The drastic impact of Eddington-limit induced mass ejections on massive star populations

TL;DR

This work tackles the long-standing challenge of LBV-like mass loss in massive stars by implementing an empirically calibrated, Eddington-limit–driven envelope-ejection prescription in the 1D stellar evolution code MESA. By tying envelope inflation to a threshold set by $R/R_\mathrm{core}$ and calibrating mass loss through a physically motivated $\dot{M}_\mathrm{eject}$, the authors reproduce key observed features of LMC/SMC massive-star populations, including the absence beyond the Humphreys-Davidson limit, WR/RSG/O-star counts, and the presence of WO stars at low $Z$, while also assessing the role of binarity via hybrid single/binary grids. The results demonstrate that Eddington-limit ejections can mitigate tensions between theory and observations, though caveats remain, such as an overproduction of bright H-free WN stars and lingering discrepancies in the WR luminosity distribution, especially at SMC metallicity. Overall, the approach offers a practical, physically motivated mechanism to improve population synthesis of massive stars and highlights the need for a more fundamental treatment of hydrogen-poor phases and SFH/binary assumptions in future work.

Abstract

Massive stars are the key engines of the Universe. However, their evolution and thus their ionizing feedback are still not fully understood. One of the largest gaps in current stellar evolution calculations is the lack of a model for the mass ejections that occur when the stars reach the Eddington limit, such as during an Luminous Blue Variable (LBV) phase. We aim to remedy this situation by providing a physically motivated and empirically calibrated method applicable in any 1D stellar evolution code to approximate the effect of such mass loss on stellar evolution. We employ the 1D stellar evolution code MESA, in which we implement a new mass-loss prescription that is acting when stellar models inflate too much when reaching the Eddington limit. Synthetic massive-star stellar populations using calculated grids of single-star models with this mass loss prescription are compared with the observed populations in the Large and Small Magellanic Clouds. In combination with already computed grids of binary evolution models, we investigate the impact of binarity on our predictions. Our single-star models reproduce key features of the observed stellar populations, namely (i) the absence of stars located beyond the Humphreys-Davidson limit, (ii) an upper limit of RSG luminosities, (iii) the faintest observed single WR stars, (iv) the absolute number of O-stars, WRs, and RSGs, (v) WO stars in low metallicity environments, and (vi) the positions of LBV stars in the HRD. Our binary population explains at the same time the 70% binary fraction of O-stars and the 40% binary fraction of WR stars. However, our synthetic population also has caveats, such as an overproduction of bright H-free WN stars. Our results show that the effect of Eddington-limit induced mass ejections on the structure and evolution of massive stars can remove tension between predicted and observed massive star populations.

Figures (12)

• Figure 1: HRDs of the massive star population (symbols) in the LMC (left), and SMC (right). The different symbols mark the positions of observed RSG dav1:18yan1:23, YSG neu1:10neu1:12, LBVs hum1:16kal1:18, OB stars (open circles and squares, eva1:04tru1:04tru1:05hun1:08bes1:11bou1:13urb1:17cas1:18sch2:18ram1:18ram1:19duf1:19bes1:20bou1:21ric1:22pau1:23ber1:24gom1:25alk1:25), partially stripped stars pau1:22ric1:23ram1:23ram1:24, and WR stars cro1:02hai1:14hai1:15tra1:15she1:16she1:19. The empirical HD limit hum1:79 is indicated by the hatched regions. Solid black and gray lines show stellar evolution tracks of the Model no-Eject until core hydrogen depletion. For clarity only the tracks with initial masses $M_\mathrm{ini}=40\,M{\odot} M$_⊙$$, $63\,M{\odot} M$_⊙$$, $100\,M{\odot} M$_⊙$$, $158\,M{\odot} M$_⊙$$, and $251\,M{\odot} M$_⊙$$ are labeled and colored in black. Dotted black lines mark the H-ZAMS and He-ZAMS. Contours in the background highlight the degree of inflation covering $R/R_\mathrm{core}=1\,\text{--}\,3$. Inflations of $R/R_\mathrm{core}=1.6$, $2.2$, and $2.8$ for stars during hydrogen burning, and $R/R_\mathrm{core}=1.05$, $1.1$, and $1.15$ for the He-ZAMS models are marked by colored lines and numbers.
• Figure 2: Sketch of the regions in the HRD where the different stellar groups are located. For reference, in the background, the stellar content of the LMC is shown. The symbols have the same meaning as in Fig. \ref{['fig:hrd_inflation']}.
• Figure 3: HRDs of the massive star population (symbols) in the LMC (left), and SMC (right), compared to the synthetic population of the Model Eject (contours). A selection of the same stellar evolution models is shown as solid lines, color-coded by their surface abundances. Small black dots on the evolution tracks mark equidistant timesteps of $\Delta t = 30000yr$. The hatched region indicates the empirical HD limit hum1:79. The different symbols mark different stellar groups and have the same sources as mentioned in Fig. \ref{['fig:hrd_inflation']}. In the SMC's population, we added the WO star DR1 from IC 1613 tra1:13, a galaxy which has SMC-like metallicity and only this WR star.
• Figure 4: Empirical luminosity distributions for the different cool supergiants (diamonds) in the LMC (left) and SMC (right) are compared to the predictions from the Model Eject (hatched bins). The error margins give the 84.13% confidence upper and lower margins of a Poissonian distribution accounting for small numbers isr1:68. The sources of the observed stars are the same as in Fig. \ref{['fig:hrd_inflation']}.
• Figure 5: Empirical luminosity distributions for the different WR subtypes (diamonds) in the LMC (left) and SMC (right) compared to the predictions from the Model Eject population (hatched bins). The error margins mark the 84% confidence intervals of a Poissonian distribution accounting for small numbers isr1:68. In the synthetic population, we differentiate between core H-burning (light dotted bins) and core He-burning stars (bold dotted bins). For definitions of the individual WR subtypes, refer to Appendix \ref{['sec:add_changes']}. The Of/WN stars are not included in the H-rich WR subtype, as they do not meet the criteria used in our models to identify the WR phase. For the LMC's WC/WO population, not all stars have been studied in detail using stellar atmosphere models, and for a large set of the WCs, we had to estimate their luminosity from their V-band photometry pau1:22. Bins containing only luminosities derived from a detailed spectral analysis are marked by dark blue diamonds, those only containing luminosities derived from the V-band photometry are marked by light blue diamonds, and those containing both are marked by half dark and half light blue diamonds. Since some of these stars might be binaries, the luminosities estimated from the V-band should be treated with caution and considered as upper limits. In the SMC's WC/WO population, we added the WO star DR1 from IC 1613 tra1:13.