Establishing a mass-loss rate relation for red supergiants in the Large Magellanic Cloud

The high mass-loss rates of red supergiants (RSGs) drastically affect their evolution and final fate, but their mass-loss mechanism remains poorly understood. Various empirical prescriptions scaled with luminosity have been derived in the literature, yielding results with a dispersion of 2-3 orders of magnitude. We determine an accurate mass-loss rate relation with luminosity and other parameters using a large, clean sample of RSGs and explain the discrepancy between previous works. We assembled a sample of 2,219 RSG candidates in the Large Magellanic Cloud, with ultraviolet to mid-infrared photometry in up to 49 filters. We determined the luminosity of each RSG by integrating the spectral energy distribution and the mass-loss rate using the radiative transfer code DUSTY. Our derived RSG mass-loss rates range from $10^{-9} M_\odot$ yr$^{-1}$ to $10^{-5} M_\odot$ yr$^{-1}$, mainly depending on the luminosity. The average mass-loss rate is $9.3\times 10^{-7} M_\odot$ yr$^{-1}$ for $\log{(L/L_\odot)}>4$. We established a mass-loss rate relation as a function of luminosity and effective temperature. Furthermore, we found a turning point in the relation of mass-loss rate versus luminosity relation at approximately $\log{(L/L_\odot)} = 4.4$, indicating enhanced rates beyond this limit. We show that this enhancement correlates with photometric variability. Moreover, we compared our results with prescriptions from the literature, finding an agreement with works assuming steady-state winds. Additionally, we examined the effect of different assumptions on our models and found that radiatively driven winds result in mass-loss rates higher by 2-3 orders of magnitude, which are unrealistically high for RSGs. Finally, we found that 21% of our sample constitute current binary candidates. This has a minor effect on our mass-loss relation.