A pilot method to determine the high mass end of the Stellar Initial Mass Function in galaxies using UVIT, H$α$-MUSE observations and applied to NGC628

We present a pilot method to estimate the high-mass initial mass function (IMF) across the arm, interarm, and spur regions in galaxies and apply it to NGC 628. We extracted star-forming complexes (SFCs) from H$α$ VLT/MUSE and UVIT (FUV and NUV) observations of NGC 628 and used ALMA observations to define the molecular gas distribution. We find that the extinction-corrected H$α$ and FUV luminosities correlate well. Using the fact that O stars have a shorter lifetime (10$^7$ yr) compared to B stars (10$^8$ yr), we estimated the approximate number of O stars from H$α$ emission, and the number of B0 ($M_{*} > 10 M_{\odot}$), and B1 ($10 M_{\odot} \geq M_{*} \geq 3 M_{\odot}$) stars using FUV, NUV observations. We derived the IMF index ($α$) for different regions using O to B0 ($α_{1}$) and B0 to B1 ($α_{2}$) stellar ratios. Our findings indicate that if we assume H$α$ arises only from O8-type stars, the resulting $α_{1}$ value is consistent with the canonical IMF index. It steepens when we assume O stars with masses up to 100 $M_{\odot}$ with mean $α_{1}= 3.16 \pm 0.62$. However, the $α_{2}$ does not change for large variations in the O-star population, and the mean $α= 2.64 \pm 0.14$. When we include only blue SFCs ($ FUV-NUV\leq0.3$), mean $α_{2}$ is $2.43 \pm 0.06$. The IMF variation for SFCs in arms and spurs is insignificant. We also find that $α_{2}$ correlates with different properties of the SFCs, the most prominent being the extinction-corrected UV color (FUV-NUV).