Clumpiness of dark matter and the positron annihilation signal

¹ Centre de Physique des Particules CPPM, CNRS-IN2P3/Université de la Méditerranée, 13288 Marseille, France e-mail: taillet@lapp.in2p3.fr
² Laboratoire de Physique des Particules LAPP, 74941 Annecy-le-Vieux, France
³ Université de Savoie, 73011 Chambéry, France
⁴ Laboratoire de Physique Théorique LAPTH, 74941 Annecy-le-Vieux, France

Received: 29 March 2006
Accepted: 20 August 2006

Abstract

Context.The small-scale distribution of dark matter in galactic halos is poorly known. Several studies suggest that it could be very clumpy, which is of paramount importance when investigating the annihilation signal from exotic particles (e.g. supersymmetric or Kaluza-Klein).

Aims.We focus on the annihilation signal in positrons. We estimate the associated uncertainty, that is due to the fact that we do not know exactly how the clumps are distributed in the Galactic halo.

Methods.We perform a statistical study based on analytical computations, as well as numerical simulations. We study the average and variance of the annihilation signal over many Galactic halos having the same statistical properties.

Results.We find that the so-called boost factor used by many authors should be used with caution, as i) it depends on energy and ii) it may be different for positrons, antiprotons and gamma rays, a fact which has not been discussed before. As an illustration, we use our results to discuss the positron spectrum measurements by the HEAT experiment.