Wind-AE: A Fast, Open-source 1D Photoevaporation Code with Metal and Multi-frequency X-ray Capabilities

TL;DR

Wind-AE delivers a fast, open-source 1D photoevaporation code that unifies multispecies and multi-frequency XUV physics with X-ray ionization, permitting rapid exploration of mass-loss rates across diverse exoplanet types. By coupling a Parker-wind relaxation framework with a detailed treatment of bolometric heating, Lyα cooling, and metal-line cooling, Wind-AE reveals that X-rays raise $\,\dot{M}$ while metals increase the mean molecular weight, often yielding comparable net mass-loss rates but with hotter, more ionized winds. The study demonstrates that the wind launch radius $R_{XUV}$ typically lies near $1.1$–$1.8\,R_P$ for HD 209458b-like planets, but can be much larger for low-gravity planets, making the energy-limited rate evaluated at $R_{XUV}$ a better estimator than at $R_P$. Mass-loss grids across planet type and flux regimes, along with thorough comparisons to existing 1D models, establish Wind-AE as a fast, versatile tool for planetary evolution studies and observational interpretation, while highlighting the importance of lower-atmosphere boundary conditions and cooling processes.

Abstract

Throughout their lives, short period exoplanets (<100 days) experience X-ray and extreme-UV (XUV) stellar irradiation that can heat and photoionize planets' upper atmospheres, driving transonic outflows. This photoevaporative mass loss plays a role in both evolution and observed demographics; however, mass loss rates are not currently directly observable and can only be inferred from models. To that end, we present an open-source fast 1D, XUV multi-frequency, multispecies, steady-state, hydrodynamic Parker Wind photoevaporation relaxation model based on Murray-Clay et al. (2009,arXiv:0811.0006). The model can move smoothly between high and low flux regimes and accepts custom multi-frequency stellar spectra. While the inclusion of high-energy X-rays increases mass loss rates ($\dot{M}$), metals decrease $\dot{M}$, and the net result for a typical hot Jupiter is a similar $\dot{M}$, but a hotter, faster, and more gradually ionized wind. We find that mulitfrequency photons (e.g., 13.6-2000eV) are absorbed over a broader range of heights in the atmosphere resulting in a wind-launch radius, $R_{XUV}$, that is of order 10 nanobars for all but the highest surface gravity planets. Grids of H/He solar metallicity atmospheres reveal that, for typical hot Jupiters like HD 209458b, $R_{XUV}$~1.1-1.8$R_P$ for low-fluxes, meaning that the energy-limited mass loss rate, $\dot{M}_{Elim}(R)$, computed at $R=R_P$ is a good approximation. However, for planets with low escape velocities, like many sub-Neptunes and super-Earths, $R_{XUV}$ can be >>$R_P$, making it necessary to use $\dot{M}_{Elim}(R=R_{XUV})$ to avoid significantly underestimating mass loss rates. For both high escape velocities and large incident fluxes, radiative cooling is significant and energy-limited mass loss overestimates $\dot{M}$.

Figures (23)

• Figure 1: Diagram of wind structure - A thermally-driven, Parker-wind-like outflow is driven by photoionization heating, primarily deposited near the wind launch radius ($R(\tau_{\rm{XUV}}) = 1$). Our relaxation code solves for the structure of this outflow by integrating between two boundary conditions, the minimum radius of the simulation ($R_{\rm{min}}$) and the sonic point ($R_{\rm{sp}}$), identified by large black 'x's. Shorter wavelengths of incident stellar irradiation, like x-rays, are represented by the magenta wave and penetrate deeper into the atmosphere than the longer wavelength dark purple (higher-energy EUV) and cyan (lower-energy EUV). Magnitude of the local velocity, $v$, relative to the local sound speed, $c_s$, is given in the middle column. Important planetary radii in the wind's structure are identified in text in the righthand column (gray semicircle, $R_P$; heavy solid, $R_{\rm{min}}$; light solid, $R_{\rm{XUV}}$; dashed, $R_{\rm{sp}}$; dotted, $R_{\mathrm{Hill}}$; heavy solid, $R_{\mathrm{cori}}$).
• Figure 2: Savitzky-Golay smoothed and binned FISM2 solar spectrum scaled to 0.05 au - Flux at 0.05 au vs. wavelength in nm (top) and vs. energy in eV (bottom). The solid purple and cyan highlights correspond to the EUV (13.6-100eV) and X-ray ($>$100eV) portions of the spectrum, respectively, and the approximate fluxes of each portion are labeled at the top of the bottom plot in $\mathrm{ergs}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$. Bin edges (heavy vertical dashed lines) are automatically set at ionization edges for species present in a given simulation for maximum accuracy in calculating ionization rates (here pure-H). Thin vertical dashed lines are the critical points in the smoothing (Appendix \ref{['appendix:spectrum']}). We crop our spectra in this investigation at 2000 eV because contributions from higher energies are negligible and most photons that high energy have $\tau_\nu=1$ surfaces below the base of the wind and do not contribute to driving the wind. The XUV smoothed spectrum for a pure-H planetary atmosphere (above) results in 59 wavelength bins and the EUV in 66.
• Figure 3: Energy Deposition Fraction for HD 209458b - Fraction of total incident stellar energy into ionizing hydrogen (black), helium (navy), heating (tan), and hydrogen excitation (light green) of which, in our model, 100$\%$ is assumed to escape as Lyman-$\alpha$ radiation. Total XUV flux over 13.6-2000 eV is 1095 $\mathrm{ergs}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$.
• Figure 4: Multi-frequency Profiles for a pure-H HD 209458 b - Black dash-dotted is the original 20eV monofrequency and pure-H rmc2009 model ($R_{\rm{min}}=1.037\ R_P$, $\rho(R_{\rm{min}})=2.7\times10^{-11}$ g cm, T($R_{\rm{min}}$)=1000 K). Gray solid is also monofrequency 20eV, but with our updated physical lower BC and bolometric heating and cooling at the base ($R_{\rm{min}}$=1.057 $R_P$, $\rho(R_{\rm{min}})=1.8\times10^{-11}$ g cm$^{-3}$, T(R$_{\rm{min}}$)=1534 K). The remaining plots all use the updated BCs. Purple is the EUV multi-frequency (13.6-100 eV) version. Because no metals are present, X-rays (cyan, dash-dotted, XUV 13.6-2000 eV) contribute relatively little to the profiles or mass loss rates of a pure-H atmosphere so the solutions overlie the EUV. Stellar spectra in all simulations are normalized to 450 $\mathrm{ergs}\ \mathrm{s}^{-1}\ \mathrm{cm}^{-2}$ between 13.6 and 40 eV (in keeping with rmc2009). Our model is not valid past the Coriolis radius (upper limit of x-axis). The sonic point and Hill sphere are given by dashed and dotted lines respectively.
• Figure 5: Energy Plot for pure-H XUV vs. Monofrequency HD 209458 b - Energy structure of multi-frequency XUV solution (top panel, cyan solution in Fig. \ref{['fig:multifreq']}) and 20eV monofrequency solution (bottom panel, gray solution in Fig. \ref{['fig:multifreq']}). The $\tau(20\mathrm{eV})=1$ surface for the XUV multispecies is at a higher radius because the deeper penetration of high energy XUV photons puffs up the atmosphere, resulting in higher densities and optical depths at higher radii than in the monofrequency solution.