The following Web Site features a calculation of the rotation curves of stars in galaxies, that matches the observed motion exactly, uses Newton's law and baryonic mass only, without the need for dark matter.
www.galaxymethods.net
The site also reviews the generally accepted calculation in Binney and Tremaine which concludes that spherical shells of dark matter are needed, and purports to show where they went wrong.
I have seen or brought attention to this site in at least 5 BAUT forums, and no one has ventured forth to challenge the calculation or raise objection to it in any way. In a phrase, "the silence is deafening". I am bringing it forward as a question to all, because I cannot find fault with the calculation, and would like to hear any scholarly discussion of it.
Thanks, TomT

Well, you can no longer say this (which I strongly doubt is even true), because:
I've looked at the "calculation", but unfortunately no details are given that would actually make it possible to check it. (Unless you want to buy the guy's book-- it's basically a shameless con game). However, assuming that the guy isn't a complete charlatan (which again, is impossible to check given the information he gives), I think the following quote is telling: (the "SMD" is the surface mass distribution, so is density integrated over disk height)
What I think this quote means is, he did not feel constrained to follow the normal mass-to-light ratio when constraining his baryonic mass! Well I have news for you, if you can use any mass-to-light ratio you want, obviously you can fit a galaxy rotation curve without "dark matter"! The dark matter is simply absorbed into a larger mass-to-light ratio. C'mon folks, this is pretty seriously brainless stuff.

Also, the link author makes great hay out of the fact that he doesn't use a spherical mass distribution, that he can get his fit using disklike mass distributions. But one-dimensional rotation curve calculations imply no constraints about whether or not the dark matter distribution is spherical (because in the plane of the disk, the gravity from a spherical shell is obviously the same, by symmetry, as the gravity from a ringlike shell that is in the plane of the disk).
You always have to make some assumption about the dark matter distribution if you are only analyzing a 1D rotation curve, a fact that the author appears to blissfully unaware of. Despite his (unsubstantiated) claims to the contrary, I'm sure that Binney and Tremaine (the conventional solution) are in fact aware of this, and chose a spherical distribution for the dark matter either for simplicity, or because it recovers the vertical disk density structure (a Gaussian distribution vertically). I don't know which, but I do note that the "solution" advocated in this link is a purely 1D rotation curve, so also does not analyze the vertical disk density structure, which is the only way to constrain non-spherical aspects of the mass distribution, as I stated.

Bottom line: the guy's an engineer, but not a very smart one, despite any credentials he might have. He may (or may not) have correctly solved the relevant equations, but it matters little because the conclusions he draws from them are completely useless, for the reasons I've stated. Given this, I wouldn't recommend driving on a bridge built by him. Sorry TomT, the link is a waste of time, and I suspect you'll be scolded for linking to a site that is merely trying to sell a book.

This is just a little comment from a complete layperson, but I was a bit turned off my his line that "astrophysics is simple compared to engineering problems." My reply would basically be, there are no trivial problems. The trivial problems get solved simply. The problems in any field are difficult, because it is the difficult problems that remain unsolved.

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As above, so below

Thanks, Ken, for making any additional perusal of the linked site unnecessary.

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Everyone is entitled to his own opinion, but not his own facts.

Good point. That's kind of a jerk statement. What is he, a transportation engineer? "Engineering" is a very, very wide field. Mechanical? Environmental? Hydro? Chemical? Bio? Structural?

__________________
Everyone is entitled to his own opinion, but not his own facts.

Besides, this raises the issue of what astrophysicists are really good at. The author of the link may be good at solving equations (and it is certainly possible that he solved them correctly), but he is not good at seeing the ramifications of his own solutions. And he has misrepresented the ramifications of the conventional solution. This is the key element that makes a good astrophysicist-- the ability to understand a larger context.

Hi Ken G,
Thanks for your response. I have a few comments on your reply, but first I see that Nicholson's web site does not give a direct link to his 3 papers which should answer your questions about the details of his calculations, and his criticism of the Binney and Tremaine calculation. I forgot that the links to the papers were given a Baut forum, so without these, I can understand that you can't say much about the calculation and assumptions. For starters, Nicholson does include variable thickness effects, and if I am not mistaken, it is Binney and Tremaine that use only a thin disk assumption to account for thickness. Correct me if I am wrong about B and T, with a reference please.
The papers can be obtained in PDF form by clicking on the following.

Errors in equations for galaxy rotation speeds

http://xxx.lanl.gov/ftp/astro-ph/pap...09/0309823.pdf

Galaxy statics without dark matter

http://xxx.lanl.gov/ftp/astro-ph/pap...09/0309762.pdf

Galaxy Mass Distributions from Rotation Speeds by Closed-Loop Convergence

http://xxx.lanl.gov/ftp/astro-ph/pap...03/0303135.pdf

One further comment for now, Nicholson will make available a CD where you can perform the calculation on you home computer and play with it to your hearts content. Notes are included. This is provided essentially at his cost.
You labelled this as a grab for money. Did you expect him to send these out for free?
Again, Thanks for your response, TomT

I don't know if he is motivated by greed, perhaps his products are fairly cheap. But there is certainly a better way to get the word out in the standard literature if one's only goal is mutual enlightenment! Anyway, I'll talk a look at those links, but note that the vertical structure business is a detail for constraining the nonspherical structure aspects. The real issue is whether or not you need dark matter, and I guarantee you that he has either made an error, or he has allowed the mass-to-light ratio to be a variable, or both. Even if there are no errors, it is perfectly obvious that increasing the mass-to-light ratio will allow solutions with no dark matter, and holding to the observed value will require dark matter. It's freshman physics.

Hi Ken G.,
I have further comments/questions on your reply.
1. Your mention of "normal mass to light ratio". I would like to dig into this one. Can you give me a reference that gives the accepted explanation and justification for this? I would like to know details, not just that it seems to be a good intuitive assumption.
2. Can you explain further what you mean by Nicholson "using a one dimensional rotation curve". I want to make sure I understand your point correctly before commenting.
3. Unfortunately, Nicholson, like so many others on either side of these debates, sometimes uses sarcastic comments in his writing. It immediately can cause hard feelings that get in the way for some. I have concluded that this is a self defeating practice, and scrupulously try to avoid doing it. I can only say, please ignore it and only pay attention to what is pertinent to the discussion.
Thanks, TomT

I've looked at the first link, and didn't get very far before I was quickly convinced this guy doesn't know much physics, even if he's good at programming equation solvers. What bothered me right off the bat was:

I learned why that statement is wrong in freshman physics, because that's where I learned how to use symmetry arguments. The geometry in question is in the plane of a thin disk at radius R from the center. If the mass distribution depends only on radius in the disk, then the gravitational force it will produce on a test mass at R in the plane of the disk will obviously be the same as if each circular shell in the mass disk was rotated around the axis from the center to the test mass, such that the circular shell becomes spread over a spherical shell. The only component of the force that can matter here is the radial component, and it is invariant under the rotation in question, proving that the circular shell yields the same gravity as the spherical shell. And we all know (I hope) that a spherical shell induces a gravity that is identical to if all the mass was concentrated at the center. Ergo, the force of gravity never diverges on a test mass in this calculation, no matter what the author may claim in the above quote.
In short, B + T never "assumed" anything, they applied the above geometric proof.

He also appears to be confused about what an integral is, because he refers to infinities that occur when the test mass R is at the same place as the integrated location r, which would only be true if the mass was actually concentrated into infinitely narrow rings rather then spread out over the plane of the disk. An integral postulates an arbitrarily narrow ring, and has no difficulty dealing with infinities that do not occur when the mass in each ring is formally zero. This is true about half of the integrals physicists deal with, but he is apparently not aware. Or is he claiming that half the integrals in physics are being done wrong? Please. I stopped reading at that point, this guy has no idea what he is talking about.

The entire idea behind dark matter is that you have matter that doesn't make light. Thus, the entire idea has presumed a mass-to-light ratio! Anything that would increase the mass-to-light ratio above what you observe from stars would therefore have to be construed as "dark matter". For a summary of the observed mass-to-light ratio, just google "mass to light ratio".
Simple-- the link you gave me only refers to a one dimensional form for the rotation curve. That is, v(r).
Personally, I'd have no problem with his sarcasm if he had been right. If he'd been right, he would have had good reason to be sarcastic. As he is not, it is others who have that right. Though I agree it shouldn't ever go "over the top", that's not productive. Believe me, I'm exercising restraint there.

[added on edit: I am looking for a better resource about the mass-to-light ratio than "googling it",which doesn't work very well in this case. Also I should be clear that the issue is a discrepancy between the M/L ratio you expect from luminous matter (stars) and what you get in actual observations of galaxy clusters (dominated by dark matter). Finally, let me note that I have no criticism of TomT here, only of the author of the badly reasoned arguments in the links. TomT's curiosity is well founded, given the extraordinary claims that abound even in mainstream astronomy!]

Hi again,
1. OK. I googled "mass to light ratio". I read through the first page of references and concluded it is not nearly as rosy a picture as you portrayed. But first could you give me your reaction to p1 and p2 of this reference from google.
"Photometric Mass-to-Light Ratio"
http://www.astro.psu.edu/users/rbc/a480/lec16n.pdf

In essence it says to me that the ML ratio can't be calculated accurately because small stars make up most of the galaxy population. What am I missing?

2. I still need clarification of what you mean by one dimensional velocity rotation curves.
Are you saying that:
(a) the rotation velocity of stars that we observe in galaxies is known in 3 dimensions (the radial, circumferential and z components). You obviously can't mean each individual star.
(b) Can you point out where Binney and Tremaine use something different than Nicholson for this. For starters, Nicholson points out the pertinent equations BandT use, B&T(2-146) through (2-174). What are they using for velocity that differs from N.

3. For further clarification of terms -
B and T find a galaxy mass distribution that simulates the observed rotation velocities. Their solution has a disc (with mass calculated from the ML ratio) that gives the Keplerian motion, plus a series of concentric spheres of dark matter. The outer sphere radius extends beyond the edge of the visible disc in the galactic plane, and the same distance above and below along the galaxy axis of rotation. The matter in the disc and spheres overlap in the galactic plane, i.e. dark matter permeates the disc also. The gravity effects from the spheres, when added to the disc effects, give the observed rotation curves. When you refer to galactic halo, are you referring to the dark matter spheres? I put the above down to make sure we are talking about the same thing. I have seen statements in the various forums that violate the B and T model, e.g. no dark matter (or bands of dark matter) in the Milky Way disc. As soon as you tinker with the model, you tinker with the velocity curves and they wont match what we observe.
Thanks, TomT

Wait a minute! B and T use a mass distribution based on the M/L ratio and it doesn't work. So they then add dark matter spheres to explain the observed rotation velocities. This has become the accepted solution.
Now you seem to be saying that there is a discrepancy between the M/L you expect from luminous matter and what we observe in actuality. This looks like the M/L ratio doesn't work after all. I thought you criticized Nicholson for not using it.
So use of the M/L ratio resulted in needing dark matter, but m/L is incorrect because dark matter effects the luminousity. Looks like pretty circular reasoning to me.
Maybe M/L is incorrect for the reason stated in the reference I quoted above, namely, most of the stars are small so the relationship doesn't hold for galaxies.
TomT

I have seen much written about this and in almost every discussion the difference between Baryonic Dark Matter (MACHOS) an Non Baryonic dark Matter is always involved.

Doesn't that need to be part of this and isn't the question really...are his calculations correct without using Non Baryonic Dark matter???

RussT

There are two totally independent issues here. The first is, how much mass do you need in your galaxy, and how must it be distributed, to get the rotation curve. That is a matter of straightforward gravity, although Nicholson seems to think the calculation has been done wrong (and in the process he makes incorrect statements that strongly suggest it is he who does not understand how to do the calculation). But none of this has anything to do with whether the matter is "dark" or not.

That brings up the second point, which is, once you know the mass, and you know the light from it, what is the "mass to light ratio"? This is where dark matter comes in. If you can't explain why you have so much mass, relative to the light, you have to say that some of the matter is "dark". So how can Nicholson say anything about dark matter without quoting his value of the M/L ration? That's what I criticized.

As a case in point, if you are right that the mass-to-light ratio is large because there are a lot of stars with very low masses that are being "missed", then that is your version of dark matter! It doesn't remove the need for dark matter, it just chooses a different explanation. It is certainly one possibility, but it is not favored for other reasons.

As for RussT's nonbaryonic dark matter, galaxy rotation curves have nothing to say about that. For that, you have to look at cosmological models, which currently strongly suggest that the dark matter must be nonbaryonic. I hope this clarifies the situation.

Hi Ken G,
I have taken the liberty to number 3 points of your reply and will give my thoughts to each.
1. I think you stopped reading Nicholson's paper based on a misunderstanding, but I will come back to that later in a future post.
2. You state "once you have so much mass". How do you know you have so much mass? Do you have an independent measure of galaxy mass, or are you saying this because the B&T calculation found dark matter necessary? I am saying that the Nicholson calculation requires only that mass be in the galactic disc, and if you read completely through the papers, you will find that his result for the total galaxy mass is about 1/3 of the value from the B&T result with dark matter. This is somewhat more than the B&T calculation for the disc contribution to the total galactic mass. This could easily be explained be the small star explanation. See point 3.
3. To clarify, I found the reference, actually a mathematical demonstration, that the M/L ratio doesn't work for galaxies when I took your suggestion to google for it. The reference I asked you to comment on was a few posts back (astro.psu.edu,etc). It isn't a question about me being right or my version of dark matter. I merely quoted a reference and what they had to say makes sense to me, and they demonstrated mathematically why they think it is correct. It also fits very nicely with Nicholson's result which requires little additional mass for the galactic disc to explain things without dark matter.
TomT

Typically, the dark matter in a galaxy is about 10 times the matter with a "normal" M/L ratio (and far more is needed for the whole galaxy cluster, but that's another matter altogether, no pun intended). Thus, if Nicholson gets 1/3 of that, he still needs dark matter! He has not changed the basic issue, just the degree. But it's still wrong, because simply putting 1/3 the mass into the disk, not spread over spherical shells, would be inadequate from the geometric proof I explained above. And whether it's 1/3 or the B+T mass, your claim that it may be explained by small stars is certainly a resolution that everyone would be very happy with, had it held up. It would have been the first resolution tried, not the last!
That reference is a nice lecture from a course that sounds pretty interesting, thanks for the link. It makes the (well-known) point that the stellar mass in a galaxy comes from low-mass stars, while the luminosity comes from high-mass stars. This indeed makes the determination of the stellar M/L ratio quite tricky. Nevertheless, efforts to determine this ratio using reasonable models of stellar populations find that the stellar M/L ratio is about a factor of 10 too low to explain the galactic M/L you need gravitationally. Had Nicholson been right, that would bring this down to a factor of 3-- you'd still have to monkey with the stellar M/L. How much leeway you have to do that is something I can't say much about, it's a very complex story involving galactic population synthesis. If you wanted to start a whole new thread on that, it would be much more interesting than the faulty Nicholson calculation, which doesn't even remove the need to consider changes in the stellar M/L!
If you think a factor of roughly 3 constitutes "little additional mass", perhaps!