On the dual nature of atmospheric escape

Abstract

Planetary atmospheres cannot remain hydrostatic at all altitudes because they approach finite density at infinite radius, implying infinite mass. Classical treatments address this in two directions: either retain a hydrostatic structure while allowing particles in the high-velocity tail to decouple and escape in a Jeans-type manner, or promote the gas to a continuum outflow to obtain a transonic Parker-type solution. The usual criterion compares the local mean free path to the sonic point radius. If the mean free path is shorter, the atmosphere is hydrostatic with an imposed Jeans escape flux; if it is longer, the gas is hydrodynamic with Jeans escape neglected. Here, we show that hydrogen-rich atmospheres do not separate cleanly into hydrodynamic and Jeans-escape regimes. At any radius, some particles still collide and behave as a fluid, while others have already experienced their last collision and move collisionlessly on ballistic trajectories. The relative importance of these two behaviors changes smoothly with radius rather than switching at a single boundary. The hydrodynamic channel accelerates and passes through a sonic point, whereas the collisionless channel decelerates under gravity and grows with altitude, removing mass and momentum from the collisional flow. As the collisionless component grows, the bulk flow speed reaches a maximum and then decelerates thereafter, producing profiles similar to Parker breeze solutions even though escape is carried by the collisionless channel. This two-channel framework provides a first step toward a self-consistent treatment that unifies hydrodynamics and kinetics in atmospheric loss models.

Figures (5)

• Figure 1: The (a) normalized sonic point radius $R_{\rm s}/R_{\rm s,0}$ (Equation \ref{['eq:Rs_R0']}), (b) decoupling fraction at the sonic point $\phi_{\rm s}$ (Equation \ref{['eq:phi_final']}), and (c) Maxwellian-tail factor at the sonic point $F_{1}(c_{\rm s,s})$ (Equation \ref{['eq:F1_final']}), as a function of the logarithm of $l_{\rm mfp,s}/R_{\rm s,0}$ with $R_{\rm s,0}{=}GM/(2c_{\rm s,s}^{2})$ and $l_{\rm mfp,s}{\equiv}(\sqrt{2}\,n_{\rm s}\sigma)^{-1}$, for $\gamma{=}1,\,1.1,\,1.2,\,1.3$ and 1.4 (blue, orange, green, red, and purple, respectively).
• Figure 2: Velocity (top) and density (bottom) profiles for three atmospheres with $\gamma{=}1$ and (left) $l_{\rm mfp,s}/R_{\rm s}{=}0.01$, (middle) $l_{\rm mfp,s}/R_{\rm s}{=}0.1$, and (right) $l_{\rm mfp,s}/R_{\rm s}{=}1$. The blue and red dashed lines show the collisional and collisionless contributions to the flow, and the black solid line shows the total bulk wind.
• Figure 3: Schematic of the two-channel picture. As the atmosphere expands and rarefies, a fraction of particles decouples from the collisional flow and streams outward ballistically. The collisional channel can remain Parker-like and transonic, while the growing collisionless channel can cause the flux-weighted bulk speed to peak at a quasi-sonic point and decrease at larger radii.
• Figure A4: Velocity (top) and density (bottom) profiles for three atmospheres with $\gamma{=}1.2$ and (left) $l_{\rm mfp,s}/R_{\rm s}{=}0.01$, (middle) $l_{\rm mfp,s}/R_{\rm s}{=}0.1$, and (right) $l_{\rm mfp,s}/R_{\rm s}{=}1$. The blue and red dashed lines show the collisional and collisionless contributions to the flow, and the black solid line shows the total bulk wind.
• Figure A5: Velocity (top) and density (bottom) profiles for three atmospheres with $\gamma{=}1.4$ and (left) $l_{\rm mfp,s}/R_{\rm s}{=}0.01$, (middle) $l_{\rm mfp,s}/R_{\rm s}{=}0.1$, and (right) $l_{\rm mfp,s}/R_{\rm s}{=}1$. The blue and red dashed lines show the collisional and collisionless contributions to the flow, and the black solid line shows the total bulk wind.