This week we are looking at the light curve of the variable star AA Ori in the Southern part of the Orion Nebula Cluster. The two figure show the long term light curve and a “zoomed in” version for just two years. We have used these images and discussed the source in a previous post in 2021.

Today we re-use the images to discuss a specific feature in light curves like these and to sent a challenge to all our users. There are many dimming events visible in this and other such light curves. It is reasonably simple to identify when dimming events occur, either using a software solution or having ‘volunteers’ look through the light curves manually. As a reminder, these dimming events are caused by structures, clumps of material in the disk. When the orbital motion of the clump moves it into alignment, it occults some of the star light. The duration of the dimming depends on two things: The physical size of the clump and the orbital speed. Hence, if we would know the orbital speed we could determine the size and structure of the clump with great precision.

There is one way of knowing the orbital speed, and this is in cases of periodic events. I.e. if there is periodic dimming, we can use Kepler’s third law to determine the radius of the orbit of the clump (lets assume we know the mass of the star from it’s spectrum), and thus the orbital velocity. And this is where the challenge is. For each of the light curves it is quite easy to produce a list of when diming events occur. These ‘dips’ can come from periodic or randomly timed occultations.  Usually clumps form and dissolve on timescales less than the orbital period. Thus, any list of times for the dimming events could contain some small number of dips that are caused by a periodic signal, as well as a number of randomly placed dips. We would like to identify which of the dips are associated with the periodic signal and what the period is. Note that even if there are periodic dips, not all of them will show up in the light curve, as the objects are not constantly monitored – there are gaps in the data. We have written a python program that is able to find periodic signals in a list of times for dips, but it does not work in some cases when we test it.

Challenge: If anyone is interested to help: Assume you have a list of dates (number of days, e.g. 17, 38, 42, 51, 63, 68, 72, 99, etc.) where dips occur, and each of these dates has an uncertainty associated (i.e. the dip happens on day 123.4, plus/minus 2 days). Write a python code that returns the most likely periodic signal in this list of dates. We will then test that code against ours to see which one works better, more reliable and/or faster 🙂