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[en] Nova LMC 2009a is confirmed as a recurrent nova (RN) from positional coincidence with nova LMC 1971b. The observational data set is one of the most comprehensive for any Galactic or extragalactic RN: optical and near-IR photometry from outburst until over 6 years later; optical spectra for the first 6 months, and Swift satellite ultraviolet (UV) and X-ray observations from 9 days to almost 1 year post-outburst. We find MV = −8.4 ± 0.8r ± 0.7s and expansion velocities between 1000 and 4000 km s−1. Coronal line emission before day 9 indicates shocks in the ejecta. Strengthening of He iiλ4686 preceded the emergence of the super-soft source (SSS) in X-rays at ∼63–70 days, which was initially very variable. Periodic modulations, P = 1.2 days, most probably orbital in nature, were evident in the UV and optical from day 43. Subsequently, the SSS shows an oscillation with the same period but with a delay of 0.28P. The progenitor system has been identified; the secondary is most likely a sub-giant feeding a luminous accretion disk. Properties of the SSS infer a white dwarf (WD) mass 1.1 M⊙ ≲ MWD ≲ 1.3 M⊙. If the accretion occurs at a constant rate, yr−1 is needed, consistent with nova models for an inter-eruption interval of 38 years, low outburst amplitude, progenitor position in the color–magnitude diagram, and spectral energy distribution at quiescence. We note striking similarities between LMC 2009a and the Galactic nova KT Eri, suggesting that KT Eri is a candidate RN.