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Flares | Max Planck Institute for extraterrestrial Physics
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Distress signals, flares and emergency beacons. Last updated 27 August Archives of long photometric surveys, such as the Kepler database, are a great basis for studying flares. However, identifying the flares is a complex task; it is easily done in the case of single-target observations by visual inspection, but is nearly impossible for several year-long time series for several thousand targets.
Although automated methods for this task exist, several problems are difficult or impossible to overcome with traditional fitting and analysis approaches. We introduce a code for identifying and analyzing flares based on machine-learning methods, which are intrinsically adept at handling such data sets. The light curves were divided into search windows, approximately on the order of the stellar rotation period.
This search window was shifted over the data set, and a voting system was used to keep false positives to a minimum: only those flare candidate points were kept that were identified as a flare in several windows. The detected flare events and flare energies are consistent with earlier results from manual inspections. Flares are energetic eruptions that occur as a result of magnetic field line reconnection. These energetic events have received increased interest since the advent of exoplanet research, as flares can have strong, deleterious effects on orbiting planets Khodachenko et al.
Flares can also continuously transform ex-oplanetary atmospheres, which is disadvantageous for hosting life see Vida et al. Currently used definitions of the habitable zone are based only on the stellar irradiation and the distance of the planet from the host star. As flares can have strong effects on planetary environments, these definitions will likely need to be revised for a more accurate definition of habitability in order to include the effects of stellar activity. To do this, and to better understand stellar magnetism itself, it is essential to characterize flares: events need to be properly identified, and their strength and frequency need to be determined.
The data from the Kepler satellite proved to be a great resource for stellar activity research because they provide an almost continuous data set of unprecedented precision over four years from about targets, which include thousands of active stars e. Studies have been performed to understand stellar activity of individual stars e.
Significant strides were made to detect the flares that are contained in the Kepler archive by Davenport , who identified events in the light curves by detecting the shape of a flare.
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However, this method can misidentify other astrophysical phenomena as flares e. Of course, there is no single perfect way to accurately detect and classify all flares: the diversity of observations e.
A manual identification of flares is also impossible in practice for a large number of observations, as in the Kepler archive. In this paper, we present an algorithm that is based on machine-learning, with which we identify flares in light curves 1 , and we present our application to the flaring, planet-hosting star TRAPPIST-1, a popular target for habitability studies, and KIC , a rotationally variable star e. The starspots, which are dark regions of suppressed convection of cool, active stars, rotate across the stellar surface in and out of view of the observer, causing periodic modulations to the light curve.
Starspots are often longer-lived than sunspots, allowing for detection during multiple rotations.
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This provides a reliable approximation for the stellar rotation period. Light-curve sections of approximately the length of the stellar rotation period typically, on the order of days are expected to be easily described by a relatively low-degree polynomial as opposed to sections covering several rotations , and their lengths are longer than the timescale of a flare event typically, on the order of hours.
The light-curve sections are specifically defined such that a flare could be easily spotted in a data set by eye. For further analysis, these light-curve windows with a length of 1. Each light-curve window must also be standardized: it is a common requirement for many machine-learning estimators that individual features should look more or less like normally distributed data Gaussian with zero mean and unit variance, see, e. For our purposes, it is enough to transform only the time axis by removing its mean and scaling the light curve by its standard deviation, since the scaling of the brightness variation is just a multiplicative factor in the coefficients of the polynomial used to fit the light-curve window.
In the case of un-derfitting, the model does not describe the data well, while in the case of overfitting, a too-complex model is used that tries to fit too many data points individually. While it might fit a training data set well, this will describe test data and future measurements poorly. This problem is generally solved by a cross-validation method.ejihybym.tk
NASS Guide to Managing Your Flares
The remaining part of the data is used for validating the model. The sets are usually created by selecting random samples of the initial data set, but this is not very useful with time series. In these cases, sets of consecutive data points are therefore used Pedregosa et al. Lengthy data sets, such as Kepler light curves, make it impractical to use all the available data for cross-validation, or to find the optimal polynomial order for each segment. Therefore, we selected a sample five, by default of light-curve windows from the observations, and performed a grid search of fit parameters on them to select the best model to describe the given data based on the median absolute error regression loss.
RANSAC is an iterative method that assumes that the data consist of inlier and outlier points generally noise, but also flare events, in this case. The algorithm works as follows: first, a sample random subset is generated from the input data set, which is fit by the model. Then, the algorithm checks which elements of the original data set fit this model based on the residuals. The points that fit the model are considered inliers for the given iteration. These steps are iterated either a maximum number of given times or until one of the stop criteria is met this can be a given number of inlier points or a stop score by a given metrics.
The final model is based on all inlier samples also called a consensus set of the previously determined best model.
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An example of the outlier selection by the algorithm is shown in the second plot of Fig. We found that while RANSAC gives a good fit even for a light-curve section with several flare events, the marked outliers are not reliable enough for searching for flare candidates alone see Fig. Thus we only used the RANSAC estimate of the inlier points for statistics and calculated the standard deviation of the light curve with the rotational modulation and most of the flare points removed.
To achieve more robust results, we shifted the search window through the light curve, by default in steps of one-fourth of the light-curve window see Fig. We note that this last step was performed only after evaluating each light-curve segment. These criteria are basically the same as those defined by Eqs.
Optionally, the rotation period can be given as an input to run the code faster, or to fix it to a chosen value if the rotational modulation is too weak, and the polynomial degree can also be fixed. The number of votes needed for a flare candidate to be kept, the window size compared to the rotation period , and the step length with which the search window is shifted cannot be changed from command line, but can be easily modified if the flare-finding function is imported to another code.
Demonstration of the algorithm on a light-curve section of KIC The top plot shows the original light-curve section. In the bottom plot , the final flare candidates are shown, which have more than a given number three, in this case of consecutive data points. These points will get a vote for this light-curve section, indicating that the feature likely is a flare.
Demonstration of the voting algorithm on a light-curve section of KIC In the bottom plot , the candidates with one light gray , two medium gray , and at least three black votes are plotted. In this setup, the flares plotted in black are kept as final flare candidates.