Burning Wimps

Malcolm Fairbairn had an interesting seminar last Wednesday here at CERN. It was about hypothetical stars whose dominant source of energy is dark matter annihilation rather than nuclear fusion. Such an object is called a dark star or, to avoid confusion with the movie, a WIMP-burner.

Dark matter is 5 times more abundant than the baryonic matter but it does not form compact objects because, interacting so feebly, it cannot efficiently dissipate energy. It can however fall onto dense baryonic objects like stars or even planets. If the dark matter particle is a WIMP, it should scatter on the nucleons that make a star and, from time to time, get captured by the gravitational field of the star. The enslaved particles form a spherical dark core of the star. Once the density in the dark core becomes large enough, the dark matter particles can efficiently annihilate with each other. It is expected that for large bodies like stars the capture rate and the annihilation rate eventually come into equilibrium. There are many unknowns in this game: the local dark matter density and velocity distribution, the mass of the dark matter particle, the scattering cross-section of dark matter on nucleons. Actually, the spin-independent cross section is constrained by XENON and CDMS to be less than $10^{-7}$ pb for a weak scale WIMP, but the spin-dependent cross-section (which is relevant for typical stars, as they are made mostly of hydrogen) can be as large as $10^{-1}$ pb. Interesting effects can be obtained provided the cross-section is close to the upper limit.

Searches for dark matter in the Earth core are sponsored by the Templeton Foundation, since a positive signal would allow us to identify the centre of the Earth as the location of Hell. There is more chance, however, to find it in the Sun. In the optimistic scenario -- a SUSY WIMP with $\sigma_{SI} = 10^{-2}$ pb and $M_{DM} = 100$ GeV -- the Sun may hold as much as $10^{13}$ tons of dark matter. The annihilation of dark matter in the core of the Sun could produce highly energetic neutrinos that are being currently searched for by terrestrial observatories, like for example the ICECUBE detector at the South Pole. Yet the Sun is hardly a dark star since, with the assumed parameters, the annihilation accounts for only $10^{-10}$ of its luminosity. In order to seriously affect the stellar dynamics one needs more infalling dark matter.

The galactic centre is expected to host much more dark matter who is attracted there by the supermassive black hole and other fireworks. The actual dark matter density at the centre is another unknown, but according to some models it can well be $10^{10}$ times larger than in the Solar System. This could be enough to make a dark star. One difficulty is that the stars move much faster close to the galactic centre which makes the capture process less efficient. However, stars with sufficiently elliptical orbits slow down from time to time and should be able to capture enough dark matter.

How would a dark star look like? As far as I understood, at first sight it's not obviously different from an ordinary star, but there are important differences in the stellar dynamics. Somewhat counterintuitively, energy release due to the annihilation makes the core temperature smaller.
As a consequence, the nuclear reactions become slower and may even shut off completely. Thus, dark stars burn more slowly so that they may live longer than ordinary stars of similar size. Therefore, one way hunt dark stars is to identify abnormally long living stars.

Astronomical observation in the galactic centre are challenging because the place is terribly polluted by dust. In the recent years, however, astronomers were able to peer behind the dust using the radio-wave and infrared observatories. Several stars orbiting around the central black hole were spotted. A few of them seem to be too massive to live long enough to wander by mistake from other places, while it's believed that new stars cannot form close to the centre because of large tidal forces due to the black hole. This is known as the youth paradox. Malcolm suggests that WIMP burning is a viable explanation of the paradox.

See also Malcolm's recent paper. The slides are here (warning: 20Mb and in fact it's all dark).