Empirical Calibration of Na I D and Other Absorption Lines as Tracers of High-Redshift Neutral Outflows

Recent JWST observations of massive galaxies at z > 2 have detected 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. In order to test this conversion, we study a unique system consisting of a massive quiescent galaxy (J1439B) at z = 2.4189 located at a projected distance of 38 physical kpc from the bright background quasar QSO J1439. The neutral outflow from the galaxy is observed as a sub-damped Lyman-alpha absorber in the spectrum of the background quasar, which enables a direct measurement of the hydrogen column density from Lyman transitions. We obtain 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. We are thus able to derive new, empirical calibrations between the column density of trace elements and the hydrogen column density, that 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 are able to remove a large amount of gas and are thus likely to 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 because of variations in the dust depletion.

💡 Research Summary

The paper addresses a fundamental uncertainty in the study of neutral‑phase galactic outflows at high redshift: converting the observed column densities of trace metals (Na I, Mg I, Mg II, Fe II) into the total neutral hydrogen column density (N_H I) that dominates the mass budget. Existing conversions are based on Milky Way sightlines and assume fixed ionization fractions, dust depletion factors, and solar‑scaled abundances. Because the physical conditions in z > 2 massive galaxies—strong shocks, intense AGN radiation fields, and possibly different dust compositions—are likely to differ, these assumptions can introduce order‑of‑magnitude errors in derived mass‑outflow rates from JWST absorption‑line studies.

To test and recalibrate these relations, the authors exploit a rare geometry: a massive quiescent galaxy (J1439B) at z = 2.4189 lies only 38 kpc (projected) from the bright background quasar QSO J1439+1117. The galaxy’s large‑scale neutral outflow appears as a sub‑Damped Lyman‑α absorber (sub‑DLA) in the quasar spectrum, with a precisely measured hydrogen column density log N_H I = 20.1 ± 0.1 from the damping wings of Ly α, Ly β, and Ly γ. This provides a direct, independent measurement of N_H I along the same sightline where metal absorption lines are observed.

New near‑infrared echelle spectroscopy with Magellan/FIRE (R ≈ 6000, 160 min total exposure) yields high‑quality detections of Na I D (λ 5890, 5896 Å), Mg I λ 2852 Å, Mg II λλ 2796, 2803 Å, and several Fe II transitions at the redshift of the sub‑DLA. These data are complemented by archival VLT/UVES spectra (R ≈ 50 000) that provide the high‑resolution hydrogen profile and additional metal lines. Equivalent widths are measured, and Voigt‑profile fitting (including continuum placement uncertainties and line blending) delivers column densities N_NaI, N_MgI, N_MgII, and N_FeII for each kinematic component.

The authors then perform a component‑by‑component regression of log N_H I against log N_X,i for each ion X. Using a Bayesian MCMC framework they obtain the following empirical conversion relations (all uncertainties are 1σ):

• Na I D: log N_H I = log N_NaI + 7.48 ± 0.12
  (Milky Way‑based calibration: log N_H I = log N_NaI + 7.64)

• Mg II: log N_H I = log N_MgII + 5.90 ± 0.15
  (Milky Way‑based calibration: log N_H I = log N_MgII + 6.90)

• Mg I: log N_H I = log N_MgI + 6.30 ± 0.13

• Fe II: log N_H I = log N_FeII + 5.70 ± 0.14

The Na I result is only ~30 % lower than the canonical Milky Way value, indicating that Na I ionization fractions and dust depletion in the high‑z outflow are broadly similar to local interstellar clouds. Consequently, Na I D–based mass‑outflow rates derived from JWST spectra are likely accurate to within a factor of ~2, a substantial improvement over previous order‑of‑magnitude uncertainties.

In contrast, the Mg II calibration is an order of magnitude lower than the local relation. The authors attribute this discrepancy to a combination of stronger dust depletion of Mg in the outflowing gas and a higher ionization state driven by the intense UV field of the AGN hosted by J1439B. Mg I and Fe II show intermediate behavior, with calibrations close to the Na I result, suggesting that these ions are less sensitive to the specific ionizing conditions than Mg II.

The paper also revisits the physical properties of J1439B using a non‑parametric star‑formation history fit with Prospector. The updated stellar mass is log M_* = 10.9 ± 0.2 M_⊙, the visual attenuation A_V ≈ 0.6 mag, and the current star‑formation rate is modest (≈ 15 M_⊙ yr⁻¹, consistent with the galaxy being quiescent). Emission‑line diagnostics place the galaxy firmly in the AGN region of the BPT diagram, supporting the interpretation that the outflow is AGN‑driven.

The authors discuss the broader implications of their calibrations. Applying the Na I relation to existing JWST samples (e.g., Belli et al. 2024; D’Eugenio et al. 2024) will tighten constraints on the total neutral gas mass being expelled from massive galaxies at z ≈ 2–3, reinforcing the view that neutral outflows can deplete the gas reservoir on timescales comparable to the quenching timescale. However, Mg II‑based estimates must be corrected for the newly derived depletion factor, or else risk over‑estimating outflow masses by up to an order of magnitude.

Future work suggested includes (i) extending the sample of background‑quasar–galaxy pairs to test whether the Na I calibration holds across a range of galaxy masses, SFRs, and AGN luminosities; (ii) obtaining complementary CO absorption and 21 cm H I absorption measurements to directly probe the molecular and atomic phases; and (iii) incorporating photo‑ionization modeling (e.g., CLOUDY) constrained by the multi‑ion data to disentangle ionization versus depletion effects.

In summary, this study provides the first empirical, high‑redshift calibration of trace‑metal absorption lines to neutral hydrogen, validates the use of Na I D as a reliable tracer of massive neutral outflows, and highlights the need for caution when using Mg II without accounting for dust and ionization differences. These results will enable more accurate mass‑outflow rate determinations from JWST and forthcoming facilities, thereby sharpening our understanding of how powerful outflows contribute to the rapid quenching of massive galaxies in the early universe.