A New Explanation for Spin-Orbit Misalignment In Planetary Systems?

  • Paper Title: Internal Gravity Waves Modulate the Apparent Misalignment of Exoplanets Around Hot Stars (arxiv: 1209.2435v1)
  • Authors: T. M. Rogers. D. N. C. Lin, H. H. B. Lau
  • First Author’s Affiliation: Department of Planetary Sciences, University of Arizona, Tucson, AZ
  • Journal: Astrophysical Journal Letters (Accepted)

Overview: This theoretical paper runs simple 2D simulations to explore an alternate explanation for the misalignment observed between the orbits of some exoplanets and the orbits of their host stars.

Introduction: The Rossiter-McLaughlin Effect and Spin-Orbit Alignment

Studying exoplanets directly is pretty difficult. Because they’re so hard to resolve from their host stars, most studies of them are indirect, usually from investigating their effects on their stellar hosts. Radial velocity studies give masses; transit studies give radii; and sometimes, secondary eclipse and transit spectroscopy can hint as to structure and composition.

One of the more clever techniques used to study exoplanets relies on the Rossiter-McLaughlin (R-M) effect. While the combination of transit and RV observations can constrain most of the details of a planet’s orbit, the one thing they can’t directly speak to is the orbit’s orientation: is it orbiting in the plane of the star’s rotation, or is it at some crazy angle relative to it? The R-M effect lets us answer this question.

Figure 1 illustrates how the R-M effect works. Consider a planet transiting a star. The star has two halves: a blueshifted half rotating towards us and a redshifted half rotating away from us. Usually the light from these two halves averages out and we don’t see any shift in the star’s spectrum. However, when the planet is in front of the blue half, it blocks only blueshifted light, and the starlight becomes slightly redshifted. Similarly, when the planet is in front of the red half, the starlight becomes slightly blueshifted. Now, if the planet’s orbit and star’s spin were perfectly aligned, you’d expect perfect symmetry in the spectral shifts as the planet transits first the blue, then the red side of the star (left panel of Figure 1). But if they are misaligned – if the planet’s orbit is tilted relative to stellar spin – the resultant shift will be asymmetric (right panel of Figure 1). By looking at the precise nature of asymmetry in the measured spectrum, scientists can back out the angle between the stellar rotation axis and the planetary orbital axis – the spin-orbit angle.

Figure 1: Schematic illustration of the Rossiter-McLaughlin effect. The left figure shows a transiting planet whose orbit is aligned with its star’s spin, while the right figure depicts a misaligned system. The bottom panel illustrates the spectral shifts expected in each case. Note how the aligned case is symmetric and the oblique case is asymmetric. Image credit: Subaru Telescope, National Observatories of Japan.

Before these measurements were conducted, scientists expected spin-orbit angles to be small; after all, the stars and planets both condensed from the same disk (which had some single direction of organized rotation), so it made sense that everything should be spinning in the same way. However, as with so many expectations in exoplanet history, this turned out to be wrong. In fact, recent studies show that particularly for hot stars (surface temperature > 6300 K), many planets exist with spin-orbit misalignment – some of which are even retrograde!

Motivation – This Work

Most of the explanations invoked to explain spin-orbit misalignment so far have appealed to planetary formation and migration. These include 1) disk migration, where planets wander due to interactions with the protoplanetary disks, 2) dynamical excitation, where planets experiencing a particular resonance have their orbits shifted about, 3) planet-planet scattering, where interactions between planets send worlds higgledy-piggeldy.

All these explanations assume the star is unchanging, and that the planet moves. This paper considers an alternate explanation. What if the planetary orbits remain aligned, and it is the star’s rotation that is causing the observed asymmetry in the star’s spectrum?

Hot, massive stars have both a convective zone in their deep interiors as well as a radiative zone near the surface. Interactions at the interface of these two zones can generate waves which carry angular momentum from the core to the surface. This can change the rotation of the surface of the star. So, even if the overall spin of the star was aligned with the orbit of the planet, the spin of the star’s surface, which is what we measure, could appear to be misaligned.

Method and Results

To test this idea, the authors ran a 2D model representing an equatorial cross-section of a 3 solar mass star. The simulation involved the full set of hydrodynamic equations, with a few reasonable approximations thrown in for computability’s sake. The authors acknowledge the limits of such a simulation, but point out that it provides a reasonable first glance at the problem.

They model first a star with a superrotating core (a core that spins faster than the surface). They find that angular momentum transport due to gravity waves rapidly increases surface spin by a factor of 10. However, due to angular momentum conservation this slows down the convective core of the star, which then eventually rotates slower than the radiative envelope. Eventually, this causes the surface spin to start decreasing. Eventually, the spin direction flips completely and the star’s rotation becomes retrograde! Similar results were found in the case of a non-superrotating core, but in this case the direction of initial acceleration – whether it was speeding up or slowing down – was random.

These results indicate that stellar internal angular momentum transport might be a viable mechanism to explain spin-orbit misalignment. It’s important to note, though, that this 2D case can only explain planets that are completely retrograde (misaligned by 180 degrees). To assess whether this mechanism can cause intermediate shifts in alignment as well requires a full 3D model and much more computer time.

The authors also propose some observational tests of their work. They note that the R-M measurements of the XO-3 planetary system have been showing variation which could be taken as a change in its spin speed – consistent with their simulations. They propose an extended study of the star. They also propose studying multi-planet systems around hot stars. If all the planets show a similar misalignment, that is a suggestion that the cause is rooted in the star and not the planets, as the uniform misalignment of planetary orbits is harder for some of the other mechanisms to explain.

Overall, this work represents an interesting new approach to the question of spin-orbit misalignments: that the apparent “misalignment” could be rooted in the star, not the planet!

About Sukrit Ranjan

I am a graduate student at Harvard University studying extrasolar planets and astrobiology. In my free time, I like books, board games, and flying over Boston. http://abstrusegoose.com/308

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