51ÁÔÆæÈë¿Ú

Abstract:

The discovery of over 5700 exoplanets has led to a boom in the field of exoplanet demographics over the past decade. Led by swaths of exoplanet discoveries from NASA\u27s Kepler space mission, astronomers have been conducting statistical studies of the exoplanet population in search of trends in various planetary and host stellar parameters. These investigations are informing our understanding of how planets form and evolve, thus putting our solar system into a galactic context. In this chapter, we review many of the major features uncovered in the distributions of physical and orbital parameters of known exoplanets including the Radius Valley, the Neptunian Desert, the Peas in a Pod pattern, dynamical properties that point toward likely formation/migration mechanisms, as well as trends with host stellar parameters such as the time-evolution of exoplanetary systems and the search for planets within the Habitable Zone. The overarching theme is that exoplanetary systems exhibit an incredible diversity of planet properties and system architectures that do not exist within our own solar system. A promising future awaits the field of exoplanet demographics with increasingly deep investigations planned following the launch of numerous dedicated space telescopes over the coming years and decades.Preprint of a chapter for the \u27Encyclopedia of Astrophysics\u27 (Editor-in-Chief Ilya Mandel, Section Editor Dimitri Veras) to be published by Elsevier as a Reference Module. 18 pages, 10 figure

Abstract:

This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective time-scale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} / t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv} / \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta(r) \sim r \omega_{\rm osc} / \left( g(r) t_{\rm conv}(r) \right)$, where g is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g/r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta(r)$ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta }$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta }$ is shown to be equal to the standard tidal dissipation factor.