Welcome to ardor
ardor is a package dedicated to detecting, modeling, and analyzing correlated flares in photometry. It featues a multi-tiered flare detection pipeline, simulation tools, statistical testing, and forward modeling functions, as well as a visualization suite. While its primary goal is to detect correlated flare arising from magnetic star-planet interactions, ardor also searches for correlation with stellar rotation.
ardor incorporates a flare detection pipeline to identify, characterize, and validate stellar flares in photometry. This pipeline uses four tiers:
- Tier 0: Light Curve Detrending
- Tier 1: Outlier identification
- Tier 2: Preliminary Model Parameterization
- Tier 3: Bayesian Modeling using
allesfitter
The end product of the ardor pipeline is a list of identified flares and flare parameters, including epoch, flare ampltidue, duration, and bolometric energy. This pipeline can be found in the Flare.py module.
ardor supports injection-recovery and precision-recall tests using simulated flares in real light curves to check performance over flare paramter space.
ardor can anaylze flare samples for a particular planetary system and determine if the flare samples are consistent with significant flare clustering. This is performed using two types of tests:
- Goodness-of-fit (GoF) tests
- Unbinned Likelihood Analysis
Both take as input phase folded flare epochs with the planetary orbital period and output their relevant test statistic and significance metric.
Three different GoF tests are supported: the Kolmolgorov-Smirnov (KS) test, the Anderson-Darling (AD) test, and the Kuiper (KU) test. These statistical tests are wrapped from the scipy, skgof, and astropy packages, respectively. ardor constructs the empirical cumulative density function (eCDF) from the given phase-folded flare epochs. The GoF tests compare the eCDF to the expected uniform distribution and determines a distance statistic between the eCDF and the uniform CDF. Each distance statistic is drawn from its own distribution which returns a p-value, which can be used to determine the significance of the flare sample. The p-value answers the question:
What is the probability that the empirical sample is drawn from a uniform distribution?
Thus, the GoF tests can answer if a sample is non-uniform to some signifiance level, but does not inform the shape of the sample.
To compliment the GoF tests, ardor uses a method called Unbinned Likelihood Analysis which aims to find the best-fit parameters that minimizes the likelihood function. Here, we directly fit a probability density function (PDF), the von Mises PDF:
$$ f(x,\kappa) = \frac{\exp{\kappa \cos{x}}}{2\pi I_{0}(\kappa)}.$$
The von Mises PDF can be thought of as a periodic Gaussian; it is unimodal and can cross periodic boundaries, ideal characterstics to find flare clustering a particular orbital phase. The likelihood function is minimized using scipy.optimize.minimize.
The development of ardor has been supported by the McDonnell Center for Space Sciences at Washington University in St. Louis.