At every public lecture on exoplanets, someone necessarily asks a question about exoplanet satellites. The question is so interesting that it deserves a separate article.
At the moment, the number of found exoplanets is approaching six thousand (including unconfirmed ones). How many large satellites should these planets have? Looking at our solar system, we can assume that about the same - we have seven satellites the size of the moon and larger for eight planets (Moon, Io, Europa, Ganymede, Callisto, Titan, Triton). What about the satellites of exoplanets? Alas, so far almost nothing. Yet the first, as yet vague, results are beginning to emerge.
The satellites of the planets are interesting because life is possible on them, even if the planet is gigantic and in itself is in no way adapted for life. For example, quite a few giant planets were found in the "habitable zone" (45 according to 2014 data). If they have large enough satellites, why shouldn't life arise on them? There should be a wonderful view: a giant planet dominating the sky, visible both night and day. Of course, such a picture inspires artists, and to some extent researchers, working with Kepler's data. Apparently, this data is the only place where an exoplanet satellite can currently be discovered.
For starters, some useful concepts.
A planet's satellite cannot revolve around it at any distance. The size of the orbit is limited from above by the so-called Hill sphere, outside which the satellite leaves the gravitational field of the planet and becomes an independent companion of the star. Here is the radius of this sphere for the simplest case, when the satellite's orbit is circular: RH = a (m / 3M) 1/3, where a is the semi-major axis of the planet's orbit, m is the planet's mass, M is the star's mass. For the Earth, the Hill radius is about 1.5 million km. A little further away are the Lagrange points L1 and L2, where space telescopes are taken out. Hill's radius near Neptune, a record in the solar system, is about 100 million km. In reality, due to various disturbing factors, the radius of the orbits, which are stable on a scale of billions of years, is less - about half or even a third of the Hill radius.
The size of the orbit is also limited from below: in a too close orbit, the satellite is torn apart by the gravity of the planet and turns into a kind of rings of Saturn. This limit is called the Roche zone, its essence: the tidal forces exceed the self-gravity of the satellite. The Roche limit depends on the rigidity of the latter: if a satellite can deform like a liquid, then the Roche limit is almost twice as large. All satellites of the solar system are outside the "hard" Roche limit, but some happily exist inside the "liquid" limit, for example, the five closest satellites of Saturn.
For the hottest Jupiters, the radius of the Hill sphere is close to the Roche limit - they certainly cannot have satellites. But there are other mechanisms for the instability of satellite orbits operating in the vicinity of the star, so that the probability of the existence of satellites in planets with an orbital period of up to 10-20 days for billions of years is negligible. It is a pity, since there are a lot of short-period exoplanets among the discovered exoplanets, and in the coming years they will dominate among new arrivals. And, most importantly, the satellites of short-period planets would be easiest to detect if they were there.
But we are most interested in the satellites of the planets in the "habitable zone". There, their orbits can be stable for many billions of years - look at the moon.
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How to find an exoplanet satellite
How big can planetary satellites be? Judging by the solar system, the typical ratio of the total mass of satellites and the mass of the planet is 1/10000. This is true for the Jupiter system, Saturn (with a slight excess due to Titan) and Uranus. Neptune and Mars have less "native" satellites (Triton is not native, it is a captured Kuiper belt object). Apparently, such a ratio is natural when satellites are formed from a dusty disk around the planet. The moon is a separate conversation, its mass is two orders of magnitude higher than the typical mass of satellites, it was formed as a result of a catastrophic collision. Then we have the right to expect that the mass of superjupiter satellites with 10 Jupiterian masses (and there are many such have been found) will be of the order of the mass of Mars. Such a body may well be noticeable during the transit of a planet - first, the star is eclipsed by the satellite, then the planet itself. The effect from the satellite will be a hundred times less, but with good transit statistics (the planet crosses the star's disk many times), it can be more or less reliably detected. Of course, a captured planet can also be a satellite, in this case it can be significantly larger, but hardly anyone is able to say what the probability of finding an abnormally large captured object is.
Another option is transit timing. If the satellite is ahead of the planet in its orbit around the star, the transit of the planet occurs a little later, if it lags behind - a little earlier. For example, if all the satellites of Jupiter are assembled into one and placed in the place of Ganymede, then the displacement of Jupiter will be plus or minus 100 km, which is expressed in a delay / advance of transits by about 7 s - 4 orders of magnitude less transit time. This is far beyond measurement accuracy. The satellite must be abnormally large. In general, this method is weaker than the previous one.
Satellites of planets, in principle, cannot be detected by the spectrometric method from the radial velocity of a star - here all conceivable effects from a satellite are negligible.
The method of gravitational microlensing remains, but it is based on rare luck. If the background star (not the host star, but the distant one in the background) passes exactly behind the planet with the satellite, a double spike will appear in the light curve of this star.
Three transits of the planet Kepler 1625b (there are only three in the Kepler database). The light curve of the star Kepler 1625 is shown. The solid line is - fitting model with a satellite the size of Neptune. The statistical significance of the model - 4.1 σ. If we remove the third transit, the significance drops to a negligible value.
In general, the most promising is the first of the listed methods - satellite transit. It requires a very large array of observations. Such an array exists, it is Kepler's archival data, which are in the public domain. Kepler worked on the main program for a little over four years. It is not enough to reliably detect satellite transits in the "zone of life", but the best data does not exist. At the moment, traces of satellites must be looked for there, and it is quite possible that one satellite has already been found.
The search for exoluns
The first hint of satellites was found near the planet with the "telephone number" 1SWASP J140747.93-394542.6 b. It is a giant planet with a mass of 20 Jupiter - on the verge of a brown dwarf1. Transits showed that it has a huge system of rings, the rings have gaps, and satellites should sit in the gaps - they eat these gaps. It's all. There is no other information about these satellites.
Another satellite was found by microlensing an orphan planet flying freely in space. It is difficult to say something about the mass of the planet and the satellite - it may be a brown dwarf with a "neptune" orbiting around it. This case is not so interesting.
In 2012, astronomers at the Pulkovo Observatory announced the possible discovery of a satellite near the exoplanet WASP 12b. It is a very hot Jupiter orbiting a Sun-class star in a day. During the transit of the planet, bursts of brightness were observed, which, according to the authors of the observations, can be interpreted as the passage of the planet through star spots or as a satellite of the planet, periodically merging with its disk. The second interpretation caused a noticeable response in the Russian press, but it is simply not physical: the Hill sphere for this planet practically coincides with the Roche zone. There can be no satellite there.
To search for exoons in the Kepler data, the HEK (Hunt for Exomoons with Kepler) project was organized. The project team has shaken up the data well and seems to have pulled some useful information out of there. True, not very optimistic. The results below were published in October 2017 in one article2.
On the one hand, an indication of the satellite of the planet Kepler 1625 b was found. The statistical significance is about 4 σ, which is rather small, given the large number of exoplanets studied. Worse, in the same study, an "antisatellite" was found near a planet of one of the stars, that is, a signal of the opposite sign with the same significance of 4 σ. It is clear that this signal is false, since there are no natural phenomena imitating the "anti-satellite". Moreover, the planet had only three transits, and only one of them is convincing enough. If the effect is confirmed, it will be a satellite the size of Neptune for a planet with a mass of at least 10 Jupiter masses (the mass is estimated from the orbit of the alleged satellite), which corresponds to the captured planet. The satellite with the planet is in the "life zone": heating is exactly the same as that of the Earth. The orbit of the putative planet is stable - deep within the Hill sphere and far beyond the Roche limit. The authors do not insist on the discovery and ordered the observation of Kepler 1625 by the Hubble telescope for October 28-29, 2017 - the time of the next transit. It took place. There is no published information, except for a conference abstract with a summary “preliminary results of observations are being reported”. This most likely means that the observation did not give an unambiguous result.that the observation did not give an unambiguous result.that the observation did not give an unambiguous result.
Another disappointing result comes from adding up the transits of many planets from the Kepler database. The authors have selected more than three hundred exoplanets, which, from their point of view, are the most promising for searching for satellites. Criteria include an orbit between 1 and 0.1 AU and good data quality. As the desired effect, the darkening of the star from the analogue of the Galilean satellites of the planet, i.e., the analogs of the Galilean satellites of Jupiter scaled by the size of the planet, were revealed. In this case, the sum of the light curves for all transits of all planets in the sample was taken.
Alas, the positive signal does not exceed 2 σ, and the result puts a scientifically significant upper limit on the abundance of large satellites. The proportion of planets with an analogue of the Galilean satellites does not exceed 0.38 at the 95% confidence level.
It seems that the shortage of exoplanet satellites in relation to the satellites of Jupiter is quite real. The simplest explanation: the population of large exoplanets within 1 AU. That is, for stars of the class of the Sun, these are most likely migrants from more distant regions. What is done with planetary satellites during migration? It is possible that they are losing stability.
Finally. A team of serious scientists combed Kepler's data for exoplanet satellites. Does this mean that the topic has been exhausted and it does not shine for anyone to find anything new in this data regarding exoluns? Nothing like this! First, any work must be repeated for verification. My friends double-checked the data of the WMAP microwave telescope, which seemed to be double-checked to the holes, and found obvious artifacts, which then had to be corrected. Secondly, this is a huge amount of work that is beyond the power of one team. Therefore, I would like to encourage volunteers: the data is open, only gray matter is required, which is still available in Russia.
Boris Stern