Research

Our approach is to model each individual system’s evolution in detail, and employ modern Bayesian analysis methods in order to account for as many observational and model uncertainties as possible. Further, we are analyzing multiple sets of data using multiple analysis methods in order to get complimentary, yet overlapping constraints that will simultaneously cover a broad range of parameters and serve as each others’ cross-checks.

Methods

Circularization Tidal dissipation acts to circularize orbits over time. The observed distributions of the eccentricities of exoplanet and binary star systems show clear signs of being shaped by tides, with all the shortest period systems in circular orbits, a gradual increase in the upper bound of the range of eccentricities encountered as the period increases, until a period is reached beyond which the eccentricity distribution is approximately period independent. As tides very quickly lose influence with increasing orbital period, this is precisely the trend predicted if all systems started with a broad range of initial eccentricities and tides were the dominant mechanism shaping their orbits. Assuming this picture is correct, an upper limit for the tidal dissipation in an individual system can be derived by requiring that for at least high initial eccentricity, tidal circularization is not so fast as to drive the present day eccentricity below its observed value. Further, assuming that there is a significant probability that the initial eccentricity is large (e.g. $latex e_{init}>0.6$) irrespective of the system components or the initial orbital period, a lower limit to the dissipation follows by requiring that such large initial eccentricity is circularized to below the envelope of eccentricity vs. period by the present system age.

Synchronization Another effect of tidal dissipation is that it causes angular momentum to be exchanged between the orbit and the spin of the dissipating object(s), typically driving the object toward synchronous rotation. The effects of this process are detectable in binary stars, and in hot–Jupiter exoplanet systems. In a nutshell, the method for using the observed spin in binary star and exoplanet systems to constrain tidal dissipation is as follows. In most cases, only the spin of the brighter primary (host) star is measured, and the effect of tides will be to cause that to differ from the expected spin for an isolated star with the same mass and age. Assuming a particular tidal dissipation efficiency, for a given system we can find initial orbital period and eccentricity such that calculating the combined spin–orbit evolution of the system forward in time reproduces the observed present day orbital period and eccentricity. Constraints on the dissipation can then be derived by tuning the assumed dissipation until the observed present day spin is also reproduced. Because the current eccentricity of the system is reproduced, this method automatically enforces the upper limit on the dissipation from the circularization method.

Inspiral For short-period exoplanet systems in particular, tidal dissipation shrinks the orbit, ultimately causing the planet to be destroyed. The timescale for destruction varies as $latex 1/Q’_\star$ and also depends sensitively on the initial period. This allows us to use the observed period distribution of hot jupiters to constrain $latex Q’_\star$, in a manner complementary to the spin-up method described in the previous section. Low values of $latex Q’_\star$ can be ruled out because they imply the unlikely conclusion that many observed planets were detected just before they are to be destroyed. High values of $latex Q’_\star$ can be excluded because they would predict more short-period planets around older stars than are observed.

Alignment Observations have revealed a wide range of obliquities for the host stars of hot jupiters, including very well-aligned systems (e.g. Winn et. al. 2006), strongly misaligned systems (Hebrard et. al. 2008), and even polar and retrograde orbits (Winn et. al. 2009 and Triaud et. al. 2010). The basis for most of these results is the Rossiter–McLaughlin (RM) effect (Queloz et. al. 2000), a spectroscopic distortion that occurs during transits.

A pattern has emerged from these results: the host stars cool enough to have outer convective zones tend to have low obliquities, while hotter stars show a broader range of obliquities (Winn et. al. 2010 and Albrecht et. al. 2012). One possible interpretation is that hot jupiters generally form with a broad range of orbital orientations, and that only the cool stars are able to tidally re-align the system due to the enhanced tidal dissipation rate associated with outer convective zones. As part of this project we will use our tidal evolution code to understand what this hypothesis implies for the value of $latex Q’_\star$