Dark Matter does not exist, what do you think?

[wolram]

http://arxiv.org/pdf/1409.6302.p

It is argued in this paper that Dark Matter does not exist, what do you think.

 

[BiGyElLoWhAt]

bad link? It arxiv says no such paper exists...

Ahhh... try this:
http://arxiv.org/pdf/1409.6302

 

[wolram]

Lessons from the Local Group (and beyond) on dark matter
Pavel Kroupa (Bonn)
Comments: 13 pages, 2 figures, invited presentation, accepted for publication in Seychelles conference on galaxy evolution, "Lessons from the Local Group", ed. K. C. Freeman, B. G. Elmegreen, D. L. Block, and M. Woolway (Dordrecht: Springer), in press, 2014
Subjects: Astrophysics of Galaxies (astro-ph.GA)
(Abridged) The existence of exotic dark matter particles outside the standard model of particle physics constitutes a central hypothesis of the current standard model of cosmology (SMoC). Using a wide range of observational data I outline why this hypothesis cannot be correct for the real Universe. Assuming the SMoC to hold, (i) the two types of dwarf galaxies, the primordial dwarfs with dark matter and the tidal dwarf galaxies without dark matter, ought to present clear observational differences. But there is no observational evidence for two separate families of dwarfs, neither in terms of their location relative to the baryonic Tully-Fisher relation nor in terms of their radius--mass relation. And, the arrangements in rotating disk-of-satellites, in particular around the Milky Way and Andromeda, has been found to be only consistent with most if not all dwarf satellite galaxies being tidal dwarf galaxies. The highly symmetric structure of the entire Local Group too is inconsistent with its galaxies stemming from a stochastic merger-driven hierarchical buildup over cosmic time. (ii) Dynamical friction on the expansive and massive dark matter halos is not evident in the data. Taking the various lines of evidence together, the hypothesis that dynamically relevant exotic dark matter exists needs to be firmly rejected
Lessons from the Local Group (and beyond) on dark matter
Pavel Kroupa (Bodwarfs with dark matter and the tidal dwarf galaxies without dark matter, ought to present clear observational differences. But there is no observational evidence for two separate families of dwarfs, neither in terms of their location relative to the baryonic Tully-Fisher relation nor in terms of their radius--mass relation. And, the arrangements in rotating disk-of-satellites, in particular around the Milky Way and Andromeda, has been found to be only consistent with most if not all dwarf satellite galaxies being tidal dwarf galaxies. The highly symmetric structure of the entire Local Group too is inconsistent with its galaxies stemming from a stochastic merger-driven hierarchical buildup over cosmic time. (ii) Dynamical friction on the expansive and massive dark matter halos is not evident in the data. Taking the various lines of evidence together, the hypothesis that dynamically relevant exotic dark matter exists needs to be firmly rejected

 

[wolram]

Try http://arxiv.org/pdf/1409.6302.pdf

 

[wolram]

http://www.thedailybeast.com/articl...ark-matter-from-space-station-experiment.html

Nothing from satellite yet either.

The experiment, which has been collecting particles for several years, has foundsomething interesting: an elevated number of positrons, the antimatter counterpart of electrons. However, fascinating as it is, AMS-02 isn’t seeing what we’d expect if dark matter was the culprit. While we can’t yet rule out the possibility that dark matter is responsible, what evidence there is seems just as likely to point to another source.

 

[Orodruin]

From what I can tell from searching around a bit the author is a fairly strong supporter of MOND and arguments between MOND and dark matter proponents can some times get a bit heated. Just as several astrophysical explanations could be possible for the dark matter "signals" that have been popping up over the years, it guess it could be possible that we do not yet understand the astrophysics to the required level - although I am speculating here as it is not my area of expertise. It should be noted that there are also several observations that seem to support dark matter over MOND (the typical example you would hear is galaxy collisions such as the bullet cluster).

In the end, if there is dark matter and it is interacting so weakly that we will never see it in the laboratory - we might never know. Certainly the "standard" SUSY WIMP paradigm is starting to look less and less appealing in my opinion.

 

[wolram]

This author may well be a proponent of MOND but let's pick out one or two of his observations that can be disproved.

 

[jeremyjr]

Dark matter and aether theories: A recurring theme in science.

In the 19th century the idea of an all pervasive medium to allow the light propagation in empty space: the aether was fully embraced by the scientific community( see Wikipedia article ), this idea was so accepted that very complicated and costly experiments were conducted to show direct evidence of its existence, for example the famous experiment of Michelson-Morley.

But Einstein’s relativity theory of 1905 showed that this idea was really superfluous and indeed if you thing about the supposedly properties of this substance you will realize in hindsight that its properties were really fantastic, but that was an idea fully accepted.

Now here we are in the 21th century and a new fantastic substance have been inserted in mainstream science: dark matter, this is just a fantastic substance, and its introduction have all the hallmarks that lead to the introduction of the aether idea: it is being introduced to “save” the current accepted theoretical framework from the inconvenient situation of the existence of observational facts that can not be explained without its introduction.

We have found some “anomalies” in the space geometry and then we are “inferring” the existence of an all pervasive mysterious substance to explain it. What about thinking that our ideas about space-time are accurate up to a certain space-time scale, but when we are dealing with very large distances and time our approximations need to be re-calibrated?

 

[bapowell]

This author may well be a proponent of MOND but let's pick out one or two of his observations that can be disproved.

Observations are not disproved. What falsifiable predictions does his theory make? Are they unique to MOND? If observations do not falsify MOND, does it enjoy the same degree of corroboration as dark matter? As a model, is MOND more or less complex than dark matter?

 

[Chronos]

I was very entertained by Milgroms MOND explanations for the bullet cluster [http://www.astro.umd.edu/~ssm/mond/moti_bullet.html] that required some 'unseen' [i.e., dark] matter. I don't believe I've heard the MOND explanation for BAO evidence of dark matter, but, expect it too would be entertaining.

 

[Vanadium 50]

See Skordis, Mota, Ferreira and Boehm "Large Scale Structure in Bekenstein's Theory of Relativistic Modified Newtonian Dynamics" where they point out that the TeVeS and LCDM cosmologies look the same with respect to structure. Each theory has one free parameter (mean density of dark matter and relative strength of the scalar term) and it turns out that the mathematical structure of the theory has the same mathematical form for these two effects. So of course the predictions are the same. Oh, and Skordis et al. published before the WMAP data.

The Bullet Cluster is a problem for MOND and likely a problem for TeVeS as well. However, it's also a problem for LCDM. It's moving too fast - see Angus and McGaugh, MNRAS, 383, 417. There's also the "anti-bullet cluster", Abell 520. Here the mass coincides with the gas, not the galaxies.

bapowell, one prediction of MOND is the Tully-Fisher relation. Another is stability of spiral disks in LSBGs - this falls out of MOND, but has to be put in each galaxy by hand in LCDM.

That said, I don't believe MOND is telling us anything about gravity. It's probably telling us something about galactic formation and evolution, much as the Drude model told us something about metals. However, much of the argument against it is unscientific snark. On the merits, it's an ugly ugly model that does about as well - perhaps slightly better than - LCDM.

 

[Drakkith]

We have found some “anomalies” in the space geometry and then we are “inferring” the existence of an all pervasive mysterious substance to explain it. What about thinking that our ideas about space-time are accurate up to a certain space-time scale, but when we are dealing with very large distances and time our approximations need to be re-calibrated?

What makes you think we aren't considering this? There are several working explanations attempting to reconcile observations with theory. Some involve modifying our current gravitational laws, while others theorize the existence of an unseen type of matter. None of these work perfectly yet, but new data is being collected all the time and work is steadily proceeding in figuring out this mystery.

 

[CKH]

MOND may well be falsified as a theory of gravity, however it's telling us that the behavior of spiral galaxies can be predicted in detail based only on the distribution of baryonic (normal) matter. In fact irregularities in rotation curves are predicted by measuring irregularities in the distribution of normal matter.

This discovery seriously challenges the theory of DM halos. Falsifying MOND in another context such as clusters or cosmology does not change the fact that spiral galaxies (across a few orders of magnitude in mass) can be empirically understood with MOND while ignoring both the amount and distribution of the theorized DM which is said to comprise 80% of galactic mass.

 

[Chronos]

MOND-ophiliacs, like Kroupa, lack compelling explanations for too much observational evidence. DM, however clumsy, is at least as good as MOND in most cases, and the only one even viable in some cases - like BAO and the bullet cluster. Theory does not trump observational evidence.

 

[cristo]

The Bullet Cluster is a problem for MOND and likely a problem for TeVeS as well. However, it's also a problem for LCDM. It's moving too fast - see Angus and McGaugh, MNRAS, 383, 417.

I don't think this is a problem anymore. There was a recent(ish) paper [Lage & Farra, ApJ 787 (2014) 144] looking at simulations of the bullet cluster. They found that there was "no need for unconventional physics or extreme infall velocities".

 

[CKH]

MOND-ophiliacs, like Kroupa, lack compelling explanations for too much observational evidence. DM, however clumsy, is at least as good as MOND in most cases, and the only one even viable in some cases - like BAO and the bullet cluster. Theory does not trump observational evidence.

You are demonstrating precisely what I stated:

Falsifying MOND in another context such as clusters or cosmology does not change the fact that spiral galaxies (across a few orders of magnitude in mass) can be empirically understood with MOND while ignoring both the amount and distribution of the theorized DM which is said to comprise 80% of galactic mass.

DM-ophilliacs falsify MOND (which may well be false as a theory of gravity) using your arguments. However, that does not change the striking predictability of rotation curves obtained through MOND's formula based only on baryonic matter distribution. MOND demonstrates that perturbations in rotation curves can be predicted directly from the observed (asymmetric) distribution of baryonic matter alone. That is a matter of observation, not theory.

Falsifying MOND in other contexts is a ploy. I've seen it widely used by DM-ophilliacs to dodge this issue. Another strategy I've seen is cherry picking rare galaxies where MOND does seem to work in order refute MOND and ignore its more general success. DM theorist are going to have a very hard time indeed using DM halos to explain the success of this formula in rotation curves and in the Tully-Fisher relation. In essence they will have to get DM to closely conspire with baryonic matter.

Kroupa may have drunk too deeply of the demon rum MOND. But, his observation-based arguments that contradict the domination of non-baryonic DM halos in galaxies are sound (IMO), but ignored by the mainstream often with the excuse that MOND is not a perfect theory of gravity. That is not Kroupa's main point, nor is it Stacy McGaugh's main point which he has repeatedly stated in papers..

 

[cristo]

However, that does not change the striking predictability of rotation curves obtained through MOND's formula based only on baryonic matter distribution.

This isn't really a matter of 'predictability' - MOND was invented purely to match the galaxy rotation curves that were observed. If MOND were written down before these observations and *then* predicted the observed rotation curves then that would be something different (you know, like DM predicts the cosmic web as observed with SDSS, or predicts the CMB anisotropies).

 

[Chronos]

No one ever said MOND is not a fit. That's why it gained popularity in the first place. Observational evidence over the last half century has, however, increasingly favored DM. MOND simply doesn't work in too many cases to be taken seriously.

 

[TrickyDicky]

No one ever said MOND is not a fit. That's why it gained popularity in the first place. Observational evidence over the last half century has, however, increasingly favored DM. MOND simply doesn't work in too many cases to be taken seriously.

Switching the words MOND an DM in this paragraph makes no difference.

 

[Chronos]

Please cite examples where MOND works and DM does not. I've already cited at least two cases where DM works and MOND does not. While there have, at least, been some attempts to shoe horn MOND into the Bullet cluster, I've not seen an account for how MOND fits into BAO, or primordial nucleosynthesis. DM, however, does a sterling job on both counts - e.g., http://www.astro.ucla.edu/~wright/BAO-cosmology.html,

 

[TrickyDicky]

Please cite examples where MOND works and DM does not. I've already cited at least two cases where DM works and MOND does not.

Mond is a fit formula for galaxy curves so it obviously works there and DM simply doesn't work in many galaxies as shown in Kroupa's (and other people's) papers. DM is an attractive fit for the LCDM model to work, and I guess that's why people are so biased towards it, there's too much at stake. The problem is that detailed observations in the last years falsify it(leaving aside the fact that it hasn't been found after years of trying hard, I'm only referring to positive observations).

While there have, at least, been some attempts to shoe horn MOND into the Bullet cluster, I've not seen a thing on how MOND fits into the BAO, or primordial nucleosynthesis. DM, however, does a sterling job on both counts.

As mentioned by V50, besides the Bullet cluster, you have the anti-bullet clusters(of which there are several examples, but just one of them would suffice to prevent using the Bullet cluster as evidence for DM). These are examples that are explained neither by MOND nor DM.

 

[wolram]

http://arxiv.org/pdf/0909.2021v2.pdf

According to this paper nothing could form without dark matter, so how did dark matter first (clump) into sufficient masses so it could capture normal matter?

 

[CKH]

You'll keep missing the point in your dismissals. It's like a blind spot. Let me try to explain once more, as clearly as I can.

Forget about cosmology.
Forget about theories of gravity.
Forget about the bullet cluster.
Think about empirical science, not theories. (Like the study of gas laws in the olden days).

We look for patterns in our observations of nature and draw conclusions concerning what accounts for the observations. For example the gas laws were originally empirical. E.g. pressure was found to be inversely proportional to volume (at a constant temperature). The early researchers did not know exactly why this was the case. It was only later that statistical mechanics provided an underlying kinetic theory explaining the gas laws.

In this case we ask: Is there some consistent relationship between observed rotation curves in spiral galaxies and the observed distribution of normal matter? There is. MOND contains an empirical formula that determines this relationship. Rotation curves in spiral galaxies don't just follow this formula roughly, they follow it very closely over a wide range of masses. The specific distribution of normal matter measured in each spiral galaxy varies. However, in each case the formula determines size and shape of the rotation curve from that distribution. Thus the rotation curves are observed to respond directly to the normal matter distribution.

So, observations of spiral galaxies show that baryon distribution determines the rotation curves. According to DM theory only 20% of galactic mass is baryons (actually less because a lot of the expected baryons are missing) and, the distribution of DM is nothing like that of baryons. If you wish to make the invisible DM determine the rotation curves, you must assume that it's distribution is very nearly the same as the normal matter. That doesn't sit well with the properties of DM.

DM theorist must recognize this problem, not sweep it under the rug by falsifying MOND as a theory of gravity. The problem with DM is raised by observations not by a theory.

 

[Chronos]

Dark matter can clump, but, not collapse like a star. It has become increasingly obvious since the mid 1900's that baryonic matter cannot explain galaxy rotation curves. Hence, it was concluded there must be a non baryonic contribution - be it MOND or DM. Your fervor is admirable, but, you appear to conveniently hand wave away facts that fail to support your views.

 

[Vanadium 50]

Here's my opinion. It is not shared by everyone, and not even by the majority of the field. But that doesn't make it wrong.

MOND is wrong. Even Milgrom would say that. It's Newtonian (even in it's name!) and we know that the universe is not Newtonian, nor is its cosmology. When people say MOND today, they mean "some relativistic theory like TeVeS that reduces to MOND in its limit."

For reasons I will explain below, I think DM is the stronger hypothesis. However, I confess to being annoyed at the behavior of the DM community towards alternatives like MOND. People will say "the Bullet Cluster proves LCDM", but these same people when presented with Abell 520 will hem and haw "you can't prove anything from a single data point..there's lots of variation in clusters...weird things can happen" I find this antiscientific - you can't have it both ways.

(By the way, statistical studies have been done and compared to simulation. One finds a few percent of the time you get Abell 520-like objects in LCDM, although usually not as dramatic. Reproducing the Bullet's infall velocity is hard, the work of Farrar notwithstanding - I'm reserving judgment on that until it's replicated, ideally by someone known for their simulation chops. I would say that this is still a win for LCDM, but not the rout that its proponents claim).

On galactic scales, MOND does better. A single number (a_0) gives very good agreement with the rotation curves, and predicts Tully-Fisher. LCDM can accommodate this, but at a cost of more parameters - it's less universal. A win for MOND.

On the scale of clusters of galaxies, LCDM wins. Everybody, even Moti Milgrom agrees that there needs to be some unseen component for the dynamics to work.

Cosmology is more complicated. LCDM has a free parameter for the average density of dark matter. TeVeS has a free parameter for the strength of the scalar piece. These parameters appear in the same spot in the equations, so any cosmology that fits one model fits the other. I am going to give this a weak win to LCDM, because there has been at least an attempt to see that the amount of dark matter is consistent at all scales (it's not all that great - you need a bit more DM than you see in galaxies or even clusters of galaxies to best fit the cosmological measurements) but as far as I know there hasn't been an equivalent test for TeVeS. So it gets a win for LCDM, but not a very strong one.

There is a long history of people looking at GR modifications. This is the only one I have seen such hostility towards - and I find this very surprising, since it's the first one that actually gets some things right!

As I think I mentioned earlier, I don't think MOND is telling us anything about gravity. It's telling us something about galaxy formation and evolution, and I think it should be taken seriously. I draw the analogy with the Drude model. It got many things right, and some things spectacularly wrong. It's central idea - "electrons in a metal behave as a gas" is within one word of being correct: "electrons in a metal behave as a quantum gas". I think the question "if MOND is wrong, why does it work so well" is worth pursuing, not dismissing.

 

[Jonathan Scott]

MOND as a predictive formula for rotation velocities in galaxies (not necessarily spiral ones) based purely on the baryonic matter is astonishingly good.

Current versions of MOND as a theory seem to be nonsense and unphysical, especially the "cut-off" aspect, even when made artificially relativistically consistent, and I think this results in the formula "baby" being thrown out with the theory "bathwater".

So my feeling is that we are missing something at the galactic scale and above, and that it does not seem to involve some independent form of matter but rather some sort of adjustment to the theory of gravity on the larger scale which reproduces the MOND formula.

I've mentioned one possible direction before, which is admittedly somewhat speculative but simple and based on GR-related concepts rather than MOND's arbitrary formula, and which people can check out for themselves rather than having to take my word for it.

The standard assumption for GR purposes using the Schwarzschild solution and its Newtonian approximation is that space is asymptotically flat at sufficient distance from a central mass. If the universe were finite and mass effectively closes it (which is admittedly not the current conventional view either), then one would expect the limiting shape of space surrounding a sufficient concentration of mass to be "conical" in the sense of a missing solid angle, proportional to the total mass enclosed (adding up to a deficit of $8 \pi$ steradians for the whole universe, as in that case something which "encloses the whole universe" is obviously an inside-out ball surrounded by the entire universe). From simple geometry, the extrinsic spatial curvature of this "cone" relative to normal lines of sight at distance $r$ from central mass $m$ which is a significant fraction of the "effective universal mass" $M$ is then $1/r \sqrt{2m/M}$. If the matching space-time curvature works as in the Einstein field equations the corresponding acceleration is therefore $c^2/r \sqrt{2m/M}$ , which varies with $m$ and $r$ in exactly the same way as the MOND acceleration formula.
If we set this equal to the corresponding MOND acceleration formula, this allows us to calculate the "effective universal mass" by feeding in the experimental value of the MOND acceleration parameter $a_o$, giving a very reasonable result:
$$\frac{c^2}{r} \sqrt{\frac{2m}{M}} = \sqrt{a_0 \frac{Gm}{r^2}}$$
$$M = 2 c^4 \frac{G}{a_0} \approx 2 \times 10^{54} \mbox{kg}$$
As should be obvious from considering the analogy of an ordinary cone, the above only applies when all of the local mass is roughly in the same direction, as at the edge of a galaxy where most of the mass is towards the middle. When there are multiple sources, including for example the case of laboratory experiments, or multiple galaxies, the terms do not add even approximately like Newtonian gravity so it is not immediately clear how to calculate the combined effect.

So this suggests to me that what we need is for someone to come up with a better theory to explain the MOND formula, based consistently on space-time curvature and quite possibly relating to the above "conical" model (which I find very interesting but don't have the time or resources to follow up).

 

[CKH]

The interesting thing about MOND in spiral galaxies is the correlation with the baryonic matter distribution. I wonder whether there might be substantial baryonic dark matter (BDM) in the disk. My idea is that the invisible matter distribution is correlated in some way with the visible matter.

Suppose spiral galaxies have a generic structure in which the M/L ratio increases with distance but is correlated with the visible matter distribution. It could be that MOND is an empirical relationship that happens to take into account this outlying BDM. Admittedly this is speculative since I haven't seen an attempt to explore this possible explanation for MOND.

The are many papers that analyze rotational curves based only on mass distribution in the disk. In fact, it is possible to derive from a rotation curve a corresponding distribution of baryonic matter in the disk. The conclusion is that the flat or rising curves are easily accounted for by BDM in the outer disk with a cutoff radius. The mass of this BDM is far less than that required by DM halos to flatten rotation curves. These papers are completely ignored by the mainstream. They are no mainstream citations nor rebuttals. Yet, theorists have approached the analysis of rotation curves in different ways and reached these same conclusions. These analyses assume the Newtonian approximation of GR is correct.

When theorist claim that DM must have five times the mass of normal matter to produce the observed rotation curves, they are implicitly assuming a huge non-baryonic roughly spherical halo. From this stance they argue that there cannot possibly be enough unseen baryonic matter to explain rotation curves. That is a poor argument since it ignores an explanation that places additional baryonic matter in the disk.

 

[zoki85]

The interesting thing about MOND in spiral galaxies is the correlation with the baryonic matter distribution. I wonder whether there might be substantial baryonic dark matter (BDM) in the disk. My idea is that the invisible matter distribution is correlated in some way with the visible matter.

Why should BDM be so substantional in the disk and not in the center of galaxy is even bigger riddle than nature of Dark matter.

 

[Chronos]

Yes, zoki, that is illogical and one of the reasons DM cannot be baryonic. Baryonic matter clumps whereas non baryonic matter does not. It flies out just as fast as it falls in, hence, spends more time in the halo region than near the center of mass.

 

[CKH]

Why should BDM be so substantional in the disk and not in the center of galaxy is even bigger riddle than nature of Dark matter.

I can't give you a precise quantitative answer, but in these disk models, the density of all baryonic matter falls off fairly rapidly from the center of the galaxy. Very little of the central mass is dark. There is lots of stellar radiation that warms the H2 clouds, plasma and dust in the visible disk. However, galactic disks extend far beyond the luminous part (which contains almost all of the visible stars). We already know this from the distribution of HI. The main unknown is how much additional matter exists far from the center that we cannot detect. While the overall density drops rapidly, the suggestion is that there may be more outer BDM than generally assumed. The mass distribution argument is mainly that the M/L ratio increases with distance, even though the total density decreases with distant.

There is no riddle here. As you get farther from the center luminosity declines. This indicates that the density at some distance is too low to form stars. However, it is not reasonable (and in fact wrong) to conclude that no mass exist outside this radius just because no stars are formed.

Here are some papers that address rotation curves of disk galaxies using baryonic matter only and standard Newtonian gravity:

http://arxiv.org/abs/1408.5054 Deficient Reasoning for Dark Matter in Galaxies (The tone of this paper seems to reflect frustration. The authors have published many related papers in the past.)
http://arxiv.org/abs/1011.1538 Galactic rotation curves inspired by a noncommutative-geometry background [this is about stability without DM halos]
http://arxiv.org/abs/1104.3236 Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies
http://arxiv.org/abs/1007.3778 Rotating thin-disk galaxies through the eyes of Newton
http://arxiv.org/abs/0906.4448 Global disc models for galaxies NGC 1365, 6946, 7793 and UGC 6446
http://arxiv.org/abs/0902.1703 The mass distribution in Spiral galaxies
http://arxiv.org/abs/0809.3135 On the axisymmetric thin disc model of flattened galaxies
http://arxiv.org/abs/0806.1131 Newtonian mechanics & gravity fully model disk galaxy rotation curves without dark matter
http://arxiv.org/abs/astro-ph/0309823 Errors in equations for galaxy rotation speeds
http://arxiv.org/abs/astro-ph/0309762 Galactic mass distribution without dark matter or modified Newtonian mechanics
http://arxiv.org/abs/astro-ph/0611113 Is Dark Matter Present in NGC 4736? An Iterative Spectral Method for Finding Mass Distribution in Spiral Galaxies

A common first order mistake is to assume that there should be Keplerian orbital speeds and that therefore we need lots of dark matter. This stems the incorrect assumption that all galactic matter closer to the center can be treated as a point mass or a uniform spherical mass and similarly that matter farther from the center can be ignored when computing the rotational velocity of a star. Both assumptions are wrong because the distribution in disk galaxies is flat rather than spherical. The situation is entirely different from the solar system where 99% of the matter is concentrated in the sun.

Computing the expected rotation curve from the mass distribution is not trivial. Some attempts have failed due to complications in the approach used. Other authors have succeeded in deriving analytic solutions and others have written numerical programs. In the later case, it is possible to begin with a known rotation curve and work backwards to compute a corresponding disk mass distribution.