A less model dependent approach to comparing dark matter and modified gravity theories to the galaxy data, which is complementary to the Radial Acceleration Relation (RAR), which is dubbed Normalized Additional Velocity (NAV) is presented in a new paper and compared to the SPARC database.
This method looks at the gap between the Newtonian gravitational expectation and the observed rotation curves of rotationally supported galaxies.
I'll review the five theories tested in the paper.
The Burkert profile (sometimes described as "pseudo-isothermal" and first proposed in 1995) is used to represent particle dark matter in a trial run of this method is a basically phenomenological distribution of dark matter particles in a halo (i.e. it was not devised to flow naturally from the plausible properties of a particular dark matter candidate), unlike the Navarro-Frank-White profile for dark matter particle halos which flows directly from a collisionless dark matter particle theory from first principles, but is a poor fit to the inferred dark matter halos that are observed. The Burkert profile has two free parameters that are set on a galaxy by galaxy basis: the core radius r0 and the central density Ï0. It systemically favors rotational velocities too high a small radii and too low a large radii, however.
MOND is familiar to readers of this blog, was proposed in 1983, is a very simple tweak of Newtonian gravity, and is purely phenomenological toy model (that doesn't have a particularly obvious relativistic generalization), but has been a good match to the data in galaxy sized and smaller systems. There are a variety of more theoretically deep gravity based explanations of dark matter phenomena out there, but this is the most widely known, is one of the oldest, and has a good track record in its domain of applicability. It has one universal constant, a(0), with units of acceleration beyond Newtonian gravity. MOND shows less dispersion in NAV than the data set does, although it isn't clear how much this is due to uncertainties in the data, as opposed to shortcomings in the theory.
The Palatini f(R) gravity and Eddington-inspired-Born-Infeld (EiBI) are theories that modify General Relativity in ways that tweak add and/or modify Einstein's field equations in ways that make plausible hypotheses to adjust them in a theoretically consistent manner and do lead to some explanation of dark matter phenomena, but very well, as this paper notes. Palatini f(R) gravity replaces the Ricci tensor and scalar with a function that has higher order terms not present in Einstein's field equations. The Eddington-inspired-Born-Infeld theory starts with the "Lagrangian of GR, with an effective cosmological constant Î = ð−1 ð , and with additional added quadratic curvature corrections. Essentially, it is a particular ð (ð
) case that fits the Palatini ð (ð
) case that was presented in the previous section, together with a squared Ricci tensor term[.]"
General relativity with renormalization group effects (RGGR) is based on a GR correction due to the scale-dependent ðš and Î couplings, and has one free parameter that varies from galaxy to galaxy that is absent in MOND. It outperforms Burkert and MOND predictions at smaller galactic radii and in the middle of the probability distribution of NAV measurements, but somewhat overstates modification of gravity at large radii at the extremes of the probability distributions.
Also, while the Burkert profile with two fitting constants, outperforms RGGR with one, and MOND with none, once you penalize that theory for the extra degrees of freedom it has to fit the data, the grounds to prefer one model over another is significantly weaker. Some of the galaxy specific fitting may simply be mitigating galaxy specific measurement errors.
Here we propose a fast and complementary approach to study galaxy rotation curves directly from the sample data, instead of first performing individual rotation curve fits. The method is based on a dimensionless difference between the observational rotation curve and the expected one from the baryonic matter (ÎīV^2). It is named as Normalized Additional Velocity (NAV). Using 153 galaxies from the SPARC galaxy sample, we find the observational distribution of ÎīV^2. This result is used to compare with the model-inferred distributions of the same quantity.
We consider the following five models to illustrate the method, which include a dark matter model and four modified gravity models: Burkert profile, MOND, Palatini f(R) gravity, Eddington-inspired-Born-Infeld (EiBI) and general relativity with renormalization group effects (RGGR).
We find that the Burkert profile, MOND and RGGR have reasonable agreement with the observational data, the Burkert profile being the best model. The method also singles out specific difficulties of each one of these models. Such indications can be useful for future phenomenological improvements.
The NAV method is sufficient to indicate that Palatini f(R) and EiBI gravities cannot be used to replace dark matter in galaxies, since their results are in strong tension with the observational data sample.
Alejandro Hernandez-Arboleda, Davi C. Rodrigues, Aneta Wojnar, "Normalized additional velocity distribution: a fast sample analysis for dark matter or modified gravity models" arXiv:2204.03762 (April 7, 2022).
Here we propose a fast and complementary approach to study galaxy rotation curves directly from the sample data, instead of first performing individual rotation curve fits. The method is based on a dimensionless difference between the observational rotation curve and the expected one from the baryonic matter (ÎīV^2). It is named as Normalized Additional Velocity (NAV). Using 153 galaxies from the SPARC galaxy sample, we find the observational distribution of ÎīV^2. This result is used to compare with the model-inferred distributions of the same quantity.
We consider the following five models to illustrate the method, which include a dark matter model and four modified gravity models: Burkert profile, MOND, Palatini f(R) gravity, Eddington-inspired-Born-Infeld (EiBI) and general relativity with renormalization group effects (RGGR).
We find that the Burkert profile, MOND and RGGR have reasonable agreement with the observational data, the Burkert profile being the best model. The method also singles out specific difficulties of each one of these models. Such indications can be useful for future phenomenological improvements.
The NAV method is sufficient to indicate that Palatini f(R) and EiBI gravities cannot be used to replace dark matter in galaxies, since their results are in strong tension with the observational data sample.
1- is Deur's model supposed to exactly reproduce MOND?
ReplyDelete2- does dark energy play any role in Deur's model of self-interaction? and in pricniple should it ?
1 - not exactly. They are nearly identical in the limit of a thin disk galaxy beyond the interpolation function region (i.e. where accelerations are very weak), but only up to about the limit of the rotating masses. The coincidence of MOND and Deur's model in highly elliptical galaxies is basically a consequence of the fact that elliptical galaxies are almost all in the Newtonian regime. Deur's model is also different in clusters, in being automatically relativistic, and in reducing the pull of gravity from systems that exhibit strong dark matter phenomena.
ReplyDelete2- In Deur's model of self-interaction, the gravitational pull of a galaxy that is not spherically symmetric is reduced outside the galaxy by an amount equal to the amount the the pull of gravity within the galaxy is enhanced, and the reduced attraction between galaxies produces dynamics that are similar to what you would expect from dark energy pulling everything apart more than in the null expectation. He is basically assuming that the cosmological constant is zero (i.e. that there is no dark energy) and that self-interaction accounts for the observations. It would be elementary to leave a non-zero value of the cosmological constant in place to be determined observationally, however, after suitably adjusting for the reduction in gravitational pull between galaxies due to self-interaction and that would have the effect, at a minimum, of very significantly reducing the best fit value of the cosmological constant, but that very difficult calculation has not been done.
Eliminating the cosmological constant entirely, however, is a quite attractive feature of Deur's model because it generalizes to quantum gravity more easily and because unlike GR and many other modified gravity theories, it conserve mass-energy globally.
ReplyDeleteMOND posits a cross over at a.o and it's not clear to me Deur reproduces this.
the issue with galaxy clusters is that there is that MOND is not enough, there needs to be more mass, such as dark matter, so it sounds like Deur is going in the wrong direction.
if there is dark energy, doesn't the energy content of empty space adds gravity and so boosts gravitational self-interaction.
how hard would it be to create a tweaked classical version of general relativity in which has an explicit self-interaction term, based on gravitational energy plus dark energy in an attempt to reproduce MOND.
I have in mind that all the gravitational energy in the galaxy, plus dark energy adds extra strength to gravity that is measureable in the MOND regime
"how hard would it be to create a tweaked classical version of general relativity in which has an explicit self-interaction term, based on gravitational energy plus dark energy in an attempt to reproduce MOND."
ReplyDeleteAccording to the textbook "Gravitation" by Charles W. Misner, John Archibald Wheeler, and Kip Thorne, which is one of the leading GR textbooks, the explicit self-interaction term based upon gravitational energy is deeply problematic even though the textbook in the same section acknowledges that the effective mass at a great distance of a system with gravitational interaction is greater than it would be with a point mass with a magnitude equal to the sum of the point masses in the system. (FWIW, I think that this claim is somewhat overstated and the analysis described in the textbook for this conclusion isn't sufficiently thoughtful although there may be literature on the issues that they are informed by but not citing that is better.)
Essentially, the issue is that the localization of gravitational energy is ill defined since it is a function of frame of reference. In a free-fall frame of reference, it should arguably be zero.
"the issue with galaxy clusters is that there is that MOND is not enough, there needs to be more mass, such as dark matter, so it sounds like Deur is going in the wrong direction."
Deur's solution to clusters is that there is an effective dimensional reduction between point masses from 3D to 1D because the gravitational field gets concentrated in a QCD flux-tube-like structure between the point masses rather than being diluted as it spreads in three dimensions as it does in the spherically symmetric case, or as it spreads in two dimensions as it does in the idealized thin disk galaxy case.
"if there is dark energy, doesn't the energy content of empty space adds gravity and so boosts gravitational self-interaction."
The simplest dark energy term is the cosmological constant in GR which is equivalent to a constant amount of energy spread over the entire volume of the universe. This is so diffuse that it would make almost no meaningful contributions even to the dynamics of even systems as large as galaxies or galaxy clusters. In conventional GR (including Deur's model) the formula is such that the cosmological constant doesn't interact with the part of GR driven by the stress-energy tensor. But, Deur thinks that the non-dark energy self-interaction effect is probably sufficient to eliminate the need for dark energy entirely (although not with a rigorous precision calculation which is not straightforward to do and instead is approximated in the manner he does in his pair of recent cosmology papers).
ReplyDelete"According to the textbook "Gravitation" by Charles W. Misner, John Archibald Wheeler, and Kip Thorne, which is one "
I understand under classical GR, but there are many alternatives to GR.
"Essentially, the issue is that the localization of gravitational energy is ill defined since it is a function of frame of reference. In a free-fall frame of reference, it should arguably be zero."
what about frame of reference involving specifically galaxy rotation curves?
"Deur's solution to clusters is that there is an effective dimensional reduction between point masses from 3D to 1D"
the papers on fractal gravity seems to be along these lines.
Gravitational force distribution in fractal structures
A. Gabrielli, F. Sylos Labini, S. Pellegrini
We study the (newtonian) gravitational force distribution arising from a fractal set of sources. We show that, in the case of real structures in finite samples, an important role is played by morphological properties and finite size effects. For dimensions smaller than d-1 (being d the space dimension) the convergence of the net gravitational force is assured by the fast decaying of the density, while for fractal dimension D>d-1 the morphological properties of the structure determine the eventual convergence of the force as a function of distance. We clarify the role played by the cut-offs of the distribution. Some cosmological implications are discussed.
arXiv:astro-ph/9809234
" the formula is such that the cosmological constant doesn't interact with the part of GR driven by the stress-energy tensor. "
this is perhaps physically wrong, as evidence by MOND
or to put it another way,
suppose I formulate another gravity theory where cosmological constant DOES interact with the part of GR driven by the stress-energy tensor, in combination perhaps with gravitational self-interaction
could this, perhaps with other concepts, give rise to MOND?
so i propose, in order to explain MOND, a form of GR where there is an explicit gravitational self-interaction term, that is strengthen by the cosmological constant.
close to galaxies explicit gravitational self-interaction term, that is strengthen by the cosmological constant gives rise to MOND.
far away from galaxies, the gravitational self-interaction term goes to zero but there is still the cosmological constant as in GR.
and then perhaps combine that with the idea that galaxies are fractals D=2
dark matter exists either as sterile neutrinos or PBH
"I understand under classical GR, but there are many alternatives to GR."
ReplyDeleteThis feature of classical GR is pretty widespread, but obviously, if you modify gravity it can do different things.
"the papers on fractal gravity seems to be along these lines."
Yes, they do.
"suppose I formulate another gravity theory where cosmological constant DOES interact with the part of GR driven by the stress-energy tensor, in combination perhaps with gravitational self-interaction
could this, perhaps with other concepts, give rise to MOND?"
No. First, dark energy is too weak. Secondly, the impact of the resulting self-interaction wouldn't correspond to MOND-like behavior. Dark energy is in the wrong places to produce a MOND-like behavior by interacting with gravitational fields.
"dark matter exists either as sterile neutrinos or PBH"
Those just don't combine properly with a MOND-like theory. There is no feasible way to get them in the right places.
Also, are you "kodama" on Physics Forums?
ReplyDelete"No. First, dark energy is too weak. Secondly, the impact of the resulting self-interaction wouldn't correspond to MOND-like behavior. Dark energy is in the wrong places to produce a MOND-like behavior by interacting with gravitational fields."
the MOND scale of acceleration ao is on the same order as the cosmological constant
the self-interaction term also includes the gravity present in the galaxy, from the baryons.
not self- interaction term solely from dark energy which would be too weak.
two other ways to strengthen this is with papers on fractals cosmology and Verlinde entropic gravity.
"dark matter exists either as sterile neutrinos or PBH"
Those just don't combine properly with a MOND-like theory. There is no feasible way to get them in the right places.
there's this paper
arXiv:0805.4014
I don't know why you say this since PBH in one form or another helps explain gravitational lensing and large scale structure and missing mass in galaxy cluster unaccounted for by MOND.
in MOND you need much less dark matter than what is needed in dark matter only models.
you can put PBH anywhere in the galaxy or galaxy clusters or filaments
assuming sterile neutrions doesn't pan out.
Also, are you "kodama" on Physics Forums?
neo was taken.
There are a lot of papers and pop sci articles on standard model and octonions by many physicists with many citations, including John Baez.
but yeah Mitchell Porter put cold water on it.
"you can put PBH anywhere in the galaxy or galaxy clusters or filaments
ReplyDeleteassuming sterile neutrions doesn't pan out."
You really can't.
For a MOND plus DM hypothesis to work you need to put PBHs (or sterile neutrinos or some other DM candidate, as the case may be) preferentially in clusters, relative to its near negligible presence in galaxies outside of clusters.
But, in the case of PBHs or sterile neutrinos, you are highly constrained in the mechanisms available to you to do the sorting (which is why LambdaCDM predicts an isotropic, homogeneous universe at large scales). PBHs interact gravitationally and by direct contact with their event horizons only. Sterile neutrinos operate via slight oscillation with other neutrinos (in some models) and gravity, but not via the weak force (which is a femtometer-ish range force itself) by hypothesis.
There is no way for gravity alone to sort PBHs or sterile neutrinos selectively into clusters relative to other parts of the universe.
If, for example, MOND didn't provide enough of an effect in early type galaxies, but was effective in late type galaxies, this could work, as the PBHs could be concentrated in places of overdensity in the early universe (the only place where they can form), while being absent in later developing galaxies that arise after the conditions in which PBHs can form are no longer present. Stacy McGaugh looked into that possibility, calling it "DD (Density begets Density)" in McGaugh and de Blok (1998a). But it didn't work. https://tritonstation.com/2022/04/08/two-hypotheses
primordial black hole or sterile neutrinos would also be in galaxies, at much lower density than DM only
ReplyDeleteit would by analogous to DM in the solar system