The Double Seasons of Kelt-9b
The already considerable amount of information available on KELT-9b and its star has recently been further enriched, thanks to a new study published in June 2020 in The Astronomical Journal, based on the accurate photometric data collected by NASA’s TESS space telescope. Between July and September 2019, TESS observed 27 transits of KELT-9b. The salient feature of the light curves acquired by the telescope during those transits is that they are asymmetric. The dip in the star luminosity is slightly more marked during the initial phase of each transit than during the final phase. How do you explain this asymmetry?

First of all, it must be considered that KELT-9, the star, is a fast rotator. The minimum rotational velocity is 111.4 ± 1.3 km/s, much higher than that of the Sun, which is just 2 km/s. The enormous centrifugal force generated by the fast rotation produces two effects: 1) it changes the shape of the star in an oblate spheroid, wider at the equator than at the poles; 2) surface gravity is less at the equator than at the poles, where more mass is compressed in a given space (a phenomenon known as gravity darkening).

As a consequence of this deformation and the gravity gradient associated with it, KELT-9 is hotter and brighter at the poles than at the equator. And not by a little: the difference is about 800 K. Here is what happens during the transits of the planet, according to the explanation reported in the study published in June:

When KELT-9 b transits its host star, it blocks a certain amount of light depending on whether it is transiting near the bright poles or dim equator. In the case of a misaligned orbit, the planet blocks varying intensities of light throughout its transit, resulting in an asymmetric transit. KELT-9 b’s transit ingress is deeper than its egress, meaning the planet begins its transit near KELT-9’s hot pole and moves toward its cooler equator.

If the orbital plane of KELT-9b had been aligned with the star’s equatorial plane, no asymmetry in the transit would have been noticed. Instead, the manifest asymmetry of the transits recorded by TESS betrays the polar orbit followed by the planet. Not only that: it allowed the study authors to obtain precise information on the star’s rotational velocity and the inclination of its axis, the flattening generated by the centrifugal force, the temperature gradient between star’s equator and the poles, and the planet’s precise orbital inclination relative to the star rotation axis. It is an incredible amount of information, considering that we see neither the star disk nor that of the planet from Earth. The only observable elements are the variations in time of KELT-9’s brightness and its radial velocity, measured through Doppler spectroscopy: a magnificent demonstration of the explanatory power of mathematics applied to physical phenomena, under the Galilean idea that the laws of Nature are written in the language of numbers and geometric shapes.

The black dots in the central box indicate the changes in the star’s brightness during KELT-9b’s transits. As you can see, the drop in light is more profound at the beginning of the transit. The asymmetrical blue curve is the best fit to the observational data, while the symmetrical red curve does not correspond as well to the data. Unlike the red one, the blue curve is modeled taking into account the gravity darkening of the star due to its oblate shape [John P. Ahlers et al 2020 AJ 160 4]

Here are the primary data obtained from the analysis of the asymmetric transits observed by TESS. The inclination of the star’s rotation axis relative to an observer on Earth is 52°, with a margin of uncertainty of +8 and −7 degrees. It means that the rotation axis is seen from the Earth inclined diagonally (the inclination would be 90° if the axis were vertical relative to us and 0° if it were horizontal). KELT-9’s actual rotation period is 16 hours, with an uncertainty of +5 and −4 hours. The star’s equatorial radius is 2.39 solar radii, that is, 1.633 million km. The oblateness, indicated with the Greek letter ζ, is equal to 0.089 ± 0.017, from which it is deduced that KELT-9’s polar radius is 148,000 km shorter than the equatorial radius. The Sun, in comparison, is an almost perfect sphere.

But the most interesting data are those concerning the effects of the variable insolation that the planet gets during its orbit. According to the study authors, when KELT-9b approaches the poles of the star, it gets a radiation flux 10% higher in the ultraviolet and 1–2% in visible light. Due to these flux variations, temperatures in the upper atmosphere of the planet are subject to radical changes during each orbit. The differences in temperature, in turn, probably produce impetuous winds, which blow at speeds of thousands of kilometers per hour: a phenomenon quite common in hot Jupiters such as KELT-9b. But the most singular effect is that the short year of this giant planet sees two summers and two winters happening in a matter of hours: a consequence of the star’s gravity darkening. In this regard, we read the explanation provided by the study authors:

The effect of gravity darkening on a planet’s insolation can be compared to the insolation of a planet with an eccentric orbit. In both scenarios the planets receive varying amounts of flux throughout their year, which can drastically impact climate. However, the frequency of changing flux is twice per orbit for gravity darkening versus once per orbit in eccentricity. […] Gravity darkening likely plays a more significant role than eccentricity for the insolation of planets such as KELT-9 b because hot Jupiter orbits are typically nearly circular.

Since during an orbit, KELT-9b passes in succession near both poles of the star, which are much hotter and brighter than the equator, its year sees two summers alternating with two winters. “Winters,” so to speak, of course, given that, in any case, KELT-9b’s temperatures are above 4,000 K.

KELT-9b’s transit geometry, as obtained from the light curves recorded by TESS. The planet begins its transit by covering a part of the stellar surface close to a pole, where temperature and brightness are higher, and progressively approaches the equator. The star temperature difference between the poles and the equator is about 800 degrees. Legend: i* is the inclination of the rotation axis of the star relative to our vantage point; b is the impact parameter; 𝜆 is the angle projected against the sky between the orbital plane of the planet and the axis of the star and corresponds to 88 ± 15° [John P. Ahlers et al 2020 AJ 160 4]

In conclusion, it would be exciting to see KELT-9b up close and study the effects on its climate of the deadly radiation flux to which it is continually exposed. Unfortunately, the enormous interstellar distances prevent us from satisfying such scientific curiosities. But the knowledge about exoplanets accumulated over the past twenty-five years allows us to form at least a general picture of the varieties of existing planetary systems. A fiery giant like KELT-9b, trapped in a polar orbit a short distance from an oblate and very hot star, shows us an example of a star/planet system utterly different from the Solar System. Such a configuration induce one to wonder what the evolutionary history of this planet was. What gravitational interactions brought the planet to that polar orbit? An issue about which, for now, we can only make educated guesses.
['Michele Diodati']
['Astronomy', 'Space', 'Astrophysics', 'Exoplanets', 'Science']