Differential rotation of solar {\alpha} sunspots and implications for stellar light curves
Differential rotation is a key driver of magnetic activity and dynamo processes in the Sun and other stars, especially as the rate differs across the solar layers, but also in active regions. We aim to accurately quantify the velocity at which round {\alpha}-spots traverse the solar disk as a function of their latitude, and compare these rates to those of the quiet-Sun and other sunspot types. We then extend this work to other stars and investigate how differential rotation affects the modulation of stellar light curves by introducing a generalized stellar differential rotation law. We manually identify and track 105 {\alpha}-sunspots in the 6173 {\AA} continuum using the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). We measure the angular velocities of each spot through center-of-mass and geometric ellipse-fitting methods to derive a differential rotation law for round {\alpha}-sunspots. Results. Using over a decade of HMI data we derive a differential rotation law for {\alpha}-sunspots. When compared to previous measurements we find that {\alpha}-sunspots rotate 1.56% faster than the surrounding quiet-Sun, but 1.35% slower than the average sunspot population. This supports the hypothesis that the depth at which flux tubes are anchored influences sunspot motions across the solar disk. We extend this analysis to other stars by introducing a scaling law based on the rotation rates of these stars. This scaling law is implemented into the Stellar Activity Grid for Exoplanets (SAGE) code to illustrate how differential rotation alters the photometric modulation of active stars. Our findings emphasize the necessity of considering differential rotation effects when modeling stellar activity and exoplanet transit signatures