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« Photometry of Contaminated Kepler Pixels

Aleksa Sarai

astronomy k2 kepler physics research tsp usyd

03 November 2015

I’ve always loved science, and have always wanted to do research ever since I was a kid. The sense of discovery and learning more about the universe speaks to me on a very fundamental level.

I recently participated in the Talented Student Program, where undergraduate students are given the opportunity to conduct real-world research. After talking to a few different research groups, I settled on an interesting project idea pitched by Tim Bedding, Daniel Huber, and Simon Murphy. Is it possible to do analysis of light coming from a star using a telescope that hasn’t explicitly collected data for the star?

Asteroseismology

Before discussing the research I’ve been working on for the past few months, I should probably explain what modern astrophysics consists of. One of the more interesting fields in astrophysics is a field called “asteroseismology”. Not unlike it’s Earth counter-part, asteroseismology is concerned with oscillations of stars.

Not all stars are not static balls of hot gas. Some are quite active, and vibrate through several different driving forces. Sound waves travel from the center of the star to the surface, which are known as p-modes (because pressure is the restoring force). Similarly, there are g-modes, where the restoring force is buoyancy. These oscillations are affected by the structure and other parameters of the star. In particular, the frequency of the oscillations (as well as which modes of oscillation are excited and the amplitude of the oscillations) are very strongly defined by stellar parameters.

As such, you should be able to convince yourself that an understanding of the underlying physics would allow for otherwise impossibly accurate measurement of stellar parameters through the measurement of the oscillation of stars. As it turns out, such an understanding does exist (you can even read very expensive textbooks on the subject).

But how do we detect these oscillations?

Photometry

One of the many techniques of detecting these oscillations is photometry. And, in a way, it’s the most obvious one: count how many photons of light you detect coming from a star over a certain exposure, do a bunch of exposures and store the timestamp of each one, and analyse that time series. There are some issues with this technique (as being limited to only detecting low-degree oscillations), but it is fairly robust and works pretty well.

Kepler and the K2 Mission

So, what is Kepler and what is K2? Kepler is a space telescope which uses photometry to try and detect transiting exoplanets. However, due to its incredibly accurate photometric detectors (CCDs) it is also an invaluable asteroseismic instrument. It’s original task was to observe a fairly uninteresting part of the sky (which contained no bright stars and was slightly above the ecliptic plane), and store photometric data for hundreds of thousands of targets.

However, by 2013 (4 years after launch) two of the four reaction wheels used to provide fine pointing control had malfunctioned. As a result, Kepler could no longer observe the original field (as radiation pressure from our Sun would make it unstable). As such, a new mission was proposed to observe fields along the ecliptic plane. As a result, Kepler would observe a very different set of stars to the original mission. This mission would be called K2, and with it would come plenty of fascinating astrophysics research.

However, for the purpose of my research, what is most interesting about K2 is that there are many more very bright stars in the new fields. Bright stars are interesting for a variety of reasons (mainly that they have been well studied from the ground for hundreds of years, and that accurate data on their oscillations can be used to improve existing models of stars).

Postage Stamps

Unfortunately, bandwidth is limited. Due to Kepler‘s distance from the Earth, and the sheer amount of data available, not all of the photometric data (which is taken every 30 minutes) can be downloaded for all Kepler pixels. To deal with this, Kepler provides only certain pre-determined pixel masks. Only about 5% of pixels captured by Kepler are actually sent to Earth. These pixel masks are called “postage stamps”.

It was generally believed that the only way to do photometry for bright stars is to count all of the light (flux) from the star. Making postage stamps for bright stars was therefore too expensive in terms of bandwidth, because bright stars have halos and other effects such that they require many more pixels (more than 100 times as many) to contain all of the light from the star.

The main point of my research project was to determine if this assumption was true, and to see if it would be possible to do bright star photometry without having all of the light from the star.

Contamination

Optics in Kepler (or any telescope for that matter) are far from perfect. Incident photons are diffracted on the supports for the sensors and internally reflected inside the actual photometric sensors. These result in the target star (which would normally be considered a point source, due to the distance from the sensor to the star being much larger than the diameter of the region of pixels its photons land on), having a “halo”. More information can be found here.

We assume that this halo has a photon count proportional to the incident photon count, as there doesn’t appear to be any bias within the optics regarding halo production. As such, it should be in principle possible to do photometry using nothing but the halo of a star (and further, only a subset of pixels in the halo of a star).

However, this idea was not known about (it’s entirely novel), so there are no nice postage stamps of subsets of halo pixels of bright stars. As a result, we had to find serendipitous postage stamps which happen to fall inside a bright stars halo. As it turns out, these postage stamps are not as rare as you might assume. While pixel bandwidth is very precious, many postage stamp proposals don’t appear to be too mindful of whether they are very close to an exceptionally bright star that will render that postage stamp useless to that researcher.

Method

So, with all of that background in order, let’s get to the nitty-gritty. The first problem to deal with is the fact that Kepler‘s pointing malfunctions result in an apparent motion of targets on the detector. This introduces a pseudo-variability, due to flux moving between pixels and crossing the postage stamp boundaries. As a result, accurate digital tracking data is required.

As the Kepler systematics are rotational in nature, a rotational model was created by Benjamin Pope (a fellow researcher) by computing the centroid of each postage stamp and tracking it for each timestamp. This apparent motion is used to accurately predict the rotational offset for each timestamp.

An aperture was manually selected to contain all halo flux which does not leave the postage stamp or become otherwise contaminated by the intended target. This aperture was then converted to a polygon with feathered edges, which is then integrated over for each cadence. From this, a time series is created which can then be analysed.

So … did it work?

Yes. Yes it did. We did only attempt this technique on a dozen postage stamps or so, due to time constraints. However, I will be continuing this research during the summer (and will hopefully get a paper published on the topic). Incidentally, I was also co-author on a paper which discusses a different technique for doing bright star photometry with Kepler smear data (which was discovered as a result of the research I’ve been doing).

I’m very excited about all of this, and have been absolutely enthralled in all of the things I’ve learnt as part of this project. While I know that I have a lot more to learn, and hopefully much more research to do, I am glad to now be able to point to something and say “I’ve done something real”.

Where’s the code at?

Of course, the code is free software and is available on GitHub, licensed under the GNU General Public License (version 2 only). The reason for using the GPL, rather than my usual choice of the MIT license is mainly philosophical, and is thoroughly explained here.