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Thread: galaxy clusters

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    galaxy clusters

    What is the math behind bound galaxies? Are galaxy clusters doomed to collide?

    I would think that the gravitational pull between two galaxies would need to create attraction exactly equal to the rate of expansion of space.

    However, the expansion of space SUPPOSEDLY does not effect bound objects.

    There must be an equalibrium right?

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    Quote Originally Posted by tommac View Post
    However, the expansion of space SUPPOSEDLY does not effect bound objects.
    I think you'll find, that on close examination, the expansion of space is not an important factor in the dynamics of bound objects... but that applies for atoms bound in crystals, more than for close orbiting stars, more than galaxies, more than clusters of galaxies, more than super-clusters. At some point, the scale and tenuousness of "an object" is such that it is just barely bound against the expansion of space.
    Forming opinions as we speak

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    Quote Originally Posted by antoniseb View Post
    I think you'll find, that on close examination, the expansion of space is not an important factor in the dynamics of bound objects... but that applies for atoms bound in crystals, more than for close orbiting stars, more than galaxies, more than clusters of galaxies, more than super-clusters. At some point, the scale and tenuousness of "an object" is such that it is just barely bound against the expansion of space.
    can you please show the math.

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    i really don't thinking they are bound to collide.They collide simple because of the gravitational force present in them.

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    Quote Originally Posted by Felix Ibe View Post
    i really don't thinking they are bound to collide.They collide simple because of the gravitational force present in them.
    Sorry used bound in two different ways ...

    bound meaning eventually
    and bound as in gravitationally bound ...

    What I was saying is that if they are gravitationally bound ... does that mean that they will eventually collide.

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    Quote Originally Posted by tommac View Post
    can you please show the math.
    I can't show full-blown math for this taking into account GR, and non-homogeneous dark energy, but just simply, take a look around you.

    Right now, the universe is locally expanding about one part in 14 billion per year, or about one part in 500 quadrillion per second. You can look at the Sun-Earth system, and see what one second's worth or perturbation would do to our orbit... slightly lower gravity, but the same momentum. It would slightly raise our orbit. The scale of the raise would be probably be small or comparable to other phenomena that raise or lower our orbit. The net impact of the expansion of space alone is about 35 feet per year away from the Sun by my rough calculation.
    Forming opinions as we speak

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    Quote Originally Posted by tommac View Post
    Sorry used bound in two different ways ...

    bound meaning eventually
    and bound as in gravitationally bound ...

    What I was saying is that if they are gravitationally bound ... does that mean that they will eventually collide.
    If the Hubble expansion is constant, then you can define a universal bound for any orbit. If the Hubble constant is changing then objects will become bound/unbound with the changing Hubble constant.

    Detailed mathematics are difficult to comprehend without parametric calculus, but there is a cute Newtonian analogy which might allow you to see how it works.

    In the strictest sense, a bound object is one where the magnitude of the kinetic energy is less than the magnitude of the potential energy (be it gravitational, chemical, whatever). Kinetic energy is related to velocity of the object squared. The Hubble Flow adds an additional velocity term v=Hd. You can imagine that it is either increasing the kinetic energy of the object or decreasing the potential energy. For our purposes, it is conceptually easier to imagine it as decreasing the potential energy. For most objects you are aware of, the Hubble flow velocity is so tiny it doesn't affect the binding energy at all so the dynamics of the situation are unchanged. For galaxies the Hubble Flow is still too small to be of importanc. For H=100 km/sec/Mpc consider the fact that our galaxy is a few kiloparsecs in size -- depending on how you measure the "size" of our galaxy. In the case of our sun which is virialized (meaning that the magnitude of the potential energy is fully twice the magnitude of the kinetic energy) the kinetic energy of our sun is associated with its orbital velocity around galactic center. Now since we are about 8 kiloparsecs away from the center of our galaxy, we can get a rough estimate of the added velocity which is about 800 meters per second for the numbers I quoted. That sounds really fast to us, but compared to the 220 kilometers per second it's nothing. In other words, the Hubble expansion is not a factor in the fact the bound nature of our galaxy. What essentially happens is as the universe expands, the Sun is given a little kick away from the center of the galaxy, but then it falls back that little way toward the center of the galaxy and regains the equilibrium state it occupied previously.

    With larger objects, the Hubble flow CAN affect the bound nature of the objects. It is affecting our attraction to the Great Attractor since it is pretty clear we haven't yet virialized and so cannot take advantage of the kick/fall-back mechanism I outlined above. When you do cosmological simulations, you have to include an expansion term to account for the dynamical effects of the expansion of the universe on large scale structure.

    In most cases, it is clear what objects will eventually collide and which will not. Simply look at the magnitude of the potential energy and compare it to the magnitude of the kinetic energy. Unfortunately, since we live in an accelerating universe, the Hubble constant is actually getting larger which means that v-correction term I talk about above is getting larger. This means that barely bound objects today will not collide because in the future the expanding universe will prevent them from collapsing. If the universe were decelerating, objects which were unbound today would eventually become bound as the v-correction got smaller. In a closed universe, the Hubble's constant becomes essentially negative which means that instead of making things less bound, the collapsing universe makes things more bound in such a way that everything ends up Bigly Crunched.
    Last edited by Astronomer; 2008-Sep-11 at 05:15 PM.

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    Huh?

    Quote Originally Posted by Astronomer View Post

    Simply look at the magnitude of the potential energy and compare it to the magnitude of the potential energy.
    ?

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    Quote Originally Posted by John Mendenhall View Post
    ?
    Awww c'mon. It made perfect sense.

    You simply look at the numbers and if they look numerical then you know that you have numbers

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    Quote Originally Posted by Astronomer View Post
    What essentially happens is as the universe expands, the Sun is given
    a little kick away from the center of the galaxy, but then it falls back
    that little way toward the center of the galaxy and regains the
    equilibrium state it occupied previously.
    The little kick and the falling back happen concurrently, of course,
    so that the result is a balance between the two. Jut in case anyone
    reading didn't get that.

    The above only happens if whatever is causing the acceleration of the
    expansion operates inside galaxies. Since we don't know the cause,
    and we have absolutely no detection of any expansion force within our
    galaxy or any other, we don't know whether there is any expansion
    force within galaxies. I have an ATM idea which implies the force is
    only between widely-separated clusters of galaxies, never within an
    individual galaxy or within a cluster, or even between closely-adjacent
    clusters.

    -- Jeff, in Minneapolis
    Last edited by Jeff Root; 2008-Sep-12 at 02:50 PM. Reason: I'm still learning how to spell 'separated'

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    Quote Originally Posted by tommac View Post
    What I was saying is that if they are gravitationally bound ... does that mean that they will eventually collide.
    I'm not sure why you say this in the first place. The earth and moon are gravitationally bound, but they will not eventually collide. If galaxies in a cluster have lateral motion, can't they just continue to "orbit" without colliding?
    As above, so below

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    Have we seen evidence of this change in orbit? How could we detect it?


    Quote Originally Posted by antoniseb View Post
    I can't show full-blown math for this taking into account GR, and non-homogeneous dark energy, but just simply, take a look around you.

    Right now, the universe is locally expanding about one part in 14 billion per year, or about one part in 500 quadrillion per second. You can look at the Sun-Earth system, and see what one second's worth or perturbation would do to our orbit... slightly lower gravity, but the same momentum. It would slightly raise our orbit. The scale of the raise would be probably be small or comparable to other phenomena that raise or lower our orbit. The net impact of the expansion of space alone is about 35 feet per year away from the Sun by my rough calculation.

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    Quote Originally Posted by Jens View Post
    I'm not sure why you say this in the first place. The earth and moon are gravitationally bound, but they will not eventually collide. If galaxies in a cluster have lateral motion, can't they just continue to "orbit" without colliding?
    Exactly.

    Of course, multiple cluster galaxies in arbitrary orbits present a very complicated scenario, and some may indeed happen to collide [termed a 'singularity' in mathematical solutions, I believe], but as you say, many or most will just continue to orbit in complicated ways within the group, roughly similar to how the planets just continue in their orbits as opposed to "eventually crashing into the Sun."
    Everyone is entitled to his own opinion, but not his own facts.

  14. #14
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    Of course, planets run on neat little railroad tracks around their stars.
    Galaxies are off the rails...

    -- Jeff, in Minneapolis

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    Lightbulb Doomsday Cosmology

    Quote Originally Posted by tommac View Post
    What is the math behind bound galaxies?


    Quote Originally Posted by tommac View Post
    Are galaxy clusters doomed to collide?
    Not when they exist in a universe that is rapidly pulling them away from each other. Since ours appears to be doing just that, then I guess in our universe the answer must be: No, they are not doomed to collide.

    Quote Originally Posted by tommac View Post
    There must be an equalibrium right?
    No. Make the "dark energy" (sometimes called phantom energy) accelerating the universe strong enough and you get the dreaded Big Rip scenario (i.e., Phantom Energy: Dark Energy with w<-1 Causes a Cosmic Doomsday; Caldwell, Kamionkowski & Weinberg, Physical Review Letters 91(7): id. 071301, August 2003). In this case the accelerated expansion becomes so furious that it not only rips apart gravitationally bound structures, it rips apart everything bound by any force, even protons & quarks.

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    Quote Originally Posted by Jens View Post
    I'm not sure why you say this in the first place. The earth and moon are gravitationally bound, but they will not eventually collide. If galaxies in a cluster have lateral motion, can't they just continue to "orbit" without colliding?
    Are galaxies orbiting one another?

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    Quote Originally Posted by tommac View Post
    Are galaxies orbiting one another?
    Not necessarily.

    Remember that scale makes a difference.

    For instance: Take two matchbox cars and roll them on the ground and slam them together.
    They bounce off eachother. They don't wreck.
    But take two automobiles and try it- Well... Let's hope you buckle up.

    The force needed to move those toy cars is Slight.
    The real cars - Great. And that great force demonstrates how great it is in a collision.

    Galaxies are huge. And heavy. At that scale, you are more likely to see a collision than an orbit.
    However, the individual "particles" (Particles?!! YIPES! I live on a particle!) will develop orbits. Some will be thrown out into space etc. Like a swirl of dust. Only big with a Whole Lotta Force!

    Ours and Andromeda are headed for this.
    In many billions of years, our Milkyway/Andromeda Galaxy will be an Enormous galaxy.
    Be proud.

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    I'm not quite sure what Neverfly was on about, there....

    In any case... Galaxies in a cluster do orbit the cluster's center of mass.
    However, as Cougar and I said, they don't orbit in neat ellipses, like trains
    on tracks, as planets orbit stars, because galaxy clusters did not collapse
    via friction into thin disks. The particles in giant molecular clouds collapse
    into thin disks when they cool off enough or when they are compressed
    by nearby supernovae. Some galaxies have apparently undergone a
    similar collapse. But elliptical galaxies, globular (star) clusters, and
    clusters of galaxies have not collapsed, and their parts move in random
    directions. Sometimes they will collide. Galaxies collide far more readily
    and often than individual stars, because galaxies are generally far larger
    in proportion to the distances between them.

    The distances between stars are stunningly enormous compared to
    their size. I haven't yet tried to calculate this to confirm it, but one
    astronomer estimated that all the stars in the visible Universe, if treated
    as massless spheres that could be packed tightly together like a big box
    full of toy balls, would all fit within our Solar System's Oort Cloud!

    Space is Big. Space is REALLY Big....

    -- Jeff, in Minneapolis

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    Quote Originally Posted by Jeff Root View Post
    I'm not quite sure what Neverfly was on about, there....


    Space is Big. Space is REALLY Big....

    -- Jeff, in Minneapolis
    Considering that we said very similar things- I'm impressed at your uncertainty

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    Quote Originally Posted by tommac View Post
    Are galaxies orbiting one another?
    Some are, some aren't.

    In the case of dwarf galaxies (closely) orbiting a normal galaxy, tidal stripping will reduce the smaller body to just its core over several orbits (details depend upon many factors).

    In the case of galaxies in, or near, the centre of a (rich) cluster, orbits are likely to be both chaotic and relatively short-lived (the inner Mpc or so of a rich cluster is not at all healthy for galaxies, other than cDs).

    For a more-or-less-equal pair such as our own MW and M31, which dominate a group that is relatively far from the nearest cluster, the orbits are likely to be many, though a 'death spiral' nonetheless, because vast amounts of energy are being lost to the system around the time of closest approach, due to many factors.

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