On the Mv(peak) versus orbital period relation for dwarf nova outbursts

We present computations for the accretion disk limit cycle model in an attempt to explain the empirical relation for dwarf nova outbursts between the peak visual absolute magnitude and orbital period found by Warner. For longer period systems one sees intrinsically brighter outbursts. This is accounted for in the limit cycle model by the scaling with radius of the critical surface density Sigma(max) that triggers the dwarf nova outbursts. During the storage phase of the instability, the accretion disk mass must be less than some maximum value, a value that scales with radius and therefore with orbital period. When the instability is triggered and the accumulated mass is redistributed into a quasi-steady state disk in outburst, the resultant peak optical flux from the disk is a measure of the total mass that was stored in quiescence. We compute light curves for a range in outer disk radius (or equivalently, orbital period), and find that our peak values of M-V are within less than 1 mag of the observed relation M-V(peak) = 5.64 - 0.259P(orbital) for 2 less than or similar to P-orbital less than or similar to 8, where P-orbital is in hours.