The Synchrotron Emission Pattern of IntraBinary Shocks

We model millisecond pulsars winds colliding with radiatively-driven companion winds in black widow and redback systems. For the redbacks, the geometry of this intrabinary shock (IBS) is quite sensitive to the expected equatorial concentration in the pulsar outflow. We thus analytically extend IBS thin-shock models to $\sim \sin^{2n}\theta$ pulsar winds. We compute the synchrotron emission from such shocks, including the build-up and cooling of the particle population as it accelerates along the IBS. For reasonable parameters, this IBS flux dominates the binary emission in the X-ray band. The modeling shows subtle variation in spectrum across the IBS peak, accessible to sensitive X-ray studies. As example applications, we fit archival CXO/XMM data from the black widow pulsar J1959+2048 and the redback PSR J2339-0533, finding that the model reproduces well the orbital light curve profiles and energy spectra. The results show a very hard injected electron spectrum, indicating likely dominance by reconnection. The light curve fitting is sensitive to the geometric parameters, including the very important orbital inclination $i$. Coupled with optical fits of the companion star, such IBS X-ray light curve modeling can strongly constrain the binary geometry and the energetics of the MSP wind.