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.