# Questions about shape of dark matter orbits in spiral galaxies

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.

• It might help you to know that the spiral shape of some galaxies does not mean that the star follow orbits in that shape. – dmckee Feb 16 '16 at 17:58
• See this search. There are already some questions very closely related to yours if not duplicates. – John Rennie Feb 16 '16 at 17:58
• dmckee: I can sense your point but do not grasp it fully. If it is possible to describe briefly here - what it means then? do some of the stars follow spiral orbits? How the spiral shape formed then? – kpv Feb 16 '16 at 18:02
• See this Wikipedia article. The spiral arms are density waves. The stars themselves move in approximately circular orbits. Dark energy probably does the same. – John Rennie Feb 16 '16 at 18:04
• What I eventually want to know is - do dark and baryonic matter often intersect in these galaxies, or they move in such a way that they do not pass through one another and always move along side. – kpv Feb 16 '16 at 18:08

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.

• If I were to pick a nit, I'd expect the DM orbits to be substantially more radially biased than the baryons in a disk galaxy. Doesn't change your conclusion at all, of course. – Kyle Oman Dec 9 '16 at 21:07

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).

• Fabrice NEYRET: I edited the question to ask next part. Please see if you can answer. – kpv Feb 16 '16 at 23:40
• The number of black holes has no importance. What counts is the total cross-section. Black-hole are very small, galaxy volume is incredibly large. Even assuming both share the same distribution in space, you can evaluate by yourself which is the total mass accumulated by the flux of DM intercepted by BH. My bet is that it's ultra-negligible. – Fabrice NEYRET Feb 16 '16 at 23:48
• Note that they are black holes, so the factor would be somewhat more than cross-section. They are eating DM all the time for billions of years, and there are 100 million of them. Even at galactic scales, it does not sound negligible. That is why, I am asking what the computations look like. – kpv Feb 16 '16 at 23:56
• @kpv: Two points are worth thinking about: (1) 100 million black holes sounds a lot, but there are 100-400 billion stars in the milky way; (2) black holes do not magically suck things in -- their gravitational field is exactly the same as that of a star of the same mass outside the surface of the star. – tfb Feb 17 '16 at 1:38
• Yes they do not suck things like that but they are in constant motion and move through dark matter. I guess, they would capture much more than cross-section though. – kpv Feb 17 '16 at 3:15