Modelling the photometric and morphological evolution of disc galaxies in the cluster environment

Observations indicate that the disc population in galaxy clusters has undergone rapid evolution, transitioning from a dominance of blue spirals to red S0s over the past $\sim7$ Gyr. We build a simplified cluster evolutionary model in the $\Lambda$CDM framework to constrain the characteristic timescales of this transformation. In our model, field spirals joining the cluster are subject to ram-pressure stripping (RPS), which removes their gas reservoir leading to the quenching of their star formation on a timescale $t_{\rm s}$, and to an (initially) unspecified mechanism that transforms them into S0s on a timescale $t_{\rm m}$. We assume that $t_{\rm s}$ and $t_{\rm m}$ are independent and both power-law functions of $M_\star/M_{\rm cl}$, the galaxy-to-cluster mass ratio. We constrain our model using the observed distribution of spirals and S0s in a color-mass plane from the OmegaWINGS and EDisCS cluster surveys at $z\simeq0.055$ and $z\simeq0.7$. Our best-fit model reproduces the data remarkably well and predicts evolutionary trends for the main morphological fractions in agreement with previous studies. We find typical $t_{\rm s}$ between $0.1$ and $1$ Gyr, compatible with previous estimates. A surprisingly strong anti-correlation between $t_{\rm s}$ and $M_\star/M_{\rm cl}$ is required in order to suppress the formation of red, low-mass spirals at low redshift, which we interpret as driven by orbit anisotropy. Conversely, $t_{\rm m}$ depends very weakly on $M_\star/M_{\rm cl}$ and has typical values of a few Gyr. The inferred morphological evolution is compatible with that resulting from the ageing of the stellar populations in galaxies abruptly quenched by ram pressure stripping: we confirm spectrophotometric ageing as a key channel for the spiral-to-S0 transition in galaxy clusters, with secular evolution playing a secondary role.