Phenomenological constraints on accretion of non-annihilating dark matter on the PSR B1257+12 pulsar from orbital dynamics of its planets

An increasing number of observations at galactic, extragalactic and cosmological scales, if interpreted in the framework of the presently accepted Newtonian/Einsteinian laws of gravitation, requires the existence of huge amounts of a peculiar kind of matter which does not emit electromagnetic radiation: the so-called Dark Matter (DM). It cannot be of baryonic nature. Indeed, measurements of the baryon density in the Universe using the Cosmic Microwave Background (CMB) spectrum and primordial nucleosynthesis constrain the baryon density to a value less than 5% of the critical density ρ crit . Instead, the total density of clustered matter, obtained from Supernovae-based measurements of the recent expansion history of the Universe, CMB measurements of the degree of spatial flatness, and measurements of the amount of matter in galaxy structures obtained through big galaxy redshift surveys, is about 27% of the critical density. Thus, about 22% of it must exist in an exotic, unknown form. For reviews of both theoretical and observational aspects of the DM paradigm, see, e.g., Bergström (2000); Gondolo (2004); Bertone et al. (2005).

If DM exists, it should be present in all astrophysical objects; it may both be there since their formation process and it may subsequently be accreted from the surrounding environment. In recent years much efforts have been devoted to investigate the phenomenon of possible capture of DM by neutron stars (Goldman & Nussinov 1989;Gould et al. 1990;Bertone & Fairbairn 2008;Kouvaris 2008;Sandin & Ciarcelluti 2009;Ciarcelluti & Sandin 2010;de Lavallaz & Fairbairn 2010;Kouvaris & Tinyakov 2010;Gonzalez & Reisenegger 2010). Indeed, such compact objects should efficiently capture DM because of their high matter density. The content of DM depend on the nature of its particles, the type of hosting celestial bodies and their history. Moreover, new precise results from observations of neutron stars are becoming more frequently available. Thus, at least in principle, they are considered as potentially useful tools to independently constraining various aspects of DM models like density, cross section and mass of their particles. Such parameters are also crucial in determining the capabilities of several Earth-based laboratory experiments like CDMSI (Akerib et al. 2003), CDMSII (Ahmed et al. 2010), DAMA/NaI (Bernabei et al. 2003) and its successor DAMA/LIBRA (Bernabei et al. 2008), XENON10 (Angle et al. 2009) and ZEPLIN III (Summer 2005) aimed to directly detect DM.

According to the widely popular Weakly Interacting Massive Particle (WIMP) scenario, DM annihilates with itself and interacts with the rest of the Standard Model (SM) via the weak interaction. The WIMP is typically defined as a stable, electrically neutral, massive particle which arises naturally in supersymmetric SM extensions (Haber & Kane 1985). A pair of WIMPs can annihilate, producing ordinary particles and gamma rays. Self-annihilating particles captured by neutron stars would contribute to alter their outward appearances because the energy released in their annihilation would affect their internal and surface temperatures (Goldman & Nussinov 1989;Kouvaris 2008;de Lavallaz & Fairbairn 2010;Kouvaris & Tinyakov 2010;Gonzalez & Reisenegger 2010). On the other hand, WIMPs do not steadily accrete onto neutron stars and do not substantially modify their inner structure by, e.g., inducing a massive DM core which may notably alter the gravitational collapse (see, instead, Section 1.3.1)..

On the other hand, models of DM exist in which it does not undergo self-annihilation (Nussinov 1985;Kaplan 1992;Hooper et al. 2005); it may happen, for example, if DM is made of fermions, without the corresponding antifermions, or if DM consists of bosons and carries one sign of an additive conserved quantum number, but not the opposite sign. Among such scenarios there is the mirror matter one (Blinnikov & Khlopov 1982;Khlopov et al. 1991;Khlopov 1999;Foot 2004a;Okun’ 2007;Foot 2008;Blinnikov 2010). The possible existence of such an exotic form of matter was envisaged for the first time in the pioneeristic works by Lee & Yang (1956) and, later, by Kobzarev et al. (1966) and Pavšič (1974); the modern form of such an idea was laid out by Foot et al. (1991). Mirror matter arises if instead of (or in addition to) assuming a symmetry between bosons and fermions, i.e. supersymmetry, one assumes that nature is parity symmetric. In such a framework, in order to restore the parity symmetry violated by the weak interactions, the number of particles in the Standard Model is doubled in such a way that the Universe is divided into two sectors with opposite handedness that interact mainly by gravity. On the other hand, parity can also be spontaneously broken depending on the Higgs potential (Berezhiani & Mohapatra 1995;Foot et al. 2000). While in the case of unbroken parity symmetry the masses of particles are the same as their mirror partners, in case of broken pa

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