The IMF-sensitive 1.14-μm Na i doublet in early-type galaxies

We present J-band spectroscopy of passive galaxies focusing on the Na i doublet at 1.14 μm. Like the Na i 0.82 μm doublet, this feature is strong in low-mass stars and hence may provide a useful probe of the initial mass function (IMF). From high signal-to-noise composite spectra, we find that Na i 1.14 μm increases steeply with increasing velocity dispersion, σ, and for the most massive galaxies (σ ≳ 300 km s−1) is much stronger than predicted from synthetic spectra with Milky Way-like IMFs and solar abundances. Reproducing Na i 1.14 μm at high σ likely requires either a very high [Na/H], or a bottom-heavy IMF, or a combination of both. Using the Na D line to break the degeneracy between IMF and abundance, we infer [Na/H] ≈ +0.5 and a steep IMF (single-slope-equivalent x ≈ 3.2, where x = 2.35 for Salpeter), for the high-σ galaxies. At lower mass (σ = 50–100 km s−1), the line strengths are compatible with Milky Way (MW)-like IMFs and near-solar [Na/H]. We highlight two galaxies in our sample where strong gravitational lensing masses favour MW-like IMFs. Like the high-σ sample on average, these galaxies have strong Na i 1.14 μm; taken in isolation their sodium indices imply bottom-heavy IMFs which are hard to reconcile with the lensing masses. An alternative full-spectrum-fitting approach, applied to the high-σ sample, recovers an IMF less heavy than Salpeter, but under-predicts the Na i 1.14 μm line at the 5σ level. We conclude that current models struggle to reproduce this feature in the most massive galaxies without breaking other constraints, and caution against over-reliance on the sodium lines in spectroscopic IMF studies.