INTRA-BINARY SHOCK HEATING OF BLACK WIDOW COMPANIONS

The low-mass companions of evaporating binary pulsars (black widows and similar) are strongly heated on the side facing the pulsar. However, in high-quality photometric and spectroscopic data, the heating pattern does not match that expected for direct pulsar illumination. Here we explore a model where the pulsar power is intercepted by an intra-binary shock (IBS) before heating the low-mass companion. We develop a simple analytic model and implement it in the popular ICARUS light curve code. The model is parameterized by the wind momentum ratio beta and the companion wind speed f(v) v(orb), and assumes that the reprocessed pulsar wind emits prompt particles or radiation to heat the companion surface. We illustrate an interesting range of light curve asymmetries controlled by these parameters. The code also computes the IBS synchrotron emission pattern, and thus can model black widow X-ray light curves. As a test, we apply the results to the high-quality asymmetric optical light curves of PSR J2215 +5135; the resulting fit gives a substantial improvement upon direct heating models and produces an X-ray light curve consistent with that seen. The IBS model parameters imply that at the present loss rate, the companion evaporation has a characteristic timescale of tau(evap) approximate to 150 Myr. Still, the model is not fully satisfactory, indicating that there are additional unmodeled physical effects.