MOND and the missing baryons problem

[Jonathan Scott]

I've also heard it alleged that the most popular interpolating function doesn't make sense relativistically but it's not my field, I wouldn't claim to know what argument they were making. If anyone more knowledgeable has any idea please feel free to enlighten me.

The interpolating function is a clearly unphysical arbitrary rule which has the sole purpose of explaining why MOND effects aren't seen in laboratory experiments and solar system results. In standard MOND, this provides a "cut-off" switch based on an unspecified function of some sort of "absolute" acceleration, which is way beyond unsatisfactory for multiple reasons.

The MOND fit to experimental data for galactic rotation curves does not require any interpolating function; one can just add the MOND acceleration to the Newtonian acceleration. In this area, MOND provides a ridiculously good predictive formula, and I had the impression (from studies a few years ago) that similar values of the acceleration parameter worked for the full range of galaxy types.

I'm not up to date on attempts to apply MOND to globular clusters and similar within the Milky Way galaxy (I need to look at those referenced papers). Unlike Newtonian theory, MOND effects are horribly non-linear and don't add up like vectors, so I wouldn't be surprised if the only case that works really well is for galaxies, where there is a single central concentration of mass being considered.

It seems to me that MOND, like the Tully-Fisher relation, should be treated for now as an empirical formula that seems to provide a surprisingly good fit for a specific set of experimental results, suggesting that there may be some sort of physical cause behind it. However, so far I'm not aware of any satisfactory theory (whether involving changes to gravity theory or dark matter) that explains it.

 

[RUTA]

However, so far I'm not aware of any satisfactory theory (whether involving changes to gravity theory or dark matter) that explains it.

There is a corresponding relativistic action for MOND produced by Bekenstein. Sean Carroll describes it at the 35:13 mark of

 

[Jonathan Scott]

There is a corresponding relativistic action for MOND produced by Bekenstein. Sean Carroll describes it at the 35:13 mark

Thanks for the reference. Carroll's presentation says "(Lorentz invariance is spontaneously violated, but okay)." To my way of thinking, that disqualifies TeVeS from being "satisfactory", although it is clearly much better than the original MOND "theory". Also, I haven't looked at TeVeS recently, but I think it had a set of parameters to be adjusted, and it was proving difficult to find a set which weren't already ruled out by experiment.

 

[RUTA]

I finally delved into the dark matter problem this summer and I would say modified gravity approaches are as reasonable as looking for non-baryonic dark matter candidates. Observations implying dark matter were first made over 80 years ago and we still don't have any confirmed non-baryonic candidates. LCDM works well for cosmology by simply assuming something exists (no one knows what), but it doesn't get the mass distribution at the galactic level correct (e.g., the core-cusp problem). The dark matter problem is very difficult, e.g., after listing its attributes, i.e., dark, cold, abundant, stable, and dissipationless, Sean Carroll concludes, “So should we be surprised that we live in a universe full of dark matter? I’m going to say: yes.” Here is a more general view of MOND recently published in PRD. Brownstein showed MOND beat metric-skew-tensor-gravity (MSTG) for galaxy rotation curves while MSTG beat MOND for the mass profiles of X-ray clusters. I like the way MSTG handles the famous Bullet Cluster, originally touted as "direct empirical proof of the existence of dark matter,'' without non-baryonic dark matter. Anyway, I think both approaches (non-baryonic dark matter and modified gravity) are reasonable at this point.

 

[RUTA]

Thanks for the reference. Carroll's presentation says "(Lorentz invariance is spontaneously violated, but okay)." To my way of thinking, that disqualifies TeVeS from being "satisfactory", although it is clearly much better than the original MOND "theory". Also, I haven't looked at TeVeS recently, but I think it had a set of parameters to be adjusted, and it was proving difficult to find a set which weren't already ruled out by experiment.

I prefer MSTG, where the gravitational "constant" varies in strength, to MOND, but I'd rather see an alternative to both that doesn't have any "gaps." By that I mean MOND has to invoke too much baryonic dark matter at the scale of galactic clusters where MSTG works well, while MSTG fits for galactic rotation curves aren't as good as MOND. Both have been applied at the cosmological level (MOND and MSTG), but I haven't seen them fit the CMB temperature power spectrum. I'm not sure they have to do that per se if they can account for Fig 1 here. In that case, the rest of the fit should follow.

 

[Jonathan Scott]

I prefer MSTG, where the gravitational "constant" varies in strength, to MOND, but I'd rather see an alternative to both that doesn't have any "gaps."

Last time I looked at this stuff I got as far as Moffat's STVG/MOG, which claims many successes but seems quite contrived with multiple adjustable parameters. Somehow the attempts to turn MOND into a "theory" rather than an empirical rule rob it of its attractive simplicity.

 

[RUTA]

Last time I looked at this stuff I got as far as Moffat's STVG/MOG, which claims many successes but seems quite contrived with multiple adjustable parameters. Somehow the attempts to turn MOND into a "theory" rather than an empirical rule rob it of its attractive simplicity.

Keep in mind that the "basic model" LCDM fit of the CMB angular power spectrum has 6 parameters and none are explained by an underlying theory (in the case of non-baryonic dark matter we don't even have a source particle). I did some MSTG fits of mass profiles of X-ray clusters this summer with only needed two parameters and that modified gravity theory has an underlying physical basis (G is a running coupling constant). So, from a theoretical standpoint, we have to pick one of two very difficult directions (non-baryonic dark matter versus modified gravity) and I don't see any reason to favor one over the other at this point.

 

[ruarimac]

The MOND fit to experimental data for galactic rotation curves does not require any interpolating function; one can just add the MOND acceleration to the Newtonian acceleration. In this area, MOND provides a ridiculously good predictive formula, and I had the impression (from studies a few years ago) that similar values of the acceleration parameter worked for the full range of galaxy types.

Can you explain how? The basic postulate in MOND is that second law is modified such that $F=m a \mu(\frac{a}{a_0})$, where $\mu$ is the interpolating function. Aside from a few boundary conditions it is a free function. As far as I can see without assuming an interpolation function MOND gives you absolutely nothing, it cannot be fit to data.

it doesn't get the mass distribution at the galactic level correct (e.g., the core-cusp problem).

That's not really clear cut, you cannot ignore the affect of the baryons of the halo. The core/cusp debate came about when dark matter only simulations were the only game in town, now we have hydro simulations which indicate dark matter is outnumbered in the cores of large galaxies and show baryons do modify the dark matter halo. There is also a lively debate about the existence of cores and cusps at low stellar masses in observation.

 

[ruarimac]

I like the way MSTG handles the famous Bullet Cluster, originally touted as "direct empirical proof of the existence of dark matter,'' without non-baryonic dark matter.

I was very curious to see how this was achieved but I'm left a little confused. It is my understanding that the difficulty with modeling the bullet cluster in a modified gravity is explaining why the lensing map is completely offset from the x-ray profile. They don't seem to explain that in the paper, their best fit convergence map doesn't seem to reproduce the offset observed or the bimodality. OK they're not modeling the gas in the subcluster but it's doesn't even fit the other cluster.

Could you explain what the power is in the result? I'm very confused by table 5 which seems to be the main result but they don't seem to quote these "HST observational upper limits" in reference to what they're doing.

 

[Jonathan Scott]

Can you explain how? The basic postulate in MOND is that second law is modified such that $F=m a \mu(\frac{a}{a_0})$, where $\mu$ is the interpolating function. Aside from a few boundary conditions it is a free function. As far as I can see without assuming an interpolation function MOND gives you absolutely nothing, it cannot be fit to data.

The interpolating function is effectively a method of turning off MOND when it would become embarrassing. In the Newtonian realm, it selects standard Newtonian gravity, and in the MOND realm it switches to a different acceleration $\sqrt(a_0 Gm/r^2)$. How it makes the transition is of interest only when investigating intermediate cases. As Newtonian gravity is weaker in the MOND realm, and MOND gravity is weaker in the Newtonian realm, it doesn't make a lot of difference whether it is switched off or not, except that we know that in solar system and laboratory experiments, which are thoroughly within the Newtonian realm, there is no evidence for MOND.

 

[RUTA]

I was very curious to see how this was achieved but I'm left a little confused. It is my understanding that the difficulty with modeling the bullet cluster in a modified gravity is explaining why the lensing map is completely offset from the x-ray profile. They don't seem to explain that in the paper, their best fit convergence map doesn't seem to reproduce the offset observed or the bimodality. OK they're not modeling the gas in the subcluster but it's doesn't even fit the other cluster.

Could you explain what the power is in the result? I'm very confused by table 5 which seems to be the main result but they don't seem to quote these "HST observational upper limits" in reference to what they're doing.

The way they present their work is different than the way I would present it :-) I would say G(r) increases farther from the center of gravity (they call it the "MOG Center"), thereby increasing the effective mass of the galaxies and pulling the kappa (lensing) peak away from the sigma (X-ray) peak. Likewise, when fitting gas mass to dynamic mass, I would say the gas mass is increased to the dynamic mass, but they say increased G(r) reduces dynamic mass to gas mass. So, to explain the shifted kappa peak, they have to show how the increased G(r) shifts the focus of the gravitational lensing (without the thin lens approximation).

 

[ruarimac]

The interpolating function is effectively a method of turning off MOND when it would become embarrassing. In the Newtonian realm, it selects standard Newtonian gravity, and in the MOND realm it switches to a different acceleration $\sqrt(a_0 Gm/r^2)$. How it makes the transition is of interest only when investigating intermediate cases. As Newtonian gravity is weaker in the MOND realm, and MOND gravity is weaker in the Newtonian realm, it doesn't make a lot of difference whether it is switched off or not, except that we know that in solar system and laboratory experiments, which are thoroughly within the Newtonian realm, there is no evidence for MOND.

Sorry there was some confusion on my part, I was talking about fitting rotation curves and while you're meaning distribution of rotational velocities. I see now, Milgrom dictates a Tully-Fisher mass relation with an exponent of 4. It seems a tiny bit circular to me to base a model on such an empirical relation and then to call it a prediction that it holds but that's just my opinion.