Barlenses and X-shaped features compared: two manifestations of boxy/peanut bulges

Aims. We study the morphological characteristics of boxy/peanut-shaped bulges. In particular, we are interested to determine whether most of the flux associated with bulges in galaxies with masses similar to those of the Milky Way at redshift z ~ 0 might belong to the vertically thick inner part of the bar, in a similar manner as in the Milky Way itself. At high galaxy inclinations, these structures are observed as boxy/peanut/X-shaped features, and when the view is near to face-on, they are observed as barlenses. We also study the possibility that bulges in some fraction of unbarred galaxies might form in a similar manner as the bulges in barred galaxies. Methods. We used the Spitzer Survey of Stellar Structure in Galaxies (S4G) and the Near-IR S0 galaxy Survey (NIRS0S) to compile complete samples of galaxies with barlenses (N = 85) and X-shaped features (N = 88). A sample of unbarred galaxies (N = 41) is also selected. For all 214 galaxies unsharp mask images were created, used to recognize the X-shaped features and to measure their linear sizes. To detect possible boxy isophotes (using the B4-parameter), we also performed an isophotal analysis for the barlens galaxies. We use recently published N-body simulations: the models that exhibit boxy/peanut/X/barlens morphologies are viewed from isotropically chosen directions that cover the full range of galaxy inclinations in the sky. The synthetic images were analyzed in a similar manner as the observations. Results. This is the first time that the observed properties of barlenses and X-shaped features are directly compared across a wide range of galaxy inclinations. A comparison with the simulation models shows that the differences in their apparent sizes, a/rbar ≳ 0.5 for barlenses and a/rbar ≲ 0.5 for X-shapes, can be explained by projection effects. Observations at various inclinations are consistent with intrinsic abl ≈ aX ≈ 0.5rbar: here intrinsic size means the face-on semimajor axis length for bars and barlenses, and the semilength of the X-shape when the bar is viewed exactly edge-on. While X-shapes are quite common at intermediate galaxy inclinations (for i = 40°−60° their frequency is about half that of barlenses), they are seldom observed at smaller inclinations. This is consistent with our simulation models, which have a small compact classical bulge that produces a steep inner rotation slope, whereas bulgeless shallow rotation curve models predict that X-shapes should be visible even in a face-on geometry. The steep rotation curve models are also consistent with the observed trend that B4 is positive at low inclination and with negative values for i ≳ 40°−60°; this implies boxy isophotes. In total, only about one quarter of the barlenses (with i ≤ 60°) show boxy isophotes. Conclusions. Our analyses are consistent with the idea that barlenses and X-shaped features are physically the same phenomenon. However, the observed nearly round face-on barlens morphology is expected only when at least a few percent of the disk mass is located in a central component, within a region much smaller than the size of the barlens itself. Barlenses contribute to secular evolution of galaxies, and might even act as a transition phase between barred and unbarred galaxies. We also discuss that the wide range of stellar population ages obtained for the photometric bulges in the literature are consistent with our interpretation