Constraining planetary mass-loss rates by simulating Parker wind profiles with Cloudy

Abstract

Models of exoplanet atmospheres based on Parker-wind density and velocity profiles are a common choice in fitting spectroscopic observations tracing planetary atmospheric escape. Inferring atmospheric properties using these models often results in a degeneracy between the temperature and the mass-loss rate, and thus provides weak constraints on either parameter. We present a framework that can partially resolve this degeneracy by placing more stringent constraints on the expected thermospheric temperature. We use the photoionization code Cloudy within an iterative scheme to compute the temperature structure of a grid of 1D Parker wind models, including the effects of radiative heating/cooling, as well as the hydrodynamic effects (expansion cooling and heat advection). We constrain the parameter space by identifying models that are not self-consistent through a comparison of the simulated temperature in the He 10830 Å line-forming region to the temperature assumed in creating the models. We demonstrate this procedure on models based on HD 209458 b. By investigating the Parker wind models with an assumed temperature between 4000 and 12000 K, and a mass-loss rate between 10 8 and 10 11 g s −1 , we are able to rule out a large portion of this parameter space. Furthermore, we fit the models to previous observational data and combine both constraints to find a preferred thermospheric temperature of T = 8200 +1200 −1100 K and a mass-loss rate of Ṁ = 10 9.84 +0.24 −0.27 g s −1 assuming a fixed atmospheric composition and no gas pressure confinement by the stellar wind. Using the same procedure, we constrain the temperatures and mass-loss rates of WASP-69 b, WASP-52 b, HAT-P-11 b, HAT-P-18 b and WASP-107 b. spheric escape to obtain a unique solution for a given set of parameters (such as Murray-Clay et al. 2009;Salz et al. 2016;Wang & Dai 2021a;Caldiroli et al. 2021a).

Observing Atmospheric Escape in Sub-Jovian Worlds with JWST

“…However, in our simulations we verified that this technique is not very constraining for sub-Jovian worlds at mild levels of irradiation like GJ 436 b and GJ 1214 b. Another technique that aims to limit the parameter space of m  versus T in unresolved metastable He spectroscopy involves taking into account the effects of radiative heating/cooling, expansion cooling, and heat advection (see Linssen et al 2022). Ideally, one-or threedimensional hydrodynamics models (such as the ones described in Salz et al 2016;Shaikhislamov et al 2021;Kubyshkina et al 2022;) break this degeneracy by calculating the outflow temperature profile and mass-loss rates self-consistently, but they are more computationally expensive and they have other free parameters as well -such as atmospheric abundances, stellar wind strength, and planetary magnetic field strength.…”

“…Ideally, higher spectral resolution is desired for He observations because resolving the planetary absorption yields stronger constraints on the outflow temperature-which in turn produces a better mass-loss constraint, since this estimate is degenerate with the outflow temperature. However, even for spectrally unresolved observations, it is still possible to obtain useful constraints for the mass-loss rate if we take into account the energetics of the outflow (Vissapragada et al 2022a;Linssen et al 2022). For the particular case of GJ 436 (J mag = 6.9), the only instrument configuration on JWST that does not result in saturation is G140H; fainter stars, such as GJ 1214, are observable at lower spectral resolutions.…”

“…Self-consistent hydrodynamic simulations do not have this degeneracy, since the outflow temperatures and escape rates are set by the underlying physics of the model (e.g., Salz et al 2016;Shaikhislamov et al 2021;Kubyshkina et al 2022). The approach described by Linssen et al (2022) may also be helpful, as they rule out part of the temperature and mass-loss parameter space by calculating the temperature structure of the outflow based on a self-consistent photoionization model.…”

Giant tidal tails of helium escaping the hot Jupiter HAT-P-32 b

“…To model the planetary outflow, we used the hydrodynamic escape parameternormalλ=GMpRpcs2where M p is the planet’s mass, R p is the planet radius, and c s is the sound speed of the outflow. We adopted λ = 8 for the planetary wind in our models, implying an outflow temperature of ≈5750 K. This is a free parameter of our current models, and we find that λ particularly affects the stream kinematics, as well as the inferred planetary mass loss rate ( 55 ). To model the much hotter (≈10 6 K), fast-expanding stellar wind, we adopted λ = 15 and replaced M p and R p to be the mass and radius of the host star, respectively, in the Eq.…”

“…At identical temperatures and EW, these 1D models predict ~2× higher planetary mass loss rate because they neglect the compression of material into tidal tails. The 1D models also suggest that the best-fitting mass-loss rate scales as M˙p∝T (i.e., M˙p0.25em∝p10.25emnormalλp−1, where T is the outflow temperature), thus giving an indication of how varying the uncertain planetary outflow thermodynamics affects the inferred planetary mass loss rate [also see ( 55 )].…”