A Non-isothermal Theory for Interpreting Sodium Lines in Transmission Spectra of Exoplanets

Abstract

We present a theory for interpreting the sodium lines detected in transmission spectra of exoplanetary atmospheres. Previous analyses employed the isothermal approximation and dealt only with the transit radius. By recognising the absorption depth and the transit radius as being independent observables, we develop a theory for jointly interpreting both quantities, which allows us to infer the temperatures and number densities associated with the sodium lines. We are able to treat a non-isothermal situation with a constant temperature gradient. Our novel diagnostics take the form of simple-to-use algebraic formulae and require measurements of the transit radii (and their corresponding absorption depths) at line center and in the line wing for both sodium lines. We apply our diagnostics to the HARPS data of HD 189733b, confirm the upper atmospheric heating reported by Huitson et al. (2012), derive a temperature gradient of $0.4376\pm 0.0154$ K km${}^{-1}$ and find densities $\sim 1$ to $10^4$ cm${}^{-3}$.

Accepted by ApJ Letters. 6 pages, 3 figures

References in corpus (7)

• Improved parameters for extrasolar transiting planets
• Sodium Absorption From the Exoplanetary Atmosphere of HD189733b Detected in the Optical Transmission Spectrum
• Rayleigh scattering in the transit spectrum of HD 189733b
• Ground-based detection of sodium in the transmission spectrum of exoplanet HD209458b
• HST/STIS Optical Transit Transmission Spectra of the hot-Jupiter HD209458b
• Determining atmospheric conditions at the terminator of the hot-Jupiter HD209458b
• Defocussed Transmission Spectroscopy: A potential detection of sodium in the atmosphere of WASP-12b

Cited by in corpus (19)

• A spectral survey of an ultra-hot Jupiter: Detection of metals in the transmission spectrum of KELT-9 b
• Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) IV. A spectral inventory of atoms and molecules in the high-resolution transmission spectrum of WASP-121 b
• Self-luminous and irradiated exoplanetary atmospheres explored with HELIOS
• Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) - II. A broadened sodium feature on the ultra-hot giant WASP-76b
• Detection of sodium in the atmosphere of WASP-69b
• Atmospheric Regimes and Trends on Exoplanets and Brown Dwarfs
• Mass loss rate and local thermodynamic state of KELT-9 b thermosphere from the hydrogen Balmer series
• A Cloudiness Index for Transiting Exoplanets Based on the Sodium and Potassium Lines: Tentative Evidence for Hotter Atmospheres Being Less Cloudy at Visible Wavelengths
• Search for water vapor in the high-resolution transmission spectrum of HD189733b in the visible
• Wind of Change: retrieving exoplanet atmospheric winds from high-resolution spectroscopy
• Into the Storm: Diving into the winds of the ultra hot Jupiter WASP-76 b with HARPS and ESPRESSO
• Exoplanetary atmospheric sodium revealed by the orbital motion. Narrow-band transmission spectroscopy of HD 189733b with UVES
• A Model of the H$\alpha$ and Na Transmission Spectrum of HD 189733b
• An HST/STIS Optical Transmission Spectrum of Warm Neptune GJ 436b
• Alkaline Exospheres of Exoplanet Systems: Evaporative Transmission Spectra
• A survey of sodium absorption in ten giant exoplanets with high-resolution transmission spectroscopy
• Assessing telluric correction methods for Na detections with high-resolution exoplanet transmission spectroscopy
• Aerosol Constraints on the Atmosphere of the Hot Saturn-mass planet WASP-49b
• On physical interpretations of the reference transit radius of gas-giant exoplanets