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Comments below this answer to How do we weigh a planet? point out that we currently cannot (or at least have not) detect moons around exoplanets, much less measure the sizes and periods of their orbits around their planets.

I commented there that:

...detecting exoplanets wasn't possible, nor did direct imaging of planetary systems, nor did making parallax measurements from the Kuiper belt, nor was the detection of gravitational waves...

my point being that impossibly challenging observations keep getting done.

So I'd like to ask what the most likely extension of observational Astronomy would be that would allow for the measurement of the period of exomoons thereby weighing exoplanets.

Is it simply a pair of space telescopes in a halo orbit with laser interferometry between them and plenty of time? Could it be done from Earth? After all, exoplanetary systems are already imaged from Earth.

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  • $\begingroup$ @AyushBhatt thanks for the edits! I like "didn't used to be possible" and I think it's not incorrect but only stylized, but your wording is better and more proper. $\endgroup$ – uhoh Sep 29 '20 at 3:36
  • $\begingroup$ Have you tried searching for papers on exomoon detection, if so what did you find? $\endgroup$ – user24157 Sep 29 '20 at 7:50
  • $\begingroup$ @antispinwards the challenge is to find enough to satisfy your request yet not enough to completely answer the question. The reason that I feel that challenge is that if I know the complete answer and don't post it, some will say that I ask in bad faith and yet others will have the opportunity to learn something, write an answer and collect some reuptation points (which I'm not after). On the other hand if I find the complete answer and do post it as an answer, others will complain that I'm gaming the system by asking and then quickly answering... $\endgroup$ – uhoh Sep 29 '20 at 8:13
  • $\begingroup$ @antispinwards and on the third hand if I find out the answer and then don't post the question because I know the answer, then everybody loses except me, and that's the worst outcome from my point of view. The first two have each happened to me more than once over the years, they are not hypothetical. I feel that an answer here will be a good thing, so I've done something to make that answer possible. Without the question, the answer can't be posted. $\endgroup$ – uhoh Sep 29 '20 at 8:14
  • $\begingroup$ @antispinwards based on my understanding of optics and interferometry, the proposed "pair of space telescopes in a halo orbit with laser interferometry between them" will certainly work in principle though quite challenging both in the hardware and the algorithms necessary to reduce the data in a model-dependent way. If you like I can elaborate on that in the question but it's simply an extension of current interferometry as addressed in answers to several of my previous questions and answers here: astronomy.stackexchange.com/search?q=user%3A7982+interferometry $\endgroup$ – uhoh Sep 29 '20 at 8:18
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My opinion (and I think there has to be a large element of that) is that the presence, and ultimately identification of the orbital period, of exomoons is going to come from very precise transit photometry.

If a sufficiently large moon orbits a planet, then this will leave its signature in the transit light curve. A "Fourier-type analysis" of the light curve might then reveal a periodic nature to the light curve shape during transit that could be attributed to the orbit of the moon. The requirements here would be a sufficiently large moon that its relative position alters the transit shape. The exoplanet also needs to be in a short period orbit so that you can observe lots of transits.

A related (and better) technique, that in practice would be used simultaneously, would be to look for the signature of a moon using changes in the duration and timing of transits that recur in a periodic way. The exoplanet-exomoon barycentre is what follows a Keplerian orbit; but the area-weighted "centre of opacity" of the system will, in general, not coincide with this barycentre because mass is proportional to $r^3$, while obscuring area is proportional to $r^2$. This will lead to a wobbling of both the time of transit and the transit duration that may again yield a periodic signal which could be identified with the exomoon period. These methods are discussed extensively by Kipping 2009, who point out that the transit timing and transit duration signatures have different dependencies on the exomoon mass and separation from the exoplanet and thus a careful measurement of both could yield the exomoon mass. i.e. Each method in its own has a degeneracy which means the exomoon mass/period could not be determined, but measured together, the degeneracy is broken.

There is a trade-off here. A wide exoplanet-exomoon separation will give bigger signatures, but of course by Kepler's third law, the orbital period will be longer and so you would likely need a longer dataset of transits to identify any periodicity and pin down the amplitude of these signatures.

At this stage, I don't think there is any likelihood of hearing about an exomoon period/mass in the next few years. Exomoon detection by these methods is though a possibility and may already have occurred (see Teachey & Kipping 2018) . Perhaps the PLATO mission, which will produce better light curves than TESS or Kepler, and have long datasets will stand a better chance (and indeed exomoon detection is one of the mission goals - see Rauer et al. 2014).

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An alternative prospect might be direct imaging, although the systems that can detect raise the question of whether or not they count as planets/exomoons. As a possible example, see Lazzoni et al. (2020) "The search for disks or planetary objects around directly imaged companions: A candidate around DH Tau B."

DH Tauri B is estimated as having 8–22 Jupiter masses (source), so is somewhere close to the deuterium-burning limit. It has a projected separation from its host star of approximately 320 au: the true separation will be larger because this does not include the component along the line-of-sight. The candidate companion is inferred to be around a Jupiter mass and has a projected separation of around 10 au from DH Tau B. If it exists, it is a rather extreme system compared to the planets and moons in our Solar System: you might argue that this is a low-mass binary brown dwarf.

Unfortunately the orbital period of the "satellite" is going to be on a timescale of centuries, so it will take quite a while to determine the orbital motion and the dynamical mass of the system.

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