Modeling photometric variations due to a global inhomogeneity on an obliquely rotating star: application to lightcurves of white dwarfs

We develop a general framework to compute photometric variations induced by the oblique rotation of a star with an axisymmetric inhomogeneous surface. We apply the framework to compute lightcurves of white dwarfs adopting two simple models of their surface inhomogeneity. Depending on the surface model and the location of the observer, the resulting lightcurve exhibits a departure from a purely sinusoidal curve that are observed for a fraction of white dwarfs. As a specific example, we fit our model to the observed phase-folded lightcurve of a fast-spinning white dwarf ZTF J190132.9+145808.7 (with the rotation period of 419s). We find that the size and obliquity angle of the spot responsible for the photometric variation are $\text{dts}\approx {60}^{\circ }$ and $\text{thetaS}\approx {60}^{\circ }$ or ${90}^{\circ }$, respectively, implying an interesting constraint on the surface distribution of the magnetic field on white dwarfs.