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jonmtkisco
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The purpose of this thread is to further discuss the concept of the Hubble expansionary flow in our local region -- which is too small to be considered homogeneous for the purposes of the Friedmann equations, say up to a radius of 100 Mpc from us. (A megaparsec (Mpc) equals about 3.25 million light years or 3E+22 meters). I have read a dozen papers on this subject by Chernin, Karachentsev, Teerikorpi, et all, as well as Sandage et al’s http://http://arxiv.org/PS_cache/astro-ph/pdf/0603/0603647v1.pdf" .
According to Sandage, a regular Hubble flow of expansion is observed over the range from 4 to 200 Mpc from the center of our Local Group. Observations of a handful of nearby dwarf galaxies suggest that this Hubble flow also remains regular to within 2 Mpc of the center of our Local Group. Our Local Group, comprised of the binary formation of the Milky Way (MW) and Andromeda (M31) massive galaxies, also contains a few small galaxies, 36 or so dwarf galaxies, and numerous star clusters which altogether add little to the total mass of the group. The MW and M31 galaxies are about .7 Mpc apart and are approaching each other at about -120km/s. At that rate they are expected to merge in 5-6Gy. The total mass of the Local Group is estimated at around 1.3E+12 solar masses. Chernin says observations of the dwarf galaxies which early in their existence gained escape velocity from the Local Group (due to the ‘Little Bang’), show that the Hubble expansion flow begins at slightly above 1 Mpc from the Local Group center, that is, just at the outskirts of the group. By about 2 Mpc from the center, the regular Hubble linear velocity-distance trend emerges. (Chernin describes this as the solution to the Sandage-de Vaucouleurs paradox).
Chernin starts with the mainstream premise that dark energy smoothly pervades all vacuum space. Dark energy’s omega = [tex]\omega = -1[/tex] equation of state creates a local effective “antigravitating” density of [tex]\rho_{v} + 3P_{v} = -2\rho_{v}.[/tex] The gravity of matter dominates at small distances, and the total acceleration is negative (inward). At large distances, the antigravity of dark energy dominates, and acceleration is positive (outward). Gravity and antigravity balance each other, with zero net acceleration, at the “zero gravity surface, which has the radius:
[tex] R _{v} = \left(\frac{3M}{8 \pi \rho_{v}}\right)^{\frac{1}{3}} [/tex]
The zero gravity surface is very close to spherical now, and has been roughly spherical over its 12.5 Gy history. When escaped particles (such as the dwarf galaxies) move beyond the zero gravity surface, the dark energy antigravity accelerates their recession, while simultaneously “cooling” their peculiar velocities. This has caused the dispersion of peculiar velocities to become quite narrow in the region.
Observations of other nearby galaxy groups show the same sort of local Hubble flow as our Local Group. There are papers dedicated to the M81/M82 group, the Centaurus A/M83 group, and the IC342-Maffei group. Chernin suggests that the same unitary zero gravity surface concept also applies to much larger rich galaxy clusters. He suggests that such clusters could have zero gravity surfaces up to 10-20 Mpc radius. There is a footnote in Teerikorpi’s paper saying “However, for a large cluster or a supercluster, the [zero gravity] spheres contain a progressively smaller fraction of the volume.”
Chernin has created a non-Friedmann equation (which is structured very similar to Friedmann) to model non-homogeneous static space-time.
[tex]\frac{1}{2}\dot{r}^{2} = GM/R + \frac{1}{2}(r/A)^{2} + \overline{E} [/tex]
where [tex]A= \left(\frac{8 \pi G}{3}\rho_{v} \right) ^{-\frac{1}{2}} [/tex]
and [tex]\overline{E} \left( \chi \right) [/tex] is the Lagrangian coordinate [tex]\chi[/tex] per its unit mass.
He points out that since the vast majority of space is dominated by a very uniform dark energy density, the universe really is much more uniform at local scales than it would appear to be based solely on matter distribution. He demonstrates that his local space-time model can be neatly embedded into the global Friedmann space-time in General Relativity, with the local universe being described as a “spherical vacuole” according to the Einstein-Straus solution. He says [Chernin 3/06]:
“… one can imagine that the whole Universe may contain not one, but many (or an infinite number) of vacuoles of various sizes and masses. Moreover, a picture is theoretically possible in which vacuoles fill almost all cosmic space without intersecting each others. Such a complex non-uniform expanding structure is exactly (!) described by the equations above. Obviously in this picture the tiny contribution of uniform matter distribution between vacuoles can be neglected, and one obtains a highly non-uniform, but completely regular, cosmological model. The model describes the global expansion in terms of the relative motions of discrete masses which are in the centres of the vacuoles. The masses move apart from each others on the uniform vacuum background, in accordance with the Hubble law and the expansion factor given by the Friedmann theory…. In fact, because the zero-gravity radius is inside the vacuole in such a model, each vacuole expulses every other one and the expansion is generally accelerating…”
The part of Chernin et al’s model which I find most difficult to conceptualize (probably because they don’t focus much discussion on it) is the scenario in which a local Hubble expansion occurs inside a gravitationally bound structure. This apparently is recognized to be the case for our Local Group, which according to Karachentsev et al is being pulled gravitationally towards the Virgo cluster at around 140 km/s, and towards the Great Attractor at around 290 km/s. It also is moving peculiarly away from the Local Void at around 200 km/s, and residually (compared to the CMB dipole) in yet another direction at around 170 km/s (towards or away from what, isn’t known). In the concordant models, all calculations of the isotropic local Hubble flow are actually adjusted to subtract out these peculiar bulk flows. This is a very significant adjustment, considering how much larger magnitude these bulk flows are than the local Hubble flow (but the adjustment for peculiar flows becomes relatively insignificant at very large distances, e.g. 1000 Mpc). In any event, my interpretation is that this adjustment is the standard treatment: gravitational peculiar flows and Hubble flows are both simply subtractions from the “real” net CMB dipole flow.
So for example, I interpret this to mean that even though our Local Group is embedded in a local region which is undergoing regular Hubble expansion, that local region also is gravitationally embedded in our Local (Virgo) supercluster, which is gravitationally contracting. This vividly demonstrates how expansion and contraction are in constant dynamic contention with each other at virtually every point in the universe. Although Hubble expansion “dominates” the local region around our Local Group, that entire region is in turn “dominated” by gravitational contraction of the Local Supercluster, which contains many regions like ours which are expanding at the Hubble rate. Thus when the expansion and contraction are netted against each other, the net flow within our local region is contractive, but at a lesser rate of contraction than would exist if the region were not simultaneously undergoing a Hubble expansion.
I would appreciate any comments or questions.
Jon
According to Sandage, a regular Hubble flow of expansion is observed over the range from 4 to 200 Mpc from the center of our Local Group. Observations of a handful of nearby dwarf galaxies suggest that this Hubble flow also remains regular to within 2 Mpc of the center of our Local Group. Our Local Group, comprised of the binary formation of the Milky Way (MW) and Andromeda (M31) massive galaxies, also contains a few small galaxies, 36 or so dwarf galaxies, and numerous star clusters which altogether add little to the total mass of the group. The MW and M31 galaxies are about .7 Mpc apart and are approaching each other at about -120km/s. At that rate they are expected to merge in 5-6Gy. The total mass of the Local Group is estimated at around 1.3E+12 solar masses. Chernin says observations of the dwarf galaxies which early in their existence gained escape velocity from the Local Group (due to the ‘Little Bang’), show that the Hubble expansion flow begins at slightly above 1 Mpc from the Local Group center, that is, just at the outskirts of the group. By about 2 Mpc from the center, the regular Hubble linear velocity-distance trend emerges. (Chernin describes this as the solution to the Sandage-de Vaucouleurs paradox).
Chernin starts with the mainstream premise that dark energy smoothly pervades all vacuum space. Dark energy’s omega = [tex]\omega = -1[/tex] equation of state creates a local effective “antigravitating” density of [tex]\rho_{v} + 3P_{v} = -2\rho_{v}.[/tex] The gravity of matter dominates at small distances, and the total acceleration is negative (inward). At large distances, the antigravity of dark energy dominates, and acceleration is positive (outward). Gravity and antigravity balance each other, with zero net acceleration, at the “zero gravity surface, which has the radius:
[tex] R _{v} = \left(\frac{3M}{8 \pi \rho_{v}}\right)^{\frac{1}{3}} [/tex]
The zero gravity surface is very close to spherical now, and has been roughly spherical over its 12.5 Gy history. When escaped particles (such as the dwarf galaxies) move beyond the zero gravity surface, the dark energy antigravity accelerates their recession, while simultaneously “cooling” their peculiar velocities. This has caused the dispersion of peculiar velocities to become quite narrow in the region.
Observations of other nearby galaxy groups show the same sort of local Hubble flow as our Local Group. There are papers dedicated to the M81/M82 group, the Centaurus A/M83 group, and the IC342-Maffei group. Chernin suggests that the same unitary zero gravity surface concept also applies to much larger rich galaxy clusters. He suggests that such clusters could have zero gravity surfaces up to 10-20 Mpc radius. There is a footnote in Teerikorpi’s paper saying “However, for a large cluster or a supercluster, the [zero gravity] spheres contain a progressively smaller fraction of the volume.”
Chernin has created a non-Friedmann equation (which is structured very similar to Friedmann) to model non-homogeneous static space-time.
[tex]\frac{1}{2}\dot{r}^{2} = GM/R + \frac{1}{2}(r/A)^{2} + \overline{E} [/tex]
where [tex]A= \left(\frac{8 \pi G}{3}\rho_{v} \right) ^{-\frac{1}{2}} [/tex]
and [tex]\overline{E} \left( \chi \right) [/tex] is the Lagrangian coordinate [tex]\chi[/tex] per its unit mass.
He points out that since the vast majority of space is dominated by a very uniform dark energy density, the universe really is much more uniform at local scales than it would appear to be based solely on matter distribution. He demonstrates that his local space-time model can be neatly embedded into the global Friedmann space-time in General Relativity, with the local universe being described as a “spherical vacuole” according to the Einstein-Straus solution. He says [Chernin 3/06]:
“… one can imagine that the whole Universe may contain not one, but many (or an infinite number) of vacuoles of various sizes and masses. Moreover, a picture is theoretically possible in which vacuoles fill almost all cosmic space without intersecting each others. Such a complex non-uniform expanding structure is exactly (!) described by the equations above. Obviously in this picture the tiny contribution of uniform matter distribution between vacuoles can be neglected, and one obtains a highly non-uniform, but completely regular, cosmological model. The model describes the global expansion in terms of the relative motions of discrete masses which are in the centres of the vacuoles. The masses move apart from each others on the uniform vacuum background, in accordance with the Hubble law and the expansion factor given by the Friedmann theory…. In fact, because the zero-gravity radius is inside the vacuole in such a model, each vacuole expulses every other one and the expansion is generally accelerating…”
The part of Chernin et al’s model which I find most difficult to conceptualize (probably because they don’t focus much discussion on it) is the scenario in which a local Hubble expansion occurs inside a gravitationally bound structure. This apparently is recognized to be the case for our Local Group, which according to Karachentsev et al is being pulled gravitationally towards the Virgo cluster at around 140 km/s, and towards the Great Attractor at around 290 km/s. It also is moving peculiarly away from the Local Void at around 200 km/s, and residually (compared to the CMB dipole) in yet another direction at around 170 km/s (towards or away from what, isn’t known). In the concordant models, all calculations of the isotropic local Hubble flow are actually adjusted to subtract out these peculiar bulk flows. This is a very significant adjustment, considering how much larger magnitude these bulk flows are than the local Hubble flow (but the adjustment for peculiar flows becomes relatively insignificant at very large distances, e.g. 1000 Mpc). In any event, my interpretation is that this adjustment is the standard treatment: gravitational peculiar flows and Hubble flows are both simply subtractions from the “real” net CMB dipole flow.
So for example, I interpret this to mean that even though our Local Group is embedded in a local region which is undergoing regular Hubble expansion, that local region also is gravitationally embedded in our Local (Virgo) supercluster, which is gravitationally contracting. This vividly demonstrates how expansion and contraction are in constant dynamic contention with each other at virtually every point in the universe. Although Hubble expansion “dominates” the local region around our Local Group, that entire region is in turn “dominated” by gravitational contraction of the Local Supercluster, which contains many regions like ours which are expanding at the Hubble rate. Thus when the expansion and contraction are netted against each other, the net flow within our local region is contractive, but at a lesser rate of contraction than would exist if the region were not simultaneously undergoing a Hubble expansion.
I would appreciate any comments or questions.
Jon
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