Over the past week I’ve been having a whale of a time looking at lightcurves at http:/www.planethunters.org (I’m on there as EDG) – well, actually I seem to be spending more time discussing them and trying to figure them out! I’ve learned a few things in the process that might be useful to other planet hunters out there:
Making sense of Eclipsing Binaries
I’ve learned a lot about the light curves of eclipsing binaries (EBs) this week, which consist of two stars orbiting eachother with one star passing in front of the other as seen from our perspective (which changes the light curve). If you’re looking through the data and want to see what the lightcurves for these EBs look like, then check out pages 18-22 of this Kepler paper (right-click the link and select “save as” to save it), which shows some typical examples of detached, semi-detached, over-contact, ellipsoid, and irregular binaries (there’s an explanation on page 17 for what these types mean – “detached” means that the stars are far enough away to be distinct from eachother, “semi-detached” means that one star has overflowed its roche lobe and is distorted, and “over-contact” means that the two stars are close enough to share a common envelope (i.e. both have overflowed their roche lobes). A dead giveaway for detached eclipsing binaries is that there may be two dips on the lightcurve, but one is shorter than the other.
I definitely recommend checking the source data for stars that are being discussed (they’ve now added a “View Star” button to the discussion pages that lets you see that!). The source data has the compressed ‘slider bar’ version of the data in which repeating patterns are very obvious (much more so than in the main graph). I’ve pointed this out in the image below (click the image to expand it):
When repeating patterns show up in the data, they can be misleading in the main graph because Kepler’s observations are often out of sync with the variability cycle, so you get what look like overlapping large-scale sine-wave patterns. A great example of this is http://www.planethunters.org/sources/SPH10026176 (you’ll need to be logged in to planethunters to see it) – compare the main graph with the compressed graph at the bottom and you’ll see the high-frequency oscillations at the bottom much more clearly. The thing to remember is that the data points on the graph are sequential and linear in time (from left to right) – your brain might see that overlapping sine-wave pattern on the main graph but if you actually follow the individual datapoints from left to right you’ll see that they’re actually going up and down very rapidly (this is what the compressed graph shows). So the moral of the story is that if you see something weird, look at the compressed view to help you understand what’s going on, and take the time to read the data points from left to right if you need to (and don’t be afraid to zoom in using the slider bars!).
The y-axis scale
The y-axis shows the normalised brightness of the star – if the average brightness of the star is “1” on the graph, then a transit would block off some of the light and create a dip in the graph (if it drops to 0.9, then 10% of the star’s light is blocked). While you can zoom in and out of the x-axis (time), the y-axis currently autoscales to the data on the graph (the highest and lowest data points mark the upper and lower boundary of the y-axis). This can be very misleading when it comes to classifying the “variability” of each star because “quiet” stars can appear very noisy – for example, the lightcurve I showed in my previous post here is actually a “Quiet” star because the y-variation is between about 0.9995 and 1.0005, but the data looks like it’s jumping up and down a lot between that range. If that lightcurve had a planetary transit in it though, it’d be rescaled to show the whole dip caused by the transit (say, to cover the range from 0.800 to 1.005), and the main lightcurve would look very flat as a result. So be sure to check the y-axis values on the graph!
Variable stars are pretty obvious – their curves rise and fall over the 35 day observation period (e.g. http://talk.planethunters.org/objects/APH10148662) and as you can see the y-variation is considerably greater than for the quiet stars. One potential issue is that variable stars can actually look like some types of eclipsing binary, so it’s hard to be sure whether you really are looking at a single star that is variable because of something going on inside it (i.e. an intrinsic variable) or an eclipsing binary. I’ve made a collection of what I think are variable stars at http://talk.planethunters.org/collections/CPHS00001v so you can see a few examples of those.
Simulating Transits in Celestia (for intermediate/advanced users)
Last night I decided to try to simulate a transit in Celestia. This turned out to be rather fiddly, but I’ve managed to get something useful working! You can download the transit.ssc file here (you’ll need to be familiar with Celestia to use this effectively).
What I did was create several “test objects” that are at fixed distances (10 AU, 100 AU, 1000 AU, 5000 AU, and 10000 AU) that are at fixed locations around the star that don’t move (they’re all on the same line drawn in space from the centre of the star, and I gave them extremely long orbital periods so their positions don’t change) . You can then go to them in Celestia and use them as vantage points to watch transits closer to the star (I’ll explain more about the transits later).
To use them, create the star in Celestia (I made one called primary.stc that you can download and edit – you might have to right-click on the link and select “save as” to save the file) and create the transiting planet in Celestia (I’ve put a planet that you can edit in the transits.ssc file). If you change the star name, make sure you edit the name in the ssc file as well! Make sure both of the files are in the extras folder in your Celestia directory.
Once you’ve sorted that out, fire up Celestia, and use Navigation/Goto Object to go to the star. Enter the star name, enter lat and lon of 0 and a distance of 0.1 AU, and press the “Go To” button. When you arrive, you can hit “Enter” to bring up the console and type your planet name and press C to centre the view on it just so you know it’s there. Then bring up the console again and type “test1” (or whichever test object you want to go to), and press G to go to it. Once there, hit F to follow the test object (you’ll be in sync orbit mode around it otherwise, which you don’t want!), Then hit “Enter” again and type the star name, and then press “:” to Lock onto the star (you should see “Lock test1 -> Primary” in the bottom right). Then press C to centre the view on the primary star. Use the “<" and ">” keys to change the magnification and zoom in on the star until it fills your field of view (you should be able to see the left and right edges of the star though), and use the K and L keys to speed up and slow down time until you see your planet come into view (use J to reverse time if you overshoot).
The aim is to watch the planet transit the star. Technically the full duration of the transit is from when the planet first touches the limb of the star as it moves in (“first contact“), to when the last part of the planet stops touching the star as it moves away (“fourth contact“) – that’s the duration when at least some of the star’s light is being blocked by the planet. Another way to do it is to measure the time between “second contact” (when the planet’s disc is entirely within the star’s disc, moving inwards) and “third contact” (when the planet’s disc is entirely within the star’s disc, moving outwards), but that only measures the length of time of the brightness minimum cause by the transit. These are illustrated in the Celestia screenshots below:
Either way, you can slow down time and note down the exact point of first (or second) contact, then speed up time and watch the planet move across the star’s disc from your vantage point, and then slow it down again and note the exact point of fourth (or third) contact, and you have your transit time as seen from that distance!
There are a few issues to be aware of here:
First, you need to pre-calculate the appropriate values for orbital period, distance, stellar and planetary radius and mass in the stc and ssc files. You’ll also need to know the star’s mass (you can estimate it from the stellar type that they give you).
Second, the transits aren’t very accurate at large distances in Celestia. test3 (at 1000 AU) is the ideal vantage point to use, because you can get the most accurate value for transit time from there – go much further than that and you can’t zoom in far enough to time the transit accurately (and the star texture gets a bit wobbly too). test4 is pushing the limit of accuracy, and test5 is probably too far (you’ll find your values are probably a bit off from there because the planet is too small and the star’s disc is too unstable in Celestia).
Transit times as viewed from increasing distance from the star.
If you measure the same transit from the different vantage points, you’ll notice that the transit times converge as the distance from the star increases. For one of the transits I was simulating, the transit (from first contact to fourth contact) took 38 hr 10 min when viewed from 10 AU. At 100 AU, it took 46h 00m. At 1000 AU, it took 47h 44m. At 5000 AU, it took 47h 52 m. Presumably if I went further out to distances of tens or hundreds or thousands of lightyears, the transit time would probably flatten out (in this case) to a value around 48 hours.
The transit time is longest when viewed from location 3 (the black dot on the line, furthest from the star), and shortest when viewed from location 1 (closest to the star). This is because 1 only sees the planet moving along the black part of the orbit within the triangle drawn from it to the edges of the star (representing the field of view from that location). Location 2, being further away, sees the black and green parts of the orbit within its triangle, and Location 3 see the black part+green parts+red parts of the orbit within its triangle. As you go even further, less and less of the planet’s orbit is added to the view, so the transit time converges as you go further (e.g. many lightyears away).
This is why viewing the transit from test3 in Celestia (1000 AU) is ideal, because it’s far enough away from the star that the transit time is close to the converged value that you’d see at even greater distances.
A few other things…
A couple more things to be aware of – the eccentricity of the planet’s orbit makes a big difference to its transit time! This is because the planet moves fastest near its pericentre (when it is closest to the star on its orbit) and slowest at its apocentre (when it is at the greatest distance from the star on its orbit). One planet I tried took about 4 hours to cross the star at its pericentre, and about 13.5 hours at its apocentre! So the orientation of the eccentric orbit is also important (you can adjust that in Celestia by changing the LongOfPericenter value) – if the orbit is oriented so that the pericentre is pointing towards the viewer then the planet will cross the disc faster than it would if it was oriented differently.
I’ve also been assuming that the planet crosses the star’s equator from the viewer’s perspective, but that’s not necessarily true – the planet is very likely to cross ‘off-centre’ or just clip the star’s disc because of the orientation of its orbit, in which case the transit won’t have a nice flat bottom and it’ll look more “pointy”. So that’s another complication to deal with when simulating them!
As you can see, there’s a lot to consider here if you want to figure out what’s going on in these lightcurves! I’m loving all this though, because this is exactly what science is all about – looking at the data, simulating things, experimenting, modelling, and learning how stuff works! 🙂