p-winds: An open-source Python code to model planetary outflows and upper atmospheres^⋆

¹ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
e-mail: ldsantos@stsci.edu
² Observatoire astronomique de l’Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
³ Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The Netherlands
⁴ School of Physics, Trinity College Dublin, the University of Dublin, College Green, Dublin-2, Ireland
⁵ Division of Geological and Planetary Sciences, California Institute of Technology, 1200 East California Blvd, Pasadena, CA 91125, USA
⁶ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
⁷ Earth and Planets Laboratory, The Carnegie Institution for Science, 5241 Broad Branch Road, Washington, DC 20015, USA
⁸ Department of Physics, and Institute for Research on Exoplanets, Université de Montréal, Montréal H3T 1J4, Canada
⁹ European Southern Observatory, Alonso de Córdova 3107, Santiago, Casilla 19001, Chile

Received: 17 August 2021
Accepted: 30 November 2021

Abstract

Atmospheric escape is considered to be one of the main channels for evolution in sub-Jovian planets, particularly in their early lives. While there are several hypotheses proposed to explain escape in exoplanets, testing them with atmospheric observations remains a challenge. In this context, high-resolution transmission spectroscopy of transiting exoplanets for the metastable helium triplet (He 2³S) at 1083 nm has emerged as a reliable technique for observing and measuring escape. To aid in the prediction and interpretation of metastable He transmission spectroscopy observations, we developed the code p-winds. This is an open-source, fully documented, scalable Python implementation of the one-dimensional, purely H+He Parker wind model for upper atmospheres coupled with ionization balance, ray-tracing, and radiative transfer routines. We demonstrate an atmospheric retrieval by fitting p-winds models to the observed metastable He transmission spectrum of the warm Neptune HAT-P-11 b and take the variation in the in-transit absorption caused by transit geometry into account. For this planet, our best fit yields a total atmospheric escape rate of approximately 2.5 × 10¹⁰ g s⁻¹ and an outflow temperature of 7200 K. The range of retrieved mass loss rates increases significantly when we let the H atom fraction be a free parameter, but its posterior distribution remains unconstrained by He observations alone. The stellar host limb darkening does not have a significant impact on the retrieved escape rate or outflow temperature for HAT-P-11 b. Based on the non-detection of escaping He for GJ 436 b, we are able to rule out total escape rates higher than 3.4 × 10¹⁰ g s⁻¹ at 99.7% (3σ) confidence.