A MISSING-LINK IN THE SUPERNOVA–GRB CONNECTION: THE CASE OF SN 2012ap

The optical light curves of supernovae have been well described by Arnett (1982) as a nearly blackbody photosphere which recedes into the ejecta, heated by γ-rays from nuclear decay and cooled by rapid expansion with a characteristic velocity of v ∼ 10⁴ km s⁻¹. The interaction of the ejecta with the circumstellar medium set up by the stellar wind of the progenitor star has been described by Chevalier (1982) using self-similar solutions. Such solutions have also successfully described the radio emission from SNe Ic (Chevalier 1998). The combination of nearly free expansion leading to decreasing optical thickness from free–free or synchrotron self absorption (SSA) and decreasing magnetic fields produces a decreasing peak frequency (the frequency at which the peak in the radio spectrum occurs), but a nearly constant flux density at the peak frequency (Chevalier 1998). In the self-similar solution, this interaction produces a shock front which expands in a power-law fashion with R ∝ t^m, where R is the radius of the shockfront, t is the time since shock breakout, and m is known as the expansion parameter (also sometimes called the deceleration parameter). In the case of SNe Ib/c, which generally have a relatively tenuous circumstellar medium, this interaction produces little deceleration, and m is close to 1. The ejecta would slow down significantly only after encountering a mass of external medium comparable to the ∼1 ${{M}_{\odot }}$ of ejecta expected for SNe Ib/c supernovae. This Sedov time (Taylor 1950) is expected to be ≳10² years for supernovae. Therefore, young supernovae are usually found in a Newtonian phase of nearly free expansion.

Gamma-ray bursts (GRBs) were discovered by Klebesadel et al. (1973) using the Vela satellites, designed for the detection of nuclear tests in space. Ultra-relativistic blast waves had already been described by fluid dynamical Blandford & McKee (1976) solutions before they were implicated in the production of GRBs (Goodman 1986; Paczynski 1986). The production of GRBs requires that the ejecta have initial bulk Lorentz factors of Γ ≳ 10² (Piran 1999) in order to overcome the pair production opacity (Ruderman 1975; Schmidt 1978). Furthermore, even a small number of baryons in the initial ejecta can soak up most of the explosion energy available for γ-rays (Shemi & Piran 1990). This is referred to as baryon poisoning. Therefore, GRB jets must have ≲10⁻⁶ ${{M}_{\odot }}$ of relativistic ejecta (Piran 1999) after breakout from the stellar progenitor surface, so as not to be baryon poisoned. In a short time, this relatively small mass of ejecta encounters a larger mass of external matter. Therefore, GRB afterglows are found in a relativistic but rapidly decelerating phase and have Γ ≲ 20. The broad-lined (high velocity) type Ic SN 1998bw was discovered in the direction of GRB 980425 (Galama et al. 1998), and was characterized by the bright radio emission from its relativistic ejecta which had Γ ∼ 2–3 (Kulkarni et al. 1998). This association between an SN Ic and a long GRB was followed by other supernovae like that of GRB 030329 with SN 2003dh (Hjorth et al. 2003) and XRF 060218 with SN 2006aj (Pian et al. 2006; Soderberg et al. 2006) also associated with GRBs. Some of these supernovae were marked by broad lines or by asphericity. However, the definitive property of this small subset of SNe Ic which allowed them to produce relativistic outflows remains elusive.

This evidence of a supernova–GRB connection inspired a systematic search for relativistic ejecta from nearby SNe Ic using radio observations, leading to the discovery of SN 2009bb by Soderberg et al. (2010) with ≳10⁴⁹ erg of energy in radio emitting relativistic ejecta. Like GRBs, SN 2009bb had relativistic ejecta (Soderberg et al. 2010), but this ejecta continued to be in nearly free expansion for ∼1 year (Bietenholz et al. 2010; Chakraborti et al. 2011), leading to the suggestion that, unlike GRBs, it is baryon loaded (Chakraborti & Ray 2011). Chakraborti et al. (2011) suggested that such engine-driven relativistic supernovae can even accelerate ultra-high-energy cosmic rays. Such a baryon loaded fireball was also implied in PTF11agg (Cenko et al. 2013). A rapid decline in flux density, faster than ∝t⁻¹ at a given radio frequency, or a decreasing peak flux density may signal the deceleration of the ejecta. Recently, the rapidly declining PTF12gzk was observed with ≲10⁴⁶ erg of energy in its fast ejecta (Horesh et al. 2013). So far, however, highly energetic (≳10⁴⁹ erg) relativistic ejecta combined with rapid deceleration has never been observed in a supernova unassociated with a GRB.

No supernova was seen in the host galaxy on a pre-explosion image taken by the Katzman Automatic Imaging Telescope on February 5 down to an upper limit of 18.7 R magnitude. A subsequent image taken on February 10, revealed SN 2012ap at 17.3 R magnitude. We therefore conclude that the explosion happened before February 10, but not much before February 5. Since one of the major claims of this work is a deceleration, we count the age of the supernova from the February 5, which is near the beginning of this range. Later dates would imply even more deceleration. Milisavljevic et al. (2014b) models the optical light curve and provides an explosion date of February 5 ± 2, which is used in this work and interpreted as a 1σ bound on the explosion date. The present uncertainties of a few days in the explosion date dominates the uncertainty in m.

Both the VLA and GMRT observations have been reduced using Astronomical Image Processing Software (AIPS) standard techniques. Radio frequency interference in data was flagged and the interferometric visibilities were amplitude and phase calibrated. Bandpass calibration was performed using BPASS based on the flux calibrators 3C48 and/or 3C147. The single source data was extracted using the AIPS task SPLIT after final bandpass and flux calibration. The single source data sets were imaged using IMAGR. The images were corrected for the residual phase calibration errors using self-calibration of visibility phases (Cornwell & Fomalont 1989). The source flux densities were extracted by fitting Gaussian using the task JMFIT assuming point sources. The errors reported on the flux density are obtained by using the image statistics from the region surrounding the source.

These radio observations were used to obtain the values reported in Table 1 and in Figures 2 and 3. Quoted uncertainties in flux densities are statistical. There may be up to 5% systematic uncertainty from flux density calibration. This dominates the error budget quoted in the final derived values for E₀ and $\dot{M}$.

The full set of radio observations were fit with an SSA model with p = 3, as has been observed in SNe Ic. Both the peak flux density and peak frequency were allowed to vary as arbitrary power laws with an origin at February 6. A good global fit is obtained with a χ² = 0.98 per degree of freedom. See Figure 1 for all of the radio observations and the fit. The radii (Figure 2) and magnetic fields (Figure 3) reported in Table 1 are derived from fits to the data at individual epochs.

The dependence of R on the ratio _e/_B and f are through a power of 1/19, and so they are likely to introduce only a negligible systematic uncertainty (Chevalier 1998). The dependence on distance is with a power 18/19, which could introduce a systematic shift but would not change the expansion parameter. The dependence on the flux density is a power of 9/19, and so a 5% error in flux density will add 2.5% of systematic error to the radii. These errors should be considered above and beyond the statistical uncertainties reported in the table. However, none of these are large enough to significantly change the results reported in this work.

Between 2012 February 05 and 2012 February 10, including both days, a total of five bursts were detected by one or more of the nine spacecraft of the (IPN: Mars Odyssey, Konus-Wind, RHESSI, INTEGRAL (SPI-ACS), Swift BAT, Suzaku, AGILE, MESSENGER, and Fermi (GBM)). All of these confirmed bursts were observed by more than one instrument on one or more spacecraft, and could be localized at least coarsely. During the same period, there were also three unconfirmed bursts which were observed by one experiment on one spacecraft (the 20 detector Suzaku HXD-WAM) in the triggered (TRN) mode. Their origin is uncertain; they could be cosmic or solar, but were too weak to be detected by other IPN spacecraft. In at least one case, it could be particle-induced. They cannot be localized accurately, but analysis of the detector responses indicates that they are unlikely to have originated from the direction of SN 2012ap. Therefore, they were excluded from further analysis. No bursts from known sources such as AXPs and SGRs were recorded during this period.

The completeness of our sample can be estimated as follows. We have three distinct sets of events: IPN bursts, Fermi GBM-only bursts, and bursts observed by the Swift BAT only within its coded field of view. The IPN is sensitive to bursts with fluences down to about 6 × 10⁻⁷ erg cm⁻², and observes the entire sky with a temporal duty cycle close to 100% (Hurley et al. 2009). This places a threshold of ∼10⁴⁷ erg on the isotropic equivalent γ-ray energy of any possibly GRB accompanying SN 2012ap if it were to be detected by the IPN. This is a factor ∼6 lower than that of GRB 980425 accompanying SN 1998bw.

The Fermi GBM detects bursts down to an 8–1000 keV fluence of about 4 × 10⁻⁸ erg cm⁻², and observes the entire unocculted sky (8.8 sr) with a temporal duty cycle of more than about 86%. The weakest burst observed by the BAT within its coded field of view had a 15–150 keV fluence of 6 × 10⁻⁹ erg cm⁻², and the BAT observes a field of view of about 2 sr with a temporal duty cycle of about 90%. Generally, the weakest bursts are short-duration GRBs; higher fluences characterize the sensitivities to long-duration GRBs.

The localization accuracies of the five confirmed bursts varied widely. None were observed within the coded fields of view of the Swift BAT, INTEGRAL IBIS, or Super-AGILE (several arcminute accuracy). None were observed by MAXI (several degree accuracy). Two were observed either by the Fermi GBM alone, or by the Fermi GBM and one near-Earth spacecraft (so that they could not be localized accurately by triangulation). These bursts had 1σ statistical-only error radii of 23.8° and 5.5°. The GBM error contours are not circles, although they are characterized as such, and have about 3.2° of systematic uncertainties associated with them. Adding the statistical and systematic uncertainties in quadrature provides a reasonable approximation to a 1σ error circle, and multiplying that radius by 3 gives a reasonable approximation to a 3σ (statistical and systematic) error circle. These two Fermi bursts have positions that are inconsistent with that of the SN (that is, the SN falls far outside the 3σ error circle as approximated above). Two were observed by interplanetary and near-Earth spacecraft, and could be triangulated to small error boxes whose positions exclude the position of SN 2012ap. One burst was observed by the Swift BAT outside the coded field of view, and by the INTEGRAL SPI-ACS. As the distance between these two spacecraft is only about 0.5 lt-s, the event can be triangulated, but not accurately. Its error annulus has an area of 1.8 sr, which includes the position of the supernova. The total area of the localizations of the five confirmed bursts was 0.5 times 4 pi sr. This implies that about 0.5 bursts can be expected to have positions which are consistent with any given point on the sky simply by chance (i.e., within the 3σ error region). In our sample, one burst has a position consistent with the SN position (Poisson probability 0.3).

There is another approach to the probability calculation. Since only 0 or 1 GRB in our sample can be physically associated with the supernova, we can calculate two other probabilities. The first is the probability that in our ensemble of five bursts, none is associated by chance with the supernova. For our ensemble, this probability is 0.54. The second probability is that any one burst is associated by chance with the SN, and that all the others are not. For our ensemble, that probability is 0.39. Since we find approximately the expected number of chance coincidences, and since there are no bursts with small error boxes whose positions are consistent with the supernova, there is no strong evidence for an SN-associated GRB within the time window down to the IPN threshold. If the supernova produced a burst below the IPN threshold and above the Fermi one, then it is possible that both Swift and Fermi would not detect it; considering their spatial and temporal coverages, the joint non-detection probability is about 0.38. Finally, if the supernova produced a burst below the Fermi threshold but above the Swift one, then the probability is about 0.86 that it would not be detected.

In summary, no confirmed coincident burst with an isotropic fluence of more than one-sixth of GRB 980425 was localized to the direction of SN 2012ap within the relevant time window. Weaker bursts were searched for, albeit with <100% duty cycle, but also not found.

As a supernova expands, its radio emitting region becomes optically thinner. The expansion also dilutes the energy density of relativistic electrons and magnetic fields. In the nearly free expansion phase, these two effects conspire (Chevalier 1998; Chakraborti & Ray 2011) to decrease the turnover frequency of the SSA spectrum but keep the peak flux density nearly constant in time. In the case of SN 2012ap, the peak flux density fell steadily over the first month of observations (see Figure 1) and the expansion is well fit by a power law of the form, R ∝ t^m, where m = 0.74 ± 0.03. Here, the 1σ statistical uncertainty is derived from the radio size determinations following Chevalier (1998). However, the determination of the explosion date derived from optical observations (Milisavljevic et al. 2014b) presents a greater 1σ systematic uncertainty of 0.07. This is determined by refitting the data with the range of explosion dates allowed by the optical studies of the supernova. Taking both into account and summing them in quadrature, the total uncertainly in m is 0.08. Therefore, our estimate of the expansion parameter is m = 0.74 ± 0.08, which incorporates our understanding of the statistical and systematic uncertainties dominated by the radio observations and time of explosion, respectively. This is 3σ away from the value near 1 expected for undecelerated expansion.

The combination of the high velocity and small expansion parameter place SN 2012ap at an unique position in Figure 4 Within the context of an ordinary SN Ic, this would imply a supernova ejecta density profile characterized by a power-law distribution of mass ejected at a particular velocity ∝v⁻⁶, where v is the velocity. However, the expulsion of stellar envelopes is expected to produce much steeper ejecta profiles (Matzner & McKee 1999). This could plausibly be explained by an extraordinarily energetic supernova with a low ejecta mass and a shallow ejecta profile extending into relativistic velocities. Our observations of SN 2012ap imply much more energy coupled to high-velocity ejecta than is expected from realistic explosion models of ordinary core collapse supernovae. The decelerating expansion is, however, consistent with a Central Engine Driven EXplosion (CEDEX; Chakraborti & Ray 2011), which places a large amount of energy in a small mass of relativistic ejecta responsible for the radio afterglow which separates itself from the non-relativistic ejecta responsible for the optical emission. The decelerating expansion of this component interacting with the wind of the progenitor star is expected to produce (see appendix) a R ∝ t^3/4 behavior consistent with the observations.

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Within the context of such a CEDEX, our radio observations allow us to perform calorimetry on the fireball responsible for this radio afterglow. The initial energy in the relativistic component can be estimated as (see the appendix for derivation and assumptions)

$$\begin{eqnarray}&&{{E}_{0}}=1.45\times {{10}^{45}}{{\left( \frac{{{F}_{\nu p}}}{{\rm mJy}} \right)}^{23/19}}{{\left( \frac{{{\nu }_{p}}}{{\rm GHz}} \right)}^{-1}}{{\left( \frac{D}{{\rm Mpc}} \right)}^{46/19}}\;{\rm erg}.\end{eqnarray} \tag{ 1 }$$

Using the SSA spectral fits from age 18 days, the epoch with the smallest fractional uncertainties in peak flux density F_νp and peak frequency ν_p, we estimate (1.0 ± 0.1) × 10⁴⁹ erg of energy in the relativistic ejecta. This estimate is robust, irrespective of whether one chooses a relativistic or Newtonian blastwave model. This energy is comparable to the energy observed in the relativistic outflows from SN 2009bb and supernovae such as SN 1998bw associated with sub-energetic GRBs in the local universe. This energy estimate forces the plausible combinations of ejected mass and initial velocity (see Figure 5) to lie in a narrow region above and parallel to the magenta line for 10⁴⁹ erg.

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In addition, the model allows us to derive (see the appendix) the mass loss rate of the progenitor responsible for the circumstellar interaction. Again, using the data from age 18 days, we estimate the pre-explosion mass loss rate between $6.0\times {{10}^{-6}}$ and $6.5\times {{10}^{-5}}\;{{M}_{\odot }}\ {\rm y}{{{\rm r}}^{-1}}$, depending on whether one uses a relativistic or Newtonian blastwave model, respectively. This range of values is consistent with the expected mass loss rate of Wolf–Rayet stars (Nugis & Lamers 2000) and is comparable to the case of SN 2009bb (Soderberg et al. 2010). The upper limit on the mass loss rate, derived by Margutti et al. (2014) using X-ray non-detection from the Chandra X-ray observations, rules out the higher mass loss rate derived from the non-relativistic model. This encourages us to prefer the lower of these values. Hence, we prefer the relativistic blaswave model. Since we find the radio afterglow of SN 2012ap in a decelerating phase, its relativistic outflow must have already swept up a mass of circumstellar matter greater than its own mass. This can place an upper limit on the mass of the relativistic ejecta, which is easily estimated since we have already determined the circumstellar density and blastwave radius. This argument constrains the mass of the relativistic ejecta to be $\lesssim 1.2\times {{10}^{-5}}\;{{M}_{\odot }}$. This restricts the allowed range of initial parameters for SN 2012ap (see yellow box in Figure 5). Hence, the mass of the ejecta component powering the radio afterglow of SN 2012ap is much less than that responsible for the optical light curve of a typical supernova and closer to the estimated mass of the relativistic component of a GRB's ejecta.

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