Sometimes you are analysing your data to find out something about it, and while contemplating your results you realise that you answered another question, much more interesting than the one you had in the first place. This is one of those cases.
About two years ago we set out to see if the variability statistics of YSO (how much do they vary on what time scale) form ‘clusters’ or not. We know that young stellar objects (YSOs) often (if not always) vary their brightness stochastically. We are using our long term light curves from HOYS and create variability fingerprints from them. A good description of this process was presented in weeks 214 and 260. These fingerprints tell you for every star how likely it is to change brightness by a given amount when observed at a given time scale.
We then used unsupervised machine learning, in particular Principle Component Analysis (PCA), and various clustering algorithms to see if there are groups of YSOs with similar fingerprints, and thus variability statistics. The short answer is: There are no groups or clusters of YSOs with similar fingerprints. Instead they form a continuum distribution. The plot above shows the distribution of 240 highly variable YSO fingerprints after PCA. In addition we added ellipses of where simulated sine-wave like light curves would lie in the distribution. One can see that they only cover a small fraction of the real YSO light curves. We knew already that the YSO light curves are usually not sine-functions, but it is good to see that the maths also tells us that this is not the case.
So, what is the interesting point about this all? Well, many people over the years have tried to classify YSO light curves based on parameters they determine from them. This gives a number of possible classifications for YSOs. However, it is not clear, if these parameters are actually any good to effectively distinguish YSO light curves from each other. If one now looks in detail what PCA is doing, one finds that it creates a parameter space that shows the most amount of variation between the objects in a sample (in our case the YSO fingerprints). We can further evaluate the meaning of the axis in the above plot. It turns out that the x-axis value is proportional to the timescale at which significant (more than 0.3mag) variation starts in a light curve. They-axis on the other hand is proportional to the long term trend in a light curve (rising, constant, fading).
Thus, without setting out to do this, we found that the most effective way to distinguish long term YSO light curves with just two numbers is to determine at what time scale variations of more than 0.3mag start and what the long term trend of the light curve is. This is not saying that other parameters are not useful (they are) but these two provide the largest amount of spread between the objects.