Chronos said:
Turbo, please elaborate. In what way is Arp's statistical analysis more 'correct' than NT's? NT made no assumptions about system dynamics, Arp did.
Arp's "assumption" about system dynamics is one that you or I would make intuitively. It is gravity and orbital motion. In a cluster of galaxies, the group's members will exhibit motions relative to each other. The members will move along geodesics in curved space-time - elliptical orbits that conserve angular momentum. This is a given. The geodesics along which these orbits lie are functions of the masses and positions of the members of the group.
Remember that the largest objects in the group will be less-perturbed than their smaller neighbors, but they too will exhibit some proper motion relative to their neighbors. To envision this, remember that the Earth is perturbed by the mass of the moon as it orbits, just as the sun is perturbed by the mass of the orbiting earth.
Now, let's take the M81 system - 13 galaxies in all, with M81 being by far the most massive. M81's companion galaxies cannot just float out in space with no angular motion relative to their more massive host - with no angular momentum, they would simply follow the path of least resistance (inward radial path) toward the gravitational center of the system and be swallowed up by their huge host.
In a more Newtonian view, we say that the objects in a gravitational system orbit around their common center of mass. In a system where one large massive galaxy dominates, the common center of mass is very near (or in) the large host, and its proper motions relative to the small companions are rather small, while the motions of the smaller objects relative to the host are much larger. Observationally, the small companions of M81 must have proper motion relative to M81. Some should be moving away from us, some toward us, and some may be moving more or less perpendicular to our line of sight. This should result in somewhat fewer than 1/2 of M81's companions being redshifted relative to the host. Arp used a simple 50:50 ratio, which while somewhat inaccurate, was generous to his critics since it should have biased the results against his theory a bit.
As I have mentioned several times in this thread, Newman-Terzian made a HUGE assumption that everybody seems to overlook. If you will read the N-T paper, you will find it on page 1, section 2 Combinatorial Considerations. The authors *assume* a fully random distribution of motion among cluster members with no dynamical pattern whatsoever. They excused this by saying in essence "the system is too complex for us to normalize" so they entirely threw out all the laws of Newtonian gravitational theory and Einstein's space-time field. By doing so, they treated M31 as if were no more massive or gravitationally influential than the Large and Small Magellanic Clouds. That is patently absurd. Newman&Terzian smugly refer in their paper to "the error in Arp's combinatory approach" - there is high irony there.
Notice that they only discussed the M31 cluster, so they could claim that the closer relative masses of M31, MW and M33 hopelessly confuse the dynamic of the cluster. The situation with the M81 system is far more straightforward, though, with a very massive central galaxy. If we look out at the M81 cluster, we should expect to find the smaller companions to have measurable proper motion relative the host galaxy. Again some should be blueshifted, some should be redshifted, and some could be neutral due to orbital inclination or present-day orbital position.
Now do you see where N-T is flawed? They make the very radical assumption that the companions of a massive host galaxy do not need to have proper motion relative to the large galaxy, and that they can treat the largest galaxy as if it had no more gravitational influence than the smallest companion. This is wrong, and Einstein and Newton both would tell them so in an instant. The universe is in constant motion, and astronomical bodies follow geodesics in space-time (or orbits if you prefer) that are determined by the mass, speed, and location of the bodies. The largest body or bodies in their neighborhood contribute the bulk of the space-time distortion (or gravitational pull, if you prefer Newton). For those companion galaxies to exist at all, they MUST be exhibiting some angular proper motion relative to the host galaxy - otherwise, they would have fallen into the host long ago.
By assuming that the members of the M81 group do not need to exhibit any classical orbital motion relative to one another (a very radical assumption, again), N-T were then able to treat the redshift excess of the companions as a problem of ordination, saying there is a one in twelve (8%) chance that the largest object will be the least redshifted. Their paper completely ignored gravitational interaction and causation. It was the only way that they could use non-substitutive ordination to arrive at their very low probability that all the companions would be redshifted relative to their hosts. Their math is very basic, accurate, and easy to follow but the statistical methods they applied are entirely inappropriate to the data.
Chronos said:
Arp offered no proof of this basic assumption. It is therefore suspect, at best, and mostly contraindicated by observational evidence. I am not a dogmatic fool, but, I am a sucker for observational facts and supporting math. So, from my reference frame, the Arp assumption is invalid.
Again, Arp's basic assumption was that galaxy clusters have to obey the classical laws of physics with regard to gravitation, motion, etc. This is not something that normally has to be stated in the introduction of any astronomy paper, so its absence should not be troubling. Newtonian gravitation and Einstein's space-time field theories are pretty well-established, so you'll have to have a pretty good reason to arbitrarily declare them invalid. The observational evidence DOES show that the companion galaxies are redshifted relative to their hosts. Arp did not make those observations - that was done a very long time ago. The observational evidence alone cannot/should not invalidate Newton/Einstein either, but there is something that does need to be re-examined - our understanding of the causes of redshift. Arp simply made the observation that if we expect the members of galactic cluster to behave in accordance with what we know about gravitation, some companions should be moving toward us and some should be moving away. The fact that all of M81s comapanions are redshifted relative to it means that either they are all somehow preferentially running away from us for some reason, OR there is something about redshift that we do not understand. It is a very simple concept. If smaller galaxies in clusters are preferentially redshifted relative to the largest members, either the Earth is at the most special place in the universe (forbidden by all credible cosmologies) OR there is something other than currently accepted causes (cosmological expansion, doppler shift, and Einstein's gravitational field effect) that must be responsible for the excess redshift.
Here's the math: if there is a 50:50 probablility of finding an object in a particular state, and you sample 11 such objects, the math is multiplicative. 1/2 x 1/2 x1/2... etc. With eleven objects with equiprobable states, that comes out to 1/(2 to the eleventh power) or 1/2048. Quite a far cry from 1/12. I used the number 11 as the number of objects because that is how many objects were included in the "analysis" that N-T gave the M31 group. There are actually 12 companion galaxies in the M81 group giving only one chance in 4096 that all of them will be redshifted relative to the host. They all are, and they all have significant recessional velocities.
Here is a link to a page on the M81 group with recessional velocities listed.
http://www.seds.org/messier/more/m081gr.html
I know I sound like a broken record talking about this N-T paper, and I wish that I could explain the basic logical flaws in it more clearly, because I seem to be missing the audience. I'll glady follow up (at the risk of boring everyone to tears!) if there are questions.