Gas density fluctuations in the Perseus Cluster: clumping factor and velocity power spectrum

X-ray surface brightness fluctuations in the core of the Perseus Cluster are analysed, using deep observations with the Chandra observatory. The amplitude of gas density fluctuations on different scales is measured in a set of radial annuli. It varies from 7 to 12 per cent on scales of similar to 10-30 kpc within radii of 30-220 kpc from the cluster centre. Using a statistical linear relation between the observed amplitude of density fluctuations and predicted velocity, the characteristic velocity of gas motions on each scale is calculated. The typical amplitudes of the velocity outside the central 30 kpc region are 90-140 km s(-1) on similar to 20-30 kpc scales and 70-100 km s(-1) on smaller scales similar to 7-10 kpc. The velocity power spectrum ( PS) is consistent with cascade of turbulence and its slope is in a broad agreement with the slope for canonical Kolmogorov turbulence. The gas clumping factor estimated from the PS of the density fluctuations is lower than 7-8 per cent for radii similar to 30-220 kpc from the centre, leading to a density bias of less than 3-4 per cent in the cluster core. Uncertainties of the analysis are examined and discussed. Future measurements of the gas velocities with the Astro-H, Athena and Smart-X observatories will directly measure the gas density-velocity perturbation relation and further reduce systematic uncertainties in this analysis.