With a spin frequency of 707 Hz, PSR J0952-0607 is the second fastest spinning pulsar known. It was discovered in radio by LOFAR in 2017 at an estimated distance of either 0.97 or 1.74 kpc and has a low-mass companion with a 6.42 hr orbital period. We report discovery of the X-ray counterpart of PSR J0952-0607 using XMM-Newton. The X-ray spectra can be well-fit by a single power law model (Gamma = 2.5) or by a thermal plus power law model (kTeff = 40 eV and Gamma = 1.4). We do not detect evidence of variability, such as that due to orbital modulation from pulsar wind and companion star interaction. Because of its fast spin rate, PSR J0952-0607 is a crucial source for understanding the r-mode instability, which can be an effective mechanism for producing gravitational waves. Using the high end of our measured surface temperature, we infer a neutron star core temperature of ~10^7 K, which places PSR J0952-0607 within the window for the r-mode to be unstable unless an effect such as superfluid mutual friction damps the fluid oscillation. The measured luminosity limits the dimensionless r-mode amplitude to be less than ~1x10^-9.
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