Cosmic rays, lithium abundance and excess entropy in galaxy clusters

We consider the production of 6Li in spallation reactions by cosmic rays in order to explain the observed abundance in halo metal-poor stars. We show that heating of ambient gas by cosmic rays is an inevitable consequence of this process, and estimate the energy input required to reproduce the observed abundance of 6Li/H ~ 10-11 to be of the order of a few hundred eV per particle. We draw attention to the possibility that this could explain the excess entropy in gas in galaxy groups and clusters. The evolution of 6Li and the accompanying heating of gas are calculated for structures collapsing at the present epoch with injection of cosmic rays at high redshift. We determine the energy required to explain the abundance of 6Li at z ~ 2 corresponding to the formation epoch of halo metal-poor stars, and also an increased entropy level of ~300 keV cm2 necessary to explain X-ray observations of clusters. The energy budget for this process is consistent with the expected energy output of radio-loud active galactic nuclei, and the diffusion length-scale of cosmic ray protons responsible for heating is comparable to the size of regions with excess entropy. We also discuss the constraints imposed by the extragalactic gamma-ray background.