several magnetospheric accretion models were developed (K¨o nigl 1991;Collier Cameron &Campbell 1993;Shu et al.1994)where material is lifted from the disc plane and is channelled along dipolar magnetic field lines onto the star,terminating in a shock at the photosphere.In an idealised model of a CTTS’s magnetic field there are closed field lines close to the star that contain the X-ray emitting corona,whilst at larger radii,there are closed field lines which thread the cir-cumstellar disc.It is along this latter set of field lines that accretion may proceed.There are also regions of open field which carry outflows in the form of a wind,and in some cases,as large collimated bipolar jets.Magnetospheric accretion models assume that CTTSs possess magnetic fields that are strong enough to dis-rupt the disc at a distance of a few stellar radii.Such strong fields have been detected in a number of systems using a variety of techniques.Average surface fields of 1-3kG have been detected most successfully by exploit-ing the Zeeman effect,both through Zeeman broaden-ing (e.g.Johns-Krull,Valenti &Koresko 1999b)and from⋆E-mail:sg64@the circular polarisation of lines which are sensitive to the presence of a magnetic field (e.g.Johns-Krull et al.1999a;Symington et al.2005;Daou,Johns-Krull &Valenti 2006).Field detections have also been made from the increase in line equivalent width (Basri,Marcy &Valenti 1992;Guenther et al.1999)and also from electron cyclotron maser emission,a coherent emission process from mildly rel-ativistic electrons trapped inside flux tubes close to the star (Smith et al.2003).The mean magnetic field strengths de-tected so far appear to be roughly constant across all stars (Valenti &Johns-Krull 2004).Traditionally magnetospheric accretion models have as-sumed the CTTSs have dipolar magnetic fields.Dipole fields (or inclined dipole fields)have been successively used to ex-plain some of the observations of CTTSs (e.g.the photopo-larimetric variability of AA Tau,O’Sullivan et al.2005),but fail to account for others.Valenti &Johns-Krull (2004)present magnetic field measurements for a number of stars,and despite detecting strong average surface fields from Zee-man broadening,often measurements of the longitudinal (line-of-sight)field component (obtained from photospheric lines)are consistent with no net circular polarisation.This can be interpreted as there being many regions of opposite polarity on the stellar surface,giving rise to oppositely po-larised signals which cancel each other out giving a net polar-isation signal of zero.This suggests that CTTSs have mag-netic fields which are highly complex,particularly close to the stellar surface;however,as Valenti &Johns-Krull (2004)point out,as the higher order multi-pole field components2S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donatiwill drop offquickly with distance from the star,the dipole component may still remain dominant at the inner edge of the disc.Also their measurements of the circular polarisa-tion of the HeI5876˚A emission line(believed to form in the base of accretion columns)are wellfitted by a simple model of a single magnetic spot on the surface of the star,suggest-ing that the accretingfield may be well ordered,despite the surfacefield being complex.The fractional surface area of a CTTS which is covered in hot spots,the accretionfilling factor f acc, is inferred from observations to be small;typically of order one percent(Muzerolle et al.2003;Calvet et al. 2004;Valenti&Johns-Krull2004;Symington et al.2005; Muzerolle et al.2005).Dipolar magneticfield mod-els predict accretionfilling factors which are too large.This,combined with the polarisation results,led Johns-Krull&Gafford(2002)to generalise the Shu X-wind model(Shu et al.1994)to include multipolar,rather than dipolar,magneticfields.With the assumption that the av-erage surfacefield strength does not vary much from star to star the generalised Shu X-wind model predicts a corre-lation between the stellar and accretion parameters of the form R2∗f acc∝(M∗˙MP rot)1/2,a prediction that matches observations reasonably well.In this paper we present a model of the accretion pro-cess using both dipolar and complex magneticfields.We apply our model to a large sample of pre-main sequence stars obtained from the Chandra Orion Ultradeep Project (COUP;Getman et al.2005),in order to test if our model can reproduce the observed correlation between mass accre-tion rate and stellar mass.An increase in˙M with M∗was originally noted by Rebull et al.(2000)and subsequently by White&Ghez(2001)and Rebull et al.(2002).The cor-relation was then found to extend to very low mass ob-jects and accreting brown dwarfs by White&Basri(2003) and Muzerolle et al.(2003),and to the higher mass,inter-mediate mass T Tauri stars,by Calvet et al.(2004).Fur-ther low mass data has recently been added by Natta et al. (2004),Mohanty,Jayawardhana&Basri(2005)and by Muzerolle et al.(2005)who obtain a correlation of the form ˙M∝M2.1∗,with as much as three orders of magnitude scatter in the measured mass accretion rate at any par-ticular stellar mass.However,Calvet et al.(2004)point out that due to a bias against the detection of higher mass stars with lower mass accretion rates,the power may be less than2.1.Further data for accreting stars in the ρ−Ophiuchus star forming region has recently been added by Natta,Testi&Randich(2006).The physical origin of the correlation between M∗and ˙M,and the large scatter in measured˙M values,is not clear;however several ideas have been put forward.First, increased X-ray emission in higher mass T Tauri stars (Preibisch et al.2005;Jardine et al.2006)may cause an in-crease in disc ionisation,leading to a more efficient magne-torotational instability and therefore a higher mass accretion rate(Calvet et al.2004).Second,Padoan et al.(2005)ar-gue that the correlation˙M∝M2∗arises from Bondi-Hoyle accretion,with the star-disc system gathering mass as it moves through the parent cloud.In their model the observed scatter in˙M arises from variations in stellar velocities,gas densities and sound speeds.Mohanty et al.(2005)provide a detailed discussion of both of these suggestions.Third,Alexander&Armitage(2006)suggest that the correlation may arise from variations in the disc initial conditions com-bined with the resulting viscous evolution of the disc.Intheir model they assume that the initial disc mass scales linearly with the stellar mass,M d∝M∗,which,upon mak-ing this assumption,eventually leads them to the conclusionthat brown dwarfs(the lowest mass accretors)should have discs which are larger than higher mass accretors.However, if it is the case that the initial disc mass increases more steeply with stellar mass,M d∝M2∗,then the stellar mass -accretion rate correlation can be reproduced with smaller brown dwarf discs of low mass(of order one Jupiter mass). Thus the Alexander&Armitage(2006)suggestion,if cor-rect,will soon be directly verifiable by observations.Fourth, Natta et al.(2006)suggest that the large scatter in the cor-relation between˙M and M∗may arise from the influence of close companion stars,or by time variable accretion.It should however be noted that Clarke&Pringle(2006)take a more conservative view by demonstrating that a steep cor-relation between˙M and M∗may arise as a consequence of detection/selection limitations,and as such˙M∝M2∗is per-haps not a true representation of the correlation between˙M and M∗.In§2we describe how magneticfields are extrapolated from observed surface magnetograms.In§3we consider ac-cretion onto an aligned,and then a tilted dipolefield,to develop a simple steady state accretion model and to inves-tigate how tilting thefield affects the mass accretion rate.In §4these ideas are extended by considering magneticfields with a realistic degree of complexity and we apply our accre-tion model to study the correlation between mass accretion rate and stellar mass,whilst§5contains our conclusions.2REALISTIC MAGNETIC FIELDSFrom Zeeman-Doppler images it is possible to extrapolate stellar magneticfields by assuming that thefield is po-tential.At the moment we do not have the necessary ob-servations of CTTSs,but we do have for the solar like stars LQ Hya and AB Dor(Donati&Collier Cameron 1997;Donati et al.1997;Donati1999;Donati et al.1999; Donati et al.2003),which have differentfield topologies (Jardine,Collier Cameron&Donati2002a;Hussain et al. 2002;McIvor et al.2003;McIvor et al.2004).Using their field structures as an example we can adjust the stellar pa-rameters(mass,radius and rotation period)to construct a simple model of a CTTS,surrounded by a thin accretion disc.The method for extrapolating magneticfields follows that employed by Jardine et al.(2002a).Assuming the mag-neticfield B is potential,or current-free,then∇×B=0. This condition is satisfied by writing thefield in terms of a scalarflux functionΨ,such that B=−∇Ψ.Thus in order to ensure that thefield is divergence-free(∇·B=0),Ψmust satisfy Laplace’s equation,∇2Ψ=0;the solution of which is a linear combination of spherical harmonics,Ψ=Nl=1l m=−l a lm r l+b lm r−(l+1) P lm(θ)e imφ,(1) where P lm denote the associated Legendre functions.It thenMass Accretion onto T Tauri Stars3 follows that the magneticfield components at any point(r,θ,φ)are,B r=−Nl=1l m=−l[la lm r l−1−(l+1)b lm r−(l+2)]P lm(θ)e imφ(2)Bθ=−Nl=1l m=−l[a lm r l−1+b lm r−(l+2)]dsinθime imφ.(4)The coefficients a lm and b lm are determined from the radial field at the stellar surface obtained from Zeeman-Doppler maps and also by assuming that at some height R s above the surface(known as the source surface)thefield be-comes radial and hence Bθ(R s)=0,emulating the effect of the corona blowing openfield lines to form a stellar wind (Altschuler&Newkirk1969).In order to extrapolate the field we used a modified version of a code originally devel-oped by van Ballegooijen,Cartledge&Priest(1998).2.1Coronal extentWe determine the maximum possible extent of the corona (which is the extent of the source surface)by determining the maximum radius at which a magneticfield could contain the coronal gas.Since a dipolefield falls offwith radius most slowly,we use this to set the source surface.For a given sur-face magnetogram we calculate the dipolefield that has the same averagefield strength.We then need to calculate the hydrostatic pressure along eachfield line.For an isothermal corona and assuming that the plasma along thefield is in hydrostatic equilibrium then,p s=p0exp 1r2+ω2r sin2θ,ω2r sinθcosθ,0 .(6) We can then calculate how the plasmaβ,the ratio of gas to magnetic pressure,changes along eachfield line.If at any point along afield lineβ>1then we assume that the field line is blown open.This effect is incorporated into our model by setting the coronal(gas)pressure to zero whenever it exceeds the magnetic pressure(β>1).We also set the coronal pressure to zero for openfield lines,which have one foot point on the star and one at infinity.The gas pressure, and therefore the plasmaβ,is dependent upon the choice of p0which is a free parameter of our model.Jardine et al. (2006)provide a detailed explanation of how p0,the coronal base(gas)pressure,can be scaled to the magnetic pressure at afield line foot point,so we provide only an outline here. We assume that the base pressure is proportional to the magnetic pressure then p0=KB20,a technique which has Table1.Data for CTTSs from Valenti&Johns-Krull(2004) DF Tau0.17 3.98.5 2.47CY Tau0.58 1.47.59.554S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati(a)(b)Figure1.Field lines which could support accretionflows for a model of a CTTS with afield topology that resembles(a)LQ Hya, obtained using the DF Tau parameters from Table1,and(b)AB Dor using the CY Tau parameters.The stellar surface is coloured to show the strength of the radial component of thefield,with red representing1kG and black-1kG.Field lines have been drawn from the corotation radius.For the lower mass star,DF Tau,the natural extent of its corona would be beyond corotation and therefore there is a mixture of open and closedfield lines threading the disc at R co.The higher mass star,CY Tau,has a more compact corona and material flows along openfield lines from corotation.measure in the same way as Jardine et al.(2006).To de-termine if afield line can accrete wefind where it threads the disc and calculate if the effective gravity along the path of thefield line points inwards,towards the star.From this subset offield lines we select those which haveβ<1along their length.In other words,for any given solid angle we assume that accretion can occur along thefirstfield line within the corotation radius which is able to contain the coronal plasma.We assume that the loading of disc mate-rial onto thefield lines is infinitely efficient,such that the firstfield line at any azimuth which satisfies the accretion conditions will accrete,and thatfield lines interior to this are shielded from the accretionflow.We also assume that the accretingfield is static and is therefore not distorted by the disc or by the process of accretion.In§3.3we consider in more detail how to determine whichfield lines are able to support accretionflows,in order to calculate mass accretion rates and accretionfilling factors.Fig.1shows thefirst set offield lines which may be accreting,obtained by surrounding thefield extrapolations of LQ Hya and AB Dor with a thin wedge-shaped accretion disc,with an opening angle of approximately10◦.In§3we develop a model for isothermal accretionflows where mate-rial leaves the disc at a low subsonic speed,but arrives at the star with a large supersonic speed.Not all of thefield lines in Fig.1are capable of supporting such accretionflows, and instead represent the maximum possible set offield lines which may be accreting.We assume a coronal temperature of10MK and obtain the gas pressure at the base of eachfield line as discussed in§2.1and by Jardine et al.(2006).The natural extent of the corona of DF Tau would be beyond the corotation radius and therefore accretion occurs along a mixture of closed and openfield lines from corotation.One suggestion for how accretion may proceed along openfield lines is that an openfield line which stretches out into the disc,may reconnect with another openfield line for long enough for accretion to occur,only to be sheared open once again.This is of particular importance for the higher mass stars,such as CY Tau,where in some cases wefind that the inner edge of the disc is sitting in a reservoir of radial openfield lines.This may have important implications for the transfer of torques between the disc and star.However more work is needed here in order to develop models for accretion along openfield lines.Thesefield extrapolations suggest that accretion may occur alongfield lines that have very different geometries. Indeed,a substantial fraction of the total mass accretion rate may be carried on openfield lines.Before developing a detailed model of the mass accretion process,however,we first consider the simple case of a tilted dipole.While this is an idealisation of the true stellarfield it allows us to clarify the role that the geometry of thefield may have in governing the mass accretion process.3ACCRETION TO A DIPOLEWe have constructed two simple analytic models as sketched in Fig.2.Thefirst case is for a star with a dipolarfield with the dipole momentµaligned with the stellar rotation axisΩ.In standard spherical coordinates thisfield may be described as,B= 2µr3sinθ,0 ,(7)Mass Accretion onto T Tauri Stars5Figure 2.An aligned and tilted dipole field geometry.The aligned dipole (left)with a field line in the star’s meridional plane,with the dipole moment µaligned with the stellar rotation axis Ω,and the perpendicular dipole (right)with a field line in the star’s equatorial plane,with µperpendicular to Ω.The averagesurfacefieldstrength matches that considered by Jardine et al.(2006)with yellow (blue)representing the positive (negative)magnetic pole.a scenario that allows us to model accretion flows along fieldlines in the star’s meridional plane.If we then take this field structure and tilt it by π/2radians such that µnow lies in the star’s equatorial plane,perpendicular to Ω,then those field lines which ran north-south in the meridional plane,now lie east-west in the equatorial plane,with,B =2µr 3sin φ.(8)Throughout we shall refer to these cases as the perpendic-ular dipole for the tilted dipole field and the aligned dipole for the aligned dipole field.To do this we consider steady isothermal accretion flows from a thin accretion disc ori-ented such that the disc normal is parallel to the stellar rotation axis.An initial sonic Mach number,M ,is ascribed to the accreting material.We then calculate the pressure and velocity profiles,relative to arbitrary initial conditions defined at the disc plane.We calculate the ratio of pressure p at each point along a field line,relative to that at the disc,p d ;and then from this we calculate how the Mach number of the flow changes along the field.The path of a field line may be described by B rrdθ=B φB d=R d4−3r2µ+1dsv 2ds+ρg ef f ·ˆs ,(14)since the Coriolis term (−2ρω×v )does not contribute for flows along the field,and where ˆs (r )is a unit vector along the path of the field line.Throughout terms with a sub-script d will denote quantities defined at the disc;for exam-ple ρd ,p d ,v d and B d are respectively the density,pressure,velocity along the field and the magnetic field strength as defined at the plane of the disc,a radial distance R d from the centre of the star.Integrating equation (14)from the disc plane to some position along the field line at a distance r from the stellar centre,and using the isothermal equation of state for an ideal gas,p =ρc 2s ,gives,lnpc 2s−1ds (ρvA )=0(16)dB=p d v dp d+1pB2M 2−1c s=Mp dB d,(20)where in both cases M =v d /c s denotes the initial sonic Mach number at which the accretion flow leaves the plane6S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati of the disc.It is then possible tofind the pressure at eachpoint along afield line,relative to the pressure at the disc(p/p d),byfinding the roots of(19).Once these roots havebeen found the velocity profile can be obtained from(20)by calculating how the Mach number of theflow varies asmaterial moves from the disc to the star.3.2Pressure and velocity profilesFor the perpendicular dipole,in the star’s equatorial plane,the effective gravity has only a radial component,g ef f= −GM∗p d +1r 6 4−3r p 2−1 R d−1R∗c2s(23)Φc=1c s 2.(24)The roots of(22)give the pressure at some point along a field line loop which is a radial distance r from the stellar centre.For the aligned dipole,in the star’s meridional plane, the effective gravity has both an r andθcomponent,g ef f= −GM∗p d +1r 6 4−3r p 2−1R d−1R d =0.(26)The only difference from the perpendicular dipole is in the final term.For a CTTS with a mass of0.5M⊙,radius2R⊙and a rotation period of7days we have calculated the pressure and velocity structure along accreting dipolefield lines,for a range of accretionflow temperatures,starting radii and ini-tial sonic Mach numbers.Figs.3(a)and3(b)show a typical pressure and velocity profile for the perpendicular dipole, whilst those for the aligned dipole are qualitatively similar. The pressure profile shows how the ratio p/p d,where p is the pressure along thefield line and p d the pressure at the disc, varies as theflow moves from the disc to the star(plotted logarithmically for clarity).The velocity profile shows how the Mach number of theflow changes along thefield line.For different accretionflow temperatures and starting radii the resulting profiles are similar,except in a few select cases, as discussed in the next section.Fig.3is for an accretion flow leaving the disc at R d=6.0R∗,which is approximately the equatorial corotation radius R co where,R co= GM∗Mass Accretion onto T Tauri Stars7(a)(b)Figure3.The resulting pressure and velocity profiles for accretion along equatorial dipolefield lines.The inner edge of the disc is at R d=6.0R∗which is approximately the corotation radius.Different lines represent different initial velocities.accretionflows.We further check to ensure that the plasma beta resulting from accretion remains<1along their length. Therefore,at any particular azimuth,accretion occurs along thefirstfield line at,or slightly within,the corotation radius; thefield line must be able to contain the coronal plasma and have a sonic point along its length.In order to determine if afield line can support a transonic accretionflow,thefirst step is tofind the pressure and velocity structure its length, which will be similar to those described in§3.2.To do this we need to determine the initial Mach number that would produce an accretionflow.We can achieve this by determin-ing if afield line has a sonic point as discussed in Appendix A.To calculate a mass accretion rate we require the veloc-ity and density of each accretionflow at the stellar surface, and also the surface area of the star covered in hot spots. For an assumed accretionflow temperature we determine the initial Mach number required to generate a transonic velocity profile,along eachfield line,and determine the in-fall velocity from(20).At every point along afield line we know the ratio of pressure at that point,to that at the disc, p/p d.For an isothermal equation of state p∝ρ,so we also know the ratio of densitiesρ/ρd at every point along the accretingfield line.Thus for a given disc midplane density ρd,we can estimate the density at the stellar surfaceρ∗. Throughout we assume a constant disc midplane density of ρd=5.0×10−9gcm−3,a resonable value at the corotation radius for T Tauri stars(e.g.Boss1996).The mass accre-tion rate may be expressed in terms of quantities defined at the disc plane,with˙M∝ρd.Therefore raising or lowering ρd directly increases or decreases˙M.We estimate the to-tal surface area of the star covered in accretion hot spots by summing the area of individual grid cells which contain accretingfield line foot points.For each grid cell i(of area A i)on the stellar surface we obtain the average in-fall ve-locity¯v∗and average density¯ρ∗of material accreting into that cell.Most grid cells do not contain any accretingfield line foot points and therefore do not contribute to the mass accretion rate.The mass accretion rate is then the sum over all cells i containing accretingfield line foot points,˙M= i˙M i= i[A¯v∗¯ρ∗]i.(28) The mass accretion rate can be expressed equivalently as ˙M=ρdv d A d,where A d is the surface area of the disc that contributes to accretion(which depends on the radial extent of accretingfield lines within the disc).Using the surface area of grid cells within the disc which contain accreting field lines to estimate A d,we obtain˙M values that are com-parable to those calculated from(28).Therefore it makes little difference which formulation for˙M is used.The accre-tionfilling factor f acc,the fractional surface area of the star covered in hot spots,is then calculated from,f acc= i A i8S.G.Gregory,M.Jardine,I.Simpson and J.-F.Donati(a)(b)(c)(d)Figure4.(a)The change in mass accretion rate and(b)the accretionfilling factor as a function ofβ,for accretion to dipolefields whereβis the obliquity-the angle between the rotation and magnetic poles,for accretionflow temperatures of1000K(solid),2500K (dotted),5000K(short dash),7500K(long dash)and10000K(dash-dot).(c)and(d)show how the contribution to the accretionfilling factor from accreting closed and openfield changes withβ.The DF Tau parameters from Table1have been used.There are no open accretingfield lines for the T acc=1000K case.ofβ.This,in part,can be attributed to the increase in theamount of openfield lines which thread the disc,and are ableto support accretion asβis increased(see Fig.4(d)).As thedipole is tilted fromβ=0◦to10◦the mass accretion rateis reduced(see Fig.4(a)).This can be understood by thechanging shape of the closedfield lines asβis increased.Foraccretion along aligned dipolefield lines,accreting materialmayflow along two identical paths from the disc to the star;that is it may accrete either onto the northern,or the south-ern hemisphere.Once the dipole has been tilted through asmall angle,the path along thefield onto each hemispherechanges,with one segment of the closedfield line loop beingshallower than before and curved towards the star,and theother being longer.This longer segment bulges out slightly,so that materialflowing along suchfield lines follows a pathwhich initially curves away from the star,before loopingback around to the stellar surface.This creates a differencein initial Mach numbers necessary to create transonic accre-tionflows along the differentfield line segments,with thenet result that some closedfield line segments are no longerMass Accretion onto T Tauri Stars9(a)(b)(c)(d)Figure 5.The stellar surface with white (black)points indicating the closed (open)accreting field line foot points for accretion to a dipole with obliquity (a)β=0◦,the aligned dipole,where accretion proceeds onto two rings in opposite hemispheres;(b)β=15◦where the accretion rings have been distorted and open field lines produce the small bands centred on 180◦and 360◦longitude;(c)β=45◦where accretion occurs predominantly along the open field lines and (d)β=90◦,the perpendicular dipole,where accretion occurs in bars around the star’s equator.All are for an accretion flow temperature of 104K.The average surface field strength matches that considered by Jardine et al.(2006)with yellow (blue)representing the positive (negative)magnetic pole.able to accrete transonically when β=10◦(see Fig.4(c)).As the dipole is tilted further from β=10◦to ≈30◦−40◦the mass accretion rate increases in all but the lowest T acc cases.This is because once the dipole has been tilted far enough the open field lines (those that have foot points at latitudes closer to the magnetic axis)begin to intersect the disc (see Fig.4(d)).There are therefore more possible paths that material can take from the disc to the star,causing anincrease in ˙M(again in all but the lower T acc cases).As βis further increased the amount of accreting closed field lines continues to reduce,whilst the amount of open field lines threading the disc reaches a maximum,and we therefore see a trend of falling mass accretion rates towards the largest values of β.The accretion flow temperature is important in deter-mining whether open field lines are able to support transonic accretion flows.From Figs.4(c)and 4(d)it is clear that the contribution to accretion from the closed field is constant for all values of T acc ,whereas the contribution from the open field depends strongly on T acc ,with more open field lines accreting at higher accretion flow temperatures.At the low-est accretion flow temperature which we consider (1000K),there are no open field lines able to support transonic ac-cretion,even for the large values of βwhere there are many such field lines passing through the disc.This can be under-stood as follows.For transonic accretion a sonic point mustexist on a field line.At a sonic point v =c s ;applying this to (20),substituting into (19)and rearranging gives,1dsv 2−c 2s=g ef f ·ˆs −c 2sds,(30)from which it can be seen that there exists some critical radius r c where either v =c s or dv/ds =0.Clearly at this critical radius the two terms on the RHS of (30)must be equal,c 2s ds=g ef f ·ˆs ,(31)where all the terms are evaluated at r c .It should be noted that (31)may also be obtained by finding the maximum turning point of (A5),consistent with our argument in Ap-pendix A.The condition for a sonic point to exist on any field line,open or closed,may be expressed as equation (31).ˆs is a unit vector along the path of the field which may be written as ˆs =B /B ,which we can use to rewrite (31)as,c 2sdB。

英语关于黑洞的作文The Mysterious and Fascinating Black Holes.In the vast and enigmatic universe, black holes standas one of the most intriguing and perplexing phenomena. These regions of space, characterized by their intense gravity and complete absence of light, have captivated the imagination of scientists and laypeople alike for centuries. Despite their otherworldly nature, black holes play acrucial role in understanding the evolution and structureof our universe.The concept of black holes emerged in the late 18th century, with the pioneering work of scientists like John Michell and Pierre-Simon Laplace. They theorized the existence of objects so massive that not even light could escape their intense gravitational pull. However, it wasnot until the 20th century that astronomers began to gather evidence that supported the existence of these mysterious objects.One of the most significant milestones in the study of black holes was the work of Albert Einstein. His theory of general relativity provided a mathematical framework to describe the behavior of gravity and its interaction with matter. This theory laid the foundation for understanding the properties of black holes, including their formation, evolution, and interaction with their environment.Black holes are formed when a massive star collapses under its own weight at the end of its life cycle. This collapse compresses the star's matter into a tiny, ultra-dense region known as a singularity. The gravity around this singularity is so intense that nothing, including light, can escape its pull. The boundary of this region, known as the event horizon, marks the point where the escape velocity exceeds the speed of light.There are two main types of black holes: stellar-mass black holes and supermassive black holes. Stellar-mass black holes are formed when a star of about 10 to 30 times the mass of the Sun collapses. These black holes have adiameter of only a few kilometers but possess a mass comparable to that of a small star. On the other hand, supermassive black holes have masses ranging from millionsto billions of times the mass of the Sun. They are believed to reside at the centers of most galaxies, including ourown Milky Way.The study of black holes has revealed much about the structure and dynamics of the universe. For instance, black holes play a crucial role in the evolution of galaxies. By accreting matter and emitting radiation, they can significantly impact the star formation and gas dynamics of their host galaxies. Additionally, the merging of black holes, a common occurrence in the universe, can emit gravitational waves, ripples in the fabric of spacetimethat can be detected by advanced telescopes like the Laser Interferometer Gravitational-Wave Observatory (LIGO).Despite their otherworldly nature, black holes are not entirely devoid of life. In fact, there are theories that suggest the existence of accretion disks around black holes. These disks are formed when matter from a nearby star orgas cloud is attracted to the black hole and begins toorbit it. As the matter spirals inward, it heats up and emits radiation, creating a bright and energetic environment.The study of black holes also holds the key to understanding some of the most fundamental questions about our universe. For instance, black holes provide a unique laboratory to test the limits of Einstein's theory of general relativity. By studying the behavior of matter and light near the event horizon, scientists can gain insights into the nature of gravity and its interaction with quantum mechanics.In conclusion, black holes are one of the most mysterious and fascinating phenomena in the universe. They challenge our understanding of gravity, matter, and the structure of the cosmos. As we continue to explore and study these enigmatic objects, we may unlock the secrets of the universe and gain a deeper understanding of our placein the cosmos.。

小学上册英语第1单元测验试卷考试时间：100分钟（总分:120）A卷一、综合题(共计100题共100分)1. 选择题：What is the capital of the United States?A. New YorkB. Los AngelesC. WashingtonD.C.D. Chicago答案：C2. 选择题：What do we call the solid part of the Earth?A. AtmosphereB. HydrosphereC. LithosphereD. Biosphere答案：C3. 填空题：The elephant's trunk is used for eating, drinking, and ________________ (交流).4. 填空题：_____ (离子) in soil can affect plant health.5. 选择题：What is the name of the famous American author known for his horror stories?A. Edgar Allan PoeB. Mark TwainC. Ernest HemingwayD. F. Scott Fitzgerald答案: A6. 听力题：She is ___ (smiling/crying) at the picture.When an acid is mixed with a base, they neutralize each other and form _______.8. 选择题：What do we call a person who draws pictures?A. IllustratorB. PainterC. Sketch ArtistD. All of the above9. 填空题：My favorite animal is a ______ (兔子) because they are gentle.10. 填空题：My dad loves to ________ (修理) cars.11. 填空题：I want to _______ (学会) how to skateboard.12. 填空题：The __________ (历史的演绎) reveals complexity.13. 选择题：What do you call a baby cat?A. PuppyB. KittenC. CubD. Calf答案: B14. 填空题：The ______ (生物多样性) of plants is essential for ecosystems.15. 填空题：I feel ______ when I learn new things.16. 听力题：A covalent bond is formed when atoms __________ electrons.17. 填空题：The __________ (挥发性) of a substance refers to how easily it evaporates.18. 听力题：A __________ is a large area of ice.The flowers are ________ (香气扑鼻).20. 听力题：A thermometer measures _______.21. 听力题：I like to ________ in the morning.22. 听力题：The chemical formula for calcium chloride is _______.23. 填空题：I love _______ (观看) the stars at night.24. 听力题：A solar system can have many _____, but usually has one star.25. 填空题：In _____ (印度), there are many active volcanoes.26. 填空题：My favorite fruit is _______ (苹果).27. 选择题：What is the capital city of Gabon?A. LibrevilleB. Port-GentilC. FrancevilleD. Moanda28. 填空题：I love my new ________ (积木). I can build many different things with it.29. 填空题：_____ (pollination) is vital for fruit production.30. 选择题：What do we call a group of stars?A. ConstellationB. GalaxyC. ClusterD. Nebula答案:AWhich of these numbers is even?A. 3B. 5C. 8D. 1132. (64) is the fastest river in the world. 填空题：The ____33. 听力题：We go _____ (swimming) in the pool.34. 听力题：A rabbit's ears are used for ______.35. 填空题：My ________ (玩具名称) is a great way to learn about feelings.36. 听力题：Chemical changes can produce new ________.37. 选择题：What do you call the person who studies the stars?A. BiologistB. AstronomerC. ChemistD. Geologist答案:B38. 听力题：I can ________ a message.39. 填空题：The __________ is a major river in Europe. (多瑙河)40. 选择题：What do we call a young horse?A. FillyB. FoalC. ColtD. All of the above答案: D41. 听力题：A rabbit has big _____ ears.The ______ (根茎的生长) supports nutrient uptake.43. 听力题：The cake is ______ with chocolate icing. (frosted)44. 选择题：What is the capital of the USA?A. LondonB. ParisC. Washington,D. C.D. New York45. 填空题：The _______ (The Gulf War) involved a coalition against Iraq in the early 1990s.46. 填空题：A ____(strategic partnership) strengthens relationships for mutual benefit.47. 选择题：Which is a large body of water?A. LakeB. PondC. RiverD. Ocean答案：D48. 听力题：A __________ is a physical change that alters the appearance.49. 听力题：The state of matter with no definite shape is ______.50. 听力题：The chemical formula for iron(III) oxide is __________.51. 选择题：What is the primary color that is a mix of blue and yellow?A. GreenB. PurpleC. OrangeD. Brown答案: A52. 听力题：We are going to ________ a concert.What is the main meal of the day?A. BreakfastB. LunchC. DinnerD. Snack答案:C54. 填空题：I like to ______ (参加) science experiments.55. 听力题：The Earth's surface is shaped by geological and ______ processes.56. 听力题：The process of extracting oil from seeds is called ______.57. 填空题：The ________ was a monument built to honor a famous leader.58. 填空题：The __________ can be quite chilly in the morning. (气温)59. 听力题：The _______ of an object can affect its movement.60. 选择题：What is the name of the famous American author known for writing about the American South?A. William FaulknerB. Harper LeeC. Tennessee WilliamsD. All of the above答案:D61. 听力题：Vikings are known for their _______ and exploration.62. 听力题：The _______ can help maintain the balance of nature.63. 选择题：What is the main ingredient in sushi?A. RiceB. NoodlesC. BreadD. Potatoes64. 听力题：The capital of Palau is __________.65. 选择题：How many wheels does a bicycle have?a. Oneb. Twoc. Threed. Four答案:b66. 选择题：What do you call a group of lions?A. PackB. PrideC. FlockD. Gaggle答案:B67. 填空题：My brother plays _______ in the band.68. 填空题：A rabbit can be very ______ (活泼) and playful.69. 听力题：My uncle is a fantastic ____ (gardener).70. 听力题：The concept of continental drift explains how continents ______ over time.71. 选择题：What do bees make?A. MilkB. HoneyC. ButterD. Sugar72. 听力题：A _______ is a chemical process that produces gas.73. 听力题：The sun rises in the ______ (east).74. 选择题：What is the capital of Libya?A. TripoliB. BenghaziC. MisrataD. Sabha75. 听力题：The teacher is ___ (kind/strict).76. 听力题：She is a great ________.77. 选择题：What is the freezing point of water?A. 0 degrees CelsiusB. 32 degrees CelsiusC. 100 degrees CelsiusD. 50 degrees Celsius答案:A. 0 degrees Celsius78. 填空题：My cat enjoys lounging in the ______ (阳光).79. 听力题：The study of the history of Earth through rock layers is known as ______.80. 听力题：The weather is very ___. (nice)81. 填空题：In a solution, the substance in the greatest amount is called the _______. (溶剂)82. 听力题：The boy likes to play ________.83. 填空题：The _____ (小鸭) quacks happily in the water.84. 听力题：The _____ (sand/gravel) is warm.85. 选择题：What do you call it when water falls from the sky?A. RainB. SnowC. HailD. Sleet答案:A86. 听力题：She brought a ________ for lunch.87. 选择题：What do you call the part of the plant that absorbs water?A. LeafB. StemC. RootD. Flower答案:C88. 选择题：How many continents are there?A. FiveB. SixC. SevenD. Eight89. 听力题：The bell is ___ (ringing) loudly.90. 听力题：I want to _____ (visit) the zoo.91. 填空题：The capital of Greece is ________ (雅典).92. 听力题：The chocolates are ______ (delicious) and rich.93. 选择题：Which animal can swim?A. DogB. CatC. FishD. Bird答案: C94. 填空题：Understanding how to care for plants can result in a flourishing ______. (了解如何照顾植物可以导致丰盛的花园。

*翻译说明:1.翻译内容为value="" 双引号里面的内容.2.一定要注意类似&#xA;&#xA这样的转换符,原文是对应哪部分的句子,翻译后还是要保持相对位置.3.标点统一用半角英文.4.人名,地名,特殊名词这些名词全部保留,并在译文最后填上,加上你觉得正确的翻译.5.基本时间定为一周,请尽量解决错字,格式错误,标点等问题,并尽量将句子完善,不要出现直译的现象.PS:这一点如果能坚持,可以很大程度的提高你的水平,当然这也是最难的一点.6.如果觉得整个文本没有问题了,请回复到原来的邮件.7.请注意,文本一旦交上,即被认为是个人最高水平,所以请尽量将文本改好再提交.8.可以鸡翻,但请修改得跟手翻一样再提交,确保审核人员看不出痕迹.9.如果有问题可以在邮件或者群里发问.<string enum="11Pan_Geo_Alpha_Centauri" value="Alpha Centauri System" /><string enum="Pan_Geo_Alpha_Centauri_Desc" value="&lt;b&gt;Distance FromEarth:&lt;/b&gt; Approximately 4.37 light-years&#xA;&#xA;&lt;b&gt;Description:&lt;/b&gt; Alpha Centauri, the brightest &quot;star&quot; in the constellation of Centaurus, when seen through a telescope, is, in fact, three stars orbiting around one another. This triple star system consists of two Sun-like stars, Alpha Centauri A and Alpha Centauri B, and a red dwarf, Alpha Centauri C." /><string enum="Pan_Geo_Alpha_Centauri_Desc02" value="&lt;b&gt;PlanetaryBodies&lt;/b&gt;&#xA;&#xA;The three gas giant planets orbiting Alpha Centauri B were discovered by terrestrial observatories. The five rocky planets were found two decades later. Since the arrangement of the planets resembled our own solar system, they were named for their counterparts: Vulcan (inside Mercury's orbit), Hermes (Mercury), Aphrodite (Venus), Gaea (Earth), Ares (Mars), Zeus (Jupiter), Cronus (Saturn), and Poseidon (chosen instead of another name for Uranus, because it occupies the equivalent of Neptune's orbit). &#xA;&#xA;The three gas giants in the system orbited far enough from ACB to be perturbed by its companion star, so their orbits were chaotic and varied wildly. Given these perturbations, there was speculation regarding the possibility of a collision between Cronus and Poseidon in the next century. Indeed, if any satellites had ever formed around these gas giants in the past, they had long ago been ejected, or drawn into the planet.&#xA;&#xA;The three gas giants around ACA were not found until after theco-orbiting synchronized telescopic interferometer network (COSTIN) went into full operation. Upon their discovery they were named Oceanus, Coeus, and Crius. &#xA;&#xA;Alpha Centauri is a trinary star system, and Earth's closest stellar neighbor outside the solarsystem.&#xA;&#xA;Its largest member, Alpha Centauri A (or &quot;ACA&quot; to astronomers), is about twenty-percent larger than our Sun, but otherwise very similar. ACA would be unremarkable were it not for the fact that it serves as the sun for 潘多拉, a large moon that orbits the planet Polyphemus. It was on 潘多拉that explorers encountered the Na'vi, the only intelligent species yet discovered in outer space. 潘多拉is also the only known source of unobtanium, a high-temperature superconductor essential for many of Earth'stechnologies.&#xA;&#xA;Alpha Centauri B (ACB) is about fifteen percent smaller than our Sun, and noticeably orange because it is 500 °K cooler than its neighboring star. Alpha Centauri C (ACC) is a red dwarf, only twenty percent of the size of the Sun and less than half its temperature. ACC gives off only a dim red glow instead of the bright yellow glare of the Sun and ACA." /> <string enum="Pan_Geo_Alpha_Centauri_Desc03"value="&lt;b&gt;Location&lt;/b&gt;&#xA;&#xA;The astronomical coordinates for the Centaurus star system are: Right Ascension 14h 39.6m; Declination -60° 50'. Alpha Centauri A and B are located approximately 4.37 light-years or 277,600 Astronomical Units from Earth. (One AU equals about 93,000,000 miles, the average distance of the Earth from the Sun.). Alpha Centauri C (also called &quot;Proxima Centauri&quot; because it is the closest of the three stars to Earth) is about 0.15 light-years closer.&#xA;&#xA;&lt;b&gt;OrbitalElements&lt;/b&gt;&#xA;&#xA;Alpha Centauri A and B have a highly elliptical orbit (e = 0.52) about their common center of mass, with their separation ranging from 11.2 to 35.6 AU; it takes slightly less than eighty years for them to complete one revolution. Recent periastrons (point of closest approach) were in 1955, 2035, 2115, and the next one will occur in 2195. Alpha Centauri C, located more than 10,000 AU away from ACA and ACB, is very weakly bound to them by gravity and takes approximately a million years to orbit the two larger stars. It is possible that perturbations by the next closer stars may eventually disrupt ACC's orbit, and free it to wander by itself." /><string enum="Pan_Geo_Alpha_Centauri_A" value="Alpha Centauri A" /><string enum="Pan_Geo_Alpha_Centauri_A_Desc" value="&lt;b&gt;Location:&lt;/b&gt; Alpha Centauri system&#xA;&#xA;&lt;b&gt;Distance From Earth:&lt;/b&gt; Approximately4.37 light-years&#xA;&#xA;&lt;b&gt;Star Classification:&lt;/b&gt; G1V&#xA;&#xA;&lt;b&gt;Description:&lt;/b&gt; Alpha Centauri A (or &quot;ACA&quot;), the brightest of the three stars comprising the Alpha Centaurus System, is similar to Earth's Sun, although it is roughly twenty percent larger. There are five planets revolving around the star, including the gas giant Polyphemus. Since Polyphemus's orbit is about twenty percent larger than Earth's, Alpha Centauri A appears almost identical to the Sun as seen from theEarth.&#xA;&#xA;&lt;b&gt;Notes:&lt;/b&gt; The planets orbiting ACA were not discovered until late in the 21st century. Home system of 潘多拉, (a moon of Polyphemus) and the Na'vi." /> <string enum="Pan_Geo_Alpha_Centauri_B" value="Alpha Centauri B" /><string enum="Pan_Geo_Alpha_Centauri_B_Desc" value="&lt;b&gt;Location:&lt;/b&gt; Alpha Centauri system&#xA;&#xA;&lt;b&gt;Distance from Earth:&lt;/b&gt; Approximately 4.37 light-years&#xA;&#xA;&lt;b&gt;Star Classification:&lt;/b&gt; K1V&#xA;&#xA;&lt;b&gt;Description:&lt;/b&gt; Alpha Centauri B (or &quot;ACB&quot;), the second brightest of the three stars that comprise Alpha Centaurus, is smaller and cooler thanEarth's Sun. It is visible in 潘多拉's daytime sky for roughly one-half of the Polyphemus year. It is visible in the night sky for most of the other half of theyear.&#xA;&#xA;&lt;b&gt;Notes:&lt;/b&gt; The star's light is noticeably orange." /><string enum="Pan_Geo_Pandora" value="潘多拉" /><string enum="Pan_Geo_Pandora_Desc" value="Although 潘多拉is a satellite of Polyphemus, it has much more in common with Earth than with our Moon. Fairly similar in size, atmosphere, and appearance, it has continents and islands surrounded by seas of a familiar bluehue. Clouds range in color from fluffy white to towering dark thunderheads. The landforms have mountains, valleys, plains, lakes, and rivers. Plant life is everywhere: forests and meadows cover much of the land, and rafts of floating seaweed dot the oceans. Vast herds of grazing animals roam the open prairie and huge flying creatures fill the skies.&#xA;&#xA;But 潘多拉is not Earth, and its paradise is deceiving. The nitrogen-oxygen atmosphere is much denser than our own. It contains so much carbon dioxide (about 19%) that humans who breathe it directly will rapidly become unconscious and die. Another toxic gas, hydrogen sulfide, is spewed out by hundreds of continually erupting volcanoes that riddle the moon.&#xA;&#xA;The lush plant life often contains chemicals that render it unfit for human food. Many of the species have poisonous thorns, or pods that burst and spray acid sap.&#xA;&#xA;The animal life is also dangerous to humans. Thickly-armored hammerheads are unstoppable with standard-issue 突击步枪s. Flying&lt;i&gt;ikran&lt;/i&gt;, or &quot;banshees,&quot; swoop down to snatch the unwary. Many smaller animals and insects, like the stingbat and hellfire wasp, have extremely potent venom. The native inhabitants are fierce warriors, and humans underestimate Na'vi capabilities at their own peril.&#xA;&#xA;Yet 潘多拉has a beauty unsurpassed by anything on Earth. On the rare completely dark nights, every living thing blazes with phosphorescence of rainbow hues – a flashing, flickering phantasmagoria of images that can quickly hypnotize a newcomer. On a spiritual level, there is a strange harmony that pervades all Pandoran life. The few humans who embrace it experience a peace they have never knownbefore.&#xA;&#xA;&lt;b&gt;Discovery&lt;/b&gt;&#xA;&#xA;When astronomers turned a powerful space-based telescope toward the Alpha Centauri system and one of its planets, Polyphemus, they were stunned to find a moon that had an atmosphere with the spectroscopic signature of free oxygen, in a concentration almost equal to Earth's. &#xA; &#xA;Given the presence of oxygen, scientists believed that the moon could harbor life. Even more intriguing was the splitting of spectographic lines that indicated the presense of intense magnetic fields, far stronger than any known outside of a star's interior.&#xA;&#xA;This spurred the construction of even larger space telescopes. They revealed 潘多拉to be a verdant earth-like world in the solar system nearest to our own. A subsequent unmanned mission led to the discovery of a world teeming with plants, animals and geological oddities. &#xA;&#xA;The research also discovered the source of the intense magnetic fields, a substance that had the remarkable property ofhigh-temperature superconductivity. It was this substance, later named 'unobtanium,' that made it financially feasible to launch the manned exploration of 潘多拉.&#xA;&#xA;But it was the image of the Na'vi that empowered the world to come together to launch the first manned mission to another star system." /><string enum="Pan_Geo_Pandora_Desc01" value="&lt;b&gt;Day-NightCycle&lt;/b&gt;&#xA;&#xA;潘多拉receives significant light from Alpha Centauri B (ACB). Because of this, for half the Polyphemian year its nights are never dark, but instead are more like Earthly dusk. At the closest point in its orbit, ACB is about 2,300 times as bright as Earth's full moon; at its farthest, it is still one hundred and seventy times as bright. During the other half of the year, when ACB is in the daytime sky, many Pandoran nights are illuminated both by Polyphemus's huge disk and reflected light from other nearby moons. Truly dark nights are uncommon. Polyphemus occasionally eclipses ACB at night for about one hundred minutes, but the light reflected by the planet still keeps the night from being dark.&#xA;&#xA; When ACB shares the daytime sky with ACA, at its closest it adds about half a percent to the total illumination.When the two stars are close together in the sky, the effect of ACB's more orange light in unnoticeable, but as they separate over the years, an orange tint may be seen in areas shadowed from ACA's direct illumination. At its most distant, ACB is about 2,700 times dimmer than ACA and does not produce noticeable lighting effects. However, it still appears as a blindingly-bright tiny orange disk in the sky.&#xA;&#xA;Because of its high axial tilt (29°), 潘多拉exhibits considerable annual variation in the day-to-night ratio. In addition, its elliptical orbit produces seasonal temperature variations and a range in daytime illumination of about tenpercent.&#xA;&#xA;&lt;b&gt;Magnetic Fields&lt;/b&gt;&#xA;&#xA;潘多拉possesses a liquid iron core, with circulating currents that produce a dipole field similar to the Earth's. This field shields the surface from cosmic rays or material ejected from Alpha Centauri A. But unlike Earth, the intense magnetic fields associated with 潘多拉's unobtanium deposits produce localized distortions to the worldwide field that can act as magnetic funnels. These anomalies can channel incoming particles ejected from the sun to the moon's surface. Any life form unlucky enough to be caught in one of these areas during a stellar flare event or C.M.E. (Coronal Mass Ejection) will be quickly irradiated with a lethal dose. Depending on the type and amount of radiation, death can occur instantly as brain tissue is ionized and effectively &quot;shortsout,&quot; or be delayed for agonizing days or weeks as dehydration and loss of electrolytes caused by intractable vomiting and diarrhea takes its toll, and blood begins to seep from mucus membranes.&#xA;&#xA;潘多拉's global field also interacts with Polyphemus's much more extensive one. This can divert radiation trapped in the planet's magnetic field to the moon's surface – also with unpleasant results. At certain times, a particular configuration of the two fields can cause a magnetic flux tube to form, linking the polar areas of the planet and satellite with an electrical current flow of millions of amperes. This causes a gigantic increase in electrical activity on both bodies, with massive lightning storms and other electromagnetic phenomena." /> <string enum="Pan_Geo_Pandora_Desc02" value="&lt;b&gt;PhysicalDescription&lt;/b&gt;&#xA;&#xA; 潘多拉's diameter is three-quarters of the Earth's. Its mass is about half of Earth's and its surface gravity about twenty percent less. The unusually high concentrations of carbon dioxide and xenon in the air make it twenty percent denser than Earth's atmosphere. 潘多拉was able to retain such a deep atmosphere in spite of its small size because it orbits between Polyphemus's two radiation belts, and they serve to deflect much of the&quot;stellar wind&quot; which normally sweeps atoms away from the outer edge of the atmosphere. &#xA;&#xA;&lt;b&gt;Internal Structure&lt;/b&gt;&#xA;&#xA;潘多拉's physical construction resembles Earth's: a liquid iron core, a plastic mantle, and a semi-rigid crust. Like Earth, it has two internal heat sources: the disintegration of radioactive isotopes, and energy from the gravitational collapse of its initial formation. But there is an additional and much larger energy input from tidal forces; the nearest inner and outer moons pull on it in contest with Polyphemus.&#xA;&#xA;This excess of energy drives continental drift at a much faster rate than Earth, causing the tectonic plates to fracture more extensively because of the increased stress. This explains the lack of large continents on 潘多拉, as well as its volcanism and geothermal activity.&#xA;&#xA;&lt;b&gt;Surface Features&lt;/b&gt;&#xA;&#xA;潘多拉's land-to-water ratio is greater than Earth's. But because the land area is broken up into a larger number of smaller continents, no land area is as far from the ocean as on Earth. The moderating influence of oceans reduces extremes in temperature; there are no deserts on 潘多拉. Polar ice caps that are smaller than Earth's exist, but because there are no land masses in the polar areas, the Pandoran ice capsare currently free-floating.&#xA;&#xA;As mentioned, 潘多拉is more volcanically active than Earth. There are vents both on the land and under the oceans. Many of the mountains and other surface features are of recent volcanic origin. Numerous hot springs and geysers dot the landscape, and there are several rivers that are almost boiling at the place where they erupt from underground aquifers. All of these serve to maintain the local concentrations of hydrogen sulfide gas that are deadly to unprotected humans.&#xA;&#xA;Landforms are shaped extensively by the higher density atmosphere – dust grains carried by the wind are larger, and strike objects with greater energy. Exposed rock weathers more rapidly, creating more sedimentary material to be carried away by rivers." />。