Happy New Year everyone and Happy 5th Birthday to the light curve of the week feature.
This week we look at an example of the work being done as part of the HOYS project to analyse the light curves through a data pipeline with a view to characterise the variability of YSOs.
The concept of fingerprinting a stars variability was introduced e.g. in week 214, where the probability that a young star will vary by a certain brightness over a given time period can be visualised. These fingerprints are used to overcome some of the issues involved in analysing the light curves, from which the fingerprints are created, themselves. Due to the surroundings of young stars they can be difficult to characterize due to the variation of their properties and behaviour. There can be dimming and brightening events on different timescales and amplitudes, as well as periodic, semi-periodic or stochastic variations. The difficulties are also exacerbated because every star has its own observing cadence with some stars being observed more often than others and some light curves containing large gaps in the data due to stars not being observable for longer periods – due to the Sun being in the way.
As part of the work being done to characterise the fingerprints using clustering algorithms it is important to ensure that the data processed by these algorithms is of sufficient quality to produce meaningful results. As well as selecting light curves that actually represent variable stars it is necessary to only retain light curve data that can produce fingerprint images with sufficiently low uncertainties. There are four figures above. The first one is an example light curve of a star that shows some positive and negative outliers from its otherwise constant brightness. The second figure is the variability fingerprint for this light curve – read the above linked post for a detailed explanation what it represents. Contrary to the earlier representations, we have not smoothed the data in the fingerprint as we want to show what is actually analysed.
We have now evaluated the relative uncertainty for each probability value in the fingerprint. There are two ways of doing this. In the third image we show the relative errors based on the assumption that the number of measurements that fall in each pixel of the fingerprint map are distributed Normally, i.e. follow a Poisson Distribution. Thus, uncertainties of the number (N) in each pixel are equal to the square root of N, and a simple error propagation can be done to determine the uncertainties. However, we do not know if the assumption of a Poisson Distribution holds. Thus, we have also determined the uncertainties using a boot strapping method – shown in the last figure. For this, one basically varies the magnitudes in the light curve randomly according to their uncertainties and determines a fingerprint for each of these random variations. After several thousand repeats one determines the mean and standard deviation from all these maps to obtain the uncertainty map.
One can see that in general the uncertainties for large parts of the fingerprint map are below 20%. This can be further improved – and we intend to do this – by increasing the size of the pixels, especially on the time (x) axis. More importantly, both error maps look very similar. Thus, we can use the simple error propagation method compared to the extremely time consuming boot strapping when determining the uncertainties of the fingerprints. Once this is all done, we will start looking at clustering the fingerprints, i.e. identifying similarly looking fingerprints to investigate if there are groups with similar behaviour, or if stars of different evolutionary stages show similar variability behaviour or not.