The problem with exomoons. They are hard to detect.
Knowing that exomoons exist and confirming that are two different things. Exomoons are moons and dwarf planets orbiting exoplanets in distant solar systems. And when we make models about those distant solar systems, we use our solar system as the model. Most of the planets in our solar system have moons. So that means moons should be a very common thing in other solar systems.
The exception is gas giants that are very close to their star. Their moons will fall into the star or vaporize because of intensive heat. But in some visions, the gas giant can have a moon similar to Earth. And that kind of moon could be an excellent place for intelligent lifeforms.
The problem with exoplanets is that they are hard to find. And their moons are far more difficult to find. The exoplanet itself must change its trajectory. Or there must be some kind of changes in reflection. The exomoon must be so massive, that it can cause changes in the exoplanet's trajectory. Or the reflection from the exoplanet must be stable enough, that those things can help to find exomoons. Confirming its existence requires complete knowledge about the brightness of the planet. And how a star's brightness changes during an overpass.
"Astronomers have detected a second exomoon candidate (depicted in blue) orbiting a giant exoplanet (right) more than 5,000 light-years from Earth. (Helena Valenzuela Widerström/ https://edition.cnn.com/2022/01/13/world/exomoon-second-candidate-scn/index.html)That means those measurements can used by benefiting the star itself or the exoplanet's reflection. When that hypothetical moon and exoplanet are in a position where both cover the planet and its star, that causes changes in the star's brightness. That means the star goes dimmer than usual. But that requires that space telescopes make intensive measurements.
And if we want to search Earth-type planets that can host lifeforms the work is very hard. Even if the planet makes an overpass in a G-2-type yellow star, that overpass is hard to detect. Detecting Earth-size planets is very hard when the star is bright. The brightness of the star covers its planetary system. And the distance to the star is long if that planet has liquid water. That means that if the planet's trajectory is oblique, that denies the overpass. And the planet is not possible to detect.
Sunspots or starspots can cause differences in other star's brightness. And that thing means that the false alarm of exoplanets can caused by those sunspots or starspots. Also, other stars have sunspots, and those sunspots can believed as exoplanets.
Seeing those moons is difficult. If we use again our solar system as a model, most moons are small irregular-shaped objects. And that means we still find new moons in our solar system. When we talk about exomoons, we should divide those moons into two categories.
1) Large and regular-shaped moons that affect their planets by gravity and tidal forces. Those moons are like Earth's moon or Titan's moon of Saturn. The problem is that, if the moon orbits a gas giant it is hard to detect especially if the gas giant is hotter than its moon. In that case, the infrared radiation from the hot gas giant or brown dwarf can cover the planet under it.
2) Small and irregular-shaped moons that do not affect their planet, except if those small, possibly potato-looking objects fall to the planet. Those small objects cannot form tidal waves. And that means they are meaningless.
The most well-known "potato moons" are Mars' moons Phobos and Deimos. Those moons have no big tidal wave effect on Mars.
But irregular moons also act as shepherds in Saturn and other gas giants' ring systems. That means other planets with surrounding ring structures should have shepherd-moons in the distant solar systems.
So the problem is this. If the planet is a gas giant even a massive moon will not give a strong enough gravitational effect, that researchers can recognize it. The exoplanet that has moons should be quite distant from its star. That makes it difficult to see its moons.
Because the star itself is very weak if the planet does not travel just between Earth and the star, it doesn't cause differences in the star's brightness. Most exoplanets are found near red dwarfs. Red dwarfs are dim stars and exoplanet that makes overpass or travels between Earth and that star causes changes in its brightness.
And that means the exoplanet with moons is a very cold and dark place. A brighter star's brightness covers those exoplanets below their shine. And that means it's hard to measure changes in a star's brightness when the planet overpasses it. Without that overpassing exoplanets are hard to detect, because they don't cause changes in the star's brightness.
https://edition.cnn.com/2022/01/13/world/exomoon-second-candidate-scn/index.html
https://www.mps.mpg.de/giant-doubts-about-giant-exomoons
https://en.wikipedia.org/wiki/Stellar_classification
https://en.wikipedia.org/wiki/Sunspot
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