The nova KT Eri Is a recurrent nova with a recurrence time-scale of 40-50 yr

KT Eridani was a very fast nova in 2009 peaking at V = 5.42 mag. We marshal large data sets of photometry to finally work out the nature of KT Eri. From the TESS light curve, as confirmed with our radial velocity curve, we find an orbital period of 2.61595 d. With our 272 spectral energy distributions from simultaneous BVRIJHK measures, the companion star has a temperature of 6200 ± 500 K. Our century-long average in quiescence has V = 14.5. With the Gaia distance (5110+920-430 pc), the absolute magnitude is MVq = +0.7 ± 0.3. We converted this absolute magnitude (corrected to the disc light alone) to accretion rates, Ṁ, with a full integration of the α-disc model. This Ṁ is very high at 3.5 × 10-7 M⊙ yr-1. Our search and analysis of archival photographs shows that no eruption occurred from 1928 to 1954 or after 1969. With our analysis of the optical light curve, the X-ray light curve, and the radial velocity curve, we derive a white dwarf mass of 1.25 ± 0.03 M⊙. With the high white dwarf mass and very-high Ṁ, KT Eri must require a short time to accumulate the required mass to trigger the next nova event. Our detailed calculations give a recurrence time-scale of 12 yr with a total range of 5-50 yr. When combined with the archival constraints, we conclude that the recurrence time-scale must be between 40 and 50 yr. So, KT Eri is certainly a recurrent nova, with the prior eruption remaining undiscovered in a solar gap of coverage from 1959 to 1969.