Constraining massive star activities in the final years through properties of supernovae and their progenitors

TL;DR

This study investigates how energy deposition in massive star envelopes shortly before supernovae influences their progenitor structures and observable properties, constraining the energy involved and suggesting secondary effects trigger mass loss.

Contribution

It provides a detailed analysis of the effects of sustained energy deposition on progenitor stars, constraining the energy levels and proposing mechanisms for mass loss prior to supernovae.

Findings

Super-Eddington energy injection alters progenitor structure significantly.

Energy budget for final-year activity is limited to about ten times the Eddington luminosity.

Moderate energy injection likely causes envelope inflation, leading to mass loss via secondary effects.

Abstract

Recent observations of supernovae (SNe) just after the explosion suggest that a good fraction of SNe have the confined circumstellar material (CSM) in the vicinity, and the pre-SN enhanced mass loss may be a common property. The physical mechanism of this phenomenon is still unclarified, and the energy deposition into the envelope has been proposed as a possible cause of the confined CSM. In this work, we have calculated the response of the envelope to various types of sustained energy deposition starting from a few years before the core collapse. We have further investigated how the resulting progenitor structure would affect appearance of the ensuing supernova. While it has been suspected that a super-Eddington energy deposition may lead to a strong and/or eruptive mass loss to account for the confined CSM, we have found that a highly super-Eddington energy injection into the envelope changes the structure of the progenitor star substantially, and the properties of the resulting SNe become inconsistent with usual SNe. This argument constrains the energy budget involved in the possible stellar activity in the final years to be at most one order of magnitude higher than the Eddington luminosity. Such an energy generation however would not dynamically develop a strong wind in the time scale of a few years. We therefore propose that a secondary effect (e.g., pulsation or binary interaction) triggered by the moderate envelope inflation, which is caused by sub-Eddington energy injection, likely induces the mass loss.

Tables

Table 1. Table 1: Summary of progenitor and explosion properties of each of the different models.

Model 111Model name.	log$T_{\mathrm{eff}}$ 222Effective temperature of the progenitor at the time of core collapse.	log $L$ 333Photospheric luminosity of the progenitor at the time of core collapse.	$R_{\mathrm{ph}}$ 444Photospheric radius of the progenitor at the time of core collapse.	$R_{\mathrm{out}}$ 555The radial coordinate of the outermost numerical cell of the progenitor at the time of core collapse.	$E_{\mathrm{bin},\mathrm{env}}$ 666Binding energy of the envelope of the progenitor at the time of core collapse. This is calculated as $E_{\mathrm{bin},\mathrm{env}}={\int }_{M_{\mathrm{He}}}^{M_{\mathrm{total}}}Gm/r𝑑m$, where $M_{\mathrm{total}}$ and $M_{\mathrm{He}}$ are the total mass and He core mass of the progenitor, respectively.	Unbound mass 777The integrated mass of the progenitor at the time of core collapse for the region in the envelope where the specific total energy is positive. Here, the total energy is the sum of the kinetic energy, internal energy, and the gravitational potential energy.	$t_{\mathrm{SB}}$ 888Time since the explosion to the shock breakout.	$L_{\mathrm{pt},50}$ 999Luminosity of the supernova at 50 days since the shock breakout.	Plateau duration 101010Duration of plateau. This is calculated as the time interval between the time of shock breakout and the time when the luminosity becomes half of $L_{\mathrm{pt},50}$.
	(K)	($L_{\odot }$)	($R_{\odot }$)	($R_{\odot }$)	(${10}^{47}$ erg)	($M_{\odot }$)	(day)	(${10}^{42}$ erg s-1)	(day)
No injection	3.52	4.93	876.3	926.9	8.67	0.00	1.68	2.35	89.1
Ldep5d39uni	3.53	6.18	3553.2	5571.0	2.14	7.14	9.02	9.04	98.7
Ldep5d39base	3.54	6.15	3282.7	3658.4	0.91	7.36	5.49	7.23	114.6
Ldep5d39middle	3.54	6.17	3363.2	6081.2	3.10	6.30	9.07	8.96	113.6
Ldep1d38uni	3.52	4.96	906.4	960.6	8.43	0.00	1.75	2.34	87.9
Ldep1d39uni	3.51	5.23	1316.7	1434.7	5.94	0.00	2.56	3.58	84.6
Ldep1d40uni	3.59	5.89	1899.7	8977.9	1.25	6.73	12.88	12.33	105.0

Equations

$${ϵ}_{\mathrm{inject}}=\frac{L_{\mathrm{dep}}}{\sigma \sqrt{2\pi }}\exp \left(-\frac{(r-R_{\mathrm{dep}}{)}^2}{2{\sigma }^2}\right)\frac{dr}{dm},$$

$$L_{\mathrm{SN}}\propto E^{5/6}{M}_{\mathrm{ej}}^{-1/2}{R}_0^{2/3}{\kappa }^{-1/3}{T}_{\mathrm{I}}^{4/3},$$

$$t_{\mathrm{SN}}\propto E^{-1/6}{M}_{\mathrm{ej}}^{1/2}{R}_0^{1/6}{\kappa }^{1/6}{T}_I^{-2/3},$$

Full text

stars: evolution — stars: massive — stars: mass-loss — supergiants — supernovae: general

††journal: ApJ††software: MESA (Paxton et al., 2011, 2013, 2015, 2018), SNEC (Morozova et al., 2015)

1 Introduction

The evolution of massive stars ($M\gtrsim 8M_{\odot}$) just a few years before the core collapse, which sets the initial condition for the ensuing supernova (SN), seems to be much more uncertain than previously believed. Recently, evidence has been accumulating that some massive stars experience the enhanced mass loss ($\dot{M}\gtrsim 10^{-4}M_{\odot}\mathrm{yr}^{-1}$) just prior ($\sim$ yr – decades) to their demise (see Smith, 2014, and references therein)

Many interacting SNe have been detected, such as SNe IIn and SNe Ibn, which are considered to be powered by the interaction of the SN ejecta with the dense circumstellar material (CSM) (Filippenko, 1997; Pastorello et al., 2008; Gal-Yam, 2012; Taddia et al., 2013; Margutti et al., 2017). The pre-SNe mass loss rates estimated for these SNe are generally high ($\dot{M}\gtrsim 10^{-4}M_{\odot}\mathrm{yr}^{-1}$; Kiewe et al., 2012; Moriya et al., 2014), which are much higher than the typical stellar wind for the red supergiants (de Jager et al., 1988; van Loon et al., 2005). Some SNe are interpreted to experience the shock breakout within a dense CSM (Ofek et al., 2010; Moriya et al., 2013). Moreover, for some SNe, the pre-SN stellar activities have been detected, probably related to the pre-SN mass loss, although the possibility remains that many of them might not be the terminal explosion (Pastorello et al., 2007; Mauerhan et al., 2013; Ofek et al., 2013, 2014; Thöne et al., 2017).

The enhanced pre-SN mass loss may also be common for SNe II, which are defined to have hydrogen lines with the P-Cygni profile in their spectra. Recent high cadence surveys, such as the intermediate Palomar Transient Factory (Law et al., 2009), have enabled us to catch SNe at the very early phase after the explosion. The spectra characterized by emission lines from highly-ionized ions (the so-called flash spectra) imply the elevated pre-SN mass loss for at least a fraction of SN IIP progenitors (Yaron et al., 2017). Khazov et al. (2016) have found such flash-ionized spectra for $18\%$ of their SNe II sample observed at ages $<$ 5 days, setting a lower limit for such phenomena. Moreover, the early-time light curves of SNe II have been proposed to be better fit with dense CSM (Morozova et al., 2017; Förster et al., 2018). Thus, the enhanced pre-SN mass loss seems to be a common property.

The underlying mechanism of such an enhanced pre-SN mass loss is not well understood. It has been claimed that energy deposition into the envelope related to the advanced burning phases might be responsible for the enhanced mass loss (Dessart et al., 2010; Smith, 2014). Various mechanisms have been proposed for the energy deposition. For example, a fraction of the gravity waves generated from the convective region in the core may tunnel towards the envelope, and deposit energy there (Quataert & Shiode, 2012; Fuller, 2017; Fuller & Ro, 2018). The energy deposition rate by this process is expected to exceed Eddington luminosity only in the last few years before the core collapse. Thus, it can naturally explain the finely tuned timing of the event close to the core collapse (Shiode & Quataert, 2014). Explosive shell burning instabilities might also create additional energy (Arnett & Meakin, 2011; Smith & Arnett, 2014). Yet as another possibility, Chevalier (2012) has proposed that common envelope interaction as the cause of mass loss. In this hypothesis, a companion deposits its orbital energy into the primary’s envelope, which then presumably unbinds the envelope.

However, many of these works mainly focus on demonstrating the validity of each idea, based on an order of magnitude estimate. How such an energy deposition affects the progenitor’s density structure and SNe light curves has not been calculated consistently. Quataert et al. (2016) have investigated the effect of near-surface super-Eddington energy deposition on the structure of the envelope. They have shown that the extended wind are developed and the properties of the wind are consistent with analytic predictions. However, they considered only the energy deposition which takes place around the constant radius near the stellar surface. Moreover, the radiation-hydrodynamic calculation of SN based on the derived density structure of the progenitor has not been done. On the other hand, there have been a lot of studies which investigated the effect of CSM on the SNe light curves. They usually attach a density structure assuming a power law profile to the stellar surface, without considering how it is produced (Chevalier & Irwin, 2011; Moriya et al., 2011; Morozova et al., 2017).

In this paper, we simulate the response of the envelope to various kinds of sustained energy deposition which hypothetically occurs within a few years before the core collapse, and investigate its effect on the nature of the SN progenitor. Furthermore, using the density profile thus derived, we calculate the light curves of the SNe self-consistently. In the present study, we do not specify those energy injection rates based on certain physical mechanisms. Rather, we artificially inject energy with parameterized forms, and investigate its effect in general. From these calculations, we aim to clarifying to what extent such energy deposition can explain the confined CSM for massive stars. Another purpose of this study is to constrain the nature of the pre-SN activity, by the requirement that the resulting progenitor and SN emission should be consistent with the existing data set, irrespective of the nature of the confined CSM.

This paper is organized as follows: in §2, we describe the procedures of calculations, both for the stellar evolution using MESA (Modules for Experiments in Stellar Astrophysics) and for the radiation hydrodynamic simulation of the SNe using SNEC (SuperNova Explosion Code). In §3, we show the results of our calculations. Firstly, we focus on one model and discuss the effect of the energy deposition in general (§3.1 – §3.3). Next, we investigate the effect of varying locations (§3.4) and the rates (§3.5) of energy injection on the progenitors and SNe. We also discuss the effect of energy injection on the location of the progenitor on the HR diagram (§3.6). In §4, we discuss the possible application of our results to peculiar SNe. We also discuss our results in relation to the hypothesis of gravity waves. Finally in §5, we summarize the content of this paper.

2 Method

2.1 Hydrodynamic stellar evolution with energy injection using MESA