That other angle
Some of the biggest exoplanet news so far this year has arrived in the form of Rossiter-McLaughlin measurements of the sky-projected misalignment angles, λ, between the orbital angular momentum vectors of transiting planets and their stellar spin vectors.
A significantly non-zero value for λ indicates that a system was subject to some rough action in the distant past. Both planet-planet scattering and Kozai migration, for example, can lead to systems with non-negligible λ’s. The recent paper by Triaud et al. (covered here) showed that such processes may be responsible for a startlingly significant fraction of the known transiting-planet systems.
The angle λ has the advantage of being measurable, but it has marked disadvantage of informing us only of the projected geometry of the system. To get a sense of the physically relevant quantity — the true degree of spin-orbit misalignment — one needs the direction of the stellar spin vector.
Kevin Schlaufman, one of the graduate students in our program here at UCSC, has worked out a very clever method of getting a proper statistically supportable guess of the complement misalignment angle between the orbit of the plant and the spin of its host star along the line of sight. I have to say that I’m quite enthusiastic about Kevin’s paper — it’s a big jump, not an incremental advance, and it’s well worth reading.
The method leverages the fact that a mature main-sequence star of given mass and age has a fairly predictable rotation period. Sun-like stars form with a wide range of rotation periods, but by the time they reach an age of ~0.5 billion years, there is a reasonably well-defined rotational period-stellar mass relation. During the remainder of their lives, main sequence stars then slow their rotation by shedding angular momentum via Alfven-like disturbances. Stellar spin-down rates are relatively large early on, and decrease with the passage of time.
A star’s projected rotational velocity can be measured by looking at the amount of rotational broadening in the spectral lines. This gives V_rot*sin(i_s), where i_s is the unknown angle between the star’s spin pole and the line of sight. The essence of the Schlaufman method is then immediately apparent. The mass and the age of the star allow you to infer V_rot. You measure V_rot*sin(i_s), and then bam! The inclination angle, i_s, is determined.
Reality, of course, is not so clear-cut. One has a host of errors and intrinsic variation to deal with, all of which blur out one’s ability to precisely determine i_s. Nevertheless, Kevin shows quite convincingly that the method has utility, and that it is possible to identify transit-bearing stars that are very likely strongly misaligned with the plane of the sky.
The results of the analysis confirm that massive and eccentric transiting planets (such as oklo.org fave HD 17156b) are substantially more likely to have significant spin-orbit misalignment than are garden variety Jupiter-mass hot Jupiters on circular orbits. Furthermore, to high confidence, it seems that systems with substantial spin-orbit misalignment tend to have host stars with masses greater than 1.2 solar masses. A reasonable conclusion is that there are two distinct and productive channels for generating short-period giant planets. The first is a disk migration process that leaves everything calm, orderly and aligned. The second, most likely involving Kozai cycling or a variant thereof, is telegenic, action packed, and leaves a system confused and misaligned, and perhaps stripped of several original fellow planets.