Dark matter density near Earth? An informal defense of Moni Bidin et al.
By Hontas Farmer | June 3rd 2012 05:06 PM | 7 comments | Print | E-mail | Track Comments

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The issue of how dense the dark matter is near Earth is far from settled. Recent work by Moni Bidin, Carraro, Mendez and Smith holds that the density of dark matter near Earth is 0.04 gigaelectron volts per cubic centimeter, the work of Bovy and Tremaine says it should be more like 0.3 gigaelectron volt per cubic centimeter. The problem is that Bovy and Tremaine make a basic logical error at the outset which invalidates what on the face of is otherwise a masterful work of theoretical astronomy/cosmology. Unfortunately that logical error of circular logic falsifies their counter argument.

Let me make it perfectly clear that this will not be an argument that there is no dark matter or for any particular model, not even one of my own (the only model that other than Moni Bidin is wrong, or dark matter is “lumpy” that could explain this.)  Moni Bidin et al are probably formulating a response of their own.  This is just my educated opinion on the whole matter.

In a nutshell, this is what Moni Bidin et al did. They measured the velocities of stars far from the galactic plane. Then, using various equations extrapolated from that data to determine how much dark matter is in the galactic disk near the sun. They found an order of magnitude less, that’s ten times less than what is typically expected in particle physics experiments that search for dark matter.

In the particle physics based  experiments large masses of normal matter are enclosed with sensors that can detect tiny flashes of light. When dark matter interacts with normal matter, and it almost never would even if there were much more of it, it generates a little bit of light. So far very little has been detected that cannot be written off as experimental noise. One way to explain this unexpected difficulty would be to question the assumption that the dark matter halo is necessarily uniform. Which is the assumption that Moni Bidin and the team at ESO tested with their project. They found a less dense halo than they.

Shortly after this, the team of Bovi and Tremaine at the institute for advanced study published a paper which points out that one of Moni Bidin et al’s assumptions may be wrong. Specifically, the assumption that the speed of a star at high above or high below the galactic plane will be constant with respect to distance from the galactic center. This is essentially true for the velocity of stars that are far enough from the galactic center and in the central plane of this or any other spiral galaxy.

To show that Moni Bidin’s analysis was wrong the team of Bovy and Tremaine repeated it without that assumption. On the face of it that sounds more robust. They assumed less and got an answer close to what everyone expects it to be if there is a uniform dark matter halo.

The problem is that Bovy and Tremaine assumed what they were trying to prove. Which is a classic and fatal mistake that everyone makes from time to time.

It is very subtle but if you carefully read their paper you can see that they have assumed that the dark matter halo near earth will have about a certain value. Namely the value that most experiments looking for dark matter have assumed all along.

They begin on the bottom of page 5 and on page six of their paper. Wherein they proceed with arguments and use numbers that could only give them the answer they desire. From the unnumbered equation

$V_{c}^2=-RF_R$

they have assumed what their paper seeks to prove.  From this point forward and given the numbers they use are cited from this paper (Jo Bovy etal arxiv:1202.2819 ) in which they did assume a dark matter halo that was uniform and of a certain density near to the one they derived in their supposed refutation of Moni bidin et al.   The answer Bovy and Tremaine found is not a surprise then, it was assumed from the beginning, their argument is a circular argument.    It's not obvious to someone who gives it a quick read, I only thought of this while weeding my garden of all things and just pondering it all long after reading this.  I don't think that this was done on purpose either.

Now while I understand their math perfectly well, I expect to be accused of not understanding it. Who am I to question them?  I freely admit to not understanding all of the subtle details they added, I’ll give any who criticize this blog that much. However, I do know basic Boolean logic very well. If your logic stars out by setting a certain answer, then your process leads you to what you assumed something’s wrong with that argument. Rather the process should lead naturally to a result. To put it terms even a casual non scientist can understand. If one wants to prove the pythagorean theorem, one cannot assume anything like it or related to it is true...no matter how mangled and different the assumption may look. (i.e. given the equation Cos^2(theta)+Sin^2(theta)=1 prove a^2 +b^2= c^2 is true if c is set equal to one. That would be more of a derivation of an expected result than a truth testing proof. That is what Bovy and Tremaine did they derived a result that fits their assumptions. Yet they, made the assumption in a subtle way that isn't very obvious.)

Let me just say that Bovy and Tremaine otherwise did very good work in that paper. It was an artful masterful derivation of just what the local density of dark matter would be assuming the halo is uniform and given Moni Bidin et al’s observations. However, it is not the death nail that it appears to be for this issue.

The question remains, as I posed and attempted a purely theoretical answer to on this blog, why is dark matter so much more elusive than anyone previously thought? That is the question of the day, not dark matter’s mere existence in some form or the other.

More work remains to be done both theoretical and observational to answer this question. Simply saying “Dark matter is dark and there’s x amount of it,” just isn’t enough for some of us.

(V_c)^2 = R * F_R, I read that as, The velocity of a star around a circle radius R, is equal to to the radius time, F_R, in the inwards (radial) Force. This is a statement of motion of a particle, in a unknown potential, with V as the velocity in the galactic plane. That is true for particle curving under a force. Its also true in cylindrical coordinates for the components of motion in the galactic plane for an ellipse, as Bovy et al use it here. How does an assumption on dark matter density appear in this equation?
Read their paper.   From that equation and for the rest of page six they proceed to use "data" from a past paper of Bovy's in which the assumption was made that there is a dark matter halo of a certain uniform density.
In a sort of graphic it's like this.

(Data from paper in which DM halo of about 0.4 GeV per cubic cm is a given)
=>
Insert into equations proposed as a test for a dark matter halo of about ten times less than that.
=>
Find that the equations give you a dark matter halo closer to 0.4 Gev per cubic centimeter.
=> which closes the loop of circular logic.

They used data from a paper which took what they were trying to show as a given and surprise, they got a number similar to their initial assumption.  An assumption contained in a prior paper that the current paper depends on.

That's my argument.
Science advances as much by mistakes as by plans.
I can see them estimating the circular speed on the same page, after quoting a density estimate but they don't use this estimate again. In the later sections they use or claim to use, three different density profiles with unknown parameters in there equations which they then solve for the unknown parameter. If equations 15 or 16 where used in later estimates they might have circular logic, but no where can i see that this has happened. Indeed 15 and 16 are first tries for consistency before they solved the Poisson equation for the surface density.
They cite a paper in which they get some of the numbers they used.  Read that paper and you will see what I am talking about.   They cite it as Bovy 2012c (_http://arxiv.org/abs/1202.2819).

Also notice the sentence in the 4th block of text on page 6.

This means that near the mid-plane, where the density is approximately 0.1M⊙ pc−3,

Uhmm :/

I do belive that right there is what they are trying to prove with this paper.  That is a number which they could only get by using data from the paper they cite as bovy 2012c (_http://arxiv.org/abs/1202.2819) in which a dark matter of a certain size shape and density is one of the assumptions.   They use that same assumption in their text of the current paper when quoting the number >~ 3.5 kpc.

In short to see this problem with their argument you can't rely on just one paper you have to read the key self citations in their paper.
Science advances as much by mistakes as by plans.
Reading the paper a third time, Bovy and Tramaine where quite clear about what assumptions they used, which of course you have to be in a scientific paper. The 0.1 Solar mass per cubic parsec comes not from Moni Bidin, but from Crezes 1998 papers and a 2000 paper, Holmberg and Flynn, who established a standard estimate for dark matter near the Solar position, note the round numbers and lack of error bars, the researchers were clear that they only had a very rough idea of the figure. Its this conventional figure that Bovy and Tramaine wanted to return to.

Its not clear how much Bovy and Tramaine used Moni's database of star positions, nor weather they had access to the source program, or wrote they own. Bovy didn't mention SEGUE sets of G class drawfs Moni used. In fact one paper discusses data, and the other mostly the quadrature (numerical integration). Whole galaxy stelllar gravity simulators are pretty hard to build, and they just using classical gravity, (how much can a Poisson Surface Gravity Integral, be used for what classes of gravity theory?, It would work for Newton of Course, but so would having the total mas acting from the center of gravity).

Just yestaday another paper came out, Silivia Garbari et al who studied K class drawfs (stars a bit more orange than our sun, and they come out with estimates of 0.025 Solar masses per cubic parsec of pure dark matter in a spherical halo.

What interests me at the moment, is not weather they is dark matter, but how the in the center of galaxies and global clusters, dark matter reaches a maximum density, so called core dark matter maximum densities, is dark matter holding itself up against gravity by some unknown force?
You keep missing my point.  The 0.1 solar masses that Bovy and Tremaine use comes from a past paper by Bovy and tremiane.  They also cited other numbers which they derived in papers which assumed a dark matter halo of a certain density shape and size.   By using numbers from papers where 0.1 solar masses is assumed they are then using that assumption in the paper which is the topic of this blog posting.   I even gave you a link to the paper that Bovy and Tremaine cited.  Read that paper.
Again

If you do an experiment that makes assumptions ABC  and get numbers XYZ.

THen use the numbers XYZ in the subsequent experiment.

You are implicitly using the assumptions XYZ.

get it.

As for this latest paper.  I would need to read it and think about it for a while. Their getting a number which is exactly what is expected... when as Sean Caroll conjectured, it's likely the dark matter is not perfectly uniformly distributed in a sphere... looks fishy to me.
Science advances as much by mistakes as by plans.
"Why is dark matter(dark energy as well??) so much more elusive than anyone previously thought?"

Perhaps the problem is a compound problem. First, the huge assumption that dark matter and energy are something exotic and strange to begin with. Second, So little is actually understood about the mechanics of mass, gravity, light, and the charge field, and how they interact. The folks at the LHC are going crazy right now trying to get bragging rights to discovery of a "Higgs particle" they can claim gives mass to mass... I wish them loads of luck with that tautilogical mess. I also struggle not to roll my eyes every time I hear about 'virtual messenger' (more like imaginary) particles that tell gravity how to work, or Einstein's dodge of the action at a distance problem, 'let's just pretend curved spacetime explains gravity... and spacetime is just a field of math soooo...er.. nope. The three body problem still is beyond present day physics except as heuristic fudge. Last I checked...a few more than three bodys in this universe are interacting gravitationally.

My question in response to your question : "Why do you think it is surprising we can't find out why galaxies move the way they do when we have no working mechanics for gravity that will explain our own solar system accurately without a million mathematical pushes and post-its tacked on?" I would also ask "Is gravity alone what determines orbits, spin, and cosmological movement? Could there be a repulsive force as well at work in orbits... based on something we already have some experience with?"

I only suggest that before dark matter geniuses crank it up, folks realize our understanding of gravity is pretty weak theoretically, and has been largely neglected since Einstein decided curved math explained curved orbits (more or less). Maybe it's time for a makeover.... not another post-it.