Two observations of V959 Mon, done using the Chandra X-ray gratings during the late outburst phases (2012 September and December), offer extraordinary insight into the physics and chemistry of this Galactic ONe nova. the X-ray flux was 1.7 x 10(-11) erg/cm(2)/s and 8.6 x 10(-12) erg/cm(2)/s, respectively at the two epochs. The first result, coupled with electron density diagnostics and compared with published optical and ultraviolet observations, indicates that most likely in 2012 September the X-rays originate from a very small fraction of the ejecta, concentrated in very dense clumps. We obtained a fairly good fit to the September spectrum with a model of plasma in collisional ionization equilibrium (CIE) with two components; one at a temperature of 0.78 keV, blueshifted by 710-930 km/s, the other at a temperature of 4.5 keV, mostly contributing to the high-energy continuum. However, we cannot rule out a range of plasma temperatures between these two extremes. In December, the central white dwarf (WD) became visible in X-rays. We estimate an effective temperature of about 680,000 K, consistent with a WD mass ~1.1 M(sol). The WD flux is modulated with the orbital period, indicating high inclination, and two quasi-periodic modulations with hour timescales were also observed. No hot plasma component with temperature above 0.5 keV was observed in December, and the blue-shifted component cooled to kT~0.45 keV. Additionally, new emission lines due to a much cooler plasma appeared, which were not observed two months earlier. We estimate abundances and yields of elements in the nova wind that cannot be measured in the optical spectra and confirm the high Ne abundance previously derived for this nova. We also find high abundance of Al, 230 times the solar value, consistently with the prediction that ONe novae contribute to at least 1/3rd of the Galactic yield of Al(26).
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