Empirical calibration of Na I D and other absorption lines as tracers of high-redshift neutral outflows

¹ Dipartimento di Fisica e Astronomia, Università di Bologna Bologna, Italy
² The Observatories of the Carnegie Institution for Science Pasadena CA, USA
³ Center for Astrophysics | Harvard & Smithsonian Cambridge MA, USA
⁴ INAF, Astrophysics and Space Science Observatory Bologna, Italy
⁵ Caltech/IPAC Pasadena CA, USA
⁶ National Centre for Nuclear Research Warsaw, Poland
⁷ SISSA Trieste, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 July 2025
Accepted: 23 December 2025

Abstract

Recent JWST observations of massive galaxies at z > 2 detect blueshifted absorption in Na I D and other resonant absorption lines, indicative of strong gas outflows in the neutral phase. However, the measured mass outflow rates are highly uncertain because JWST observations can only probe the column density of trace elements such as sodium, while most of the gas is in the form of hydrogen. The conversion between the column density of sodium and that of hydrogen is based on observations of gas clouds within the Milky Way, and has not been directly tested for massive galaxies at high redshift. To test this conversion, we studied a unique system consisting of a massive quiescent galaxy (J1439B) at z = 2.4189, located at a projected distance of 38 physical kiloparsecs from the bright background quasar QSO J1439+1117. The neutral outflow from the galaxy is observed as a sub-damped Lyman-α absorber (sub-DLA) in the spectrum of the background quasar, which enables a direct measurement of the hydrogen column density from Lyman transitions. We obtained new near-infrared spectroscopy with Magellan/FIRE and detect Na I D and other resonant absorption lines from Mg II, Mg I, and Fe II. This dataset allows us to derive new empirical calibrations between the column densities of trace elements and hydrogen, which can be used to estimate the mass and the rate of neutral gas outflows in other massive quiescent galaxies at high redshift. The calibration we derive for Na I is only 30% lower than the local relation that is typically assumed at high redshift, confirming that the neutral outflows observed with JWST at z > 2 can remove a large amount of gas and likely play a key role in galaxy quenching. However, using the local calibration for Mg II yields an order-of-magnitude discrepancy compared to the empirical calibration, possibly due to variations in dust depletion.