RELATIVISTIC SUPERNOVAE HAVE SHORTER-LIVED CENTRAL ENGINES OR MORE EXTENDED PROGENITORS: THE CASE OF SN 2012ap

The vast majority of supernova explosions (SNe) arising from hydrogen- and helium-stripped progenitors (i.e., type Ic SNe; see Filippenko 1997 for the spectral classification of SNe) can be explained by the hydrodynamical collapse of the massive progenitor star (e.g., Tan et al. 2001). In a very limited percentage of cases (≲ 1%; Berger et al. 2003; Coward 2005; Guetta & Della Valle 2007; Soderberg et al. 2010b), the explosion is instead powered by an engine able to accelerate a tiny portion of the ejecta with typical mass⁶M ≈ 10⁻⁵–10⁻⁶ M_☉ to velocities v ≳ 0.6 c. Engine-driven explosions (hereafter E-SNe) are thus uncommon. Furthermore, only a small fraction of E-SNe (≲ 10%; e.g., Soderberg et al. 2006a; see also Cobb et al. 2006; Pian et al. 2006; Liang et al. 2007; Virgili et al. 2009) harbor a fully relativistic jet and give origin to gamma-ray bursts (GRBs). The peculiar circumstances that cause a hydrogen-stripped, massive progenitor star to produce a relativistic jet at the time of the collapse are still not fully understood. High angular momentum seems to be a key ingredient (e.g., MacFadyen & Woosley 1999; MacFadyen et al. 2001; Woosley & Heger 2006; Dessart et al. 2008).

E-SNe have historically been detected through their prompt X-ray and γ-ray emission produced by energy dissipation within the jet (ordinary GRBs) and by the SN shock break out (which is relevant at least for some sub-energetic, sub-E, GRBs; e.g., Kulkarni et al. 1998; Matzner & McKee 1999; MacFadyen et al. 2001; Tan et al. 2001; Campana et al. 2006; Wang et al. 2007; Waxman et al. 2007; Katz et al. 2010; Bromberg et al. 2011; Nakar & Sari 2012). More recently, two E-SNe have been discovered through their bright later-time radio emission (i.e., the relativistic SNe 2009bb and 2012ap; Soderberg et al. 2010b; Bietenholz et al. 2010; Chakraborti et al. 2011; Chakraborti et al. 2014, hereafter C14). Here, we specifically ask the following questions. What is the nature of relativistic SNe, and what is their connection with the other classes of E-SNe known so far?

The two known relativistic SNe 2009bb and 2012ap share with sub-E GRBs evidence for mildly relativistic ejecta powering a bright radio emission (Soderberg et al. 2006a, 2010b; Bietenholz et al. 2010; C14) and a very energetic optical explosion with E_k ∼ 10⁵² erg coupled to material moving at v ∼ a few 10⁴ km s⁻¹ (Pignata et al. 2011; Milisavljevic et al. 2014b). These properties dynamically distinguish relativistic SNe and sub-E GRBs from ordinary SNe and put these explosions between the highly relativistic, collimated GRBs and the more common type Ic SNe.

On the theoretical side, state-of-the art simulations of jet-driven stellar explosions (e.g., Lazzati et al. 2012) associate classic GRBs with fully developed, highly relativistic jets and suggest that sub-E GRBs likely represent the cases where the jet is just barely able to pierce through the stellar envelope (Bromberg et al. 2011; Nakar & Sari 2012). In particular, it was suggested by Lazzati et al. 2012 that a different lifetime of the central engine might be able to explain the entire zoo of E-SNe (i.e., relativistic SNe, sub-E GRBs, and ordinary GRBs). However, it is unclear if relativistic SNe represent a new class of explosions, or if, instead, they are the equivalent of sub-E GRBs for which we missed the high-energy trigger because of line-of-sight effects or incomplete coverage of the γ-ray satellites (see, e.g., the discussion for SN 2009bb in Soderberg et al. 2010b). This still open question motivates this study.

We present late-time, deep X-ray observations of the relativistic SN 2012ap. These observations allow us to identify for the first time a distinctive property of relativistic SNe that clearly sets them apart from all the other known engine-driven explosions. We find that relativistic SNe are characterized by a significantly fainter X-ray emission at late times (t ∼ 20 days), even compared to sub-E GRBs (SN 2012ap is ∼100 times fainter than the faintest sub-E GRB at the same epoch), and show no evidence for an excess of X-ray radiation that has been recently reported for the sub-E GRBs 060218 (Soderberg et al. 2006a; Fan & Piran 2006) and 100316D (Margutti et al. 2013a).

We describe our observations in Section 2 and constrain the progenitor mass-loss rate in Section 3. Finally, we put SN 2012ap in the context of engine-driven explosions in Sections 4 and 5 and discuss how our findings clearly suggest that relativistic SNe constitute a separate class of engine-driven explosions with intrinsic differences with respect to sub-E GRBs. Conclusions are drawn in Section 6.

Uncertainties are quoted at the 1σ confidence level, unless otherwise noted. We employ standard cosmology with H₀ = 71 km s⁻¹ Mpc⁻¹, Ω_Λ = 0.73, and Ω_M = 0.27. Throughout the paper, we use 2012 February 5 as the explosion date of SN 2012ap, as inferred by Milisavljevic et al. (2014b), hereafter M14) from extensive optical observations. Following C14, we assume a distance of 40 Mpc (Springob et al. 2007, 2009). A detailed discussion of the optical and radio properties of SN 2012ap can be found in M14 and C14, respectively. Finally, we note that sub-E GRBs are also called low-luminosity GRBs in the literature (see, e.g., Bromberg et al. 2011). However, the physical parameter that is relevant to your analysis is the (modest) kinetic energy of their fastest ejecta, which is surely related to the low luminosity of their prompt γ-ray emission. For this reason, we will refer to this class as sub-E GRBs.

2.1. Swift-XRT

2.2. Chandra

We initiated deep X-ray follow-up of SN 2012ap with the Chandra X-ray Observatory on 2012 February 29.2 UT, δt ≈ 24 days after the explosion (Program 13500648; PI: Soderberg). Chandra ACIS-S data were reduced with the CIAO software package (v4.5) and relative calibration files, applying standard ACIS data filtering. Using wavedetect, we find no evidence for X-ray emission at the position of SN 2012ap (Figure 1), with a 3σ limit of 8.0 × 10⁻⁴cps (0.5–8 keV energy range, total exposure time of 9.9 ks). Employing the spectral parameters above, the corresponding absorbed (unabsorbed) flux limit in the 0.3–10 keV energy range is F_x < 6.8 × 10⁻¹⁵ erg s⁻¹cm⁻² (F_x < 1.3 × 10⁻¹⁴ erg s⁻¹cm⁻²). The luminosity limit is L_x < 2.4 × 10³⁹ erg s⁻¹ (0.3–10 keV).

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At δt ≲ 30 days, inverse Compton (IC) is the dominating X-ray emission mechanism for ordinary SNe arising from hydrogen-stripped progenitors exploding in low-density environments (Björnsson & Fransson 2004; Chevalier & Fransson 2006). In the case of central-engine-powered SNe, additional sources of X-ray power are represented by continued central engine activity (as in the case of sub-E GRBs like 100316D; Margutti et al. 2013a) and interaction of the explosion jet with the environment (as in the case of ordinary GRBs; see, e.g., Margutti et al. 2013b). In the following, we use the deep Chandra limit of Section 2.2 and conservatively assume that IC is responsible for the entire X-ray emission to derive a solid upper limit to the mass-loss rate of the progenitor star of SN 2012ap.

In the IC scenario, the X-ray emission is originated by the up-scattering of optical photons from the SN photosphere by a population of relativistic electrons and depends on the density structure (1) of the SN ejecta and (2) of the circumstellar medium (CSM); (3) the details of the electron distribution responsible for the up-scattering; (4) the explosion parameters (ejecta mass M_ej and kinetic energy⁷ E_k); and (5) the bolometric luminosity of the SN: L_IC∝L_bol. We adopt the formalism by Margutti et al. (2012) modified to account for the outer density structure of SNe with compact progenitors that has been shown to scale as ρ_SN∝R⁻ⁿ with n ∼ 10 (see, e.g., Matzner & McKee 1999; Chevalier & Fransson 2006).

Assuming a wind-like CSM structure ρ_CSM∝R⁻² as appropriate for massive stars, a power-law electron distribution n_e(γ) = n₀γ^−p with p ∼ 3 as indicated by radio observations of type Ib/c SNe (Chevalier & Fransson 2006) and by radio observations of SN 2012ap (C14), and a fraction of energy into relativistic electrons _e = 0.1 as supported by well-studied SN shocks (e.g., Chevalier & Fransson 2006), the Chandra non-detection of SN 2012ap at δt ≈ 24 days implies $\dot{M}/v_w <5\times 10^{-6}(M_{\odot }\,{\rm y}^{-1}/1000\,\rm {km\,s^{-1}})$. $\dot{M}$ is the mass-loss rate of the progenitor star, and v_w is the wind velocity. We renormalize the mass loss to v_w = 1000 km s⁻¹ as appropriate for Wolf–Rayet progenitor stars. In this calculation, we used the bolometric luminosity we derived in M14, E_k ∼ 10⁵² erg and M_ej ∼ 3 M_☉ as obtained by modeling the bolometric luminosity in M14.

The inferred limit to the mass-loss rate $\dot{M} <5\times 10^{-6}(M_{\odot }\,{\rm y}^{-1})$ is independent from any assumption on magnetic-field-related parameters; it is not affected by possible uncertainties on the SN distance and indicates that the pre-explosion mass loss of SN 2012ap lies at the low end of the interval of values derived by C14 ($4\times 10^{-6}\,{M_{\odot }\,{\rm y}^{-1}}<\dot{M} <5\times 10^{-5}\,{M_{\odot }\,{\rm y}^{-1}}$) and is based on the modeling of the radio observations with synchrotron emission.⁸ This result is in line with the value derived for the relativistic SN 2009bb ($\dot{M}\sim 2\times 10^{-6} \,{M_{\odot }\,{\rm y}^{-1}}$; Soderberg et al. 2010b) and is consistent with the wide range of values inferred for sub-E GRBs ($10^{-7}\,{M_{\odot }\,{\rm y}^{-1}}\lesssim \dot{M} \lesssim 10^{-5}\,{M_{\odot }\,{\rm y}^{-1}}$).

The radio observations of SN 2012ap are well modeled by synchrotron emission arising from the interaction of the SN shock with the environment (C14). C14 derive E_k = (1.6 ± 0.1) × 10⁴⁹ erg carried by mildly relativistic ejecta with velocity v ∼ 0.7c at δt = 1 d. By modeling the observed optical emission, M14 infer E_k ∼ 10⁵² erg in slow moving (v ≈ 20, 000 km s⁻¹) material. These two values define an E_k profile significantly flatter than what was expected in the case of a pure hydrodynamical collapse (E_k∝(Γβ)^−5.2; e.g., Tan et al. 2001), thus pointing to the presence of an engine driving the SN 2012ap explosion (see Figure 2).

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Engine-driven SNe constitute a diverse class of explosions that includes relativistic SNe, sub-E GRBs, and ordinary GRBs. SN 2012ap is intermediate between ordinary non-relativistic SNe and fully relativistic GRBs and falls into a region of the parameter space populated by sub-E GRBs and the other known relativistic SN, SN 2009bb (Figure 2).⁹ With reference to Figures 3 and 4, we find the following.

• 1.  
  The radio luminosity of SN 2012ap and sub-E GRBs is comparable. SN 2012ap is significantly more luminous than ordinary Ic SNe at the same epoch and even more luminous than the sub-E GRBs 100316D and 060218 (Figure 3, right panel). With E_k ∼ 10⁵² erg and evidence for broad spectral features (M14), the properties of SN 2012ap in the optical band are also reminiscent of the very energetic SNe associated with sub-E GRBs and ordinary GRBs.
• 2.  
  At δt ∼ 20 days, the X-ray emission from SN 2012ap is, however, a factor ⩾100 fainter then the faintest sub-E GRB ever detected, GRB 980425 (Figure 3, left panel).
• 3.  
  Along the same line, from C14, the prompt γ-ray energy released by the SN 2012ap explosion is E_{γ, iso} < 10⁴⁷ erg, a factor ⩾10 fainter then the faintest sub-E GRB 980425 (Figure 4).

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In addition, in Milisavljevic et al. (2014a) and M14, we showed the following.

• 1.  
  Contrary to sub-E GRBs and GRBs, SN 2012ap exploded in a solar–metallicity environment. Interestingly, the metallicity of the environment of SN 2009bb was also super-solar (Levesque et al. 2010b).
• 2.  
  Different from sub-E GRBs and GRBs, our analysis of multi-epoch spectroscopy strongly favors the presence of helium in the ejecta of SN 2012ap. Helium was also reported in the early-time spectra of SN 2009bb (Pignata et al. 2011).

Relativistic SNe and sub-E GRBs are thus clearly distinguished in terms of their high-energy (X-rays and γ-rays) properties, a higher metallicity environment, and the conspicuous presence of helium in their ejecta.

The different levels of X-ray emission between relativistic SNe and sub-E GRBs cannot be ascribed to beaming collimated emission away from our line of sight. Radio observations of sub-E GRBs support the idea of quasi-spherical explosions (e.g., Kulkarni et al. 1998; Soderberg et al. 2004, 2006a; Margutti et al. 2013a), and there is no evidence for beaming of the non-thermal emission from relativistic SNe (Soderberg et al. 2010b; C14). Furthermore, on a timescale of ∼20 days, the blastwave arising from both relativistic SNe and sub-E GRBs is sub-relativistic, and the geometry of emission is effectively spherical, independent from the initial conditions. The different levels of X-ray emission between sub-E GRBs and relativistic SNe at t ≳ 10 days are thus intrinsic.

While both relativistic SNe and sub-E GRBs are intermediate between ordinary type Ic SNe and GRBs, these findings point to a diversity in the properties of the progenitors and/or the engines that drive their explosion. This topic is discussed below.

At δt ≳ 10 days, the detected X-ray emission from sub-E GRBs like 060218 and 100316D has been suggested to originate from the activity of the explosion central engine (Soderberg et al. 2006a; Fan & Piran 2006; Fan et al. 2011; Margutti et al. 2013a), which dominates over synchrotron emission from the shock–CSM interaction.¹⁰ The nature of the central engine is currently not known. For the sub-E GRBs 060218 and 100316D, the observations support either a magnetar central engine or continued accretion onto a newly formed black hole.

Figure 5 clearly shows that the X-ray emission from SN 2012ap is instead consistent with the shock–CSM model that best fits the radio observations. For SN 2012ap, the deep X-ray limit thus rules out the presence of an additional, luminous X-ray component arising from the engine activity, contrary to sub-E GRBs like 100316D portrayed in Figure 5. This finding suggests that the engine that powers SN 2012ap is short lived and unable to survive for such a long time.

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We propose that relativistic SNe like 2009bb and 2012ap represent weak engine-driven explosions, where the engine activity stops before being able to produce a successful jet breakout. The result is a stellar explosion that is able to accelerate a tiny fraction of ejecta to mildly relativistic velocities, thus dynamically different from ordinary Ic SNe and more similar to sub-E and classical GRBs (Figure 2). In contrast to GRBs, however, the jet is not able to pierce through the stellar envelope, and a very limited fraction of energy is dissipated at γ-ray frequencies, consistent with the deep limit E_{γ, iso} < 10⁴⁷ erg from C14. This phenomenology can either be due to an intrinsically short-lived engine or to a different progenitor structure/properties between relativistic SNe and GRBs. We discuss these two possibilities in Sections 5.1–5.3.

5.1. Central Engine Lifetime

5.2. Progenitor Properties: Metallicity

5.3. Progenitor Properties: Helium-rich Ejecta

5.4. A Continuum of Stellar Explosions Originating from Hydrogen-stripped Progenitors

The class of E-SNe collects a rare variety of SN explosions (≲ 1% of type Ic SNe) and includes relativistic SNe, sub-E GRBs, and ordinary GRBs. E-SNe are characterized by a significantly shallower kinetic energy profile of the explosion ejecta than expected in the case of a pure hydrodynamic collapse of the progenitor star (Figure 2), indicating that E-SNe are able to accelerate a tiny but important fraction of their ejecta to higher velocities (v ≳ 0.6 c). E-SNe otherwise show a diverse phenomenology.

Relativistic SNe and sub-E GRBs share a bright radio emission and evidence for mildly relativistic ejecta that clearly set them apart from ordinary SNe Ic (non-relativistic). The thermal properties of relativistic SNe are also analogous to the very energetic, fast expanding SNe associated with sub-E GRBs and ordinary GRBs (Soderberg et al. 2010b; M14). However, a distinctive property of relativistic SNe is their significantly fainter X-ray emission (Figure 3) that implies the lack of a luminous X-ray components arising from the central engine activity at late times (δt ∼ 20 days; Figure 5). With E_{γ, iso} < 10⁴⁷ erg, the prompt γ-ray energy released by the relativistic SN 2012ap is also considerably below the level of sub-E GRBs (Figure 4).¹⁴ The higher metallicity of the environment and the conspicuous presence of helium in the ejecta of the two known relativistic SNe also sets them apart from sub-E GRBs and GRBs.

These findings call for some crucial diversity in the properties of the engines and/or of the progenitors of relativistic SNe and sub-E GRBs (and ordinary GRBs as well). We showed that the observations of relativistic SNe are consistent with the picture of jet-driven explosions where the jet just barely fails to break out from the progenitor star. This scenario naturally explains (1) the lack of evidence for central engine activity at late times and (2) the deep limit to the promptly released γ-ray energy.

The failed jet breakout might be due to an intrinsically short-lived engine (but the same progenitor properties) or to a different progenitor structure between relativistic SNe and sub-E GRBs. At the time of writing, with only two relativistic SNe discovered so far (through targeted optical surveys), observations do not allow us to distinguish between these two scenarios. A significantly larger sample of relativistic SNe found through untargeted SN searches in the optical and radio band is clearly needed to deeply understand their connection to GRBs, build a complete picture of E-SNe, and constrain which unique property differentiates failed breakouts from successful, fully relativistic jets. The Large Synoptic Survey Telescope (Ivezic et al. 2008) is expected to discover hundreds of SNe Ic every year, thus, in principle, providing the significantly larger sample of E-SNe that is needed to deeply understand the connection between relativistic SNe and GRBs. However, as we demonstrate here, coordinated radio and X-ray follow-up is essential to identify E-SNe from their ordinary counterparts and determine the properties of the engines that power their explosion.

We thank the referee for useful comments and suggestions that improved the quality of our paper. R.M. is grateful to the Aspen Center for Physics and NSF grant 1066293 for hospitality during the completion of this work. Support for this work was provided by the David and Lucile Packard Foundation Fellowship for Science and Engineering awarded to A.M.S.