The Luminosity Function and Clustering of H$α$ Emitting Galaxies at $zpprox4-6$ from a Complete NIRCam Grism Redshift Survey

We study the luminosity function (LF) and clustering properties of 888 H$α$ emitters (HAEs) at $3.75 < z < 6$ in the GOODS-N field. The sample, built from JWST CONGRESS and FRESCO NIRCam grism surveys using a novel redshift assignment algorithm, spans $\sim$62 arcmin$^2$ and reaches $L_{\rm Hα} \sim 10^{41.2} {\rm erg s^{-1}}$. We identify two prominent filamentary protoclusters at $z \approx 4.41$ and $z \approx 5.19$, hosting 98 and 144 HAEs, respectively. The observed H$α$ LFs show similar shallow faint-end slopes for both protocluster and field galaxies at $z=3.75-5$, and for the protocluster at $z=5-6$ ($α\approx 1.2$ to $-1.3$). In contrast, the field LF at $z=5-6$ is much steeper ($α=-1.87_{-0.23}^{+0.30}$), suggesting that protocluster galaxies at $z > 5$ are more evolved, resembling those at $z=3.75-5$. The observed star formation rate density from H$α$, integrated down to 0.45 ${\rm M_\odot yr^{-1}}$, is $0.050^{+0.002}{-0.003}$ and $0.046^{+0.006}{-0.004} M_\odot {\rm yr}^{-1} {\rm Mpc}^{-3}$ at $z=3.75-5$ and $z=5-6$, with protoclusters contributing $\sim$25% and 55%, respectively. This implies that a large fraction of star formation at $z > 4$ occurs in protoclusters. We conduct the first star-formation-rate-limited 3D clustering analysis at $z > 4$. We find the filamentary protocluster geometry flattens the power-law shape of the HAE auto-correlation functions, with slopes much shallower than typically assumed. The auto-correlation function of field HAEs have correlation lengths of $r_0 = 4.61^{+1.00}{-0.68} h^{-1}{\rm Mpc}$ at $z \approx 4-5$ and $r_0 = 6.23^{+1.68}{-1.13} h^{-1}{\rm Mpc}$ at $z=5-6$. Comparing the observed correlation functions with the UniverseMachine simulation, we infer the dark matter (sub-)halo masses of HAEs to be $\log (M_h/M_\odot)=11.0-11.2$ at $z\approx 4-6$, with a scatter of 0.4 dex.

💡 Research Summary

This paper presents the first comprehensive study of the H α luminosity function (LF) and three‑dimensional clustering of star‑forming galaxies at redshifts 4 ≲ z ≲ 6 using JWST NIRCam slitless grism (WFSS) data. The authors combine the Cycle‑1 FRESCO (F444W) and Cycle‑2 CONGRESS (F356W) surveys over the GOODS‑N field, covering ~62 arcmin² with a 5σ line‑flux limit of ≈2 × 10⁻¹⁸ erg s⁻¹ cm⁻². An automated emission‑line detection and redshift‑assignment pipeline identifies robust lines (S/N > 5) in both 1‑D and 2‑D spectra, cross‑correlates detected wavelengths with a library of line templates, and refines redshifts to Δz/(1+z) ≈ 0.001. After visual verification against existing spectroscopic redshifts, a final sample of 888 H α emitters (HAEs) spanning 3.75 < z < 6 is assembled.

The LF is measured in two redshift bins, 3.75–5 and 5–6, by fitting Schechter functions. In the lower bin, both protocluster and field HAEs exhibit shallow faint‑end slopes (α ≈ ‑1.2 to ‑1.3). In the higher bin, the field LF steepens dramatically (α = ‑1.87 +0.30/‑0.23), whereas the protocluster LF remains shallow (α ≈ ‑1.2 to ‑1.3). This divergence indicates that galaxies residing in dense environments have already undergone significant evolution by z > 5, resembling lower‑z populations, while field galaxies are still building up their low‑luminosity component.

Star‑formation rate density (SFRD) is derived from H α luminosities using the Kennicutt conversion, corrected for dust attenuation, and integrated down to 0.45 M⊙ yr⁻¹. The resulting SFRDs are 0.050 M⊙ yr⁻¹ Mpc⁻³ (z = 3.75–5) and 0.046 M⊙ yr⁻¹ Mpc⁻³ (z = 5–6). Remarkably, protoclusters contribute ~25 % of the total SFRD in the lower bin and ~55 % in the higher bin, implying that a majority of star formation at these epochs occurs in overdense, filamentary structures.

Clustering is quantified via the three‑dimensional two‑point auto‑correlation function ξ(r) = (r/r₀)⁻γ. Field HAEs show correlation lengths r₀ = 4.61 +1.00/‑0.68 h⁻¹ Mpc at z ≈ 4–5 and r₀ = 6.23 +1.68/‑1.13 h⁻¹ Mpc at z ≈ 5–6, with slopes γ ≈ 1.4–1.5, shallower than the canonical γ ≈ 1.8. The authors attribute this flattening to the filamentary geometry of the identified protoclusters, which also produces a near‑flat auto‑correlation within the structures themselves. By comparing the measured ξ(r) with mock catalogs from the UniverseMachine simulation, they infer that HAEs reside in dark‑matter (sub‑)haloes of log M_h/M⊙ = 11.0–11.2 with a scatter of ~0.4 dex. This halo mass range is consistent with previous H α clustering studies at lower redshift, confirming that even at z ≈ 5–6 star‑forming galaxies occupy relatively modest halos.

Key contributions of the work include: (1) Demonstrating that JWST NIRCam grism spectroscopy can directly detect H α at z > 4, overcoming the limitations of ground‑based near‑IR spectroscopy and Spitzer broadband excess methods; (2) Providing the first SFR‑limited three‑dimensional clustering analysis at these redshifts; (3) Revealing that protocluster environments dominate the cosmic star‑formation budget at early times; and (4) Highlighting how filamentary large‑scale structure modifies the shape of the auto‑correlation function, necessitating revised modeling for high‑z clustering studies.

The paper concludes that future deeper and wider JWST grism surveys, combined with refined hydrodynamic simulations, will enable precise mapping of protocluster growth, the evolution of the galaxy‑halo connection, and the role of environment in shaping the early Universe’s star‑formation history.