One H ₂ molecule per ten million H atoms reveals sub-parsec-scale cold overdensities at <i>z</i> ∼ 4

We present the detection and analysis of H 2 absorption at z = 4.24 towards the bright quasar J 0007−5705, which was observed with the Very Large Telescope as part of the ESPRESSO QUasar Absorption Line Survey (EQUALS). The high resolving power of R ≈ 120 000 enables the identification of extremely weak H 2 lines in several rotational levels at a total column density of N (H 2 )≈2 × 10 14 cm −2 , which is among the lowest ever measured in quasar absorption systems. Remarkably, this constitutes the highest redshift H 2 detection to date. Two velocity components are resolved that are separated by only 3 km s −1 : a narrow ( b ∼ 1.7 km s −1 ) and a broader ( b ≃ 6.2 km s −1 ) component. Modelling the rotational population of H 2 yields a density of log n H /cm −3 ∼ 2.8 and temperature of ∼40 K (typical of the cold neutral medium) for the narrow component and log n H /cm −3 ∼ 1.4, T ∼ 600 K for the warmer, more turbulent component under a moderate ultraviolet (UV) field, suggesting at least a several-megaparsec distance from the quasar. This system reveals the existence of tiny (down to ∼0.01 pc), cold overdensities in the neutral medium. Their detection among only seven damped Lyman- α systems in EQUALS suggests that they may be widespread yet usually remain undetected. H 2 provides an exceptionally sensitive probe of these structures: even a minute molecular fraction produces measurable Lyman-Werner absorption lines along the extremely narrow optical beam –the size of the quasar’s accretion disc– when observed at sufficiently high spectral resolution. High-resolution spectroscopy on extremely large telescopes may routinely detect and resolve such structures in the distant Universe, where 21-cm absorption traces the collective contribution of many cold cloudlets towards larger radio background sources.