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By controlling instrumental errors to below 10 cm/s, the EXtreme PREcision Spectrograph (EXPRES) allows for a more insightful study of photospheric velocities that can mask weak Keplerian signals. Gaussian Processes (GP) have become a standard tool for modeling correlated noise in radial velocity datasets. While GPs are constrained and motivated by physical properties of the star, in some cases they are still flexible enough to absorb unresolved Keplerian signals. We apply GP regression to EXPRES radial velocity measurements of the 3.5 Gyr old chromospherically active Sun-like star, HD 101501. We obtain tight constraints on the stellar rotation period and the evolution of spot distributions using 28 seasons of ground-based photometry, as well as recent $TESS$ data. Light curve inversion was carried out on both photometry datasets to reveal the spot distribution and spot evolution timescales on the star. We find that the $> 5$ m/s rms radial velocity variations in HD 101501 are well-modeled with a GP stellar activity model without planets, yielding a residual rms scatter of 45 cm/s. We carry out simulations, injecting and recovering signals with the GP framework, to demonstrate that high-cadence observations are required to use GPs most efficiently to detect low-mass planets around active stars like HD 101501. Sparse sampling prevents GPs from learning the correlated noise structure and can allow it to absorb prospective Keplerian signals. We quantify the moderate to high-cadence monitoring that provides the necessary information to disentangle photospheric features using GPs and to detect planets around active stars., 25 pages, 16 figures, accepted to AJ

Nearby, active stars with relatively rapid rotation and large starspot structures offer the opportunity to compare interferometric, spectroscopic, and photometric imaging techniques. In this paper, we image a spotted star with three different methods for the first time. The giant primary star of the RS Canum Venaticorum binary $\sigma$ Geminorum ($\sigma$ Gem) was imaged for two epochs of interferometric, high-resolution spectroscopic, and photometric observations. The light curves from the reconstructions show good agreement with the observed light curves, supported by the longitudinally-consistent spot features on the different maps. However, there is strong disagreement in the spot latitudes across the methods., Comment: Accepted to ApJ, 19 pages, 16 figures, 5 tables

The Kepler target KIC 5110407, a K-type star, shows strong quasi-periodic light curve fluctuations likely arising from the formation and decay of spots on the stellar surface rotating with a period of 3.4693 days. Using an established light-curve inversion algorithm, we study the evolution of the surface features based on Kepler space telescope light curves over a period of two years (with a gap of .25 years). At virtually all epochs, we detect at least one large spot group on the surface causing a 1-10% flux modulation in the Kepler passband. By identifying and tracking spot groups over a range of inferred latitudes, we measured the surface differential rotation to be much smaller than that found for the Sun. We also searched for a correlation between the seventeen stellar flares that occurred during our observations and the orientation of the dominant surface spot at the time of each flare. No statistically-significant correlation was found except perhaps for the very brightest flares, suggesting most flares are associated with regions devoid of spots or spots too small to be clearly discerned using our reconstruction technique. While we may see hints of long-term changes in the spot characteristics and flare statistics within our current dataset, a longer baseline of observation will be needed to detect the existence of a magnetic cycle in KIC 5110407., 32 pages, 15 figures, accepted to ApJ

We present the results of a study of differential rotation on the K2 IV primary of the RS CVn binary II Pegasi (HD 224085) performed by inverting light curves to produce images of the dark starspots on its surface. The data were obtained in the standard Johnson B and V filter passbands via the Tennessee State University T3 0.4-m Automated Photometric Telescope from JD 2447115.8086 to 2454136.6221 (1987 November 16 to 2007 February 5). The observations were subdivided into 68 data sets consisting of pairs of B and V light curves, which were then inverted using a constrained non-linear inversion algorithm that makes no a priori assumptions regarding the number of spots or their shapes. The resulting surface images were then assigned to 21 groups corresponding to time intervals over which we could observe the evolution of a given group of spots (except for three groups consisting of single data sets). Of these 21 groups, six showed convincing evidence of differential rotation over time intervals of several months. For the others, the spot configuration was such that differential rotation was neither exhibited nor contraindicated. The differential rotation we infer is in the same sense as that on the Sun: lower latitudes have shorter rotation periods. From plots of the range in longitude spanned by the spotted regions vs. time, we obtain estimates of the differential rotation coefficient k defined in earlier work by Henry et al., and show that our results for its value are consistent with the value obtained therein., Submitted to The Astronomical Journal