Revisiting the Photometric Modulation Amplitudes of Kepler Planet Hosts: A Confounder-Adjusted Test of Stellar Spin-Orbit Alignment

T. Mazeh and coworkers pioneered a method using rotational photometric modulation as a proxy to infer stellar obliquities in Kepler transiting planetary systems, based on the expected positive correlation between spot-induced modulation amplitudes and stellar inclinations. They found that planet hosts cooler than the Sun showed larger modulation amplitudes than comparison stars, consistent with low stellar obliquities. For hotter hosts, however, they reported the opposite - a negative amplitude difference (hosts minus comparison stars) - which is difficult to interpret in terms of viewing geometry. We show that this comparison is affected by confounding variables not controlled for in the sample selection. One such confounder is apparent magnitude, whose distributions differ markedly between the two samples for hotter stars and affect the observed modulation amplitudes. We develop resampling and likelihood-based approaches that enable comparison of the amplitude distributions at fixed apparent magnitude, stellar radius, and rotation period. The previously reported negative amplitude difference for hot hosts is no longer present in either analysis. The likelihood-based analysis finds a positive amplitude difference up to $\sim 6100\,\mathrm{K}$ that becomes consistent with zero at higher temperatures, while the resampling analysis shows a similar but less pronounced trend. This result is qualitatively consistent with independent $v\sin i$ analyses suggesting low obliquities for cooler super-Earth and sub-Neptune hosts and broader obliquity distributions for hotter ones. This may also indicate a gradual change in the obliquity distribution with stellar temperature, although changes in spot distributions or selection effects could also contribute to the photometric trends in hot stars.