2026ApJ...997..207L

We study the luminosity function (LF) and clustering properties of 888 Hα 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 ∼62 arcmin² and reaches L_Hα ∼ 10^41.2 erg s^–1. We identify two prominent filamentary protoclusters at z ≈ 4.41 and z ≈ 5.19, hosting 98 and 144 HAEs, respectively. The observed Hα LFs show similar shallow faint-end slopes for both protocluster and field galaxies at 3.75 < z < 5, and for the protocluster at 5 < z < 6 (α ≈ -1.2 to -1.3). In contrast, the field LF at 5 < z < 6 has a much steeper slope ($\alpha =-1.8{7}_{-0.23}^{+0.30}$), suggesting that protocluster galaxies at z > 5 are more evolved, resembling the populations at 3.75 < z < 5. The observed star formation rate density from Hα integrated down to 0.45 M_⊙ yr^–1, is $0.05{0}_{-0.003}^{+0.002}\,{M}_{\odot }\,{{\rm{yr}}}^{-1}\,{{\rm{Mpc}}}^{-3}$ at 3.75 < z < 5 and $0.04{6}_{-0.004}^{+0.006}\,{M}_{\odot }\,{{\rm{yr}}}^{-1}\,{{\rm{Mpc}}}^{-3}$ at 5 < z < 6, with protoclusters contributing about 25% and 55%, respectively. This implies a large fraction of star formation at z > 4 occurs in protoclusters. For the first time, we conduct the star formation-rate-limited three-dimensional clustering analysis at z > 4. We find that the filamentary geometry of protoclusters flattens the power-law shape of the HAE autocorrelation functions, with slopes much shallower than the typically assumed value. The autocorrelation function of field HAEs has a correlation length of ${r}_{0}=4.6{1}_{-0.68}^{+1.00}\,{h}^{-1}\,\mathrm{Mpc}$ at z ≈ 4-5 and ${r}_{0}=6.2{3}_{-1.13}^{+1.68}\,{h}^{-1}{\rm{Mpc}}$ 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 ${\mathrm{log}}({M}_{h}/{M}_{\odot })=11.0-11.2$ at z ≈ 4-6, with a scatter of 0.4 dex.