Wednesday, February 6, 2019

Galaxies Are Stable In Modified Gravity Theories

A new preprint examines the stability of galaxy-likes structures under a variety of modified gravity theories and finds that some are more stable than they would be with Newtonian dynamics and no dark matter, while others are less stable.
The local stability of stellar and fluid discs, under a new modified dynamical model, is surveyed by using WKB approximation. The exact form of the modified Toomre criterion is derived for both types of systems and it is shown that the new model is, in all situations, more locally stable than Newtonian model. In addition, it has been proved that the central surface density of the galaxies plays an important role in the local stability in the sense that LSB galaxies are more stable than HSBs. Furthermore, the growth rate in the new model is found to be lower than the Newtonian one. We found that, according to this model, the local instability is related to the ratio of surface density of the disc to a critical surface density Σ cr it . We provide observational evidence to support this result based on star formation rate in HSBs and LSBs.
Hossein Shenavar, Neda Ghafourian, "Local Stability of Galactic Discs in Modified Dynamics"
(February 5, 2019).
From the conclusion:
In this work, we considered the local stability of a modified dynamical model which is based on imposing Neumann BC on GR field equations. Both fluid and stellar discs in this model are found to be locally more stable compared to pure Newtonian discs. For the gaseous (stellar) discs, when βg ( β⋆) increases the maximum value that is needed for Q to make the system stable decreases. Thus, regions with larger βg or β⋆ are more stable. Also, LSB galaxies which show a high value of Freeman ratio RF ≡ Σ† Σ0 are predicted to be more stable than HSBs. The growth rate were found to be smaller than Newtonian model for both fluid and stellar discs. We tested the model by using THINGS data of (Leroy et. al. 2008) and showed that the general behaviour of star formation rate per surface density (ΣSFR) agrees with the predictions of the model. 
Other modified theories too have tried to explain the issue of local stability and many interesting results have been reported. For example, Milgrom (1989) reports that MONDian discs are more stable than Newtonian ones. Also, in the deep MOND limit the stability criteria becomes independent of the acceleration. Furthermore, Milgrom (1989) argues that when Σ ≫ Σ†, or equivalently when RF is small, the Newtonian regime prevails and the disc becomes unstable. It is then proposed that the rarity of discs with small RF is due to their unstable nature. Using Lelli, McGaugh & Schombert (2016) data, we observed the same behaviour here as shown in Fig. 6. Also, Fig. 6 provided a chance to compare the role of Σ† in MOND and the present model. 
Roshan & Abbassi (2015a, 2014) show that although MOG provides more attracting force compared to Newtonian theory, it is interestingly less stable than Newtonian case. However, they argue that the difference between the two theories is too small to be detected at galactic scale. This is shown by introducing a parameter βMOG ≡ µ0v/κ, counterpart to β in this work, in which µ0 = 0.042 ± 0.004 kpc−1 is a fundamental constant of MOG derived by Moffat & Rahvar (2013). Any difference between the stability of MOG and Newtonian models is proportional to βMOG, and it would be negligible because of the smallness of µ0 at galactic scales. If, however, this parameter is dependent to the system, say for instance µ0 ∝ 1/Rd in analogy with our analysis, then the instability of MOG could be studied at galactic scales. In fact, Haghi & Amiri (2016) suggest that to fit MOG to the observed velocity dispersion of dwarf spheroidal galaxies, one needs to consider µ0 as a varying parameter. This possibility, however, complicates the MOG model even more. In the case of f (R) theories, on the other hand, Roshan & Abbassi (2015b) show that the discs in a specific class of these theories are generally more stable than Newtonian discs. 
Another challenge facing modified gravity/dynamics models is the problem of global stability. For example, Roshan et al. (2016) develop a semi-analytic method to study the response of a Maclaurin disc to linear nonaxisymmetric perturbations for the theory of MOG. Their results show that Maclaurin discs are less stable in MOG compared to Newtonian gravity and especially the bar mode, i.e. m = 2, is strongly unstable and unlike in Newtonian gravity cannot be avoided. Also Ghafourian & Roshan (2017) study the global stability of Mestel and exponential discs in MOG from numerical point of view. In future works, we will examine the global stability of the present model in analytical and numerical studies. The equilibrium configuration of our model is reported in Shenavar (2018).
Despite slower galaxy growth,  structure formation is not necessarily slower.


neo said...

what i'd like to see is if MOND like theoriest can reproduce large scale structures with only baryons like CDM

andrew said...

Still unknown but not unknowable. From

ΛCDM is cosmology, while MOND doesn't have a cosmology. Given the history of cosmology, I'm not sure that should be considered a shortcoming. But certainly ΛCDM fits the expansion history and geometry of the universe, by construction. The only objection is to the particular parameters (Ω, Λ) we're stuck with. Totally bizarre, though familiarity seems to be taking the edge off of that. The one place where it is not so obvious that ΛCDM is better is in the baryon density from big bang nucleosynthesis (BBN). BBN was arguably the first example of precision cosmology, and for decades before WMAP, it was known that Ωb h2 = 0.0125. WMAP says it is 0.02258. That's right - the baryon density basically doubled while gaining an extra significant digit. This creates a tention between the baryon density measured by fitting WMAP and that found from the 7Li abundance in low metallicity stars. Since it is widely presumed that ΛCDM is correct and that WMAP is the definitive word on everything, the 7Li abundances must somehow be wrong (most likely through some sort of mixing that exposes 7Li to thermonuclear processing). This tension does not exist in MOND - the CMB behaved as predicted for the BBN baryon density that is consistent with all of the relevant isotopes. As an added bonus, the missing baryon problem disappears in MOND.

Structure Formation
The formation of large scale strucure is one of the success stories of ΛCDM. Simulations in this context do a nice job of growing the sort of filamentary structure that is observed in large redshift surveys. MOND has less mass to work with, but a stronger long range force. The result isn't terribly different - MOND is just a tweak of Newton after all - but it is much harder to quantify. Unlike ΛCDM, MOND structure formation is completely non-linear, and gastrophysics cannot be avoided. It is quite possible that MOND may overshoot, in the sense that it may produce too much structure for the same initial condition. That is not entirely clear as of yet, but two salient difference seem to be that MOND is more efficient at emptying out the voids and more likely to form structure early: both testable predictions."

andrew said...

Continued . . .

"The Cosmic Microwave Background
The CMB provides another frustrating example of irreconcilable merits. ΛCDM fits the acoustic power spectrum of the CMB very well. It did not correctly predict its shape, however. The only successful a priori predicion concerning that was by MOND, which nailed the first-to-second peak amplitude ratio. (Fitting for this is what drove up the baryon density in ΛCDM.) However, the same model that correctly predicted the second peak also predicted a third peak that is much lower than subsequently observed. ΛCDM is flexible enough to fit the observations, though if you look at the history of WMAP releases it was pretty lousy at predicting itself. (That is to say, the fit to the year 1 data did a poor job of predicting the new parts of the year three data, year three doesn't extrapolate well to year 5, and so on.) On the one hand, that is a good thing: it was worthwhile to keep operating WMAP as there was new information to be gained (proivided that systematic effects like foreground subtraction and PSF corrections don't dominate the signal at large ℓ). On the other hand, the most that should be claimed here is that ΛCDM "wins ugly" by virtue of its greater flexibility in fitting the data.
Note added 11/12:
Looking again at this table a year later, I have been quite generous to ΛCDM. For example, I grade early reionization as "promising." Really? Early reionization was a huge surprise. "Certainy not before redshift 7" multiple prominent cosmologists assured us shortly before the data contradicted them. Concern over early reionization launched a thousand papers about Pop. III stars. But now nobody worries about it, because ΛCDM is so flexible it can be adjusted to account for just about anything. Maybe it is true, but is it still science?

Note added 4/13:
We now have Planck, which basically sees the same power spectrum as WMAP just with smaller error bars. So nothing above changes significantly. It will be interesting to see if the small error bars lead to any tension with independent data, or if "independent" measurements simply start migrating towards what Planck says they should be, as has happened with the baryon density from BBN. We've seen that happen historically with cosmic parameters like the Hubble constant. As of this writing, Planck reports 67.3 ± 1.2 while Riess et al. (2011) give 73.8 ± 2.4 km/s/Mpc.""

andrew said...

I call particular attention to this statement: "It is quite possible that MOND may overshoot, in the sense that it may produce too much structure for the same initial condition. That is not entirely clear as of yet, but two salient difference seem to be that MOND is more efficient at emptying out the voids and more likely to form structure early: both testable predictions."

My intuition is that Deur's approach, of seeing MOND-like enhancements of gravity within large systems like galaxies and galaxy clusters arising from something analogous to the confinement of quarks and gluons in hadrons in QCD, resulting in reduced gravitational attraction between these large systems (because gravitons stay inside the system to bind components more strongly rather than escaping the large systems) which in turn is the source of dark energy phenomena probably also solves the "too much structure" problem described above. (I also think that systemic error in measurements of "dark energy" are underestimated based on a paper I've cited previously at this blog, which reduces the magnitude difference between dark matter and dark energy phenomena.)

But better MOND-like cosmology modeling is necessary.

Fortunately, this doesn't really taking anything more than generic computational power to accomplish with large chunks of existing N-body simulation software being salvageable for inclusion in much more computationally difficult non-linear N-body simulations. Nobody needs to build a billion dollar collider or telescope and a cast of thousands to work it out and compare the simulations with data that have already been gathered for other purposes. This is a project that requires half a dozen to a dozen astrophysicists and/or IT experts, and two to five years of work, and tens of millions of dollars of funding, all of which is not easy to come by, but is also not insurmountable. We are talking on the order of 1% to 0.1% of the resources involved in a next generation collider and less than a third the time necessary to do it.

andrew said...

A more rigorous development and vetting of Deur's work sufficient to elevate it from an obscure footnote in the field to a centerpiece of active research and prominence as a solution to the dark matter and dark energy problems could probably be accomplished with half a dozen or less investigators in three years or less, with a mid-single digit million dollar budget. If I had $5 million to spend, I'd happily fund it myself.

andrew said...

There are about 44 papers addressing the subject cited in McGaugh's bibliography, although I would add some additional papers about F(R) theories and scalar graviton models as well.

andrew said...

Scholarpedia also has a good sub-entry on MOND Cosmology.

neo said...

thanks, i'm digesting this.

what i had in mind when i asked this question, is the earlier post and paper you cited,

"Monday, December 10, 2018
Reproducing MOND with Conformal Gravity

James G. O'Brien, et al., "Radial Acceleration and Tully-Fisher Relations in Conformal Gravity" (December 7, 2018)."

i'd like to see how conformal gravity, the version that reproduces MOND, RAR, etc., can handle simulation, CMB, etc.

IMO the fact conformal gravity has been researched by a large group of physicists over decades and is grounded in conformal invariance, has explicit derviations, including RAR, makes it more promising than Deur, in getting MOND like physics.

there's more recent papers on explicit derviation of McGaugh RAR from conformal gravity, i'm not aware of Deur doing so with his model.

speaking of colliders, what do you think of bee's claims, and i agree 20 billion or however much it is is a lot of money, but i did ask her, what about the HE-LHC, simply reusing the LHC tunnel and using stronger 16 tesla magnets, upgrade from LHC 8 tesla for 28 TEV.

i'd like to see an experiment that can somehow directly test MOND

andrew said...

You can't directly test MOND in an experiment because you need to get to a place where the gravitational field is sufficiently weak which means a long way from any large object like a planet or moon or star. You can only have observational evidence and rule out alternatives with some direct experiments.

Doing cosmology with any modified gravity theory that reproduces empirically observed dark matter phenomena without dark matter presents the same difficulty as MOND. All such theories, generically, must be non-linear. This makes the coding of (and finding processing power to conduct) a simulation profoundly more difficult than GR (where the big non-linearities can be modeled in simple cases analytically and found to be too small to be relevant in most other cases where a simply Newtonian approximation can be used). And, there is no straightforward way to model this analytically either (generically in these kinds of modified gravity theories).

All theories that do reproduce observe dark matter phenomena should have, broadly speaking, similar cosmology implications. TeVeS (a relativistic extension of MOND) and Conformal Gravity, for example, should have similar cosmologies because they are modifying gravity in similar ways even if there are differences in the details. Deur's approach is qualitatively different for simulation purposes than most other modified gravity theories because stronger fields in one place are always matched by weaker fields somewhere else a feature absent from almost all other theories in this class. But, it too should have a cosmology similar in broad outline to MOND or any other modified gravity theory in the class of MOND-like theories that can produce the RAR.

My intuition is that the fact that modified gravity theories look quite similar to dark matter particle theories at galaxy scales and smaller scales implies that it is very likely that they also have cosmologies similar to dark matter, although this is hard to prove rigorously and has some limits (e.g. modified gravity theories tend to form structure more quickly than DM particle theories).

andrew said...

"speaking of colliders, what do you think of bee's claims, and i agree 20 billion or however much it is is a lot of money, but i did ask her, what about the HE-LHC, simply reusing the LHC tunnel and using stronger 16 tesla magnets, upgrade from LHC 8 tesla for 28 TEV."

Any new collider has costs sin the billions with thousands of people needed to operate it and process its data even on the cheapest possible basis.

I agree with Bee that this is not a sensible investment at this time. If people become more affluent and the costs go down, it would be nice. A new collider has some value in more precisely modeling physical constants and heavy hadrons, that data is in my view somewhat more useful than she gives it credit for being, and there is always a remote change that new discoveries will be made although indirect tests of high energy physics like muon g-2 strongly disfavor new physics in the potentially possible energy range. A linear lepton collider could also be a lot cleaner for some measurement than the LHC is. Still, it isn't worth the money now given alternative available ways to spend science $$s. Investments in QCD computation power and astronomy research will do more to establish fundamental physics as will lower cost small projects.

It should be revised in a decade or two to see if the situation has changed with new tech, new economics, or new hints of new physics.

neo said...


i know Deur is your fav, but has Deur produced a paper similar to this

"arXiv:1901.01228 [pdf, ps, other] physics.gen-ph

Conformal Gravity and the Radial Acceleration Relation

Authors: James G. O'Brien, Thomas L. Chiarelli, Mark A. Falcone, Muhannad H. AlQurashi

Abstract: During the 2016 International Workshop on Astronomy and Relativistic Astrophysics (IWARA), the question was raised as to if conformal gravity could explain the timely result of McGaugh et. al. 2016 which showed a universal nature found in the centripetal accelerations of spiral galaxies. At the time of the conference, the McGaugh result was only published for two weeks. Since then, the result has become known as the Radial Acceleration Relation (RAR) and has been considered tantamount to a natural law. In this work, we summarize how conformal gravity can explain the Radial Acceleration Rule in a fashion consistent with the findings of the original authors without the need for dark matter"

in otherwords has Deur shown his theory can reproduce RAR as conformal gravity has?

i think conformal gravity is the most promising way to get MOND out of gravity.

neo said...

re: collider

if you read the blog there are plenty of counter arguments, including statements from other HEP and blogger ethan siegal among others.

i think the HE-LHC is an affordable upgrade to the magnets of the LHC, to explore 14tev to 28tev.

one thing i'm a bit unclear on,

so CERN plans to build both a compact ee linear collider for $10 billion or so in Geneva, and plans to spend $20 billion or so on a FCC also in Geneva near where LHC is located, all in the same time frame?

wow. that's a lot of money and electrical power.

China is interested in the 100TEV collider bc of its technical expertise to build one.

it might be worth it for them as it will advance their engineering and technical training.

neo said...

when i spoke of testing MOND,

i had something like this in mind

arXiv:1901.02604 [pdf] gr-qc

Evidence for Modified Newtonian Dynamics from Cavendish-type gravitational constant experiments

Authors: Norbert Klein

Abstract: Recent experimental results for the gravitational constant G from Cavendish-type experiments were analysed in the framework of MOND (Modified Newtonian Dynamics). "

andrew said...

Re 1901.02604

Deeply skeptical that this experiment is seeing what it says it is, and it isn't applying any orthodox version of MOND because it is taking place in a strong external field which should eliminate the effect. Cavandish type experiments shouldn't work to test the theory. The paper is an interesting footnote and I don't absolutely rule out the possibility that this effect has similar quantum gravity or modified inertia roots. But, due to the external field effect, no inner solar system based experimental test of MOND should work in the accepted toy-model version of MOND. It is inherently an effect limited to very weak fields.

"it might be worth it for them as it will advance their engineering and technical training."

This is the only really strong argument, but if the best we can do to justify an experiment is as make work for highly trained and skilled professionals who could do other valuable things, I'm not impressed. The bottom line is that the odds of seeing new physics with a one order of magnitude increase in energy scale are very low and the cost is very great and we have other places we can spend money that we know will provide much greater value. There is lots of stuff that a long run at a low energy collider like BESIII or LHCb or GlueX could produce in terms of QCD results as QCD is far behind the curve of other fields (a huge lattice computation effort would also produce sure gains at a reasonable price). But, between 13-14 TEV and ten times that energy, we know from indirect measurements that basically show that there isn't anything interesting to see. You need extremely baroque and contrived models to get new physics between 14 TeV and 100 TeV conditional on the experimental results we've seen today. You really need to get to something like 300 TeV to 1000 TeV to have any realistic chance of seeing new physics that aren't indirectly ruled out by existing measurements. So, it's better to wait.

"Deur shown his theory can reproduce RAR as conformal gravity has?"

As I stated before, yes. Any theory that produces a gravitational force law in a galaxy context that reproduces a MOND-like potential reproduces the RAR. It isn't that hard to do and you don't have to run a lot of simulations with data to know that. The comparisons have been done with MOND which produces RAR, so any other theory that has a similar gravitational field strength of MOND in weak fields will have the same effect.

"i think conformal gravity is the most promising way to get MOND out of gravity."

It is certainly a promising possibility that shouldn't be ruled out. Like Deur's work is a quite conservative tweak of GR. Also, I have already blogged about 1901.01228

neo said...

well i'm skeptical of the cavendish experiment as well.

i wonder if conformal gravity can reproduce the third peak in cmb, or deal with mass discrepancy in galaxy clusters or gravitational lensing.

conformal gravity can be loop quantized.