<p>Feng and Gallo and others before them ask the question, what is the expected mass distribution derived from the rotation profile, assuming that the matter is distributed entirely in the disk (ie. in a plane).  There is a solution with the density falling roughly as an exponential.  The problem is that it does not follow the density law that we get from the light distribution.   From the light distribution, including spectral information from UV to radio we know the stellar distribution and the gas distribution.  The Feng and Gallo finds a density falloff that is shallower.  In other words, it also needs a "missing mass" component (albeit less than dark matter), but now it has to be distributed in a flat disk.  Is this preferred?</p>

<p>Then there is the issue that it would not help to explain the high velocity dispersion in groups and clusters.   And, on top of that, it would not help to explain how galaxies and clusters formed so quickly given that the density of the universe started out so highly uniform.</p>

CC BY-SA 3.0
2014-12-24T21:34:09.360Z
2014-12-24T22:02:28.523Z
2014-12-24T22:02:28.523Z
eshaya
<p>Feng &amp; Gallo have published a series of extremely similar papers, all of which essentially claim that they have "discovered" a major flaw in the way (some) astrophysicists think about rotation curves. Instead of assuming spherical symmetry, they try to solve for the mass distribution, using a rotation curve, without assuming spherical symmetry, instead adopting a planar geometry with cylindrical symmetry.</p>

<p>Of course they <em>do</em> have a point; statements that the flat rotation curve can be compared with a Keplerian prediction (that assume spherical symmetry, or that all the mass is concentrated at the centre) are overly simplistic. So far so good, but they then go on to claim that their analysis is compatible with the total <em>stellar</em> mass of galaxies and that dark matter is not required.</p>

<p>So, in their planar model (and obviously this is open to criticism too) they invert rotation curves to obtain a radially dependent surface density distribution that drops pseudo-exponentially.</p>

<p>Problem 1: They concede (e.g. in <a href="http://arxiv.org/abs/1104.3236" rel="nofollow noreferrer">Feng &amp; Gallo 2011</a>) that "the surface mass density decreases toward the galactic periphery at a slower rate than that of the luminosity density. In other words, the mass-to-light ratio in a disk galaxy is not a constant". This is an understatement! They find exponential scale lengths for the mass that are <em>around twice</em> (or more for some galaxies) the luminosity scalelengths, so this implies a <em>huge, unexplained</em> increase in the average mass to light ratio of the stellar population with radius. For the Milky way they give a luminosity scalelength of 2.5 kpc and a mass scale length of 4.5 kpc, so the <span class="math-container">$M/L$</span> ratio goes as <span class="math-container">$\exp[0.18r]$</span>, with radius in kpc (e.g. increases by a factor 4 between 2 kpc and 10 kpc). They argue this may be due to the neglect in their model of the galactic bulge, but completely fail to explain how this could affect the mass-to-light ratio in such an extreme way.</p>

<p>Problem 2: In their model they derive a surface mass density of the disk in the solar vicinity as between 150-200 <span class="math-container">$M_{\odot}/pc^2$</span>. Most (<span class="math-container">$\sim 90$</span>%) of the stars in the solar neighbourhood are "thin disk" stars, with an exponential scale height of between <span class="math-container">$z_0= 100-200$</span>pc. If we assume the density distribution is exponential with height above the plane and that the Sun is near the plane (it is actually about 20pc above the plane, but this makes little difference), a total surface mass density of <span class="math-container">$\sigma = 200M_{\odot}/pc^2$</span> implies a local volume mass density of <span class="math-container">$\rho \simeq \sigma/2z_0$</span>, which is of order <span class="math-container">$0.5-1 M_{\odot}/pc^3$</span> for the considered range of possible scale heights.  The <em>total</em> mass density in the Galactic disk near the Sun, derived from the dynamics of stars observed by Hipparcos, is actually only <span class="math-container">$0.076 \pm 0.015 M_{\odot}/pc^3$</span>  (<a href="http://adsabs.harvard.edu/abs/1998A%26A...329..920C" rel="nofollow noreferrer">Creze et al. 1998</a>), <em>which falls short of Feng &amp; Gallo's requirements by an order of magnitude</em>. (This does not bother the cold, non-baryonic dark matter model because the additional (dark) mass is not concentrated in the plane of the Galaxy).</p>

<p>Problem 3: For the most truncated discs that they consider, with an edge at <span class="math-container">$r=15$</span> kpc, the total Galaxy mass is <span class="math-container">$1.1\times10^{11}\ M_{\odot}$</span> (again from <a href="http://arxiv.org/abs/1104.3236" rel="nofollow noreferrer">Feng &amp; Gallo 2011</a> ). The claim is then that this "is in very good agreement with the Milky Way <em>star counts</em> of 100 billion (Sparke &amp; Gallagher 2007)". I would not agree. Assuming "stars" covers the full stellar mass range, then I wouldn't dissent from the 100 billion number; but the average stellar mass is about <span class="math-container">$0.2\ M_{\odot}$</span> (e.g. <a href="http://adsabs.harvard.edu/abs/2003PASP..115..763C" rel="nofollow noreferrer">Chabrier 2003</a>), so this implies <span class="math-container">$\sim 5$</span> times as much mass as there is in stars (i.e. essentially the same objection as problem 2, but now integrated over the Galaxy). Gas might close this gap a little, white dwarfs/brown dwarfs make minor/negligible contributions, but we still end up requiring some "dark" component that dominates the mass, even if not as extreme as the pseudo-spherical dark matter halo models. Even if a factor of 5 additional baryonic dark matter (gas, molecular material, lost golf balls) were found this still leaves the problem of points 1 and 2 - why does this dark matter not follow the luminous matter and why does it not betray its existence in the kinematics of objects perpendicular to the disc. </p>

<p>Problem 4: Feng &amp; Gallo do not include any discussion or consideration of the more extended populations of the Milky Way. In particular they do not consider the motions of distant globular clusters, halo stars or satellite galaxies of the Milky Way, which can be at 100-200 kpc from the Galactic centre (e.g. <a href="http://iopscience.iop.org/0004-637X/785/1/63?rel=sem&amp;relno=2" rel="nofollow noreferrer">Bhattachargee et al. 2014</a>). At these distances, any mass associated with the luminous matter in the disk at <span class="math-container">$r \leq 15$</span> kpc <em>can</em> be well approximated using the Keplerian assumption. Proper consideration of these seems to suggest a much larger <em>minimum</em> mass for the Milky way independently of any assumptions about its distribution, though perhaps not in the inner (luminous) regions where dark matter appears not to be dominant and which is where F&amp;G's analysis takes place. i.e the factor of 5-10 "missing" mass referred to above may be quite consistent with what others say about the total disk mass and the required dark matter <em>within 15kpc</em> of the Galactic centre (e.g. <a href="http://adsabs.harvard.edu/abs/2014ApJ...794...59K" rel="nofollow noreferrer">Kafle et al. 2014</a>). To put it another way, the dynamics of these very distant objects require a large amount of mass in a spherical Milky Way halo, way more than the luminous matter and way more even than derived by Feng &amp; Gallo. For instance, Kafle et al. model the mass (properly, using the Jeans equation) as a spheroidal bulge, a disk and a spherical (dark) halo using the velocity dispersions of halo stars out to 150 kpc. They find the total Galaxy mass is <span class="math-container">$\sim 10^{12} M_{\odot}$</span> and about 80-90% is in the spherical dark halo. Yet this dark halo makes almost no contribution to the mass density in the disk near the Sun.</p>

<p>Problem 5: (And to be fair I do think this is beyond the scope of what Feng &amp; Gallo are doing) Feng &amp; Gallo treat this problem in isolation without considering how their rival ideas might impact on all the other observations that non-baryonic dark matter was brought in to solve. Namely, the dynamics of galaxies in clusters, lensing by clusters, the CMB ripples, structure formation and primordial nucleosynthesis abundances to state the obvious ones. A new paradigm needs to do at least as well as the old one in order to be considered competitive.</p>

CC BY-SA 3.0
2015-02-18T17:00:39.473Z
This answer provides plenty of "food for thought". Many thanks. My problem = I don't know enough to be convinced either way.
steveOw
CC BY-SA 3.0
2015-02-18T17:28:00.920Z
Re: "...that dark matter is not required". Seems to me that "missing mass" can hypothetically be explained by (a) assumption of over-large luminosity/mass ratios for stuff with detectable luminosity (=ordinary bright stuff) (b) under-estimate of objects and matter without detectable luminosity (=ordinary dark stuff) (c) presence of  non-baryonic matter (=strange dark stuff).  Presumably Feng & Gallo seek to exclude (c) but not (b).
steveOw
CC BY-SA 3.0
2015-03-02T11:10:00.683Z
@steveOw If you don't know enough to be convinced, then carefully note the opinion of those that do. Your option (b) helps with rotation curves, but not with other puzzles that non-baryonic dark matter can solve. There are also massive (pun) problems besides that of wondering what could it be; for example if it is baryonic dark matter, why isn't it following the same spatial distribution as the luminous matter?
ProfRob
CC BY-SA 3.0
2015-03-02T12:20:15.523Z
I most certainly do value your opinion and generous contribution and have accepted your answer.  Fortunately it is not essential that I be convinced either way and so I am content to register the weaknesses which you have pointed out (while remaining sceptical about nbdm).  Re: your last question, spatial distributions of bdm and luminous matter are quite different in the Solar system so why not allow different distributions in a galaxy (even if an evolving dynamic mechanism to explain such distributions has yet to elucidated)?
steveOw
CC BY-SA 3.0
2015-03-02T12:36:36.223Z
@steveOw How so? The Sun contributes ~100% of the luminosity and ~100% of the mass ? The planets etc. make a negligible contribution to either.
ProfRob
CC BY-SA 3.0
2015-03-03T14:13:04.143Z
I was challenging the perceived (by me) qualitative suggestion in your previous question: that bdm and lumious matter would normally be expected to have similar spatial distributions (in a galaxy).  In the Solar system ~ 100% of the bdm and ~ 0% of luminous mass is outside the luminous core. If F&G's dynamic model suggests differing spatial distributions of bdm and luminous mass in a galaxy then present lack of explanatory evolutionary mechanisms should not preclude formal consideration of the dynamic model. Of course the debate should employ quantitative arguments rather than the qualitative.
steveOw
CC BY-SA 3.0
2015-03-03T14:22:56.963Z
@steveOw But the bdm in the solar system is a negligible trifle. I have no problem at all with someone suggesting that there is a *negligible* amount of bdm spread about in any way they please - lost golf balls. All *significant* amounts of baryonic mass that we know about are not dark. Why is it preferable to postulate unknown and unseen bdm that has no power to explain (i) primordial abundances, (ii) structure formation, (iii) cluster dynamics? F+Gs model requires huge amounts of this "stuff" to be *in* the disk, but observations other than rotation curves preclude this.
ProfRob
CC BY-SA 3.0
2015-03-03T17:56:39.770Z
I dont know about explaining (i) (ii) or (iii). One class of "unknown" ordinary matter is that which is simply "under-estimated" because of (a) obscuration, (b) low-detectability by present technology or (c) use of incorrect rules for estimating quantities. I am just arm-waving here but it leads to another question:(http://astronomy.stackexchange.com/questions/10042 ./how-do-astronomers-estimate-the-total-mass-of-dust-in-clouds-and-galaxies).
steveOw
CC BY-SA 3.0
2015-03-06T21:31:21.877Z
@steveOw All of these things have been addressed by 1000s of astronomers, working for decades on these problems. It is not good enough to say that you don't know about explaining (i), (ii) and (iii). Any competing model *must* do this. As stated in "Problem 2" of my answer - the dark matter *cannot* be in the disk as claimed by F+G, because it would utterly change dynamics of stars perpendicular to the plane. But then what could cause *baryonic* dark matter not to be in the plane - it should have collapsed to a disk with everything else. Round in circles we go.
ProfRob
CC BY-SA 3.0
2015-03-07T15:45:45.560Z
Apologies for my ambiguous language.  By "I don't know about..." I meant to express " I don't know enough to argue sensibly about..." rather than "I disagree with and dismiss...".  Certainly a mature model should address all evidence but can even be useful even if it contradicts other useful models. An immature model can be improved by debate. F&G's immature model seems to have been dismissed without formal (i.e. in good journals) debate. Yet exotic non-baryonic dark matter is still entertained despite depending on such things as the quality of being "dissipationless".  It doesn't seem fair.
steveOw
CC BY-SA 3.0
2015-03-07T16:59:44.007Z
@steveOw If you want to overthrow a paradigm (and it has been done a number of times) you need to (a) consider all the evidence, not just what suits you; (b) have a model that does at least as well as the prevailing one. Ideas that are non-starters because they do nor even nealy satisfy (a) aren't going to make it into proper journals. NBDM of course has satisfied(a) and (b) because
ProfRob
CC BY-SA 3.0
2015-10-25T10:57:41.620Z
Not sure how this comment answers the question (this is a Q+A site not a discussion site). The paper you refer to (http://arxiv.org/abs/1507.05095 non paywall version). The conclusions of this paper are far more equivocal than you state. In any case,  I think molecular gas is a fairly small contributor to the baryonic mass budget of the Galactic disk and it absolutely follows the same distribution of luminous baryonic matter.
ProfRob
CC BY-SA 3.0
2015-10-25T11:21:32.840Z
As such, the discovery of very significant extra mass in molecular gas would only address point 3 in my answer, not points 1,2,4. Note that to explain the dynamical evidence, relatively little dark matter is required where most of the luminous matter is. It is required elsewhere. I.e. dark halos.
ProfRob
CC BY-SA 3.0
2015-10-26T00:34:20.903Z
@Hilton Thanks, that is interesting. I suggest the label "previously-dark ordinary matter" in place of "previously ordinary dark matter" ;-).  This is an example of what I referred to in another comment as "under-estimated" ordinary matter.
steveOw
CC BY-SA 4.0
2014-12-25T10:45:05.623Z
2018-10-19T16:09:34.537Z
2018-10-19T16:09:34.537Z
ProfRob
<p>The well-known <strong>galaxy rotation problem</strong> is described <a href="http://en.wikipedia.org/wiki/Galaxy_rotation_curve" rel="nofollow noreferrer">here</a>. Basically (as one moves outward from the galactic centre, $R$ increasing) the <strong>observed</strong> pattern of variation in orbital speed $V$ is very different from the pattern <strong>expected</strong> on the basis of the distribution of mass inferred from detectable radiation. This is illustrated by the two curves in the following figure.
<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/M33_rotation_curve_HI.gif/420px-M33_rotation_curve_HI.gif" alt="galactic rotation curve"></p>

<p><strong>Feng and Gallo</strong> in several papers such as <a href="http://arxiv.org/abs/1007.3778" rel="nofollow noreferrer">this 2010 article</a> have proposed a method for modelling mass distributions in discoidal galaxies.  The method can be applied to an individual galaxy to produce a "tailor-made" mass distribution which (by applying basic Newtonian physics) predicts a galactic rotation curve matching the curve observed for the galaxy. They explain the failure of other attempts, using "ordinary" physics, to predict observed galactic rotations on the use of crude luminosity:mass assumptions and on the inappropriate application of Keplerian models to galaxies.</p>

<p>"Mysterious" explanations of the galaxy rotation problem such as <a href="http://en.wikipedia.org/wiki/Dark_matter" rel="nofollow noreferrer">Dark Matter</a>  and <a href="http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics" rel="nofollow noreferrer">MOND</a> are still being considered seriously. Presumably therefore Feng and Gallo's ideas are not widely accepted.  What are the reasons for the rejection of their explanations?</p>

CC BY-SA 3.0
2015-02-02T21:03:30.593Z
Feng and Gallo are honest scientists who follow the evidence wherever it takes them. The other commentators should be less concerned with the referee's bonifides and more concerned with the truth. Many claim that the rotation curves of spiral galaxies can only be obtained if there are large amounts of non-Baryonic dark matter contained in galactic halos. Feng and Gallo show that the rotation curves can be predicted from thin-disk normal matter without invoking dark matter halos. It seems that the onus should be upon those who claim non-Baryonic dark matter is necessary.
Bill Lama
CC BY-SA 3.0
2015-02-03T18:45:56.403Z
No. Absolutely not. They show that the rotation curves can be explained by enormous amount of non-luminous (i.e. dark) matter *in* the disks of galaxies. In what form is their dark matter - golf balls? Because it is certainly not stars, planets, black holes, or anything else that astronomers have studied. So which explanation is better? The non-baryonic dark matter explanation has to account for lots of observations, not *just* the rotation curves of galaxies - growth of structure, big-bang nucleosynthesis yields, motions of galaxies within clusters.
ProfRob
CC BY-SA 3.0
2015-02-03T22:46:20.393Z
@Bill Lama The "onus" is on both sides. Feng & Gallo are free to try to convince others. However, I am also free to point out that IMO there are big holes in their arguments that need filling. A few other points: the baryonic, or not, nature of DM is not addressed by rotation curves; I suspect serious work (i.e. not addressed at "lay people") does not (usually) make the "Keplerian mistake"; the question is not about honesty, it *is* about evidence; lastly, *I* do not have a dog in this fight, or a vested interest beyond curiosity - not my field at all. You however appear to know the authors?
ProfRob
<gravity><galactic-dynamics>
What are the arguments against the Feng and Gallo thin disk explanation of galactic rotation curves?
steveOw
# What are the arguments against the Feng and Gallo thin disk explanation of galactic rotation curves?

(Asked by: username_0 on 2014-12-07)

The well-known **galaxy rotation problem** is described [here](http://en.wikipedia.org/wiki/Galaxy_rotation_curve). Basically (as one moves outward from the galactic centre, $R$ increasing) the **observed** pattern of variation in orbital speed $V$ is very different from the pattern **expected** on the basis of the distribution of mass inferred from detectable radiation. This is illustrated by the two curves in the following figure.
![galactic rotation curve](https://upload.wikimedia.org/wikipedia/commons/thumb/e/ec/M33_rotation_curve_HI.gif/420px-M33_rotation_curve_HI.gif)

**Feng and Gallo** in several papers such as [this 2010 article](http://arxiv.org/abs/1007.3778) have proposed a method for modelling mass distributions in discoidal galaxies. The method can be applied to an individual galaxy to produce a "tailor-made" mass distribution which (by applying basic Newtonian physics) predicts a galactic rotation curve matching the curve observed for the galaxy. They explain the failure of other attempts, using "ordinary" physics, to predict observed galactic rotations on the use of crude luminosity:mass assumptions and on the inappropriate application of Keplerian models to galaxies.

"Mysterious" explanations of the galaxy rotation problem such as [Dark Matter](http://en.wikipedia.org/wiki/Dark_matter) and [MOND](http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics) are still being considered seriously. Presumably therefore Feng and Gallo's ideas are not widely accepted. What are the reasons for the rejection of their explanations?

**Tags:** gravity, galactic-dynamics

> **Comments:**
> **username_1**: Feng and Gallo are honest scientists who follow the evidence wherever it takes them. The other commentators should be less concerned with the referee's bonifides and more concerned with the truth. Many claim that the rotation curves of spiral galaxies can only be obtained if there are large amounts of non-Baryonic dark matter contained in galactic halos. Feng and Gallo show that the rotation curves can be predicted from thin-disk normal matter without invoking dark matter halos. It seems that the onus should be upon those who claim non-Baryonic dark matter is necessary.  
> **username_2**: No. Absolutely not. They show that the rotation curves can be explained by enormous amount of non-luminous (i.e. dark) matter *in* the disks of galaxies. In what form is their dark matter - golf balls? Because it is certainly not stars, planets, black holes, or anything else that astronomers have studied. So which explanation is better? The non-baryonic dark matter explanation has to account for lots of observations, not *just* the rotation curves of galaxies - growth of structure, big-bang nucleosynthesis yields, motions of galaxies within clusters.  
> **username_2**: @username_1 The "onus" is on both sides. Feng & Gallo are free to try to convince others. However, I am also free to point out that IMO there are big holes in their arguments that need filling. A few other points: the baryonic, or not, nature of DM is not addressed by rotation curves; I suspect serious work (i.e. not addressed at "lay people") does not (usually) make the "Keplerian mistake"; the question is not about honesty, it *is* about evidence; lastly, *I* do not have a dog in this fight, or a vested interest beyond curiosity - not my field at all. You however appear to know the authors?  

---

## 2 answers

### Answer by username_2 on 2014-12-25. Score: 7 | Accepted answer

Feng & Gallo have published a series of extremely similar papers, all of which essentially claim that they have "discovered" a major flaw in the way (some) astrophysicists think about rotation curves. Instead of assuming spherical symmetry, they try to solve for the mass distribution, using a rotation curve, without assuming spherical symmetry, instead adopting a planar geometry with cylindrical symmetry.

Of course they *do* have a point; statements that the flat rotation curve can be compared with a Keplerian prediction (that assume spherical symmetry, or that all the mass is concentrated at the centre) are overly simplistic. So far so good, but they then go on to claim that their analysis is compatible with the total *stellar* mass of galaxies and that dark matter is not required.

So, in their planar model (and obviously this is open to criticism too) they invert rotation curves to obtain a radially dependent surface density distribution that drops pseudo-exponentially.

Problem 1: They concede (e.g. in [Feng & Gallo 2011](http://arxiv.org/abs/1104.3236)) that "the surface mass density decreases toward the galactic periphery at a slower rate than that of the luminosity density. In other words, the mass-to-light ratio in a disk galaxy is not a constant". This is an understatement! They find exponential scale lengths for the mass that are *around twice* (or more for some galaxies) the luminosity scalelengths, so this implies a *huge, unexplained* increase in the average mass to light ratio of the stellar population with radius. For the Milky way they give a luminosity scalelength of 2.5 kpc and a mass scale length of 4.5 kpc, so the $M/L$ ratio goes as $\exp[0.18r]$, with radius in kpc (e.g. increases by a factor 4 between 2 kpc and 10 kpc). They argue this may be due to the neglect in their model of the galactic bulge, but completely fail to explain how this could affect the mass-to-light ratio in such an extreme way.

Problem 2: In their model they derive a surface mass density of the disk in the solar vicinity as between 150-200 $M\_{\odot}/pc^2$. Most ($\sim 90$%) of the stars in the solar neighbourhood are "thin disk" stars, with an exponential scale height of between $z\_0= 100-200$pc. If we assume the density distribution is exponential with height above the plane and that the Sun is near the plane (it is actually about 20pc above the plane, but this makes little difference), a total surface mass density of $\sigma = 200M\_{\odot}/pc^2$ implies a local volume mass density of $\rho \simeq \sigma/2z\_0$, which is of order $0.5-1 M\_{\odot}/pc^3$ for the considered range of possible scale heights. The *total* mass density in the Galactic disk near the Sun, derived from the dynamics of stars observed by Hipparcos, is actually only $0.076 \pm 0.015 M\_{\odot}/pc^3$ ([Creze et al. 1998](http://adsabs.harvard.edu/abs/1998A%26A...329..920C)), *which falls short of Feng & Gallo's requirements by an order of magnitude*. (This does not bother the cold, non-baryonic dark matter model because the additional (dark) mass is not concentrated in the plane of the Galaxy).

Problem 3: For the most truncated discs that they consider, with an edge at $r=15$ kpc, the total Galaxy mass is $1.1\times10^{11}\ M\_{\odot}$ (again from [Feng & Gallo 2011](http://arxiv.org/abs/1104.3236) ). The claim is then that this "is in very good agreement with the Milky Way *star counts* of 100 billion (Sparke & Gallagher 2007)". I would not agree. Assuming "stars" covers the full stellar mass range, then I wouldn't dissent from the 100 billion number; but the average stellar mass is about $0.2\ M\_{\odot}$ (e.g. [Chabrier 2003](http://adsabs.harvard.edu/abs/2003PASP..115..763C)), so this implies $\sim 5$ times as much mass as there is in stars (i.e. essentially the same objection as problem 2, but now integrated over the Galaxy). Gas might close this gap a little, white dwarfs/brown dwarfs make minor/negligible contributions, but we still end up requiring some "dark" component that dominates the mass, even if not as extreme as the pseudo-spherical dark matter halo models. Even if a factor of 5 additional baryonic dark matter (gas, molecular material, lost golf balls) were found this still leaves the problem of points 1 and 2 - why does this dark matter not follow the luminous matter and why does it not betray its existence in the kinematics of objects perpendicular to the disc.

Problem 4: Feng & Gallo do not include any discussion or consideration of the more extended populations of the Milky Way. In particular they do not consider the motions of distant globular clusters, halo stars or satellite galaxies of the Milky Way, which can be at 100-200 kpc from the Galactic centre (e.g. [Bhattachargee et al. 2014](http://iopscience.iop.org/0004-637X/785/1/63?rel=sem&relno=2)). At these distances, any mass associated with the luminous matter in the disk at $r \leq 15$ kpc *can* be well approximated using the Keplerian assumption. Proper consideration of these seems to suggest a much larger *minimum* mass for the Milky way independently of any assumptions about its distribution, though perhaps not in the inner (luminous) regions where dark matter appears not to be dominant and which is where F&G's analysis takes place. i.e the factor of 5-10 "missing" mass referred to above may be quite consistent with what others say about the total disk mass and the required dark matter *within 15kpc* of the Galactic centre (e.g. [Kafle et al. 2014](http://adsabs.harvard.edu/abs/2014ApJ...794...59K)). To put it another way, the dynamics of these very distant objects require a large amount of mass in a spherical Milky Way halo, way more than the luminous matter and way more even than derived by Feng & Gallo. For instance, Kafle et al. model the mass (properly, using the Jeans equation) as a spheroidal bulge, a disk and a spherical (dark) halo using the velocity dispersions of halo stars out to 150 kpc. They find the total Galaxy mass is $\sim 10^{12} M\_{\odot}$ and about 80-90% is in the spherical dark halo. Yet this dark halo makes almost no contribution to the mass density in the disk near the Sun.

Problem 5: (And to be fair I do think this is beyond the scope of what Feng & Gallo are doing) Feng & Gallo treat this problem in isolation without considering how their rival ideas might impact on all the other observations that non-baryonic dark matter was brought in to solve. Namely, the dynamics of galaxies in clusters, lensing by clusters, the CMB ripples, structure formation and primordial nucleosynthesis abundances to state the obvious ones. A new paradigm needs to do at least as well as the old one in order to be considered competitive.

> **Comments:**
> **username_0**: This answer provides plenty of "food for thought". Many thanks. My problem = I don't know enough to be convinced either way.  
> **username_0**: Re: "...that dark matter is not required". Seems to me that "missing mass" can hypothetically be explained by (a) assumption of over-large luminosity/mass ratios for stuff with detectable luminosity (=ordinary bright stuff) (b) under-estimate of objects and matter without detectable luminosity (=ordinary dark stuff) (c) presence of  non-baryonic matter (=strange dark stuff).  Presumably Feng & Gallo seek to exclude (c) but not (b).  
> **username_2**: @username_0 If you don't know enough to be convinced, then carefully note the opinion of those that do. Your option (b) helps with rotation curves, but not with other puzzles that non-baryonic dark matter can solve. There are also massive (pun) problems besides that of wondering what could it be; for example if it is baryonic dark matter, why isn't it following the same spatial distribution as the luminous matter?  
> **username_0**: I most certainly do value your opinion and generous contribution and have accepted your answer.  Fortunately it is not essential that I be convinced either way and so I am content to register the weaknesses which you have pointed out (while remaining sceptical about nbdm).  Re: your last question, spatial distributions of bdm and luminous matter are quite different in the Solar system so why not allow different distributions in a galaxy (even if an evolving dynamic mechanism to explain such distributions has yet to elucidated)?  
> **username_2**: @username_0 How so? The Sun contributes ~100% of the luminosity and ~100% of the mass ? The planets etc. make a negligible contribution to either.  
> **username_0**: I was challenging the perceived (by me) qualitative suggestion in your previous question: that bdm and lumious matter would normally be expected to have similar spatial distributions (in a galaxy).  In the Solar system ~ 100% of the bdm and ~ 0% of luminous mass is outside the luminous core. If F&G's dynamic model suggests differing spatial distributions of bdm and luminous mass in a galaxy then present lack of explanatory evolutionary mechanisms should not preclude formal consideration of the dynamic model. Of course the debate should employ quantitative arguments rather than the qualitative.  
> **username_2**: @username_0 But the bdm in the solar system is a negligible trifle. I have no problem at all with someone suggesting that there is a *negligible* amount of bdm spread about in any way they please - lost golf balls. All *significant* amounts of baryonic mass that we know about are not dark. Why is it preferable to postulate unknown and unseen bdm that has no power to explain (i) primordial abundances, (ii) structure formation, (iii) cluster dynamics? F+Gs model requires huge amounts of this "stuff" to be *in* the disk, but observations other than rotation curves preclude this.  
> **username_0**: I dont know about explaining (i) (ii) or (iii). One class of "unknown" ordinary matter is that which is simply "under-estimated" because of (a) obscuration, (b) low-detectability by present technology or (c) use of incorrect rules for estimating quantities. I am just arm-waving here but it leads to another question:(http://astronomy.stackexchange.com/questions/10042 ./how-do-astronomers-estimate-the-total-mass-of-dust-in-clouds-and-galaxies).  
> **username_2**: @username_0 All of these things have been addressed by 1000s of astronomers, working for decades on these problems. It is not good enough to say that you don't know about explaining (i), (ii) and (iii). Any competing model *must* do this. As stated in "Problem 2" of my answer - the dark matter *cannot* be in the disk as claimed by F+G, because it would utterly change dynamics of stars perpendicular to the plane. But then what could cause *baryonic* dark matter not to be in the plane - it should have collapsed to a disk with everything else. Round in circles we go.  
> **username_0**: Apologies for my ambiguous language.  By "I don't know about..." I meant to express " I don't know enough to argue sensibly about..." rather than "I disagree with and dismiss...".  Certainly a mature model should address all evidence but can even be useful even if it contradicts other useful models. An immature model can be improved by debate. F&G's immature model seems to have been dismissed without formal (i.e. in good journals) debate. Yet exotic non-baryonic dark matter is still entertained despite depending on such things as the quality of being "dissipationless".  It doesn't seem fair.  
> **username_2**: @username_0 If you want to overthrow a paradigm (and it has been done a number of times) you need to (a) consider all the evidence, not just what suits you; (b) have a model that does at least as well as the prevailing one. Ideas that are non-starters because they do nor even nealy satisfy (a) aren't going to make it into proper journals. NBDM of course has satisfied(a) and (b) because  
> **username_2**: Not sure how this comment answers the question (this is a Q+A site not a discussion site). The paper you refer to (http://arxiv.org/abs/1507.05095 non paywall version). The conclusions of this paper are far more equivocal than you state. In any case,  I think molecular gas is a fairly small contributor to the baryonic mass budget of the Galactic disk and it absolutely follows the same distribution of luminous baryonic matter.  
> **username_2**: As such, the discovery of very significant extra mass in molecular gas would only address point 3 in my answer, not points 1,2,4. Note that to explain the dynamical evidence, relatively little dark matter is required where most of the luminous matter is. It is required elsewhere. I.e. dark halos.  
> **username_0**: @Hilton Thanks, that is interesting. I suggest the label "previously-dark ordinary matter" in place of "previously ordinary dark matter" ;-).  This is an example of what I referred to in another comment as "under-estimated" ordinary matter.  

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### Answer by username_3 on 2014-12-24. Score: 2

Feng and Gallo and others before them ask the question, what is the expected mass distribution derived from the rotation profile, assuming that the matter is distributed entirely in the disk (ie. in a plane). There is a solution with the density falling roughly as an exponential. The problem is that it does not follow the density law that we get from the light distribution. From the light distribution, including spectral information from UV to radio we know the stellar distribution and the gas distribution. The Feng and Gallo finds a density falloff that is shallower. In other words, it also needs a "missing mass" component (albeit less than dark matter), but now it has to be distributed in a flat disk. Is this preferred?

Then there is the issue that it would not help to explain the high velocity dispersion in groups and clusters. And, on top of that, it would not help to explain how galaxies and clusters formed so quickly given that the density of the universe started out so highly uniform.


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