One of my day-to-day jobs as an exoplanet astronomer is to look through transiting exoplanet candidates and find those that are actually from exoplanets. However, scrolling through Kepler, K2 or TESS lightcurves is something anyone can do – professionals and amateurs alike. Therefore, it may be useful for me to go through a few of the steps we use as professionals to determine what makes, and what kills, a good planet candidate.

First some key points:

• The majority of “dips” found by photometric surveys are not planets – they are false positives like eclipsing binaries (stars crossing stars), or even just junk noise from the detector.
• Even good-looking planet candidates are not, on their own, interesting or publishable. To confirm a planet there needs to be a lot of follow-up time on ground-based telescopes, as well as a lot of complex data analysis.
• But you can still make a contribution to exoplanet science by finding previously-missed planet candidates and passing them to astronomers.

So let’s get started…

1. What makes a transiting planet candidate?

Planets can be found by searching the shadow they cast as they pass in front of their parent star – effectively blocking a bit of starlight for a few hours. This is the famous “transit” effect. However, we don’t see the shadow directly (except during transits within our solar system – i.e. the transit of Venus which is shown below). Instead, the star is seen as a “point source” with all the light from the star smeared onto a few pixels on a detector. But, by adding up the light from the star across those pixels and plotting it against time (this is “photometry” and produces a so-called “light curve”) we can see the “transit” in the data – a U-shaped dip. We can immediately throw out signals that jump up (instead of down), or asymmetric events which drop down without ever jumping back up again – planets only ever cause symmetrical dips.

Planets are also strictly periodic – their signals repeat precisely once every orbit. Therefore, good planet candidates should have repeating dips as is shown below. However, this isn’t strictly necessary – long-period planets may transit only once. But we can still assess these monotransits with the same rules.

This strictly periodic nature means we typically search do not find planets by looking at lightcurves – instead we search through a range of potential periods and stack data together (e.g. using BLS or TLS). If the period matches the real period, each transit stacks together, and their combined signal is strong, producing a spike on a periodogram. This lets us delve into the noise and find shallower transits.

2. Information from the transit

So you have found a dip… The most useful information now comes from the depth of the dip. The reason for this is obvious when you think about the geometry of a transit – the bigger the transiting object is, the more light it blocks.

Using geometry, the area of the star emitting light is πR_s², while the area of that star being blocked by the planet is πR_p², so the depth is the ratio of these, i.e. (R_p/R_s)².

Planets are, by definition, objects smaller than stars. Typically, giant planets top out at about 20 earth radii, or about 0.2 solar radii. So, for a star like the Sun, the maximum possible depth from a planet transit is 0.2² = 0.04. So if you found an interesting dip which seems to drop by greater than 4%, then it’s not a planet – it’s one star orbiting another, or what we call an eclipsing binary (or EB). And even dips between 1% and 4% are far more likely due to EBs than planets.

Not every star is like the Sun. But thanks to Gaia there are estimates of stellar radii for almost every star in the sky. If you’re looking at TESS data you can check the TESS ID in ExoFop-TESS, while MAST has data for K2/EPIC IDs and for Kepler IDs. Now you have a transit depth and a stellar radius you can estimate a planetary radius (R_p= R_s√depth).

Giant stars 10 times the radius of the Sun will effectively never have detectable transiting planets around as the limit drops from (0.2/1)²=4% to (0.2/10)²=0.04%. Smaller M-dwarf stars could host planet that are almost as large as their stars themselves, however giant planets are extremely rare around M-dwarfs, and typically the <4% rule holds for all stars smaller than the Sun too.

3. Transit Shape

It’s not only the depth of the lightcurve which contains information about the transiting object – the shape of the transit does too. Typically, us astronomers would model the lightcurve with a transit model, and this would produce parameters including a better estimate of planetary radius, period, as well as all the transit geometry. For this modelling, programs like Jason Eastmans’s exofast2 are good places to start.

However, for just a simple sense of what else the transit tells us, here’s a couple of points:

• V-shaped dips are caused by objects that do not fully traverse the stellar disc. This means their radius is larger than the radius calculated using (R_p/R_s)². The exact boundary depends on many parameter, but even a 1%-deep V-shaped dip (i.e. one that does not have a flat bottom) is far more likely to be a binary than an exoplanet.

• Transit duration (t_dur) should match the stellar density (ρ_s). There is a bit of weird geometry to do before it’s obvious why this is the case, but transit duration is proportional to the stellar density & planet period where P/t_dur³ ~ 5000 ρ_s. So for a P=10d transiting planet with a 0.1-day transit duration (2.4hrs), the computed density roughly suggests a star slightly denser than the sun (with ρ_s~2). If this is hugely discrepant with the actual density of the star (as provided on ExoFop or MAST), it suggests the object is in fact an EB. However, the transit duration can vary by a factor of 2-3 here, so only really large discrepancies (a factor of >10) are useful.

4. Out-of-transit features

Transiting planets can be thought of as simple black spheres which are only seen when they cross the star and block it’s light. Eclipsing binaries, however, are due to stars of their own and emit their own light, and therefore we often see their effects out of transit as well. So if there are any of the following features in the lightcurve, we can safely call this candidate an eclipsing binary and not a planet:

Secondary Eclipses

While planets cause one dip per year, eclipsing binaries often cause two – one when the dimmer star passes in front of the brighter star (the “primary eclipse”), and another smaller dip when the smaller star passes behind it’s larger host (the “secondary eclipse”). This might look like one of two things:

1. A smaller dip seen consistently at the same place between each “transit”:

2. A slight difference in depth between odd transits and even transits (caused by two similar-sized stars):

For circular orbits, the secondary eclipse should happen when a star is half way round its orbit (i.e. at phase 0.5). But this is not always the case – eccentric orbits mean that often that the position of the secondary eclipse is offset from this mid-point.

Synchronised sinusoidal variations

Stars are typically variable due to starspots & other effects. However, for planets, those up-and-down wiggles are never linked to the planet’s period. If the wiggles in the lightcurve are synchronised with the transit period, then that’s a sure sign that you’re looking at an eclipsing binary.

That’s because, when the transiting object is massive enough to influence the primary star and bright enough to produce its own light, they can produce sinusoidal signals linked to the binary period due to:

• tidal effect of the smaller star synchronising the stellar rotation of the primary star so starspots spin with the companion;
• a hot-spot located at the noon position of the smaller star;
• the gravitational pull of each star on the other stretching the stars into elongated ovals creating two cycles of “ellipsoidal” variation per period;
• the velocity of the smaller star’s orbit causing a “beaming” effect where light is red- & blue-shifted into & out-of the colour range that the spacecraft observes;
• some combination of all of these effects.

5. Extra Checks

There are a couple of final checks which require a little more effort than merely looking at the lightcurve.

One of the key things to check is: is this already a known candidate? For TESS & K2, this should be obvious on the ExoFop page for that target. For Kepler you can check if it’s on the Kepler candidate list. In both cases, these catalogues should also contain a disposition – i.e. whether the Kepler or TESS vetters have also determined it to be a planet (PC), or a false positive (FP, NTP, EB, etc). If it has already been detected (and at a period and epoch that matches), there is not much that you can do – astronomers already have this on their lists and it will be (or will have been already) published without your help. That’s the way it goes sometimes!

If it’s not known, then there’s a chance you have an interesting target that astronomers missed!

One of the key points is that the dip should be occurring on the brighter target star in the field you’re looking at. If a star which only contributes a small fraction of the light is causing the dip, it must be dimming proportionately by a large amount. For exmple, if you see a 1% dip but it’s actually coming from a nearby star which only provides 4% of the light, then that star must have dimmed by 25% – far too deeply to be a planet! The best way to do this check is to:

1. Check the lightcurves of nearby stars to see if they are causing the dip.
2. Check the “centroid position”. The centroid is a weighted average of the flux coming from the star onto the detector, and any shift in this between the in-transit images & out-of-transit images moves is a sign that a nearby unresolved star is causing the dip and not the target star.
3. See if the depth of the transit increases as a function of the “aperture” size (i.e. the number of pixels used to compute the lightcurve). A larger depth at larger apertures suggests the star is a blended nearby star not at the position of the target star.

Another useful check is using Gaia’s radial velocity and astrometry error – if these are high it’s typically because the target star is in fact two stars which are constantly in motion. This can be done by typing the coordinates into a Gaia cone search and scrolling down to the astrometric_excess_noise_sig and dr2_radial_velocity_error parameters. If either of these are higher than about 5, it’s a sign that the object is a binary (though this is not always true).

6. What Now?

So you’ve found a candidate which seems to pass most of these tests… What now?

As I mentioned at the start, it isn’t just a case of “upload it to the exoplanet database and move onto the next one” – these databases only contain planets that have been published in the academic literature, and have been independently & statistically verified.

So, if you’re simply an amateur scrolling through lightcurves for fun, what do you do now? One nice next step would be to share it on the planethunters message boards as the interesting cases will make their way to astronomers. Alternatively you can directly email the candidate to an exoplanet astronomer (like me), and we’ll let you know if we think the candidate is interesting, and likely pass it on to someone better suited to studying (and eventually publishing) that candidate as a planet. But – fair warning – even if you think your candidate is awesome, and even if an astronomer agrees that it’s likely a planet, that doesn’t necessary mean that it’s easy or interesting enough to get published. Some cases are very tricky and require a lot of extra observations – something that typically only happens for interesting cases.

Another avenue, only to be taken for candidate you are sure are real, is to propose it as a Community TOI through ExoFop-TESS. However, it’s best to get confirmation from an exoplanet astronomer and TESS member before doing this.

I hope this proves a useful guide! Happy hunting.

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For more basic info on transiting exoplanets, check out Andrew Vanderburg’s light curve tutorial and Paul Wilson’s exoplanet transit method page.