Galactic Accelerometers Probe Milky Way’s Dark Side

Interesting, but then I'm not a fan of dark matter. I'd be wondering about whether one could ignore the ( tremendously strong ) magnetic field of a pulsar. It's a magnet moving in the magnetic field of the galaxy so it'll suffer a force due to that. Is that comparable to some alleged 'dark matter' component ? That's a problem with the definition of dark matter - it is the bit left over when you account for all that you can think of.  Maybe dark  matter is no more mysterious than a failure of imagination.

[back of the envelope partial calculation]

The magnetic field of the galaxy is of the order of 10 uG ie. 10^-5 Gauss. But a neutron star has a magnetic field of order 10¹⁴ Gauss, and it's the main reason we 'see' these things at all : from radiation processes that are proportional to massive induced currents ie. the pulsar is a dynamo. But it's hard to estimate the magnitude of those currents if you don't have a good idea of neutron star matter properties .... and if one knew the current then one could gauge the force on the star.

A quick/slick guess would use F = B * I * L, where F is the force on the neutron star, B is the galaxy's magnetic field strength^*, I is the 'effective' current in question, and L is the 'length of the conductor' ( a neutron star's diameter is ~ 20km ). If M_n is the mass of the neutron star^** then F/M_n gives the acceleration of interest. Hmmmmm .....

.... or you could flip the question and estimate the current from the measured residual acceleration ( call it A_n ) using the methods in the paper :  

I = (M_n * A_n)/(B * L ) ~ 10³⁰ * An /(10^-5 * 10^-5 * 2 * 10⁴) = A_n * 5 *  10³⁷ 

and then decide if I was a 'reasonable' measure. An epic number of amperes for every 1 m/s² of acceleration. Now given "Over a year, they may amount to a few centimeters per second" gives

A_n ~ 10^-2/(seconds per year) ~ 10^-2/(3 * 10⁷) ~ 3 * 10^-10 m/s²

Thus I = 3 * 10^-10 * 5 *  10³⁷ = 15 * 10²⁷ ~ 10²⁸ Amps

Now I'm not saying this is right, but it gives a feel for the tremendous numbers that follow from my assumptions. That's a staggering amount of current. To restate : to account for the alleged dark matter effect on the acceleration as not due to gravity but good old EM effects then a neutron star has to carry ~ 10²⁸ Amps. If I'm wrong then we at least know by how much ! :-)

* not forgetting that 10⁵ Gauss is one Tesla = 1 volt second per square meter, or 1 Gauss = 10^-5 Tesla 

^** Call it one solar mass = 10³⁰ kg

[/back of the envelope partial calculation]

Cheers, Mike.

( edit ) Numbers that beggar belief are common when one studies neutron stars. Black holes too. But one can only measure three things about an isolated black hole : mass, angular momentum and charge. Neutron stars are nearly black holes but have ever so many measurable things, especially if they are in company.