arXiv:1001.2737v3 [hep-ph] 26 May 2010 Capture of Inelastic Dark Matter in White Dwarves Matthew McCullough ∗ Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK Malcolm Fairbairn † Physics, King’s College London, Strand, WC2R 2LS, UK (Dated: October 31, 2018) We consider the capture of inelastic dark matter in white dwarves by inelastic spin-independent scattering on nuclei. We show that if the dark matter annihilates to standard-model particles then, under the assumption of primordial globular cluster formation, the observation of cold white dwarves in the globular cluster M4 appears inconsistent with explanations of the observed DAMA/LIBRA annual modulation signal based on spin-independent inelastic dark matter scattering. Alternatively if the inelastic dark matter scenario were to be confirmed and it was found to annihilate to standard- model particles then this would imply a much lower dark matter density in the core of M4 than would be expected if it were to have formed in a dark matter halo. Finally we argue that cold white dwarves constitute a unique dark matter probe, complementary to other direct and indirect detection searches. Many models of dark matter (DM), in particular those models where the DM abundance is a consequence of thermal freeze-out, require the annihilation of DM into standard-model particles which usually implies a non- zero DM-nucleon interaction cross-section. These two properties can be constrained by a variety of observa- tions. The annihilation cross-section and products can be constrained by the requirement that DM particles are not overproduced during thermal freeze-out and/or by limits on fluxes of standard model particles that would arise from DM annihilation in the galactic halo. The DM-nucleon cross-section can be constrained by direct detection experiments which search for the recoil energy deposited when DM scatter off nuclei. Limits on a com- bination of the DM-nucleon cross-section and the partic- ular annihilation products can be placed by considering the flux of neutrinos that would result from DM capture and subsequent annihilation in the Sun or Earth. It has also been pointed out in [1, 2] that as white dwarves (hereafter WDs) have no internal energy source, and many cold WDs have now been observed, it is pos- sible to set limits on the DM-nucleon cross-section by showing that the energy released by the annihilation of DM particles in their core could contribute significantly to the luminosity of the star. An interesting possibility for DM-nucleon interactions is that the DM could predominantly scatter off nucleons inelastically to an excited energy state, so-called ‘inelas- tic dark matter’ (iDM). This idea has been proposed as a possible explanation [3–5] for the annual modulation signal observed by the DAMA collaboration [6, 7]. The key feature in iDM is the mass splitting, δ , between DM The converse is true for limits on capture in WDs as it is the deposited energy that is used to set the lim- its, and annihilation to neutrinos will only deposit a small amount of energy in the WD. Therefore models of DM that attempt to explain the DAMA annual modula- tion observation with the iDM mechanism, in particular models that also aim to offer an explanation of recent PAMELA [13] and Fermi LAT [14] observations through DM annihilation, are subject to limits from capture in WDs. Limits on iDM from capture in the Sun [8–10] are promising as the escape velocity of the Sun, v$_{esc}$ ∼ 600 − 1300 km s − $^{1}$, is large enough to provide sufficient energy to in-falling DM particles to overcome inelastic splittings δ ∼ 100 keV. Although these limits are ham- pered by the difficulty of detecting neutrinos, progress in neutrino telescope exposure means strong limits exist on particular models of iDM, for example, limits on sneu- trino iDM have been studied in [11]. However, models of iDM that annihilate predominantly to e $^{+}$e $^{−}$, µ $^{+}$µ $^{−}$, γγ , light hadrons or gluons are immune to these limits as these particles either stop before decaying and produc- ing neutrinos or don’t produce neutrinos at all. In these cases the energy deposited in the Sun from DM annihi- lations is swamped by the internal energy due to fusion. Therefore models of the class described in [12] can evade limits from solar capture. The main physical consequence of the inelastic split- ting is that the minimum velocity for a DM particle to scatter off a nucleus and impart an energy E$_{R}$ is in- creased. This can severely weaken the sensitivity of di- rect detection experiments as the number of particles in the halo with a large enough velocity to scatter can be very small, or even zero in some cases. As a consequence the allowed DM-nucleon cross-sections can be orders of magnitude larger than for elastic scattering. particles that scatter off nuclei. For iDM explanations of the DAMA/LIBRA annual modulation δ is of the order 30 − 130 keV (depending on DM mass and couplings). $^{∗}$Electronic address: mccull@thphys.ox.ac.uk $^{†}$Electronic address: malcolm.fairbairn@kcl.ac.uk I. INTRODUCTION