The stellar masses of galaxies from the 3.4 μm band of the WISE All-Sky Survey

We study the rest-frame 3.4 mu m band infrared luminosity as an indicator of the stellar masses of galaxies. We cross-match the Wide-field Infrared Survey Explorer All-Sky catalogue with the MPA-JHU Sloan Digital Sky Survey catalogue to produce a sample of 542 757 galaxies. We find that up to z similar to 0.35, the stellar mass (log(10)M(*)) is strongly correlated with the rest-frame 3.4 mu m luminosity [log(10)nu L-nu(3.4 mu m)]. We have derived the formulae for using the log(10)nu L-nu(3.4 mu m) to calculate the stellar mass of the total galaxy sample. We can improve the calculation of stellar mass by classifying the sample into H ii galaxies, composite galaxies, AGNs, absorption line galaxies and low-signal-to-noise (S/N) emission line galaxies, or by classifying the sample into early-type galaxies and late-type galaxies. The composite galaxies, AGNs, absorption galaxies and low-S/N emission line galaxies have similar peak values of log(10)M(*)/nu L-nu(3.4 mu m) as early-type galaxies have. H ii galaxies and late-type galaxies also have similar peak values. For the same luminosity, slightly higher stellar mass estimates will result for composite galaxies, AGNs, absorption line galaxies and low-S/N emission line galaxies than for H ii galaxies. Similarly, the mass estimates for early-type galaxies are higher than for late-type galaxies. The mass-to-luminosity ratio, log(10)M(*)/nu L-nu(3.4 mu m), correlates with [22]-[3.4] mu m colour, g - r and u - r colour in the rest frame. We give the quadratic regression fitting of these quantities, which can also be used to estimate the stellar mass. The ratio also has a relationship with EQW(H alpha) and weaker relationships with log(10)nu L-nu(22 mu m), oxygen abundances, the intrinsic extinction of galaxies and the strength of AGN features.