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From the TNG50 cosmological simulation we build a sample of 191 well-resolvedbarred galaxies with a stellar mass $\log M_\star > 10$ at $z=0$. We search forbox/peanut bulges (BPs) in this sample, finding them in 55 per cent of cases.We compute $f_\mathrm{BP}$, the BP probability for barred galaxies as afunction of $M_\star$, and find that this rises to a plateau, as found inobservations of nearby galaxies. The transition mass where $f_\mathrm{BP}$reaches half the plateau value is $\log M_\star = 10.14$, consistent with theobservational value within measurement errors. We show that this transition in$f_\mathrm{BP}$ can be attributed to the youth of the bars at low $M_\star$,which is a consequence of downsizing of galaxies. Young bars, being generallyshorter and weaker, have not yet had time to form BPs. At high mass, while wefind a plateau, the value is at $\sim 60$ per cent, whereas observationssaturate at 100 per cent. We attribute this difference to excessive heating inTNG50, due to merger activity and to numerical resolution effects. BPs in TNG50tend to occur in galaxies with more quiescent merger histories. As a result,the main driver of whether a bar hosts a BP in TNG50 is not the galaxy mass,but how long and strong the bar is. Separating the BP sample into those thathave visibly buckled and those that have not, we find that fully half of BPgalaxies show clear signs of buckling, despite the excessive heating andlimited vertical resolution of TNG50.

The interplay between accretion, galaxy downsizing and the formation of box/peanut bulges in TNG50