WIMP annihilation and cooling of neutron stars

Since Zwicky proposed the problem of the ‘‘missing mass’’ in 1933, a lot of theoretical and experimental effort has been made in order to unveil the nature of dark matter. Today, WMAP has provided very accurate data regarding the matter density in the Universe [1]. The energy density of the Universe is composed of 4% atoms and roughly 22% dark matter. Data from recent observations indicate that dark matter cannot be attributed more than 20% to dim objects like black holes, brown dwarfs, and giant planets [2]. From a theoretical point of view, several candidates rise from different theories, such as neutralinos [3,4], Majorana neutrinos, and, lately, technibaryons provided by theories that are not ruled out by the electroweak precision measurements [5–10]. From the experimental point of view, the focus is on the direct and indirect detection of dark matter particles. The direct detection might occur in underground experiments like CDMS that, in principle, can detect recoil energies from collisions between weakly interacting massive particles (WIMPs) and nuclei, or atmospheric experiments like the X-ray Quantum Calorimeter (XQC), where strongly interacting particles might collide with the detector. The indirect detection might occur via gamma-ray and neutrino telescopes, where the presence of WIMPs can be detected indirectly, by observing products of WIMP annihilations. In particular, provided that WIMPs can annihilate and because they can be trapped inside the Earth or the sun, such annihilations would produce jets of particles and more specifically neutrinos coming straight from the center of the Earth or the sun, that could possibly be detected by neutrino telescopes [11–13]. On the other hand, gammaray telescopes can, in principle, detect gamma rays produced by WIMP annihilation at the center of the Galaxy [14]. Both direct and indirect detection experiments can impose strong constraints on the cross section of the WIMP with the nuclei. For instance, heavy Dirac neutrinos have been excluded as WIMPs for masses up to several TeV, because their elastic cross section with nuclei is sufficiently large and therefore they should have been detected by now in CDMS [15]. In this paper we investigate the possibility of a different kind of indirect signature of WIMP annihilation. Instead of looking at the indirect signals from the annihilation of trapped WIMPs inside the Earth or the sun, we examine the consequences of WIMP annihilation on the temperature of neutron stars. The neutron stars are massive compact objects with very low temperatures. Naively one might expect that, since the mass of the trapped WIMPs inside a neutron star represents a tiny fraction of the overall mass of the star, such an effect should be negligible. However, the annihilation of massive particles inside the star releases a huge amount of energy that is heating up the star. As we shall argue, once the accretion rate of dark matter particles equilibrates the rate of annihilation, the amount of released energy is independent of the star’s temperature, and therefore at late times the WIMP annihilation can keep the star at a constant temperature that depends on the mass and the radius of the star, the cross section of annihilation, and the local dark matter density of the star. The paper is organized as follows: First we calculate the rate of dark matter accretion onto the neutron star including general relativity corrections. Then we calculate the annihilation rate for the WIMPs, and we calculate the effect of the WIMP annihilation on the cooling curves of a typical neutron star made of regular nuclear matter. We present our conclusions in the last section.