We report the discovery of the first short period binary in which a hot subdwarf star ( sdOB ) fills its Roche lobe and started mass transfer to its companion .
The object was discovered as part of a dedicated high-cadence survey of the Galactic Plane named the Zwicky Transient Facility and exhibits a period of P = 39.3401 ( 1 ) min , making it the most compact hot subdwarf binary currently known .
Spectroscopic observations are consistent with an intermediate He-sdOB star with an effective temperature of T _ { eff } = 42 , 400 \pm 300 K and a surface gravity of \log ( g ) = 5.77 \pm 0.05 .
A high-signal-to noise GTC+HiPERCAM light curve is dominated by the ellipsoidal deformation of the sdOB star and an eclipse of the sdOB by an accretion disk .
We infer a low-mass hot subdwarf donor with a mass M _ { sdOB } = 0.337 \pm 0.015 M _ { \odot } and a white dwarf accretor with a mass M _ { WD } = 0.545 \pm 0.020 M _ { \odot } .

Theoretical binary modeling indicates the hot subdwarf formed during a common envelope phase when a 2.5 - 2.8 M _ { \odot } star lost its envelope when crossing the Hertzsprung Gap .
To match its current P _ { orb } , T _ { eff } , \log ( g ) , and masses , we estimate a post-common envelope period of P _ { orb } \approx 150 min , and find the sdOB star is currently undergoing hydrogen shell burning .
We estimate that the hot subdwarf will become a white dwarf with a thick helium layer of \approx 0.1 M _ { \odot } and will merge with its carbon/oxygen white dwarf companion after \approx 17 Myr and presumably explode as a thermonuclear supernova or form an R CrB star .