Black holes can cause dark matter to annihilate in their vicinity by concentrating the dark matter and enhancing the collision rate between dark matter particles. The best observational candidates are supermassive black holes, such as the 4 million solar mass black hole found at the center of our Milky Way galaxy. Some galaxies have much larger supermassive black holes, reaching as high as several billion or even tens of billions of solar masses. Most massive galaxies appear to have supermassive black holes in their centers.
We infer the existence of supermassive black holes through their effect on nearby stellar or molecular cloud orbits. And we more directly detect supermassive black holes (SMBHs) by the radiation emitted from ordinary matter that is near the black hole (BH), but has not yet fallen into the BH’s event horizon (from which nothing, not even light, can escape). Such matter will often form a hot accretion disk around the SMBH. The disk or other infalling matter can be heated to millions of degrees by the strong gravitational potential of the BH as the kinetic energy of infall is converted to thermal energy by frictional processes. Ordinary matter (OM) heated to such high temperatures will give off X-rays.
Now if OM is being pulled into a SMBH, so is dark matter, which pervades every galaxy. Dark matter (DM) responds to the same gravitational potential from the SMBH. The difference is that OM is collisional since it easily interacts with other OM via the electromagnetic force, whereas DM is generally collisionless, since it does not interact via electromagnetism.
Nevertheless DM – DM collisions can occur, rarely, via a ‘direct hit’ (as if two bullets hit each other in mid-air) and this leads to annihilation. Two DM particles meet directly and their entire energy content, from their rest mass as well as their kinetic energy of motion, is converted into other particles. The cross-section strength is not known, but it must be small due to observational limits, yet is expected to be non-zero. The most likely candidates for decay products are expected to be photons, neutrinos, and electrons.
The leading candidate for DM is some sort of weakly interacting massive particle with a mass of perhaps 5 to 300 GeV; this is the range where DM searches from satellites and on Earth are focused. (The proton mass is a little less than 1 GeV = billion electron Volts.) So if two DM particles mutually annihilate, there is of order 10 GeV to 600 GeV of available rest mass energy to produce highly energetic gamma rays.
The likelihood of a direct hit is proportional to the square of the density of the DM. A SMBH’s gravitational potential acts as a concentrator for DM, allowing the density to be high enough that there could be a significant number of annihilation events, resulting in a detectable flux of escaping photons reaching Earth. Relativistic effects work to further increase the annihilation rate. And it is possible that the annihilation signal could scale as M³ (mass of the SMBH cubed), and thus the most massive SMBHs would be very strong gamma ray emitters. These would be highly energetic gamma rays with well over 1 GeV of energy.
Movie from NASA Goddard showing Dr. Jeremy Schnittman’s simulation
Dr. Jeremy Schnittman of the NASA Goddard Space Flight Center has investigated possible annihilation rates and the nature of the observable gamma ray spectrum for some simple dark matter models. He used a compute cluster to simulate hundreds of millions of DM particles moving in the general direction of a SMBH. One of his remarkable findings is that much higher gamma ray energies can be produced than previously believed, in the case of SMBHs which are rapidly spinning.
This is a result of something known as the Penrose process, which allows energy to be extracted from a rotating BH. There is a region called the ergosphere outside of the event horizon and when two DM particles annihilate in this region and produce two gamma rays, one gamma ray photon would fall into the event horizon (into the BH), and the other photon would escape to infinity, possibly in the direction of Earth. Dr. Schnittman’s simulation indicates that the energy boost can be as high as 6 times or more. The faster the SMBH is spinning, the greater the potential energy boost.
He also has looked at DM particles on bound orbits, which are likely to form into a (donut-shaped) corotating torus around the SMBH, aligned with its spin vector. The bound DM particle annihilations lead to lower energy gamma ray production, as compared to the unbound particles.
One of the important considerations is that the influence radius of the BH is very large. The size of the BH itself (event horizon or Schwarzschild radius) is small, even for SMBHs. The radius is proportional to the mass, via the relation 2GM/R = c² (G is the gravitational constant, c the speed of light and M and R are the BH mass and radius, respectively). A SMBH with a mass of 10 million solar masses will have a radius of only around 30 million kilometers, or about 1/5 of the Earth-Sun distance (an AU, or astronomical unit).
But the gravitational influence is much greater, since DM particles are typically expected to be moving at around only a couple of hundred kilometers per second far away from the SMBH. Thus DM particles that are 1 million times further away than the SMBH will have their orbits in their galaxy perturbed by the SMBH. And the scale of influence is thus parsecs (1 parsec = 3.26 light-years) or tens of parsecs or even hundreds of parsecs, depending on the SMBH mass.
The most energetic gamma rays can be produced by unbound DM particles. These are on orbits which can approach near to the SMBH after falling from far away (a “swan dive” toward the SMBH) and these DM particles would then typically head out away from the SMBH in the opposite direction. But before they are able to, they have a direct hit with another DM particle and annihilate into gamma rays or some other decay products.
The search for gamma rays from annihilating DM around SMBHs is already underway. There is in fact a possible detection by the Fermi telescope at 130 GeV in our Milky Way galaxy, from the direction of the Sagittarius A* SMBH. Future more sensitive gamma ray surveys may lead to many detections, helping us to better understand both dark matter and black holes.
J.D. Schnittman, 2015. “The Distribution and Annihilattion of Dark Matter around Black Holes”, http://arxiv.org/abs/1506.06728
J.D. Schnittman, 2014. Phys. Rev. Letters 113, 261102, “Revised Upper Limit to Energy Extraction from a Kerr Black Hole”