We have a curiosity about whether there is life on exoplanets, but how could we tell? Obviously, we have to know that the planet is there, then we have to know something about it. We have discovered the presence of a number of planets through the Doppler effect, in which the star wobbles a bit due to the gravitational force from the planet. The problem, of course, is that all we see is the star, and that tells us nothing other than the mass of the planet and its distance from the star. A shade more is found from observing an eclipse, because we see the size of the star, and in principle we get clues as to what is in an atmosphere, although in practice that information is extremely limited.
If you wish to find evidence of life, you have to first be able to see the planet that is in the habitable zone, and presumably has Earth-like characteristics. Thus the chances of finding evidence of life on a gas giant are negligible because if there were such life it would be totally unlike anything we know. So what are the difficulties? If we have a star with the same mass as our sun, the planet should be approximately 1 AU from the star. Now, take the Alpha Centauri system, the nearest stars, and about 1.3 parsec, or about 4.24 light years. To see something 1 AU away from the star requires an angular separation of about one arc-second, which is achievable with an 8 meter telescope. (For a star x times away, the required angular resolution becomes 1/x arc-seconds, which requires a correspondingly larger telescope. Accordingly, we need close stars.) However, no planets are known around Alpha Centauri A or B, although there are two around Proxima Centauri. Radial velocity studies show there is no habitable planet around A greater than about 53 earth-masses, or about 8.4 earth-masses around B. However, that does not mean no habitable planet because planets at these limits are almost certainly too big to hold life. Their absence, with that method of detection, actually improves the possibility of a habitable planet.
The first requirement for observing whether is life would seem to be that we actually directly observe the planet. Some planets have been directly observed but they are usually super-Jupiters on wide orbits (greater than10 AU) that, being very young, have temperatures greater than 1000 degrees C. The problem of an Earth-like planet is it is too dim in the visible. The peak emission intensity occurs in the mid-infrared for temperate planets, but there are further difficulties. One is the background is higher in the infrared, and another is that as you look at longer wavelengths there is a 2 – 5 times coarser spatial resolution due to the diffraction limit scaling. Apparently the best telescopes now have the resolution to detect planets around roughly the ten nearest stars. Having the sensitivity is another question.
Anyway, this has been attempted, and a candidate for an exoplanet around A has been claimed (Nature Communications, 2021, 12:922 ) at about 1.1 AU from the star. It is claimed to be within 7 times Earth’s size, but this is based on relative light intensity. Coupled with that is the possibility that this may not even be a planet at all. Essentially, more work is required.
Notwithstanding the uncertainty, it appears we are coming closer to being able to directly image rocky planets around the very closest stars. Other possible stars include Epsilon Eridani, Epsilon Indi, and Tau Ceti. But even then, if we see them, because it is at the limit of technology, we will still have no evidence one way or the other relating to life. However, it is a start to look where at least the right sized planet is known to exist. My personal preference is Epsilon Eridani. The reason is, it is a rather young star, and if there are planets there, they will be roughly as old as Earth and Mars were when life started on Earth and the great river flows occurred on Mars. Infrared signals from such atmospheres would tell us what comprised the atmospheres. My prediction is reduced, with a good amount of methane, and ammonia dissolved in water. The reason is these are the gases that could be formed through the original accretion, with no requirements for a bombardment by chondrites or comets, which seemingly, based on other evidence, did not happen here. Older planets will have more oxidized atmospheres that do not give clues, apart possibly if there are signals from ozone. Ozone implies oxygen, and that suggests plants.What should we aim to detect? The overall signal should indicate the temperature if we can resolve it. Water gives a good signal in the infrared, and seeing signals of water vapour in the atmosphere would show that that key material is present. For a young planet, methane and ammonia give good signals, although resolution may be difficult and ammonia will mainly be in water. The problems are obvious: getting sufficient signal intensity, subtracting out background noise from around the planet while realizing the planet will block background, actually resolving lines, and finally, correcting for other factors such as the Doppler effect so the lines can be properly interpreted. Remember phosphine on Venus? Errors are easy to make.