The ALMA-QUARKS survey: Investigating Thermal Feedback of Massive Protostars in Hot Molecular Cores

We identify a sample of 83 spatially resolved hot molecular cores (HMCs) in the QUARKS survey, aiming at investigating thermal feedback from massive stars. Using CH$_3$CN\,(12--11) line emission together with 1.3\,mm continuum data we derive the radial temperature, volume density and \ch3cn{} abundance profiles for the 83 HMCs. Based on the envelope temperature and density profiles, we compute the luminosities of the embedded massive protostars with \radmc{} radiation transfer model. The derived luminosities are comparable (within $\sim1$ dex) to the bolometric luminosities of their natal clumps and show strong correlations with several core-scale properties, including the HMC mass ($Log[ M_\mathrm{env}] = 1.01\,Log [L_\star] - 4.80$), the inner core radius (the flat radius of Plummer-like volume density profile) ($Log[a] = 0.46\,Log[L_\star] + 0.52$) and the central density $ (Log[n_c] = -0.55 Log[L_\star] +10.47) $. These empirical relations provide useful observational constraints for physical models of protostellar objects. Importantly, we find a strong positive correlation between the massive protostellar luminosity and the local thermal Jeans mass. The derived Jeans masses, $M_\mathrm{Jeans}$, exceed the HMC masses $M_\mathrm{env}$, with the average $M_\mathrm{Jeans}$ being two times larger than the average $M_\mathrm{env}$. This provides observational evidence that thermal feedback from massive protostars can effectively suppress further fragmentation of HMCs, thereby promoting massive star formation. In addition, the positive correlation between massive protostellar luminosity and natal clump mass suggests that more massive clumps preferentially host more luminous protostars, leading to stronger thermal feedback.