Globular Cluster UVIT Legacy Survey (GlobULeS) $-$ II. Evolutionary status of hot stars in M3 and M13

We present a far-ultraviolet (FUV) study of hot stellar populations in the second parameter pair globular clusters (GCs) M3 and M13, as a part of the Globular cluster UVIT Legacy Survey program (GlobULeS). We use observations made with F148W and F169M filters of the Ultraviolet Imaging Telescope (UVIT) onboard {\em AstroSat} along with ground-based data (UBVRI filters), {\em Hubble Space Telescope (HST)} GC catalogue, and {\em Gaia} EDR3 catalogue. Based on the FUV-optical colour-magnitude diagrams, we classify the sources into the horizontal branch (HB) stars, post-HB stars, and hot white dwarfs (WDs) in both the GCs. The comparison of synthetic and observed colours of the observed HB stars suggests that the mass-loss at the red giant branch (RGB) and He spread in both clusters have a simultaneous effect on the different HB distributions detected in M3 and M13, such that, HB stars of M13 require a larger spread in He (${\rm 0.247-0.310}$) than those of M3 (${\rm Y= 0.252-0.266}$). The evolutionary status of HB stars, post-HB stars, and WDs are studied using SED fit parameters and theoretical evolutionary tracks on the H-R diagram. We found that the observed post-HB stars have evolved from zero-age HB (ZAHB) stars of the mass range $0.48-0.55$ \Msun\ in M3 and M13. We detect 24 WD candidates in each cluster having ${\rm \log(L_{bol}/L_\odot)}$ in the range $-0.8$ to $+0.6$ and ${\rm \log(T_{eff}/K)}$ in the range of 4.2 to 5.0. Placing the WDs on the H-R diagram and comparing them with models suggest that M13 has a population of low-mass WDs, probably originating from binary evolution.