Questions about shape of dark matter orbits in spiral galaxies

kpv 02/16/2016. 2 answers, 115 views
black-holes dark-matter galaxies galaxy-rotation-curve

Could someone please describe what the proposed (calculated) orbits of dark matter are? Are they exactly as those of baryonic matter (i.e. spiral), or are they different from those of baryonic matter? If they are not the same, are they in the same plane? I mean do the orbits of dark and baryonic matter intersect?

What I eventually want to know is: do dark and baryonic matter often intersect in these galaxies, or do they move in such a way that they do not pass through one another and always move along side?

Then next part of question is:

Figured out via comments, and an answer, that baryonic matter does cross with DM all the time.

I read that our own Milky Way galaxy (which is also spiral galaxy) has ~100 million stellar mass black holes orbiting it. Black holes and DM keep intersecting with one another. Due to this continuous intersection, the stellar black holes would be continually feeding on DM. We are talking about ~100 million black holes over billions of years. It may not affect the uniform speed curve, due to conservation of angular momentum, but a change in ratio of the BM (Baryonic Matter) to DM (Dark MAtter) should be part of DM models. Has that change been accounted for in the models? What do those computations look like?

Note that these are black holes and so the impact area should be more than the cross-section.

2 Answers

Rob Jeffries 12/09/2016.

I thought I'd have an order of magnitude attempt at answering your edit.

First, there is nothing magical about its orbit in the galactic potential - dark matter particles (if that's what they are) should orbit just like any other point (baryonic) mass. But, the baryonic mass is predominantly in orbits confined to a disc, whereas dark matter is thought to be much more spherically symmetric. All these orbits will not be exact Keplerian ellipses, since the Galactic potential is not that of a point mass.

The typical velocities of dark matter will be similar to that of normal matter at the same galactocentric radius, but in pseudo-random directions. The net result is that from the point of view of a star at the radius of the Sun, the dark matter is like a wind blowing at $\sim 220$ km/s.

So now to the black hole problem. Black holes are the endpoints of massive stars. Empirically, they seem to cluster in mass at a little below $10 M_{\odot}$ (but let's just assume 10). The number of Galactic black holes is highly uncertain, dependent on the form of the stellar initial mass function (as a function of epoch and perhaps metallicity) and the uncertain physics of mass loss from massive stars (again, as a function of metallicity). However, $10^8$ is not unreasonable.

Massive stars are predominantly formed, live and die in the disc. Let's conservatively assume no "kick" from any supernova and that black holes orbit in the disc with a similar speed to the stars around them. Thus they will pass through a dark matter medium, at a speed of 220 km/s, with an estimated density at the Sun's position is about 0.3 GeV/cm$^3 = 5\times 10^{-28}$ kg/m$^3$ (e.g. Read 2014).

We can treat the gravitational interaction in terms of Bondi-Hoyle accretion. Thus $$ \dot{M} = \pi R^2 \rho v,$$ where $\rho$ is the dark matter density, $v$ is the relative speed, and $R$ is the Bondi-Hoyle radius, which can be estimated by equating the escape speed at $R$ with $v$. i.e. $$ R = \frac{2GM}{v^2}$$ and hence $$ \dot{M} = 4\pi \frac{(GM)^2 \rho}{v^3}.$$

Putting in the numbers, I get $\dot{M} \simeq 1$ kg/s or $1.6\times 10^{-23} M_{\odot}$/yr. Thus $10^{8}$ such black holes, accreting for $10^{10}$ years will accrete a tiny fraction of a solar mass of dark matter in the lifetime of the Galaxy.

There are perhaps caveats. The dark matter density is a bit higher nearer the Galactic centre, but on the other hand the rotation curve is quite flat, so it can't make many orders of magnitude difference to the result. The velocity used will have a distribution, so accretion will be stronger for slower dark matter. On the other hand, kicks from supernovae will increase $v$.Thus,I think the effect you are talking about is demonstrably negligible.

Fabrice NEYRET 02/16/2016.

Galaxies cores and disks, stars, planets can form because the energy accumulated by their gravitational collapse can be dissipated, thanks to friction (or pseudo-friction), i.e. interactions.

But dark matter doesn't interact (beside via gravity), so has no friction, so cannot dissipate it's energy, so it can not easily collapse or form structures. That's why it is assumed that it roughly keeps the shape of a spherical halo around galaxies, of quite larger radius than the baryonic matter.

So the trajectories are differents. But even when they traverse the same location, there is no interaction, which mean, even less than with neutrinos (which most of the time traverse Earth without even noticing it).

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