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Register a new userStellar Evolution and Tidal Dissipation in REBOUNDx
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We introduce two new features to REBOUNDx, an extended library for the N-body integrator REBOUND. The first is a convenient parameter interpolator for coupling different physics and integrators using numerical splitting schemes. The second implements a constant time lag model for tides (without evolving spins) from Hut (1981). We demonstrate various examples of these features using post-main sequence stellar evolution data from MESA (Modules for Experiments in Stellar Astrophysics). These additional effects are publicly available as of REBOUNDxs latest release.
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Stars with hot Jupiters tend to be rotating faster than other stars of the same age and mass. This trend has been attributed to tidal interactions between the star and planet. A constraint on the dissipation parameter $Q_star$ follows from the assumption that tides have managed to spin up the star to the observed rate within the age of the system. This technique was applied previously to HATS-18 and WASP-19. Here we analyze the sample of all 188 known hot Jupiters with an orbital period $< 3.5$ days and a cool host star ($T_{eff} < 6100$ K). We find evidence that the tidal dissipation parameter ($Q_star$) increases sharply with forcing frequency, from $10^5$ at 0.5 day$^{-1}$ to $10^7$ at 2 day$^{-1}$. This helps to resolve a number of apparent discrepancies between studies of tidal dissipation in binary stars, hot Jupiters, and warm Jupiters. It may also allow for a hot Jupiter to damp the obliquity of its host star prior to being destroyed by tidal decay.
In recent years it has been shown that the tidal coupling between extrasolar planets and their stars could be an important mechanism leading to orbital evolution. Both the tides the planet raises on the star and vice versa are important and dissipation efficiencies ranging over four orders of magnitude are being used. In addition, the discovery of extrasolar planets extremely close to their stars has made it clear that the estimates of the tidal quality factor, Q, of the stars based on Jupiter and its satellite system and on main sequence binary star observations are too low, resulting in lifetimes for the closest planets orders of magnitude smaller than their age. We argue that those estimates of the tidal dissipation efficiency are not applicable for stars with spin periods much longer than the extrasolar planets orbital period. We address the problem by applying our own values for the dissipation efficiency of tides, based on our numerical simulations of externally perturbed volumes of stellar-like convection. The range of dissipation we find for main-sequence stars corresponds to stellar $Q_*$ of $10^8$ to $3{times}10^9$. The derived orbit lifetimes are comparable to, or much longer than the ages of the observed extrasolar planetary systems. The predicted orbital decay transit timing variations due to the tidal coupling are below the rate of ms/yr for currently known systems, but within reach of an extended Kepler mission provided such objects are found in its field.
The architecture of many exoplanetary systems is different from the solar system, with exoplanets being in close orbits around their host stars and having orbital periods of only a few days. We can expect interactions between the star and the exoplanet for such systems that are similar to the tidal interactions observed in close stellar binary systems. For the exoplanet, tidal interaction can lead to circularization of its orbit and the synchronization of its rotational and orbital period. For the host star, it has long been speculated if significant angular momentum transfer can take place between the planetary orbit and the stellar rotation. In the case of the Earth-Moon system, such tidal interaction has led to an increasing distance between Earth and Moon. For stars with Hot Jupiters, where the orbital period of the exoplanet is typically shorter than the stellar rotation period, one expects a decreasing semimajor axis for the planet and enhanced stellar rotation, leading to increased stellar activity. Also excess turbulence in the stellar convective zone due to rising and subsiding tidal bulges may change the magnetic activity we observe for the host star. Here I review recent observational results on stellar activity and tidal interaction in the presence of close-in exoplanets, and discuss the effects of enhanced stellar activity on the exoplanets in such systems.
Tidal interactions in close star-planet or binary star systems may excite inertial waves (their restoring force is the Coriolis force) in the convective region of the stars. The dissipation of these waves plays a prominent role in the long-term orbital and rotational evolution of the bodies involved. If the primary star rotates as a solid body, inertial waves have a Doppler-shifted frequency restricted to the range $[-2Omega, 2Omega]$ ($Omega$ being the angular velocity of the star), and they can propagate in the entire convective region. However, turbulent convection can sustain differential rotation with an equatorial acceleration (as in the Sun) or deceleration that modifies the frequency range and propagation domain of inertial waves and allows corotation resonances for non-axisymmetric oscillations. In this work, we perform numerical simulations of tidally excited inertial waves in a differentially rotating convective envelope with a conical (or latitudinal) rotation profile. The tidal forcing that we adopt contains spherical harmonics that correspond to the case of a circular and coplanar orbit. We study the viscous dissipation of the waves as a function of tidal frequency for various stellar masses and differential rotation parameters, as well as its dependence on the turbulent viscosity coefficient. We compare our results with previous studies assuming solid-body rotation and point out the potential key role of corotation resonances in the dynamical evolution of close-in star-planet or binary systems.
Most stars form and spend their early life in regions of enhanced stellar density. Therefore the evolution of protoplanetary discs (PPDs) hosted by such stars are subject to the influence of other members of the cluster. Physically, PPDs might be truncated either by photoevaporation due to ultraviolet flux from massive stars, or tidal truncation due to close stellar encounters. Here we aim to compare the two effects in real cluster environments. In this vein we first review the properties of well studied stellar clusters with a focus on stellar number density, which largely dictates the degree of tidal truncation, and far ultraviolet (FUV) flux, which is indicative of the rate of external photoevaporation. We then review the theoretical PPD truncation radius due to an arbitrary encounter, additionally taking into account the role of eccentric encounters that play a role in hot clusters with a 1D velocity dispersion $sigma_v > 2$ km/s. Our treatment is then applied statistically to varying local environments to establish a canonical threshold for the local stellar density ($n_{c} > 10^4$ pc$^{-3}$) for which encounters can play a significant role in shaping the distribution of PPD radii over a timescale $sim 3$ Myr. By combining theoretical mass loss rates due to FUV flux with viscous spreading in a PPD we establish a similar threshold for which a massive disc is completely destroyed by external photoevaporation. Comparing these thresholds in local clusters we find that if either mechanism has a significant impact on the PPD population then photoevaporation is always the dominating influence.
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