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An approximation of the dimming of exoplanet transits can be obtained by dividing the areas of the disks of the exoplanet and star by each other.

Taking the radii of Jupiter and our sun results in an area ratio of (69,911 km)^2 / (696,340 km)^2 = 0.0101, so a brightness change in the 1%-5% range most exoplanets detected by the transit method are in.

This is possible to observe even with amateur telescopes, but Earth-like planets seem to be much more difficult:

Earth's ratio to the sun, having an area only a tenth of Jupiter (6,371 km), is 0.0000837, or roughly 1/12000, approximately 100 times smaller.

Assuming one uses a 16-bit camera, if the exposure time is optimized to be just below saturation, this would amount to a 5-6 count difference - which seems incredibly small, but perhaps possible to reliably detect/confirm with statistical methods?

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How many Earth-sized planets have been discovered with ground-based telescopes using the transiting techique? The answer will be somewhere between zero (around solar-type stars) and not many if you restrict the sample strictly to Earth-radius and below.

The problem is not the signal-to-noise ratio in your data. If you had a big enough telescope you can easily collect enough counts to significantly detect a 0.01% dip in light - though you would need to make sure the starlight was spread over many pixels on your detector, since a dip of 6 counts in 60,000 is not statistically significant.

No, the problem for a ground-based telescope is that there are all sorts of other things that cause the brightness of a star to vary by much more than 0.01% over the period of a few hours as a pnaet moves into transit and then out again.

Your only hope with ground based telecopes is to choose much smaller and less luminous stars, so that the transit depth is more like 1%. This is how the TRAPPIST small telescope at La Silla in Chile works and it has discovered Earth-sized planets around very low-mass and small stars (e.g. Trappist-1).

So your best best is to chase small planets that are orbiting very small stars. You will not be able to spot a transit of an Earth-sized planet around a Sun-like star using a ground-based telescope.

To illustrate the problem - here is discovery data and follow-up photometry for the Trappist-1 planets from Gillon et al. (2016). The upper transit is I guess representative of the discovery data, taken in the near-infrared with a 0.6-m telescope in the near-infrared. The subsequent transits are follow up on a 2-m, a 3.8-m and an 8.2-m telescope resepectively. The light curves improve a bit in quality, but not massively and not in proportion to the factor of 100 gain in aperture area. The problem is that the star is also variable at some level as well as the problem of controlling for variations in atmospheric extinction. And these observations have been performed as carefully as possible.

Transit curves for Trappist-1

The upper curve is probably representative of what a really good, dedicated amateur programme could produce. The scatter on the data is of order 0.1% and thus you can see a 1% transit reasonably well. A 0.01% transit would not be detected with any significance.

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    $\begingroup$ Yep. That's why we put TESS in cislunar space. The cameras are small by amateur telescope standards. The effective camera aperture is only 10 cm, but that's enough to collect the necessary light. One good thing about being out that far is that you're not only above the atmosphere, you're far from it, so scattered light is minimized. Also, the thermal environment is extremely stable. Temperature affects optics and electronics, so keeping it stable is a key to accurate relative photometry. $\endgroup$
    – John Doty
    Jan 21, 2023 at 15:15
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You analyse the main challenge in detecting or re-detecting exoplanets quite well - and you also present the solution: a decently sensitive-enough camera to resolve these brightness changes.

Five to six counts could be challenging but should be just enough enough difference from my experience on this kind of project: It's a good student or amateur project. Some years ago, I did this as part of the practical exercise for our students as a joint project with the local observatory. While we chose the larger exoplanets for this project (thus around 1% darkening), we also had a camera which had 16 bit, so that the signal for these large planets was quite clear. Further, the stars are not visible as a single-pixel object, but cover several pixel in the view. Thus integrating their total signal improved signal-to-noise (SNR) also quite a bit. The cooling functionality of the SBIG8 camera helped, too, in order to reduce the SNR.

I'd recommend to keep the exposure time reasonably short though (like up to 10 minutes at most) in order to get a decently enough time-resolved light curve - and you will need enough of comparison stars in the FOV in order to compensate for the inevitable change of atmospheric influence (be that different elevation of your FOV as the night progresses, or simply change in water content etc - they all have a similar effect on brightness, and you need your reference stars to detect this).

Doing proper dark frame and possibly bias frame reduction also helps your results.

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