KurtLudwig said:
Please explain above paragraph. Are you implying that at the outer reaches of our galaxy gravity decreases by about 1/distance not by 1/distance^2?
The dynamics of objects at the outer reaches of our galaxy are consistent with that assumption, although the reason for that is disputed.
There is a phenomenological toy model which makes this assumption and does a very good job of describing phenomena that are observed from solar system scale to large galaxies that is called MOND invented
by Mordeci Milgrom in 1983. The abstract of the original paper is as follows:
MOND is absolutely and admittedly not a complete and accurate theory of gravity (in its simplest form, for example, it does not have many fully established properties of general relativity, although it can be generalized as
Jacob Bekenstein did in 2004 which address some of the most superficial flaws of MOND, although not its deeper problem with galactic cluster sized systems) and Milgrom himself doesn't claim otherwise. (Sadly, Milgrom's junior and much younger colleague, Bekenstein, predeceased him
in 2015.)
But, any correct solution to dark matter phenomena, be it from dark matter particles or a modification of gravity, needs to explain why this reality, also called the
radial acceleration relation, holds true so generally beyond a certain threshold gravitational acceleration constant called a0, with its domain of applicability which spans many order of magnitude.
The Radial Acceleration Relation in Rotationally Supported Galaxies
Stacy McGaugh,
Federico Lelli,
Jim Schombert
(Submitted on 19 Sep 2016)
We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons. The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions. The correlation persists even when dark matter dominates. Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxies.
Other more sophisticated modifications of gravity reproduce the radial acceleration relation without many of the shortcomings of toy model MOND.
What Does A Complete Dark Matter Theory Look Like?
Also, to be clear, you can explain almost any kind of galaxy dynamics in any particular galaxy, simply by putting dark matter particles in places needed to produce those dynamics. So, a proposed dark matter particle theory is really not a complete operational physics model unless it also provides some way of explaining why the dark matter particles ended up in the places that they did, and why they stay in the configuration.
Thus, for example, you could have two dark matter particle theories both of which have precisely the same particles with precisely the same properties. But, one of those theories might have dark particles of that type that are produced in thermal freeze out, and another might have them produced in some other manner that would cause the dark matter to be distributed in a different manner. One might be supported by some piece of astronomy evidence, while another might be contradicted by a piece of astronomy evidence.
One of the main distinctions between dark matter particle theories (cold, warm and hot) concerns not the intrinsic properties of the particles themselves, but the mean velocity of those particles (which is correlated tightly with dark matter particle mass in thermal freeze out scenarios).
This is important, because, for example, the theory needs to explain why the radical acceleration relation arises with the kind of dark matter particle in question, i.e. why the inferred distribution of dark matter in galaxies is so tightly correlated with the distribution of ordinary matter over so many order of magnitude of galaxy scale. This is challenging because, almost by definition, any non-gravitational interactions that dark matter has with ordinary matter are extremely feeble, and naively, it is challenging to produce such a tight correlation exclusively through gravitational interactions.
Similarly, unless dark matter interacts with itself (another property of dark matter that is often assumed to not be the case, except, of course, in self-interacting dark matter a.k.a. SIDM theories), or with ordinary matter, dark matter should have what is called a
Navarro-Frenk-White (NFW) distribution (a.k.a. profile) within a galaxy. But, while the evidence isn't entirely one sided, there is considerable data to support the conclusion that the inferred distribution of dark matter in most galaxies is inconsistent with an NFW profile, and instead usually has an inferred "isothermal distribution" that is also not perfectly spherical.
As a third example, elliptical galaxies have less dark matter relative to the amount of ordinary matter in them than spiral galaxies do, which in turn tend to have less dark matter relative to the amount of ordinary matter in low surface brightness dwarf galaxies (with a handful of notable exceptions in which dwarf galaxies appear to have no dark matter). And, among elliptical galaxies, more spherical elliptical galaxies have less inferred dark matter relative to the ordinary matter content than more oval shaped galaxies. But, galactic clusters have much more inferred dark matter relative to their ordinary matter content than spiral and elliptical galaxies do, and the inferred dark matter phenomena effects in galaxy clusters are stronger than MOND would predict. So, your dark matter particle theory needs to be able to explain why that is the case.
None of those properties of dark matter distributions were predicted in advance by dark matter theories, all of them, except the excess of apparent dark matter phenomena in galaxy clusters, was predicted (in multiple cases before data was available) by MOND.
Proposing a dark matter particle with particular properties that would evade direct detection experiments is easy.
But, explaining how it came to be distributed in the manner that it must be reproduce what we see in terms of galaxy, etc. dynamics and cosmology observations is a non-trivial process of limited accuracy as both analytical approaches to doing this, and N-body simulations, are more art than science with current computational power and methods even in the abstract. And, given the considerable observational constraints regarding the inferred distribution of dark matter in galaxies, this is a particularly challenging task.
