A Virgo Environmental Survey Tracing Ionised Gas Emission (VESTIGE) XVIII. Reconstructing the star formation history of early-type galaxies through the combination of their UV and H$\alpha$ emission

We reconstruct the SFHs of 7 massive ($M_{\star}\gtrsim 10^{10} M_{\odot}$) early-type galaxies (ETGs) in the Virgo cluster by analysing their spatially resolved stellar population (SP), including their UV and H$\alpha$ emission. As part of the VESTIGE survey, we used H$\alpha$ images to select ETGs that show no signs of ongoing star formation. We combined VESTIGE with images from Astrosat/UVIT, GALEX and CFHT from the NGVS to analyse radial spectral energy distributions (SEDs) from the FUV to the NIR. The UV emission in these galaxies is likely due to old, low mass stars in post main sequence (PMS) phases, the UV upturn. We fit the radial SEDs with novel SP models that include an old, hot stellar component of PMS stars with various temperatures and energetics. This way, we explore the main stellar parameters responsible for UV upturn stars irregardless of their evolutionary path. Standard models are not able to reproduce the galaxies' central FUV emission (SMA/$R_{eff}\lesssim1$), while the new models well characterise it through PMS stars with temperatures T$\gtrsim$25000 K. All galaxies are old (mass-weighted ages $\gtrsim10$ Gyr) and the most massive M49 and M87 are supersolar within SMA/$R_{\rm eff}\lesssim0.2$. Overall, we found flat age gradients ($\nabla$Log(Age)$\sim -0.04 - 0$ dex) and shallow metallicity gradients ($\nabla$Log(Z)$<-0.2$ dex), except for M87 ($\nabla$Log($Z_{\rm M87}$)$\simeq-0.45$ dex). Our results show that these ETGs formed with timescales $\tau\lesssim1500$ Myr, having assembled between $\sim40-90\%$ of their stellar mass at $z\sim5$. This is consistent with recent JWST observations of quiescent massive galaxies at high$-z$, which are likely the ancestors of the largest ETGs in the nearby Universe. The derived flat/shallow gradients indicate that major mergers might have contributed to the formation and evolution of these galaxies.