Kepler Mission Options

[brellis]

Consider Uranus, and entire system tipped 90 degrees relative to our star. Pancake-shaped systems might be the exception?

[Hungry4info]

The assumption arises out of a rejection of anthropocentric ideas of the Universe. If the planet-planet inclinations in transiting systems are different then planet-planet inclinations in non-transiting systems, then there is something fundamentally different about planet formation in systems that are aligned a certain way relative to Earth, at this certain moment in time.

I think it is safe to reject this idea.

Put simply: there is no reason to expect transiting and non-transiting systems to be intrinsically different.

[Ondaweb]

These two planets have the same semi-major axis but different inclinations (and thus different impact parameters)
image

http://arxiv.org/abs/1207.5250

Let me put it another way. Your diagram above shows the chord transiting planet (as distinct from the one crossing the diameter) as crossing on a path parallel to the planet crossing at the diameter. But neither you nor Kepler have any way knowing (at least that I know of, or has been demonstrated yet) that that is in fact the case. In actuality, the two planes might be perpendicular to each other and, again, neither you nor Kepler could know whether THAT is the case or not. If there is some way to KNOW the planets MUST be nearly coplanar, and not simply ASSUME it, that's what I'd like to know. Indeed, to assume that they are is in fact to hold to the anthropocentric principle because it's based on what we've seen in our one system.

And to go further, even if you some how KNOW that two are in fact coplanar, what prevents there from being any number of other planets in highly inclined orbits in the same system that would therefore be NOT transiting and therefor not detectable by Kepler?

[Hungry4info]

Yes it's possible that a multi-planet system only appears well aligned and only transit at their nodes, however you would then expect secular interactions to produce very visible transit timing and transit duration variations. Furthermore, only a small percentage of multiplanet systems will transit right at the nodes, in such a way that the impact parameter will behave as we expect (decreasing for longer periods).

what prevents there from being any number of other planets in highly inclined orbits in the same system that would therefore be NOT transiting and therefor not detectable by Kepler?

Stability arguments would require them to orbit further out then, and I agree fully with JRehling here:

"BUT, any Kepler results are confined to inner systems, which includes planets whose orbits are tidally influenced by the star's rotation. This need not apply to planets further out."

Obviously, the completeness of our understanding of planetary system architecture from transits decays with increasing semi-major axis.

[Ondaweb]

OK, we're making progress here. What I described was indeed a system with two planets in it in perpendicular planes and where the intersection of the two plane happened to point right at us. I agree that even if planetary systems had planets whizzing around like electrons around the old Bohr atom, such alignments would be rare. And it would also be true that the gravitational interactions (is that what you mean by "secular interactions"?) would most probably produce observable differences int the difference and timing of transits that could discriminate between the two possibilities. However, if that calculation was made and was part of the evidence for "pancake" systems, it wasn't mentioned in the brief. However I'm pretty sure that FOR THE SYSTEMS SHOWN, such calculations have in been done, because variations in transit times are seen as evidence that additional planets are in the system. However, none of this solves the problem anyway.

Kepler and Doppler studies both have a bias in favor of larger planets with short periods (which probably are "tidally influenced by the star's rotation", but that's not the basis of the bias.) Further, both have a bias in favor of planetary orbital planes the intersect earth. Kepler can ONLY detect such planets and the observable Doppler shift goes to 0 for planets, no matter how large or close in, in orbits perpendicular to our line of sight. These facts are well known and exactly why I STILL don't understand how Frank has CALCULATED the flatness of planetary systems.

Although it is true that the information available about exoplanetary architecture mainly applies to planets close to their stars (and, I'm willing to bet, their may be dynamical models of planetary interactions that severely limit, if not exclude, non coplanar planets in close to a star) it's the very fact that these limitations are known to exist that make me very uncertain what, exactly, is being claimed by Frank's article.

Put another way, how does she claim to constrain the inclination of orbits of planets about which we (apparently) know nothing?

[Hungry4info]

I am not exactly sure what specifically you are confused about, so let me try to state what is known in as clear and concise a manor as I can.

I think the most accurate way to state it is that multi-planetary systems like those Kepler is sensitive to -- not exclusively ones Kepler can detect, but rather the typical system of several low-mass planets in periods < 200 days -- have minimum mutual inclinations that are very low, consistent with being very coplanar. Yes there are degeneracies that can prevent you from knowing the true mutual inclination, but statistical arguments alone imply that a great deal of the systems we see are truly rather coplanar.

As a singular test example, the Kepler-30 system is found to be well-aligned and coplanar based on the detection of transits of planets across star spots.
http://arxiv.org/abs/1207.5804

(and yes gravitational perturbations = secular interactions.)

[JRehling]

I'll try to make this as simple as possible.

In the presence of noise and with sparse data, it is certainly a challenge to determine the typical flatness. But with enough and good enough data, it is definitely possible in principle. Consider the following ideal situation:

We have a vast number of systems which contain one planet with a period arbitrarily close to 50 days, and that planet transits right through the middle of the star's disc (which we can determine by the transit duration).

Now we consider these systems in terms of inner planets (or lack thereof) with a period of 25 days. In each system we either find or do not find such a planet. If we do find one, we can measure the impact (distance of the transit alignment from going right through the middle of the star's disc) on the basis of the transit duration. If we do not find such a planet, we can't know whether or not there's one which fails to transit or if there is none at all.

The data we CAN collect is the distribution of impacts for the inner planet where there is a transiting inner planet.

If the flatness of all systems is absolute, then all such inner impacts will be, like the impact of the outer planet, zero. It must be in the exact same planet.

If the flatness of all systems is as non-flat as possible, then the observed transits will display a completely flat distribution (and moreover, be very rare). We will see the inner planet display an impact of zero in the extremely small fraction of cases where the orbits either happen to be coplanar or non-coplanar orbits happen to cross our line of sight.

The distribution of impacts for the observed inner planets will tell us where in between these two extremes actual systems lie.

Now, to revoke those assumptions: We would never find so many systems with such precise constraints, so the analysis is complicated by allowing the varied periods of all observed systems. And we have serious errors in calculating impact precisely, because of observational noise (in luminosity as well as time) and because stellar parameters are uncertain. Finally, as I noted earlier, we can only gauge such work as valid for the types of systems and periods we observe. We have no proof that it won't be considerably otherwise for longer periods.

So I don't necessarily see as obvious if/that it is possible in practice, but it is definitely possible in principle.

[Ondaweb]

I think I understand your argument, but need clarity about a few points first.

Could you be more precise about the distribution of impacts in the "non-flat" as possible case? What do you mean by a "flat distribution" in this case? Linear? Gaussian?

Also, I assume by "non-flat as possible" you mean that the observed planets transit the star. Is that correct? If not, what, precisely, do you mean by non-flat as possible flatness?

Finally, doesn't the argument you put forth REQUIRE the assumption that the (unobservable) paths of the observed transits of the 25 day period planets are parallel to the (unobserved/unobservable) path of the 50 day period planet?

Thanks

Also, I want to make clear that I do not doubt that some of the observed multi-planet systems (i.e., those planets that have been observed) are in fact nearly co-planar. It is generalizing those results to other planetary systems, or indeed to other planets in those systems that, as far as I understand, MIGHT exist, but not be observable by Kepler (since they don't transit). This is what the report seemed to me to be implying, though I could be wrong about that too.

[JRehling]

I think the difficulty in picturing 3D spatial geometry creates snags.

Even if two planets' orbits around the star are non-coplanar,even if they were at right angles, there is a probability that they will both transit as seen from Earth. I think this may be the elusive fact. For some observer s(in either of two directions which are separated from one another by 180 degrees) both Earth and Pluto will appear to transit the Sun, even though the orbits of Earth and Pluto are non-coplanar. The coplanarity governs the probability that an observer will see both transit, not that they may or may not.

And given impact=0 for the first planet, A, we consider, coplanarity will determine the distribution of the impacts for the second planet, B. If the orbits in all systems are perfectly coplanar, and impactA=0, then impactB=0. If the orbits were always at right angles, then the distribution of impactB would be flat: It would just as likely be 0.8 as 0.4 as 0.2 as 0. So the observed distribution will tell us precisely how coplanar or non-coplanar the orbits are across all systems.

[hendric]

Could transiting a fast-rotating star give an opportunity to determine the angle crossed by the planet? Second order effects, such as the shape of the entry/exit curve could determine the location of the entry, the speed of entry could determine the length, and the two taken together could provide information on the angle the planet takes with respect to the centroid of the star. A planet diving straight vertical across the star would have a transit time similar to a planet at some latitude north/south of the star's equator. However, the entry curve of the vertical planet would be more abrupt, while the horizontal planet more gradual.

[Hungry4info]

Yes indeed. Look at KOI-13 for an example of a planet transiting a rapidly rotating, oblate star.
http://arxiv.org/abs/1105.2524

[NGC3314]

Could transiting a fast-rotating star give an opportunity to determine the angle crossed by the planet? Second order effects, such as the shape of the entry/exit curve could determine the location of the entry, the speed of entry could determine the length, and the two taken together could provide information on the angle the planet takes with respect to the centroid of the star. A planet diving straight vertical across the star would have a transit time similar to a planet at some latitude north/south of the star's equator. However, the entry curve of the vertical planet would be more abrupt, while the horizontal planet more gradual.

It hasn't come up for a while in this thread (IIRC), but the Rossiter-Mclaughlin effect is measurable in many transiting systems (of Jupiter size, anyway). This is the change in a star's mean Doppler shift as the planet covers up portions of it at varying locations. The sign and amplitude of the effect (which can be many times larger than the Doppler signature caused by the perturbation from the planet) tells the angle between the stellar equator and planetary orbit, and can also distinguish planet transits at such a steep angle that they only ever cross the star's leading or trailing half. The remaining uncertainty is the star's axial inclination to us, where there is some information from the rotational line broadening.

For the recently-reported PH1 system around an eclipsing binary, there was the interesting wrinkle that the sense of the correlation between transit times and phase of the central eclipsing binary (and a similar correlation with transit duration) says that the planet orbit has to be roughly aligned with the binary orbit. Unfortunately, the secondary star is too faint for Kepler to see transits against it alone, which would nail down whether they are coplanar at the 2-degree level or so.

[0101Morpheus]

New analysis of close in planets around M dwarfs suggest over 100 billion such planets exist in our galaxy.

http://arxiv.org/pdf/1301.0023v1.pdf

It seems that a majority of planets in the Milky Way orbit M dwarfs.

[JRehling]

This result, which has been echoed in the mainstream media the past few days, certainly needs a bit more qualification than it's getting. Kepler has thus far told us next to nothing about planets with periods >500d (where, as a point of reference, most of the solar system's planets exist) so it is not even capable of telling us anything about a total number of planets per stellar class... unless that conclusion is qualified with a period threshold.

The fact that M dwarf stars outnumber other stellar classes, however, makes it "easy" for the claim to hold true that they collectively hold most of the planets. They could have fewer than half as many planets per star and that would still be true.

We may also note the microlensing survey by [Cassan et al. 2012] which found 1.6 planets per K-M star including only Super Earths and larger at distances 0.5-10.0 AU. Adding in such planets found inside 0.5 AU is likely to raise the total to about 2 planets per star and including smaller planets is likely to raise the total considerably.

I'm interested to see the details here about origins beyond the ice line for planets of this size. [Ida & Lin, 2010] hypothesize that embryos (solid protoplanetary bodies smaller than the Earth... how small depends on the model) migrate inwards from about 2 AU to about 0.5 AU. This would create a relative dearth of Super Earths in that zone, which of course is of great interest because of the whole "Eta Earth" question. Would it mean that Earths are more or less common in that zone? I don't think the models are sufficiently well-validated to say. [Mayor et al, 2011] found a relative dearth of Super Earths in that range based on the HARPS radial velocity survey whereas [Dong and Zhu, 2012] found no such dearth in the Q1-Q6 Kepler data. I plan on performing an analysis of the Q1-Q8 data when it's released which should answer the question. If HARPS and Kepler find differences, note that it is always possible that there is an important difference in the samples, namely that HARPS probably observes more high-metal stars and Kepler more low-metal stars.

The next few months will be very interesting.

[0101Morpheus]

I wouldn't say it has found nothing per-se. Places like Planet Finders have found some interesting transits but it may not be possible for them to become bona fide candidates before the end of the mission.

Forgive me, but the more I hear people talking about the ice line the less I believe we have a solid concept of it yet. I don't perceive it as a rigid barrier any more. Icy material is perfectly capable of interacting with terrestrial material, especially in the presence of massive bodies like planets. This has implications for water worlds because how I see it there are two different ways to form one. One is that the planet can form in stu and acquire water by accretion of planetesimals or by out gassing. Or an icy planet can form beyond the snow line and then migrate inward until its crust melts. We don't know yet how large terrestrial planets or Super-earths can get before there is a transition from a rocky crust to a fluid one because there is no example in the solar system we can study.

Now I am not a scientist, but I feel the reason there are no icy planets or hot Neptunes in the solar system is because of Jupiter. Jupiter has always been the most massive gas giant in the solar system well as the most inward one. I feel the second characteristic is the most important one. Imagine a solar system without a Jupiter analog. In the place of Jupiter many icy and Neptune sized planets would form. These would gravitationally interact with each other and start migrating. This would in turn lead to the terrestrial portion of the system being influenced, especially so if any icy planet migrated into the region. If a Jupiter sized planet were to form further out than our Jupiter did there would still plenty of icy material at the inner part of the ice line to form planets. In fact it may magnify the effect.

I feel my hypothesis explains explains what were seeing from Kepler. Neptunes, sub-Neptunes and icy planets are very common. In our solar system Jupiter acted as the gravitational blockage that prevented the chaos that was occurring across the ice line from entering the terrestrial system. Who knows what happens without a Jupiter analogue.