While we are still repairing the server hard disks, we look at some interesting technique of analysing our light curves. We call this variability fingerprinting.
The young star light curves do come in all sorts of “shapes and sizes”, i.e. they can have dimming and brightening events on different timescales and amplitudes, as well as periodic, semi-periodic or stochastic variations. Each light curve is hence completely unique and and stars also can change their behaviour over time. It is hence very difficult to characterise these data, in particular since every star also has it’s own observing cadence (some are observed more often then others, some have large gaps in the data due to the Sun being in the way).
The variability fingerprinting tries to overcome these issues. We first look at every pair of observations of a star in the light curve. We calculate the time difference between the observations and the change in the magnitude between the two data points, and plot this in a delta(t) vs. delta(m) graph. This usually results in a vast number of these pairs. With N data points we have N*(N-1)/2 pairs. Hence, in this plot we determine the density of points, which we then can normalise to determine the probability that a star changes its brightness by a certain amount if observed a time delta(t) apart. This is what is shown in th above plot. The colour code is the probability, and the x-axis is the time difference in days – in logarithmic units.
For the example shown we see that on short time scales (less than one day, or 0 on the x-axis) the star barely varies. Then there is an ever increasing probability for larger variations at increasing time differences between observations. At x=1.5 we then see that the star has an increased probability to again not be variable. A similar ‘spot’ appears at x=1.8 and 2.1. The reason for this is that the star varies with a period of about 31 days – log(31)=1.5 – an hence always returns to its normal brightness after one period. the other values represent two and four periods, respectively. We can also see that after about one quarter period (x=0.9) the maximum and minimum variations do not change anymore and remain constant. In other words the star varies by no more than 1mag.
We are looking into statistical tools that allow us to compare these ‘fingerprint’ plots, which are unique for each star, in order to group stars with similar behaviour in these plots for analysis……