The Dependence of Bar Frequency on Galaxy Mass, Colour, and Gas Content -- and Angular Resolution -- in the Local Universe

I use distance- and mass-limited subsamples of the Spitzer Survey of Stellar Structure in Galaxies (S4G) to investigate how the presence of bars in spiral galaxies depends on mass, colour, and gas content and whether large, SDSS-based investigations of bar frequencies agree with local data. Bar frequency reaches a maximum of $\approx 0.70$ at $M_{\star} \sim 10^{9.7} M_{\odot}$, declining to both lower and higher masses. It is roughly constant over a wide range of colours ($g - r \approx 0.1$-0.8) and atomic gas fractions ($\log (M_{HI} / M_{\star}) \approx -2.5$ to 1). Bars are thus as common in blue, gas-rich galaxies are they are in red, gas-poor galaxies. This is in sharp contrast to many SDSS-based studies of $z \sim 0.01$-0.1 galaxies, which report f_bar increasing strongly to higher masses (from $M_{\star} \sim 10^{10}$ to $10^{11} M_{\odot}$), redder colours, and lower gas fractions. The contradiction can be explained if SDSS-based studies preferentially miss bars in, and underestimate the bar fraction for, lower-mass (bluer, gas-rich) galaxies due to poor spatial resolution and the correlation between bar size and stellar mass. Simulations of SDSS-style observations using the S4G galaxies as a parent sample, and assuming that bars below a threshold angular size of twice the PSF FWHM cannot be identified, successfully reproduce typical SDSS f_bar trends for stellar mass and gas mass ratio. Similar considerations may affect high-redshift studies, especially if bars grow in length over cosmic time; simulations suggest that high-redshift bar fractions may thus be systematically underestimated.