Photoelectric heating for dust grains at high redshifts
  Lyman-$\alpha$ absorption systems at $z \sim 3$ with $N_{HI} \ga 3 \times 10^{14}$ cm$^{-2}$ have been found to be enriched with a mean metallicity of $Z/Z_{\odot} \sim 10^{-2.5}$, and a large scatter in the metallicity. It is reasonable to assume that the process of initial enrichment of the intergalactic medium (IGM) at $z \ga 3$ also produced dust grains. We explore the implications of the presence of dust grains in the IGM at high redshift, in particular, the contribution of photoelectric emission from grains by hard background photons to the net heating rate of the IGM.   We show that (i) the charge on dust particles and the characteristics of photo-emitted electrons differ substantially from those in the interstellar medium (ISM) in several respects: a) grains are exposed to and charged by photons beyond the Lyman limit, and b) because of this, the photoelectrons have typical energy of tens of eV. We also show that ii) silicates are more efficient heating agents than graphites; iii) small grains contribute mostly to the net heating; iv) at densities typical of the IGM at $z\sim 3$ and for Lyman-$\alpha$ absorbers, dust heating can be comparable or exceed photoionization heating within an order of magnitude; v) this increases the temperature of overdense regions, compared to the case of no dust heating, by factor of $\sim 2$. We discuss the implications of this extra heating source in Lyman-$\alpha$ absorbing systems. 
Biman Nath (RRI, India), Shiv Sethi (IAP, France) and Yuri Shchekinov   (OAA, Italy; Rostov State University, Russia)