Classical novae from the POINT-AGAPE microlensing survey of M31; 2 Rate and statistical characteristics of the nova population

We report the results of our statistical study of the POINT-AGAPE CNe catalogue. The first Sloan $r'$ and $i'$ analysis of the MMRD relationship in M31 is performed using the resulting POINT-AGAPE CN catalogue. Good fits are produced to the MMRD in the two filters. However, we are unable to verify the $t_{15}$ relationship for either Sloan filter. The subsequent analysis of our automated CN detection pipeline has provided us with the most thorough knowledge of the completeness of a CN survey to-date. In addition, the large field of view of the survey has permitted us to probe the outburst rate well into the galactic disk, unlike previous CCD imaging surveys. Using this analysis we are able to probe the CN distribution of M31 and evaluate the global nova rate. Using models of the galactic surface brightness of M31, we show that the observed CN distribution consists of a separate bulge and disk population. We also show that the M31 bulge CN eruption rate per unit $r'$ flux is more than five times greater than that of the disk. We deduce a global M31 CN rate of $65^{+16}_{-15}$ year$^{-1}$, a value much higher than found by previous surveys. Using the global rate, we derive a M31 bulge rate of $38^{+15}_{-12}$ year$^{-1}$ and a disk rate of $27^{+19}_{-15}$ year$^{-1}$. Given our understanding of the completeness and an analysis of other sources of error, we conclude that the true global nova rate of M31 is at least 50% higher than was previously thought and this has consequent implications for the presumed CN rate in the Milky Way. We deduce a Galactic bulge rate of $14^{+6}_{-5}$ year$^{-1}$, a disk rate of $20^{+14}_{-11}$ year$^{-1}$ and a global Galactic rate of $34^{+15}_{-12}$ year$^{-1}$.