ROSAT PSPC observations of the outer regions of the Perseus cluster of galaxies

We present an analysis of four off-axis ROSAT PSPC observations of the Perseus cluster of galaxies (Abell~426). We detect the surface brightness profile to a radius of 80 arcmin ($\sim 2.4 h_{50}^{-1}$ Mpc) from the X-ray peak. The profile is measured in various sectors and in three different energy bands. Firstly, a colour analysis highlights a slight variation of $N_{H}$ over the region, and cool components in the core and in the eastern sector. We apply the $\beta$-model to the profiles from different sectors and present a solution to the, so-called, $\beta$-problem. The residuals from an azimuthally-averaged profile highlight extended emission both in the East and in the West, with estimated luminosities of about 8 and 1 $\times 10^{43} erg/s$, respectively. We fit several models to the surface brightness profile, including the one obtained from the Navarro, Frenk and White (1995) potential. We obtain the best fit with the gas distribution described by a power law in the inner, cooling region and a $\beta$-model for the extended emission. Through the best-fit results and the constraints from the deprojection of the surface brightness profiles, we define the radius where the overdensity inside the cluster is 200 times the critical value, $r_{200}$, at $2.7 h_{50}^{-1}$ Mpc. Within $2.3 h_{50}^{-1}$ Mpc ($0.85 r_{200}$), the total mass in the Perseus cluster is $1.2 \times 10^{15} M_{\odot}$ and its gas fraction is about 30 per cent.