Correction to: ‘A new mass-loss rate prescription for red supergiants’

Abstract

The paper ‘A new mass-loss rate prescription for red supergiants’ was published in MNRAS 492, 5994–6006 (2020). Recent discussions with L. Decin have alerted us to a numerical error in the derivation of the mass-loss rate prescription. The error arose when combining the individual mass-loss prescriptions into the final initial-mass dependent prescription. This caused the slope of the mass-loss rate (⁠|$\dot{M}$|⁠) prescription to be too steep and the errors on the relation to be overestimated. In addition, the individual luminosity and mass-loss rate values are not explicitly stated in the paper, though they do appear in figures. To ensure the usefulness of the prescription and repeatability of the results we detail the updated formula below, including the individual mass-loss and luminosity data used for calculation. The main result of this correction is that the amount of mass lost via quiescent winds throughout the red supergiant (RSG) phase is predicted to be even lower than in the original paper, though the numbers are consistent to within the errors. This change, therefore, strengthens our original conclusion that RSG winds are ineffective at removing the H envelope. In Beasor et al. (2020, hereafter B20) we combined previously measured |$\dot{M}$| and Lbol values from RSGs in clusters NGC 2100 (Beasor & Davies 2016, hereafter B16), NGC 7419 and χ Persei (Beasor & Davies 2018, hereafter B18) with new measurements for Milky Way cluster RSGC1. Following publication of B16 and B18, a number of luminosity values for the RSGs within these papers were updated due to the use of a different technique, namely deriving luminosities from integrating under the observed spectral energy distribution (SED) rather than taking the values from the best fit DUSTY model (for more detail see Davies & Beasor 2018). In addition, we recalculated the distances and foreground extinctions for NGC 7419 and χ Per following the release of Gaia DR2 (Gaia Collaboration 2018). As such, the luminosities and mass-loss rates for the objects in these clusters was adjusted, but the numbers were not explicitly published in B20. The |$\dot{M}$| and Lbol values for the stars in NGC 2100 and RSGC1 are not affected. In Table 1 we state the cluster properties used in this work. In Tables 2 and 3 we list the luminosities and mass-loss rates derived for all RSGs in the B20 sample. Cluster properties. Notes. 1Pietrzyński et al. (2013), 2Beasor et al. (2019), 3Davies & Beasor (2019), 4Davies et al. (2008), 5Niederhofer et al. (2015), 6Figer et al. (2006) †Converted from AK using the extinction law of Koornneef (1983). Luminosities and mass-loss rates for the stars in NGC 7419 and χ Persei. Same as Table 1 but for NGC 2100 and RSGC1. We also note that the derived mass-loss rates in B20 for NGC 7419 and χ Persei were erroneously scaled, resulting in the numbers being too high in the Lbol-|$\dot{M}$| figures. In particular the |$\dot{M}$| value for MY Cep was overstated by a factor of 10 in B20 (this can be seen when comparing to B18), also contributing to the individual Lbol-|$\dot{M}$| relation for NGC 7419 being too steep. Here, to ensure reliability, we have rerun the DUSTY fitting procedure on all of the stars in NGC 7419 and χ Per. We note that as the only parameters that have changed are the luminosities—which affect only the final |$\dot{M}$| derived, not the shape of the spectral energy distributions—the best fit DUSTY parameters (Tin, τV) have not changed from those presented in B18. Repeating the fitting process using IDL routine FITEXY we re-derive individual relations for each cluster (see Table 4) as well as the following initial mass dependent |$\dot{M}$|-prescription: |$\dot{M}$| relation parameters for each cluster. The |$\dot{M}$|-luminosity relation is in the form |$\log (\dot{M}/M_\odot \,\rm{yr}^{-1})= a + b\log (L_{\rm bol}/L_\odot)$|⁠. where b = 3.6 ± 0.8. In Fig. 2 we show the gradient averaged |$\dot{M}$|-prescriptions for each cluster. |$\dot{M}$| versus Lbol for all clusters. Solid lines show relation after the gradient has been fixed. Change in mass of stars between 12–25M|$_{\odot }$| as a function of time for Geneva mass tracks. The solid lines show the mass lost through the Ekström et al. (2012) mass-loss implementation, while the coloured dashed lined show the amount of mass lost using the prescription presented here. Grey dashed lines show the predicted mass-loss using the former B20 prescription. To demonstrate the effect this updated prescription has on our conclusions, in Fig. 2 we remake fig. 7 from B20 with the results from the updated prescription also plotted. This figure shows the change in mass for stars of 12, 15, 20 and 25M|$_{\odot }$| in the Geneva models (solid lines) and for our prescription (dashed lines). Here, the grey dashed lines represent the prescription from B20, while the colored dashed lines represent the corrected results from this erratum. As can be seen, we find that correcting the prescription does not affect our main conclusions; that even the most massive RSGs do not lose more than ∼ 1 M|$_{\odot }$| of H-envelope through quiescent winds. The results only change for the two most massive stars, 20 and 25 M|$_{\odot }$|⁠, which both have the total amount of mass lost reduced from 1.40 M|$_{\odot }$| to 0.79 M|$_{\odot }$|⁠, and from 1.45 M|$_{\odot }$| to 0.92 M|$_{\odot }$|⁠, respectively. We also remake fig. 4 from B20 in Fig. 3, showing the |$\dot{M}$| residuals for each star with each prescription. This figure demonstrates the B20 prescription has less scatter than the dJ88 |$\dot{M}$|-prescriptions. Remake of fig. 4 from B20. Residual |$\dot{M}$| values, defined as log(⁠|$\dot{M}$|measured) – log(⁠|$\dot{M}$|prescription), for each star using the |$\dot{M}$|-prescriptions from this work and de Jager, Nieuwenhuijzen & Van Der Hucht (1988). While the exact numbers have changed we note that the main conclusions of our work remain unchanged: RSGs do not lose enough mass through their quiescent winds to steer them away from the red. These objects would not return to the blue of the HRD and die as hot stars. The amount of H-envelope remaining at core-collapse directly correlates with the initial mass of the star. The authors would like to thank Leen Decin for bringing the error in B20 to our attention.

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