We present the second Swift Burst Alert Telescope (BAT) catalog of gamma-ray bursts (GRBs), which contains 476 bursts detected by the BAT between 2004 December 19 and 2009 December 21. This catalog (hereafter the BAT2 catalog) presents burst trigger time, location, 90% error radius, duration, fluence, peak flux, time-averaged spectral parameters, and time-resolved spectral parameters measured by the BAT. In the correlation study of various observed parameters extracted from the BAT prompt emission data, we distinguish among long-duration GRBs (L-GRBs), short-duration GRBs (S-GRBs), and short-duration GRBs with extended emission (S-GRBs with E.E.) to investigate differences in the prompt emission properties. The fraction of L-GRBs, S-GRBs, and S-GRBs with E.E. in the catalog are 89%, 8%, and 2%, respectively. We compare the BAT prompt emission properties with the BATSE, BeppoSAX, and HETE-2 GRB samples. We also correlate the observed prompt emission properties with the redshifts for the GRBs with known redshift. The BAT T90 and T50 durations peak at 70 s and 30 s, respectively. We confirm that the spectra of the BAT S-GRBs are generally harder than those of the L-GRBs. The time-averaged spectra of the BAT S-GRBs with E.E. are similar to those of the L-GRBs. Whereas, the spectra of the initial short spikes of the S-GRBs with E.E. are similar to those of the S-GRBs. We show that the BAT GRB samples are significantly softer than the BATSE bright GRBs and that the time-averaged E obs peak of the BAT GRBs peaks at 80keV, which is significantly lower energy than those of the BATSE sample, which peak at 320keV. The time-averaged spectral properties of the BAT GRB sample are similar to those of the HETE-2 GRB samples. By time-resolved spectral analysis, we find that only 10% of the BAT observed photon indices are outside the allowed region of the synchrotron shock model. We see no obvious observed trend in the BAT T90 and the observed spectra with redshifts. The T90 and T50 distributions measured at the 140-220keV band in the GRB rest frame from the BAT known redshift GRBs peak at 19 s and 8 s, respectively. We also provide an update on the status of the on-orbit BAT calibrations.
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