What's our Hubble Flow Vector?

[George]

I suppose some assumptions must be made. Should we assume that the center of gravity of our Local Group is moving with zero velocity relative to the Hubble Flow?

If so, what is our galactic center vector (V_MW) relative to this c.g.?

Then, what is our solar system's orbital vector (V_S) relative to our galactic center?

We know the daily orbital vector of the Earth, so what would be the net vector relative to the HF?

[mugaliens]

Normally I never approach an OP with "Wow! Great Questions!" Most don't deserve it.

So, George: Wow! Great Questions!

Just some questions so I'll be able to follow the ensuing discussion:

By "Local Group" are you referring to the local galactic cluster? And no, I don't think we should assume a zero velocity, though I suspect it's very slight relative to the Hubble flow.

"We know the daily orbital vector of the Earth, so what would be the net vector relative to the HF?"

Sum of movement around the Sun, through the Galaxy, Galaxy through the cluster, and cluster through interstellar space. Add a fudge factor for observed kicks (variances) and I think you'll have nailed it.

[DrRocket]

I suppose some assumptions must be made. Should we assume that the center of gravity of our Local Group is moving with zero velocity relative to the Hubble Flow?

If so, what is our galactic center vector (V_MW) relative to this c.g.?

Then, what is our solar system's orbital vector (V_S) relative to our galactic center?

We know the daily orbital vector of the Earth, so what would be the net vector relative to the HF?

You have identified the cg of the local group as a reference point, presumably the origin of some reference frame, and you have assumed that the Hubble flow is radially outward from that point. What do you propose as the axes for your coordinate system ?

[grant hutchison]

Seems like you're looking for the COBE dipole: the asymmetry in the cosmic microwave background generated by the Earth's peculiar motion relative to the "rest of the Universe".
This reference gives a velocity of 369 km.s^-1 towards galactic longitude 264.3°, latitude 48.0°. Our orbital movement around the galaxy is orientated in roughly the opposite direction, at about 220 km.s^-1, which accounts (I think) for the deduced ~600 km.s^-1 for the Local Group quoted on the APOD page.
The Sun has a peculiar motion relative to that Local Standard of Rest on the order of ten km.s^-1. (The LSR is difficult to measure precisely, since it's derived by averaging the peculiar motion of stars which are felt to be "typical" for our galactic neighbourhood.)

Grant Hutchison

[Jeff Root]

The May 1978 'Scientific American' had a good article about this:
"The Cosmic Background Radiation and the New Aether Drift", by
Richard A. Muller (pages 64-74). The numbers have probably
been updated since then, with data from COBE and WMAP.

-- Jeff, in Minneapolis

[Cougar]

This reference gives a velocity of 369 km.s^-1 towards galactic longitude 264.3°, latitude 48.0°.

This is the resultant vector. I recall reading that it results from a number of gravitational vectors, including the Virgo supercluster and the Great Attractor. The assumption that the center of gravity of our Local Group is moving with zero velocity relative to the Hubble Flow would be incorrect.

[grant hutchison]

This is the resultant vector. I recall reading that it results from a number of gravitational vectors, including the Virgo supercluster and the Great Attractor. The assumption that the center of gravity of our Local Group is moving with zero velocity relative to the Hubble Flow would be incorrect.

That's right; as I said, The Local Group has quite a large velocity.

Grant Hutchison

[Cougar]

That's right; as I said, The Local Group has quite a large velocity.

Yes. I hope my previous post did not imply any difference of opinion (or fact) with what you previously said.

As for the component vectors of the Local Group's resultant "peculiar" motion, the following article investigates this in some detail:

Our Peculiar Motion Away from the Local Void -- Brent Tully, et al.

Introduction
The dipole anisotropy seen in the cosmic microwave background (CMB) temperature map (Fixsen et al. 1996) is compelling evidence that the solar system has a large peculiar motion with respect to the overall cosmic expansion. There are known local components to this motion, including the orbital velocity of the Sun in the Milky Way, and the attraction of our Galaxy toward M31. Once these components are taken into account, it is found that the Local Group of galaxies has a peculiar motion of over 600 km s^–1 in a well-established direction.

[grant hutchison]

As for the component vectors of the Local Group's resultant "peculiar" motion, the following article investigates this in some detail:

Our Peculiar Motion Away from the Local Void -- Brent Tully, et al.

Ah, that's handy. Thanks. (Here's a link to the paper.)

Grant Hutchison

[George]

You have identified the cg of the local group as a reference point, presumably the origin of some reference frame, and you have assumed that the Hubble flow is radially outward from that point. What do you propose as the axes for your coordinate system ?

I think I understand your point, and I could suggest that Grant's dipole will allow an axes, but I'm not quite ready to do so.

So, George: Wow! Great Questions!

It's best to wait till folks like grant give their answer before being wowed.

Seems like you're looking for the COBE dipole: the asymmetry in the cosmic microwave background generated by the Earth's peculiar motion relative to the "rest of the Universe".

Darn, good answer, I plum forgot about it.

Ok, but the 369 kps result assumes an isotropic expansion. The dipole is 13.7 billion years in the making and may or may not be simply due to our peculiar motion, not that my Local Group c.g. free floating point is a good assumption, admittedly.

This reference gives a velocity of 369 km.s-1 towards galactic longitude 264.3°, latitude 48.0°. Our orbital movement around the galaxy is orientated in roughly the opposite direction, at about 220 km.s-1, which accounts (I think) for the deduced ~600 km.s-1 for the Local Group quoted on the APOD page.

[Using a 225 million year galactic orbital period and a 27,000 lyr. radius, I get close to the 220 kps figure (226 kps).] Assuming the 600 kps is an indpendent figure from the doppler shifts of our Local Group of galaxies -- from your link in your post, #9, this is implied and may be explicit if I were to read it fully -- then the 369 kps dipole amount seems to match beautifully. [The small difference due to being off-axis.]

Does this mean then that the c.g. of the Local Group is indeed "floating" with the flow, like a cork in a river? It seems like it to me, but then...

As for the component vectors of the Local Group's resultant "peculiar" motion, the following article investigates this in some detail:

Our Peculiar Motion Away from the Local Void -- Brent Tully, et al.

Introduction
The dipole anisotropy seen in the cosmic microwave background (CMB) temperature map (Fixsen et al. 1996) is compelling evidence that the solar system has a large peculiar motion with respect to the overall cosmic expansion. There are known local components to this motion, including the orbital velocity of the Sun in the Milky Way, and the attraction of our Galaxy toward M31. Once these components are taken into account, it is found that the Local Group of galaxies has a peculiar motion of over 600 km s–1 in a well-established direction.

So the 600kps is the vector result of the three motions: Sheet movement from the Void, MW galaxy motion within the Sheet, and our Sun's orbital motion around the MW. Is this right? [I assume the 3000 kps is the study's galactic redshift range.]

But the 369 kps dipole may still be an accurate value for our motion relative to the Hubble Flow, and consistent, with some reservation, with the other evidence (galaxy reshifts, I assume). Am I close?

[grant hutchison]

Ok, but the 369 kps result assumes an isotropic expansion. The dipole is 13.7 billion years in the making and may or may not be simply due to our peculiar motion ...

I'm not sure what you mean. You're looking for our motion relative to a comoving observer (that is, an observer at rest in the Hubble flow). Such observers see the Universe as isotropic (no dipole in the CMB). So the observed COBE dipole is our measure of motion relative to the Hubble flow.

Grant Hutchison

[George]

I'm not sure what you mean. You're looking for our motion relative to a comoving observer (that is, an observer at rest in the Hubble flow). Such observers see the Universe as isotropic (no dipole in the CMB). So the observed COBE dipole is our measure of motion relative to the Hubble flow.

[Is this reverse logic?] Is the premise correct? On a large scale, would such a "floating" observer indeed measure no dipole? Do observations allow us to say there can be no trivial speed variation between hemispheres in the expansion after 13.7 billion years? [Why am I not surprised you're still awake? ]

[grant hutchison]

Is the premise correct? On a large scale, would such a "floating" observer indeed measure no dipole? Do observations allow us to say there can be no trivial speed variation between hemispheres in the expansion after 13.7 billion years?

The assumption of isotropy is quite fundamental, I think. See, for instance, Jones & Lambourne's textbook on this topic.

Grant Hutchison

[George]

The assumption of isotropy is quite fundamental, I think. See, for instance, .... on this topic.

[The link leads me to an unavailable page in the book.] I don't doubt that isotropy is a fundamental case, but so is the anisotropy. Is it funamental that no large scale anisotropy as I imagine can exist with just a few hundred kps difference after inflation?

[grant hutchison]

Is it funamental that no large scale anisotropy as I imagine can exist with just a few hundred kps difference after inflation?

It would be remarkable if such an anisotropy produced the polar alignment and smooth transition between poles we oberve. Removing the dipole on the mathematical assumption that it is generated by our peculiar velocity leaves a symmetrically distributed and much small residual anisotropy, having characteristics which accords with theory of the early Universe. That would be a remarkable global conspiracy by the surface of last scattering, if it isn't a local Doppler effect.

Grant Hutchison

[George]

It would be remarkable if such an anisotropy produced the polar alignment and smooth transition between poles we oberve.

Why would it be remarkable if the dynamics creating this imagined difference happens to transition smoothly from one hemisphere to another, especially after inflation? [Or is it because of ....]

Removing the dipole on the mathematical assumption that it is generated by our peculiar velocity leaves a symmetrically distributed and much small residual anisotropy, having characteristics which accords with theory of the early Universe. That would be a remarkable global conspiracy by the surface of last scattering, if it isn't a local Doppler effect.

Agreed, unless there were two dipoles perhaps, which seems unlikely.

As I mentioned earlier, I think the vector math does a nice job of arguing for peculiar motion. Choosing the Void is a logical HF reference point and better than the Local Group c.g.

I do appreciate the vector you have given me. I haven't mapped it to see if the vector sum from here to the Void is the 369 kps, and whether or not it aligns with the dipole, but I am assuming for now that this is the case.

[grant hutchison]

Why would it be remarkable if the dynamics creating this imagined difference happens to transition smoothly from one hemisphere to another, especially after inflation?

What mechanism in the wider Universe places the two poles precisely opposite each other in our sky, and induces the apparent temperature to vary between those points, all around the sky, in a way which reproduces the variation we'd predict from Doppler? This is either a very finely tuned anisotropy in the sky, an amazing accident, or a straightforward local effect.

Grant Hutchison

[George]

What mechanism in the wider Universe places the two poles precisely opposite each other in our sky, and induces the apparent temperature to vary between those points, all around the sky, in a way which reproduces the variation we'd predict from Doppler? This is either a very finely tuned anisotropy in the sky, an amazing accident, or a straightforward local effect.

Again, I agree. Both this argument and the observed combined peculiar motions rule out a large-sized small hemispherical anisotropy, though perhaps a tiny one may exist. [I hope I didn't sound like an ATMer.]

So it sounds as if the 369 kps is likely close to what might be our true HF vector. The Great Void should make a nice reference for if it itsn't at rest with the flow what is?

Assuming this speed is correct, can we claim, using SR, that our clocks are slower by 7.5x10^-5% than a Great Voider? [At least at the present time. Perhaps an average time dilation would be a little different over the last 13 billion years.]

[John Jaksich]

Hello George,

The new post in Reviews of Modern Physics ---Volume 82, January--March 2010---

might give some new references as well as some of the work in regards to the "so-called" Pioneer anomaly (Pioneer 10 & 11). The authors dismiss cosmological parameters as being the origin of the "so-called" anomaly.

The article is entitled:

Influence of Global Cosmological Expansion on Local Dynamics and Kinematics

Authors: Matteo Carrera & Domenico Guilini

The introduction of the article states that the "Hubble flow is a red-shift which grows linearly with distance . . . "

I am wading through the piece and --although I am a neophyte in this area-- I thought that it would be of interest to you and others who posted on it ---earlier in the thread.

[John Jaksich]

Here is a link to it from http://aps.arxiv.org/abs/0810.2712 the Physics Pre-print server:

[George]

Authors: Matteo Carrera & Domenico Guilini

The introduction of the article states that the "Hubble flow is a red-shift which grows linearly with distance . . . "

I am wading through the piece and --although I am a neophyte in this area-- I thought that it would be of interest to you and others who posted on it ---earlier in the thread.

They seem to be attempting to address only the localized effects of the Hubble Flow. [The Hubble Constant is the velocity per unit linear distance for the redshift discovered.]

[John Jaksich]

Upon further inspection that is what they seem to be doing . . . attempting to look at dynamic/kinematic effects of Hubble flow on man-made objects in the Solar System. They conclude (Section VII) that there are no "genuine relativistic effects" upon solar system phenomena (Pioneer 10 & 11) on the levels of present precision, however; other results were reached: local inhomogeneities within cosmological expansion may "essentially influence cosmological observation." "An example that the authors mention is the recent efforts to interpret the cosmological constant within realistic inhomogeneities"---in short: Measuring the Cosmological Constant as a series of inhomogeneous values within a frame of reference. (my bold) See the following two reference for more information:

Celerier, M.-N., 2000, "Do we really see a cosmological constant in supernova data?," Astron. Astrophys. 353 63 - 71

Wiltshire, D. L., 2007, "Exact solution to the averaging problem in cosmology," Phys. Rev. Lett. 99, 25101

I will try to provide links:

[John Jaksich]

Here is a link to Celerier's paper:

from the Physics Preprint Server:


Preprint Server

[Nereid]

You might also like to explore "Void Cosmology" - the idea that we are at (or near) a particularly large (and deep) cosmological inhomogeneity. For one thing, the metric to use is not the familiar RWFL one!