Gravitational instability and star formation in NGC 628

The gas-stars instability criterion for infinitesimally thin disc was applied to the galaxy NGC 628. Instead of using the azimuthally averaged profiles of data the maps of the gas surface densities (THINGS, HERACLES), of the velocity dispersions of stars (VENGA) and gas (THINGS) and of the surface brightness of the galaxy (S$^4$G) were analyzed. All these maps were collected for the same region with a noticeable star formation rate and were superimposed on each other. Using the data on the rotation curve values of $Q_\mathrm{eff}$ were calculated for each pixel in the image. The areas within the contours $Q_\mathrm{eff}<3$ were compared with the ongoing star formation regions ($\Sigma_\mathrm{SFR}> 0.007 \, M_{\odot}$yr$^{-1}$kpc$^{-2}$) and showed a good coincidence between them. The Romeo-Falstad disc instability diagnostics taking into account the thickness of the stellar and gas layers does not change the result. If the one-fluid instability criterion is used, the coincidence is worse. The analysis was carried out for the area $r < $ 0.5$r_{25} $. Leroy et al. (2008) using azimuthally averaged data obtained $Q_\mathrm{eff} \approx 3-4$ for this area of the disc, which makes it stable against non-axisymmetric perturbations and gas dissipation, and does not predict the location of star forming regions. Since in the galaxies the distribution of hydrogen and the regions of star formation is often patchy, the relationship between gravitational instability and star formation should be sought using data maps rather than azimuthally averaged data.