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Register a new userA pragmatic Bayesian perspective on correlation analysis: The exoplanetary gravity - stellar activity case
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We apply the Bayesian framework to assess the presence of a correlation between two quantities. To do so, we estimate the probability distribution of the parameter of interest, $rho$, characterizing the strength of the correlation. We provide an implementation of these ideas and concepts using python programming language and the pyMC module in a very short ($sim$130 lines of code, heavily commented) and user-friendly program. We used this tool to assess the presence and properties of the correlation between planetary surface gravity and stellar activity level as measured by the log($R_{mathrm{HK}}$) indicator. The results of the Bayesian analysis are qualitatively similar to those obtained via p-value analysis, and support the presence of a correlation in the data. The results are more robust in their derivation and more informative, revealing interesting features such as asymmetric posterior distributions or markedly different credible intervals, and allowing for a deeper exploration. We encourage the reader interested in this kind of problem to apply our code to his/her own scientific problems. The full understanding of what the Bayesian framework is can only be gained through the insight that comes by handling priors, assessing the convergence of Monte Carlo runs, and a multitude of other practical problems. We hope to contribute so that Bayesian analysis becomes a tool in the toolkit of researchers, and they understand by experience its advantages and limitations.
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The architecture of many exoplanetary systems is different from the solar system, with exoplanets being in close orbits around their host stars and having orbital periods of only a few days. We can expect interactions between the star and the exoplanet for such systems that are similar to the tidal interactions observed in close stellar binary systems. For the exoplanet, tidal interaction can lead to circularization of its orbit and the synchronization of its rotational and orbital period. For the host star, it has long been speculated if significant angular momentum transfer can take place between the planetary orbit and the stellar rotation. In the case of the Earth-Moon system, such tidal interaction has led to an increasing distance between Earth and Moon. For stars with Hot Jupiters, where the orbital period of the exoplanet is typically shorter than the stellar rotation period, one expects a decreasing semimajor axis for the planet and enhanced stellar rotation, leading to increased stellar activity. Also excess turbulence in the stellar convective zone due to rising and subsiding tidal bulges may change the magnetic activity we observe for the host star. Here I review recent observational results on stellar activity and tidal interaction in the presence of close-in exoplanets, and discuss the effects of enhanced stellar activity on the exoplanets in such systems.
The key goals of the astrobiology community are to identify environments beyond Earth that may be habitable, and to search for signs of life in those environments. A fundamental aspect of understanding the limits of habitable environments and detectable signatures is the study of where such environments can occur. Thus, the need to study the creation, evolution, and frequency of environments hostile to habitability is an integral part of the astrobiology story. The study of these environments provides the opportunity to understand the bifurcation between habitable and uninhabitable conditions on planetary bodies. The archetype of such a planet is Earths sibling planet, Venus, which provides a unique opportunity to explore the processes that created a completely uninhabitable environment and thus define the conditions that rule out bio-related signatures. We advocate a continued comprehensive study of our neighboring planet, to include models of early atmospheres, compositional abundances, and Venus-analog frequency analysis from current and future exoplanet data. Critically, new missions to Venus that provide in-situ data are necessary to address the major gaps in our current understanding, and to enable us to take the next steps in characterizing planetary habitability.
We discuss the impact that the next generation of Extremely Large Telescopes will have on the open astrophysical problems of resolved stellar populations. In particular, we address the interplay between multiband photometry and spectroscopy.
The search for Earth-like planets around late-type stars using ultra-stable spectrographs requires a very precise characterization of the stellar activity and the magnetic cycle of the star, since these phenomena induce radial velocity (RV) signals that can be misinterpreted as planetary signals. Among the nearby stars, we have selected Barnards Star (Gl 699) to carry out a characterization of these phenomena using a set of spectroscopic data that covers about 14.5 years and comes from seven different spectrographs: HARPS, HARPS-N, CARMENES, HIRES, UVES, APF, and PFS; and a set of photometric data that covers about 15.1 years and comes from four different photometric sources: ASAS, FCAPT-RCT, AAVSO, and SNO. We have measured different chromospheric activity indicators (H$alpha$, Ca~{sc II}~HK and Na I D), as well as the FWHM of the cross-correlation function computed for a sub-set of the spectroscopic data. The analysis of Generalized Lomb-Scargle periodograms of the time series of different activity indicators reveals that the rotation period of the star is 145 $pm$ 15 days, consistent with the expected rotation period according to the low activity level of the star and previous claims. The upper limit of the predicted activity-induced RV signal corresponding to this rotation period is about 1 m/s. We also find evidence of a long-term cycle of 10 $pm$ 2 years that is consistent with previous estimates of magnetic cycles from photometric time series in other M stars of similar activity levels. The available photometric data of the star also support the detection of both the long-term and the rotation signals.
In this work we test the most widely used methods for fitting the composition fraction in data, namely maximum likelihood, $chi^2$, mean value of the distributions and mean value of the posterior probability function. We discuss the discrimination power of the four methods in different scenarios: signal to noise discrimination; two signals; and distributions of Xmax for mixed primary mass composition. We introduce a distance parameter, which can be used to estimate, as a rule of thumb, the precision of the discrimination. Finally, we conclude that the most reliable methods in all the studied scenarios are the maximum likelihood and the mean value of the posterior probability function.
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