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Photometric rotational modulations due to starspots remain the most common and accessible way to study stellar activity. Modelling rotational modulations allows one to invert the observations into several basic parameters, such as the rotation period, spot coverage, stellar inclination and differential rotation rate. The most widely used analytic model for this inversion comes from Budding (1977) and Dorren (1987), who considered circular, grey starspots for a linearly limb darkened star. That model is extended to be more suitable in the analysis of high precision photometry such as that by Kepler. Macula, a Fortran 90 code, provides several improvements, such as non-linear limb darkening of the star and spot, a single-domain analytic function, partial derivatives for all input parameters, temporal partial derivatives, diluted light compensation, instrumental offset normalisations, differential rotation, starspot evolution and predictions of transit depth variations due to unocculted spots. The inclusion of non-linear limb darkening means macula has a maximum photometric error an order-of-magnitude less than that of Dorren (1987) for Sun-like stars observed in the Kepler-bandpass. The code executes three orders-of-magnitude faster than comparable numerical codes making it well-suited for inference problems.
MAH calculates the posterior distribution of the "minimum atmospheric height" (MAH) of an exoplanet by inputting the joint posterior distribution of the mass and radius. The code collapses the two dimensions of mass and radius into a one dimensional term that most directly speaks to whether the planet has an atmosphere or not. The joint mass-radius posteriors derived from a fit of some exoplanet data (likely using MCMC) can be used by MAH to evaluate the posterior distribution of R_MAH, from which the significance of a non-zero R_MAH (i.e. an atmosphere is present) is calculated.
The Beta Inverse code solves the inverse cumulative density function (CDF) of a Beta distribution, allowing one to sample from the Beta prior directly. The Beta distribution is well suited as a prior for the distribution of the orbital eccentricities of extrasolar planets; imposing a Beta prior on orbital eccentricity is valuable for any type of observation of an exoplanet where eccentricity can affect the model parameters (e.g. transits, radial velocities, microlensing, direct imaging). The Beta prior is an excellent description of the current, empirically determined distribution of orbital eccentricities and thus employing it naturally incorporates an observer’s prior experience of what types of orbits are probable or improbable. The default parameters in the code are currently set to the Beta distribution which best describes the entire population of exoplanets with well-constrained orbits.
ECCSAMPLES solves the inverse cumulative density function (CDF) of a Beta distribution, sometimes called the IDF or inverse transform sampling. This allows one to sample from the relevant priors directly. ECCSAMPLES actually provides joint samples for both the eccentricity and the argument of periastron, since for transiting systems they display non-zero covariance.
Flicker calculates the mean stellar density of a star by inputting the flicker observed in a photometric time series. Written in Fortran90, its output may be used as an informative prior on stellar density when fitting transit light curves.
LDC3 samples physically permissible limb darkening coefficients for the Sing et al. (2009) three-parameter law. It defines the physically permissible intensity profile as being everywhere-positive, monotonically decreasing from center to limb and having a curl at the limb. The approximate sampling method is analytic and thus very fast, reproducing physically permissible samples in 97.3% of random draws (high validity) and encompassing 94.4% of the physically permissible parameter volume (high completeness).
ExoPriors calculates a log-likelihood penalty for an input set of transit parameters to account for observational bias (geometric and signal-to-noise ratio detection bias) of transiting exoplanets. Written in Python, the code calculates this log-likelihood penalty in one of seven user-specified cases specified with Boolean input parameters for geometric and/or SNR bias, grazing or non-grazing events, and occultation events.
Transit Clairvoyance uses Artificial Neural Networks (ANNs) to predict the most likely short period transiters to have additional transiters, which may double the discovery yield of the TESS (Transiting Exoplanet Survey Satellite). Clairvoyance is a simple 2-D interpolant that takes in the number of planets in a system with period less than 13.7 days, as well as the maximum radius amongst them (in Earth radii) and orbital period of the planet with maximum radius (in Earth days) in order to predict the probability of additional transiters in this system with period greater than 13.7 days.
Forecaster predicts the mass (or radius) from the radius (or mass) for objects covering nine orders-of-magnitude in mass. It is an unbiased forecasting model built upon a probabilistic mass-radius relation conditioned on a sample of 316 well-constrained objects. It accounts for observational errors, hyper-parameter uncertainties and the intrinsic dispersions observed in the calibration sample.