The Unique Cataclysmic Variable V Sge is Increasing Its Accretion With a Doubling Timescale of 89 Years and Will In-Spiral To Make a Red-Nova

The cataclysmic variable (CV) V Sagittae has a ~3.3 solar-mass main sequence star accreting by Roche lobe overflow onto a ~0.9 solar-mass carbon/oxygen white dwarf in a 0.514 day orbital period that shows eclipses. V Sge is unique in having a high mass ratio (q~3.3), with this necessarily driving unstable runaway accretion. Currently, V Sge is incredibly luminous for a CV with absolute magnitude up to -2.2, has an unprecedentedly large mass overflow rate of over 10^-5 solar-mass per year, and is driving a stellar wind at a rate up to 2.3x10^-5 solar-mass per year. We report on a light curve of 1531 Johnson B magnitudes from 1890-2017 and 68016 Johnson V magnitudes from 1904-2019. Both colors shows a clear brightening at an average rate of -0.84 ± 0.10 mag/century, so the accretion rate is rising with a doubling time of 89 ± 11 years. Further, we report on 162 eclipse times from 1909-2017 (showing a steady period change of -4.73x10^-10 days/cycle), the spectral energy distribution from radio to X-rays (with the single power law from radio to ultraviolet arising from the powerful stellar wind), and the distance of 2380 pc from the Gaia parallax (2240-2610 pc one-sigma). With this, we see V Sge to be in the late stages of its in-spiral, with the runaway accretion increasing exponentially on a fast time scale. The inevitable future evolution of V Sge is to keep in-spiraling, transferring mass at an ever-increasing rate, while in the last few months and days having most of the mass of the secondary star fall off to form a common envelope, then having the remaining CO core in-spiral on a time scale of days, ultimately reaching a configuration of a red giant (a CO white dwarf core surrounded by a massive envelope with a hydrogen burning layer). The star will appear as a so-called 'red nova', with the red giant left behind to last for many millions of years. The primary open question is the time from now until the final in-spiral, and the usual calculations and programs (e.g., MESA) are unable to handle this unique case.