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Gravitational collapse, star precipitation and black hole formation.

  1. May 24, 2006 #1
    Could the process of star formation in a collapsing gas cloud transform the process of virialisation and ultimately promote the formation of a central black hole?

    Consider the following idealised and oversimplified scenario.

    Suppose a gas cloud massive enough to generate vast numbers of stars is drawn together by gravity. Variations in density from place to place may cause overdense regions of the cloud to collapse into stars. In this process the escape into intergalactic space of radiation from such individual overdense regions promotes the virialisation of stellar matter and the formation of stable stars.

    But once matter has precipitated into stars, the cloud, now composed of infalling stellar particles, as it were, can only be virialised by the escape from the cloud of the surplus kinetic energy of the particles themselves, i.e. of whole stars. Until this happens collapse must proceed adiabatically. Star formation thus quenches virialisation of the cloud as a whole and promotes adiabatic collapse.

    Eventually, however, the density of infalling stars must become high enough for close encounters between stars to become common. A new mechanism for virialisation of the cloud can now activated. Tidal kneading
    during close encounters between stars renders such encounters inelastic, and tranforms surplus kinetic energy of stellar motion into radiation which can escape from the cloud. The dissipation of surplus kinetic energy can gradually damp out any adiabatic oscillations and the star cloud as a whole can eventually settle into a stable and localised configuration.

    The end result might be a globular cluster of stars.

    But if the collapsing gas cloud were massive enough to generate billions of stars the density of stars in a central adiabatically-collapsing region might become large enough for an event horizon to form, in which case the collapsing cloud of stars could acquire a black hole at its centre, as its core collapses towards a singularity.

    Is it possible that the classical virial theorem is at the heart of the pervasive presence of black holes at the centres of galaxies?
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  3. May 25, 2006 #2


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    I've never heard of this being a dominant energy sink in a star cluster -- even in the core of an evolved globular cluster, close encounters are pretty rare. The core collapse of a star cluster is usually driven by stars in the tail of the Maxwellian distribution escaping the potential well.

    At a given size, a system with more stars will taken longer to relax and, therefore, collapse. Core collapse to the size of a black hole in an object with billions of stars would take much longer than a Hubble time. Anyway, energy input from close binaries is known to halt core collapse in globular clusters -- I see no reason why they wouldn't also prevent it in a more massive star system.
  4. May 25, 2006 #3
    Black holes at galaxy centres

    Neither had I. I suggested this as a possibility, but clearly my betters have thought of simpler ways of removing energy from a collapsing cluster. Thanks for the heads up..

    No. I wasn’t suggesting that billions of stars collapse into a black hole over much longer than the Hubble time. I was proposing that when in such a collapsing system stars have formed, perhaps early in the life of the universe,the nature of virialisation changes. As you wrote in your post #8 in the thread "The Virial theorem and Cosmology" “A star is its own self-gravitating system, so has its own virial eqilibrium”. Just so.

    Therefore the virial equilibrium of a star-filled collapsing structure is one in which the stars themselves can be treated as particles to be virialised. I propose that it is then that rapid? adiabatic collapse can set in, and that the inner core of the collapsing object, which might contain only a
    few million stars, could become dense enough to generate an event horizon enclosing only a tiny fraction of the total mass in the collapsing cloud.

    Lastly, re energy input from close binaries: here again my ignorance shows.

    Is the energy input you refer to coming from the formation of such binaries and the consequent release of surplus kinetic energy, along the lines introducing the thread “The Virial theorem and Cosmology”, namely: “Whenever a diffuse gravitating system condenses into a stable and more compact object, energy must be removed from it”?

    If so, just how does this energy escape from the core and halt its collapse?
  5. May 25, 2006 #4


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    That's about how many you would need to form the most massive black holes in the centers of galaxies (and you'd need to do it in much less than a Hubble time). Unless I misunderstood you, that was what you were proposing?

    I don't see what you're getting at. What part of virialization would be different in the early universe? The primary difference I'm aware of is the lack (or low abundance of) heavy elements. This is where the whole "Population III stars" debate comes in. These stars would be more massive and perhaps a bit larger on average, but they shouldn't behave too differently when in a cluster.

    The core collapse I described for a globular cluster does occur under virial equilibrium.

    Hard binaries (ones with orbital velocities greater than the velocity dispersion of the cluster) will generally add energy to the globular cluster after three-body interactions with other stars. Basically, energy is taken from the oribt of the two stars and put into the random motion of a third star in the cluster. In a dense globular cluster, these interactions are quite common. Again, by the simple arguments of the virial theorem presented in your cosmology thread, an increase in energy will lead to an increase in radius.
    Last edited: May 25, 2006
  6. May 26, 2006 #5
    Gravitational collapse, star precipitation and black hole format

    Well, not quite. In my ignorance I thought that galaxies were composed of billions of stars, but their black holes only of millions of star-masses. I stand corrected.

    Again, I thought that galaxies started out as gas clouds that stayed virialised as they collapsed, but that such virialisation would be quenched by star formation, to be followed by adiabatic collapse of the star-cloud inwards, until a different kind of virialisation (along the lines you have described for star clusters) took over, or a black hole formed.

    I clearly have only a poor idea of how galaxies do form. I’ve looked at Peebles’ Principles of Physical Cosmology for enlightenment, but this is written by a master for the cognoscenti, and his section on galaxy formation is too densely fact-filled for me to see the wood among the trees, as it were. I don’t mind the algebra; it’s the plethora of relevant stuff that confuses me.

    Yes, I understand now. Thanks.
  7. May 30, 2006 #6
    How do cosmologists think galaxies form?

    I am now beginning to believe that professional cosmologists also have only a poor idea of how galaxies form........... after making the remark quoted above I've also looked through Peacock's Cosmological Physics only to find that he tackles this problem from a general perspective of the gravitational amplification of overdense regions, focusing on the variation of density enhancement (delta) with time. He treats several models (pancake formation and spherical infall) as if they were processes in a continuous fluid.

    This approach is like, in another branch of physics, treating the phase change of say a liquid into a solid as if the result were always a featureless glass. A good start, but oversimplified. Galaxies, like most real solids, are highly structured entities. In such cases it is essential also to consider how the nature and behaviour of the condensing phase affects the process and the products of condensation.

    I'd love to have the answers to a few questions about the present state of knowledge:

    Is it known how long (roughly) galaxies take to form, and when during the evolution of the universe this occurs?

    Is the nature of the condensing phase known for galaxies ? (Gas, dust, a star-cloud or, if a mixture, in what proportions?) Or do stars form during condensation?

    Is the origin of cental black holes well understood, and if so, is it a simple and inevitable adjunct to galaxy formation?
  8. May 31, 2006 #7


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    No, not very precisely, and it would depend on the size of the galaxy. In the most popular scenario right now, small galaxies formed quickly (order 100 million years) in the early universe. In general, larger objects take longer to collapse and virialize -- I would guess around a billion years for the largest galaxies.

    Dust (which requires elements other than hydrogen and helium) wouldn't have been very abundant in the early stages of galaxy formation. The first stars (and smallest galaxies) would have been formed from extremely low metallicity gas (probably [itex][Fe/H]\lesssim-3[/itex]). Both gas and stars would have been involved, but the proportions would have depended on environment (e.g. proximity to AGN, dark matter halo, or starburst).

    They do, but our understanding of early star formation is very crude. We can say that we expect early stars to be more massive (on average) due to the lack of cooling from heavy elements.

    No, we're still not sure whether the dominant growth mechanism is accretion or mergers with other black holes, though we're now leaning towards the former. The mechanism for this accretion is still not understood -- that is, the mechanism by which the accreted matter's angular momentum is reduced to the point where it reaches the last stable orbit.
  9. Jun 3, 2006 #8

    First. let me thank you for the trouble you and your fellow (grad. students? post-docs? researchers? academics?) have taken in this thread and two others to help me to a better, albeit sceptical, understanding of some aspects of cosmology and astrophysics, and of current thinking.

    Your remarks have been greatly appreciated.

    Finally, let me propose that keen astrophysicists ask themselves two simple questions:

    First, why do galaxies have centres at all? (Many things don't .. continents, trees, ourselves, for example).

    Second: what formation mechanism labels these centres with compact objects?

    And that is my last post (for a while) ...
  10. Jun 3, 2006 #9


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    It appears that "oldman" has now checked out for the time being.
    One might then offer some information and discuss the topic without feeling like one is interupting the discussion which oldman wants to have.

    I think it is a good topic. One should try to understand galaxy formation, which to a large extent means the formation of GROUPS OF GALAXIES (because AFAIK at least half of galaxies occur in groups, it is very common of them) and also the process of MERGER

    merger seems to be very common----to a significant extent it is how galaxies grow----and there are a lot of computer simulation studies of how the merging is inelastic and somehow they collide softly and stick together rather than just passing thru and continuing on their separate ways.

    also one should know about the bigtime N-body simulation of structure formation called MILLENNIUM. ultimately the only way to really understand how the universe curdled is with computer simulations IMHO

    That said, I will try to get a raw bunch of links. I didnt sift these to find the goodies----it is an unselective bunch
    Galaxy Formation
    Authors: Eric Gawiser (Yale University)
    Comments: Invited review to appear in New Horizons in Astronomy, ASP Conference Series (13 pages)
    I summarize current knowledge of galaxy formation with emphasis on the initial conditions provided by the Lambda CDM cosmology, integral constraints from cosmological quantities, and the demographics of high-redshift protogalaxies. Tables are provided summarizing the number density, star formation rate and stellar mass per object, cosmic star formation rate and stellar mass densities, clustering length and typical dark matter halo masses for Lyman break galaxies, Lyman alpha emitting galaxies, Distant red galaxies, Sub-millimeter galaxies, and Damped Lyman alpha absorption systems. I also discuss five key unsolved problems in galaxy formation and prognosticate advances that the near future will bring."

    The broken hierarchy of galaxy formation
    Authors: R. G. Bower (1), A. J. Benson (2), R. Malbon (1), J. C. Helly (1), C. S. Frenk (1), C. M. Baugh (1), S. Cole (1), C. G. Lacey (1) ((1) ICC, Durham, (2) Dept. of Physics, Oxford)
    Comments: 10 pages, 6 colour figures. Submitted to MNRAS

    "Recent observations of the distant Universe suggest that much of the stellar mass of bright galaxies was already in place at $z>1$. This presents a challenge for models of galaxy formation because massive halos are assembled late in hierarchical cosmologies such as cold dark matter (CDM). In this paper, we discuss a new implementation of the Durham semi-analytic model in which feedback due to active galactic nuclei (AGN) is assumed to quench cooling flows in massive halos. This mechanism naturally creates a break in the local galaxy luminosity function at bright magnitudes. The model is implemented within the Millennium N-body simulation; the accurate dark matter merger trees and large number of realizations of the galaxy formation process that the simulation provides results in highly accurate statistics. After adjusting the values of the physical parameters in the model by reference to the properties of local galaxies, we use it to investigate the evolution of the K-band luminosity and galaxy stellar mass functions. We also calculate the volume averaged star formation rate density of the Universe as a function of redshift and the way in which this is apportioned amongst galaxies of different mass. The model robustly predicts a substantial population of massive galaxies out to redshift $z\sim 5$ and a star formation rate density which rises with increasing redshift in objects of all masses. Although observational data on these properties have been cited as evidence for ``anti-hierarchical'' galaxy formation, we find that when AGN feedback is taken into account, the fundamentally hierachical CDM model provides a very good match to these observations."

    Galaxy Formation and Dark Matter
    Authors: Joseph Silk
    Comments: To be published in "The Invisible Universe: Dark Matter and Dark Energy", proceedings of the Third Aegean Summer School, Chios, 26 September-1 October, 2005
    "The challenge of dark matter may be addressed in two ways; by studying the confrontation of structure formation with observation and by direct and indirect searches. In this review, I will focus on those aspects of dark matter that are relevant for understanding galaxy formation, and describe the outlook for detecting the most elusive component, non-baryonic dark matter. Galaxy formation theory is driven by phenomenology and by numerical simulations of dark matter clustering under gravity. Once the complications of star formation are incorporated, the theory becomes so complex that the brute force approach of numerical simulations needs to be supplemented by incorporation of such astrophysical processes as feedback by supernovae and by active galactic nuclei. I present a few semi-analytical perspectives that may shed some insight into the nature of galaxy formation."

    The Formation Histories of Galaxy Clusters
    Authors: J.D.Cohn, Martin White
    Comments: 24 pages, final version to appear in Astroparticle Physics
    Journal-ref: Astropart.Phys. 24 (2005) 316-333
    "A sample of hundreds of simulated galaxy clusters is used to study the statistical properties of galaxy cluster formation. Individual assembly histories are discussed, the degree of virialization is demonstrated and various commonly used formation times are measured and inter-compared. In addition, the fraction of clusters which have ``recently'' undergone a major merger or significant mass jump is calculated as a function of lookback time and interval. The fraction of three- and four-body mergers is also studied."

    Modeling the formation of galaxy clusters in MOND
    Authors: Adi Nusser, Etienne Pointecouteau
    Comments: 8 pages, 7 figures, MNRAS submitted
    Journal-ref: Mon.Not.Roy.Astron.Soc. 366 (2006) 969-976

    The History of Galaxy Formation in Groups: An Observational Perspective
    Authors: Christopher J. Conselice
    Comments: Invited review, 16 pages, to be published in ESO Astrophysics Symposia: "Groups of Galaxies in the Nearby Universe", eds. I. Saviane, V. Ivanov, J. Borissova
    "We present a pedagogical review on the formation and evolution of galaxies in groups, utilizing observational information from the Local Group to galaxies at z~6. The majority of galaxies in the nearby universe are found in groups, and galaxies at all redshifts up to z~6 tend to cluster on the scale of nearby groups (~1 Mpc). This suggests that the group environment may play a role in the formation of most galaxies. The Local Group, and other nearby groups, display a diversity in star formation and morphological properties that puts limits on how, and when, galaxies in groups formed. Effects that depend on an intragroup medium, such as ram-pressure and strangulation, are likely not major mechanisms driving group galaxy evolution. Simple dynamical friction arguments however show that galaxy mergers should be common, and a dominant process for driving evolution. While mergers between L_* galaxies are observed to be rare at z < 1, they are much more common at earlier times. This is due to the increased density of the universe, and to the fact that high mass galaxies are highly clustered on the scale of groups. We furthermore discus why the local number density environment of galaxies strongly correlates with galaxy properties, and why the group environment may be the preferred method for establishing the relationship between properties of galaxies and their local density."

    Simulations of Early Galaxy Formation
    Authors: Romeel Davé
    Comments: 9 pages, to appear in the proceedings of UC Irvine May 2005 workshop on "First Light & Reionization", eds. E. Barton & A. Cooray, New Astronomy Reviews
    Journal-ref: New Astron.Rev. 50 (2006) 24-28
    We present the predictions for the photometric and emission line properties of galaxies present during the latter stages of reionization from z=8 to 6. These preliminary predictions are made from cosmological hydrodynamic simulations that include star formation and feedback, but not the effects of radiative transfer. We find significant numbers of galaxies that have stellar masses exceeding 10^8 Mo by z=8, with metallicities in the range of one-tenth solar. These galaxies are just beyond the reach of current near-infrared surveys, but should be found in large numbers by next-generation programs. The Lyman alpha luminosity function does not evolve much from z=6 to z=8, meaning that it should also be possible to detect these objects in significant numbers with upcoming narrow band surveys, unless the escape fraction of Ly-alpha evolves significantly between those epochs.

    Understanding Galaxy Formation and Evolution
    Authors: V. Avila-Reese (Instituto de Astronomia, U.N.A.M., Mexico)
    Comments: 50 pages, 10 low-resolution figures (for normal-resolution, DOWNLOAD THE PAPER (PDF, 1.9 Mb) FROM this http URL). Lectures given at the IV Mexican School of Astrophysics, July 18-25, 2005 (submitted to the Editors on March 15, 2006)

    remember that when most of this stuff happened THE UNIVERSE HAD NOT EXPANDED SO MUCH SO STUFF WAS CLOSER TOGETHER

    also remember that this is a randomly assembled unselective biblio of titles and abstracts :smile:
    you have to do the picking and choosing. I don't recommend. Except e.g. in Joe Silk's case because he's famous and I respect him, but i didnt yet read this particular paper of his so I can't vouch. He's a discerning scholar so at least his citation REFERENCE list should be good.

    I would be curious to know what is the shockabsorb mechanism when two galaxies collide!!!!

    what about the presence of a THIRD GALAXY?

    computer animation of two galaxies merging that I have seens end up with some pieces of arms flung out wide. I guess that carries off some of the energy

    another thing is they DONT COLLIDE VERY FAST because they are diffuse bodies and not point masses so the acceleration of their fall towards each other kind of stops as they begin to merge.

    I've read that people think collisions trigger waves of star-formation, which I suppose suggests other mechanisms to make it inelastic.
    Last edited: Jun 3, 2006
  11. Jun 3, 2006 #10


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    And how many event horizons have been observed?
  12. Jun 3, 2006 #11


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    Unlike trees, people, and continents, galaxies are self-gravitating. We are bound by electromagnetic forces, but these forces are local. By contrast, a star (for example) in a galaxy will feel non-negligible gravitational forces from the entire galaxy.

    In the absence of a preferred axis or point in space, the minimum energy configuration for a self-gravitating system is a sphere, which of course has a center. Similarly, a system with net angular momentum tends to organize itself into a disk, which also has a center.

    They need not have formed in the center. If you put a supermassive black hole in the outer parts of a disk galaxy, a variety of mechanisms (most importantly, dynamical friction), will cause that object to migrate towards the center.
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