Limits on non-canonical heating and turbulence in the intergalactic medium from the low redshift Lyman α forest

We examine the column density distribution function (CDDF) and Doppler parameter distribution from hydrodynamical simulations and Cosmic Origins Spectrograph (COS) observations of the Ly alpha forest at redshift 0 <= z <= 0.2. Allowing for a factor of two uncertainty in the metagalactic H I photoionization rate, our hydrodynamical simulations are in good agreement (1-1.5 sigma) with the shape and amplitude of the observed CDDF at H I column densities 10(13.3 )cm(-2) <= N-H I <= 10(14.5) cm(-2). However, the Doppler widths of the simulated lines remain too narrow with respect to the COS data. We argue that invoking AGN feedback does not resolve this discrepancy. We also disfavour enhanced photoheating rates as a potential solution, as this requires an unphysically hard UV background spectrum. If instead appealing to a non-canonical source of heating, an additional specific heat injection of u less than or similar to 6.9 eV m(p)(-1) is required at z less than or similar to 2.5 for gas that has N-H I similar or equal to 10(13.5) cm(-2) by z = 0.1. Alternatively, there may be an unresolved line of sight turbulent velocity component of nu(turb) less than or similar to 8.5 km s(-1) (N-H I/10(13.5) cm(-2))(0.21) for the coldest gas in the diffuse IGM.