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If Doppler searches for earth-mass, habitable planets are to succeed, observers must be able to identify and model out stellar activity signals. Here we demonstrate how to diagnose activity signals by calculating the magnitude-squared coherence $\hat{C}^2_{xy}(f)$ between an activity indicator time series $x_t$ and the radial velocity (RV) time series $y_t$. Since planets only cause modulation in RV, not in activity indicators, a high value of $\hat{C}^2_{xy}(f)$ indicates that the signal at frequency $f$ has a stellar origin. We use Welch's method to measure coherence between activity indicators and RVs in archival observations of GJ 581, alpha Cen B, and GJ 3998. High RV-H$\alpha$ coherence at the frequency of GJ 3998 b, and high RV-S index coherence at the frequency of GJ 3998 c, indicate that the planets may actually be stellar signals. We also replicate previous results showing that GJ 581 d and g are rotation harmonics and demonstrate that alpha Cen B has activity signals that are not associated with rotation. Welch's power spectrum estimates have cleaner spectral windows than Lomb-Scargle periodograms, improving our ability to estimate rotation periods. We find that the rotation period of GJ 581 is 132 days, with no evidence of differential rotation. Welch's method may yield unacceptably large bias for datasets with $N < 75$ observations and works best on datasets with $N > 100$. Tapering the time-domain data can reduce the bias of the Welch's power spectrum estimator, but observers should not apply tapers to datasets with extremely uneven observing cadence. A software package for calculating magnitude-squared coherence and Welch's power spectrum estimates is available on github., Comment: Submitted to AJ, responded to input from referee. 35 pages (29 in main body of article) include 21 figures

Measured spectral shifts due to intrinsic stellar variability (e.g., pulsations, granulation) and activity (e.g., spots, plages) are the largest source of error for extreme precision radial velocity (EPRV) exoplanet detection. Several methods are designed to disentangle stellar signals from true center-of-mass shifts due to planets. The EXPRES Stellar Signals Project (ESSP) presents a self-consistent comparison of 22 different methods tested on the same extreme-precision spectroscopic data from EXPRES. Methods derived new activity indicators, constructed models for mapping an indicator to the needed RV correction, or separated out shape- and shift-driven RV components. Since no ground truth is known when using real data, relative method performance is assessed using the total and nightly scatter of returned RVs and agreement between the results of different methods. Nearly all submitted methods return a lower RV RMS than classic linear decorrelation, but no method is yet consistently reducing the RV RMS to sub-meter-per-second levels. There is a concerning lack of agreement between the RVs returned by different methods. These results suggest that continued progress in this field necessitates increased interpretability of methods, high-cadence data to capture stellar signals at all timescales, and continued tests like the ESSP using consistent data sets with more advanced metrics for method performance. Future comparisons should make use of various well-characterized data sets -- such as solar data or data with known injected planetary and/or stellar signals -- to better understand method performance and whether planetary signals are preserved., Comment: 33 pages (+12 pages of Appendix), 10 figures, 8 tables, accepted for publication in AJ

Radial-velocity (RV) planet searches are often polluted by signals caused by gas motion at the star's surface. Stellar activity can mimic or mask changes in the RVs caused by orbiting planets, resulting in false positives or missed detections. Here we use Gaussian process (GP) regression to disentangle the contradictory reports of planets vs. rotation artifacts in Kapteyn's star (Anglada-Escude et al. 2014, Robertson et al. 2015, Anglada-Escude et al. 2016). To model rotation, we use joint quasi-periodic kernels for the RV and H-alpha signals, requiring that their periods and correlation timescales be the same. We find that the rotation period of Kapteyn's star is 125 days, while the characteristic active-region lifetime is 694 days. Adding a planet to the RV model produces a best-fit orbital period of 100~years, or 10 times the observing time baseline, indicating that the observed RVs are best explained by star rotation only. We also find no significant periodic signals in residual RV data sets constructed by subtracting off realizations of the best-fit rotation model and conclude that both previously reported "planets" are artifacts of the star's rotation and activity. Our results highlight the pitfalls of using sinusoids to model quasi-periodic rotation signals., Comment: 15 pages, including 10 figures. Accepted for publication in Astronomical Journal

gamma Draconis, a K5III star, showed radial velocity (RV) variations consistent with a 10.7 Jupiter mass planet from 2003-2011. After 2011, the periodic signal decayed, then reappeared with a phase shift. Hatzes et al. (2018) suggested that gamma Dra's RV variations could come from oscillatory convective modes, but did not fit a mathematical model. Here we assess whether a quasi-periodic Gaussian process (GP)---appropriate when spots with finite lifetimes trace underlying periodicity---can explain the RVs. We find that a model with only one quasiperiodic signal is not adequate: we require a second component to fit the data. The best-fit model has quasi-periodic oscillations with P1 = 705 days and P2 = 15 days. The 705-day signal may be caused by magnetic activity. The 15-day period requires further investigation., Comment: to be published in RNAAS

This study uses students performance on standardized tests as evidence of the quality of education and introduces a methodology based on the comparison of performance distributions to produce indicators for both the level achieved by the students and the learning gap between social groups, two inseparable dimensions of quality of education. In the first case, the study compares the distribution of the group observed with a reference distribution, which represents an ideal situation of where students should be. In the second, it compares the performance distribution of students belonging to social groups defined by socioeconomic characteristics. This article uses the Kullback-Leibler divergence to characterize the differences between the distributions. This measure takes into account types of diferences not considered by other measures and have solid conceptual justifications. The proposed methodology is used to describe the quality of Brazilian basic education using the test results applied biannually to all Brazilian students of basic education.