Photometric determination of rotation axis inclination, rotation rate, and mass of rapidly rotating intermediate-mass stars (2307.00082v2)

Abstract: Intermediate-mass stars are often fast rotators, and hence are centrifugally flattened and affected by gravity darkening. To analyse this kind of stars properly, one must turn to 2D models to compute the visible radiative flux and to take the geometrical effect of the star inclination into account. Assuming a given stellar age and chemical composition, we aim to derive the mass and rotation rates of main sequence fast rotating stars, along with their inclination, from photometric quantities. We chose three observables that vary with mass, rotation, and inclination: the infrared flux method temperature T_IRFM, the Str\"omgren c1 index, and a second index c2 built in the same way, but sensitive to the UV side of the Balmer jump. These observables are computed from synthetic spectra produced with the PHOENIX code and rely on a 2D stellar structure from the ESTER code. These quantities are computed for a grid of models in the range 2 to 7~M_Sun, and rotation rates from 30% to 80% of the critical rate. Then, for any triplet (T_IRFM, c1, c2), we try to retrieve the mass, rotation rate, and inclination using a Levenberg-Marquardt scheme, after a selection step to find the most suitable starting models. Hare-and-hound tests showed that our algorithm can recover the mass, rotation rate, and inclination with a good accuracy. The difference between input and retrieved parameters is negligible for models lying on the grid and is less than a few percent otherwise. An application to the real case of Vega showed that the u filter is located in a spectral region where the modelled and observed spectra are discrepant, and led us to define a new filter. Using this new filter and subsequent index, the Vega parameters are also retrieved with satisfactory accuracy. This work opens the possibility to determine the fundamental parameters of rapidly rotating early-type stars from photometric space observations.