The frequency and sizes of inner bars and nuclear rings in barred galaxies and their dependence on galaxy properties

ABSTRACT Using a volume- and mass-limited (D < 30 Mpc, $\log \, (M_{\star }/M_{\odot })\ge 9.75$) sample of 155 barred S0–Sd galaxies, I determine the fraction with secondary structures within their bars. Some 20 ± 3 per cent have a separate inner bar, making them double-barred; an identical fraction have nuclear rings, with $11^{+3}_{-2}$ per cent hosting both. The inner-bar frequency is a strong, monotonic function of stellar mass: only $4^{+3}_{-2}$ per cent of barred galaxies with $\log \, (M_{\star }/M_{\odot })= 9.75$–10.25 are double-barred, while 47 ± 8 per cent of those with $\log \, (M_{\star }/M_{\odot })\gt 10.5$ are. The nuclear-ring frequency is a strong function of absolute bar size: only $1^{+2}_{-1}$ per cent of bars with semimajor axes