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tommac
2008-Sep-11, 03:30 PM
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?

antoniseb
2008-Sep-11, 03:37 PM
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.

tommac
2008-Sep-11, 03:42 PM
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.

Felix Ibe
2008-Sep-11, 03:49 PM
i really don't thinking they are bound to collide.They collide simple because of the gravitational force present in them.

tommac
2008-Sep-11, 03:57 PM
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.

antoniseb
2008-Sep-11, 04:18 PM
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.

Astronomer
2008-Sep-11, 04:19 PM
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.

John Mendenhall
2008-Sep-11, 04:55 PM
Simply look at the magnitude of the potential energy and compare it to the magnitude of the potential energy.



?

Neverfly
2008-Sep-11, 05:26 PM
?

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:)

Jeff Root
2008-Sep-12, 07:32 AM
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

Jens
2008-Sep-12, 08:39 AM
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?

tommac
2008-Sep-12, 01:46 PM
Have we seen evidence of this change in orbit? How could we detect it?



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.

Cougar
2008-Sep-12, 02:14 PM
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."

Jeff Root
2008-Sep-12, 02:55 PM
Of course, planets run on neat little railroad tracks around their stars.
Galaxies are off the rails...

-- Jeff, in Minneapolis

Tim Thompson
2008-Sep-12, 09:44 PM
What is the math behind bound galaxies?

Future Evolution of Bound Superclusters in an Accelerating Universe (http://ads.ari.uni-heidelberg.de/abs/2008arXiv0809.1417A); Araya-Melo, et al., preprint, September 2008.
The return of a static universe and the end of cosmology (http://ads.ari.uni-heidelberg.de/abs/2007GReGr..39.1545K); Krauss & Scherrer, General Relativity and Gravitation 39(10): 1545-1550, Oct 2007.
Cosmological expansion and local physics (http://ads.ari.uni-heidelberg.de/abs/2007PhRvD..76f3510F); Faraoni & Jacques, Physical Review D 76(6): id. 063510, September 2007.
Redshift-space limits of bound structures (http://ads.ari.uni-heidelberg.de/abs/2007MNRAS.376.1577D); DŁnner, et al., Monthly Notices of the Royal Astronomical Society 376(4): 1577-1587, April 2007.
The limits of bound structures in the accelerating Universe (http://ads.ari.uni-heidelberg.de/abs/2006MNRAS.366..803D); DŁnner, et al., Monthly Notices of the Royal Astronomical Society 366(3): 803-811, March 2006.
Future Evolution of Cosmic Structure in an Accelerating Universe (http://ads.ari.uni-heidelberg.de/abs/2003ApJ...596..713B); Busha, et al., The Astrophysical Journal 596(2): 713-724, October 2003.



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.


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 (http://ads.ari.uni-heidelberg.de/abs/2003PhRvL..91g1301C); 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.

tommac
2008-Sep-15, 08:51 PM
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?

Neverfly
2008-Sep-15, 09:12 PM
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.

Jeff Root
2008-Sep-15, 09:35 PM
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

Neverfly
2008-Sep-15, 10:13 PM
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:doh:

Nereid
2008-Sep-15, 10:57 PM
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.