Evolved Massive Stars at Low-metallicity V. Mass-Loss Rate of Red Supergiant Stars in the Small Magellanic Cloud

We assemble the most complete and clean red supergiant (RSG) sample (2,121 targets) so far in the Small Magellanic Cloud (SMC) with 53 different bands of data to study the MLR of RSGs. In order to match the observed spectral energy distributions (SEDs), a theoretical grid of 17,820 Oxygen-rich models (``normal'' and ``dusty'' grids are half-and-half) is created by the radiatively-driven wind model of the DUSTY code, covering a wide range of dust parameters. We select the best model for each target by calculating the minimal modified chi-square and visual inspection. The resulting MLRs from DUSTY are converted to real MLRs based on the scaling relation, for which a total MLR of $6.16\times10^{-3}$ $M_\odot$ yr$^{-1}$ is measured (corresponding to a dust-production rate of $\sim6\times10^{-6}$ $M_\odot$ yr$^{-1}$), with a typical MLR of $\sim10^{-6}$ $M_\odot$ yr$^{-1}$ for the general population of the RSGs. The complexity of mass-loss estimation based on the SED is fully discussed for the first time, indicating large uncertainties based on the photometric data (potentially up to one order of magnitude or more). The Hertzsprung-Russell and luminosity versus median absolute deviation diagrams of the sample indicate the positive relation between luminosity and MLR. Meanwhile, the luminosity versus MLR diagrams show a ``knee-like'' shape with enhanced mass-loss occurring above $\log_{10}(L/L_\odot)\approx4.6$, which may be due to the degeneracy of luminosity, pulsation, low surface gravity, convection, and other factors. We derive our MLR relation by using a third-order polynomial to fit the sample and compare our result with previous empirical MLR prescriptions. Given that our MLR prescription is based on a much larger sample than previous determinations, it provides a more accurate relation at the cool and luminous region of the H-R diagram at low-metallicity compared to previous studies.