# Analyzing Tidal Circularization In Exoplanet Systems To Determine The Tidal Dissipation Efficiency Of Giant Planets

## Abstract

A planet in the gravitational field of its parent star experiences a tidal force due to the variation of the gravitation at different points on it at different distances from the star. The planet gets distorted, being stretched by this difference of gravity. This distortion raises two bulges (called “tidal bulges”) along the star-planet joining line on two opposite sides of the planet (p). When it (p) revolves in an eccentric orbit, the tidal distortion varies since the tidal force varies with the distance from the star. The repetitive tidal distortion causes a periodic variation of the amplitude of the tidal bulges. The difference between the planet’s rotational angular speed and the system’s orbital angular speed also varies with the planet-star distance. It causes the tidal bulges to move around the planet, creating a tidal wave. The friction and viscous force within the different layers of the planet resist the motion of the tidal wave and the variation of its amplitude, resulting in the generation of heat. Ultimately, some portion of the system’s orbital energy converts into heat. The gradual loss of the system’s orbital energy reduces the orbital eccentricity and semimajor axis. A ubiquitously used term that parameterizes tidal dissipation is the modified tidal quality factor (Q′ pl). Q′ pl is inversely proportional to the tidal dissipation rate. In this project, we determined a possible range of Q′ pl of short-period gas giants. The periodically varying tide acting on different parts of the planet, sometimes coupling with other forces (like Coriolis force), generates multiple components of the tidal wave that depend on the time-dependent tidal frequency. So we prescribe an empirical model where Q′ pl may depend on the frequency to consider different possible tidal wave components. We applied our analysis to 78 exoplanet systems consisting of a single planet orbiting a single host star. We worked out an allowed range of the frequency-dependent Q′ pl for each system and combined them to find general constraints on Q′ pl. We determined the upper limit of Q′ pl by requiring that if the system starts evolution with a sufficiently high initial eccentricity, then the eccentricity simulated at the present age for which the simulated orbital period matches the measured value of the orbital period, should be lower than the envelope observed in the ‘eccentricity vs. semimajor axis to planetary radius scatter plot’ of a collection of exoplanet systems. We determined the lower limit of the same parameter by requiring that it should not be lower than the measured orbital eccentricity at the present age. We find that the value of log10 Q′ pl for HJs is 5.0 ± 0.5 for the range of tidal period from 0.8 to 7 days. We do not see any clear sign of frequency dependence of Q′ pl within the mentioned uncertainties.