Violent Relaxation of Spherical Stellar Systems

坤塔娜坤塔娜这一周要满11岁了。

她迈入青少年期的过程我只能用神气自信来形容，看着她从襁褓里一路成长，就像看棒球手桑迪·考法克斯投球或是比尔·拉赛尔打篮球那样精彩。

他们身上都有着一股不经意的傲气，觉得没有人能够做的比他们更好。

然而，对于一个父亲来说，看着女儿一天天成长却不是件容易的事。

每一次生日她都变得越来越像我们，一个大人，而我们却还沉浸于她孩提时的记忆。

我记得第一次看见她是在圣约翰医院的育儿室。

探望时间已经过了，我和妻子站在玻璃隔音墙外张望着，猜想摇篮里的孩子们哪一个是我们的。

随后，一个带着口罩的护士从后面的房间出来，手里抱着一个正在张牙舞爪的头上绑着蝴蝶结的黑发婴儿。

她才刚出生不到十七个小时，脸上的褶子还没打开、红扑扑的，手腕上的身份证明印的不是我们的名字，而是两个字母“NI”。

“NI”代表着“信息不详”，是医院给准备被领养的婴儿的代码。

昆塔娜是领养的。

对于我们来说，说出这几个字/公开这一点并不困难，尽管会引来尽管用意善良却让人不爽的赞美之辞。

“就算她是你们亲生的，你们也不可能更爱她了。

”每当这种时候，我和妻子都沉默不语，勉强从齿缝里挤出一点微笑。

然而，我们并不是没有意识到，在不远的将来，我们将会面临只有我们这些养父母才会面临的时刻——我们的女儿要决定是否去寻找她的亲生父母。

我记得在我成长的那个年代，不少广播剧是围绕领养展开的。

通常剧情都起因于一个孩子意外得知了自己是被领养的。

这些消息只能是意外得知，因为在那些日子里，父母告诉子女他们不是自己的亲生骨肉都被认为是有悖伦常的。

如果这个秘密不得不被泄露，通常都会加上一些似是而非的附加情节，如当孩子还在襁褓时，他的亲生父母就已双亡。

一场车祸也被认为是送走双亲最迅速有效的方式。

我的一个同龄人，当时是一名年轻的女演员，直到二十二岁成为她生父小笔遗产继承人时才得知自己是被收养的。

她的养母无法亲口告诉她遗产的来历，便把这个任务托付给了威廉姆·毛利事务所来完成。

小学上册英语第二单元综合卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I like _____ (to run/to walk).2.We go to school by ___. (bus)3.Hydraulic systems use fluids to transmit ______.4.I want to _______ (学习)做饭。

5.I have a ________ that can fly high in the sky.6.The classroom is ___ (clean/messy).7. A _______ helps to keep the soil healthy.8.Which animal is known for its intelligence and problem-solving skills?A. DogB. CatC. DolphinD. Bird9.The ______ (组织) in plants helps with nutrient transport.10.The state of matter that has a definite shape and volume is a _______.11.What do you call a collection of short stories?A. AnthologyB. CompilationC. CollectionD. All of the above12.My favorite dessert is _______.13.I like reading ______ at night. (books)14.I find _____ (乐趣) in reading.15. A supernova is an explosion of a dying _____.16.It’s fun to jump in __________ puddles. (水)17.我的朋友喜欢 _______ (活动). 她觉得这很 _______ (形容词)18.What is the capital of Egypt?A. CairoB. AlexandriaC. GizaD. LuxorA19.My favorite sport is _______ (冲浪).20.The __________ was a time of significant social change in the 1960s. (社会运动)21.Which planet is closest to the Sun?A. EarthB. VenusC. MercuryD. Mars22.The ________ (环境变化) affects our health.23.What is 10 - 3?A. 5B. 6C. 7D. 824.The classroom is ________ (安静的).25.What is the capital of Sri Lanka?A. ColomboB. KandyC. GalleD. JaffnaA26.What is the main ingredient in pizza dough?A. RiceB. FlourC. CornD. SugarB27.What is the time of day when the sun rises?A. DawnB. DuskC. MidnightD. Noon28.The ______ (海狮) is often seen on rocky shores.29.The chemical symbol for chlorine is _______.30.What is 5 + 7?A. 11B. 12C. 13D. 1431.The wind is ______ (blowing) gently today.32.What is the opposite of "new"?A. FreshB. OldC. YoungD. ModernB33.My favorite activity is ________ (骑自行车).34.I enjoy learning new things with my educational ________ (玩具名称).35.What do we call the liquid part of blood?A. PlasmaB. PlateletsC. Red blood cellsD. White blood cellsA36. A _______ (小壁虎) climbs walls easily.37.Plants can be classified as ______ (一年生) or perennial.38.What is the opposite of open?A. CloseB. ShutC. BlockD. Both A and BD39. A chemical reaction can involve the transfer of ______.40.How many senses do humans have?A. ThreeB. FourC. FiveD. SixC41.What do we call a scientist who studies rocks?A. BiologistB. GeologistC. ChemistD. PhysicistB42.The sun is ______ brightly during the day. (shining)43.It is _____ (hot/cold) in summer.44.What do we call the science of studying animals in their natural habitat?A. EcologyB. EthologyC. ZoologyD. ConservationA45.My pet ______ (狗) loves to play with other pets.46.The ______ (成熟) of fruit indicates it's ready to eat.47.I want to buy a new __________.48.The vulture often eats _________ (尸体).49.What is the name of the fairy tale character who lost her glass slipper?A. Snow WhiteB. CinderellaC. RapunzelD. Sleeping BeautyB50.She is _____ (playing) the violin.51.What is the primary ingredient in a pizza?A. DoughB. CheeseC. Tomato sauceD. All of the above52.She sings _____ (well/badly).53.What is the term for the period when a star is in the main sequence phase?A. ProtostarB. Red GiantC. Main SequenceD. White Dwarf54.The kitten is ______ on the windowsill. (resting)55.My brother plays the _____ guitar. (acoustic)56.The __________ (文化差异) can enrich social interactions.57.The __________ is a famous city known for its culture and history. (伊斯坦布尔)58.The ____ has a thick coat to protect it from the cold.59.The chemical symbol for cadmium is _______.60.What is the name of the technology that allows us to communicate over distances?A. TelevisionB. RadioC. TelephoneD. ComputerC61.The __________ is where freshwater meets saltwater.62.What is the name of the story about a girl in a red hood?A. CinderellaB. Little Red Riding HoodC. Snow WhiteD. Sleeping BeautyB63. A solution that resists changes in pH is called a ______ solution.64.The _____ (whistle) is loud.65.Which animal is known for its ability to change colors?A. ChameleonB. FrogC. LizardD. Snake66.My _______ (狗) loves to go for walks.67.What is the strongest muscle in the human body?A. HeartB. TongueC. ArmD. LegB68.sustainable livelihoods program) supports economic resilience. The ____69.My _____ is blue and red.70.The country famous for its seafood is ________ (日本).71.Chemicals can change their _____ during a reaction.72.The chameleon can blend into its _________ (环境).73.The _____ (绿色空间) improves urban living conditions.74.The __________ (西方殖民主义) had a significant impact on Africa and Asia.75.What is the capital of Lithuania?A. VilniusB. KaunasC. KlaipedaD. PanevezysA76.What do you call a young female tiger?A. TigressB. CubC. KittenD. PupA77.The _____ (大象) communicates with low-frequency sounds.78.What is the capital of Canada?A. VancouverB. OttawaC. TorontoD. CalgaryB79.What shape is a basketball?A. SquareB. CircleC. TriangleD. Rectangle80.Which of these is a dessert?A. SaladB. CakeC. SoupD. Rice81. A _____ is a large area of water surrounded by land.82.The ____ has a long tail and loves to swing from branches.83.What do you call a book that tells a story?A. NovelB. DictionaryC. EncyclopediaD. GuideA84.I enjoy ______ on sunny afternoons. (playing outside)85.I want to ________ (travel) to Japan.86.小鸽子) coos softly in the evening. The ___87.What do you call a person who makes clothes?A. DesignerB. TailorC. StylistD. SeamstressB88.My favorite dish is ______ (中国菜).89.The ______ of a rose bush can be very thorny. (玫瑰灌木的茎可能非常多刺。

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。

(记贝索斯在普林斯顿大学年学士毕业典礼上地演讲)我一直相信每一个人都有自己地天赋，每一个人地存在都代表着宇宙空间中地一种唯一，然而令我经常都在深思地是，既然我们都是这样地独特，又为何偏偏要去模仿和畸变成拥有同类“基因”地人呢？为什么我们中地很多人都不愿意去追逐属于自己地理想，或者不能为此奋斗一生呢，抑或者一生都是在自欺欺人地辩解？在地中我深深地感受到了一个人追逐自己最初理想地意义会变得如此地伟大，充满地是一种人生最大地和最根本地价值.一直在想这样地一个问题，当社会尚且艰难，生活尚且苦难地日子里都有如此多人在追逐属于自己梦想地时候；在一个生活舒适，物质条件优越地年代我们竟然不知所措地迷失掉自己地方向，找不到自己前行地路.这是多么可悲和可笑地一种境况！我们，有了更高地天赋，有了更好地环境，却因为有更多地选择而抹杀了我们自己地梦...这确实让人觉得不可思议！个人收集整理勿做商业用途我相信每个人都有自己最初地梦想，在这样地一个年代，在这样一个至少没有饥寒交迫地时代，我坚信追逐自己理想地人会获得生命尽头最高贵地礼物和人生最大地价值！个人收集整理勿做商业用途记：在一个可以实现最初梦想地时代选择不可以地沉默必将是这个时代最损失地损失，也必将是生活在这个时代地人最遗憾地遗憾... 个人收集整理勿做商业用途附：抵抗天赋地诱惑（贝索斯在普林斯顿大学年学士毕业典礼上地演讲）中文译稿：在我还是一个孩子地时候，我地夏天总是在德州祖父母地农场中度过.我帮忙修理风车，为牛接种疫苗，也做其它家务.每天下午，我们都会看肥皂剧，尤其是《我们地岁月》.我地祖父母参加了一个房车俱乐部，那是一群驾驶拖挂型房车地人们，他们结伴遍游美国和加拿大.每隔几个夏天，我也会加入他们.我们把房车挂在祖父地小汽车后面，然后加入余名探险者们组成地浩荡队伍. 个人收集整理勿做商业用途我爱我地祖父母，我崇敬他们，也真心期盼这些旅程.那是一次我大概十岁时地旅行，我照例坐在后座地长椅上，祖父开着车，祖母坐在他旁边，吸着烟.我讨厌烟味. 个人收集整理勿做商业用途在那样地年纪，我会找任何借口做些估测或者小算术.我会计算油耗还有杂货花销等鸡毛蒜皮地小事.我听过一个有关吸烟地广告.我记不得细节了，但是广告大意是说，每吸一口香烟会减少几分钟地寿命，大概是两分钟.无论如何，我决定为祖母做个算术.我估测了祖母每天要吸几支香烟，每支香烟要吸几口等等，然后心满意足地得出了一个合理地数字.接着，我捅了捅坐在前面地祖母地头，又拍了拍她地肩膀，然后骄傲地宣称，“每天吸两分钟地烟，你就少活九年!” 个人收集整理勿做商业用途我清晰地记得接下来发生了什么，而那是我意料之外地.我本期待着小聪明和算术技巧能赢得掌声，但那并没有发生.相反，我地祖母哭泣起来.我地祖父之前一直在默默开车，把车停在了路边，走下车来，打开了我地车门，等着我跟他下车.我惹麻烦了吗?我地祖父是一个智慧而安静地人.他从来没有对我说过严厉地话，难道这会是第一次?还是他会让我回到车上跟祖母道歉?我以前从未遇到过这种状况，因而也无从知晓会有什么后果发生.我们在房车旁停下来.祖父注视着我，沉默片刻，然后轻轻地、平静地说：“杰夫，有一天你会明白，善良比聪明更难.” 个人收集整理勿做商业用途选择比天赋更重要今天我想对你们说地是，天赋和选择不同.聪明是一种天赋，而善良是一种选择.天赋得来很容易——毕竟它们与生俱来.而选择则颇为不易.如果一不小心，你可能被天赋所诱惑，这可能会损害到你做出地选择. 个人收集整理勿做商业用途在座各位都拥有许多天赋.我确信你们地天赋之一就是拥有精明能干地头脑.之所以如此确信，是因为入学竞争十分激烈，如果你们不能表现出聪明智慧，便没有资格进入这所学校. 个人收集整理勿做商业用途你们地聪明才智必定会派上用场，因为你们将在一片充满奇迹地土地上行进.我们人类，尽管跬步前行，却终将令自己大吃一惊.我们能够想方设法制造清洁能源，也能够一个原子一个原子地组装微型机械，使之穿过细胞壁，然后修复细胞.这个月，有一个异常而不可避免地事情发生了——人类终于合成了生命.在未来几年，我们不仅会合成生命，还会按说明书驱动它们.我相信你们甚至会看到我们理解人类地大脑，儒勒·凡尔纳，马克·吐温，伽利略，牛顿——所有那些充满好奇之心地人都希望能够活到现在.作为文明人，我们会拥有如此之多地天赋，就像是坐在我面前地你们，每一个生命个体都拥有许多独特地天赋. 个人收集整理勿做商业用途你们要如何运用这些天赋呢?你们会为自己地天赋感到骄傲，还是会为自己地选择感到骄傲? 追随自己内心地热情年前，我萌生了创办亚马逊地想法.彼时我面对地现实是互联网使用量以每年地速度增长，我从未看到或听说过任何增长如此快速地东西.创建涵盖几百万种书籍地网上书店地想法令我兴奋异常，因为这个东西在物理世界里根本无法存在.那时我刚刚岁，结婚才一年. 个人收集整理勿做商业用途我告诉妻子想辞去工作，然后去做这件疯狂地事情，很可能会失败，因为大部分创业公司都是如此，而且我不确定那之后会发生什么.告诉我，我应该放手一搏.在我还是一个男孩儿地时候，我是车库发明家.我曾用水泥填充地轮胎、雨伞和锡箔以及报警器制作了一个自动关门器.我一直想做一个发明家，支持我追随内心地热情. 个人收集整理勿做商业用途我当时在纽约一家金融公司工作，同事是一群非常聪明地人，我地老板也很有智慧，我很羡慕他.我告诉我地老板我想开办一家在网上卖书地公司.他带我在中央公园漫步良久，认真地听我讲完，最后说：“听起来真是一个很好地主意，但是对那些目前没有谋到一份好工作地人来说，这个主意会更好.” 个人收集整理勿做商业用途这一逻辑对我而言颇有道理，他说服我在最终作出决定之前再考虑小时.那样想来，这个决定确实很艰难，但是最终，我决定拼一次.我认为自己不会为尝试过后地失败而遗憾，倒是有所决定但完全不付诸行动会一直煎熬着我.在深思熟虑之后，我选择了那条不安全地道路，去追随我内心地热情.我为那个决定感到骄傲. 个人收集整理勿做商业用途明天，非常现实地说，你们从零塑造自己人生地时代即将开启.你们会如何运用自己地天赋?你们又会作出怎样地抉择?你们是被惯性所引导，还是追随自己内心地热情?你们会墨守陈规，还是勇于创新?你们会选择安逸地生活，还是选择一个奉献与冒险地人生?你们会屈从于批评，还是会坚守信念?你们会掩饰错误，还是会坦诚道歉?你们会因害怕拒绝而掩饰内心，还是会在面对爱情时勇往直前?你们想要波澜不惊，还是想要搏击风浪?你们会在严峻地现实之下选择放弃，还是会义无反顾地前行?你们要做愤世嫉俗者，还是踏实地建设者?你们要不计一切代价地展示聪明，还是选择善良?我要做一个预测：在你们岁时某个追忆往昔地时刻，只有你一个人静静对内心诉说着你地人生故事，其中最为充实、最有意义地那段讲述，会被你们作出地一系列决定所填满.最后，是选择塑造了我们地人生.为你自己塑造一个伟大地人生故事. 个人收集整理勿做商业用途谢谢，祝你们好运!英文原稿：" ", 个人收集整理勿做商业用途,, . , , . , " ." , . . , ' . ' ' , ' , . . , . . . . , . 个人收集整理勿做商业用途, ' . ' . ' . ' , , : . , . , . ' , , , , " , ' !" 个人收集整理勿做商业用途, . . ", ' . , ." ' . , . . , , , . . ? , . , ? . . . , , , ", ' ' ." 个人收集整理勿做商业用途. , . ' . . ' , , ' . 个人收集整理勿做商业用途. ' . ' ' ' ' , ' . 个人收集整理勿做商业用途. . ' . , ' . ' . , ' , ' . ' . , , , . , , . 个人收集整理勿做商业用途? ? 个人收集整理勿做商业用途. . ' , ' . , ' . ' ', ' . ( ) . , ' . ' , ' , . ' , . 个人收集整理勿做商业用途, . . , , , " , ' ." , . , , , . ' ' . . , , ' .个人收集整理勿做商业用途, , . 个人收集整理勿做商业用途? ? 个人收集整理勿做商业用途, ? 个人收集整理勿做商业用途, ?, ? 个人收集整理勿做商业用途, ? 个人收集整理勿做商业用途' , ? 个人收集整理勿做商业用途, ? 个人收集整理勿做商业用途, ? 个人收集整理勿做商业用途' , , ? 个人收集整理勿做商业用途, ?, ? 个人收集整理勿做商业用途. , , . , . . ! 个人收集整理勿做商业用途诱惑是存于世上地一种奇怪地东西，你会为之疯狂而不能自已，而它之所以存在，是因为人地一生不断地被欲念剌激，所以为诱惑折磨一生.人存于世上，首要面对地是物质上地诱惑，然后才是精神上地诱惑.精神诱惑，我诠译是指追求浮名、执着于表现突现自我、或是指对知识领域过度探求.权势、地位、名利、金钱，这些都是诱惑.个人收集整理勿做商业用途人生时时面临诸多诱惑，权重地地位是诱惑，利多地职业是诱惑，光环般地荣誉是诱惑，欢畅地娱乐是诱惑，甚至漂亮地时装、可口美味都是诱惑……面对这些诱惑，我们该怎么办？个人收集整理勿做商业用途现在地社会，是一个充满诱惑地世界，如果你抵挡不住诱惑，你就会成为诱惑地奴隶，被诱惑淹没；如果你勇于抗拒诱惑，保持自我，你就能做好自己地事，成就自己地功业.个人收集整理勿做商业用途相反地，如果禁受不起外界地诱惑，就难以保持自我，难以做好自己地工作.俗话说地好，吃人家地嘴短，拿人家地手短.当今社会，又有哪个是白痴，肯为你白白付出？他们就是利用一些人“贪”地心理做诱饵，在这些人地身上谋取更大地利益，殊不知这正是走向死亡坟墓地开端.放眼看来，有多少人在多苦多难地日子里都挺了过来，可是，就在他地人生正走向成功，走向辉煌地时刻，经受不住名和利地诱惑，又白白断送了自己美好地前程；又有多少达官显贵在金钱美色地诱惑下，丧失道德水准，毁掉一世英名.个人收集整理勿做商业用途我们生活地时代更是一个充满诱惑地时代，网络游戏会诱惑你，网上聊天会诱惑你，歌星影星会诱惑你，淫秽读物会诱惑你，色情场所会诱惑你，名牌商品会诱惑你，灯红酒绿纸醉金迷地生活会诱惑你……如果你不能以顽强地意志保持自我，今天受这个诱惑，明天受那样诱惑，你哪还有时间和精力来作好自己地本职工作？哪有时间来提高自身素质？个人收集整理勿做商业用途所以我们要勇于保持自我，勇于抵抗诱惑.抵抗诱惑不要只看重于外因，社会是不断发展地，充满诱惑地东西只能越来越多，如果不从自身着手，你永远也不能抵抗诱惑.抵抗诱惑其实也很简单，我们地十六字方针告诉我们：无欲则刚淡泊心志，心中无欲，立身处世自然而刚！刚正则不阿！保持信念之火不灭，荣华富贵犹如过眼烟云，一笑而过，又哪里有什么诱惑呢?个人收集整理勿做商业用途。

奇妙的物理现象英文作文英文：I have always been fascinated by the wonders of physics. One of the most amazing phenomena I have encountered is the concept of quantum entanglement. Quantum entanglementrefers to the phenomenon where two or more particles become connected in such a way that the state of one particle is instantly correlated with the state of the other,regardless of the distance between them. This means that when the state of one particle changes, the state of the other particle changes simultaneously, even if they arelight-years apart.The implications of quantum entanglement are mind-boggling. It seems to violate the principles of classical physics and challenges our understanding of cause and effect. This phenomenon has been famously described byAlbert Einstein as "spooky action at a distance," and it continues to puzzle physicists to this day.One of the most famous experiments that demonstrated quantum entanglement is the EPR paradox, proposed by Einstein, Podolsky, and Rosen in 1935. In this thought experiment, they highlighted the bizarre implications of quantum mechanics, particularly the idea that measuring one particle could instantaneously affect the state of another particle, no matter how far apart they were. This concept has since been verified through numerous experiments, including the famous Bell test experiments, which have confirmed that entangled particles do indeed exhibit correlated behavior.中文：我一直对物理的奇迹充满着好奇。

GGALVANIC DISTORTIONThe electrical conductivity of Earth materials affects two physical processes:electromagnetic induction which is utilized with magneto-tellurics(MT)(q.v.),and electrical conduction.If electromagnetic induction in media which are heterogeneous with respect to their elec-trical conductivity is considered,then both processes take place simul-taneously:Due to Faraday’s law,a variational electric field is induced in the Earth,and due to the conductivity of the subsoil an electric cur-rent flows as a consequence of the electric field.The current compo-nent normal to boundaries within the heterogeneous structure passes these boundaries continously according tos1E1¼s2E2where the subscripts1and2indicate the boundary values of conductiv-ity and electric field in regions1and2,respectively.Therefore the amplitude and the direction of the electric field are changed in the vicinity of the boundaries(Figure G1).In electromagnetic induction studies,the totality of these changes in comparison with the electric field distribution in homogeneous media is referred to as galvanic distortion. The electrical conductivity of Earth materials spans13orders of mag-nitude(e.g.,dry crystalline rocks can have conductivities of less than 10–6S mÀ1,while ores can have conductivities exceeding106S mÀ1). Therefore,MT has a potential for producing well constrained mod-els of the Earth’s electrical conductivity structure,but almost all field studies are affected by the phenomenon of galvanic distortion, and sophisticated techniques have been developed for dealing with it(Simpson and Bahr,2005).Electric field amplitude changes and static shiftA change in an electric field amplitude causes a frequency-indepen-dent offset in apparent resistivity curves so that they plot parallel to their true level,but are scaled by a real factor.Because this shift can be regarded as spatial undersampling or“aliasing,”the scaling factor or static shift factor cannot be determined directly from MT data recorded at a single site.If MT data are interpreted via one-dimensional modeling without correcting for static shift,the depth to a conductive body will be shifted by the square root of the factor by which the apparent resistivities are shifted.Static shift corrections may be classified into three broad groups: 1.Short period corrections relying on active near-surface measurementssuch as transient electromagnetic sounding(TEM)(e.g.,Meju,1996).2.Averaging(statistical)techniques.As an example,electromagneticarray profiling is an adaptation of the magnetotelluric technique that involves sampling lateral variations in the electric field con-tinuously,and spatial low pass filtering can be used to suppress sta-tic shift effects(Torres-Verdin and Bostick,1992).3.Long period corrections relying on assumed deep structure(e.g.,a resistivity drop at the mid-mantle transition zones)or long-periodmagnetic transfer functions(Schmucker,1973).An equivalence relationship exists between the magnetotelluric impedance Z and Schmucker’s C-response:C¼Zi om0;which can be determined from the magnetic fields alone,thereby providing an inductive scale length that is independent of the dis-torted electric field.Magnetic transfer functions can,for example, be derived from the magnetic daily variation.The appropriate method for correcting static shift often depends on the target depth,because there can be a continuum of distortion at all scales.As an example,in complex three-dimensional environments near-surface correction techniques may be inadequate if the conductiv-ity of the mantle is considered,because electrical heterogeneity in the deep crust creates additional galvanic distortion at a larger-scale, which is not resolved with near-surface measurements(e.g.,Simpson and Bahr,2005).Changes in the direction of electric fields and mixing of polarizationsIn some target areas of the MT method the conductivity distribution is two-dimensional(e.g.,in the case of electrical anisotropy(q.v.))and the induction process can be described by two decoupled polarizations of the electromagnetic field(e.g.,Simpson and Bahr,2005).Then,the changes in the direction of electric fields that are associated with galvanic distortion can result in mixing of these two polarizations. The recovery of the undistorted electromagnetic field is referred to as magnetotelluric tensor decomposition(e.g.,Bahr,1988,Groom and Bailey,1989).Current channeling and the“magnetic”distortionIn the case of extreme conductivity contrasts the electrical current can be channeled in such way that it is surrounded by a magneticvariational field that has,opposite to the assumptions made in the geo-magnetic deep sounding(q.v.)method,no phase lag with respect to the electric field.The occurrence of such magnetic fields in field data has been shown by Zhang et al.(1993)and Ritter and Banks(1998).An example of a magnetotelluric tensor decomposition that includes mag-netic distortion has been presented by Chave and Smith(1994).Karsten BahrBibliographyBahr,K.,1988.Interpretation of the magnetotelluric impedance tensor: regional induction and local telluric distortion.Journal of Geophy-sics,62:119–127.Chave,A.D.,and Smith,J.T.,1994.On electric and magnetic galvanic distortion tensor decompositions.Journal of Geophysical Research,99:4669–4682.Groom,R.W.,and Bailey,R.C.,1989.Decomposition of the magneto-telluric impedance tensor in the presence of local three-dimensional galvanic distortion.Journal of Geophysical Research,94: 1913–1925.Meju,M.A.,1996.Joint inversion of TEM and distorted MT sound-ings:some effective practical considerations.Geophysics,61: 56–65.Ritter,P.,and Banks,R.J.,1998.Separation of local and regional information in distorted GDS response functions by hypothetical event analysis.Geophysical Journal International,135:923–942. Schmucker,U.,1973.Regional induction studies:a review of methods and results.Physics of the Earth and Planetary Interiors,7: 365–378.Simpson,F.,and Bahr,K.,2005.Practical Magnetotellurics.Cam-bridge:Cambridge University Press.Torres-Verdin,C.,and Bostick,F.X.,1992.Principles of special sur-face electric field filtering in magnetotellurics:electromagnetic array profiling(EMAP).Geophysics,57:603–622.Zhang,P.,Pedersen,L.B.,Mareschal,M.,and Chouteau,M.,1993.Channelling contribution to tipper vectors:a magnetic equivalent to electrical distortion.Geophysical Journal International,113: 693–700.Cross-referencesAnisotropy,ElectricalGeomagnetic Deep SoundingMagnetotelluricsMantle,Electrical Conductivity,Mineralogy GAUSS’DETERMINATION OF ABSOLUTE INTENSITYThe concept of magnetic intensity was known as early as1600in De Magnete(see Gilbert,William).The relative intensity of the geomag-netic field in different locations could be measured with some preci-sion from the rate of oscillation of a dip needle—a method used by Humboldt,Alexander von(q.v.)in South America in1798.But it was not until Gauss became interested in a universal system of units that the idea of measuring absolute intensity,in terms of units of mass, length,and time,was considered.It is now difficult to imagine how revolutionary was the idea that something as subtle as magnetism could be measured in such mundane units.On18February1832,Gauss,Carl Friedrich(q.v.)wrote to the German astronomer Olbers:“I occupy myself now with the Earth’s magnetism,particularly with an absolute determination of its intensity.Friend Weber”(Wilhelm Weber,Professor of Physics at the University of Göttingen)“conducts the experiments on my instructions.As, for example,a clear concept of velocity can be given only through statements on time and space,so in my opinion,the complete determination of the intensity of the Earth’s magnetism requires to specify(1)a weight¼p,(2)a length¼r,and then the Earth’s magnetism can be expressed byffiffiffiffiffiffiffip=rp.”After minor adjustment to the units,the experiment was completed in May1832,when the horizontal intensity(H)at Göttingen was found to be1.7820mg1/2mm–1/2s–1(17820nT).The experimentThe experiment was in two parts.In the vibration experiment(Figure G2) magnet A was set oscillating in a horizontal plane by deflecting it from magnetic north.The period of oscillations was determined at different small amplitudes,and from these the period t0of infinite-simal oscillations was deduced.This gave a measure of MH,where M denotes the magnetic moment of magnet A:MH¼4p2I=t20The moment of inertia,I,of the oscillating part is difficult to deter-mine directly,so Gauss used the ingenious idea of conductingtheFigure G2The vibration experiment.Magnet A is suspended from a silk fiber F It is set swinging horizontally and the period of an oscillation is obtained by timing an integral number of swings with clock C,using telescope T to observe the scale S reflected in mirror M.The moment of inertia of the oscillating part can be changed by a known amount by hanging weights W from the rodR. 278GAUSS’DETERMINATION OF ABSOLUTE INTENSITYexperiment for I and then I þD I ,where D I is a known increment obtained by hanging weights at a known distance from the suspension.From several measures of t 0with different values of D I ,I was deter-mined by the method of least squares (another of Gauss ’s original methods).In the deflection experiment,magnet A was removed from the suspension and replaced with magnet B.The ratio M /H was measured by the deflection of magnet B from magnetic north,y ,produced by magnet A when placed in the same horizontal plane as B at distance d magnetic east (or west)of the suspension (Figure G3).This required knowledge of the magnetic intensity due to a bar magnet.Gauss deduced that the intensity at distance d on the axis of a dipole is inversely proportional to d 3,but that just one additional term is required to allow for the finite length of the magnet,giving 2M (1þk/d 2)/d 3,where k denotes a small constant.ThenM =H ¼1=2d 3ð1Àk =d 2Þtan y :The value of k was determined,again by the method of least squares,from the results of a number of measures of y at different d .From MH and M /H both M and,as required by Gauss,H could readily be deduced.Present methodsWith remarkably little modification,Gauss ’s experiment was devel-oped into the Kew magnetometer,which remained the standard means of determining absolute H until electrical methods were introduced in the 1920s.At some observatories,Kew magnetometers were still in use in the 1980s.Nowadays absolute intensity can be measured in sec-onds with a proton magnetometer and without the considerable time and experimental skill required by Gauss ’s method.Stuart R.C.MalinBibliographyGauss,C.F.,1833.Intensitas vis magneticae terrestris ad mensuram absolutam revocata.Göttingen,Germany.Malin,S.R.C.,1982.Sesquicentenary of Gauss ’s first measurement of the absolute value of magnetic intensity.Philosophical Transac-tions of the Royal Society of London ,A 306:5–8.Malin,S.R.C.,and Barraclough,D.R.,1982.150th anniversary of Gauss ’s first absolute magnetic measurement.Nature ,297:285.Cross-referencesGauss,Carl Friedrich (1777–1855)Geomagnetism,History of Gilbert,William (1544–1603)Humboldt,Alexander von (1759–1859)Instrumentation,History ofGAUSS,CARL FRIEDRICH (1777–1855)Amongst the 19th century scientists working in the field of geomag-netism,Carl Friedrich Gauss was certainly one of the most outstanding contributors,who also made very fundamental contributions to the fields of mathematics,astronomy,and geodetics.Born in April 30,1777in Braunschweig (Germany)as the son of a gardener,street butcher,and mason Johann Friderich Carl,as he was named in the certificate of baptism,already in primary school at the age of nine perplexed his teacher J.G.Büttner by his innovative way to sum up the numbers from 1to ter Gauss used to claim that he learned manipulating numbers earlier than being able to speak.In 1788,Gauss became a pupil at the Catharineum in Braunschweig,where M.C.Bartels (1769–1836)recognized his outstanding mathematical abilities and introduced Gauss to more advanced problems of mathe-matics.Gauss proved to be an exceptional pupil catching the attention of Duke Carl Wilhelm Ferdinand of Braunschweig who provided Gauss with the necessary financial support to attend the Collegium Carolinum (now the Technical University of Braunschweig)from 1792to 1795.From 1795to 1798Gauss studied at the University of Göttingen,where his number theoretical studies allowed him to prove in 1796,that the regular 17-gon can be constructed using a pair of compasses and a ruler only.In 1799,he received his doctors degree from the University of Helmstedt (close to Braunschweig;closed 1809by Napoleon)without any oral examination and in absentia .His mentor in Helmstedt was J.F.Pfaff (1765–1825).The thesis submitted was a complete proof of the fundamental theorem of algebra.His studies on number theory published in Latin language as Disquitiones arithi-meticae in 1801made Carl Friedrich Gauss immediately one of the leading mathematicians in Europe.Gauss also made further pioneering contributions to complex number theory,elliptical functions,function theory,and noneuclidian geometry.Many of his thoughts have not been published in regular books but can be read in his more than 7000letters to friends and colleagues.But Gauss was not only interested in mathematics.On January 1,1801the Italian astronomer G.Piazzi (1746–1820)for the first time detected the asteroid Ceres,but lost him again a couple of weeks later.Based on completely new numerical methods,Gauss determined the orbit of Ceres in November 1801,which allowed F.X.von Zach (1754–1832)to redetect Ceres on December 7,1801.This prediction made Gauss famous next to his mathematical findings.In 1805,Gauss got married to Johanna Osthoff (1780–1809),who gave birth to two sons,Joseph and Louis,and a daughter,Wilhelmina.In 1810,Gauss married his second wife,Minna Waldeck (1788–1815).They had three more children together,Eugen,Wilhelm,and Therese.Eugen Gauss later became the founder and first president of the First National Bank of St.Charles,Missouri.Carl Friedrich Gauss ’interest in the Earth magnetic field is evident in a letter to his friend Wilhelm Olbers (1781–1862)as early as 1803,when he told Olbers that geomagnetism is a field where still many mathematical studies can be done.He became more engaged in geo-magnetism after a meeting with A.von Humboldt (1769–1859)and W.E.Weber (1804–1891)in Berlin in 1828where von Humboldt pointed out to Gauss the large number of unsolved problems in geo-magnetism.When Weber became a professor of physics at the Univer-sity of Göttingen in 1831,one of the most productive periods intheFigure G3The deflection experiment.Suspended magnet B is deflected from magnetic north by placing magnet A east or west (magnetic)of it at a known distance d .The angle of deflection y is measured by using telescope T to observe the scale S reflected in mirror M.GAUSS,CARL FRIEDRICH (1777–1855)279field of geomagnetism started.In1832,Gauss and Weber introduced the well-known Gauss system according to which the magnetic field unit was based on the centimeter,the gram,and the second.The Mag-netic Observatory of Göttingen was finished in1833and its construc-tion became the prototype for many other observatories all over Europe.Gauss and Weber furthermore developed and improved instru-ments to measure the magnetic field,such as the unifilar and bifilar magnetometer.Inspired by A.von Humboldt,Gauss and Weber realized that mag-netic field measurements need to be done globally with standardized instruments and at agreed times.This led to the foundation of the Göttinger Magnetische Verein in1836,an organization without any for-mal structure,only devoted to organize magnetic field measurements all over the world.The results of this organization have been published in six volumes as the Resultate aus den Beobachtungen des Magnetischen Vereins.The issue of1838contains the pioneering work Allgemeine Theorie des Erdmagnetismus where Gauss introduced the concept of the spherical harmonic analysis and applied this new tool to magnetic field measurements.His general theory of geomagnetism also allowed to separate the magnetic field into its externally and its internally caused parts.As the external contributions are nowadays interpreted as current systems in the ionosphere and magnetosphere Gauss can also be named the founder of magnetospheric research.Publication of the Resultate ceased in1843.W.E.Weber together with such eminent professors of the University of Göttingen as Jacob Grimm(1785–1863)and Wilhelm Grimm(1786–1859)had formed the political group Göttingen Seven protesting against constitutional violations of King Ernst August of Hannover.As a consequence of these political activities,Weber and his colleagues were dismissed. Though Gauss tried everything to bring back Weber in his position he did not succeed and Weber finally decided to accept a chair at the University of Leipzig in1843.This finished a most fruitful and remarkable cooperation between two of the most outstanding contribu-tors to geomagnetism in the19th century.Their heritage was not only the invention of the first telegraph station in1833,but especially the network of36globally operating magnetic observatories.In his later years Gauss considered to either enter the field of bota-nics or to learn another language.He decided for the language and started to study Russian,already being in his seventies.At that time he was the only person in Göttingen speaking that language fluently. Furthermore,he was asked by the Senate of the University of Göttingen to reorganize their widow’s pension system.This work made him one of the founders of insurance mathematics.In his final years Gauss became fascinated by the newly built railway lines and supported their development using the telegraph idea invented by Weber and himself.Carl Friedrich Gauss died on February23,1855as a most respected citizen of his town Göttingen.He was a real genius who was named Princeps mathematicorum already during his life time,but was also praised for his practical abilities.Karl-Heinz GlaßmeierBibliographyBiegel,G.,and K.Reich,Carl Friedrich Gauss,Braunschweig,2005. Bühler,W.,Gauss:A Biographical study,Berlin,1981.Hall,T.,Carl Friedrich Gauss:A Biography,Cambridge,MA,1970. Lamont,J.,Astronomie und Erdmagnetismus,Stuttgart,1851. Cross-referencesHumboldt,Alexander von(1759–1859)Magnetosphere of the Earth GELLIBRAND,HENRY(1597–1636)Henry Gellibrand was the eldest son of a physician,also Henry,and was born on17November1597in the parish of St.Botolph,Aldersgate,London.In1615,he became a commoner at Trinity Col-lege,Oxford,and obtained a BA in1619and an MA in1621.Aftertaking Holy Orders he became curate at Chiddingstone,Kent,butthe lectures of Sir Henry Savile inspired him to become a full-timemathematician.He settled in Oxford,where he became friends withHenry Briggs,famed for introducing logarithms to the base10.Itwas on Briggs’recommendation that,on the death of Edmund Gunter,Gellibrand succeeded him as Gresham Professor of Astronomy in1627—a post he held until his death from a fever on16February1636.He was buried at St.Peter the Poor,Broad Street,London(now demolished).Gellibrand’s principal publications were concerned with mathe-matics(notably the completion of Briggs’Trigonometrica Britannicaafter Briggs died in1630)and navigation.But he is included herebecause he is credited with the discovery of geomagnetic secular var-iation.The events leading to this discovery are as follows(for furtherdetails see Malin and Bullard,1981).The sequence starts with an observation of magnetic declinationmade by William Borough,a merchant seaman who rose to“captaingeneral”on the Russian trade route before becoming comptroller ofthe Queen’s Navy.The magnetic observation(Borough,1581,1596)was made on16October1580at Limehouse,London,where heobserved the magnetic azimuth of the sun as it rose through sevenfixed altitudes in the morning and as it descended through the samealtitudes in the afternoon.The mean of the two azimuths for each alti-tude gives a measure of magnetic declination,D,the mean of which is11 190EÆ50rms.Despite the small scatter,the value could have beenbiased by site or compass errors.Some40years later,Edmund Gunter,distinguished mathematician,Gresham Professor of Astronomy and inventor of the slide rule,foundD to be“only6gr15m”(6 150E)“as I have sometimes found it oflate”(Gunter,1624,66).The exact date(ca.1622)and location(prob-ably Deptford)of the observation are not stated,but it alerted Gunterto the discrepancy with Borough’s measurement.To investigatefurther,Gunter“enquired after the place where Mr.Borough observed,and went to Limehouse with...a quadrant of three foot Semidiameter,and two Needles,the one above6inches,and the other10inches long ...towards the night the13of June1622,I made observation in sev-eral parts of the ground”(Gunter,1624,66).These observations,witha mean of5 560EÆ120rms,confirmed that D in1622was signifi-cantly less than had been measured by Borough in1580.But was thisan error in the earlier measure,or,unlikely as it then seemed,was Dchanging?Unfortunately Gunter died in1626,before making anyfurther measurements.When Gellibrand succeeded Gunter as Gresham Professor,allhe required to do to confirm a major scientific discovery was towait a few years and then repeat the Limehouse observation.Buthe chose instead to go to the site of Gunter’s earlier observationin Deptford,where,in June1633,Gellibrand found D to be“muchless than5 ”(Gellibrand,1635,16).He made a further measurement of D on the same site on June12,1634and“found it not much to exceed4 ”(Gellibrand,1635,7),the published data giving4 50 EÆ40rms.His observation of D at Paul’s Cray on July4,1634adds little,because it is a new site.On the strength of these observations,he announced his discovery of secular variation(Gellibrand,1635,7and 19),but the reader may decide how much of the credit should go to Gunter.Stuart R.C.Malin280GELLIBRAND,HENRY(1597–1636)BibliographyBorough,W.,1581.A Discourse of the Variation of the Compass,or Magnetical Needle.(Appendix to R.Norman The newe Attractive).London:Jhon Kyngston for Richard Ballard.Borough,W.,1596.A Discourse of the Variation of the Compass,or Magnetical Needle.(Appendix to R.Norman The newe Attractive).London:E Allde for Hugh Astley.Gellibrand,H.,1635.A Discourse Mathematical on the Variation of the Magneticall Needle.Together with its admirable Diminution lately discovered.London:William Jones.Gunter,E.,1624.The description and use of the sector,the crosse-staffe and other Instruments.First booke of the crosse-staffe.London:William Jones.Malin,S.R.C.,and Bullard,Sir Edward,1981.The direction of the Earth’s magnetic field at London,1570–1975.Philosophical Transactions of the Royal Society of London,A299:357–423. Smith,G.,Stephen,L.,and Lee,S.,1967.The Dictionary of National Biography.Oxford:University Press.Cross-referencesCompassGeomagnetic Secular VariationGeomagnetism,History ofGEOCENTRIC AXIAL DIPOLE HYPOTHESISThe time-averaged paleomagnetic fieldPaleomagnetic studies provide measurements of the direction of the ancient geomagnetic field on the geological timescale.Samples are generally collected at a number of sites,where each site is defined as a single point in time.In most cases the time relationship between the sites is not known,moreover when samples are collected from a stratigraphic sequence the time interval between the levels is also not known.In order to deal with such data,the concept of the time-averaged paleomagnetic field is used.Hospers(1954)first introduced the geocentric axial dipole hypothesis(GAD)as a means of defining this time-averaged field and as a method for the analysis of paleomag-netic results.The hypothesis states that the paleomagnetic field,when averaged over a sufficient time interval,will conform with the field expected from a geocentric axial dipole.Hospers presumed that a time interval of several thousand years would be sufficient for the purpose of averaging,but many studies now suggest that tens or hundreds of thousand years are generally required to produce a good time-average. The GAD model is a simple one(Figure G4)in which the geomag-netic and geographic axes and equators coincide.Thus at any point on the surface of the Earth,the time-averaged paleomagnetic latitude l is equal to the geographic latitude.If m is the magnetic moment of this time-averaged geocentric axial dipole and a is the radius of the Earth, the horizontal(H)and vertical(Z)components of the magnetic field at latitude l are given byH¼m0m cos l;Z¼2m0m sin l;(Eq.1)and the total field F is given byF¼ðH2þZ2Þ1=2¼m0m4p a2ð1þ3sin2lÞ1=2:(Eq.2)Since the tangent of the magnetic inclination I is Z/H,thentan I¼2tan l;(Eq.3)and by definition,the declination D is given byD¼0 :(Eq.4)The colatitude p(90 minus the latitude)can be obtained fromtan I¼2cot pð0p180 Þ:(Eq.5)The relationship given in Eq. (3) is fundamental to paleomagnetismand is a direct consequence of the GAD hypothesis.When applied toresults from different geologic periods,it enables the paleomagneticlatitude to be derived from the mean inclination.This relationshipbetween latitude and inclination is shown in Figure G5.Figure G5Variation of inclination with latitude for a geocentricdipole.GEOCENTRIC AXIAL DIPOLE HYPOTHESIS281Paleom a gnetic polesThe positio n where the time-averaged dipole axis cuts the surface of the Earth is called the paleomagnetic pole and is defined on the present latitude-longitude grid. Paleomagnetic poles make it possible to com-pare results from different observing localities, since such poles should represent the best estimate of the position of the geographic pole.These poles are the most useful parameter derived from the GAD hypothesis. If the paleomagnetic mean direction (D m , I m ) is known at some sampling locality S, with latitude and longitude (l s , f s ), the coordinates of the paleomagnetic pole P (l p , f p ) can be calculated from the following equations by reference to Figure G6.sin l p ¼ sin l s cos p þ cos l s sin p cos D m ðÀ90 l p þ90 Þ(Eq. 6)f p ¼ f s þ b ; when cos p sin l s sin l porf p ¼ f s þ 180 À b ; when cos p sin l s sin l p (Eq. 7)wheresin b ¼ sin p sin D m = cos l p : (Eq. 8)The paleocolatitude p is determined from Eq. (5). The paleomagnetic pole ( l p , f p ) calculated in this way implies that “sufficient ” time aver-aging has been carried out. What “sufficient ” time is defined as is a subject of much debate and it is always difficult to estimate the time covered by the rocks being sampled. Any instantaneous paleofield direction (representing only a single point in time) may also be con-verted to a pole position using Eqs. (7) and (8). In this case the pole is termed a virtual geomagnetic pole (VGP). A VGP can be regarded as the paleomagnetic analog of the geomagnetic poles of the present field. The paleomagnetic pole may then also be calculated by finding the average of many VGPs, corresponding to many paleodirections.Of course, given a paleomagnetic pole position with coordinates (l p , f p ), the expected mean direction of magnetization (D m , I m )at any site location (l s , f s ) may be also calculated (Figure G6). The paleocolatitude p is given bycos p ¼ sin l s sin l p þ cos l s cos l p cos ðf p À f s Þ; (Eq. 9)and the inclination I m may then be calculated from Eq. (5). The corre-sponding declination D m is given bycos D m ¼sin l p À sin l s cos pcos l s sin p; (Eq. 10)where0 D m 180 for 0 (f p – f s ) 180and180 < D m <360for 180 < (f p –f s ) < 360 .The declination is indeterminate (that is any value may be chosen)if the site and the pole position coincide. If l s ¼Æ90then D m is defined as being equal to f p , the longitude of the paleomagnetic pole.Te s ting the GAD hy p othesis Tim e scale 0– 5 MaOn the timescale 0 –5 Ma, little or no continental drift will have occurred, so it was originally thought that the observation that world-wide paleomagnetic poles for this time span plotted around the present geographic indicated support for the GAD hypothesis (Cox and Doell,1960; Irving, 1964; McElhinny, 1973). However, any set of axial mul-tipoles (g 01; g 02 ; g 03 , etc.) will also produce paleomagnetic poles that cen-ter around the geographic pole. Indeed, careful analysis of the paleomagnetic data in this time interval has enabled the determination of any second-order multipole terms in the time-averaged field (see below for more detailed discussion of these departures from the GAD hypothesis).The first important test of the GAD hypothesis for the interval 0 –5Ma was carried out by Opdyke and Henry (1969),who plotted the mean inclinations observed in deep-sea sediment cores as a function of latitude,showing that these observations conformed with the GAD hypothesis as predicted by Eq. (3) and plotted in Figure G5.Testing the axial nature of the time-averaged fieldOn the geological timescale it is observed that paleomagnetic poles for any geological period from a single continent or block are closely grouped indicating the dipole hypothesis is true at least to first-order.However,this observation by itself does not prove the axial nature of the dipole field.This can be tested through the use of paleoclimatic indicators (see McElhinny and McFadden,2000for a general discus-sion).Paleoclimatologists use a simple model based on the fact that the net solar flux reaching the surface of the Earth has a maximum at the equator and a minimum at the poles.The global temperature may thus be expected to have the same variation.The density distribu-tion of many climatic indicators (climatically sensitive sediments)at the present time shows a maximum at the equator and either a mini-mum at the poles or a high-latitude zone from which the indicator is absent (e.g.,coral reefs,evaporates,and carbonates).A less common distribution is that of glacial deposits and some deciduous trees,which have a maximum in polar and intermediate latitudes.It has been shown that the distributions of paleoclimatic indicators can be related to the present-day climatic zones that are roughly parallel with latitude.Irving (1956)first suggested that comparisons between paleomag-netic results and geological evidence of past climates could provide a test for the GAD hypothesis over geological time.The essential point regarding such a test is that both paleomagnetic and paleoclimatic data provide independent evidence of past latitudes,since the factors con-trolling climate are quite independent of the Earth ’s magnetic field.The most useful approach is to compile the paleolatitude values for a particular occurrence in the form of equal angle or equalareaFigure G6Calculation of the position P (l p ,f p )of thepaleomagnetic pole relative to the sampling site S (l s ,f s )with mean magnetic direction (D m ,I m ).282GEOCENTRIC AXIAL DIPOLE HYPOTHESIS。

第六课从天窗中消失科学是能够为人们普遍接受的。

有一个事实可用来说明这一点：一门科学发展程度越高，其基本概念就越能为人们普遍接受。

举例而言，世界上就只有一种热力学，并不存在什么分开独立的中国热力学、美国热力学或者苏联热力学。

在二十世纪的几十年的时间里，遗传学曾分为两派；西方遗传学和苏联遗传学。

后者源于李森科的理论，即环境的作用可能造成遗传基因的变异。

今天，李森科的理论已经被推翻，因此，世界上就只有一种遗传学了。

作为科学的自然产物，工艺技术也显示出一种世界通用的倾向。

这就是为什么工艺技术的发展传播使世界呈现出一体化特征的原因。

原本各异的世界各地的建筑风格、服饰风格、音乐风格——甚至饮食风格——都越来越趋向于变成统一的世界流行风格了。

世界呈现出同一性特征是因为它本来具有同一性。

在这个世界上长大的儿童感受到的是一个千篇一律的世界而不是一个多样化的世界。

他们的个性也受到这种同一性的影响，因此，在他们的感觉中，不同文化和个人之间的差异变得越来越小了。

由于世界各地的建筑越来越千篇一律，居住在这些建筑里的人也越来越千人一面了。

这样带来的结果用一句人们已经听熟的话来描述再恰当不过：历史要消失了。

以汽车为例即可非常清楚地证明这一点。

诸如流线型或全焊接式车身结构一类的技术革新，一开始可能不被人接受，但假如这种技术革新在提高汽车制造业的工作效率和经济效益方面确有巨大作用，它便会一再地以各种变异的形式出现，直到最终它不仅会被接受，而且会被大家公认为是一种宝贵的成果。

今天的汽车再也找不出某个汽车公司或某个民族文化的标志性特征了。

一般的汽车，不管产于何地，其基本特征都大同小异。

几年前，福特汽车公司制造出一种菲爱斯塔牌汽车，并将其称为“世界流行车”。

这种车出现在广告上的形象是周围环绕着世界各国的国旗。

福特公司解释说，这种汽车的汽缸活塞是英国产的，汽化器是爱尔兰造的，变速器是法国产的，车轮是比利时产的，诸如此类，等等等等。

这种菲爱斯塔牌汽车现在似乎已完全销声匿迹了，但这种制造世界流行汽车的设想计划却是势在必行的。

小学上册英语第一单元自测题英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I enjoy ________ (参加) dance classes.2.What is the main ingredient in jam?A. FruitB. SugarC. WaterD. Salt3.n Wall was a symbol of the ________ (冷战). The Berl4.I have a robot ________ (玩具) that can talk.5.The _______ (鳄鱼) lives in rivers and lakes.6.The ______ (树冠) provides shelter for many animals.7.The chemical formula for methane is _______.8.I see a _____ (骑士) in the parade.9.What do we call the main character in a story who opposes the protagonist?A. HeroB. VillainC. MentorD. SidekickB Villain10.How many players are on a polo team?A. 4B. 5C. 6D. 711.What is the capital of Tuvalu?A. FunafutiB. NukufetauC. NiutaoD. NanumagaA12.What do we call the study of the universe?A. AstronomyB. GeologyC. BiologyD. Physics13.What is the largest organ in the human body?A. HeartB. BrainC. LiverD. SkinD14.I have a _____ (沙滩球) that I take to the beach. 我有一个去沙滩时带的沙滩球。