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When the disc's away, the stars will play: dynamical masses in the nova-like variable KR Aur with a pinch of accretion

We obtained time-resolved optical photometry and spectroscopy of the nova-like variable KR Aurigae in the low state. The spectrum reveals a DAB white dwarf and a mid-M dwarf companion. Using the companion star's $i$-band ellipsoidal modulation we refine the binary orbital period to be $P = 3.906519 \pm 0.000001$ h. The light curve and the spectra show flaring activity due to episodic accretion. One of these events produced brightness oscillations at a period of 27.4 min, that we suggest to be related with the rotation period of a possibly magnetic white dwarf at either 27.4 or 54.8 min. Spectral modelling provided a spectral type of M4-5 for the companion star and $T_{1}=27148 \pm 496$ K, $\log g=8.90 \pm 0.07$, and $\log (\mathrm{He/H})= -0.79^{+0.07}_{-0.08}~~$ for the white dwarf. By simultaneously fitting absorption- and emission-line radial velocity curves and the ellipsoidal light curve, we determined the stellar masses to be $M_1 = 0.94^{+0.15}_{-0.11}~$ $M_\odot$ and $M_2 = 0.37^{+0.07}_{-0.07}~$ $M_\odot$ for the white dwarf and the M-dwarf, respectively, and an orbital inclination of $47^{+1^{\rm o}}_{-2^{\rm o}}$. Finally, we analyse time-resolved spectroscopy acquired when the system was at an $i$-band magnitude of 17.1, about 1.3 mag brighter than it was in the low state. In this intermediate state the line profiles contain an emission S-wave delayed by $\simeq 0.2$ orbital cycle relative to the motion of the white dwarf, similar to what is observed in SW Sextantis stars in the high state.