Local Dark Matter Clumps and the Positron Excess

1. Positron spectra from neutralino annihilation Positron fraction vs. HEAT observations In figures 3-6, we display the local positron fraction, calculated for four benchmark MSSM models. We compare these to the observations by HEAT, recorded during its 1994 -1995 flight (red points) and its 2000 flight (blue points), where the bars correspond to 1σ error ranges. In each case the normalisation of the positron flux was left as a free parameter and altered to deduce the best-fitting (solid lines) and 1σ range (dashed) of positron fraction’s. Positrons resulting from neutralino annihilation can result from the decay of gauge bosons in the processes χ χ →ZZ or χ χ →W + W - , producing positrons of energy ~mχ /2. Alternatively, they can also be produced with a continuum of energies resulting from the cascades of particles produced in the initial annihilations. In figure1, we display the positron spectra utilised in our study. Fig. 1The solid lines represent the positron yield, per annihilation, dφ/dEe+ from the process χ χ → , for 50, 150 and 600GeV neutralinos (bottom to top). Dotted lines are the same, but correspond to the process χ χ → τ+ τ -. The dashed line correspond to the process χ χ →W+W- (or χ χ →ZZ) for a 150GeV neutralino. Fig. 4 Positron fraction as a function of energy (in GeV), for a 150GeV neutralino which annihilates to 96% of the time and 4% to t+t-. Fig. 3 Positron fraction as a function of energy (in GeV), for a 50GeV neutralino which annihilates to 96% of the time and 4% to t+t-. Positron propagation in the ISM Cosmic ray positrons diffuse through the interstellar medium under the influence of the Galactic magnetic field and background radiation, losing energy through synchrotron emission and inverse Compton scattering processes. We solve the diffusion-loss equation for the local positron flux resulting from dark matter annihilations within substructures located within the Galactic halo. We utilise the substructure mass distribution determined from the high-resolution simulations conducted by Diemand et al. (Nature, 433, 389 (2005)). The resulting distribution proved to be very similar to that of the present Galactic halo, which scales approximately as dn/dlgMM-1. Therefore, we adopted this distribution to describe the present Galactic subhalo population for the range of subhalo masses investigated by Diemand et al., which were as light as 10-6 solar masses. The rate of dark matter annihilations within a dark matter clump crucially depends on its density profile. Here, we utilised the widely adopted NFW profile, which, as displayed in figure 2, provides a good fit to the profiles of the lightest clumps produced in Diemand et al.'s simulations. Fig. 5 Positron fraction as a function of energy (in GeV), for a 600GeV neutralino which annihilates to bb 87% of the time and 13% to t+t- or . Fig. 6 Positron fraction as a function of energy (in GeV), for a 150GeV neutralino which annihilates entirely to W + W - or ZZ. Fig. 2 Radial density profile of the clumps utilised in our study. The profile, deduced in simulations conducted by Diemand et al. (Nature, 433, 389 (2005)), is typical of the Earth-mass clumps produced. The profile is well approximated to a radial power-law of slope ~1.61, which is shown here fitted to the simulation data. Local Dark Matter Clumps and the Positron Excess astro-ph/0602320, accepted by Monthly Notices of the RAS D.T Cumberbatch (dtc@astro.ox.ac.uk) and J. Silk(silk@astro.ox.ac.uk)Department of Astrophysics, University of Oxford, Keble Road, Oxford, OX1 3RH. It has been proposed that the excess in cosmic ray positrons, occurring at approximately 8 GeV, observed on both flights of the HEAT balloon experiment, may be associated with the annihilation of dark matter within the Milky Way. In this paper we demonstrate how the annihilation of neutralino dark matter within local substructures can account for this excess, and we estimate the range of annihilation cross-sections necessary to reconcile with observations, for several benchmark minimal supersymmetric (MSSM) models. We also demonstrate the changes in the permitted parameter space as substructures become increasingly tidally disrupted. Can stripped clumps produce a positron excess? We incorporated the effects of tidal-stripping by stars passing clumps as they orbited the Galactic halo, estimated using the model outlined by Zhao et al. (astro-ph/0508215). Our results indicate that neutralino annihilations within local dark matter substructure can give rise to local positron fluxes, which reconcile with observations, for values of ranging from 3x10-28 cm3 s-1, for 50 GeV neutralinos, to 4x10-26 cm3 s-1, for 600 GeV neutralinos. Despite the fact that the majority of these values are at least an order of magnitude smaller than the canonical value of 3x10-26 cm3 s-1, we highlight that many conventional MSSM models exist in which this approximation is grossly violated and are easily able to accommodate our results, where the number of such models rapidly increases for lighter neutralinos. We observed that even with up to 99% stripping, and varying the clump concentration over a range consistent with simulations, the best-fit values of do not change by more than a factor of 2. We also observed that even if we change the lower mass cut-off in our subhalo mass distribution from 8x10-6 solar masses to 106 solar masses, the best-fit values of increase by no more than a factor of 5, but are consequently consistent with a larger region of MSSM parameter space.