Characterizing AGB stars in Wide-field Infrared Survey Explorer (WISE) bands

Aims. Since asymptotic giant branch (AGB) stars are bright and extended infrared objects, most Galactic AGB stars saturate the Wide-field Infrared Survey Explorer (WISE) detectors and therefore the WISE magnitudes that are restored by applying point-spread-function fitting need to be verified. Statistical properties of circumstellar envelopes around AGB stars are discussed on the basis of a WISE AGB catalog verified in this way. Methods. We cross-matched an AGB star sample with the WISE All-Sky Source Catalog and the Two Mircon All Sky Survey catalog. Infrared Space Observatory (ISO) spectra of a subsample of WISE AGB stars were also exploited. The dust radiation transfer code DUSTY was used to help predict the magnitudes in the W1 and W2 bands, the two WISE bands most affected by saturation, for calibration purpose, and to provide physical parameters of the AGB sample stars for analysis. Results. DUSTY is verified against the ISO spectra to be a good tool to reproduce the spectral energy distributions of these AGB stars. Systematic magnitude-dependent offsets have been identified in WISE W1 and W2 magnitudes of the saturated AGB stars, and empirical calibration formulas are obtained for them on the basis of 1877 (W1) and 1558 (W2) AGB stars that are successfully fit with DUSTY. According to the calibration formulas, the corrections for W1 at 5 mag and W2 at 4 mag are -0.383 and 0.217 mag, respectively. In total, we calibrated the W1/W2 magnitudes of 2390/2021 AGB stars. The model parameters from the DUSTY and the calibrated WISE W1 and W2 magnitudes are used to discuss the behavior of the WISE color-color diagrams of AGB stars. The model parameters also reveal that O-rich AGB stars with opaque circumstellar envelopes are much rarer than opaque C-rich AGB stars toward the anti-Galactic center direction, which we attribute to the metallicity gradient of our Galaxy.