What Determines the Sizes of Bars in Spiral Galaxies?

I use volume- and mass-limited subsamples and recently published data from the Spitzer Survey of Stellar Structure in Galaxies (S4G) to investigate how the size of bars depends on galaxy properties. The known correlation between bar semi-major-axis $a$ and galaxy stellar mass (or luminosity) is actually bimodal: for $\log M_{\star }<10.1$, bar size is almost independent of stellar mass ($a\propto M_{\star }^{0.1}$), while it is a strong function for higher masses ($a\propto M_{\star }^{0.6}$). Bar size is a slightly stronger function of galaxy half-light radius $r_e$ and (especially) exponential disc scale length $h$ ($a\propto h^{0.8}$). Correlations between stellar mass and galaxy size can explain the bar-size–$M_{\star }$ correlation – but only for galaxies with $\log M_{\star }<10.1$; at higher masses, there is an extra dependence of bar size on $M_{\star }$ itself. Despite theoretical arguments that the presence of gas can affect bar growth, there is no evidence for any residual dependence of bar size on (present-day) gas mass fraction. The traditional dependence of bar size on Hubble type (longer bars in early-type discs) can be explained as a side-effect of stellar-mass–Hubble-type correlations. Finally, I show that galaxy size ($r_e$ or $h$) can be modeled as a function of stellar mass and both bar presence and bar size: barred galaxies tend to be more extended than unbarred galaxies of the same mass, with larger bars correlated with larger sizes.