Scripts

Mass–Luminosity Calculator

We provide a Python script and an online calculator that enable users to compute mass–luminosity relations (MLRs), which can predict the minimum, maximum, and pure-helium (He) mass for a given luminosity and surface composition — and vice versa.

These results are based on the stellar structure models presented in Sabhahit et al. (2025b) and build upon existing MLRs in the literature by incorporating models that feature a helium core and hydrogen shell. These configurations may result from partial envelope stripping and can break simple homology relations, appearing more luminous than pure-He stars despite having a lower mean molecular weight.

A detailed description of our additional structure models by taking into account partial envelope stripping and the resulting new MLRs can be found here.

For comparison, we also provide a Python script implementing the minimum and maximum MLRs from Gräfener et al. (2011).

VMS Mass-Loss Implementations

Mass loss for classical massive stars (10-50 M☉) with optically-thin winds is typically taken from Vink et al. (2000, 2001), which show a shallow scaling with the Eddington parameter. However, a steeper scaling of mass loss in proximity to the Eddington limit has been found in Vink et al. (2011). This study implements a switch in the mass loss from a shallow to steeper scaling at the transition mass loss point where the single scattering limit is approximately breached as proposed in Vink & Gräfener (2012).

We use two different ways to estimate the transition mass loss point based on the presence or absence of observed VMSs:

For high metallicity (Z = 0.02 to 0.008, GAL and LMC-like): The transition mass-loss rate is obtained using the observed luminosities of the Of/WNh stars in the Arches cluster in our own galaxy and the 30 Dor in the LMC. We use η ~ 0.6 to get the transition mass-loss rate from the luminosity. The Github repository containing the MESA input files for the high metallicity case is provided at GitHub Repository - VMS_paper1. The paper is available at Sabhahit et al. (2022) - Mass-loss implementation and temperature evolution of very massive stars.

For low metallicity (Z = 0.004 to 0.0002, SMC-like or below): We do not have observed individual VMS in low metallicity environments to get the transition point. In the absence of such a large sample of VMS, we make use of both the concepts of transition mass loss point from Vink & Gräfener (2012) and hydro-dynamically consistent PoWR atmosphere models to construct the new implementation. The Github repository containing the MESA input files for the low metallicity case is provided at GitHub Repository - VMS_paper2. The paper is available at Sabhahit et al. (2023) - Very Massive Stars and Pair-Instability Supernovae: Mass-loss Framework for Low Metallicity.

RSG Mass-Loss Implementation

Mass loss for red supergiants (RSGs) oft use empirical prescriptions like de Jager et al. (1988) with mass-loss scaling with luminosity. However, Yang et al. 2023 showcase an empirical mass-loss kink with the mass loss scaling steeply above log(L/L☉) of 4.5. We formulate a mass loss scaling with the luminosity to current mass ratio based on these empirical rates transitioning from a shallow to steep scaling. The Github repository containing the MESA input files for the high metallicity case is provided at GitHub Repository - RSG. The paper is available at Vink & Sabhahit (2023) - Exploring the Red Supergiant wind kink. A Universal mass-loss concept for massive stars.