Science

discussion

RINGS & MOONS

Started by ggccg
Default_user
over 6 years ago

I've been following this discussion here with some interest, but I thought I'd introduce a reality check. The size of an exomoon compared to its host planet is extremely small, e.g. our Moon, or Luna, compared to the Earth is just 7% of its circular area, and if an Earth-sized planet were to transit a Sun-like star, the drop in flux is only 0.000085. A similar-sized moon would cause a dimming of just 0.000006. Here's how the Earth and Moon look like. Sizes and separation are to scale, with the moon at 380,000 km away:

However, the size of the Sun is huge compared to us - and in the next image, the Sun has been scaled so that the moon represents just one pixel, the Earth comes out at 3.67 pixels, but I've rounded it up to 4.

I've added a red circle to highlight the moon because it's barely visible. Looking at the relative sizes, it seems virtually impossible to discern the light flux difference. In fact, I'm not even sure if an Earth-sized transit is at the signal-noise level. Judging from the size of the error bars on the Kepler flux, they are larger than an Earth-sized ∆flux! But that's another discussion.

Based on this, I'm quite skeptical whether the sensitivity of the Kepler CCDs will let us detect a Luna-sized exomoon. Using TTV or TDV to determine the presence of exomoons might be a better bet, although still quite a long shot.

Default_user
over 6 years ago

I agree completely with kianjin. Detecting a Luna sized exomoon transit of a star (as the diagram accurately illustrates) is certainly out of the question. Still, l think that observing an exomoon completing a transit of its planet (while the planet itself it transiting its star) may be detectable. In this case, the planet transiting exomoon (being non-luminous) would have no effect on the light curve as the planet enters transit. However, as the exomoon finishes its transit of the the planet and moves into the disk of the star, it will block more light and show up as an additional drop in luminosity within the planet transit signature. Using the Earth/Luna example, this situation would result in a relatively sudden drop in luminosity of an additional 7.4%... probably an undetectable change at Earth/Luna scale, but how about if the planet and it's exomoon were a scaled-up version of Earth?

Default_user
over 6 years ago
pauldrye in response to kianjin

kianjin:

I've been following this discussion here with some interest, but I thought I'd introduce a reality check.

Not that I disagree with you, but an exomoon detection is, I think, just within Kepler's reach.

The smallest radius of any planet in the Planetary Candidate list is 0.6 R<sub>e</e>: There's two of them, KOI-70.04 and KOI-388.01. A histogram of the radii of all the planets in the list suggests to me that that's about as small as Kepler can see (i.e., it's not that the sample size isn't big enough and it just hasn't observed any smaller).

Now Ganymede is the largest moon in our solar system at 0.41R<sub>e</e>, which is not quite up to snuff but not ridiculously under the limit of the instruments. It's likely there are some moons of the 1200+ planets found that sneak above 0.6.

I think we'd be darned lucky to see one as the geometry would have to be right for both the planet and the star and it would have to be a relatively dim star in the first place (KOI-70 is 0.358 solar luminosities, so probably a late K-class star, and KOI-388 is 0.684 solar luminosities, which is early K or late G). But I would figure a really big moon around a red dwarf would be do-able.

Default_user
over 6 years ago

Thanks a lot kianjin! Those figures are very useful when it comes to visualizing the problem (yours are good too ggccg). I don't think it should be any more difficult to detect an exomoon than it is to detect an exoplanet aside from the fact that the moons are in general a lot smaller of course. If there are Earth sized moons out there they should create a dip the same size as an Earth sized planet (though the transit duration might appear weird). The question is, however, if such large moons exists.

I am curious to know your thoughts on my and Gerald's debate about the "shape" of an exomoon event, kianjin. The distance between the Earth and the moon is 380,000 km whilst the distance between Jupiter and Ganymede is closer to 1,000,000 km. Do you think Ganymede (if the noise had been a lot lower and it had been perhaps a bit further out from Jupiter) would be observable as a completely separate transit event or would it "overlap" Jupiter's transit? I agree with ggccg though that for exomoons closer to their host planet any observable exomoon event would only be seen as a change to the planetary transit shape. As the moon passes in front of the planet I think we could see a sharp rise in brightness and then the curve would go back to its ordinary shape as the moon positions itself on one of the sides of the planet. Ganymede takes 7 days to orbit Jupiter so I think it would seldom have the time to make a complete pass in front of Jupiter. Note that I am not saying it will be easy to detect exomoons with our method, just that it might be theoretically possible. We shouldn't be able to find a moon the size of Ganymede I think. Thanks for reading!

Default_user
over 6 years ago

Let me illustrate my point about the larger planets and the possibility of seeing rather small changes in flux by revisiting our old friend APH22714177. Everyone seems to be in agreement that there something out of the ordinary going on there, but for this example, just what that something is is irrelevant (although I do have a theory that I'll post at another time). Here is a close-up of one of the transits showing the the dFlux values at two different points amidst the event of interest.

Would we be able to detect this 12% change in luminosity outside of the transit? I doubt it. But here, the difference is crystal clear.

Granted, a 12% dFlux value would suggest a rather large exomoon since you'd need a body in the range of 30% of the diameter of the planet to get to 10%. But the point is, we would be able to see this difference here even if it was just 7.4% of the total drop.

Hence, my request for examples of large planet transits.

Default_user
over 6 years ago
ggccg in response to AsAsAsBjornTh

AsAsAsGalaxyZoo:

"... I agree with ggccg though that for exomoons closer to their host planet any observable exomoon event would only be seen as a change to the planetary transit shape. As the moon passes in front of the planet I think we could see a sharp rise in brightness and then the curve would go back to its ordinary shape as the moon positions itself on one of the sides of the planet."


Ahhhh... you were doing so good there for a while! Let me clarify a couple of points:

  1. It doesn't matter what the orbital distance of the moon is since I am only looking for exomoons that are entering or exiting a transit of their planet. At that point, they are, from our point of view, cheek by jowl.

  2. If an exomoon begins a transit of its planet while the planet is transiting its star, you will see an INCREASE in luminosity during the exomoon transit because during that time, only the planet will be blocking light from the star (exomoons are non-luminous). When exomoons are on either side of a planet while the planet is transiting its star (assuming the exomoon is at a point of it's orbit that is visually close enough to be included in the transit) luminosity will be lower because both bodies are acting to reduce the light we see from the star.

Default_user
over 6 years ago

Speaking of the two smallest Kepler candidates, I thought I'd have another look at them. KOI-70 has, IIRC, been subject to some doubt because of possible contamination from a nearby star, so its transit depth could be diluted, so I focused on KOI-388 which seems free of contamination. So I detrended the curve and folded it at the published period..

Looks good doesn't it? Is this how a 0.6 RE planet's transit should look like?

(Continued next msg...)

Default_user
over 6 years ago

So I import this folded curve into Excel, plotted it and zoomed into the transit.

The bottom of the transit is irregular, so I took a close estimate and I measure a transit depth of 0.000325. Based on the star's size (0.89 Rs), this works out to a planet that is 1.75 RE, not 0.6 RE! Could the Kepler team be wrong about this candidate?

In fact, to get a planet that is 0.6 RE, the transit depth has to be 0.00004 or less, and in the chart above, that's the horizontal line. The transit would have to be much shallower, so shallow that it might be hard to pick out, unless there were many instances, in this case, the short period makes it easier, but would such a shallow transit be lost in the noise?

Needless to say, a Ganymede-sized exomoon transit would be even shallower than this, slightly less than 0.000025.

Default_user
over 6 years ago

@kianjin

What star radius did you use? I don't find it listed on the "Kepler archives". Perhaps the Kepler team used the wrong value here?

@ggccg

You make a very good case for studying the planetary transit shapes. I like. I still think the exomoon orbit period is important as this tells the chances of having the exomoon travel in front (or behind) the planet during the actual planet transit. With a 7 day orbit for the moon and say a 12 hour transit duration for the planet finding the exomoon in front of the planet would be quite rare.

The largest moons in our solar system and their orbital periods

Ganymede 7 days

Titan 16 days

Callisto 17 days

Io 42 hours

Moon 27 days

I think this would mean that some exomoons often affect the planet transit shape where as others much more often just produce a dip of their own. There should also be a middle ground where the exomoon sometimes gives rise to an asymmetry of the planet transit shape (in some cases the moon will not have the time to make a complete pass in front of the planet). In the extreme case where we have the moon very close to the planet I think we should see a quick rise in received light as the moon passes in front or behind it's host planet (as you say) and then the transit will go back to normal (moons spend a relatively small amount of time in front of their planet)?

What do you guys think of my reasoning? All in all, I think we agree on a lot of things and that we are on the right track here. Also, I agree that APH22714177 is worth a lot of interest.

Default_user
over 6 years ago
ggccg in response to AsAsAsBjornTh

AsAsAsGalaxyZoo:

@ggccg

"You make a very good case for studying the planetary transit shapes. I like. "

Some might call it Transit Phrenology ;-)

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