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Abstract

Using a volume- and mass-limited (D < 30 Mpc, log(M-star/M-circle dot)>= 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 11-2+3 per cent hosting both. The inner-bar frequency is a strong, monotonic function of stellar mass: only 4-2+3 per cent of barred galaxies with log(M-star/M-circle dot)=9.75-10.25 are double-barred, while 47 +/- 8 per cent of those with log(M-star/M-circle dot)>10.5 are. The nuclear-ring frequency is a strong function of absolute bar size: only 1-1+2 per cent of bars with semimajor axes <2 kpc have nuclear rings, while 39-5+6 per cent of larger bars do. Both inner bars and nuclear rings are absent in very late-type (Scd-Sd) galaxies. Inner bar size correlates with galaxy stellar mass, but is clearly offset to smaller sizes from the main population of bars. This makes it possible to define 'nuclear bars' in a consistent fashion, based on stellar mass. There are eight single-barred galaxies where the bars are nuclear-bar-sized; some of these may be systems where an outer bar failed to form, or previously double-barred galaxies where the outer bar has dissolved. Inner bar size is even more tightly correlated with host bar size, which is likely the primary driver. In contrast, nuclear ring size is only weakly correlated with galaxy mass or bar size, with more scatter in size than is true of inner bars.