Models of type I X-ray bursts from 4U 1820-30

I present ignition models for type I X-ray bursts and superbursts from the ultracompact binary 4U 1820-30. A pure helium secondary is usually assumed for this system (which has an orbital period approximate to11 minutes); however, some evolutionary models predict a small amount of hydrogen in the accreted material (mass fraction X similar to 0.1). I show that the presence of hydrogen significantly affects the type I burst recurrence time if X greater than or similar to 0.03 and the CNO mass fraction greater than or similar to3 x 10(-3). When regularly bursting, the predicted burst properties agree well with observations. The observed 2-4 hr recurrence times are reproduced for a pure He companion if the time-averaged accretion rate is ((M))over dot approximate to (7-10) x 10(-9) M(circle dot) yr(-1) or a hydrogen-poor companion if ((M))over dot approximate to (4-6) x 10(-9) M(circle dot) yr(-1). This result provides a new constraint on evolutionary models. The burst energetics are consistent with complete burning and spreading of the accreted fuel over the whole stellar surface. Models with hydrogen predict similar to10% variations in burst fluence with recurrence time, which could perhaps distinguish the different evolutionary scenarios. I use the accretion rates determined by matching the type I burst recurrence times to predict superburst properties. The expected recurrence times are approximate to1-2 yr for pure He accretion (much less than that found by Strohmayer Brown) and approximate to5-10 yr if hydrogen is present. Determination of the superburst recurrence time would strongly constrain the local accretion rate and thermal structure of the neutron star.