Gravity-Darkened Seasons on Planets

Title: Gravity-Darkened Seasons: Insolation Around Rapid Rotators
Authors: John P. Ahlers
First Author’s Institution: Physics Department, University of Idaho

On Earth, our seasons come about due to the Earth’s tilted rotational axis relative to its orbital plane (and not due to changes in distance from the Sun, as it is commonly mistaken!) Essentially, this is due to the varying amounts of radiation that the Earth receives from the Sun in each hemisphere. But what would happen if the Sun were to radiate at different temperatures across its surface?

It’s hard to imagine such a scenario, but a phenomenon known as gravity darkening causes rapidly spinning stars to have non-uniform surface temperatures due to their non-spherical shape. As a star spins, its equator bulges outwards as a result of centrifugal forces (specifically, into an oblate spheroid). Since a star is made of gas, this has interesting implications for its temperature. If its equator is bulging outwards, the gas at the equator experiences a lower surface gravity (being slightly further away from the star’s center) a lower density and temperature. The equator of a spinning star is thus considered to be “gravitationally darkened”. The gas at the star’s poles on the other hand, has a slightly higher density and temperature (“gravitational brightening”) since it is closer to the center of the star relative to the gas at the equatorial bulge. Thus, there is a temperature gradient between the poles and equator of a rapidly rotating star.

While this is an interesting phenomenon in itself, the author of today’s paper introduces a new twist: what if there’s a planet orbiting such a star, and what implication does this gravity darkening have on a planet’s seasonal temperature variations? Compared to Earth. exoplanets have potentially more complex factors governing its surface temperature variations. For example, if a planet’s orbit is inclined relative to the star’s equator (see Figure 1), it can preferentially receive radiation from different parts of its star during the course of its orbit.

Fig 1: All the parameters describing a planet's orbit. In this paper, the author mainly focuses on the inclination i, which is the angle of a planet's orbital plane relative to the star's equator. (Image courtesy of Wikipedia)

Fig 1: All the parameters describing a planet’s orbit. In this paper, the author mainly focuses on the inclination i, which is the angle of a planet’s orbital plane relative to the star’s equator. (Image courtesy of Wikipedia)

The author claims that this effect can cause a planet’s surface temperature to vary as much as 15% (Figure 2). This essentially doubles the number of seasonal temperature variations a planet can experience over the course of an orbit. However, the author does not attempt to model the complex heat transfer that occurs on the planets surface due to the atmosphere and winds.

Fig. 2: Some examples of seasonal temperature changes of a planet for various orbital parameters. The top left figure shows the orientation of the planet’s tilt (precession angle, color-coded to match the plots), and the times corresponding to one orbit around the host star. In each subplot, the author shows the flux a planet would receive for different orbital inclinations (i.e. the angle i in Fig. 1). 

Not only that, but there is also some variation in the type of radiation that a planet receives during the course of its orbit. Since the poles of rotating star are at a higher temperature, it will radiate relatively more UV radiation compared to the equatorial regions. The author claims that a planet orbiting in a highly inclined orbit will alternate receiving radiation preferentially from a star’s poles or equator, causing the amount of UV radiation to vary as much as 80%. High levels of UV radiation can cause a planet’s atmosphere to evaporate, as well as other complex photochemical reactions (such as those responsible for the hazy atmosphere on Saturn’s moon Titan).

As we discover new exoplanets over the course of the coming years, we will likely find examples of planets potentially experiencing these gravitationally darkened seasons. This will have interesting implications on how we view the habitability of these other worlds.

[Update (9/30/2016): Fig. 2 has been updated to correctly match Fig. 4 given in the paper]

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  1. In your fig.2, I think the obliquity measures the tilt of the planet’s pole relative to its orbit, not the tilt of the orbit relative to the star’s equator (that is the inclination which, checking the original paper, was set to 90° for all curves).

    • Oops, thanks for pointing that out. I’ve updated the post to include the link.

  2. Very interesting research!

  3. Hello Anson, thank you for writing this article about my research. I would like to politely request that Figure 2 of your article be changed to Figure 5 of my paper. That figure will correctly match the caption you have written. It’s the more interesting figure anyway 😉

    • Hi John,
      I appreciate the feedback! I apologize for the inaccuracy. Just to clarify, are you referring to Fig. 4 of your paper? The figure that I posted is Fig. 5 of your paper. I’m happy to update it of course.

      – Anson

      • Hi Anson, I’m not sure if my previous reply went through. Yes, please change Figure 2 of your article to Figure 4 of my paper (sorry about the typo above). Thanks!

        • I’ve updated the figure, so hopefully it should be accurate now. Thanks again for your help and feedback! 🙂


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