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KELT-9b: ‘Gravity Darkening’ and an Asymmetric Light Curve

Perhaps the hottest planet ever discovered spotlights yet another way to interpret light curves produced by transiting worlds. KELT-9b comes out of data gathered by the KELT transit survey, the acronym standing for Kilodegree Extremely Little Telescope. KELT consists of two robotic telescopes, one at Winer Observatory in southeastern Arizona, the other at the South African Astronomical Observatory in Sutherland, South Africa. The planet orbits an A-class star in Cygnus about 670 light years away and turned up in the KELT data in 2017.

We’ve learned a lot more about KELT-9b thanks to the TESS mission, allowing us to understand just how unusual this planet is. 2.9 times as massive as Jupiter, the world orbits its star in 36 hours, receiving 44,000 times the energy from its host that Earth receives from the Sun. Reaching 4,300 degrees Celsius, this is a tidally locked planet whose dayside is hotter than the surfaces of some stars. Its orbital path takes it almost directly above both the star’s poles.

But this mix gets even more intriguing. The primary, KELT-9, is roughly twice the size of the Sun, 56 percent hotter, and spins 38 times as fast. That makes for a complete stellar rotation in 16 hours. As you would imagine, the rapid spin causes the star to deform, flattening at the poles and broadening at the equator. As a result, we run into the phenomenon known as gravity darkening — the poles brighten as the equatorial region cools and dims by comparison.

We get a temperature differential of almost 800 degrees Celsius. The effects on the transit light curve are interesting. Beginning near the star’s poles, the transit blocks less light as KELT-9b travels over the stellar equator. We have an asymmetry here we can work with to gain information about the temperature and brightness changes over the surface of the star, learning more about its shape and orientation.

Jason Barnes (University of Idaho) is a co-author of the paper on this work:

“Of the planetary systems that we’ve studied via gravity darkening, the effects on KELT-9 b are by far the most spectacular. This work goes a long way toward unifying gravity darkening with other techniques that measure planetary alignment, which in the end we hope will tease out secrets about the formation and evolutionary history of planets around high-mass stars.”

Image: Observations from NASA’s Transiting Exoplanet Survey Satellite (TESS) have revealed new details about KELT-9b’s environment. The planet follows a close, polar orbit around a squashed star with different surface temperatures, factors that make peculiar seasons for KELT-9b. The planet’s transits begin near one of the star’s hot, bright poles and progress toward the cooler, dimmer equator. Credit: NASA’s Goddard Space Flight Center.

Depending on which part of the star is being referenced, the phenomenon behind gravity darkening is sometimes called gravity brightening, reflecting the fact that the oblate shape of such a rapidly spinning star causes higher surface gravity at the poles, producing higher temperature and brightness; by contrast, the equator is darker. Because of the temperature differential on the surface of the star, KELT-9b experiences an unusual kind of seasonality, hotter over the poles, colder over the star’s equator. A kind of summer, a kind of winter, with each season lasting nine hours, only to repeat during the brief year.

A planet like this is going to be useful for research into hot Jupiters. There is a clear trend among such worlds in that they are often spin-orbit misaligned. The paper continues:

“Its high dayside temperature provides excellent opportunities for phase curve and secondary eclipse analyses (Hooton et al. 2018; Wong et al. 2019; Mansfield et al. 2020). The high signal-to-noise ratio of its transit makes KELT-9 b a top target for transmission spectroscopy (Hoeijmakers et al. 2018, 2019; Cauley et al. 2019). In this work, we model KELT-9 b’s Transiting Exoplanet Survey Satellite (TESS) light curve including rapid stellar rotation to measure the hot Jupiter’s transit parameters, and we take advantage of the transit asymmetry caused by gravity darkening to robustly constrain the planet’s orbital geometry including its true spin–orbit orientation.

Thus this paper is unusual in being one of the few that deal with gravity darkening in analyzing an exoplanet lightcurve. Using it, the authors measure the planet’s alignment angle and discuss the effects of gravity darkening on the hot Jupiter’s atmospheric processes. In the figure below, the effects of gravity darkening are apparent in the transit.

Image: This is Figure 2 from the paper. Caption: (Left) KELT-9 b begins its transit near the star’s hot pole and moves toward the star’s cooler equator. Our transit analysis directly measures the stellar inclination ( i ), the planet’s projected alignment (λ), and the orbital inclination (i.e., the impact parameter b). We find that KELT-9 varies in effective temperature by ∼800 K between its hot poles and cooler equator. (Right) KELT-9 b’s phase-folded primary transit from TESS. The transit depth steadily decreases throughout the eclipse, indicating that KELT-9 b begins its transit near one of the host star’s hotter poles and moves toward the dimmer stellar equator. Credit: Ahlers et al.

Models of rapidly rotating stars are still being developed, but will be needed to analyze the high number of such stars expected to be discovered by TESS. In fact, I was surprised to learn that in a previous paper, lead author John Ahlers (NASA GSFC) had estimated on the order of 2,000 exoplanets will turn up orbiting A/F stars in the TESS data, and the expectation is that a large number of these will be spin-orbit misaligned. Thus KELT-9b gives us a window into fast rotators, which are expected to comprise a large number of the A/F systems discovered.

The paper is Ahlers et al., “KELT-9 b’s Asymmetric TESS Transit Caused by Rapid Stellar Rotation and Spin–Orbit Misalignment,” The Astronomical Journal Vol. 160, No. 1 (5 June 2020). Abstract.

{ 13 comments… add one }
  • charlie July 7, 2020, 12:54

    “As a result, we run into the phenomenon known as gravity darkening — the poles brighten as the equatorial region cools and dims by comparison. ”
    Ok, I’ll bite ; HOW does gravity darkening WORK?

    • Bruce D Mayfield July 7, 2020, 18:55

      Some stars rotate so fast that they have a significant bulging at their equators. Points closer to a star’s core will be hotter than more distant points, therefore the poles are hotter and brighter than points near the equator.

    • Ron S. July 7, 2020, 19:02
    • Mike Serfas July 8, 2020, 7:43

      In the paper (ArXiv: https://arxiv.org/pdf/2004.14812.pdf ) the authors explain gravity darkening is actually a combination of two effects. In addition to the polar surface being brighter, the radius around the equator (which is seen from the pole) is also larger.

  • Bruce D Mayfield July 7, 2020, 13:49

    “I was surprised to learn that in a previous paper, lead author John Ahlers (NASA GSFC) had estimated on the order of 2,000 exoplanets will turn up orbiting A/F stars in the TESS data, and the expectation is that a large number of these will be spin-orbit misaligned.”

    I find that surprising as well. Not that so many exoplanets orbiting A and F stars are expected to be found by TESS, but that so many of these “will be spin-orbit misaligned.” What is thought to be the cause of all these projected misalignments?

    • Paul Gilster July 7, 2020, 20:20

      Bruce, see my response to Ron S. above on this.

  • Ron S. July 7, 2020, 14:11

    “I was surprised to learn that in a previous paper, lead author John Ahlers (NASA GSFC) had estimated on the order of 2,000 exoplanets will turn up orbiting A/F stars in the TESS data, and the expectation is that a large number of these will be spin-orbit misaligned.”

    The misalignment is also surprising to me. What is the proposed mechanism whereby this is predicted to be likely?

    • Paul Gilster July 7, 2020, 20:19

      Ron, I haven’t read the earlier paper from Ahlers yet, where he makes the case for the TESS findings in the range of 2,000. Re the mechanism for misalignment, he points to a lot of earlier scholarship going back to 2010 to back up the idea that “giants around high-mass stars are frequently spin–orbit misaligned.” Digging in on those citations might make for a good entry here in the future.

      Re KELT-9b itself, he sees three possibilities for the misalignment:

      1) “KELT-9 b likely misaligned into its polar orbit through one of three possible scenarios. One possibility is that an outside body torqued the system’s protoplanetary disk out of alignment, and then KELT-9 b formed inside the misaligned plane.”

      2) “Another possibility is that the host star’s rotation axis torqued out of alignment. In such a scenario, KELT-9 b and ny other planet in that system ostensibly remained in their formation plane, and the star instead misaligned from the system.”

      3) “The third general idea for explaining KELT-9 b’s spin–orbit misalignment is that some mechanism misaligned the planet after formation. For example, Kozai–Lidov resonance involves bodies exchanging angular momentum by driving up inclinations and eccentricities, which could explain KELT-9 b’s polar

      • Ron S. July 7, 2020, 22:56

        Of these only the third sounds plausible to me, at least off hand. Both the second and third hypotheses can be tested with numerical models to determine whether the misalignment is probable or rare. The first hypothesis would be rare, not frequent. There is a lot of angular momentum in the disk planets (as in our solar system) but I wonder how it would tip the stellar axis that much and leave the disk a disk.

        Obviously I haven’t dug into this and thought the author would have a better reference to claim that misalignment would be frequent in this class of system. It looks like at least several people were surprised by the claim.

        Thank you for the rapid follow up, Paul.

      • Aleksandar Shulevski July 8, 2020, 6:05

        What about the possibility of capture? The planet could have been a rogue, captured in a polar orbit…

        • Paul Gilster July 8, 2020, 6:34

          An interesting thought. I want to follow up on the question of how common these orbital misalignments are among hot Jupiters, though Ahlers implies they’re common enough that planetary capture would seem unlikely. Much to learn here.

  • FrankH July 7, 2020, 15:03

    It’s amazing that this star was discovered using an inexpensive telephoto lens (and a very expensive CCD).

  • Geoffrey Hillend July 8, 2020, 17:24

    I think explanation two is the most probable. Maybe the orbital misalignment was caused by the stronger gravity of the star at the poles, the gravity darkening . The plane of the accretion formed normally around the equator, but when the star formed the gravity was stronger at the poles which caused the angle orbit of axis of KELT-9-b to precess or move closer to the poles of the star. I don’t like the idea that the star’s obliquity or angle of axis being changed because of the KELT-9-b or the smaller body moving the more massive one. On the other hand, a star is made of hot gases so maybe the gas giant can perturb a smaller part of the star, so the exoplanet could still torque or change axis or obliquity of the star? It would be important to see if there are any other planets around this star and see if their orbit inclinations are perpendicular to KELT-9-b or not.

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