The Rest-frame Optical (900 nm) Galaxy Luminosity Function at z ∼ 4-7: Abundance Matching Points to Limited Evolution in the M STAR/M HALO Ratio at z ≥ 4

We present the first determination of the galaxy luminosity function (LF) at z ∼ 4, 5, 6, and 7, in the rest-frame optical at {λ }_{rest}∼ 900 {nm} (z‧ band). The rest-frame optical light traces the content in low-mass evolved stars (∼stellar mass—M _*), minimizing potential measurement biases for M _*. Moreover, it is less affected by nebular line emission contamination and dust attenuation, is independent of stellar population models, and can be probed up to z ∼ 8 through Spitzer/IRAC. Our analysis leverages the unique full-depth Spitzer/IRAC 3.6-8.0 μm data over the CANDELS/GOODS-N, CANDELS/GOODS-S, and COSMOS/UltraVISTA fields. We find that, at absolute magnitudes where {M}_z^\prime is fainter than ≳ -23 mag, {M}_z^\prime linearly correlates with {M}_{UV,1600}. At brighter {M}_z^\prime , {M}_{UV,1600} presents a turnover, suggesting that the stellar mass-to-light ratio {M}_* /{L}_{UV,1600} could be characterized by a very broad range of values at high stellar masses. Median-stacking analyses recover an {M}_* /{L}_z^\prime roughly independent on {M}_z^\prime for {M}_z^\prime ≳ -23 mag, but exponentially increasing at brighter magnitudes. We find that the evolution of the LF marginally prefers a pure luminosity evolution over a pure density evolution, with the characteristic luminosity decreasing by a factor of ∼ 5× between z ∼ 4 and z ∼ 7. Direct application of the recovered {M}_* /{L}_z^\prime generates stellar mass functions consistent with average measurements from the literature. Measurements of the stellar-to-halo mass ratio at fixed cumulative number density show that it is roughly constant with redshift for {M}_h≳ {10}¹²{M}_⊙ . This is also supported by the fact that the evolution of the LF at 4≲ z≲ 7 can be accounted for by a rigid displacement in luminosity, corresponding to the evolution of the halo mass from abundance matching.