One’s small telescope is another’s exoplanet hunter

Are we alone? This project is part of one of the biggest efforts of modern astronomy, which is trying to answer questions such as “can we find another Earth?” and “is the Solar System common?”. But these are very general questions, and there are many ways to look for the answers. For instance, we can turn into the closest stars in our own Galaxy, and look for signatures that indicate the presence and characteristics of (exo-)planets orbiting them.

The majority of exoplanets discovered in the latest decades are hot Jupiters, massive gaseous planets that orbit in a very tight trajectory around their host star. This was unexpected to us, when we first got these results, because we were very used to our own Solar System, with its rocky planets in the inner part of the system, and each one relatively far away from the Sun. A hot Jupiter can be as close to their host star as a fraction of Mercury’s orbit. So, yes, that is weird. The following plot shows a compilation of the exoplanetary systems that we have discovered so far. Most of what we see are single planets instead of various planets orbiting a star, but this is probably a bias, due to limitations of our instrumentation and methods.

All the exoplanets we had discovered until September 2014. Lissauer, J.; Dawson, R.; Tremaine, S. Data provided by J. Rowe. Nature 513, 336–344

When we look at these stars, sometimes we see variability in their brightness, and there are many phenomena that can cause it. One of the causes is an exoplanetary transit, and the variability this case is very tiny, of the order of millimagnitudes. But they can be observed, and this is what many astronomical surveys do: they look for dips in stars’ brightness, all through the sky.

Although there is Kepler to perform surveys from space, there are too telescopes here on ground doing this work, which is the case of KELT, the Kilodegree Extremely Little Telescope. And when I say little, I really mean it: the telescope is as tiny as a photographic camera. When I first saw a picture of it, I though “wow, that’s a cool mount, but why the hell did they put the picture of the mount without a scope”? It came to me as a surprise when I took a better look at the picture and noticed that the telescope was already there, and it’s actually just the CCD box with lenses attached to it. There are actually two KELTs, one in the northern hemisphere and one in the south. “Kilodegree” is because the field of view of the telescope is very big, which is caused by the awfully short focal length of the scope. It’s tiny after all, so no surprise there. But we should not think little of this instrument: it is powerful enough to see very slight brightness variability in many stars at the same time, and this is where its power resides.

The Kilodegree Extremely Little Telescope. Yup, it’s that tiny. But it is powerful. Credit: KELT Team.

The problem with KELT is that, sometimes, it’s difficult to disentangle variability from other possibles causes. And this is where we come. KELT needs other instruments to make follow-up observations of their candidate targets. We are using the B&C 0.60 m telescope from Pico dos Dias Observatory to make follow-up observations for KELT South (which is located in South Africa). Our job is to observe stars for which transits are predicted, and make light curves of them.

If you are not familiar with light curves, they are plots of a star’s brightness through time. They are important tools in the study of variability, and many discoveries of exoplanets were done using such plots. There are various ways to construct these. One of them is to take consecutive observations (generally in the same night and in the same instrument) of a target star, and compare its brightness with other stars (let’s call it the “standard stars”) in the same field. The standard stars must not have an intrinsic variability, otherwise we will not be able to compare their brightness in time with our target star. This method is called differential photometry, and it is much more accurate when compared to absolute photometry, which consists on calculating the brightness of a star from “principles”, directly taking into account effects of atmosphere and instrumentation – the problem with this method is that the uncertainties will be much wider than the variability we are trying to observe (remember it’s of the order of a few millimagnitudes).

When we have two stars in the same field of view, if it is small enough, we can assume that they are affected in the same way by the atmosphere and the instruments, and this approximation is, most of the time, good enough. Because we want to compare brightness, what we do to minimize the uncertainties as best as possible is to try to get as much light as we can in an image. Getting photons is like counting, which is a Poisson process, and statistics geeks will remember that the uncertainty in a Poisson process is proportional to the square root of the number of occurrences. An exoplanetary transit takes some time: from a few dozen of minutes to a couple of hours, so we should aim for a time resolution of a few minutes, generally. But if the star is too bright, the CCD can saturate in just a few seconds. In order to gather more light as possible in a single image, we can try de-focusing the telescope a little bit, so that the CCD doesn’t saturate quickly and we keep on a linear scale for a longer time. All this contributes to having an accurate photometry, which is what we are aiming for.

Data reduction follows the usual algorithm: bias subtraction followed by flat-fielding. But after that comes the most interesting part: doing the actual photometry. As I said, we are using differential photometry, but there are some subtleties to it. The way we do it is to measure the brightness of the target star and the standard stars inside of circles or, say, apertures in the image (which is why this sub-procedure is called aperture photometry). We then follow to compare their measured brightness by subtraction in a log-scale, and this results in differences in the scale of magnitudes. These differences are then plotted, and what we have is, hopefully, a “rough draft” light curve of the target star. The plot will be, however, in an arbitrary unit for the magnitude. What we do is to normalize the differences in magnitude, by establishing that the highest values of differences should be zero (which is the same as saying that the difference of brightnesses of two non-variable stars should be null). If our target star has a variability, the difference in brightness will be seen as a shift from zero.

We have performed two observation sessions so far. The first one was more of a test, to see if the B&C telescope would be suitable for this kind of research. Most of our results at this point come from this first session. The second session was performed in the beginning of April and had two targets that were exoplanet host candidates, but the weather was crap. The following plots show the light curves that we have obtained so far. These results are very preliminary, though, because the observations weren’t, well, very good. We weren’t very experienced with transit observations, so we messed up on something very important: we didn’t get many exposures before and after the transit, so the bulk of the data is too concentrated during the event. Also, the plotted uncertainties are completely systematic, no statistical uncertainties were obtained thus far. Conditions were not photometric in either sessions.

Data reduction was done in IRAF. We performed differential photometry of the target star using the software AstroImageJ. Plots were created with Python, using NumPy, Matplotlib and Seaborn.

Light curve for the confirmed exoplanet host WASP 19, with a predicted transit depth of ~20 mmag. Notice that the y-axis contains the apparent magnitude of the star (obtained through comparison with another star in the field of view).
Light curve for the eclipsing binary KS21C009352. Notice the y-axis contains difference between the star’s current magnitude against its before/after transit magnitude. The predicted magnitude depth is ~30 mmag.
Light curve of the confirmed exoplanet host WASP 104. Notice the y-axis contains difference between the star’s current magnitude against its before/after transit magnitude. The predicted magnitude depth is ~15 mmag. Cloudiness affected this observation.

WASP-19 is a confirmed exoplanet host, with a transit depth of approximately 20 mmag. In our observation, we could only get the end of the transit, because the beginning was washed out by twilight. And we can see that the observed transit depth agrees very well with the predicted. Additionally, we observed KS21009352, which is an eclipsing binary with a depth of 30 mmag. Again, as we can see in the light curve, our observed depth agrees very well with the prediction.

Another interesting result is for the light curve of the confirmed exoplanet host WASP-104, which has a transit depth of approx. 15 mmag. The photometry we performed produced these weird outliers, and it was caused by cloudiness (it also happens for the targets of the second observation session, but it is even worse, reason why I didn’t plot them here). However, if we get rid of these outliers on the transit of WASP-104b, we can see that we managed to get a reasonably good agreement with the predicted depth (but the uncertainties are bigger when compared with WASP 19 and the eclipsing binary). I wonder if there is a way to improve the uncertainties (if you know something, please let me know in the comments).

We plan to have several other observation sessions throughout the year, this time observing actual exoplanet candidates for KELT South, so more results are coming. And hopefully better ones. I’m keeping a project page about this research that I will keep updated as things go on.

One’s small telescope is another’s exoplanet hunter