I didn't find a definition of SFR on TNG or Illustris website,so I wonder what's the physical meaning of M⊙/yr, new stars with 1M⊙ generated from the designated gas cell per year?
I also read Donnari's paper, but I don't understand the meaning of this sentence in the paper: The SFR of a gas cell is inversely proportional to a density-dependent time-scale for star formation and is proportional to the subgrid estimate of cold gas mass.
The star formation rate is the same as you will find in any observational or theoretical work related to galaxies.
It is the rate, in solar masses per year, that stars are forming. If you are looking at this value for a single gas cell, then it is the rate that gas mass of that cell is being converted into stellar mass. If you are looking at this value for an entire galaxy or halo, then it is that rate summed up over the respective object.