The FAST Ursa Major supergroup HI survey (FUMaS): catalog and HI mass function

Using the Five-hundred-meter Aperture Spherical radio Telescope (FAST), we have performed an Ursa Major supergroup HI Survey (FUMaS) covering the entire UMa region centered at RA=11$^h$59$^m$28$^s$.3, DEC=49$^\circ$05'18" with a radius of 7.5$^\circ$. We have obtained the most complete catalog of HI sources in the UMa supergroup, containing 178 HI sources with velocities in the range 625-1213.4 km s$^{-1}$ and masses in the range 10$^{6.0}$-10$^{10.1}$ M$_{\odot}$ assuming a distance of 17.4 Mpc. Among them, 55 HI sources were detected for the first time, of which 32 do not have known optical redshifts. For these 32 sources, we have searched the DESI Legacy Surveys and found optical counterparts for 25 of them (with optical images, but no redshifts), with the remaining 7 sources to be pure HI clouds without an optical counterpart. We detected HI distributions in some interacting systems and discussed four small groups in detail. We computed the HIMF of the UMa supergroup using the 1/V$_\mathrm{max}$ method and fitting it with the non-linear least squares (NLLS) and modified maximum likelihood (MML) methods. We obtained the following HIMF parameters: log$_{10}$($\phi_*$/Mpc$^{-3}$) = -0.78 $\pm$ 0.15, $\alpha$ = -1.05 $\pm$ 0.07 and log$_{10}$($M_*$/$M_{\odot}$) = 9.87 $\pm$ 0.19 for the NLLS method, and log$_{10}$($\phi_*$/Mpc$^{-3}$) = -0.70 $\pm$ 0.11, $\alpha$ = -1.05 $\pm$ 0.05 and log$_{10}$($M_*$/$M_{\odot}$) = 9.77 $\pm$ 0.13 for the MML method. This result is similar to that derived from the VLA blind survey, but the slope is steeper because we detected more low-mass galaxies. The slope is flatter than that of the global HIMF, which agrees with the theoretical prediction that galaxies in high-density regions are stripped of gas due to interactions.