View Full Version : A strange planet Kepler found, and some strange things about it

Roger E. Moore
2018-Nov-06, 02:01 AM

The above paper is a recent one on a sunlike star named Kepler-1656 and its planet, "b". Kepler-1656, the star, is slightly bigger and more massive than the Sun, about (if I did the math right) 186.8774644 pc = 609.22 ly away. The Kepler spacecraft caught a transiting planet, and the current paper follows up with more astrometric detail to pin down the details as best as possible.

Kepler-1656 b is about 48.6 times the mass of Earth (=0.511 Saturns or 2.834 Neptunes), just over 5 times the radius of Earth, and has an eccentricity of 0.836, a real roller-coaster. The semimajor axis is 0.197 AU, so it gets pretty hot. Its closest approach to its sun is a*(1-e) = 0.03231 AU, and its greatest distance is about 0.3617 AU. Mercury's distance from the Sun ranges from 0.3075 AU to 0.4667 AU, so K-1656 b is toasted nicely. I cannot find out what spectral type the star is, but I looked at other papers on it and it's an F or G.

The authors of the paper call Kepler-1656 b a "sub-Saturn" but it isn't really. In any other research paper on "Saturn-like" exoplanets, that phrase means the exoplanet is large in diameter but very low in density and mass, as Saturn is to Jupiter. This planet is not. It is on the extreme high end of mini-gas giant mass, a very strange critter, more properly a giant/massive Neptune. The authors believe K-1656 b is the complete amalgamation of all inner planets the system ever had, as none could escape the gravity well where K-1656 b is even if slingshot-ed away by the planet. The other planets and planetoids eventually collided with K-1656 b and that was it. It literally mopped up its inner planetary system. No other worlds have been detected around the star, yet, but there's plenty of room for them farther out.

I wanted to figure out if this massive mini-gas giant might have any moons. Attached is the Roche limit table for it. Moons could have been formed by giant impacts, which this world likely had, or captured as debris in 3-body problems.

More in a bit.

Roger E. Moore
2018-Nov-06, 03:29 AM
Temperature of Kepler-1656 is 5,731 60 K, and our Sun is 5,800 K, so I guess it is a G-something. None of the exoplanet archives or stellar archives give any spectral info or even estimate luminosity. Life is hard.

Hill sphere calculations tomorrow. That was a surprise.

John Mendenhall
2018-Nov-06, 04:17 AM
Thought provoking, indeed. Thanks.

Roger E. Moore
2018-Nov-06, 01:50 PM
Attached are the Hill sphere calculations, with comparative data for Earth. I was stunned to see how compacted the Hill sphere is for K-1656 b, as a result of its extreme eccentricity and closeness to its sun. Earth has a bigger Hill sphere.

Here is a quote from the Wikipedia page on Hill spheres: "True region of stability: The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius. The region of stability for retrograde orbits at a large distance from the primary, is larger than the region for prograde orbits at a large distance from the primary. This was thought to explain the preponderance of retrograde moons around Jupiter; however, Saturn has a more even mix of retrograde/prograde moons so the reasons are more complicated."

I have no located references to all of the above data, but I included reduced Hill sphere values in the attachment, at the far right end. Earth's Moon, as can be seen, is well within the minimal fractional value for the Hill sphere.

Roger E. Moore
2018-Nov-06, 02:03 PM
Kepler-1656b: a Dense Sub-Saturn With an Extreme Eccentricity
Madison T. Brady, et al. (Submitted on 22 Sep 2018)

QUOTES: Kepler-1656b has a mass of 48.6 +4.2/-3.8 M-earth, making it one of the most massive sub-Saturns known. Its high mass also implies a high density, which at... 2.13 +0:87/-0:57 g cm-3 makes Kepler-1656b one of the densest sub-Saturns known and denser than any gaseous object in the solar system.

Following Petigura et al. (2017a), we quantified the core and envelope fractions of Kepler-1656b using the Lopez & Fortney (2014) planet structure models, which assume an Earth composition core and a envelope of primordial H/He. In the sub-Saturn size range, derived envelope fractions are not sensitive to the precise composition of the core (Petigura et al. 2016). Under these assumptions, we found that 82 +/- 6% of the planet’s mass is in the core. This value is on the high end of what is observed among sub-Saturns.


Given the above, it's sure that Kepler-1656 b has a thick atmosphere, but I cannot guess how deep it goes. This is important in sorting out Roche limits above the planet's surface.

Given how hot the planet gets and how close to its sun, my guess is that no volatiles remain on any satellites it has, if it has any, so its moons are rocky.

Comparing the Roche limit table with the Hill sphere table to get outer and inner margins for moon orbits....

Roger E. Moore
2018-Nov-06, 02:34 PM
...the orbital range is extremely narrow and open only to stony, ice-free moons. Taking a conservative stance, the maximum stable altitude above K-1656 b's core would be 58,238.51 km (0.3 Hill sphere radius), down to whatever maximum height to which the atmosphere will rise at perihelion. It is expected that the atmosphere will expand at perihelion, with air drag pulling down moons that get too close, in the same way that human spacecraft will enter Earth's atmosphere and decay when the Earth warms and the atmosphere height increases during periods of increase solar activity. The Roche limit for a basalt-density moon is 21,000-22,000 km above K-1656b's core.

This is a really narrow range. Could moons form naturally in this range around a massive world subjected to massive impacts in its past?

We do have the example of Uranus. It was likely smacked with an Earth-size impactor to cause it to tilt, and satellites could have sprung from such a collision. If it worked for planet Uranus, it might have worked for K-1656 b, but again the range of stable orbits is pretty narrow.



NOTE: Explaining why the Uranian satellites have equatorial prograde orbits despite the large planetary obliquity

Alessandro Morbidelli, Kleomenis Tsiganis, Konstantin Batygin, Aurelien Crida, Rodney Gomes (Submitted on 23 Aug 2012)

We show that the existence of prograde equatorial satellites is consistent with a collisional tilting scenario for Uranus. In fact, if the planet was surrounded by a proto-satellite disk at the time of the tilting and a massive ring of material was temporarily placed inside the Roche radius of the planet by the collision, the proto-satellite disk would have started to precess incoherently around the equator of the planet, up to a distance greater than that of Oberon. Collisional damping would then have collapsed it into a thin equatorial disk, from which the satellites eventually formed. The fact that the orbits of the satellites are prograde requires Uranus to have had a non-negligible initial obliquity (comparable to that of Neptune) before it was finally tilted to 98 degrees.

Roger E. Moore
2018-Nov-06, 02:38 PM
In the end, as eccentric as K-1656 b is, it's hard to see anything big surviving around it. My guess is that any moons it has are caught in resonance with the planet's perihelion with its sun; if they get too close to perfect resonance, they might get pulled out of orbit and crash into K-1656 b. The moons would have to be tidally locked to face K-1656 b as our Moon faces Earth.

Was just thinking that K-1656 b itself would be in captured resonance with its sun, either in a 1:1 or 3:2 spin-orbit capture, like Mercury (3:2).

Roger E. Moore
2018-Nov-06, 02:45 PM

This NOAA segment on satellite drag is important when looking at debris in orbit around K-1656 b when it reaches perihelion and its atmosphere reaches maximum expansion, and during periods of solar storms on Kepler-1656 itself. I doubt this planet has a ring system or much small debris around it, all cleaned up long ago.

Roger E. Moore
2018-Nov-06, 04:24 PM
Extra table showing possible orbital periods for any existing stable moons around Kepler-1656 b, within the boundaries of its Hill sphere (0.3 value).

Just a few hours at most, whirling around this heavy planet.

Roger E. Moore
2018-Nov-07, 03:18 PM
This is weird. New paper came out discussing new mass-radius relations. Check out the graphs on pages 7 & 9. Kepler-1565 b is WAY off the graph for anything. Wow.

Predicting Exoplanets Mass and Radius: A Nonparametric Approach
Bo Ning, Angie Wolfgang, Sujit Ghosh (Submitted on 6 Nov 2018)

Roger E. Moore
2018-Nov-07, 03:21 PM
Assumed (a bad thing, I know) that the luminosity of K-1656 (the star) was about that of the Sun, did the following table showing insolation at different AU from the star (aphelion & perihelion).

2018-Nov-22, 10:42 AM
This is weird. New paper came out discussing new mass-radius relations. Check out the graphs on pages 7 & 9. Kepler-1565 b is WAY off the graph for anything. Wow.

Predicting Exoplanets Mass and Radius: A Nonparametric Approach
Bo Ning, Angie Wolfgang, Sujit Ghosh (Submitted on 6 Nov 2018)
Unfortunately, that paper neglects to show where the Solar System's planets are in its graphs. It shows separate results for mass as a function of radius, M(R), and radius as a function of mass, R(M). The curves are close, but somewhat different. From Planetary Fact Sheet - Ratio to Earth (https://nssdc.gsfc.nasa.gov/planetary/factsheet/planet_table_ratio.html) (radius, mass):
Mercury (0.383,0.0553), Mars (0.532,0.107), Venus (0.949,0.815), Earth (1,1), Neptune (3.88,17.1), Uranus (4.01,14.5), Saturn (9.45,95.2), Jupiter (11.21,317.8).

Jupiter and Saturn are right on the dot for both M(R) and R(M), but Uranus and Neptune are more massive than average for M(R) and about right for R(M). Venus and the Earth are about right for both, but both planets are where the data get scanty.

Kepler-1565 b is (5.02+0.53-0.53, 48.6 4.2-3.8) and that's well off from the average for both M(R) and R(M).

2018-Nov-22, 11:59 AM
I will now estimate equilibrium temperatures. I will use a naive equilibrium estimate that assumes uniform heating and uniform reradiation, both with the same albedo. That estimate gives 278 K or 5 C for the Earth, close to our actual value of 15 C.

Kepler-1565 b has a mean distance of 0.197 AU and an eccentricity of 0.844, and it orbits between 0.031 and 0.363 AU, giving equilibrium temperatures of 480 K, 650 K, and 1700 K. If the planet has moons, they must be rocky ones.

The Hill-sphere stability limit corresponds to an unperturbed period of sqrt(3) or 1.732 times less than the planet's orbit period, assuming a circular orbit. For an eccentric orbit, one must use the period corresponding to the planet's closest distance, and that is 1.95 days.

Using the Hill-sphere limit as a guide, one can construct an empirical estimate using the Solar System's moons. I have done so, and by that estimate, Jupiter has the farthest moons.

Jupiter's period: 4332.59 d, eccentricity: 0.0489, perihelion-distance period: 4018.71 d
S/2003 J 2 (lost, retrograde): period 981.55 d, ratio 4.09
Megaclite (XIX, retrograde): period 792.44 d, ratio 5.07
Valetudo (LXII, direct); period 532.00 d, ratio 7.55

Using Valetudo's period ratio, Kepler-1565 b's farthest stable moon would have a period of 0.26 days or 6.2 hours. With Megaclite's, that becomes 0.38 days or 9.2 hours.

2018-Nov-22, 12:24 PM
I will now calculate the lower limit of the period that a moon of Kepler-1565 b can possibly have. This is the surface-satellite period, and for the Earth, it is 1.41, and for this planet, 2.3 hours. There is not much of a range between that value and the period limits that I derived from Jupiter's outermost moons.

Doing the inner limit more carefully requires working with the Roche limit. That limit's radius is (some factor) * (planet radius) ((planet density) / (moon density))^(1/3). For a rigid sphere, that factor is 1.260 (gravity-only) and 1.442 (with synchronous rotation), while for a fluid, it is 2.423 (gravity-only) and 2.455 (with synchronous rotation).

The planet's mean density is 2.16 g/cm^3, and that of the Earth's upper mantle is 3.5 g/cm^3. Stony meteorites vary, but that is a rough average for them also. Using 3.5 g/cm^3 as a plausible best case, the surface-satellite period is 1.8 hours and the Roche limits are 3 hours (rigid) and 7 hours (fluid or rubble pile). For a moon density the same as the planet's density, the numbers become 4 hours and 9 hours.

A solid-rock moon may be able to orbit Kepler-1565 b, but a rubble-pile one would not be able to.

Roger E. Moore
2018-Nov-22, 01:08 PM
:) Weird planet for sure. Thank you!

Roger E. Moore
2019-Jun-11, 12:50 PM
This paper just came out, and from my reading it appears to well explain the existence of Kepler-1656b as the result of multiple planetary collisions.


Signatures of a planet-planet impacts phase in exoplanetary systems hosting giant planets

Renata Frelikh, Hyerin Jang, Ruth A. Murray-Clay, Cristobal Petrovich (Submitted on 7 Jun 2019)

Exoplanetary systems host giant planets on substantially non-circular, close-in orbits. We propose that these eccentricities arise in a phase of giant impacts, analogous to the final stage of Solar System assembly that formed Earth's Moon. In this scenario, the planets scatter each other and collide, with corresponding mass growth as they merge. We numerically integrate an ensemble of systems with varying total planet mass, allowing for collisional growth, to show that (1) the high-eccentricity giants observed today may have formed preferentially in systems of higher initial total planet mass, and (2) the upper bound on the observed giant planet eccentricity distribution is consistent with planet-planet scattering. We predict that mergers will produce a population of high-mass giant planets between 1 and 5 au from their stars.