On the mass of supernova progenitors: the role of the $^{12}$C$+^{12}$C reaction

TL;DR

This paper refines the mass limits of supernova progenitors by incorporating recent insights into the $^{12}$C+$^{12}$C reaction, impacting our understanding of stellar evolution and supernova origins.

Contribution

It provides new stellar models for 7-10 solar mass stars and revises the mass bounds for supernova progenitors considering recent nuclear reaction rate improvements.

Findings

Revised upper bound for CO white dwarf progenitors.

Revised lower bound for type II supernova progenitors.

Impact of $^{12}$C+$^{12}$C reaction rate on stellar evolution.

Abstract

A precise knowledge of the masses of supernova progenitors is essential to answer various questions of modern astrophysics, such as those related to the dynamical and chemical evolution of Galaxies. In this paper we revise the upper bound for the mass of the progenitors of CO white dwarfs (\mup) and the lower bound for the mass of the progenitors of normal type II supernovae (\mups). In particular, we present new stellar models with mass between 7 and 10 \msun, discussing their final destiny and the impact of recent improvements in our understanding of the low energy rate of the \c12c12 reaction.

Full text

1 Introduction

$M_{up}$ is the minimum stellar mass that, after the core-helium burning, develops temperature and density conditions for the occurrence of a hydrostatic carbon burning. Stars whose mass is lower than this limit are the progenitors of C-O white dwarfs and, when they belong to a close binary system, may give rise to explosive phenomena, such as novae or type Ia supernovae. Stars whose mass is only slightly larger than $M_{up}$ ignite C in a degenerate core and, in turn, experience a thermonuclear runaway. Their final destiny may be either a massive O-Ne white dwarf or an e-capture supernova. More massive objects ignite C in non-degenerate conditions and, after the Ne, O and Si burning, they produce a degenerate Fe core. These stars are the progenitors of various type of core-collapse supernovae among which the well known type IIp. In spite of their importance, a precise evaluation of $M_{up}$ and $M_{up}^{\star}$ is still missing (see,e.g., [1], [2]). It relies on our knowledge of various input physics used in stellar modelling, such as the plasma neutrino rate, responsible of the cooling of the core, the equation of state of high density plasma, which affects the compressibility and the consequent heating of the core, and the 12C$+^{12}$C reaction rate. In addition $M_{up}$ and $M_{up}^{\star}$ depend on the C-O core mass, which is determined by the extension of the convective instabilities during the H and He-burning phases, such as convective overshoot, semiconvection or rotational induced mixing. In this paper, we revise the theoretical predictions of $M_{up}$ and $M_{up}^{\star}$ . New stellar models of stars whose initial mass ranges between 7 and 10 $M_{\odot}$ and nearly solar composition, i.e., Z=0.02 and Y=0.27, are presented. Finally we provide a quantitative evaluation of the effects of the latest 12C$+^{12}$C reaction rate as revised after the new experimental studies based on the Trojan Horse Method [3].

2 Carbon burning in degenerate C-O cores

All the models here presented have been computed with the latest version of the FUNS code (see [4] and [5]). Rotation is here neglected, but its effects will be discussed in a fothcoming paper. The Kippenhahn diagram of the C burning phase of the 8.5 $M_{\odot}$ stellar model is shown in figure 1 (left). C ignites at about 0.15 $M_{\odot}$ from the center, where the temperature attains its maximum value. More inside, the cooling induced by the emission of plasma-neutrinos prevents the C burning. Suddenly, a quite extended convective shell develops, powered by the thermonuclear runaway. This episode lasts for about 4000 yr. Then, for a short period of time the C burning dies down, meanwhile the contraction and the consequent heating restart, until a new off-center C ignition follows. This time, the released thermal energy diffuses inward, so that the maximum temperature moves toward the center and a convective core develops. After about 500 yr, the convective core disappears. Later on, the maximum temperature moves outside again, giving rise to 3 distinct convective C-burning episodes. The final composition of the resulting O-Ne core is shown in figure 1 (right). The main components are 16O and 20Ne, with a lower, but non-negligible, amount of 24Mg. Note that in the innermost 0.5 $M_{\odot}$ , the original carbon has not besn fully consumed.

3 $M_{up}$ and $M_{up}^{\star}$

In order to determine the values of $M_{up}$ and $M_{up}^{\star}$ , we have computed 2 sets of models, with masses ranging between 7.0 and 10.0 $M_{\odot}$ (step 0.5 $M_{\odot}$ ), and different choices of the 12C$+^{12}$C reaction rate, namely, the Caughlan and Fowler (CF88) [6] and the Trojan Horse (THM) [3] rates. Figure 2 reports the final composition of the cores for the models 7.0, 7.5 and 8.0 $M_{\odot}$ . With the CF88 rate (left panels), the lighter model never attains the conditions for the C ignition and proceeds its evolution entering the AGB phase. Then, the 7.5 and the 8.0 $M_{\odot}$ undergo an incomplete C burning. In particular, in the 7.5 $M_{\odot}$ model, the C burning remains confined within a small shell located near the external border of the C-O core. Only for $M\geq 8.5$ $M_{\odot}$ , after the usual off-center ignition, the C burning propagates inward down to the center, and a complete C burning takes place, resulting in the formation of an O-Ne core. When the THM rate is adopted (right panels in figure 2), we find similar final compositions but for models $\sim 0.5$ $M_{\odot}$ less massive.

Concerning $M_{up}^{\star}$ , figure 3 shows the final compositions of the 9.5 and 10 $M_{\odot}$ models. In this case we find little differences between the CF88 and the THM models. In both cases, the 9.5 $M_{\odot}$ model never attains the conditions for the Ne photo-dissociation. On the contrary the 10 $M_{\odot}$ models ignite C at the center. Then, they experience a complete C burning. Later on, the Ne photo-dissociation starts at about 1 $M_{\odot}$ and the evolution proceeds through the more advanced burning phases (note that we stopped the computations when the O burning was still moving inward).