The Impact of Realistic Red Supergiant Mass Loss on Stellar Evolution

The mass-loss rates ($\dot{M}$) of massive single stars above 8M_⊙ have long been considered a fundamental influence in stellar evolution, with the potential to change the fate of a star by peeling away the hydrogen envelope ⁵ (see reviews by Chiosi & Maeder 1986; Heger et al. 2003; Langer 2012; Smith 2014; Meynet & Maeder 2003). Stellar evolutionary models incorporate mass loss by utilizing empirical and analytical $\dot{M}$-prescriptions, and ultimately make predictions about which initial masses of stars are expected to end their lives as certain flavors of supernovae (SNe). Importantly, the usefulness of these predictions depends on how accurately the input physics reflects observations of real stars.

For massive stars with initial masses <30M_⊙, winds during the main sequence (MS) are minimal (removing only ≤ 0.8 M_⊙), so the only opportunity to significantly impact onward evolution via mass loss is during the cool supergiant phases (T_eff< 10,000K). At present, there is no first-principles model for cool supergiant mass loss in this region of the Hertzsprung–Russell diagram (although considerable progress is being made, see e.g., Kee et al. 2021). Evolutionary models such as Geneva (Meynet & Maeder 2000; Ekström et al. 2012) and BPASS (Eldridge & Stanway 2009) have therefore been forced to choose from a number of empirical prescriptions (e.g., Nieuwenhuijzen & de Jager 1990; van Loon et al. 2005; Kudritzki & Reimers 1978; Reimers 1975; de Jager et al. 1988; Goldman et al. 2017), with $\dot{M}$ s spanning up to an order of magnitude for a given luminosity (see Figure 1 within Mauron & Josselin 2011). The most commonly used prescription is that of de Jager et al. (1988), but this prescription contains large amounts of internal scatter (Mauron & Josselin 2011) and has recently been shown to vastly overestimate the total amount of mass lost post-MS for the highest mass objects (Beasor et al. 2020). Further, the de Jager et al. prescription contains $\dot{M}$ and L_bol measurements for only a handful of 15 RSGs. The sample itself is heterogeneous in terms of both mass and metallicity, as well as the method used to determine $\dot{M}$, and relies on highly uncertain distances, corresponding to a large source of error in the luminosities. Beasor & Davies (2016) suggested that the scatter in these relations is due to a lack of constraint on the initial masses of the stars used to derive the $\dot{M}$–L_bol relation. ⁶ When measuring $\dot{M}$–L_bol relations for RSGs in clusters, where the RSGs can be assumed to be the same age, metallicity, and initial mass, the dispersion on the relation is greatly reduced (Beasor & Davies 2016, 2018). Recently, we have combined the $\dot{M}$–L_bol relations for RSGs in four Galactic and LMC clusters of different ages, and derived a new initial mass-dependent $\dot{M}$-prescription (Beasor et al. 2020). This $\dot{M}$-prescription is calibrated to RSGs with initial masses between 10 and 25M_⊙, covering the observed mass range for Type II-P SN progenitors. ⁷

Zoom In Zoom Out Reset image size

Once a prescription has been selected, further complications can arise in the way in which it is implemented in evolutionary models. For example, the most recent Geneva models (Ekström et al. 2012) utilize a combination of both de Jager et al. (1988) and van Loon et al. (2005), both of which have been shown to overestimate RSG mass loss (Beasor et al. 2020). The van Loon et al. (2005) prescription is calibrated using stars with extreme mass loss (>10⁻⁴ M_⊙yr⁻¹) that are very rarely seen in unbiased RSG samples, and this prescription therefore is likely not applicable for normal RSG evolution (Beasor & Davies 2016, 2018; Beasor et al. 2020, Beasor & Smith 2021, submitted). Ekstrom et al. also take the additional step of increasing $\dot{M}$ by a factor of 3 when the luminosity of a star exceeds the Eddington luminosity. While this strategy has been duplicated in other studies (e.g., Dorn-Wallenstein et al. 2020) there is no observationally motivated reason for this increase in $\dot{M}$ during the RSG phase (e.g., Beasor et al. 2020). The result of artificially enhancing the RSG mass-loss rates in this way is to force single stars with masses ≥ 20M_⊙ back to the blue, where they die as H-poor SNe (e.g., Ekström et al. 2012).

Recently (Beasor et al. 2020, hereafter B20), derived a new $\dot{M}$-prescription for RSGs, calibrated to objects with initial masses between 10 and 25M_⊙. This prescription benefits from a number of improvements upon the dJ88 prescription. First, B20 measured the mid-IR excess ⁸ of RSGs in clusters rather than relying on field stars, providing a sample that is unbiased toward high $\dot{M}$ objects. Second, accurate luminosities allow stringent constraints to be placed on both the age of the cluster and therefore the initial masses of the stars (see Beasor et al. 2019). Further, this new prescription is calibrated from a larger sample of RSGs. In total, Beasor et al. (2020) measured $\dot{M}$ and L_bol for 34 RSGs in four different clusters (two Galactic, two LMC), whereas the dJ88 prescription is calibrated using only 15. Finally, whereas previous studies relied on field stars with uncertain distances, Beasor et al. (2020) use only RSGs in clusters for which distance is more accurately known. For two of the three Galactic clusters, new Gaia (Gaia Collaboration et al. 2018) measurements are available, leading to more precise L_bol measurements (Davies & Beasor 2019).

In this current paper, we investigate the effect of implementing the new $\dot{M}$-prescription from Beasor et al. (2020) for the cool supergiant (CSG) phase, using the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code (Paxton et al. 2010, 2013, 2015), and from this we make predictions about the progenitors of Type II SN. The paper will be organized as follows: in Section 2 we describe the model grid incorporating the new $\dot{M}$-prescription, in Section 3 we briefly describe our results and in Section 4 we discuss the implications of our finding on massive star evolution and SN characterization.

2.1. The Model Grid

We compute a new grid of stellar models using MESA (Paxton et al. 2010, 2013, 2015). For the input physics, we utilize the inlists for the MIST models from Choi et al. (2016) using MESA vr7503; therefore, our work can be considered a comparative study with that of Choi et al. In this work, we consider only the effect of changing mass loss during the CSG phase, defined as where T_eff< 10,000K (see below for full description), all other parameters remain identical to that of the MIST models. As the B20 $\dot{M}$-prescription is calibrated using clusters where M_init is between 10 and 25M_⊙, we compute models for stars with initial masses 12, 15, 18, 21, and 24M_⊙. This also covers the observationally inferred mass range for Type II-P SN progenitors (e.g., Maund et al. 2004; Fraser et al. 2011; Smartt 2015).

In the MIST models, the mass-loss rates for high mass stars (defined as objects with M_init > 10M_⊙) are implemented using a combination of wind mass-loss prescriptions named Dutch. This combination includes $\dot{M}$ prescriptions for hot phases (Vink et al. 2000, 2001), cool phases (de Jager et al. 1988, hereafter dJ88), and another for Wolf–Rayet phases (Nugis & Lamers 2000). When stars reach T_eff < 10,000K, the Dutch recipe switches on the cool phase $\dot{M}$, for which the empirically derived prescription of de Jager et al. (1988) is utilized,

$$\begin{eqnarray}&&{\dot{M}}_{\mathrm{dJ}}={10}^{-8.158}(L/{L}_{\odot })\,{T}_{\mathrm{eff}}^{-1.676}\,{{M}_{\odot }{yr}}^{-1}.\end{eqnarray} \tag{ 1 }$$

Below, we discuss the new $\dot{M}$-prescription from Beasor et al. (2020).

2.2. The Updated $\dot{M}$-prescription

Beasor et al. (2020) derived an $\dot{M}$-prescription that is dependent on the initial mass of the object as well as luminosity, given by,

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{log}(\dot{M}/{M}_{\odot }{\mathrm{yr}}^{-1}) & = & a+b({M}_{\mathrm{init}}/{M}_{\odot })\\ & & +c\mathrm{log}({L}_{\mathrm{bol}}/{L}_{\odot }),\end{array}\end{eqnarray} \tag{ 2 }$$

where a = −26.4 ± 0.7, b = −0.23 ± 0.05, and c = 4.8 ± 0.6. Importantly, Beasor et al. (2020) demonstrated that $\dot{M}$ prescriptions that are based on field stars, e.g., dJ88, vastly overpredict the mass loss, particularly for the highest luminosity objects, i.e., the highest initial mass stars. For example, the dJ88 prescription overpredicts the mass loss of 25M_⊙ RSGs by a factor of 40 (see Figure 4 within Beasor et al. 2020). ⁹

We now take the B20 prescription and investigate the effect of lower $\dot{M}$ across the CSG phase on the final fate of massive stars. We compute the models using the same inlists as for the MESA MIST models (Choi et al. 2016) until the cool supergiant phase, where the Dutch prescription kicks in. At this point, we switch the mass loss to the prescription presented in B20, Equation (2).

In Figure 1 we show the HRDs for each set of models; those with standard MIST parameters, i.e., utilizing the Dutch $\dot{M}$ recipe only (dashed tracks); and those where the cool $\dot{M}$ phase uses the B20 prescription (solid tracks). The $\dot{M}$-prescriptions switch from the hot star regime to the cool-star regime at 10,000 K (log T_eff = 4.0). As can be seen, the effects of switching the mass-loss recipes has a minimal effect on the location of tracks in the HRD, indeed there are only slight temperature changes for the higher mass stars. Renzo et al. (2017) and Sukhbold et al. (2018) also showed that even dramatic downward revisions in CSG mass loss have a minimal effect on the HRD and the final luminosity of RSGs. In the mass range 12–27M_⊙, there is no noticeable difference between the end point for RSGs between the models employing only the Dutch prescription (dashed lines), and the new models utilizing a combination of Dutch and B20 (solid lines). We also do not see any significant difference in the luminosity time evolution of the two model grids.

Though the final temperatures and luminosities of the stars do not change significantly when the new $\dot{M}$ law is implemented, the terminal envelope mass is substantially altered. The amount of H-envelope at the end of a star's life is an important parameter in determining the rates of various flavors of SNe. For example, should a star retain a large amount of H-envelope (mass) it will appear as a H-rich Type II supernovae, likely a Type II-P. On the other hand, if a star sheds nearly all of its H-envelope, it may appear as a Type IIb and the progenitor may appear as a yellow or blue supergiant instead of an RSG. In Figure 2 we show the mass of the H-envelope remaining at core-carbon burning for the standard $\dot{M}$ implementation (dJ88) and for the new B20 prescription. While the evolutionary paths of the RSGs do not change (i.e., in both model grids the stars would all explode in the RSG phase) the amount of H-envelope remaining changes drastically.

Zoom In Zoom Out Reset image size

3.1. Low Mass-loss Rates Prevent RSGs Returning to the Blue

3.2. Correlation of H-envelope with Initial Mass

3.3. Metallicity

In this work, we have explored the impact of incorporating the Beasor et al. (2020) RSG mass-loss rates into stellar evolution calculations. Our main findings are as follows:

• 1.  
  We confirm the results of previous studies, that even vastly reducing mass loss during the CSG phases has a minimal effect on the final position of the star on the HRD, and the M_init–L_fin relation remains unchanged.
• 2.  
  The amount of H-envelope lost due to cool supergiant mass loss is not enough to cause a star to evolve back to the blue, effectively ruling out the single-star pathway for the production of WRs and stripped-envelope SNe at masses below 27M_⊙.
• 3.  
  We find a clear correlation of initial mass with envelope mass at core collapse for single RSGs. We discuss several implications of the higher H-envelope mass for SNe and SN progenitors.

We would like to thank the anonymous referee whose comments helped improve the paper. The authors would also like to thank Luc Dessart for useful comments on the manuscript. E.R.B. is supported by NASA through Hubble Fellowship grant HST-HF2-51428 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This work makes use of the IDL software and astrolib.