Professor Stacy McGaugh, Department of Astronomy, Computer & Space Sciences Bldg, University of Maryland [19Aug2010]

That is a very thorough examination of disk dynamics. You appear to have hit upon at least two important ideas that come up once and a while, but never seem to get much attention. Angris Kalnijs pointed out in IAU 100 that disk rotation curves could often be fit with just the stars if one actually bothers to build a proper mass model (which was not yet done back then; this would have been 1981 or so). The counter argument offered by Bosma and others was that the rotation curves that were measured to very later radii remained flat even after the flat portion of proper mass models had ceased being flat and started their Keplerian decline.

The other thing is that indeed, a disk surface mass distribution that falls off as 1/r gives a flat RC. Hoekstra looked into this in some detail about a decade ago, and was able to fit many RCs. Even though the stars fall off exponentially, the HI gas tends to be close to 1/r where it needs to be. The trick there is that the HI mass is not itself sufficient, so one needs to scale up its contribution (this is sometimes called "HI scaling" in the literature). This implies a dark component that follows the same distribution as the HI; this would presumably be some sort of baryons or even gas - indeed, this is part of the reasoning that went into the suggestion that very cold molecular gas (which might remain undetecable) might be this disk dark matter (as advocated by Pfenniger & Combes). In my own experience, this hasn't always worked so well; in Hoekstra's work you can see deviations that will grow severe if RCs stay flattish even a bit further than observed; this is what I encountered in LSB cases like UGC 128.

In the case of LSBs, I'm impressed you can do so well with a pure exponential. The trick here is the scale length. Your fits want scale length that are rather larger than that of the observed star light. So I think this might work if again we are willing to invoke some dark baryonic component. Which is not at all unreasonable... indeed, everyone I know who has seriously studied disk dynamics (Rubin, Sancisi, Bosma, Freeman, etc.) has come to some variation of the same conclusion at some point.

This has, of course, been completely ignored in cosmology.

Professor Tom Shanks, University of Durham [16Mar2011]

I have just had a quick look - do you mention the model that I have always been keen on? Here all mass is in the disk and the surface density in the disk is proportional to r^-1. Then M(<r)= Integral of 2pi rdr x surface density ie M(<r) is proportional to r ie like the spherical case with rho(r)=r^-2 and this also gives flat rotation curve. This fits with the maximum disk models in the centre where stars dominate

Now interestingly the HI surface density in the Galaxy has surface density proportional to r^-1 but the amplitude is too low by a factor of 6-7. The question is whether molecular hydrogen follows the HI better than its usual tracer CO. If so, it could provide missing mass in the disk.

You have to hide the H2 from being detectable by FUSE via UV absorption lines. But if it’s in a fractal ie in small dense clumps with low cross-section then this can be done- see work a few years ago by Francoise Combes and Daniel Pfenniger. There may even be evidence in the Galaxy that H2 is distributed like this.

Professor Stacy McGaugh, Department of Astronomy, Computer & Space Sciences Bldg, University of Maryland [19Aug2010]

I try to be open minded. Certainly I don't know for certain what the right answer is. I used to think, as most others still do, that it had to be CDM, probably WIMPs. So I was greatly humbled to find that it was MOND's predictions that came true in my LSB data. That is the only theory that got its *a priori* predictions right there, so I certainly consider it a leading candidate.

I have difficulties with a baryonic DM solution (doesn't solve the entire mass discrepancy problem on cosmic scales unless we abandon BBN [though maybe Prof. Shanks has given us an out for that]; the stability of disks is hard to maintain if we put all the mass there [this might be OK in HSBs but not LSBs]) but after such an humbling experience I don't want to be too sure of what "has" to be the right answer when none of us really know.

Professor Tom Shanks, University of Durham [17Mar2011]

It seems like Stacy is saying something very similar to me in terms of surface density going as r^-1 etc. Max disk is what Kalnajs was doing ....

Dr. Dilip Banhatti, Madurai-Kamaraj University, India [18Mar2011]

I guess it is quite important to genuinely see if known Newtonian physics + gravitation can reasonably model disk galaxy rotation curves without invoking ad hoc modifications like MoND or postulating rather intricate theories like some scalar-vector-tensor theories or postulating electrodynamic-luminiferous-etherlike entities like dark matter / dark energy & so on. In all these elaborate exercises, Occam's razor just rusts - & that's by no means real science!

Professor Anatoly Zasov, Sternberg Astronomical Institute, Moscow, Russia [20Mar2011]

MOND theory will be seriously demanded only if a classical description of a weak gravitation comes to deadlock, which is not the case yet. The conclusion of the existence of a dark matter by itself is not a deadlock. Besides, there are known problems with MOND if to apply it to clusters of galaxies: it also cannot avoid the conclusion about the presence of a dark matter there.

As to HI scaling, this problem really exists, however in any case it is not in favour of MOND, because it does not connect DM with low acceleration. This scaling may have a more simple and classical explanation. Indeed, the observed proportionality between column densities of HI and DM may appear just because both densities follow R {-1} law; the former one may reflect that gas density is close to its critical value needed for stability, which, if to follow Toomre's criterion, changes as 1/R for a disc with flat rotation curve, the latter (DM column density profile) is due to the presence of a pseudo-isothermal halo which also follows 1/R law at large R.

A short comment to Marr's picture and his paper:

It is evident that practically any shape of rotation curve may be explained within the frame of Newtonian mechanics without invoking DM. It is not a shape of V(R) that forces to propose DM. The problem is that the observed curves usually do not correspond to those expected for stellar (+gas) disc for normal stellar M/L ratio, that's where DM enters. Even if we propose that the stellar M/L grows significantly along the radius (by some puzzling reason), we came either to non-stable thin disk, or to a very thick and low luminous disk which is practically equal to a dark halo.

Professor Anatoly Zasov, Sternberg Astronomical Institute, Moscow, Russia[22Mar2011] I'm glad that my point of view is close to yours. The only remark I want to give is that the stability condition should be verified for any concrete galaxy to be sure that its disk can include the dark matter, at least its significant part. As my experience shows, this is not the case for most spiral galaxies at least for radial distance R>2 radial scale lengths. Indeed, the measured stellar velocity dispersion gives evidence that as a rule, a surface density of stellar disc only (that is a disc with stellar M/L without any DM) already keeps disc near the margin of stability, which excludes a large amount of additional mass (DM) within a disk. Of course, some exceptions may exist. See the details in 2010arXiv1010.5179 and references therein.