# Constraints on the Progenitor System of SN 2016gkg

from a Comprehensive Statistical Analysis

###### Abstract

Type IIb supernovae (SNe) present a unique opportunity for understanding the progenitors of stripped-envelope (SE) SNe as the stellar progenitor of several Type IIb SNe have been identified in pre-explosion images. In this paper, we use Bayesian inference and a large grid of non-rotating solar-metallicity single and binary stellar models to derive the associated probability distributions of single and binary progenitors of the Type IIb SN 2016gkg using existing observational constraints. We find that potential binary star progenitors have smaller pre-SN hydrogen-envelope and helium-core masses than potential single-star progenitors typically by and , respectively. We find no strong constraint on the nature of the companion star. We demonstrate that the range of progenitor helium-core mass inferred from observations could help improve constraints on the progenitor. We find that the probability that the progenitor of SN 2016gkg was a binary is 25% when we use constraints only on the progenitor luminosity and effective temperature. Imposing the range of pre-SN progenitor hydrogen-envelope mass and radius inferred from SN light-curves the probability the progenitor was a binary increases to 48%. However, there is no clear preference for a binary progenitor. Our analysis demonstrates the importance of statistical inference methods in order to constrain progenitor channels.

###### Subject headings:

binaries: general – stars: massive – supernovae: general – supernovae: individual (SN 2016gkg)## 1. Introduction

The mechanisms driving the stripping of the progenitor stars of stripped-envelope (SE) supernovae (SNe) remain an open reserach question. Currently, stellar winds, close binary interactions, and nuclear burning instabilities are leading candidates to explain the mass loss (e.g., Claeys et al., 2011; Arnett & Meakin, 2011; Quataert & Shiode, 2012; Shiode et al., 2013; Groh et al., 2013; Smith, 2014; Smith & Arnett, 2014; Fuller, 2017). Among SE SNe, Type IIb SNe explode with a low-mass but extended residual hydrogen-envelope (e.g., Podsiadlowski et al., 1992; Woosley et al., 1994). The progenitors of six Type IIb SNe have been identified in pre-explosion images: 1993J (Aldering et al., 1994), 2001ig (Ryder et al., 2006), 2008ax (Folatelli et al., 2015), 2011dh (Maund et al., 2011), 2013df (Van Dyk et al., 2014), and 2016gkg (Kilpatrick et al., 2017). Furthermore, there is evidence for the presence of binary companions to the progenitors of SNe 1993J and 2011dh (Fox et al., 2014; Folatelli et al., 2014). This makes Type IIb SNe ideal candidates to test theories of binary evolution.

SN 2016gkg was discovered on 2016 September 20.18 UT in NGC 613. Kilpatrick et al. (2017) identified a source in pre-explosion Hubble Space Telescope (HST) images as its progenitor and inferred its luminosity and effective temperature^{1}^{1}1Note that Tartaglia et al. (2017), using the same images, conclude they cannot confirm the source as the progenitor star..
Arcavi et al. (2017) fit analytic models to the light curve of SN 2016gkg and derived a radius and residual hydrogen-envelope mass for the progenitor star (see Table 1).

K | |||
---|---|---|---|

5.14 | 9500 | 40 – 150 | 0.02 – 0.4 |

References. – Kilpatrick, C. D., private communication (uncertainties are one-third of , see Section 2.2); Arcavi et al. (2017).

In this paper, given observational constraints on its progenitor properties, we use Bayesian inference to derive the distribution of properties of potential progenitor systems (both singles and binaries) of SN 2016gkg. We also calculate the probability that the progenitor was a binary. We assume that the constraints derived by Kilpatrick et al. (2017) corresponds to the progenitor. We discuss the effect of using the pre-SN progenitor hydrogen-envelope and helium-core mass constraints to distinguish between single and binary star progenitor channels.

## 2. Method

### 2.1. Single and Binary Star Models

We compute a large grid of non-rotating solar-metallicity^{2}^{2}2We choose the value of solar metallicity () to be 0.02. The metallicity of the host galaxy of SN 2016gkg is (Kilpatrick et al., 2017). The results presented here are strongly dependent on metallicity (see Yoon et al., 2017). The choice of solar metallicity was motivated by the goal of comparing our results with previous studies of Type IIb SN progenitors. single and binary star models with Modules for Experiments in Stellar Astrophysics (MESA^{3}^{3}3Release 9575., Paxton et al., 2011, 2013, 2015). We briefly summarize the models in what follows.

We start the evolution of the star(s) at the zero-age main sequence (ZAMS). We stop the evolution if any of the following conditions are met: the carbon mass fraction at (any) star’s center is lower than , the hydrogen-envelope mass of any star drops below (in which case we assume the system is completely stripped Type Ibc progenitor), or, in binaries, the accretor overfills its Roche-lobe. We assume the surface properties of the star at carbon depletion match those of the pre-supernova progenitor. This is because the thermal timescale of the envelope is large compared to the time between carbon depletion and iron core-collapse. Note however that it has recently been proposed that waves could efficiently transport energy outwards during core neon and oxygen burning, potentially producing outbursts and large changes in the progenitor surface luminosity and effective temperature months or years prior to the explosion (Quataert & Shiode, 2012; Shiode & Quataert, 2014; Fuller, 2017)

We use the basic.net, approx21.net, and co_burn .net nuclear networks in MESA. We adopt the standard mixing-length theory and the Ledoux criterion to model convection, with set to 1.5. When convective regions approach the Eddington limit, the efficiency of convection is enhanced (Paxton et al., 2013). To account for the nonzero momentum of a convective element at the Hydrogen burning convective core boundary, we extend this region by 0.335 of the pressure scale height (Brott et al., 2011). We adopt the value of dimensionless free parameter for semi-convection, , to be 1.0 (Yoon et al., 2006). We use radiative opacity tables from the OPAL project (Iglesias & Rogers, 1996). We adopt surface effective temperature and abundance dependent stellar wind prescriptions. When K, we adopt the prescription of Vink et al. (2001) if the surface hydrogen mass fraction 0.4 and Nugis & Lamers (2000) otherwise. If K we adopt the prescription of de Jager et al. (1988).

We use the model of Kolb & Ritter (1990) to calculate the mass transfer rate due to Roche-lobe overflow (RLO) in our binary star models. The efficiency of mass transfer (the ratio of mass accreted by the secondary to the mass transferred via RLO by the primary), , is assumed to be constant during the evolution. The mass not accreted is assumed to be lost as stellar winds. Stellar winds carry away with them the specific angular momentum of the corresponding component. All orbits are assumed to be circular.

We compute single-star models with = 1.28 – 1.40 ( 19 – 25) in intervals of 0.0005 dex and binary star models with initial primary mass = 1.0 – 1.4 ( 10 – 25) in intervals of 0.02 dex, initial mass ratio, = 0.225 – 0.975 in intervals of 0.05, and initial orbital period d = 2.5 – 3.8 (d 316 – 6310) in intervals of 0.02 dex. We compute the models for = 0.5 and 0.1. We choose this parameter space based on a broader scan. Models that reach core carbon exhaustion () with at least of residual hydrogen-envelope are defined as Type IIb SN progenitors (Groh et al., 2013).

### 2.2. Statistical Method

We use Bayesian inference to derive the distribution of the potential progenitors (and their binary companions) of SN 2016gkg. We adopt luminosity and effective temperature constraints on the progenitor as derived from observations of the progenitor system before explosion (Kilpatrick, C. D., private communication). We assume that luminosity and effective temperature are independent variables for simplicity, though this assumption is not accurate. We do not apply the progenitor hydrogen-envelope mass and radius constraints derived from the SN light-curves as these are model-dependent. However, we discuss the implications of applying them when appropriate.

For each Type IIb SN progenitor model (see above for definition) we calculate an unnormalized posterior probability ():

(1) |

where, is the vector of observed luminosity and effective temperature of the progenitor of SN 2016gkg, is the vector of luminosity and effective temperature of the model progenitor, and is the vector of model parameters. We assume that

(2) |

for , where is the vector of spacing in the parameter space scan for .

We adopt the split normal distribution^{4}^{4}4, = when and = when . for and one-third of the constraints on the progenitor luminosity and effective temperature as (Kilpatrick, C. D., private communication) constraints (Table 1).
The prior probability is computed for the range . For a single-star with initial mass, ,:

(3) |

and for a stellar binary with initial primary mass, , initial mass ratio, , and initial orbital period, ,:

(4) |

where, is the fraction of stars in binaries.

We assume to be a constant and independent of , , and . The distribution of is taken to be the Salpeter Initial Mass Function (Salpeter, 1955)

(5) |

We assume that the minimum ZAMS mass needed to undergo core-collapse is (Woosley et al., 2002). We adopt a power-law distribution for the initial mass ratio, ,

(6) |

This distribution is assumed to be followed for (Kobulnicky et al., 2014). Finally, the distribution of initial orbital period, , is chosen according to Kobulnicky et al. (2014)

(7) |

This distribution is assumed to hold^{5}^{5}5The upper limit for the validity of this distribution if 2000 days (Kobulnicky et al., 2014). However, due to poor constraints for wide binaries we assume that this distribution holds upto 10,000 days. for d.

## 3. Results

We compute posterior probabilities for SN 2016gkg using our model Type IIb SN progenitors (see Section 2.1 for definition) using the method described above. Unless otherwise mentioned, we assume , (Salpeter, 1955), = -1, and (Kobulnicky et al., 2014).

Some binary star models experience very little interaction, transferring only small amounts of mass when the atmosphere Roche-lobe overflows. Therefore their evolution largely resembles that of single stars. We therefore require that primaries transfer at least 1% of their initial mass in RLO to qualify as a ‘binary’ progenitors. The exact choice for this number does not affect our results significantly; lowering it by an order of magnitude adds some mass binaries with net posterior probabilities 3% more for our fiducial priors.

In figure 1 we show the distribution of the parameter space of potential single and binary star progenitors of SN 2016gkg. There are three peaks in the distribution of initial primary mass for binary star progenitors. The first is favored by the prior on initial primary mass (Eq. 5), the second is due to the likelihood for , and the third results from mildly interacting binaries with relatively undisturbed primaries whose evolution largely resembles their single-star counterparts. There are fewer binary star progenitors with , , and d as they experience unstable mass transfer or evolve into contact, which lead to a merger.

In figure 2 we show the distribution of pre-SN properties of potential single and binary star progenitors of SN 2016gkg. The three peaks in the distributions of initial primary mass (Figure 1) of binary star progenitors roughly translates to the distributions of pre-SN hydrogen-envelope and helium-core mass. Pre-SN hydrogen-envelope and helium-core mass for potential binary star progenitors are clearly smaller than for potential single-star progenitors typically by and , respectively. Therefore, these can be used to distinguish progenitor scenarios. While progenitor helium-core mass constraints are currently unavailable for SN 2016gkg, their existence could increase the likelihood of a binary progenitor of SN 2016gkg significantly by ruling out several single-star progenitors (see below for a discussion on rates). The distribution of all binary star properties shown in Figures 1 and 2 remain roughly the same regardless of whether or not we apply the progenitor hydrogen-envelope mass and radius constraints.

In figure 3 we show the distribution of locations on the Hertzsprung-Russell (H-R) diagram of potential single and binary star progenitors of SN 2016gkg. The luminosities of binary progenitors are smaller than of single-star progenitors. This is a consequence of smaller pre-SN helium-core masses for binary progenitors (see Figure 2). The secondaries of binary progenitors mostly lie on the main-sequence and are less luminous than their primaries. Some binary progenitors with initial mass ratios have evolved secondaries that are on the RGB. We note that no strong constraints can be placed on the companion’s location the H-R diagram.

X-ray/radio observations can be used to infer the CSM density around SN progenitors and thus trace the mass loss history of the progenitor star. We use our models to infer the CM density at cm to compare with results of Margutti et al. (2017) (example Figure 6). Our models have a SN Ibc-like mass loss history: km s and yr. This is because most of the potential binary progenitors detach before core-collapse. If future measurements indicate than SN 2016gkg also experienced high mass loss rates ( yr) as those for other Type IIb SNe in the aforementioned study, then it would indicate that the progenitor experienced a period of enhanced mass-loss just before explosion.

Finally, we compute the probability that the progenitor of SN 2016gkg was a binary: the total posterior probability of all model binary star progenitors divided by total posterior probability of all model single and binary star progenitors. In Table 2 we list probabilities of a binary star progenitor of SN 2016gkg not applying and applying progenitor hydrogen-envelope mass and radius constraints, for and various values of , , and . We find that the probability of a binary star progenitor of SN 2016gkg with = 0.1 and 0.5 not-given (given) progenitor hydrogen-envelope mass and radius constraints is 25% (48%) and 15% (32%), respectively, for our fiducial values of (2.3), (-1.0), and (-0.22).

## 4. Conclusions

We use Bayesian inference and a large grid of single and binary star models to derive the distributions of potential progenitors and companions of SN 2016gkg. We find that potential binary star progenitors have lower initial primary mass and pre-SN hydrogen-envelope and helium-core mass than single-star progenitors. The probability that the progenitor of SN 2016gkg was a binary with = 0.1 (0.5) is 25% (15%) if we only use luminosity and effective temperature constraints on the progenitor star. Applying observational constraints on the progenitor hydrogen-envelope mass and radius rule out several single-star progenitors, favoring a binary as the progenitor of SN 2016gkg (48% for = 0.1 and 32% for = 0.5). In either case, there is no clear preference for a binary star progenitor for SN 2016gkg. Constraints on the progenitor helium-core mass can help tighten constraints on the progenitor. Similarly, improved constraints on the progenitor luminosity can significantly narrow the parameter space for progenitors. We would like to stress that the parameter space for Type IIb SN progenitors is strongly dependent on the progenitor metallicity. At lower metallicities, the parameter space for binary progenitors of Type IIb SNe widens significantly (Yoon et al., 2017). We expect that the results presented here will differ strongly at low metallicities. This would be an interesting line of investigation in the future.

-2.0 | 0.00 | 0.16 | 0.10 | 0.34 | 0.22 | |

-0.22 | 0.14 | 0.08 | 0.31 | 0.19 | ||

1.6 | -1.0 | 0.00 | 0.23 | 0.14 | 0.45 | 0.29 |

-0.22 | 0.20 | 0.12 | 0.41 | 0.26 | ||

0.0 | 0.00 | 0.30 | 0.18 | 0.54 | 0.35 | |

-0.22 | 0.27 | 0.15 | 0.50 | 0.31 | ||

-2.0 | 0.00 | 0.20 | 0.12 | 0.41 | 0.27 | |

-0.22 | 0.17 | 0.11 | 0.37 | 0.24 | ||

2.3 | -1.0 | 0.00 | 0.28 | 0.17 | 0.52 | 0.35 |

-0.22 | 0.25 | 0.15 | 0.48 | 0.32 | ||

0.0 | 0.00 | 0.36 | 0.22 | 0.60 | 0.41 | |

-0.22 | 0.32 | 0.19 | 0.57 | 0.37 | ||

-2.0 | 0.00 | 0.25 | 0.16 | 0.48 | 0.33 | |

-0.22 | 0.22 | 0.14 | 0.44 | 0.30 | ||

3.0 | -1.0 | 0.00 | 0.34 | 0.22 | 0.59 | 0.42 |

-0.22 | 0.31 | 0.19 | 0.55 | 0.38 | ||

0.0 | 0.00 | 0.42 | 0.27 | 0.67 | 0.48 | |

-0.22 | 0.38 | 0.23 | 0.63 | 0.44 |

Note. – , and , , and are parameters for the priors on the initial mass, , initial mass ratio, , and initial orbital period, , respectively (see Eqs. 5, 6, and 7).

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