By Jeffrey Cummings (STSCI and Johns Hopkins University).
Stars evolve through many phases in their lifetime. Towards the end, when they have fused all of the Hydrogen (H) in their cores to Helium (He), they expand, cool down, and become giants. During these final stages, stars also begin to lose a significant amount of mass from their surfaces. A star like our Sun will lose approximately 50% of their mass, while more massive stars (> 8 Msun) will lose as much as 80% to 85%. Nearly all stars will eventually shed their outer layers and expose their hot and ultrahigh density cores. These remnants are called white dwarfs and, unless they experience mass transfer from a companion, their fate is to slowly cool with time.
However, a small percentage (approximately less than 2%) of high-mass stars can reach the necessary high densities and pressures in their cores to undergo a different fate: iron (Fe) will be created in their central core, but because it cannot undergo fusion to continue to generate energy, the star eventually becomes unstable and gravitationally collapses on itself creating a core-collapse supernova (CCSN). While it is commonly adopted in astronomy that stars with initial masses greater than 8 Msun will end their lives as a CCSN, we still do not fully understand at which stellar mass this transition occurs.
Knowledge of this transition mass is important because it sheds light on stellar evolution processes like mass-loss and convection/dredge up, and on the CCSN rate and how large of an effect these supernovae have on the production of elements (important to understand chemical evolution), on the energetics/feedback in galaxies, and on star formation.
Determination of the CCSN Mass Transition
There are three main methods to determine this mass. They all have their challenges and limitations, but jointly they may be able to begin to precisely constrain this transition mass:
1) Supernova studies. With the ability of the Hubble Space Telescope to resolve stars out to nearby galaxies, when a nearby CCSN occurs there is likely deep and resolved archival images of the progenitor star. Additionally, the stellar population of lower-mass stars that formed with the progenitor can subsequently be observed. Using stellar evolutionary models and the photometry of the progenitor and/or of the nearby lower-mass stars that formed with it, it is possible to infer the progenitor’s mass (e.g., Smartt 2009, Smartt 2015, Williams et al. 2014, Jennings et al. 2014). Within the past several years, the sample of nearby supernova has increased enough to provide meaningful statistics, indicating that the lowest-mass stars that undergo supernova have masses of ~9.5 Msun (Smartt 2015; Figure 1). These data also suggest that stars more massive than 18 Msun likely collapse but do not undergo an observable supernova.
Figure 1: Nearby supernovae are displayed with their inferred initial masses and errors. These masses are based on STARS and Geneva models (Eldridge & Tout 2004; Hirschi et al. 2004). In solid black, a trend is fit to the data suggesting a lower limit of ~9.5 Msun. In dashed black a second trend illustrates the expected number of stars at each initial mass based on a Salpeter initial mass function. This shows that such a large number of 10 to 17 Msun supernovae progenitors should be accompanied by a smaller but observable number of higher mass supernovae progenitors. This suggests that stars with mass greater than ~18 Msun may not undergo standard observable supernovae.
2) Stellar evolution models. A second method to estimate the CCSN transition mass is to use stellar evolution models to determine at which mass the core will reach the necessary conditions to create an Fe core and induce core-collapse (or produce an electron-capture CCSN). While a variety of models currently exist to account for the complex physical processes involved, many of them are beginning to converge around 9.3–9.8 Msun (Eldridge & Tout 2004, Poelarends 2007, Ibeling & Heger 2013, Doherty et al. 2015). Figure 2 illustrates the models from Doherty et al. (2015) and the transition masses at differing composition, with solar being represented by Z = 0.02.
Figure 2: This diagram illustrates the evolutionary result of a star with an initial mass at a given composition (Z = total mass fraction of a star that is not H or He), where solar composition is Z = 0.02. This model distinguishes between the different types of white dwarfs (WDs) and illustrates where white dwarf formation ends and supernovae begin. These models suggest a narrow region where electron-capture supernovae (ECSN) occur followed by the traditional Fe-core CCSN and shows that composition is an important secondary variable in these mass transitions.
3) White dwarf studies. Another way to constrain the transition mass is to study the remnants of the stars that do not undergo CCSN, i.e. white dwarfs. Spectroscopic analysis of high-mass white dwarfs in star clusters, together with evolutionary models, allow us to both directly determine the mass of the white dwarf and to infer the mass of the white dwarf’s progenitor. This is known as the initial-final mass relation (IFMR). Figure 3 illustrates the IFMR derived from white dwarfs across multiple clusters and a broad range of masses (Cummings et al. 2015; 2016a; 2016b; in prep.), and with evolutionary timescales based on PARSEC stellar models (Bressan et al. 2012). The IFMR provides a direct constraint on the mass loss that occurs during stellar evolution and how it varies with initial mass. In terms of constraining the CCSN transition mass, there currently are very few ultramassive white dwarfs that have been discovered in star clusters, but our current project is to survey for more white dwarfs approaching the highest mass a white dwarf can stably have (the Chandrasekhar mass limit at 1.375 Msun). The initial mass of a star that will create a Chandrasekhar mass white dwarf will also define the CCSN transition mass, which will provide a critical check of the other methods. However, based on cautious extrapolation, we note that our current relation suggests a consistency with the CCSN mass transition occurring near 9.5 Msun.
Figure 3: The current IFMR based on the spectroscopic analysis of white dwarfs that are members of star clusters. Comparison of the spectroscopically determined mass and age of the white dwarf can in comparison to the age of the cluster be traced back to the mass of the star that would have formed a white dwarf at that time. The solid line represents a fit to the data while the dashed line represents the theoretical IFMR of Choi et al. (2016). This shows a relatively clean relation with the clear formation of larger and larger white dwarfs from larger and larger stars. The highest-masses, however, remain poorly constrained, but precise measurement of where this relation reaches the Chandrasekhar mass (1.375 Msun; the upper limit of the y-axis), will define the progenitor mass at which stars begin to undergo CCSN.
The three methods described above, mostly independent from each other, are beginning to suggest a convergence around a CCSN transition mass of ~9.5 Msun. This implies that the commonly adopted value of 8 Msun, which is based on older and more limited data and theoretical models, has led us in the past to overestimate the number of CCSN by ~30%. Such an overestimation would greatly affect our understanding of the chemical evolution, energetics, and feedback in galaxies. Furthermore, the maximum mass for CCSN inferred by Smartt (2015), 18 Msun, further decreases the number of expected CCSN in a stellar population. This may solve the supernova rate problem that resulted from assuming that all stars with a mass greater than 8 Msun should undergo a CCSN. Under that assumption, the number of predicted CCSN is twice the observed rate (Horiuchi et al. 2011). But if only stars in the 9.5–18 Msun mass range undergo CCSN, based on the standard Salpeter stellar initial mass function, the new estimated CCSN rate is almost exactly half of the original estimate. This would bring observations and models into remarkable agreement.
Significant work remains to be done. More nearby supernovae need to be observed, with subsequent study of their progenitors, to further constrain their lower and upper mass limits. More ultramassive white dwarfs need to be discovered in star clusters, a focus of our research group, to refine our understanding of higher-mass stars and their mass-loss processes. Increasing the white dwarf sample size will provide an independent measurement of the CCSN transition mass, and it may also begin to provide an important observational test for the effects of differing stellar composition on mass-loss, evolution, and this mass transition. For stellar evolution models, a more coordinated approach between these observations and theory will improve the models, which also affects the inference of progenitor masses in the supernova and white dwarf studies. An iterative process, aiming for self-consistency across all steps, will ideally bring a more precise convergence of the mass transition at which supernova begin to occur. In any case, the assumption that all stars with mass greater than 8 Msun will undergo a CCSN is appearing more and more inaccurate.
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