Progenitors of Type IIb Supernovae. I. Evolutionary Pathways and Rates

We compute solar-metallicity single-star models with initial mass, ${\mathrm{log}}_{10}$(M_ZAMS/M_⊙) = 1.2–1.5 (M_ZAMS/M_⊙ ≃ 16–31.5) in intervals of 0.0005 dex.

We compute solar-metallicity binary-star models with initial primary mass, ${\mathrm{log}}_{10}({M}_{\mathrm{ZAMS},1}/{M}_{\odot })$ = 1.0–1.4 (M_ZAMS,1/M_⊙ ≃ 10–25) in intervals of 0.02 dex, initial mass ratio, q_ZAMS ≡ M_ZAMS,2/M_ZAMS,1 = 0.225–0.975 in intervals of 0.05, and initial orbital period, ${\mathrm{log}}_{10}({P}_{\mathrm{orb},\mathrm{ZAMS}}/$day) = 2.5–3.8 (P_orb,ZAMS/day ≃ 316–6310) in intervals of 0.02 dex. We only consider case B or later mass transfer (i.e., mass transfer after core hydrogen exhaustion) in this work; a systematic investigation of case A mass transfer (i.e., mass transfer before core hydrogen exhaustion) toward SNe IIb is beyond the scope of this paper and would be an interesting line of future investigation. As a result, the upper limit on the initial primary mass is set to the mass of the most massive single-star model that is stripped by its own stellar winds (M_ZAMS = 25.6M_⊙), since case B or later mass transfer will only result in additional mass loss as the core is already established in these models. We compute the models for  = 1.0 (fully conservative mass transfer), 0.5, 0.1, and 0.01.

Models with  = 0.5 and 0.1 are the same as those analyzed in Sravan et al. (2018), where we show that they successfully reproduce the observed properties of the progenitor of SN 2016gkg derived from pre-explosion photometry and its light curve.

We compute low-metallicity single-star models with initial mass, ${\mathrm{log}}_{10}({M}_{\mathrm{ZAMS}}/{M}_{\odot })$ = 1.4–1.7 (M_ZAMS/M_⊙ ≃ 25–50) in intervals of 0.0005 dex. Within this mass range, only models with initial masses >40M_⊙ lose enough of their hydrogen envelopes to qualify as SN IIb progenitors, but at low metallicities, these are expected to directly collapse into black holes rather than explode as SNe (Heger et al. 2003).

We compute low-metallicity binary-star models with the same initial primary masses and initial mass ratios as at solar. However, we compute a broader range in initial orbital period than at solar metallicity, ${\mathrm{log}}_{10}$(P_orb,ZAMS/day) = 1.0–3.7 (P_orb,ZAMS/day ≃ 10–5012, because of the wider parameter space that leads to SNe IIb at low metallicity. In addition, we use coarse (0.1 dex) and fine (0.02 dex) intervals for initial orbital periods below and above ${\mathrm{log}}_{10}({P}_{\mathrm{orb},\mathrm{ZAMS}}/$day) = 2.7 (P_orb,ZAMS ≃ 501 days), respectively, to reduce computational demand for modeling short orbital period binaries (experiencing early case B mass transfer) while adequately resolving long orbital period binaries (experiencing late case B and case C mass transfer). As for solar metallicity, our coverage of the range in orbital periods does not capture case A mass transfer. We limit the initial primary mass to M_ZAMS,1 ≃ 25M_⊙, even though our single-star models at low metallicity retain large envelopes at this mass and can potentially lead to SNe IIb after mass transfer, to reduce computational demand. In addition, we show in Section 5 that potential SN IIb progenitors with M_ZAMS,1 ≳ 25M_⊙ are relatively very few and do not affect our inference for SN IIb progenitors significantly. We compute all of the aforementioned low-metallicity models for  = 0.5 and 0.1. We do not use  = 1.0 and 0.01, because, as we show in Section 4, the parameter spaces at  = 0.01 and 0.1 are quite similar and the parameter space at  = 1.0 is quite small at solar metallicity. In addition, mass transfer is expected to be nonconservative due to rapid spin-up of the secondary to critical rotation during mass transfer (Packet 1981; Petrovic et al. 2005; Ritchie et al. 2012, also see Popham & Narayan 1991 for a counter argument).

We introduce a couple of definitions to aid our discussion of SN IIb progenitors.

First, we define which pre-CC models are interpreted as SN IIb progenitors. The connection between the pre-SN progenitor structure and the explosion's spectroscopic properties is a subject of ongoing investigation (e.g., Dessart et al. 2018). Therefore, here we adopt a conservative criterion using the pre-SN hydrogen-envelope mass to define an SN IIb progenitor. Specifically, models with primaries that reach CC with residual hydrogen-envelope mass⁶ 0.01M_⊙ ≤ M_{H env,preSN(,1)} ≤ 1M_⊙ are defined as SN IIb progenitors. This is our "fiducial SN IIb progenitor definition."

Our adopted definition was chosen to be a conservative one. Inferred hydrogen-envelope masses for SNe IIb with detected progenitors are ≲0.5M_⊙ (Woosley et al. 1994; Houck & Fransson 1996; Bersten et al. 2012; Morales-Garoffolo et al. 2014; Arcavi et al. 2017; Bersten et al. 2018). These SNe IIb represent those with the most massive, and thus most extended (Yoon et al. 2017), envelopes, as more compact progenitors would be harder to detect. In addition, the inferred hydrogen-envelope masses from a larger population SNe IIb are also <0.5M_⊙ (Bufano et al. 2014; Morales-Garoffolo et al. 2015; Fremling et al. 2019).

We also test the effect of changing the "fiducial definition" of SN IIb progenitors in later sections by applying a tighter cut on the residual hydrogen-envelope mass (0.01M_⊙ ≤ M_{H env,preSN(,1)} ≤ 0.5M_⊙) and the helium core mass (2M_⊙ ≤ M_{He core,preSN(,1)} ≤ 6M_⊙; Nomoto et al. 1993; Woosley et al. 1994; Morales-Garoffolo et al. 2014; Ergon et al. 2014, 2015; Folatelli et al. 2015). These constraints are motivated by values derived for SNe IIb with detected progenitors, computed by analyzing their light curves numerically (using hydrodynamical models), analytically or semi-analytically.

Second, in addition to the case C binaries defined earlier, we introduce a further distinction between binaries experiencing case B mass transfer:

• 1.  
  Case early-B (EB): models initiating mass transfer while the primary is crossing the Hertzsprung Gap (HG)⁷ : the time between exhausting hydrogen in its core and the start of its rise on the giant branch
• 2.  
  Case late-B (LB): models initiating mass transfer after the primary begins its rise on the giant branch but before it exhausts helium in its core

Once again, case C binaries are those where the primary initiates mass transfer after core helium exhaustion.

Figure 1 shows H–R tracks for single stars at solar and low metallicity. It demonstrates two well-understood phenomena related to producing single stripped stars. First, increasing ZAMS mass drives stronger winds and results in more stripped progenitors. Second, lowering metallicity drives weaker winds and results in less stripped progenitors.

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Our single-star solar-metallicity models transition from SN II to SN IIb at ZAMS mass of 22M_⊙, then to SN Ibc at ZAMS mass of 26M_⊙ (see definitions in Sections 2 and 2.3). In Figure 1, the 23 M_⊙ model is an SN IIb progenitor. At low metallicity, none of our models lose enough of their envelope to explode as SE SNe. We emphasize that the mass range leading to a given SN type at any metallicity is strongly dependent on the wind mass-loss prescription used and these are known to be quite uncertain (see also discussion in Section 6.2).

Figure 2 shows typical evolutionary pathways via case EB, LB, and C mass transfer to SNe IIb at low metallicity. These channels also exist at solar metallicity; however, case EB mass transfer channels are strongly suppressed, as in several cases stronger winds remove the remaining hydrogen envelope after detachment (Yoon et al. 2017). Case C mass transfer is only possible for a narrow range in initial primary mass (see also Section 4). This is because only lower primary masses can expand significantly after core helium exhaustion. Despite their rarity, case C SNe IIb warrant discussion because they have the attractive property of having recently undergone or still undergoing mass transfer at CC. Recent studies indicate that many SNe IIb experience strong mass loss close to CC (e.g., Kamble et al. 2016). This channel was also initially suggested as the likely progenitor of the prototypical SN IIb: 1993J (Podsiadlowski et al. 1993; Maund et al. 2004).

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Many of these channels were first discussed for solar-metallicity models by Claeys et al. (2011). However, unlike this work, Claeys et al. (2011) also found channels to SNe IIb via case A and EB mass transfer.⁸ The difference in outcomes is largely due to the adopted wind mass-loss prescription. Claeys et al. (2011) adopted the prescription of de Jager et al. (1988) during the entire stellar evolution, which is about two orders of magnitude lower than our WR mass-loss prescription of Nugis & Lamers (2000) and drives most of the stripping in our case. More recently, Yoon et al. (2017) extended the analysis for SN IIb progenitors to low metallicity. They found a significant difference in the availability of case EB mass transfer channels toward SNe IIb between solar and low metallicities. Specifically, though after the mass transfer phase primary stars at both metallicities detach with similar amounts of hydrogen envelope, strong winds at high metallicity strip many of them before CC. This results in a sharp narrowing of the parameter space for binary SNe IIb at solar metallicity as case EB binaries span ∼2 orders of magnitude in initial orbital period. We show the full parameter space of binary SNe IIb as a function of metallicity (including mass transfer efficiency and mass ratio) in Section 4 and quantify the effect of the above mentioned phenomenon on theoretical SN IIb rates in Section 5.

Our parameter space coverage allows us to investigate the effect of mass ratio and mass transfer efficiency on binary SN IIb channels at both solar and low metallicities. We find that the viability of all three channels mentioned above (case EB, LB, and C) increases with increasing initial mass ratio and decreasing mass transfer efficiency. We find that mass transfer efficiency plays an important role for the viability of case EB SNe IIb. The left and right panels of Figure 3 show the difference in evolution when mass transfer begins early and late on the HG for different values. The primary in these models initiates mass transfer on its thermal timescale, which is shorter later on the HG (Wellstein et al. 2001). In late EB mass transfer scenarios (right panels), if is high enough that accretion occurs significantly faster than the thermal timescale of the secondary, then the binary will enter contact. Given the wide parameter space spanned by case EB binaries, this phenomenon has an important secondary effect on the parameter space and rates for SNe IIb.

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At solar metallicity, single stars with initial mass ${\mathrm{log}}_{10}({M}_{\mathrm{ZAMS}}/{M}_{\odot })$ = 1.3445–1.409 (M_ZAMS/M_⊙ ≃ 22–26) are SNe IIb progenitors according to our fiducial definition (primaries that reach CC with residual hydrogen-envelope mass 0.01M_⊙ ≤ M_{H env,preSN(,1)} ≤ 1M_⊙). At low metallicity, our most massive model (M_ZAMS ≃ 50M_⊙) barely gets stripped enough to be labeled an SN IIb progenitor. However, we expect that stars as massive as these (helium core masses ≳26M_⊙) will not experience successful explosions but will instead collapse directly into black holes (Fryer 1999). We adopt this assumption for the remainder of this work.

We also explore the effect of adopting different criteria for defining SN IIb progenitors as the mapping between progenitor structure and ensuing SN spectra is not clear. Adopting the cut 0.01M_⊙ ≤ M_{H env,preSN(,1)} ≤ 0.5M_⊙ for defining SN IIb progenitors, only models with M_ZAMS ≃ 23–25.5 M_⊙ at solar metallicity qualify as SN IIb progenitors. Applying the 2M_⊙ ≤ M_{He core,preSN(,1)} ≤ 6M_⊙ cut qualifies no single stars, either at solar or low metallicity, as SN IIb progenitors: M_{He core,preSN(,1)} = 9.5M_⊙for the least massive SN IIb progenitor (using our fiducial definition) at solar metallicity. This fact has been noted several times in the literature to motivate the need for additional mass-loss mechanisms (including binary interactions) to create SN IIb progenitors at lower ZAMS masses (e.g., Lyman et al. 2016; Prentice et al. 2019).

Claeys et al. (2011) found single SN IIb progenitors with ZAMS masses ∼33M_⊙. This is again due to the difference in adopted wind mass-loss prescription, where their formulation is two orders of magnitude lower than ours. Lowering wind mass-loss rates increases the minimum ZAMS mass that produces SNe IIb.

Figures 4 and 5 show the parameter space for binary SN IIb progenitors using our fiducial definition (primaries that reach CC with residual hydrogen-envelope mass $0.01{M}_{\odot }\leqslant {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}\leqslant 1{M}_{\odot }$) at solar and low metallicity, respectively.

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Case LB mass transfer toward SNe IIb are the dominant production scenarios at solar metallicity. However, case C mass transfer channels, though observationally interesting, have not previously been discussed in the context of a parameter space analysis. As expected, case C SNe IIb are limited to lower initial primary masses and arise from a small range in initial orbital periods that shrinks with increasing initial primary mass. Case C SNe IIb are also favored for lower initial mass ratios (q_ZAMS ≲ 0.65).

The parameter space for binary SNe IIb increases dramatically with decreasing metallicity. This is due to channels to SNe IIb via case EB mass transfer that are only viable at low metallicity (see Section 3). Due to the large change in primary radius that occurs when crossing the HG, the range of initial orbital periods that permit mass transfer during this phase is very large. The difference in parameter space due to metallicity has a primary dominant effect on theoretically computed SN IIb rates (see Section 5).

Once again, we explore the effect of adopting different criteria for defining SN IIb progenitors. For example, the SN IIb parameter space with q_ZAMS ≲ 0.4 is almost entirely progenitors with M_{H env,preSN(,1)} ≤ 0.5M_⊙ at both metallicities. Case EB SNe IIb also dominantly have M_{H env,preSN(,1)} ≤ 0.5M_⊙. Applying the cut 2M_⊙ ≤ M_{He core,preSN(,1)} ≤ 6M_⊙, effectively excludes the parameter space above M_ZAMS,1 ≃ 16 M_⊙ at both metallicities. This is because the core is already established before the onset of interaction in the binary models considered in this work (see Section 2.1).

Finally, while it is difficult to directly compare our results to those of Claeys et al. (2011) and Yoon et al. (2017) due to differences in modeled binary parameters, definitions for SNe IIb progenitors, and adopted physics in stellar modeling, there is broad agreement with respect to all of the above results.

4.2.1. Effect of Mass Transfer Efficiency

Mass transfer efficiency plays an important role in shaping the parameter space toward SNe IIb, especially at low metallicity. The gap in the parameter space between ${\mathrm{log}}_{10}({P}_{\mathrm{orb},\mathrm{ZAMS}}/$day) ≃ 1.5 (2)–3 at low metallicity when  = 0.5 in Figure 5 is due to the occurrence of contact in these binaries (see Section 3 and Figure 3 for details). In other words, low-metallicity EB SN IIb are favored at lower . Also, overall, the parameter space for SNe IIb decreases with increasing at both metallicities. This is because of increasing likelihood of contact in the binaries when the secondary is unable to thermally relax with its acquired mass at higher (Braun & Langer 1995) and the decreasing stabilizing effect of orbit widening (from loss of angular momentum) due to inefficient mass transfer.

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Interestingly, for the subset of high initial mass ratio (q_ZAMS = 0.975) EB SNe IIb at low metallicity, higher has the opposite effect, i.e., it helps avoid contact. Specifically, in models with  = 0.1, the secondary accretes relatively small amounts of mass when it is close to the terminal main sequence, with a negligible effect on its evolution, and expands as it leaves the main sequence and enters contact while on the HG. However, in models with  = 0.5, the secondary accretes enough mass to rejuvenate as a main-sequence star, allowing the primary to evolve to CC while the secondary is still on the main sequence. This phenomenon results in the absence of several case EB SNe IIb in the topmost-right panel of Figure 5, as compared to the topmost-left panel of the same figure.

Notably, whether binaries with  = 1.0 and high mass ratios (q_ZAMS ≳ 0.7) at high metallicity are able to avoid contact depends sensitively on their evolutionary history, which dictates whether convective mixing in the secondary is able to carry the accreted material to the core, allowing them to rejuvenate and contract. Specifically, rejuvenation occurs over a series of discrete events where the convective core grows in mass and merges with an outer convection zone. The discrete nature of this process leads to non-monotonic behavior in terms of the initial parameters, resulting in the patchy distribution that can be seen in the panel for q_ZAMS = 0.725 and  = 1.0 in Figure 4.

We note that the SN IIb parameter space for  = 0.1 and 0.01 at solar metallicity is quite similar.

4.2.2. Effect of Mass Ratio

Table 2 summarizes our results for SNe IIb relative rates. Tables 3 and 4 list single- and binary-star (with  = 0.5 and 0.1) SN IIb rates at solar and low metallicity, respectively, for all values for f_bin, α, β, and γ and four definitions for SN IIb progenitors (see Section 3), namely

• 1.  
  $0.01{M}_{\odot }\leqslant {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}\leqslant 1{M}_{\odot }$ ("fiducial definition"),
• 2.  
  $0.01{M}_{\odot }\leqslant {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}\leqslant 0.5{M}_{\odot }$,
• 3.  
  $0.01{M}_{\odot }\leqslant {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}\leqslant 1{M}_{\odot }$ and $2{M}_{\odot }\leqslant {M}_{\mathrm{He}\mathrm{core},\mathrm{preSN}(,1)}\leqslant 6{M}_{\odot }$, and
• 4.  
  $0.01{M}_{\odot }\leqslant {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}\leqslant 0.5{M}_{\odot }$ and $2{M}_{\odot }\leqslant {M}_{\mathrm{He}\mathrm{core},\mathrm{preSN}(,1)}\leqslant 6{M}_{\odot }$.

Values shown in the tables correspond to lower limits on SN IIb rates, where we assume that all secondaries explode as SNe of a different type. The upper limit on SN IIb rates, assuming that none of the secondaries explode as SNe, can be obtained by multiplying the rates by (1 + f_bin).

Table 2.  Theoretical vs. Observationally Inferred SN IIb Relative Rates

	Theoretical (This Paper)				Observational
Metallicity	Single	Binary		Single+binary	Li et al. (2011)	Smith et al. (2011)	Graur et al. (2017)
high (Z⊙)	0–3.6	0.1–2.2		0.1–4.1	${11.9}_{-3.6}^{+3.9}$	${10.6}_{-3.1}^{+3.6}$	${10}_{-3}^{+3}$
		= 0.5	= 0.1
		0.1–1.2	0.1–2.2
low (Z⊙/4)	0	0.4–15		0.5–15	⋯	⋯	${19}_{-10}^{+15}$
		= 0.5	= 0.1
		0.4–4.7	2–15

Notes.

(1) SN IIb relative rate is defined as the percentage of SNe IIb out of all CC SNe.

(2) Low-metallicity rates are lower limits (see the text).

(3) We quote rates from Graur et al. (2017) using their cut of 3 × 10⁹M_⊙ on SN host galaxy stellar mass, as this cut separates galaxies below and above mass of the LMC.

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Table 3.  SN IIb Relative Rates at Solar Metallicity

				MHe core ≥ 0M⊙						2M⊙ ≤ MHe core ≤ 6M⊙
				MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙			MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙
fbin	α	β	γ	single	binary		single	binary		single	binary		single	binary
					= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1
		−1.0	0.0	2.8	0.14	0.21	1.9	0.11	0.16	0.0	0.12	0.17	0.0	0.08	0.13
	1.6		−0.22	2.8	0.12	0.18	1.9	0.09	0.14	0.0	0.1	0.14	0.0	0.07	0.11
		0.0	0.0	2.8	0.2	0.33	1.9	0.14	0.26	0.0	0.16	0.26	0.0	0.1	0.2
			−0.22	2.8	0.17	0.28	1.9	0.12	0.22	0.0	0.13	0.22	0.0	0.09	0.17
		−1.0	0.0	2.8	0.22	0.31	1.9	0.16	0.24	0.0	0.18	0.26	0.0	0.13	0.2
0.25	2.3		−0.22	2.8	0.18	0.27	1.9	0.13	0.21	0.0	0.15	0.23	0.0	0.11	0.17
		0.0	0.0	2.8	0.29	0.49	1.9	0.2	0.38	0.0	0.24	0.41	0.0	0.16	0.31
			−0.22	2.8	0.25	0.42	1.9	0.17	0.32	0.0	0.2	0.35	0.0	0.13	0.27
		−1.0	0.0	2.0	0.23	0.34	1.3	0.17	0.26	0.0	0.21	0.3	0.0	0.14	0.22
	3.0		−0.22	2.0	0.2	0.29	1.3	0.14	0.22	0.0	0.17	0.26	0.0	0.12	0.19
		0.0	0.0	2.0	0.32	0.53	1.3	0.22	0.41	0.0	0.27	0.46	0.0	0.18	0.35
			−0.22	2.0	0.27	0.46	1.3	0.18	0.35	0.0	0.23	0.4	0.0	0.15	0.3
		−1.0	0.0	1.6	0.24	0.35	1.1	0.18	0.27	0.0	0.2	0.28	0.0	0.14	0.21
	1.6		−0.22	1.6	0.2	0.3	1.1	0.15	0.23	0.0	0.17	0.24	0.0	0.12	0.18
		0.0	0.0	1.6	0.33	0.55	1.1	0.24	0.43	0.0	0.26	0.44	0.0	0.17	0.33
			−0.22	1.6	0.28	0.47	1.1	0.2	0.37	0.0	0.22	0.37	0.0	0.15	0.29
		−1.0	0.0	1.6	0.36	0.52	1.0	0.26	0.4	0.0	0.3	0.44	0.0	0.21	0.33
0.50	2.3		−0.22	1.6	0.3	0.45	1.0	0.22	0.34	0.0	0.26	0.38	0.0	0.18	0.28
		0.0	0.0	1.6	0.49	0.81	1.0	0.34	0.63	0.0	0.4	0.68	0.0	0.26	0.51
			−0.22	1.6	0.41	0.7	1.0	0.29	0.54	0.0	0.34	0.59	0.0	0.22	0.44
		−1.0	0.0	1.1	0.39	0.57	0.74	0.28	0.43	0.0	0.34	0.5	0.0	0.24	0.37
	3.0		−0.22	1.1	0.33	0.49	0.74	0.24	0.37	0.0	0.29	0.43	0.0	0.2	0.32
		0.0	0.0	1.1	0.53	0.89	0.74	0.36	0.68	0.0	0.45	0.77	0.0	0.29	0.58
			−0.22	1.1	0.45	0.76	0.74	0.31	0.59	0.0	0.38	0.67	0.0	0.25	0.5
		−1.0	0.0	1.0	0.29	0.41	0.68	0.21	0.32	0.0	0.23	0.33	0.0	0.16	0.25
	1.6		−0.22	1.0	0.24	0.35	0.68	0.18	0.28	0.0	0.2	0.28	0.0	0.14	0.21
		0.0	0.0	1.0	0.39	0.64	0.68	0.28	0.5	0.0	0.31	0.51	0.0	0.2	0.39
			−0.22	1.0	0.33	0.55	0.68	0.24	0.43	0.0	0.26	0.44	0.0	0.17	0.34
		−1.0	0.0	1.0	0.42	0.62	0.66	0.31	0.47	0.0	0.36	0.52	0.0	0.25	0.39
0.65	2.3		−0.22	1.0	0.36	0.53	0.66	0.26	0.41	0.0	0.3	0.44	0.0	0.22	0.33
		0.0	0.0	1.0	0.58	0.96	0.66	0.4	0.74	0.0	0.47	0.81	0.0	0.31	0.61
			−0.22	1.0	0.49	0.83	0.66	0.34	0.64	0.0	0.4	0.69	0.0	0.27	0.52
		−1.0	0.0	0.72	0.46	0.67	0.47	0.33	0.51	0.0	0.4	0.59	0.0	0.28	0.43
	3.0		−0.22	0.72	0.39	0.58	0.47	0.28	0.44	0.0	0.34	0.5	0.0	0.24	0.38
		0.0	0.0	0.72	0.62	1.1	0.47	0.43	0.8	0.0	0.53	0.91	0.0	0.35	0.69
			−0.22	0.72	0.53	0.9	0.47	0.36	0.69	0.0	0.45	0.79	0.0	0.29	0.59
		−1.0	0.0	0.53	0.32	0.47	0.36	0.24	0.36	0.0	0.26	0.37	0.0	0.19	0.28
	1.6		−0.22	0.53	0.27	0.4	0.36	0.2	0.31	0.0	0.22	0.32	0.0	0.16	0.24
		0.0	0.0	0.53	0.44	0.73	0.36	0.31	0.57	0.0	0.34	0.58	0.0	0.23	0.44
			−0.22	0.53	0.37	0.62	0.36	0.27	0.49	0.0	0.29	0.5	0.0	0.2	0.38
		−1.0	0.0	0.52	0.48	0.69	0.35	0.35	0.53	0.0	0.41	0.58	0.0	0.29	0.44
0.80	2.3		−0.22	0.52	0.41	0.59	0.35	0.3	0.46	0.0	0.34	0.5	0.0	0.24	0.38
		0.0	0.0	0.52	0.65	1.1	0.35	0.45	0.84	0.0	0.53	0.91	0.0	0.35	0.69
			−0.22	0.52	0.55	0.93	0.35	0.39	0.72	0.0	0.45	0.78	0.0	0.3	0.59
		−1.0	0.0	0.38	0.52	0.76	0.25	0.38	0.58	0.0	0.46	0.66	0.0	0.32	0.49
	3.0		−0.22	0.38	0.44	0.65	0.25	0.32	0.5	0.0	0.39	0.57	0.0	0.27	0.42
		0.0	0.0	0.38	0.7	1.2	0.25	0.48	0.91	0.0	0.6	1.0	0.0	0.39	0.77
			−0.22	0.38	0.59	1.0	0.25	0.41	0.78	0.0	0.51	0.89	0.0	0.33	0.67

Note. f_bin is fraction of binary systems, and α, β, and γ are parameters for the priors on the initial mass, ${\mathrm{log}}_{10}{M}_{\mathrm{ZAMS}}$, initial mass ratio, q_ZAMS, and initial orbital period, P_orb, respectively (see Equations (1), (2), and (3)). SN IIb rate is defined as fraction of SNe IIb versus all CC SNe percent.

(1) ${M}_{\mathrm{He}\mathrm{core}}\equiv {M}_{\mathrm{He}\mathrm{core},\mathrm{preSN}(,1)}$: Residual hydrogen-envelope mass in the progenitor at CC.

(2) ${M}_{{\rm{H}}\mathrm{env}}\equiv {M}_{{\rm{H}}\mathrm{env},\mathrm{preSN}(,1)}$ : Helium core mass of the progenitor at CC.

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Table 4.  SN IIb Relative Rates at Low Metallicity

				MHe core ≥ 0M⊙						2M⊙ ≤ MHe core ≤ 6M⊙
				MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙			MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙
fbin	α	β	γ	single	binary		single	binary		single	binary		single	binary
					= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1
		−1.0	0.0	0.0	0.65	2.7	0.0	0.54	2.5	0.0	0.51	2.1	0.0	0.46	2.0
	1.6		−0.22	0.0	0.64	2.5	0.0	0.54	2.4	0.0	0.51	2.1	0.0	0.48	2.0
		0.0	0.0	0.0	1.0	3.4	0.0	0.89	3.2	0.0	0.83	2.7	0.0	0.76	2.6
			−0.22	0.0	1.0	3.3	0.0	0.91	3.1	0.0	0.83	2.6	0.0	0.78	2.5
		−1.0	0.0	0.0	0.71	2.9	0.0	0.6	2.7	0.0	0.59	2.4	0.0	0.54	2.3
0.25	2.3		−0.22	0.0	0.71	2.8	0.0	0.62	2.6	0.0	0.59	2.3	0.0	0.55	2.2
		0.0	0.0	0.0	1.1	3.7	0.0	1.0	3.4	0.0	0.96	3.1	0.0	0.9	2.9
			−0.22	0.0	1.1	3.6	0.0	1.0	3.3	0.0	0.97	3.0	0.0	0.91	2.8
		−1.0	0.0	0.0	0.73	2.9	0.0	0.64	2.7	0.0	0.64	2.5	0.0	0.58	2.4
	3.0		−0.22	0.0	0.73	2.8	0.0	0.65	2.7	0.0	0.64	2.5	0.0	0.59	2.4
		0.0	0.0	0.0	1.2	3.7	0.0	1.1	3.5	0.0	1.0	3.2	0.0	0.97	3.0
			−0.22	0.0	1.2	3.6	0.0	1.1	3.4	0.0	1.0	3.1	0.0	0.99	3.0
		−1.0	0.0	0.0	1.1	4.4	0.0	0.91	4.1	0.0	0.84	3.6	0.0	0.78	3.4
	1.6		−0.22	0.0	1.1	4.3	0.0	0.91	4.0	0.0	0.86	3.5	0.0	0.8	3.3
		0.0	0.0	0.0	1.7	5.7	0.0	1.5	5.3	0.0	1.4	4.5	0.0	1.3	4.3
			−0.22	0.0	1.7	5.5	0.0	1.5	5.1	0.0	1.4	4.4	0.0	1.3	4.2
		−1.0	0.0	0.0	1.2	4.8	0.0	1.0	4.5	0.0	0.98	4.0	0.0	0.9	3.8
0.50	2.3		−0.22	0.0	1.2	4.6	0.0	1.0	4.4	0.0	0.99	3.9	0.0	0.92	3.8
		0.0	0.0	0.0	1.9	6.2	0.0	1.7	5.7	0.0	1.6	5.1	0.0	1.5	4.8
			−0.22	0.0	1.9	5.9	0.0	1.7	5.5	0.0	1.6	5.0	0.0	1.5	4.7
		−1.0	0.0	0.0	1.2	4.8	0.0	1.1	4.6	0.0	1.1	4.2	0.0	0.98	4.0
	3.0		−0.22	0.0	1.2	4.7	0.0	1.1	4.4	0.0	1.1	4.1	0.0	1.0	3.9
		0.0	0.0	0.0	1.9	6.2	0.0	1.8	5.8	0.0	1.7	5.4	0.0	1.6	5.1
			−0.22	0.0	1.9	6.0	0.0	1.8	5.6	0.0	1.7	5.2	0.0	1.6	4.9
		−1.0	0.0	0.0	1.3	5.2	0.0	1.1	4.9	0.0	1.0	4.2	0.0	0.91	4.0
	1.6		−0.22	0.0	1.3	5.0	0.0	1.1	4.7	0.0	1.0	4.1	0.0	0.94	3.9
		0.0	0.0	0.0	2.0	6.8	0.0	1.8	6.2	0.0	1.6	5.4	0.0	1.5	5.0
			−0.22	0.0	2.0	6.5	0.0	1.8	6.0	0.0	1.6	5.2	0.0	1.5	4.9
		−1.0	0.0	0.0	1.4	5.7	0.0	1.2	5.3	0.0	1.2	4.8	0.0	1.1	4.5
0.65	2.3		−0.22	0.0	1.4	5.5	0.0	1.2	5.1	0.0	1.2	4.6	0.0	1.1	4.4
		0.0	0.0	0.0	2.2	7.3	0.0	2.0	6.7	0.0	1.9	6.1	0.0	1.8	5.7
			−0.22	0.0	2.2	7.0	0.0	2.0	6.5	0.0	1.9	5.9	0.0	1.8	5.6
		−1.0	0.0	0.0	1.4	5.7	0.0	1.3	5.4	0.0	1.3	5.0	0.0	1.2	4.8
	3.0		−0.22	0.0	1.4	5.5	0.0	1.3	5.2	0.0	1.3	4.9	0.0	1.2	4.6
		0.0	0.0	0.0	2.3	7.4	0.0	2.1	6.8	0.0	2.0	6.4	0.0	1.9	6.0
			−0.22	0.0	2.3	7.1	0.0	2.1	6.6	0.0	2.0	6.2	0.0	1.9	5.8
		−1.0	0.0	0.0	1.4	5.9	0.0	1.2	5.5	0.0	1.1	4.7	0.0	1.0	4.5
	1.6		−0.22	0.0	1.4	5.7	0.0	1.2	5.3	0.0	1.1	4.6	0.0	1.1	4.4
		0.0	0.0	0.0	2.3	7.7	0.0	2.0	7.0	0.0	1.8	6.1	0.0	1.7	5.7
			−0.22	0.0	2.3	7.3	0.0	2.0	6.8	0.0	1.8	5.9	0.0	1.8	5.6
		−1.0	0.0	0.0	1.6	6.4	0.0	1.4	6.0	0.0	1.3	5.4	0.0	1.2	5.1
0.80	2.3		−0.22	0.0	1.6	6.2	0.0	1.4	5.8	0.0	1.3	5.2	0.0	1.2	5.0
		0.0	0.0	0.0	2.5	8.2	0.0	2.2	7.6	0.0	2.1	6.9	0.0	2.0	6.4
			−0.22	0.0	2.5	7.9	0.0	2.3	7.4	0.0	2.1	6.6	0.0	2.0	6.3
		−1.0	0.0	0.0	1.6	6.4	0.0	1.4	6.1	0.0	1.4	5.6	0.0	1.3	5.4
	3.0		−0.22	0.0	1.6	6.2	0.0	1.4	5.9	0.0	1.4	5.5	0.0	1.3	5.3
		0.0	0.0	0.0	2.6	8.3	0.0	2.3	7.7	0.0	2.3	7.2	0.0	2.1	6.7
			−0.22	0.0	2.6	8.0	0.0	2.4	7.5	0.0	2.3	7.0	0.0	2.2	6.6

Note. Table notes and notation are the same as in Table 3.

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Table 5 lists single- and binary-star (with  = 0.5 and 0.1) SN IIb rates at solar and low metallicity computed using the distributions of Moe & Di Stefano (2017) for all values of α and all four definitions for SN IIb progenitors. For these, we compute and quote lower and upper limits on the rates, assuming that all or none of the secondaries explode as SNe, respectively. These rates are typically 2–5 times lower than those from our "fiducial distributions" (using f_bin = 0.88; computed value for our simulated population).

Table 5.  SN IIb Relative Rates at Solar and Low Metallicities Using 10⁶ Single and Binary Stars Generated from Distributions of Moe & Di Stefano (2017)

		MHe core ≥ 0M⊙						2M⊙ ≤ MHe core ≤ 6M⊙
		MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙			MH env ≤ 1.0M⊙			MH env ≤ 0.5M⊙
Z	α	single	binary		single	binary		single	binary		single	binary
			= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1		= 0.5	= 0.1
	1.6	0.21–0.4	0.12–0.22	0.15–0.29	0.14–0.26	0.09–0.17	0.12–0.22	0.0	0.1–0.19	0.12–0.24	0.0	0.07–0.14	0.09–0.17
Z⊙	2.3	0.18–0.33	0.15–0.28	0.2–0.37	0.11–0.22	0.11–0.21	0.15–0.28	0.0	0.13–0.25	0.17–0.32	0.0	0.1–0.18	0.13–0.24
	3.0	0.13–0.24	0.16–0.3	0.22–0.41	0.08–0.15	0.12–0.23	0.17–0.31	0.0	0.14–0.27	0.19–0.36	0.0	0.11–0.2	0.14–0.26
	1.6	0.0	0.81–1.6	2.8–5.3	0.0	0.73–1.4	2.6–5.1	0.0	0.67–1.3	2.2–4.3	0.0	0.64–1.2	2.2–4.2
Z⊙/4	2.3	0.0	0.8–1.5	2.6–5.0	0.0	0.72–1.4	2.5–4.8	0.0	0.67–1.3	2.2–4.2	0.0	0.64–1.2	2.2–4.1
	3.0	0.0	0.83–1.6	2.7–5.0	0.0	0.77–1.4	2.6–4.8	0.0	0.74–1.4	2.3–4.4	0.0	0.71–1.3	2.3–4.2

Note. Table notes and notation same as in Table 3. The lower (upper) limit on rates is from assuming that all (none) of the secondaries explode as SNe.

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The computed rates increase by <0.01% when we require that primary stars transfer at least 0.1% (instead of 1%) of their initial mass in RLO to qualify as a "binary." The low-metallicity rates are more strongly robust to this definition; there are relatively few mildly interacting binaries at low metallicity. As mentioned in Section 2.2, we limit the initial primary mass to M_ZAMS,1 ≃ 25M_⊙ in our low-metallicity models even though the corresponding single-star models retain large envelopes. If we assume that all binaries in the unmodeled parameter space lead to SNe IIb (i.e., M_ZAMS,1 ≳ 25M_⊙, q_ZAMS = 0.4–1.0, and ${\mathrm{log}}_{10}({P}_{\mathrm{orb},\mathrm{ZAMS}}/$ day) = 3.0–3.7), they would contribute at most 2.7% in rates for the most favorable priors and assuming that no secondaries lead to SNe.

In Table 2, we report conservative ranges for theoretical SNe IIb relative rates. The lower limits are the smallest values from Tables 3 and 4 and assuming that all secondaries explode as SNe of a type other than IIb, while the upper limits are the largest values from those tables and assuming that no secondaries explode as SNe. Therefore, values in Table 2 span the range of theoretical SN IIb rates obtained by varying prior distributions of single- and binary-star birth properties and structural criteria for defining SN IIb progenitors.

We note that our binary SN IIb rates at low metallicity represent lower limits, as we do not compute progenitors arising via case A mass transfer. We do not expect SN IIb progenitors via case A mass transfer at solar metallicity because their residual hydrogen envelope after the mass transfer phase will be roughly as massive as that for binary stars that initiate mass transfer on the HG (Götberg et al. 2017) and will therefore also be stripped by winds before CC.

Overall, our model (single and binary) SNe IIb contribute to 0%–4.1% and 0.4%–15% of all CC SNe at solar and low metallicity, respectively. The SN IIb rate from observations is ∼11% (Li et al. 2011; Smith et al. 2011; Graur et al. 2017) at high metallicity. Our solar-metallicity models can account for less than half the observationally inferred rate at high metallicity. On the other hand, there is evidence that SN IIb rates may be higher in galaxies less massive than the LMC (Arcavi et al. 2010; Graur et al. 2017). Note that observationally inferred rates as a function of galaxy mass/metallicity should be interpreted with caution as they are affected by small sample sizes. However, if this trend holds up in future investigations using large sample sizes, our models can account for the implied SNe IIb rates at low metallicity. However, this is only true for models with low mass transfer efficiency.

Applying the most restrictive criteria for defining SN IIb progenitors [M_{H env,preSN(,1)} ≤ 0.5M_⊙ and $2{M}_{\odot }\leqslant {M}_{\mathrm{He}\mathrm{core},\mathrm{preSN}(,1)}\leqslant \,6{M}_{\odot }$], makes the disagreement between theoretical (0.1%–1.4%) and observed rates at solar metallicity worse. At low metallicity, however, though theoretical rates (0.5%–12%) also decrease, our most optimistic rates are still consistent with observed rates. An analogous result was also found by Lyman et al. (2016), who found that low-metallicity binaries with primary masses 8–20M⊙ can explain the observed distribution of SN IIb (and also SE SN generally) ejecta masses.

In this paper, we use non-rotating single- and binary-star models at solar and low metallicities covering a broad parameter space (see Table 1) to investigate evolutionary channels and parameter space for progenitors of SNe IIb. We find that metallicity and mass transfer efficiency play important roles in shaping the parameter space toward SNe IIb. Both of these affect the evolution of case EB binaries (binaries that initiate MT on the HG), where lower metallicities and mass transfer efficiencies are favorable for the production of SNe IIb. Since the range of binary configurations that lead to case EB mass transfer is very wide, these binaries have a strong effect in shaping the parameter space and, therefore, rates for SNe IIb.

We use our models to compute theoretical SN IIb rates and compare them to observationally constrained values. We attempt to account for the uncertainties in the prior distributions of single- and binary-star birth properties and criteria used to define SN IIb progenitor structures by spanning possible values for them. This allows us to investigate to what extent our models are a priori able to explain observed SN IIb rates.

We find that solar-metallicity single- and binary-star models, by themselves or together, account for less than half of the observed SN IIb rate at solar metallicity. Our most optimistic rate is inconsistent within 2σ of the observationally inferred rates. Also, at high metallicity, singles and binaries contribute to roughly equal numbers (singles slightly more) of SNe IIb. At low metallicity, however, our models can account for the implied rate. Here, binaries are the sole producers of SNe IIb. The group of case EB binary SNe IIb (which in turn is courtesy of lower wind mass-loss rates at low metallicity) is responsible for this change. Further, even using our most restrictive criterion on an SN IIb progenitor structure, theoretical rates at low metallicity are still consistent with observed rates within the reported uncertainties (though these are quite large).

If wind mass-loss rates are lower than those used in our models (which may be the case as discussed in Section 6.2), it might be instructive to compare observed rates at high metallicity to our low-metallicity models (Yoon et al. 2017). We find that rates for our low-metallicity and low mass transfer efficiency models are consistent with observed rates at high metallicity. This is true even after using our most restrictive definition of an SN IIb progenitor. However, this requires f_bin > 0.5 and priors favoring equal mass binaries and favoring a flat orbital period distribution to be consistent within reported uncertainties for observationally inferred rates. We discuss implications of this in Section 6.3.

Although we have tried to be conservative in our predicted upper and lower limits for rates, it is instructive to point out additional physical uncertainties in our models.

Wind mass-loss rates have an important effect on single- and binary-star channels toward SNe IIb. Stellar winds in our MESA models are computed using different wind mass-loss prescriptions at various evolutionary phases. WR mass-loss rates have the strongest impact on evolutionary outcomes. However, these rates are also known to be quite uncertain, particularly for low mass WR stars. Most estimates, including those used in this work are expected to be overestimated due to clumping in the winds (Smith 2014). Lower wind mass-loss rates would expand the parameter space for binary SNe IIb (Yoon et al. 2017; Gilkis et al. 2019). In addition, though it is commonly assumed that mass-loss rates from red supergiants decrease with metallicity, some studies suggest that they are more or less metallicity independent (van Loon 2000; van Loon et al. 2005; Goldman et al. 2017). If this is the case, we would expect low-metallicity single stars to produce SN IIb at a relative rate similar to that of high-metallicity single stars.

Another important point is that we have not included stellar rotation. Rotation is thought to play an important role in massive star evolution, with very rapidly rotating stars even being predicted to evolve chemically homogeneously due to rotationally enhanced mixing (Maeder 1987). Rotationally enhanced mass-loss rates can also reduce the minimum mass required for a single star to remove its hydrogen envelope (Meynet & Maeder 2003), thus increasing the rate of SN IIb progenitors from single stars. However, Groh et al. (2013a) found that the initial mass range that produces SNe IIb does not change much for their rotating models with v_rot ∼ 250 km s⁻¹. Further, observations show that the bulk of the massive star population rotates at lower velocities (Ramírez-Agudelo et al. 2013, 2015), and that stars rotating at faster rates can potentially be accounted for in terms of spun-up secondaries in post-mass transfer systems (de Mink et al. 2013). Properly assessing the impact of rotation, along with the effect of tides and eccentricity (which is likely small due to the wide orbits considered here) would require future calculations that include these effects, but they are beyond the scope of the present study.

Our results have the following implications for progenitor channels to SNe IIb. In order to account for the observationally inferred SN IIb rates

• 1.  
  Solar-metallicity wind mass-loss rates need to be lower than those used in our models: lower wind mass-loss rates increase the contribution of binaries to SNe IIb, by populating the parameter space available via case EB mass transfer, while driving down the contribution from single stars.
• 2.  
  Low mass transfer efficiencies are needed: this allows case EB accretors to thermally adjust to the transferred mass and avoid contact.

We note that it is likely that even after accounting for robust mass-loss rates, the uncertainty in prior distributions of stellar birth properties and SN IIb definitions will still pose significant challenges for comparing theoretical models to observations. Therefore, in order to address the question of SNe IIb progenitors, we need four pieces of information: (1) accurate determinations of mass-loss rates for stripped stars as a function of metallicity, (2) constraints on structural properties of SN IIb progenitor stars, (3) robust distributions for single- and binary-star birth properties, and (4) on the observational side, SN IIb rates as a function of metallicity. An exploration of case A mass transfer toward SNe IIb at low metallicity and merger channels would also be worthwhile.

In this paper, we focused on understanding the evolutionary channels and parameter space of SN IIb progenitors. In a follow-up paper, we will focus on using our models to draw statistical comparisons to all three independent observational probes into SN IIb progenitors: (1) direct progenitor detections in archival images, (2) progenitor structure and explosion parameters from analyzing multi-band light curves, and (3) circumstellar medium properties from X-ray/radio observations. The aim would be to confirm that our models are able to reproduce the full range of observational constraints for SNe IIb, that the results of such comparison is consistent with conclusions in this paper, and finally, to identify regions in the observational parameter space that are implied from our models but remain unprobed by observations to help guide observing strategies.

The advent of high-cadence surveys like the ZTF (Bellm 2014; Bellm & Kulkarni 2017), ASSA-SN (Kochanek et al. 2017), DLT40 (Valenti et al. 2017), KAIT (Filippenko et al. 2001), and, at the turn of the decade, LSST (Tyson 2002; Ivezić et al. 2019) have created the need for a comprehensive database of theoretical models to provide reliable progenitor characterization and in the case of binary progenitors, their companions. Conversely, the wealth of data that will be available will provide unprecedented statistics on progenitor properties, along with their dependence on properties such as host galaxy metallicity. Efforts such as the one undertaken here are therefore imperative in order to understand the physics of massive star evolution.