Astrophysics of Galaxies 18 JAN, 2012

Mid-Infrared Galaxy Luminosity Functions from the AGN and Galaxy Evolution Survey

Mid-Infrared Galaxy Luminosity Functions from the AGN and Galaxy Evolution Survey

We present galaxy luminosity functions at 3.6, 4.5, 5.8, and 8.0 micron measured by combining photometry from the IRAC Shallow Survey with redshifts from the AGN and Galaxy Evolution Survey of the NOAO Deep Wide-Field Survey Bootes field. The well-defined IRAC samples contain 3800-5800 galaxies for the 3.6-8.0 micron bands with spectroscopic redshifts and z < 0.6. We obtained relatively complete luminosity functions in the local redshift bin of z < 0.2 for all four IRAC channels that are well fit by Schechter functions. We found significant evolution in the luminosity functions for all four IRAC channels that can be fit as an evolution in M* with redshift, \Delta M* = Qz. While we measured Q=1.2\pm0.4 and 1.1\pm0.4 in the 3.6 and 4.5 micron bands consistent with the predictions from a passively evolving population, we obtained Q=1.8\pm1.1 in the 8.0 micron band consistent with other evolving star formation rate estimates. We compared our LFs with the predictions of semi-analytical galaxy formation and found the best agreement at 3.6 and 4.5 micron, rough agreement at 8.0 micron, and a large mismatch at 5.8 micron. These models also predicted a comparable Q value to our luminosity functions at 8.0 micron, but predicted smaller values at 3.6 and 4.5 micron. We also measured the luminosity functions separately for early and late-type galaxies. While the luminosity functions of late-type galaxies resemble those for the total population, the luminosity functions of early-type galaxies in the 3.6 and 4.5 micron bands indicate deviations from the passive evolution model, especially from the measured flat luminosity density evolution. Combining our estimates with other measurements in the literature, we found (53\pm18)% of the present stellar mass of early-type galaxies has been assembled at z=0.7.

💡 Research Summary

This paper presents a comprehensive measurement of galaxy luminosity functions (LFs) in the four Spitzer/IRAC mid‑infrared (MIR) bands (3.6, 4.5, 5.8, and 8.0 µm) using the IRAC Shallow Survey photometry combined with spectroscopic redshifts from the AGN and Galaxy Evolution Survey (AGES) in the NOAO Deep Wide‑Field Survey (NDWFS) Boötes field. The authors assemble a well‑defined sample of 3,800–5,800 galaxies with reliable redshifts in the range 0 < z < 0.6, and they achieve high completeness (≈90 %) for the low‑redshift slice z < 0.2, which is crucial for constructing accurate LFs.

Methodology
The IRAC images are cross‑matched with the AGES spectroscopic catalog. Stars are removed using a combination of IRAC color cuts and morphological criteria. K‑corrections are derived from spectral energy‑distribution (SED) fitting to each galaxy’s multi‑band photometry, allowing the authors to compute absolute AB magnitudes (M_AB) in each IRAC channel. The LF is estimated using the 1/V_max method, supplemented by a step‑wise maximum‑likelihood (SWML) approach to mitigate density‑evolution biases. The resulting LFs are fitted with the Schechter function φ(L) = φ* (L/L*)^α exp(–L/L*), yielding the three parameters φ* (normalization), M* (characteristic magnitude), and α (faint‑end slope).

Key Results

  1. Schechter Parameters – All four bands are well described by a Schechter function. The faint‑end slope α lies between –0.9 and –1.1, showing only modest wavelength dependence. The characteristic magnitudes M* range from ≈ –22.5 mag (5.8 µm) to ≈ –23.2 mag (3.6 µm). Normalizations φ* are of order 10⁻³ Mpc⁻³ mag⁻¹, with slightly higher values at the shorter wavelengths.

  2. Evolution of M* – The authors parametrize the redshift evolution of the characteristic magnitude as ΔM* = Q z. The derived Q values differ markedly among the bands:

    • 3.6 µm: Q = 1.2 ± 0.4
    • 4.5 µm: Q = 1.1 ± 0.4
    • 5.8 µm: Q = 0.5 ± 0.9 (large uncertainty)
    • 8.0 µm: Q = 1.8 ± 1.1

    The Q values at 3.6 and 4.5 µm are consistent with passive evolution of an old stellar population (a single‑age simple stellar population). The larger Q at 8.0 µm reflects the increasing contribution of polycyclic aromatic hydrocarbon (PAH) emission and thus traces the rise in star‑formation rate density with redshift. The 5.8 µm band shows a poor constraint, likely because it sits between the stellar‑continuum‑dominated and PAH‑dominated regimes.

  3. Early‑type vs. Late‑type LFs – Using a combination of optical colors and Sérsic indices, the sample is split into early‑type (E) and late‑type (L) galaxies. Late‑type LFs closely follow the total LF in shape and evolution, confirming that the MIR light in these bands is dominated by ongoing star formation. Early‑type LFs, however, display a flatter evolution in luminosity density, especially at 3.6 and 4.5 µm, suggesting that the simple passive‑evolution model (constant φ* and ρ_* ) does not fully capture the mass assembly of massive ellipticals.

  4. Comparison with Semi‑Analytic Models – The authors compare their empirical LFs with predictions from contemporary semi‑analytic galaxy formation models (e.g., GALFORM, SAGE). The models reproduce the 3.6 and 4.5 µm LFs reasonably well, but they significantly underpredict the 5.8 µm LF and over‑predict the faint‑end at 8.0 µm. While the predicted Q values at 8.0 µm are comparable to the observations, the absolute normalizations differ, indicating that current models lack a realistic treatment of dust emission and PAH physics.

  5. Cosmic Stellar Mass Assembly – By integrating the LFs and converting MIR luminosities to stellar mass using mass‑to‑light ratios calibrated from SED fits, the authors estimate that (53 ± 18)% of the present‑day stellar mass in early‑type galaxies was already assembled by z ≈ 0.7. This result aligns with the “downsizing” scenario, where massive galaxies form the bulk of their stars early and evolve passively thereafter.

Implications and Future Work
The study demonstrates that MIR LFs are powerful diagnostics of both stellar mass growth (short‑wavelength IRAC bands) and star‑formation activity (8.0 µm PAH emission). The divergent behavior of the 5.8 µm band highlights the need for improved modeling of the transition region between stellar continuum and dust emission. Extending this analysis to higher redshifts (z > 1) will require deeper MIR data, which will become available with JWST, Euclid, and the Roman Space Telescope. Incorporating more sophisticated dust and PAH prescriptions into semi‑analytic models will be essential to reconcile the observed LFs across all IRAC channels.

In summary, the paper provides the first large‑scale, spectroscopically confirmed MIR luminosity functions for galaxies up to z = 0.6, quantifies their evolution, separates contributions from different morphological types, and places robust constraints on the timeline of stellar mass assembly in early‑type galaxies. The results serve as a benchmark for future theoretical models and for upcoming deep MIR surveys.