Do You Know The Minimum Dark Matter Evaporation Mass For Celestial Objects? (Cosmology / Astronomy)

The possibility of capture of dark matter (DM) particles by celestial bodies has a long history dating back to the mid 1980s. Already in the late 1970s, some of the potential effects of DM annihilations and scatterings on energy transport within the Sun were realized and then further proposed to alleviate the so-called solar neutrino problem. Nevertheless, these early works did not consider the process of DM capture, but assumed the required amount of accumulated DM particles. The process of capture of galactic DM particles by the Sun and the Earth was first studied by Gould and colleagues, which set the ground of further calculations. After that, it has been studied for other celestial bodies, such as, other solar system planets and satellites, exoplanets, brown dwarfs, main-sequence and post-main sequence stars, and compact objects such as white dwarfs and neutron stars.

The scattering of DM particles in galactic halos with the nuclei (or electrons) of celestial objects could bring those particles into close orbits and finally result in their gravitational capture within the objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape.

Now, Garani and Sergio, computed the DM evaporation mass for a wide range of celestial bodies, from the smallest objects with spherical shape that can be in hydrostatic equilibrium (small satellites), M ≃ 10¯10 M, to the most massive main-sequence stars, M ≃ 100 M. They also discussed the DM evaporation mass for post-main sequence stars, white dwarfs and neutron stars. In addition, they considered a range of DM-nucleon scattering cross sections that covers ten decades, 10¯41 cm² ≤ σp ≤ 10¯31 cm², and which runs over the thin and thick regimes. Their study recently appeared on journal Arxiv.

For planetary bodies, brown dwarfs and main-sequence stars, spanning the mass range is 10¯10 M ≤ M ≤ 10² M, they obtained that for a wide range of DM-nucleon cross sections, 10¯41 cm² ≤ σp ≤ 10¯31 cm², the absolute minimum for the DM evaporation mass is mevap ≃ 350 MeV. This minimum value is obtained for the largest cross section they considered and for super-Jupiters and low-mass brown dwarfs. For very compact objects, such as white dwarfs and neutron stars, smaller DM evaporation masses are found, with values as low as mevap ≃ 1 MeV and mevap ≃ 1 keV, respectively.

© Garani and Sergio

They have also discussed the critical importance of the exponential tail of the DM evaporation rate (Fig. 1), which had already been studied for the case of the Sun, although its importance has not always been appreciated. These early papers obtained a DM evaporation mass for the Sun which is approximately given by Ec/Tχ ≃ 30, where Ec is the escape energy at the core of captured DM particles and Tχ is their temperature. Similar values are found for the DM evaporation masses obtained for the Earth and the Moon. This estimate approximately corresponds to the geometric cross section,

Here, they generalize this result for all round celestial bodies in hydrostatic equilibrium. The virial theorem is at the core of this finding.

In addition, they have also studied the dependence with other parameters, as the position of the celestial body in the galactic halo (DM density and velocity), the DM annihilation cross section, and the type of interaction (SI and SD). The DM evaporation mass, however, depends only logarithmically on these parameters, so its value is rather stable against variations of them.

© Garani and Sergio

For the geometric value of the scattering cross section, they obtained the minimum value of the DM evaporation mass for super-Jupiters and low-mass brown dwarfs (Fig. 2), mevap ≃ 0.7 GeV. According to Garani and Sergio, the fact that, these objects are optimal sites to search for effects of capture of light DM particles has been pointed out recently in many papers. Nevertheless, those papers neglected the crucial exponential tail of the evaporation rate and estimated a DM evaporation mass as low as ∼ 4.5 MeV, which represents an underestimation of the correct result by two orders of magnitude. Similarly, a too low DM evaporation mass for planets has also been suggested using similar arguments. Therefore, they argued that the conclusions reached in those papers for masses below the correct DM evaporation mass are not valid.

Finally, they stressed again, the general and robust result they obtained: for the geometric cross section, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by the simple expression Ec/Tχ ∼ 30, which provides the correct result within ≲ 30% in the mass range 10¯10 M ≤ M ≤ 10² M and in the SI scattering cross section range 10¯41 cm² ≤ σp ≤ 10¯31 cm². The dependence on the local galactic DM density, velocity, and on the scattering and annihilation cross sections is only logarithmic.

Reference: Raghuveer Garani, Sergio Palomares-Ruiz, “Evaporation of dark matter from celestial bodies”, Arxiv, pp. 1-31, 2021.

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