Weak Lensing Determination of the Mass in Galaxy Halos

a r X i v :0806.1707v 1 [g r -q c ] 10 J u n 2008arXiv:08mm.nnnn[astro-ph]High Longevity Microlensing Events and Dark Matter Black Holes Paul H.Frampton Department of Physics and Astronomy,University of North Carolina,Chapel Hill,NC 27599-3255.Abstract Gravitational microlensing has been employed to identify mas-sive halo objects by their amplilification of distant sources;MACHO searches have studied event times 2h <∼t 0<∼2y corresponding masses in the range 10−6M ⊙<∼M <∼100M ⊙.We suggest that larger masses up to 106M ⊙are also of considerable interest.It has not been excluded that there is a significant number of halo black holes with such masses as suggested by cosmological entropy considerations and potentially detectable by high longevity microlensing events.1Introduction.Attempts to unify gravity with the other interactions of Nature may be guided by the holographic[1]principle which provides an(unproven)upper limit on the amount of information which can be contained is a given three-dimensional volume in terms of its two-dimensional surface area.Although the principle is not proven rigorously,it provides the best available guide to estimates of cosmological entropy and hence to suggest which future obser-vations can help to quantify where the entropy lies.It may well be objects not yet detected for want of a motivation to make the requisite observations. One such set of observations is the subject of the present Letter.Here we assume throughout the holographic principle is physically correct that the upper limit of entropy,taking into account all degrees of freedom, both gravitational and non-gravitational,is the area of the surface surround-ing a volume in units of the Planck area.Taking a standard estimate for the volume and area of the visible universe,this gives an upper limit for the entropy of the universe.The value is(S U)max∼10123.The conventional wisdom is that the present entropy of the universe is overwhelmingly dominated by the supermassive black holes(SMBHs)at the cores of galaxies.This provides a lower limit on the cosmological entropy which,taking for simplicity1012galaxies each containing a SMBH of mass 107M⊙,gives(S U)min∼10102.If we further acknowledge that the galaxies are receding from one another at an accelerated rate such that coalescence is,in general,unlikely and they can be regarded as totally segregated and disentangled then the upper limit on S U is refined to(S U)max∼10112.This provides the cosmological entropy range102<∼log10S U<∼112(1)thefirst of two interesting windows which are the subject for this Letter. Conventional wisdom is S U∼(S U)min=10102.Dark Matter Black HolesIf we consider normal baryonic matter,other than black holes,contri-butions to the entropy are far smaller.The background radiation and relic neutrinos each provide∼1088.We have learned in the last decade about the dark side of the universe.WMAP[2]suggests that the pie slices for the overall energy are4$baryonic matter,24%dark matter and72%dark energy.Dark energy has no known microstructure,and especially if it ischaracterized only by a cosmological constant,may be assumed to have zero entropy.As already mentioned,the baryonic matter other than the SMBHs contributes far less than(S U)min.This leaves the dark matter which is concentrated in halos of galaxies and clusters.It is counter-intuitive that essentially all the entropy of the universe is concentrated in SMBHs.The Schwarzschild radius for a107M⊙SMBH is ∼3×107km and so1012of them occupy only∼10−36of the volume of the visible universe.Cluster halos have scales∼1Mpc and sofill out closer to ∼10−3of the total volume and the galcatic halos∼10−6.Several years ago important work by Xu and Ostriker[3]showed by nu-merical simulations that DMBHs with masses above106M⊙would have the property of disrupting the dynamics of a galactic halo leading to runaway spiral into the center.This provides an upper limit(M DMBH)max∼106M⊙.Gravitational lensing observations are amongst the most useful for deter-mining the mass distributions of dark matter.Weak lensing by,for example, the HST shows the strong distortion of radiation from more distant galaxies by the mass of the dark matter and leads to astonishing three-dimensional maps of the dark matter trapped within clusters.At the scales we consider ∼3×107km,however,weak lensing has no realistic possibility of detecting DMBHs in the forseeable future.Gravitational microlensing presents a much more optimistic possibility. This technique which exploits the amplification of a distant source wasfirst emphasized in modern times(Einstein considered it in1912unpublished work)by Paczynski[4].Subsequent observations[5]found many exam-ples of MACHOs,yet insufficient to account for all of the halo by an or-der of magnitude.These MACHO searches looked for masses in the range 10−6M⊙<∼M<∼102M⊙.According to[4]the time t0of a microlensing event is given byr Et0≡M⊙ 1/2(3)so that,for the MACHO masses considered,2h<∼t0<∼2y.Although some of the already observed MACHOs may be DMBHs,they do not saturate the possible mass or entropy for dark matter so let us set as definition (M DMBH)min∼102M⊙.This provides the range for DMBH mass2<∼log10η=log10(M DMBH/M⊙)<∼6(4)which,after Eq.(1),provides a second window of interest.It corresponds to 2y<∼t0<∼200y.Ranges(1)and(4)are related in the next section. Cosmological entropy considerationsAs mentioned already,the key guide will be the holographic principle[1] which informs us that the cosmological entropy is in the window(1).It cannot be at the absolute maximum value because that is possible only if every halo has already completely collpsed into a single black hole.Also,the absolute minimum although not excluded seems intuitively im-plausible because all the entropy is compressed into10−36V U.The natural suggestion is that there exist DMBHs in the mass region(4). The number is limited by the total halo mass1012M⊙.The total entropy is higher for higher DMBH mass because S∝M2.Let n be the number of DMBHs per halo,ηbe the ratio(M DMBH/M⊙),S U be the total entropy for1012halos and t0be the microlensing longevity.The Table showsfive possibilitiesDark Matter Black Holes and Microlensing Longevitylog10n max log10S halo21022310364104205105606106200Note that ten billion DMBHs with100M⊙mass contribute the same entropy as one SMBH but105times the mass.With the maximim allowed DMBH mass there can be up to a million DMBHs each with106M⊙mass, contributing104times as much entropy as the SMBH.Microlensing observationSince microlensing observations[5]already impinge on the lower end of the range(4)and the Table,it is likely that observations which look at longer time periods,have higher statistics or sensitivity to the period of maximum amplification can detect heavier mass DMBHs in the halo.If this can be achieved,and it seems a worthwhile enterprise,then the known entropy of the universe could be increased by up to four orders of magnitude.To my knowledge,the DMBHs are not excluded by existing observations although the actual number,if not zero,can be significantly below the maximum allowed by the Table.AcknowledgementsThis work was supported in part by the U.S.Department of Energy under Grant No.DG-FG02-06ER41418.References[1]G.’t Hooft,in Salamfestschrift,Editors:A.Ali,J.Ellis and S.Ranjbar-Daemi.World Scientific(1994).p.284.gr-qc/9310026.[2]D.N.Spergel,et al.(WMAP Collboration),Astrophysical J.Suppl.170,377(2007).astro-ph/0603449.[3]G.H.Xu and J.Ostriker,Astrophys.J.437,184(1994).[4]B.Paczynski,Astrophys.J.304,1(1986).[5]C.Alcock,et al.Astrophys.J.542,281(2000).astro-ph/0001272.[6]P.H.Frampton and T.W.Kephart,JACP(2008,in press).arXiv:0711.0193[gr-qc]P.H.Frampton,S.D.U.Hsu,T.W.Kephart and D.Reeb.arXiv:0801.1847[hep-th].。

"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius -- and a lot of courage -- to move in the opposite direction.""Imagination is more important than know ledge.""Gravitation is not responsible for people falling in love.""I w ant to know God's thoughts; the rest are details.""The hardest thing in the world to understand i s the income tax.""Reality is merely an illusion, albeit a very persi s tent one.""The only real valuable thing is intuition.""A person starts to live when he can live outside himself.""I am convinced that He (God) does not play di c e.""God is subtle but he i s not malicious.""Weakness of attitude becomes w eakness of character.""I never think of the future. It comes soon enough.""The eternal mystery of the w orld is its comprehensibility.""Sometimes one pays most for the things one gets for nothing.""Science w ithout religion is lame. Religion w ithout science is blind.""Anyone who has never made a mistake has never tried anything new.""Great spirits have often encountered violent opposition from w eak minds.""E verything should be made as simple as possible, but not simpler.""Common sense is the collection of prejudices acquired by age eighteen.""Science i s a wonderful thing if one does not have to earn one's living at it.""The secret to creati v ity is knowing ho w to hide your sources.""The only thing that interferes with my learning is my education.""God does not care about our mathematical difficulties. He integrates empirically.""The w hole of science is nothing more than a refinement of everyday thinking.""Technological progress is like an axe in the hands of a pathological criminal.""P eace cannot be kept by force. It can only be achieved by understanding.""The most incomprehensible thing about the world is that it is comprehensible.""We can't solve problems by using the same kind of thinking w e used when w e created them.""E ducation is w hat remains after one has forgotten everything he learned in school.""The important thing is not to stop questioning. Curiosity has its own reason for existing.""Do not w orry about your di f ficulties in Mathematics. I can assure you mine are still greater.""E quations are more important to me, because politics is for the present, but an equation is something for eternity." "If A i s a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut.""T w o things are infinite: the universe and human stupidity; and I'm not sure about the the universe.""As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality.""Whoever undertakes to set himself up as a judge of Truth and Kno w ledge is shipwrecked by the laughter of the gods.""I know not with what weapons World War III w ill be fought, but World War IV will be fought w i t h sti c ks and stones." "In order to form an immaculate member of a flock of sheep one must, above all, be a sheep.""The fear of death is the most unjusti f ied of all fears, for there's no risk of accident for someone who's dead.""Too many of us look upon Americans as dollar chasers. This is a cruel libel, even i f it is reiterated thoughtlessl y by the Americans themselves.""Heroism on command, senseless violence, and all the loathsome nonsense that goes by the name of patriotism -- how passionately I hate them!""No, this trick w on't work...How on earth are you ever going to explain in terms of chemistry and physics so important a biological phenomenon as first love?""My religion consi s ts of a humble admiration of the illimitable superior spi r it who reveal s himself in the slight details we are able to perceive w ith our frail and feeble mind.""Yes, we have to di v ide up our time like that, betw een our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.""The release of atom power has changed everything except our w ay of thinking...the solution to thi s problem lies in the heart of mankind. If only I had know n, I should have become a watchmaker.""Great spirits have al w ays found violent opposition from mediocrities. The latter cannot understand it when a man does not thoughtlessly submit to hereditary prejudices but honestly and courageousl y uses hi s intelligence.""The most beautiful thing we can experience i s the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, w ho can no longer pause to w onder and stand rapt in awe, i s as good as dead: his eyes are closed.""A man's ethical behavior should be based effectually on sympathy, education, and social ties; no religious basis i s necessary. Man w ould indeeded be in a poor w ay i f he had to be restrained by fear of punishment and hope of reward after death.""The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational know ledge.""Now he has departed from this strange world a little ahead of me. That means nothing. P eople like us, who believe in physi c s, kno w that the distinction between past, present, and future is only a stubbornly persistent illusion.""You see, w i r e telegraph is a kind of a very, very long cat. You pull his tail in New York and hi s head i s meow ing in Los Angeles. Do you understand thi s? And radio operates exactly the same way: you send signal s here, they receive them there. The only di f ference is that there i s no cat.""One had to cram all this stuff into one's mind for the examinations, whether one liked it or not. This coercion had such a deterring effect on me that, after I had passed the final examination, I found the consideration of any scientifi c problems distasteful to me for an entire year.""...one of the strongest motives that lead men to art and science i s escape from everyday life w ith its painful crudity and hopeless dreariness, from the fetters of one's own ever-shi f ting desires. A finely tempered nature longs to escape from the personal life into the w orld of objective perception and thought.""He w ho joyfully marches to music rank and file, has already earned my contempt. He has been given a large brain by mistake, since for him the spinal cord w ould surely suffice. This di s grace to civilization should be done away with at once. Heroism at command, how violently I hate all this, how despicable and ignoble war is; I would rather be torn to shreds than be a part of so base an action. It is my conviction that killing under the cloak of war is nothing but an act of murder.""A human being is a part of a whole, called by us _universe_, a part limited in time and space. He experiences himself, his thoughts and feelings as something separated from the rest... a kind of opti c al delusion of his consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a fe w persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of compassion to embrace all living creatures and the whole of nature in its beauty.""Not everything that counts can be counted, and not everything that can be counted counts." (Sign hanging inE instein's office at P rinceton)Copyright: Kevin Harris 1995 (may be freely distributed with this acknowledgement)∙一个物体的质量就是其所含能量的度量单位。

Investigating the Nature of DarkMatterThe phrase “dark matter” has become a buzzword in modern astrophysics as well as popular culture, and yet we still know very little about what dark matter really is. It is a mysterious substance that makes up 27% of the universe and that cannot be observed directly, but can only be inferred from the gravitational effects it has on visible matter. Therefore, dark matter is a topic of intense research and debate in the scientific community. In this article, we will explore the key aspects of dark matter and the different ways scientists are working to uncover its nature.What is Dark Matter?As mentioned, dark matter is a substance that does not emit, absorb or reflect light, hence its name. It does not interact strongly with electromagnetic forces, but it does with gravity, which is why its presence can be inferred from the gravitational effects it has on visible matter. One of the most well-known examples of this is the rotation curve of spiral galaxies. According to the laws of classical mechanics, the velocity of stars and gas in a galaxy should decrease as one moves away from the center, as the gravitational attraction of the visible matter decreases. However, observations have shown that the velocity remains constant or even increases, suggesting that there is an invisible mass that is causing this anomaly. This invisible mass is the dark matter.Another piece of evidence for the existence of dark matter is the distribution of matter in the universe as revealed by the cosmic microwave background radiation, which is the afterglow of the Big Bang. The pattern of temperature fluctuations in this radiation shows that the matter in the universe is not distributed evenly, but is rather clumped up in large structures such as galaxies and clusters of galaxies. However, this clumping up cannot be explained solely by the gravitational influence of visible matter; there must be an additional source of gravity, i.e. dark matter, to explain the observed distribution.Moreover, measurements of the large-scale structure of the universe, such as the distribution of galaxies and galaxy clusters, also point to the existence of dark matter.What is Dark Matter Made of?Despite its importance in shaping the structure of the universe, the identity of dark matter remains unknown. There are several hypotheses about what dark matter might be made of, but none of them has been conclusively proven yet. One popular hypothesis is that dark matter is composed of weakly interacting massive particles (WIMPs), which are hypothetical particles that would interact with normal matter only through the weak nuclear force and gravity. The idea is that WIMPs were produced in the early universe when it was hot and dense, and have been moving around freely ever since. If they collide with normal matter, they would transfer some of their energy and momentum, producing detectable signals. In fact, several experiments have been designed to detect WIMP interactions, such as the Large Underground Xenon (LUX) experiment and the Super Cryogenic Dark Matter Search (SuperCDMS).Another hypothesis is that dark matter is made of axions, which are theoretical particles that were originally proposed to explain a different problem in physics, the strong CP problem. The idea is that axions would be very light and weakly interacting, making them difficult to detect, but would still affect the motion of galaxies and other cosmic structures. The Axion Dark Matter eXperiment (ADMX) is currently searching for evidence of axions in a laboratory at the University of Washington.A third hypothesis is that dark matter is composed of primordial black holes, which are black holes that were formed by the collapse of a density fluctuation in the early universe. The idea is that these black holes could have a mass range that would make them more likely to be dark matter, and that their interactions with normal matter could produce observable effects. However, this hypothesis is less favored by most researchers, as the formation and stability of such black holes would require very specific conditions.ConclusionDespite decades of research, the nature of dark matter remains one of the most intriguing and elusive topics in astrophysics. It remains a theoretical construct that cannot be directly observed, but its effects on the motion and structure of the cosmos are undeniable. Researchers are continuing to study dark matter using a variety of tools and techniques, from telescopes that measure gravitational lensing to underground experiments that look for WIMP interactions. The hope is that someday we will finally be able to unravel the mystery of what dark matter is made of, and in doing so, gain a better understanding of the universe and our place in it.。