We present an analysis of the X-ray spectrum and long-term variability of the nearby dwarf starburst galaxy Henize 2-10. Recent observations suggest that this galaxy hosts an actively accreting black hole with mass ~10^6 M_sun. The presence of an AGN in a low-mass starburst galaxy marks a new environment for active galactic nuclei (AGNs), with implications for the processes by which seed black holes may form in the early Universe. In this paper, we analyze four epochs of X-ray observations of Henize 2-10, to characterize the long-term behavior of its hard nuclear emission. We analyze observations with Chandra from 2001 and XMM-Newton from 2004 and 2011, as well as an earlier, less sensitive observation with ASCA from 1997. Based on detailed analysis of the source and background, we find that the hard (2-10 keV) flux of the putative AGN has decreased by approximately an order of magnitude between the 2001 Chandra observation and exposures with XMM-Newton in 2004 and 2011. The observed variability confirms that the emission is due to a single source. It is unlikely that the variable flux is due to a supernova or ultraluminous X-ray source, based on the observed long-term behavior of the X-ray and radio emission, while the observed X-ray variability is consistent with the behavior of well-studied AGNs.
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