Superclusters and Voids - same curvature?

[Jorrie]

Hi Jon.

Beyond that [the central observer], logic still seems to me to require that in addition to the gravitational collapse you described, there must be a second "overlay" effect of a quasilocal (Hubble) scale contraction factor within the hypothetical cluster.

Nope, I don't think so. For the quasi-homogeneous and isotropic scenario with static initial conditions that you described, Newton says that the collapse will [edit] appear to be isotropic in the frame [/edit] of any locally comoving observer inside the 'cloud' (ignoring a possible observable edge and keeping it non-relativistic). No other effects are needed, [edit] provided that one has given enough time for light to have traveled through the whole cloud since t0.[/edit]

Hypothetically, if the same cluster were enlarged (adding more stars) to a size equal to our observable horizon, the observable universe would be above critical density and FRW would calculate a global scale contraction factor.

Newton dynamics does not hold all the way to the observable universe size, because the FRW metric and Newton are not quite compatible at that size. Also, the static initial conditions that you chose mean that it has a closed geometry (over critical density) for any size.

If hypothetically, the size of the cluster were then reduced repeatedly by eliminating successive outer shells (layers) of stars, at some point the observable universe would no longer qualify as "homogeneous", and we would no longer trust in the FRW equations.

If you take away all but a spherical collection of stars (anywhere inside the cloud, still many of them, initially static and uniformly spaced), things will remain homogeneous until it becomes relativistic. The only inhomogeneity will be inside the stars. If you include the (now empty space around the cloud), then the total is obviously not homogeneous, but that was not part of the original scenario.

The possibilities 1 to 3 that you listed are largely based on your views that I discussed above. Without agreeing on the correctness of those views, the discussion cannot continue fruitfully, I'm afraid.

Jon, you are again using a 'funny' term (to me at least): "scale expansion factor". What's that? If you meant 'scale factor' or 'expansion factor' (a), it does not make sense in the context you used it.

Jorrie

 

[jonmtkisco]

Hi Jorrie,

Sorry if the term "scale expansion factor" sounds funny to you. Due to Wallace's repeated admonition I feel constrained to minimize use of terms like "Hubble flow" and "expansion of space." I used the term "scale expansion factor" to have the same meaning as a Hubble constant: dot a / a , with the expansion rate being linear with distance from the observer.

For the quasi-homogeneous and isotropic scenario with static initial conditions that you described, Newton says that the collapse will [edit] appear to be isotropic in the frame [/edit] of any locally comoving observer inside the 'cloud' (ignoring a possible observable edge and keeping it non-relativistic).

OK, I didn't realize that a straight Newtonian collapse will appear "Hubble flow-like" (approach rate linear with distance) to any non-central observer (except for the visible edge). So why isn't it correct to interpret this as constituting a de facto (or pseudo-)Hubble scale contraction of a spherical subset of the observable universe? Why would that interpretation be necessarily wrong?

If you include the (now empty space around the cloud), then the total is obviously not homogeneous, but that was not part of the original scenario.

Yes, including the (almost) empty region outside the cloud (as I described it in my last post) is now part of my revised scenario. That's the question I'm asking now: Based on physics as we currently understand it, would we predict that the outside region would behave more like possibility 1, 2, or 3? Or if you think all three are incorrect, then please describe what you think is the most likely behavior for the region outside the cloud.

Jon

 

[Jorrie]

Hi Jon.

I used the term "scale expansion factor" to have the same meaning as a Hubble constant: dot a / a , with the expansion rate being linear with distance from the observer.

I suggest you rather use dot a / a, except that in your hypothetical scenario, there is no well defined a... I guess recession speed/distance ratio is a better option, which will not confuse anyone.

So why isn't it correct to interpret this as constituting a de facto (or pseudo-)Hubble scale contraction of a spherical subset of the observable universe? Why would that interpretation be necessarily wrong?

I don't think it is wrong, provided you pick a large enough subset so that it can be taken as approximately homogeneous and not so large that recession (or in-fall) velocities become relativistic. I think some structure formation studies are done more or less like this, but I'm uncertain of that.

Yes, including the (almost) empty region outside the cloud (as I described it in my last post) is now part of my revised scenario.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.

Jorrie

 

[jonmtkisco]

Hi Jon.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.
Jorrie

Hi Jorrie,

The Shell Theory equations seem straightforward enough for regions outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

As far as I can tell, my "possibility #3" is consistent with the mainstream expectation of how an isolated mass is supposed to behave. For example, in their paper "Fractal Approach to Large-Scale Galaxy Distribution" (5/05), Baryshev and Teerikorpi cite the Lemaitre-Toman-Bondi (LTB) model, which is an exact solution of Einstein's dequations and a generalization of the FRW models with a non-zero density gradient. They say:

"The LTB model has been used for understanding the kinematics and dynamics of galaxies around individual mass concentrations. For example, Teerikorpi et al. (1992), and Ekholm et al. (1999) could put in evidence the expected behaviour in the Virgo supercluster: 1) Hubble law at large distances, 2) retardation at smaller distances, 3) zero-velocity surface, and 4) collapsing galaxies at still smaller distances." (p.71)

Of course, observations of our Local Group find results that seem inconsistent with the LTB model. That is the Sandage-de Vaucouleurs (S-V) paradox which Wiltshire refers to. Observations show that the Hubble scale expansion of local galaxies is quite close to the overall Hubble value, seemingly with little or no influence from the gravitation of the obviously significant local clumpiness.

Wiltshire claims that his model gives an "implicit" solution of the S-V paradox. But on further consideration his "solution" is not what I would have expected. The point of the S-V paradox is that less variation from the Hubble rate is observed locally than what is expected to be produced by local clumpiness. Wiltshire seems to be saying that even though "wall observers" like us observe significant quasilocal variations in expansion rates, that the underlying expansion rates are actually identical in voids and clusters, and it is the differences in clocks which distorts our observations. But I would think that doesn't solve the S-V paradox, on the contrary it makes it worse. Wilthire says that the "real" variance in expansion rates is smaller than we observe; but S-V says that the observed variance is already too small. Making the variance smaller only exacerbates the paradox. If anyone understands what Wiltshire really means on this point, I'd appreciate an explanation.

There is another point where I think Wiltshire is trying to duck a possible contradiction. He says that the universe is void-dominated, which seems right. A void-dominated universe should be below critical density and therefore have negative overall curvature. But negative overall curvature would conflict with the WMAP CMB observations. So instead, he proposes that the universe is flat overall, but that our entire observable horizon is inside of a single underdense perturbation which has negative curvature. So we have to go to scales larger than our observable horizon to verify that the universe is indeed flat. While his logic seems sound, I can't help being skeptical about how neatly such a duex ex machina solves an otherwise intractible conflict for him. Essentially he's putting all of his eggs in a single basket which may prove impossible to verify.

It also seems to me that it is just a matter of time before any region of the full universe becomes void-dominated. Even if a region the size of our observable universe starts out somewhat overdense, the voids will expand faster than the bound clusters, and eventually it will be void-dominated and underdense on average. I don't see how the current (supposed) underdensity of our observible universe can be tracked back in any definitive way to prove that our observable universe was initially overdense, underdense, or pretty much exactly at critical density.

Jon

 

[Jorrie]

Hi Jon.

Hi Jorrie,
The Shell Theory equations seem straightforward enough for regions outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

The Shell Theorem works perfectly well inside any spherically symmetrical mass concentration, provided that the conditions are within the weak-field, low-speed (Newtonian) limit. I'm not sure what a relativistic Shell Theorem entails.

I'll leave the rest of your post for Wallace to consider...

Jorrie

 

[jonmtkisco]

Hi Jon.

Your hypothetical scenario is now the same as if your original 'cloud of stars' had one very dense clump of stars somewhere inside it. You can now still approximate it by Newtonian gravity (within limits), but you can no longer use the homogeneous density approximation, but need to integrate the non-homogeneous http://en.wikipedia.org/wiki/Shell_theory" for a sphere. It is obvious that the FRL metric does not hold and in order to understand this cosmologically, I think you must look at the studies that Wallace referred you to (through the Wiltshire paper). To speculate about it without doing the computations would not be very useful.
Jorrie

Hi Jorrie,

The Shell Theory equations seem straightforward enough for a point outside of the sphere; the sphere is treated as a gravitational point source. That is what I had understood.

As far as I can tell, my "possibility #3" is consistent with the mainstream expectation of how an isolated mass is supposed to behave. For example, in their paper "Fractal Approach to Large-Scale Galaxy Distribution" (5/05), Baryshev and Teerikorpi cite the Lemaitre-Tolman-Bondi (LTB) model, which is an exact solution of Einstein's equations and a generalization of the FRW models with a non-zero density gradient. They say:

"The LTB model has been used for understanding the kinematics and dynamics of galaxies around individual mass concentrations. For example, Teerikorpi et al. (1992), and Ekholm et al. (1999) could put in evidence the expected behaviour in the Virgo supercluster: 1) Hubble law at large distances, 2) retardation at smaller distances, 3) zero-velocity surface, and 4) collapsing galaxies at still smaller distances." (p.71)

Of course, observations of our Local Group find results that seem inconsistent with the LTB model. That is the Sandage-de Vaucouleurs (S-V) paradox which Wiltshire refers to. Observations show that the Hubble scale expansion of local galaxies is quite close to the overall Hubble value, seemingly with little or no influence from the gravitation of the obviously significant local clumpiness.

Wiltshire claims that his model gives an "implicit" solution of the S-V paradox. But on further consideration his "solution" is not what I would have expected. The point of the S-V paradox is that less variation from the Hubble rate is observed locally than what is expected to be produced by local clumpiness. Wiltshire seems to be saying that even though "wall observers" like us observe significant quasilocal variations in expansion rates, the underlying expansion rates are actually identical in voids and clusters, and it is the differences in clocks which distorts our observations. But I would think that doesn't solve the S-V paradox, on the contrary it makes it worse. Wilthire says that the "real" variance in expansion rates is smaller than we observe; but S-V says that the observed variance is already too small. Making the variance smaller only exacerbates the paradox. If anyone understands what Wiltshire really means on this point, I'd appreciate an explanation.

There is another point where I think Wiltshire is trying to duck a possible contradiction. He says that the universe is void-dominated, which seems right. A void-dominated universe should be below critical density and therefore have negative overall curvature. But negative overall curvature would conflict with the WMAP CMB observations. So instead, he proposes that the universe is flat overall, but that our entire observable horizon is inside of a single underdense perturbation which has negative curvature. So we have to go to scales larger than our observable horizon to verify that the universe is indeed flat. While his logic seems sound, I can't help being skeptical about how neatly such a duex ex machina solves an otherwise intractible conflict for him. Essentially he's putting all of his eggs in a single basket which may prove impossible to verify.

It also seems to me that it is just a matter of time before any region of the full universe becomes void-dominated. Even if a region the size of our observable universe starts out somewhat overdense, the voids will expand faster than the bound clusters, and eventually it will be void-dominated and underdense on average. I don't see how the current (supposedly) underdensity of our observible universe can be tracked back in any definitive way to prove that our observable universe is overdense, underdense, or pretty much exactly at critical density.

Jon

 

[jonmtkisco]

Hey Wallace,

It's your turn to weigh in here...

 

[jonmtkisco]

Jorrie found the 2005 article http://arxiv.org/PS_cache/astro-ph/pdf/0507/0507364v1.pdf" by A.D. Chernin et al which provides a clear explanation for a model of very local scale expansion which resolves the Sandage-de Vaucouleurs paradox. Apparently this model of cluster formation is referred to as the "Little Bang", a term I had not heard. The model says that only the small core of the Local Group is gravitationally bound, out to a Zero Gravity Surface at 1.5-2 Mpc from the Milky Way - Andromeda barycenter. So pretty much only these two galaxies are gravitationally bound together. The remainder of the local group (including 86-some small galaxies) is not gravitationally bound together, and these outer galaxies are expanding away from us at the general Hubble rate.

This model predicts that the universe is dominated by low mass structures like our Local Group; each such structure contains only a handful of large galaxies. As a result, only these small core clusters are gravitationally bound; clusters and superclusters themselves are not. Other galaxies contained in a cluster probably originated within the Zero Gravity Surface core; the chaotic mix of high peculiar velocities inside the core caused most of the galaxies to exit the core radially. Later the cosmic expansion (including the cosmological constant at larger distances) cooled and normalized exited galaxies' peculiar velocities, and they asymptotically rejoined the cosmic Hubble flow. So today we see these cluster structures which appear to be bound but in fact are mostly expanding at the Hubble rate.

I think this model makes a lot of sense. I would think that it still works with the Wiltshire model, although as far as I can tell it says that the fraction of the volume of the observable universe which is gravitationally bound must be a tiny percentage of the 20-25% figure Wiltshire uses in his paper. I'm not sure if that affects the general outcome of Wiltshire's results...

Chernin defines the Zero Gravity Surface as the surface where "the gravity of the Local Group dark matter and baryons is balanced by the antigravity of the vacuum. Observations show that these are just the distances [1.5-2 Mpc] from which the observed Hubble flow takes start."

They say:

"These considerations suggest that cosmic vacuum may control the dynamics of the observed Universe at both global spatial scales approaching the observation horizon and local scales deep inside the cell of matter uniformity. Because of this, the cosmological expansion may be not only a global phenomenon, but also a local one..."

Very interesting.

Jon

 

[jonmtkisco]

Is anyone on this Forum aware of observational data or theoretical logic which challenges the 'Little Bang' model described in Chernin (et al)'s paper?

The paper says: "low mass groups, like the Local Group, dominate, and the Hubble flow is not significantly disturbed around them." I interpret this to mean that, in general, individual clusters and superclusters are not unitary, gravitationally bound structures. Instead, the largest gravitationally bound physical structures (in general) are individual galaxies and small local groups containing a handful of large galaxies. For example, the gravitational influence of our Local Group, comprised essentially of the Milky Way and Andromeda large galaxies, extends only about 1.5-2 Mpc from its barycenter.

Mainstream estimates of the mass of clusters are mostly based on the virial theorem, which assumes that clusters are in gravitational equilibrium with their virial kinetic energy. But if only multiple individual subsets of clusters are internally gravitationally bound, the virial theorem would not yield an accurate mass estimate for an entire cluster. The cluster's total mass should be somewhat smaller than if it were gravitationally bound. This in turn might indicate that the intra-cluster medium (ICM) contains less dark matter than normally supposed (and perhaps less dark matter than galactic halos contain). Which in turn could require adjusting the LCDM ratios of cold dark matter and baryonic matter for the observable universe as a whole.

[edit: Also requiring an explanation is why most clusters are observed to have a tightly bound core of very hot ICM gas at their physical center. If the physical center of a large cluster is but one of many galaxy group cores in the cluster, then why would the ICM gas be heavily skewed towards that single center, rather than distributed more evenly around each of the galaxy group cores?]

It seems to me that Chernin's model must be very controversial, but I'm not aware of any specific commentary.

And, I haven't seen any other logically compelling solution for the Sandage-de Vaucouleurs paradox.

Jon