Not difficult to compute: Sun diameter is slightly below 1% of Earth orbit radius, so the tilt angle allowing for transit (observed from an "infinite distance") is almost 0,01 radians; assuming random orbit tilt distribution, transit-observing probability will be this angle divided by 3.14 or 0.3%...

PS: hey, last Brellis post was the 1000th of this thread!

Let's see. Radius of Fomalhaut is about 1.27e+6 km and the semimajor axis of Fomalhaut-b's orbit is about 1.72e+10 km. Taking the ratio and the arctan, I figure the half-angle to be about 74 microradians. Multiply by 2 and divide by pi (not 2 pi) I get a probability of 4.72e-5. Out of 150,000 stars, I'd figure one chance in 7--assuming every star actually had such a planet. Of course we'd have to watch for 1,000 years to witness such a transit.

At 115 from Fomalhaut (twice solar mass) it ought to have sqrt(2/115) Earth's velocity, or about 4 kps. I figure an equatorial transit should last just under four days.

As always, someone should check these figures before planning their own mission. :-)

--Greg

"First two extrasolar worlds ever confirmed to be the size of our own Earth or smaller?"

What happened to the planets of PSR B1257+12? I think it has one confirmed small planet about 2% of Earth's mass... (Maybe the intent is 'first two extrasolar planets around a main-sequence star ever confirmed to be, etc.'?)

Yes, pulsar planets are generally excluded from these sorts of announcements, (and not without reason, too)!

Planet of PSR B1257+12 D is estimated at 0.0004 of Earth's mass.

http://en.wikipedia.org/wiki/PSR_B1257%2B12_D

That makes it less than 3x the mass of Ceres! I'm amazed they can measure anything that small. Given that, it surprises me that there are only five or six pulsar planets--and four of them are around the same pulsar. Is it just that no one is looking?

--Greg

Maybe there will be some announcements along precisely those lines at this conference in a few weeks...

http://www.mpia-hd.mpg.de/PLANETS2012/index.html

P

http://www.sciencedaily.com/releases/2012/...20126155915.htm

WONDEROUS! and WEIRD ... What a Universe we inhabit.

NASA's Kepler announces 11 planetary systems hosting 26 planets

From the KEPLER web site - more details
http://kepler.nasa.gov/news/index.cfm?Fuse...&NewsID=182

Papers:
Kepler-23 and Kepler-24 - Transit Timing Observations from Kepler: II. Confirmation of Two Multiplanet Systems via a Non-parametric Correlation Analysis. Confirms KOI-168=Kepler-23 and KOI 1102=Kepler-24
http://arxiv.org/pdf/1201.5409.pdf

Kepler-25, 26, 27 and 28 - Transit Timing Observations From Kepler: IV. Confirmation Of 4 Multiple Planet Systems By Simple Physical Models
http://arxiv.org/pdf/1201.5412.pdf

Kepler-29, 30, 31 and 32 - Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations
http://arxiv.org/pdf/1201.5415v1.pdf

kepler-33 - Almost All of Kepler's Multiple Planet Candidates are Planets, and Kepler-33 5-planet system
http://arxiv.org/pdf/1201.5424v1.pdf

Enjoy

Kepler has found lots of 'Hot Jupiters' in its survey thus far. Are there models that would indicate the chance that the equivalent of our Kuiper Belt might exist in those systems?

What if 'hot KBOs' are floating in 'habitable zones'?

Wouldn't a hot KBO just be a really big comet?

...yep. And unless they were MUCH rockier than our KBOs are thought to be, they wouldn't last very long in terms of geological time...they'd become garden-variety asteroids in short order.

Let's not go off the deep end on the speculation front, please. Hot Jupiters, Neptunes, super-Earths, etc. are acceptable discussion topics since there is considerable observational evidence that they exist. I'm sure as time marches on exo-solar system research will provide even more surprises for us to discuss.

Seems like the very shallow end of speculation to me. Actually, just an innocent question.

One interesting answer to the 'Hot Jupiter planetary model' question exists here:

http://astronomy.stackexchange.com/questio...their-host-star



Sorry I asked.

http://arxiv.org/abs/1202.5852

New release: more planets, developing trends.

Thanks for the link!

KEPLER 02.28.2012 release news
http://kepler.nasa.gov/news/index.cfm?Fuse...&NewsID=190

Go to Nasa Planet Archive to download a spreadsheet with updated Kepler candidate data from the 02.28.2012 release.
Need to use firefox browser
http://exoplanetarchive.ipac.caltech.edu/c...xotbls?kepler=1

Craig

One report out today on Space Daily suggests that exact earth analogs are relatively rare. Less than one per cent of all stellar systems will have one, if this analysis turns out to be correct.

Earthlike Planets Very Rare

Not what most of us want, but if it's true, then it is what it is.

Edit: When I posted I hadn't noticed who the author of the paper was. If I had, I certainly would have mentioned it. Sorry about that John.

How many of the 158,000 stars are tilted enough that their planets wouldn't transit Kepler's pov?

I'm glad I'm just a musician, I'm sticking with my optimism!

It's worth noting (a point I trimmed from the article) that the bin for earth-sized planets with periods of 64 to 128 days has zero observed candidates although in the 407 days of observations, any such world must have transited between three and seven times while Kepler was watching (discounting the possible lapses of downtime), and so we aren't actually waiting, as the mission goes on, to see any new transits there: As the mission goes on, any such planet will only repeat what it's already done (e.g., transit, and be missed in the noise, or not transit... or not exist).

That's a bin two slots to the left (two powers of two shorter) than the Earth itself, and Kepler found none. The prospects for the Earth's actual bin are distinctly poorer. Kepler did, however, find five candidates in the bin corresponding to periods of 64 to 128 days and sizes one notch larger than Earth: worlds with radii 1.2 to 1.4 Re. That corresponds to a 2% abundance of such worlds, and every trend indicating continued drop-off with smaller sizes and greater distance.

re: Brellis's question, the probability of a randomly-placed observer being situated for the geometry to allow them to witness the Earth transiting the Sun is 0.29%. For a world twice as far out, the probability is half that. For a world twice as close, the probability is double that. In our solar system, the easiest worlds for Kepler to detect would be, in descending order: Venus, Earth, Jupiter, Saturn. As of this release, an exact Venus analogue *could* have been detected, but wasn't.

Kepler could detect exact analogues of almost any of the planets in the solar system, given the right luck and an un-noisy enough star. At levels of noise in the present analyses, it now seems quite unlikely that the abundance of terrestrial worlds in the habitable zone will be high enough for us to get good statistics on the frequency function out that far. We could always luck into a single detection, but getting statistical significance seems very unlikely. This highlights the importance either of ways to find repeated transits buried deep in the noise or follow-up missions that monitor a yet-larger number of stars.

John,
I was unsure in the article what you did to de-bias the frequency (or is that a reference to a pre-processed value provided by the Kepler team?). Are you modifying each frequency bin by the chance to detect an earth-like planet at that bin?

Edit:
I also repeat the question left on the article - Are these sun-like stars, or is there a bias in this dataset to stars of a different size than the sun? Many more small stars in the galaxy, larger stars are easier to see at a distance. Really needs a 3-d representation with star's mass or radius as another axis, and possibly a 4D representation with the star's metallicity or distance from Earth.

Edit^2: Nevermind, I see where you responded that the data is all stars lumped together, and that there isn't enough data to separate the stars into separate bins.

Great to see you posting again JRehling. Here's what I take from the Kepler release.
1/ 0.7% is plenty. I reckon that means about 100 within 100LY
2/ The estimate is premature. Let's wait for the full data set and the long analysis.
3/ I've heard it stated (in the infamous IAU debate on the definition of "planet") that the solar system is dynamically 'full' in the sense that the planets are packed together as closely as possible apart from the gap where the asteroid belt is located. The dense compact systems Kepler has found seem to contradict this hypothesis, unless in fact they are young systems that will in due course eject or swallow most of the objects now observed.
4/ I love all these planets and their extreme diversity, no doubt arising from peculiar histories yet to be elucidated. (Just look at the Iapetus 'fairy tale' for an example of reality exceeding imagination.)

hendric, the raw count of observed candidates is biased in two (and a half) ways from the actual frequency of planets in a given bin:

1) The geometric bias takes into account that for most orbital inclinations, transits will never be observable. The extent of this is a factor of distance from the primary. Happily, we can model this exactly: It's straight-up Euclidean geometry. A planet orbiting at 1AU has a probability of 0.29% of transiting a sun-sized star. For each distance we consider, this bias can be calculated exactly. If we observe N planets at 1AU, and that count is statistically significant, we can be sure that about (N / 0.29%) planets exist (and we missed almost all of them).

It may help to imagine if, say, Mercury and Neptune were in the exact same plane, and for some observer, Mercury transited the Sun but appeared to slice across latitude 60 North. For that observer, Neptune will fail to transit by a great margin, several Sun radii, passing far above the Sun's disc each time it passed across the Sun's central meridian.

1 and a half) Planets in further-out orbits orbit more slowly, so the time required to witness N transits will vary with the orbital period. This, too, is pretty easy to model. It also, in many cases, does not matter, if the ratio of the observation period to the orbital period is high. For periods of, say, two days, the planet has had hundreds of chances to transit: If it's going to happen, it's already happened a lot. For periods of, say, ten years, this factor is quite significant, because while the team could report a giant planet very far out on the basis of a single transit, most such planets have not had a chance to perform their transit. 15 of the published candidates actually have orbital periods longer than the observation period: For each such observation, there are likely (far) more at that distance that will happen but haven't had a chance to yet.

2) Noise bias: Variability in the star and our measurements exist: When a large planet transits, it blots out a larger area with almost perfect blackness than when a smaller planet transits. With smaller planets, the transit is insignificant compared to the star's baseline variability, and in such cases, detection is impossible. The devil is in the details here, and the noise happens to be greater, for many stars, than we expected.

For each size bin, I calculated this by taking the SNR of observed large planets. Each such positive event allows us to say how much smaller of a planet *could* have been detected, with its correspondingly smaller transit effect. By sampling all of the largest planet candidates, I got a distribution of star noise. For each candidate size, we can say what fraction of stars allow detection of that size. This is another de-bias factor, a bit less certain than the geometric one, but it should be correct to a first order. I also performed this with the four-month release and found very similar values. We can't be totally sure that the stars hosting larger planets are precisely the same as the stars which do not have larger planets... that is an unconstrained possibility, but there's no reason, either, to assume that they are different than the other stars with respect to noise.

For each bin, then, we have an expected bias factor: What fraction of existing planets we would expect to find. By multiplying the observed candidates by the reciprocal of the bias factor, we get an estimate of the total number of planets in that bin, counting all of the ones we missed because of misalignment or noise.

There's a gaping hole inward of Mercury that is oddly void of planets. Kepler and HARPS have shown us that low-mass planets are common in this region, so our solar system seems slightly odd in this respect, too, regarding the "packed planetary system hypothesis." It's also worth noting that the Kepler planets, being typically closer to the star than the planets in our solar system, will have smaller Hill Spheres, and can therefore be packed in tighter than what you see for the Solar System without destabilising.

You can also look at the satellite systems of Jupiter, Saturn, and Uranus: Packed in very tight. It's not absolute worlds per orbital-radius that poses a limit, but a more complex relationship between the distances and masses.

The relationship between neighboring planets as seen in Kepler data is also interesting. The ratio of orbital periods peaks sharply at 1.5, with a resonance that is seen in our solar system between Neptune and KBOs, but not among the inner/major planets. There is also a desert at a ratio of about 1.97 picking up against at/after 2.0.

The kicker in your analysis is the assumption that planetary systems are a single normally distributed population. As you say in your piece a second distinct population with loads of earth-analogues could be in there, we simply don't know at this point.

Cool work though.

My understanding of current planetary systems formation theories is that the predominant planet (e.g. Jupiter) migrates inward and pushes all other planets closer to the star; hence all the "hot Jupiters". In case of the solar system, Saturn came to the rescue and the gravitational interaction between Saturn and Jupiter stopped the inward migration early and there might even caused a phase of outward migration. I don't know if there is any evidence to support this theory in Kepler data.

Giant planet formation and migration occurs before terrestrial planet formation. If there are planets already formed inward, then it's early enough for them to become giant planets.

When the big planet forms (the so called oligarchs), it cleans a large swath of the protoplanetary disk and slows the growth of any other planet in the vicinity. And when it migrates inward, the "vicinity" is a very large area.

Blair, there are unfortunately a lot of kickers... Wes Traub's paper lists a lot of possible factors which are currently unconstrained and which he assumes, therefore, to be nonexistent. I happened to include two factors that he did not:

F1 Noise as a nonlinear bias regarding planet size
F2 Separate orbital radius distribution functions for different planet sizes

He included one factor that I did not:

F3 Class of star
(But note, the majority of stars in the release are fairly sunlike.)

And there are many more factors which are unconstrained in either study. Particularly, those regarding the variation in noise across various circumstances are potentially very thorny. We might hope and expect that that factor is not psychopathic with respect to any key independent variables, but it's a risky assumption. Any extrapolation is: There could be a second peak in the distribution for any of these planet sizes: We also have yet to prove that the number of Earth-sized planets orbiting at Earth-like distances from Sun-like stars is not arbitrarily close to zero! (In fact, Venus is still the best Earth surrogate we've actually found.)

I will take some effort to model the known sources of variation in more detail. Two that I think are particularly worthwhile are F3 and

F4 The effect of transit "latitude" on SNR: Transits which skim the top/bottom of the stellar disc feature less signal and perhaps different distributions of noise.

Conceivably, we may see important cumulative effects in the bias that either raise or lower the estimation of absolute frequencies. I think the main qualitative result of my analysis will stand: Terrestrial planet frequency drops off with distance much faster than giant planet frequency; but the quantitative models may merit considerable revision. I'll be working on this, and I'm sure I won't be alone.

"F4 The effect of transit "latitude" on SNR: Transits which skim the top/bottom of the stellar disc feature less signal and perhaps different distributions of noise."

I've been curious how transit latitude can be ascertained. I keep googling my questions, always get pointed to this thread, lol

Question: Might not a tiny planet making a quick equatorial transit create a similar transit signal to a larger planet in a longer orbit skimming the top/bottom of the stellar disc? Would subsequent observations from land-based scopes detect a larger wobble from the latter?

Nice thought: Similar to the Hubble database, as time goes on and software improves, the database established by Kepler may subsequently reveal more planets, especially the harder-to-find nuggets we're hoping to identify.

The same transit depth, but the shape of the transit curve is different. For an equitorial transit, the transit curve is "flat bottom", whereas a skimming transit curve looks "round". Of course, you need a good signal to noise ratio to get the shape of the transit curve. On the other hand, if SNR is really good, one may also model smaller effects like limb darkening and such.

Not to mention that if we have the orbital period, we would know how long an equatorial transit "should" take, assuming the stellar diameter expected for the star's brightness and spectral class, and a circular stellar disk (or one that is elongated according to the theoretical prediction for its mass and rotation rate). Given the expected and actual transit times it is simple geometry to calculate the impact factor. With additional data (the Rossiter-McLaughlin effect) we can also determine the angle of the projected planetary orbit to the star's polar axis.

Thanks for the answers!

Initially it's difficult to accept the transit method as a reliable way to 'see' an exo-planet, until one realizes that the scientific process of elimination (as so elegantly described here) rules out other possibilities. On the other hand, it's quite easy to accept images derived from UV or infrared wavelength.

As I have tried to explain what I'm learning here to *real* n00bies (if you think I ask silly questions sometimes! ), a effective analogy to cite is how rare it is to see a lunar or solar eclipse.

Thanks again,

-Brad

siravan and Mongo are right, but there are a couple of additional complicating factors.

(1) Many planetary orbits are significantly elliptical, so the planet's distance from the star is not very close to the semimajor axis at the time of the transit. Without additional information, this variation is unconstrained, so some transits seem to take up to twice as long as would be possible if the planet were in a circular orbit with the same period.

(2) there are some inconsistencies between the stellar properties as published and my understanding of the relationships between temperature, radius, and mass. This seems to say that there's a lot of variation around the expected means, so it is harder to characterize any particular Kepler candidate and we need, instead, to build a more complex statistical model taking that variability into account.

For example, we have some grazing transits of large planets that imply that a, say, Neptune-sized planet making the same transit would not have adequate SNR for candidacy. That implicitly "blames" the star for the decreased SNR of an off-center transit. It would be preferable to model the star's noise taking into account that each observed candidate has a degree of centrality to its transits ("impact", the Kepler team calls it) which can (for reasons 1 and 2 above) not be determined accurately in any given case.

To handle these factors, it's important to know about typical planetary eccentricity, which radial velocity methods constrain for large planets, but not for small ones, and more about stellar noise, for which the best, newest source of information is Kepler itself.

Kepler was extended through 2016!

Money well spent, for sure!

An extension is really great news.

As I get deeper into the weeds of the data analysis, I understand what that means. The Signal to Noise Ratio improves as a function of the square root of the number of observed transits. So, for a small body with an orbital period of less than 1 year, this means that the SNR that might be accomplished for a body of radius r with a 3-year mission, the same SNR will be achieved with an 8-year mission for a body of radius 0.6 r. In circumstances where the threshold might have been a Venus-sized object, we will see a Mars-sized object.

For larger bodies in more distant orbits, this will push the outer threshold of large planet detections by a factor of about 1.5... actual detections will depend on luck.

The outer threshold of earth-sized bodies will also move outwards... again, actual detections will depend upon luck and the actual frequency of such worlds, but this allows the detection of earth-sized bodies orbiting sun-like stars beyond 1.5 AU, which may be an important part of the range where earth-like surface temperatures occur. I suspect the bottleneck on detections here will be the frequency of such worlds and the unfortunate but unavoidable geometric bias against favorable alignments for worlds farther out.

As a larger comment, the issue of noise is a very thorny one. Top reasons include:

1) The time granularity of observations is 29 minutes, so measuring a transit duration is inherently noisy.
2) The reported stellar parameters are not only inaccurate on an individual basis but almost certainly systematically skewed, but it is not clear how to correct these errors. See Plavchan et all: http://arxiv.org/abs/1203.1887

In the work for my SpaceDaily piece, I took a very holistic approach to all sources of noise. In contrast, Catanzarite and Shao broke the noise down by the key factors, but because there is unconstrained uncertainty other than variations in stellar brightness, their approach also leads to some inconsistencies in analyzing the full data set. (They limit their analysis to data from a region of candidate parameter space where noise is inconsequential.)

This is to say that even the best work on the Kepler data will not give us a crystal-clear measure of what types of worlds we're seeing: The error bars remain large. It will be an ongoing effort to see if we can correct for the systematic biases and end up with a good statistical encapsulation of planetary types.

http://swri.org/9what/releases/2012/unseen-planet.htm

Gravitational perturbation method that utilizes Kepler transit variations to detect additional planets.

Small Planets Don't Need 'Heavy Metal' Stars to Form

"PASADENA, Calif. - The formation of small worlds like Earth previously was thought to occur mostly around stars rich in heavy elements such as iron and silicon. However, new ground-based observations, combined with data collected by NASA's Kepler space telescope, show small planets form around stars with a wide range of heavy element content and suggest they may be widespread in our galaxy."

http://www.jpl.nasa.gov/news/news.cfm?release=2012-171

a reaction wheel appears to be malfunctioning Kepler glitch may lower odds of finding Earth's twin

Well, any anomaly is a concern. But I remember when one of Cassini's reaction wheel showed anomalous torque, and we switched to the backup (in principle leaving us with very little redundancy, although not none as the wheel didnt actually fail)
That was back in 2000, so don't panic, Kepler folks!

Here is the Mission Manager's Report on the incident. It sounds like the problem may be other than mechanical. By that I mean it may not be wear and tear on the wheel, but some other hardware or software problem. The mission can proceed just fine with three working wheels.

UPDATE came out this afternoon. LINK

Hopefully, the nominal operations can continue much longer. I am planning an analysis of the potential of the long-term discoveries as part of another publication.

Note that Kepler has an extraordinary requirement for stable pointing. We've seen useful imaging of the outer solar system from missions with degraded pointing: You get a blurrier image, and that's worse than a sharp image, but often useful. Kepler data could be degraded tremendously with less reliable pointing. In fact, the pointing has varied over the mission duration already, with the mission team figuring out ways to improve this from the first couple of quarters by Q4 or so (IIRC).

The problem is that an individual star's signal is what you want to be tracking, hourly. If the light from the star is known to fall on a certain pixel, then this is straightforward. Inevitably, some stars' light will fall across 2 or more pixels. If that varies over time, then working backwards to get that star's signal could be hard or impossible, and even if you do reconstruct the signal, there's more noise, which could make smaller planets' signal basically disappear.

Hoping for the best on this...

One Of Our Planets Is Missing

Possible Disintegrating Short-Period Super-Mercury Orbiting KIC 12557548

We report here on the discovery of stellar occultations, observed with Kepler, that recur periodically at 15.685 hour intervals, but which vary in depth from a maximum of 1.3% to a minimum that can be less than 0.2%. The star that is apparently being occulted is KIC 12557548, a K dwarf with T_eff = 4400 K and V = 16. Because the eclipse depths are highly variable, they cannot be due solely to transits of a single planet with a fixed size. We discuss but dismiss a scenario involving a binary giant planet whose mutual orbit plane precesses, bringing one of the planets into and out of a grazing transit. We also briefly consider an eclipsing binary, that either orbits KIC 12557548 in a hierarchical triple configuration or is nearby on the sky, but we find such a scenario inadequate to reproduce the observations. We come down in favor of an explanation that involves macroscopic particles escaping the atmosphere of a slowly disintegrating planet not much larger than Mercury. The particles could take the form of micron-sized pyroxene or aluminum oxide dust grains. The planetary surface is hot enough to sublimate and create a high-Z atmosphere; this atmosphere may be loaded with dust via cloud condensation or explosive volcanism. Atmospheric gas escapes the planet via a Parker-type thermal wind, dragging dust grains with it. We infer a mass loss rate from the observations of order 1 M_E/Gyr, with a dust-to-gas ratio possibly of order unity. For our fiducial 0.1 M_E planet, the evaporation timescale may be ~0.2 Gyr. Smaller mass planets are disfavored because they evaporate still more quickly, as are larger mass planets because they have surface gravities too strong to sustain outflows with the requisite mass-loss rates. The occultation profile evinces an ingress-egress asymmetry that could reflect a comet-like dust tail trailing the planet; we present simulations of such a tail.

Evidence for the disintegration of KIC 12557548 b

Context. The Kepler object KIC 12557548 b is peculiar. It exhibits transit-like features every 15.7 hours that vary in depth between 0.2% and 1.2%. Rappaport et al. (2012) explain the observations in terms of a disintegrating, rocky planet that has a trailing cloud of dust created and constantly replenished by thermal surface erosion. The variability of the transit depth is then a consequence of changes in the cloud optical depth. Aims. We aim to validate the disintegrating-planet scenario by modeling the detailed shape of the observed light curve, and thereby constrain the cloud particle properties to better understand the nature of this intriguing object. Methods. We analysed the six publicly-available quarters of raw Kepler data, phase-folded the light curve and fitted it to a model for the trailing dust cloud. Constraints on the particle properties were investigated with a light-scattering code. Results. The light curve exhibits clear signatures of light scattering and absorption by dust, including a brightening in flux just before ingress correlated with the transit depth and explained by forward scattering, and an asymmetry in the transit light curve shape, which is easily reproduced by an exponentially decaying distribution of optically thin dust, with a typical grain size of 0.1 micron. Conclusions. Our quantitative analysis supports the hypothesis that the transit signal of KIC 12557548 b is due to a variable cloud of dust, most likely originating from a disintegrating object.

More on the above peculiar object:

Modelling the light-curve of KIC012557548: an extrasolar planet with a comet like tail

An object with a very peculiar light-curve was discovered recently using Kepler data from first two quarters. Authors argue that this object may be a transiting disintegrating planet with a comet like dusty tail. The aim of the present paper is to verify the model suggested by the discoverers by the light-curve modelling and put constraints on the geometry of the dust region and various dust properties. We modify the code Shellspec designed for modelling of the interacting binaries to calculate the light-curves of stars with planets with comet like tails. We take into account the Mie absorption and scattering on spherical dust grains of various sizes assuming realistic dust opacities and phase functions and finite radius of the source of light (star). The light-curve is reanalysed using first six quarters of the Kepler data. We prove that the peculiar light-curve of this objects is in agreement with the idea of a planet with a comet like tail. Light-curve has a prominent pre-transit brightening and a less prominent brightening after the transit. Both are caused by the forward scattering and are a strong function of the particle size. Dust density in the tail is a steep decreasing function of angle (distance) from the planet which indicates significant dust destruction along the tail caused by the star. The particle size of the grains in the tail is about 0.1 micron but can be slightly larger if data with the shorter exposure (short cadence) were available. The orbital period of the planet was slightly improved. This light-curve with pre-transit brightening is analogous to the light-curve of $\epsilon$ Aur with mid-eclipse brightening and forward scattering plays significant role in both of them.

At the daily press conferences put on by the Division of Planetary Sciences over the past week there was a discussion of results from Kepler that confused me as well as many others. The recording can be found here http://www.ustream.tv/recorded/26175189.
It is the first briefing of the day.
In it, Julia Frank describes how using Kepler data she shows that the range of inclinations of detected planets is "small" so that planetary systems look like something between "pancakes" and "crepes". Later, in the Q and A part someone asks how inclination angles are determined, i.e., compared to what. Julia says an arbitrary plane. The questioner persists, pointing out that since Kepler can only see transiting planets, those in orbits whose angle of inclination is greater that the diameter of the star won't be seen in the first place. This is verified here.. Further, I do not see how it's possible for a transit time to translate into an angle of inclination (when you can't see the path of the transit across the disc of the star since Kepler can't resolve the stellar disc).

Answers provided by Julia and others did not aid my understanding (or the questioners and others in the audience). So I'm posting this here in the hopes that someone could direct me to a reference that might explain how the reported results were obtained.

Thanks

The part of the conference you mention confused me a bit too, but I later realised that the speaker may have misunderstood the question. I think the audience member was asking about the inclination of the orbit of a planet, and the speaker thought he was talking about the inclination of the orbits of two planets to each other.

Inclination of an exoplanet's orbit is defined relative to the plane of the sky. 0 degrees (or 180 degrees) is a face-on orbit. 90 degrees is an edge-on, transiting orbit. 89 degrees may still transit the star if the star is large enough or the planet orbit is close enough. But because it's not exactly 89 degrees, the transit will not be a central transit (the impact parameter will be > 0), and thus the planet will spend less time on the stellar disc.

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

If you know the orbital period, and you have a value for the stellar mass, you can get its semi-major axis. Based on this, you can get the orbital velocity. With an estimate of the stellar radius, you can predict how long a transit should last depending on what impact parameter the planet's orbit has (or where it transits on the stellar disc), where the impact parameter is calculated with b = a cos i.

Edit: Wording.

Edit2: As for the coplanarity results, they just simulated various planetary system architectures and matched it to what they see in Kepler data, taking into account the observational biases.
http://arxiv.org/abs/1207.5250

First, thanks a lot for your detailed response.
I think I get most of what you are saying. I can see how, by observing the star, you can get it's temperature/spectral class. How you can plot that on a H_R diagram and get an estimate of the mass (though I admit I was surprised to discover that such an estimate is considered accurate enough to make the subsequent calculations. I always saw the main sequence as a broad band.) Then you can use the mass and period to get the semi-major axis. Per what you say, I can see know how it's possible to use that same mass estimate to also estimate volume and hence diameter. Then the estimated diameter can be combined with the observed transit time to calculate the angle of inclination of the planet from a line/plane from Earth to the center of of the star.

As you note, however, any such angle is going to be very small; i.e., an orbital plane very close to 90 degrees.

All that said however, since the only planets that can be detected in a system are those in that narrow range of transiting orbital planes and since planets, at least in theory (e.g., Pluto, if it were still a planet) can have orbits highly inclined to other orbital planes, I don't see how Kepler data can lead to the conclusion Frank describes (i.e., that planetary systems are like pancakes [rather than, say, bagels]).
Put as the questioner put it, Kepler can only detect planets that transit (and hence must be in one highly constrained planar orientation) so how can anything be said about undetected planets in possible non-transiting planes? As you may recall, the more senior responder basically described what you illustrated by your diagram below.

If a planetary system is perfectly coplanar and there's a small inclination away from 90 degrees, then each transiting planet out from the star will have an increasingly large impact parameter. If planetary systems are well-aligned, then you would expect that, in general, the impact parameters of outer planets are greater than for inner planets. Otherwise, you need orbit planes to be inclined relative to each other.

If, amongst the transiting multi-planet systems, you observe a typical distribution of the difference in inclination between two planets, then it's reasonable to assume that this distribution applies to non-transiting planets as well.

Hungry4info's answer is right on the money on the technical details. (Not sure about the various speakers' intentions; I didn't hear that audio.)

I'll add a couple of notes:
1) Kepler's time resolution is actually pretty coarse as far as timing transit durations, so a single measurement has considerable error. Given many transits, however, the accuracy increases.

2) 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.

3) There are also major discrepancies seen in the estimated stellar properties and observed transit durations. Peter Plavchan and his colleagues have been researching this. All told, the stellar properties estimated contain errors, and likely contain some systematic errors. As a simple demonstration of this: If you estimate that a planet should transit the star for a maximum of 2 hours and its observed to transit for 3 hours, then your estimate of the star's radius is probably too low (or your estimate of the star's mass is too high, or both). And there are such cases.

It's that "assume" in your quote above that defines my problem. If you assume that all the planets in a multi-planet system are in the same plane, then the math will prove your assumption true. But the interest in the "pancake" result stems, I believe, from the fact that this is yet to be determined. We only have one system in which we know the planes of all the orbiting planets and they are pretty much co-planar. But to know that this is also a fact for other systems goes a long way towards verifying our planetary formation models. Thus proving it is so is quite important.) Further, just as indicated by the post above, some of our assumptions about stellar mass (as a function of spectral type) are quite clearly incorrect, so too must we be cautious about any assumptions of orbital inclinations.

So in my mind, I'm still unclear how it is possible to say anything about the orbital inclinations of UNSEEN planets based on only those observed transiting stars.