V746 Cas is known to be a triple system composed of a close binary with an alternatively reported period of either 25\hbox{$.\!\!^{\rm d}$}4 or 27\hbox{$.\!\!^{\rm d}$}8 and a distant third component in a 170 yr (62 000 d) orbit. The object was also reported to exhibit multiperiodic light variations with periods from 0\hbox{$.\!\!^{\rm d}$}83 to 2\hbox{$.\!\!^{\rm d}$}50, on the basis of which it was classified as a slowly pulsating B star. Interest in further investigation of this system was raised by the recent detection of a variable magnetic field. Analysing spectra from four instruments, earlier published radial velocities, and several sets of photometric observations, we arrived at the following conclusions: (1) The optical spectrum is dominated by the lines of the B-type primary (Teff 1 ~ 16 500(100) K), contributing 70% of the light in the optical region, and a slightly cooler B tertiary (Teff 3 ~ 13 620(150) K). The lines of the low-mass secondary are below our detection threshold; we estimate that it could be a normal A or F star. (2) We resolved the ambiguity in the value of the inner binary period and arrived at a linear ephemeris of \hbox{$T_{\rm super.\,conj.}={\rm HJD}~2\,443\,838.78(81)+25\fd41569(42)\times E$}. (3) The intensity of the magnetic field undergoes a sinusoidal variation in phase with one of the known photometric periods, namely 2\hbox{$.\!\!^{\rm d}$}503867(19), which we identify with the rotational period of the tertiary. (4) The second dominant photometric 1\hbox{$.\!\!^{\rm d}$}0649524(40) period is tentatively identified with the rotational period of the broad-lined B-type primary, but this interpretation is much less certain and needs further verification. (5) If our interpretation of photometric periods is confirmed, the classification of the object as a slowly pulsating B star should be revised. (6) Applying an N-body model to different types of available observational data, we can constrain the orbital inclination of the inner orbit to ~60°<i1< 85° even in the absence of binary eclipses, and we estimate the probable properties of the triple system and its components.
Semiclassical 3D Neumann Laplacian with Variable Magnetic Field: A Toy Model
