We have used the Advanced Camera for Surveys on board the Hubble Space Telescope to image the core of the globular cluster M15 in the far-ultraviolet (FUV) waveband. Based on these observations, we identify the FUV counterpart of the recently discovered low-mass X-ray binary M15 X-2. Our time-resolved FUV photometry shows a modulation with 0.062+/-0.004 mag semi-amplitude and we clearly detect a period of 22.5806+/-0.0002 min. We have carried out extensive Monte Carlo simulations which show that the signal is consistent with being coherent over the entire observational time range of more than 3000 cycles. This strongly suggests that it represents the orbital period of the binary system. M15 X-2 is FUV bright (approx. 17 mag) and is characterized by an extremely blue spectral energy distribution (F_lambda ~ lambda^{-2.0}). We also find evidence for an excess of flux between 1500 and 1600 AA and probably between 1600 and 2000 AA, which might be due to CIV 1550 and HeII 1640 emission lines. We also show that M15 X-2s X-ray luminosity can be powered by accretion at the rate expected for gravitational-wave-driven mass transfer at this binary period. The observed FUV emission appears to be dominated by an irradiated accretion disk around the neutron star primary, and the variability can be explained by irradiation of the low-mass white dwarf donor if the inclination of the system is approx. 34 degree. We conclude that all observational characteristics of M15 X-2 are consistent with it being an ultracompact X-ray binary, only the third confirmed such object in a globular cluster.
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