A massive AGB donor in Scutum X-1: Identification of the first Mira variable in an X-ray binary

The symbiotic X-ray binary Sct X-1 was suggested as the first known neutron star accreting from a red supergiant companion. Although known for nearly 50 years, detailed characterization of the donor remains lacking, particularly due to the extremely high reddening towards the source ($A_V\gtrsim25$ mag). Here, we present i) improved localization of the counterpart using Gaia and Chandra observations, ii) the first broadband infrared spectrum ($\approx1-5\,\mu$m; $R\approx 2000$) obtained with SpeX on the NASA Infrared Telescope Facility and iii) $J$-band light curve from the Palomar Gattini-IR survey. The infrared spectrum is characterized by i) deep water absorption features (H$_2$O index $\approx 40$%), ii) strong TiO, VO and CO features, and iii) weak/absent CN lines. We show that these features are inconsistent with known red supergiants, but suggest a M8-9 III type O-rich Mira donor star. We report the discovery of large amplitude ($\Delta J\approx3.5$ mag) periodic photometric variability suggesting a pulsation period of $621\pm36\,{\rm(systematic)}\pm8\,{\rm(statistical)}$ days, which we use to constrain the donor to be a relatively luminous Mira ($M_K=-8.6\pm0.3$ mag) at a distance of $3.6^{+0.8}_{-0.7}$ kpc. Comparing these characteristics to recent models, we find the donor to be consistent with a $\approx 3-5$ M$_\odot$ star at an age of $\approx 0.1-0.3$ Gyr. Together, we show that Sct X-1 was previously mis-classified as an evolved High Mass X-ray Binary; instead it is an intermediate mass system with the first confirmed Mira donor in an X-ray binary. We discuss the implications of Mira donors in symbiotic X-ray binaries, and highlight the potential of wide-field infrared time domain surveys and broadband infrared spectroscopy to unveil their demographics.