# The 2.4 $\mu$m Galaxy Luminosity Function as Measured Using WISE. III. Measurement Results

## TL;DR

This study measures the galaxy luminosity function at 2.4 micrometers using WISE data, providing highly accurate parameters that relate closely to stellar mass, and offers new insights into galaxy distribution and density.

## Contribution

The paper introduces precise measurements of the 2.4 μm galaxy luminosity function using spectroluminosity functional methods applied to WISE data, improving accuracy over previous estimates.

## Key findings

- Luminosity function parameters: φ* = 5.8e-3 Mpc^-3, L* = 6.4e10 L_sun, α = -1.050.
- Galaxy number density brighter than 10^6 L_sun is 0.08 Mpc^-3.
- Luminosity density at 2.4 μm is 3.8×10^8 L_sun Mpc^-3.

## Abstract

The WISE satellite surveyed the entire sky multiple times in four infrared wavelengths (3.4, 4.6, 12, and $22\,\mu$m; Wright et al. 2010). The unprecedented combination of coverage area and depth gives us the opportunity to measure the luminosity function of galaxies, one of the fundamental quantities in the study of them, at $2.4\ \mu$m to an unparalleled level of formal statistical accuracy in the near infrared. The big advantage of measuring luminosity functions at wavelengths in the window $\approx 2$ to $3.5\,\mu$m is that it correlates more closely to the total stellar mass in galaxies than others. In this paper we report on the parameters for the $2.4\,\mu$m luminosity function of galaxies obtained from applying the spectroluminosity functional based methods defined in Lake et al. (2017b) to the data sets described in Lake et al. (2017a) using the mean and covariance of $2.4\,\mu$m normalized SEDs from Lake & Wright (2016). In terms of single Schechter function parameters evaluated at the present epoch, the combined result is: $\phi_\star = 5.8 \pm [0.3_{\mathrm{stat}},\, 0.3_{\mathrm{sys}}] \times 10^{-3} \operatorname{Mpc}^{-3}$, $L_\star = 6.4 \pm [0.1_{\mathrm{stat}},\, 0.3_{\mathrm{sys}}] \times 10^{10}\, L_{2.4\,\mu\mathrm{m}\,\odot}$ ($M_\star = -21.67 \pm [0.02_{\mathrm{stat}},\, 0.05_{\mathrm{sys}}]\operatorname{AB\ mag}$), and $\alpha = -1.050 \pm [0.004_{\mathrm{stat}},\, 0.03_{\mathrm{sys}}]$, corresponding to a galaxy number density of $0.08\operatorname{Mpc}^{-3}$ brighter than $10^6\, L_{2.4\,\mu\mathrm{m}\,\odot}$ ($10^{-3} \operatorname{Mpc}^{-3}$ brighter than $L_\star$) and a $2.4\,\mu$m luminosity density equivalent to $3.8\times10^{8}\,L_{2.4\,\mu\mathrm{m}\,\odot}\operatorname{Mpc}^{-3}$. $\ldots$