COSMOS-Web: MIRI Data Reduction and Number Counts at 7.7$\mu$m using JWST

The COSMOS-Web survey is the largest JWST Cycle 1 General Observer program covering a contiguous ~0.54 deg$^2$ area with NIRCam imaging in four broad-band filters and a non-contiguous ~0.2 deg$^2$ with parallel MIRI imaging in a single broad-band filter, F770W. Here we present a comprehensive overview of the MIRI imaging observations, the data reduction procedure, the COSMOS-Web MIRI photometric catalog, and the first data release including the entire COSMOS-Web MIRI coverage. Data reduction is predominantly based on the JWST Science Calibration Pipeline with an additional step involving custom background subtraction to mitigate the presence of strong instrumental features and sky background in the MIRI images. We reach 5$\sigma$ (point source) limiting depths ($m_{F770W}$~25.51 based on $r$~0.3'' circular apertures) that are significantly better than initial expectations. We create a COSMOS-Web MIRI catalog based on the images presented in this release and compare the F770W flux densities with the Spitzer/IRAC CH4 measurements from the COSMOS2020 catalog for CH4 detections with S/N $>5$. We find that these are in reasonable agreement with a small median offset of $<0.05$ mag. We also derive robust 7.7$\mu$m number counts spanning five orders of magnitude in flux ($\sim$0.2-2300 $\mu$Jy) $\unicode{x2013}$ making COSMOS-Web the only JWST survey to date to efficiently sample such a large flux range $\unicode{x2013}$ which is in good agreement with estimates from other JWST and IRAC surveys.