The X-ray Variability and Luminosity Function of High Mass X-ray Binaries in the Dwarf Starburst Galaxy IC 10

We present an analysis of $\sim$235 ks of Chandra observations obtained over $\sim$19 years of the nearby dwarf starburst galaxy IC 10 in order to study the X-ray variability and X-ray luminosity function (XLF) of its X-ray binary (XRB) population. We identify 23 likely XRBs within the 2MASS $K_S$ isophotal radius and find the distributions of their dynamic ranges and duty cycles are consistent with a young, high-mass XRB population dominated by supergiant (sg)-fed systems, consistent with previous work. In general, we find that brighter HMXBs (those with $L_X\gtrsim$several$\times10^{36}$ erg s$^{-1}$) have higher duty cycles (i.e., are more persistent X-ray sources) than fainter objects, and the dynamic ranges of the sgHMXBs in the lower metallicity environment of IC 10 are higher than what is observed for comparable systems in the Milky Way. After filtering out foreground stars on the basis of Gaia parallaxes we construct, for the first time, the XLF of IC 10. We then use the XLF to model the star formation history of the galaxy, finding that a very recent (3-8 Myr) burst of star formation with rate of $\sim$0.5 $M_{\odot}$ yr$^{-1}$ is needed to adequately explain the observed bright-end ($L_X\sim10^{37}$ erg s$^{-1}$) of the HMXB XLF.