2016A&A...587A.160D

Stellar bars play an essential role in the secular evolution of disk galaxies because they are responsible for the redistribution of matter and angular momentum. Dynamical models predict that bars become stronger and longer in time, while their rotation speed slows down. We use the Spitzer Survey of Stellar Structure in Galaxies (S⁴G) 3.6µm imaging to study the properties (length and strength) and fraction of bars at z=0 over a wide range of galaxy masses (M_*≃10⁸-10¹¹M_☉) and Hubble types (-3≤T≤10). We calculated gravitational forces from the 3.6µm images for galaxies with a disk inclination lower than 65°. We used the maximum of the tangential-to-radial force ratio in the bar region (Q_b) as a measure of the bar-induced perturbation strength for a sample of ∼600 barred galaxies. We also used the maximum of the normalized m=2 Fourier density amplitude (A₂^max) and the bar isophotal ellipticity (ε) to characterize the bar. Bar sizes were estimated i) visually; ii) from ellipse fitting; iii) from the radii of the strongest torque; and iv) from the radii of the largest m=2 Fourier amplitude in the bar region. By combining our force calculations with the Hi kinematics from the literature, we estimated the ratio of the halo-to-stellar mass (M_h/M_*) within the optical disk and by further using the universal rotation curve models, we obtained a first-order model of the rotation curve decomposition of 1128 disk galaxies. We probe possible sources of uncertainty in our Q_b measurements: the assumed scale height and its radial variation, the influence of the spiral arms torques, the effect of non-stellar emission in the bar region, and the dilution of the bar forces by the dark matter halo (our models imply that only ∼10% of the disks in our sample are maximal). We find that for early- and intermediate-type disks (-3≤T<5), the relatively modest influence of the dark matter halo leads to a systematic reduction of the mean Q_b by about 10-15%, which is of the same order as the uncertainty associated with estimating the vertical scale height. The halo correction on Q_b becomes important for later types, implying a reduction of ∼20-25% for T=7-10. Whether the halo correction is included or not, the mean Q_b shows an increasing trend with T. However, the mean A₂^max decreases for lower mass late-type systems. These opposing trends are most likely related to the reduced force dilution by bulges when moving towards later type galaxies. Nevertheless, when treated separately, both the early- and late-type disk galaxies show a strong positive correlation between Q_b and A₂^max. For spirals the mean ε≃0.5 is nearly independent of T, but it drops among S0s (≃0.2). The Q_b and ε show a relatively tight dependence, with only a slight difference between early and late disks. For spirals, all our bar strength indicators correlate with the bar length (scaled to isophotal size). Late-type bars are longer than previously found in the literature. The bar fraction shows a double-humped distribution in the Hubble sequence (∼75% for Sab galaxies), with a local minimum at T=4 (∼40%), and it drops for M_*≲10^9.5–10 M_☉. If we use bar identification methods based on Fourier decomposition or ellipse fitting instead of the morphological classification, the bar fraction decreases by ∼30-50% for late-type systems with T≥5 and correlates with M_h/M_*. Our M_h/M_* ratios agree well with studies based on weak lensing analysis, abundance matching, and halo occupation distribution methods, under the assumption that the halo inside the optical disk contributes roughly a constant fraction of the total halo mass (∼4%). We find possible evidence for the growth of bars within a Hubble time; as (1) bars in early-type galaxies show larger density amplitudes and disk-relative sizes than their intermediate-type counterparts; and (2) long bars are typically strong. We also observe two clearly distinct types of bars, between early- and intermediate-type galaxies (T<5) on one side, and the late-type systems on the other, based on the differences in the bar properties. Most likely this distinction is connected to the higher halo-to-stellar ratio that we observe in later types, which affects the disk stability properties.