The double-peaked radio light curve of PTF11qcj
N. T. Palliyaguru A. Corsi D. A. Frail J. Vinkó J. C. Wheeler A. Gal-Yam S. B. Cenko S. R. Kulkarni M. M. Kasliwal











    The double-peaked radio light curve of PTF11qcjPalliyaguru et al.Texas Tech University, Physics Department, Box 41051, Lubbock, TX 79409, USAArecibo Observatory, HC3 Box 53995, Arecibo, PR 00612, USATexas Tech University, Physics Department, Box 41051, Lubbock, TX 79409, USANational Radio Astronomy Observatory, 1003 Lopezville Road, Socorro, NM 87801, USAKonkoly Observatory, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, Konkoly-Thege M. út 15-17, Budapest, 1121, HungaryDepartment of Optics and Quantum Electronics, University of Szeged, Dómtér 9, Szeged, 6720 HungaryDepartment of Astronomy, University of Texas at Austin, Austin, TX, 78712, USADepartment of Astronomy, University of Texas at Austin, Austin, TX, 78712, USABenoziyo Center for Astrophysics, Weizmann Institute of Science, 76100 Rehovot, IsraelAstrophysics Science Division, NASA Goddard Space Flight Center, Mail Code 661, Greenbelt, MD 20771, USAJoint Space-Science Institute, University of Maryland, College Park, MD 20742, USADivision of Physics, Math and Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USADivision of Physics, Math and Astronomy, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125, USA
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    We present continued radio follow–up observations of PTF11qcj, a highly energetic broad-lined Type Ic supernova (SN), with a radio peak luminosity comparable to that of the γ–ray burst (GRB) associated SN 1998bw. The latest observations, carried out with the Karl G. Jansky Very Large Array (VLA), extend up to ∼5 years after the PTF11qcj optical discovery.
    The radio light curve shows a double–peak profile, possibly associated with density variations in the circumstellar medium (CSM), or with the presence of an off-axis GRB jet.
    Optical spectra of PTF11qcj taken during both peaks of the radio light curve do not show the broad Hα features typically expected from H–rich circumstellar interaction. Modeling of the second radio peak within the CSM interaction scenario requires a flatter density profile and an enhanced progenitor mass–loss rate compared to those required to model the first peak. Although our radio data alone cannot rule out the alternative scenario of an off–axis GRB powering the second radio peak, the implied off-axis GRB parameters are unusual compared to typical values found for cosmological long GRBs. Deep X–ray observations carried out around the time of the second radio peak could have helped distinguish between the density variation and off-axis GRB scenarios. Future VLBA measurements of the PTF11qcj radio ejecta may unambiguously rule out the off-axis GRB jet scenario. 
    
    
    
    § INTRODUCTION
    
    The reason why some massive stars explode as supernovae (SNe) and others as rare γ–ray bursts (GRBs) remains a mystery.
    Type Ib/c supernovae (SNe) are the result of the core collapse of massive stars, specifically the ones that have shed their hydrogen, and possibly helium, envelopes.
    Massive Wolf Rayet (WR) stars and stars in close binary systems, that have completely lost their outer hydrogen layer due to stellar wind or through Roche-lobe overflow, respectively, are possible progenitors of these SNe <cit.>.
    Long duration (≳ 2 s) GRBs, with their engine–driven collimated outflows, are also thought to originate from the core collapse of massive stars <cit.>, being a rare subset of Type Ib/c SNe.
    The leading scenario is that all long GRBs are accompanied by core–collapse SNe (though not all Ib/c SNe are accompanied by GRBs). In some long GRBs, the SN light may go undetected due to reasons such as large distances, poor localizations, dust extinction and galaxy contamination <cit.>. It is noteworthy, however, that some nearby, well-localized GRBs without significant dust obscuration have been identified without a SN association <cit.>.
    
    So far,  ∼ 11 Type Ib/c SNe have been discovered in connection with GRBs <cit.>, pointing to a relationship between the two events.
    These include SN 1998bw <cit.> associated with GRB 980425, and a few more SNe <cit.>. SNe with a GRB association are generally more energetic than typical Type Ib/c SNe <cit.>, with explosion kinetic energies of ∼10^52 erg <cit.> for the former, and ∼10^51 erg <cit.> for the latter, and
    also have broad features in their optical spectra <cit.> that imply high photospheric velocities.
    
    In the radio, most "ordinary" BL-Ic SNe go undetected or are "radio quiet" <cit.>. On the other hand, the GRB-associated SN 1998bw was three orders of magnitude more radio luminous than, for example, the ordinary BL-Ic SN 2002ap, although a few orders of magnitude less radio-luminous than cosmological GRB afterglows <cit.>.  Because radio emission probes the fastest ejecta, radio-loud BL-Ic SNe are more likely to be engine-driven (i.e., associated with GRBs). However, the radio-loud Ib/c SN 2009bb showed no clear evidence for an association with a (high-luminosity) GRB <cit.>, opening the question of whether there is  a class of core-collapse explosions with properties in between ordinary BL-Ic SNe and GRBs. In fact, the γ-ray energy of several GRBs with a spectroscopic SN association is also lower than that of typical cosmological GRBs <cit.>. This suggests that low-luminosity GRBs themselves may represent a distinct population of intrinsically lower-energy events <cit.>, although (for at least some of them) an interpretation as ordinary GRBs observed off-axis is also possible <cit.>.
    
    Off-axis GRBs are a natural expectation of the fireball model <cit.>. An off-axis GRB accompanying a relativistic (engine-driven) BL-Ic SN should become visible at late times in the radio <cit.>, thus representing a potential source of radio-loud emission with characteristic timescales (≳ 100 d since explosion) much longer than the radio peak time of 1998bw-like SNe <cit.>.  The discovery of an off-axis long GRB associated with a BL-Ic SN remains, as of today, yet to be achieved.
    In fact, all previous claims of off-axis GRB discoveries  <cit.> have subsequently been ruled out <cit.>. 
    
    One of the challenges in searching for off-axis events is the fact that the characteristic late-time peaking radio light curve of an off-axis GRB (whose emission enters our line of sight after substantial deceleration has occurred) may, at first glance, look similar to that of a non-relativistic SN whose ejecta are interacting strongly with a dense CSM. In radio SNe powered by synchrotron self-absorbed emission, the radio peak luminosity and the peak timescale probe the ejecta speed. Particularly, for a given radio luminosity, the later the peak time, the smaller the ejecta speed <cit.>. A relatively slow turn–on in the radio has been observed in radio-bright non-relativistic Ib/c SNe such as SN 1979C and SN 1988Z <cit.>, thought to be  powered by shock interaction with a high-density medium <cit.>. 
    SN 2001em, SN 2003bg, SN 2004cc, SN 2004dk, SN 2004gq, and SN 2007bg <cit.> are other more recent examples of (non-relativistic) SNe that exhibit late–time radio emission arising from CSM density variations. In summary, distinguishing between CSM-interaction and off-axis GRB jets requires an accurate analysis of broad-band datasets.
    
    Here, we present late-time radio observations of PTF11qcj, a bright BL-Ic SN for which the radio luminosity is ∼ 10^29erg s^-1 Hz^-1, comparable to that of SN 1998bw <cit.>. Our extended radio follow-up observations of PTF11qcj show evidence for the presence of a second, late-time peak in its radio light curve. While the first radio peak pointed to a speed of the fastest ejecta of ≈ 0.3-0.5 c and a high progenitor mass-loss rate (∼ 10^-4 M_⊙ yr^-1) indicative of strong CSM interaction  <cit.>, here we focus on the analysis of the second late-time radio peak within the two possible scenarios of strong CSM interaction and off-axis GRB. Our extensive radio dataset is presented in Section 2; modeling of the radio data is discussed in Section 3; and results are presented in Section 4.
    In Section 5 we conclude.
    
    
    
    § OBSERVATIONS
    
    PTF11qcj was discovered by the Palomar Transient Factory <cit.> on November 1st, 2011 UTC (MJD 55866), at α=13^h13^m41.51^s, δ=+47^∘ 17 57.0, and at a redshift of z=0.028, corresponding to a luminosity distance of d_L≈124 Mpc <cit.>.
    Early optical observations and VLA follow–up data are presented in <cit.>.
    In this Section we describe later radio follow–up observations and spectroscopic data.
    
    
    
     §.§ Radio follow–up
    
    The VLA follow–up observations presented here were carried out between June 1st 2014 (MJD 56809) and December 7th 2016 (MJD 57729).
    The data were taken at the nominal central frequencies of 2.5, 3.5, 7.4, 13.5 and 16 GHz with a nominal bandwidth of 2 GHz.
    3C286 and J1327+4326 were used as flux and phase calibrators, respectively.
    
    
    
    The Common Astronomy Software applications <cit.>[Available online at http://casa.nrao.edu]
     was used to calibrate, flag and image the data.
    The automated VLA calibration pipeline for CASA was used to calibrate the raw data.
    Images were formed from the visibility data using the CLEAN algorithm <cit.>.
    The image size was set to (1024×1024) pixels, and the pixel size was determined as 1/4 of the nominal beam width.
    The images were cleaned using natural weighting for 10000 iterations or until a threshold of ∼0.03 mJy (∼3σ) was reached.
    
    The source flux was calculated as the flux corresponding to the brightest pixel
    within a circle centered around the PTF position with a radius of 2<cit.>.
    Figure <ref>
    shows the radio light curves of PTF11qcj, with the new
     data from MJD 56809 onwards plotted along with the data from <cit.>.
    Flux errors are calculated as the quadratic sum of the rms map error and a 5% fractional error that accounts for errors in the flux calibration <cit.>.
    We note that results from imfit, that fits a two dimensional elliptical Gaussian to a source, do not show evidence for extended emission, confirming that the radio counterpart of PTF11qcj is a point source up to ≈ 0.27 arcsec, which is the beam size in the VLA A array configuration at 7.4 GHz.
    The fluxes at each MJD and frequency for the latest observations are reported in Table <ref>.
    
    
    
     §.§ Spectroscopic follow–up
    
    The location of PTF11qcj was observed with the Low Resolution Spectrograph-2 (LRS-2) attached to
    the Hobby-Eberly Telescope (HET) on February 22, 2017 UT.
    LRS-2 is a twin IFU spectrograph having
    two arms each:  LRS2-B covers the range between 3700–4700 Å  (blue arm) and 4600–7000 Å 
    (orange arm) with resolving power of 1900 and 1100, respectively, while LRS2-R covers the range from
    6500 to 8400 Å  (red arm) and from 8200 to 10500 Å  (far-red arm) at a resolution of
    1800 in each arm <cit.>. Each IFU maps a 12" × 6" area on
    the sky covered by 280 fibers. The coverage is complete, so no dithering is required.
    
    We utilized the red arm of LRS2-R to collect spectra in the vicinity of the SN.
    Figure <ref> shows the SDSS r-band frame of the host galaxy of PTF11qcj with the
    SN position marked in red. The blue rectangle indicates the position of the LRS2-R IFU (it was
    not completely centered on the SN due to a minor pointing issue). A spectrum at the SN position was extracted by median-combining the signal of
    the three closest fibers. Wavelength calibration was computed using FeAr spectral
    lamp observations. Flux calibration was performed by comparing the
    observed and flux-calibrated catalogued spectra of the standard star HD 84937.
    
    The final LRS2 spectrum of PTF11qcj is plotted in Figure <ref> together with the
    spectrum obtained with the Keck2-DEIMOS on 2012-03-20 <cit.>.
    This plot suggests that the broad SN features that were clearly visible
    in the Keck spectrum 5 years ago (typical nebular features due to forbidden transitions of
    neutral oxygen [O I] λλ 6300,6364 and ionized [Ca II] λλ 7291,7324), may still be present in the new HET-LRS2 spectrum although with a smaller signal–to–noise.
    Also, the bright, narrow Hα feature present in both spectra appears basically
    unchanged (in both strength and width). No broad Hα feature can be identified in the HET-LRS2 spectrum of PTF11qcj (as was the case for the older Keck spectrum during the first radio peak), thus excluding H-rich CSM interaction similar to SN 2014C <cit.>.  As discussed in what follows,  interaction with an
     H-poor CSM may explain the late-time radio re-brightening.
    
    
    
    § RADIO MODELING
    
    As shown in  in Figure <ref>, the higher-frequency (13.5 and 16 GHz) radio light curves of PTF11qcj appear double–peaked. At lower frequencies, a late-time re-brightening is also evident.
    We thus identify two phases in the evolution of the radio emission, with the first peak in between ∼MJD 55842 and ∼MJD 56101, and the second starting from ∼MJD 56101.
    
    As discussed in Section <ref>, bright radio emission in a SN may be powered by the presence of a central engine, or via the interaction of the ejecta with the the CSM. Within the CSM-interaction scenario, a double-peaked radio light curve may be attributed to density variations in the CSM  <cit.> due to variable (potentially eruptive) mass loss from the SN progenitor, or clumping due to turbulence in the medium and violent outbursts <cit.>. In the case of a binary SN progenitor, variable radio emission may occur due to two different wind components from the two stars in the binary and/or the interaction of the shock with the common envelop or the wind termination shock <cit.>. On the other hand, in the engine-driven scenario, a late–time peak in the radio light curve may be expected from an off–axis GRB: as the ultra-relativistic jet transitions to the sub-relativistic regime, it also spreads sideways resulting in a re-brightening of the radio SN light curve <cit.>.
    
    In light of the above, in what follows we model the PTF11qcj light curves within both the synchrotron self-absorption (SSA) model with CSM density variations <cit.>, and the off-axis GRB afterglow model <cit.>.
    
    
    
    
     §.§ CSM-interaction SSA model
    <cit.> model describes the radio emission from SN ejecta interacting with the CSM.
    The radio flux density at time t and frequency ν is given by:
    
        F(t,ν)=C_f(t-t_e/t_0)^(4α_r-α_B)/2[1-exp^-τ_ν^ξ(t)]^1/ξν^5/2F_3(x)F_2^-1(x),
    
    with the optical depth given by
    
        τ_ν(t)=C_τ(t-t_e/t_0)^(3+p/2)α_B+(2p-3)α_r-2(p-2),
    
    where C_f, C_τ are normalization constants, F_2, F_1 are Bessel functions and x=2/3(ν/ν_m) where ν_m is the critical synchrotron frequency, t_0 is a reference epoch, t_e is the explosion time, p is the electron energy index, ξ=[0,1] describes the sharpness of the spectral break between optically thin and thick regimes <cit.>.
    In the above equations, α_r and α_B are the temporal indices of the shock radius r and the magnetic field B respectively, such that
    
        r=r_0(t-t_e/t_0)^α_r,
    
    and
    
        B=B_0(t-t_e/t_0)^α_B,
    
    where r_0 and B_0 the radius and magnetic field at the reference epoch t_0.
    The expansion of the SN shock is described by: 
    
        α_r=n-3/n-s,
    
    where ρ_ej∝ r^-n is the density profile of the outer SN ejecta, and
     ρ_CSM∝ n_e ∝ r^-s that of the shocked CSM (or shocked electron density).
    The self–similar conditions s<3 and n>5<cit.> result in α_r<1. 
    
    In the standard scenario, the magnetic energy density and the relativistic
    electron energy density are constant fractions, ϵ_B and ϵ_e respectively, of the post-shock energy density. Under these assumptions:
    
        α_B=(2-s)/2α_r-1,
    
    and the minimum Lorentz gamma factor and the critical synchrotron frequency of the radiating electrons read:
    
        γ_m=γ_0(t-t_e/t_0)^2 (α_r-1),
    
        ν_m=ν_m,0(t-t_e/t_0)^(10α_r-sα_r-10)/2.
    
    
    The electron number density within the shocked CSM is given by:
    
        n_e=p-2/p-1(ϵ_e/ϵ_B) B_0^2/8π m_ec^2γ_m,0(t-t_e/t_0)^-sα_rcm^-3,
    
    where m_e is the electron mass, and c the speed of light.
    The SN progenitor mass loss rate reads:
    
        Ṁ=8π n_e m_pr_0^2v_w/η(t-t_e/t_0)^α_r(2-s),
    
    where m_p is the proton mass, v_w is the wind velocity,
    while
    η describes the thickness, r/η, of the radiating shell at radius r. Finally, the ejecta energy reads:
    
        E=4π r_0^2B_0^2/η 8πϵ_B(t-t_e/t_0)^5α_r -s α_r - 2.
    
    Hereafter, we work under the equipartition hypothesis and set ϵ_e=ϵ_B=0.33. We note that departures from equipartition would imply ϵ_e/ϵ_B≳ 1 and likely point to ϵ_B≲ 0.33, thus increasing both the shocked electron number density  (and, in turn, the estimated mass-loss rate; see Eqs. (9)-(10)), and the energy budget (Eq. (11)).
    
    
    As evident from the Equations (1)-(2) and (4)-(8), the observed flux at a given frequency ν and time t depends on C_f, C_τ, p, s, α_r, ν_m,0, ξ and t_e. Since
    C_f, C_τ can be expressed in terms of r_0 and B_0 (see <cit.> Equations 6-8), the observed flux ultimately depends on r_0, B_0, p, s, α_r, ν_m,0, ξ and t_e, which we determine by comparison with the observed data using a χ^2 minimization procedure <cit.>.
    In modeling the radio emission from PTF11qcj, following <cit.>, we set t_0=10 days and ν_m,0≈ 1 GHz.
    When deriving the mass-loss rate and energy implied by the best-fit results (from Equations (8)-(9)), we also assume a shell thickness of η=10.
    
    
    
     §.§ Off-axis GRB afterglow model
    
    In a scenario in which PTF11qcj is powered by a central engine, we may interpret its double-peaked radio light curves as a combination of
    radio emission from an uncollimated (non relativistic) SN shock interacting with a dense CSM <cit.>, and that of an off-axis relativistic jet entering our line of sight at late times, as the jet decelerates and spreads sideways <cit.>.  The jet dynamics in the relativistic regime is described by the Blandford-Mckee solution <cit.>, and in the late non-relativistic regime by the Sedov-von Neumann–Taylor (SNT) solution <cit.>.
    
    Because analytical solutions for the dynamics of a spreading and decelerating relativistic jet cannot fully capture the details (sideways expansion and transition to the non-relativistic regime) of the blast wave evolution, hereafter we use the high-resolution relativistic hydrodynamic simulations by <cit.> and <cit.> for a jet expanding in a constant density ISM. These two-dimensional simulations include the transition from the relativistic to non-relativistic regime, which is essential to accurately model the GRB outflow at late times <cit.>. The observed flux can be modeled as a function of eight parameters: the isotropic equivalent kinetic energy of the explosion, E_ iso; the circumburst medium number density, n_ ISM; the jet half-opening angle, θ_0; the observer's angle, θ_obs; the fraction of internal energy in the shock going into magnetic fields; ϵ_e; the fraction of internal energy going into accelerating electrons, ϵ_B; the fraction of electrons shock–accelerated in a power–law energy distribution, ξ_N∼1;  and the power-law index of the accelerated electron energy distribution, p. These parameters are determined by comparison with the observed fluxes (at each observed frequency and time) using a χ^2 minimization procedure <cit.>.
    
    
    
    § RESULTS
    
    
     §.§ CSM-interaction radio fits
    
    In Table <ref> and Figure <ref> we report fit results for the second radio peak of PTF11qcj within the synchrotron SSA scenario described in Section 3.1 (Model 1). We impose a smooth radial evolution of the SN shock, i.e. we require that  that r_0 and α_r remain unchanged with respect to what found during the first radio peak (Model 0), and attempt to model the second radio peak by varying the wind density profile (s and, in turn, α_B; see Eq. (5)) and the magnetic field (B_0). This is justified by the consideration that a change in these parameters at fixed r_0 and α_r effectively corresponds to a change in CSM density as  F_ν∝ B^4 ∝ n^2_e<cit.>. We also allow for variations in ξ. The model was fit to the data obtained after MJD 56429, which is around the time re-brightening occurs, yielding a χ^2/ dof=575/35 (see Table <ref>). We note that including the rising data points in the fit results in B_0≈1.9, s≈0.87 and ξ≈0.17, and a χ^2/ dof=1703/49.
    
    The physical parameters derived from Model 1 best fit results are shown in Figure <ref>. As evident from this Figure, the best-fit requires an increase in energy and mass-loss rate during the second radio peak. This is similar to what observed in e.g. the CSM-interacting SN 2003bg <cit.>. In Figure <ref> we show the uncertainties in the best fit results for s and B_0, which shows that during the second radio peak a flattening in the CSM profile is also required (compared to the first peak). We note that a flattening in the density profile may be attributed to passage  through a termination shock <cit.>, although the simplified analytical model used here does not allow us to properly account for other sources of possible density profile variations such as e.g. clumpiness in the stellar wind.
    
    
    
    
     §.§ Off-axis GRB radio fits
    
    We use the off-axis afterglow model described in Section 3.2 to model the second radio peak in the PTF11qcj light curve. In our fits, ϵ_e=ϵ_B=0.33, and p are held fixed.
    
    For a fireball expanding in a constant density medium, we find a best fit with an explosion energy of E_ iso≈7×10^52 erg, θ_0≈0.3 rad, ISM density n_ ISM≈3×10^-5  cm^-3, θ_ obs≈0.6 rad, and a χ^2/ dof=1167/36 (Figure <ref>, dashed curve). The ISM density predicted by this model is rather low compared to typical long GRBs which have n_ ISM≳1  cm^-3. Low ISM densities, although peculiar, are not unseen in long GRBs broad-band afterglow modeling <cit.>. For completeness, we have also carried out a fit where n_ ISM is set to the typical long GRB value of 1  cm^-3, and E_iso, θ_0, and θ_ obs are allowed to vary. This fit returns E_ iso≈2×10^53 erg, θ_0≈0.05 rad, θ_ obs≈0.17 rad, and a χ^2/ dof=4154/37.
    
    
    § DISCUSSION AND CONCLUSION
    
    We have presented PTF11qcj late–time VLA observations up to ∼5 years since optical discovery, and late–time spectroscopic follow–up with the HET at ≈ 5 yr post explosion.
    The radio luminosity of PTF11qcj is as high as that of the GRB–associated SN 1998bw.
    The radio light curves show a double–peak profile, with the first peak emerging at ≈100 days since explosion, and the second at ≈2000 days (≈ 5.5 yrs) since explosion. We model the second radio peak (i) with CSM density variations in the standard synchrotron SSA model <cit.>, and (ii) within
    an off–axis GRB model  <cit.>.
    
    We find that density enhancements alone (Model 1) may explain the late–time re-brightening of PTF11qcj.
    Radio modeling suggests an enhanced mass-loss rate during the second radio peak.
    Even though precursor eruptions have mostly been detected in type IIn SNe, evidence for pre–SN activity was detected in the pre-explosion images of PTF11qcj around May–July 2009 <cit.> hinting at the possibility of such mass–loss episodes being responsible for the enhanced mass–loss rate during the second peak.
    Assuming the explosion took place on MJD 55842, and with r_0∼10^16 cm and α_r≈0.8,  the shock radius would have reached r≈4× 10^17 cm around 1000 days since the explosion (i.e., around the peak of the re-brightening phase).
    If material from the pre-SN activity observed in 2009 (∼ 860 d before the explosion) was responsible for the radio re-brightening, the progenitor wind would have traveled at a speed ∼ 24,000  km s^-1, which is way to high compared to typical stellar winds for stripped-envelope core-collapse SN progenitors (∼ 1000 km s^-1).
    The non–detection of H-rich material (to a level distinguishable by our HET/LRS2 spectrum) during the second radio peak also imply that H-rich layers would have been shed well before the 2009 pre-SN activity.
    
    If an off–axis GRB is invoked to explain the late–time radio re-brightening, a
    very low n_ ISM value is required to fit the data. We note that the off–axis afterglow scenario predicts a detectable X–ray flux of 5×10^-6 mJy at ∼500 days since the explosion, corresponding to ≈1×10^-14  erg s^-1 cm^-2 at 1 keV - detectable with a 10 ks observation with Chandra. On the other hand, in the SSA model extrapolating the peak radio flux to the X-ray band with a spectral index of β∼1 (where β=-(p-1)/2, with p=3), gives an expected flux of ∼4×10^-7 mJy at 1 keV (corresponding to 8×10^-16  erg s^-1 cm^-2).
    Therefore, we emphasize the importance of observing future events at X–ray frequencies close to the radio peak[While we have secured a late-time Chandra ToO observation of PTF11qcj, execution of our ToO was delayed to 2018 due to scheduling issues.].
    
    <cit.> pointed out that in GRB-SNe, the SN carries most of the energy compared to the γ–ray energy of the jet - an indication that the SN is powered by a central engine.
    Since we cannot rule out the off-axis GRB scenario for PTF11qcj, we attempt to estimate the γ–ray energy of a hypothetical GRB associated with PTF11qcj under the assumption that this was an engine-driven SN.
    From the analysis of four GRB-SNe, <cit.> finds that the peak spectral energy of GRBs and the peak bolometric luminosity of the underlying supernova are related by
    ν_γ,peak=90.2   keV(L_ SN,peak/10^43  erg s^-1)^4.97.
    Considering the peak bolometric luminosity of PTF11qcj ≳10^9.3L_⊙<cit.>, the peak γ-ray energy of a hypothetical GRB can be expected to be ≳ 23 keV.
    Then assuming the correlation between the ν_γ, peak and E_ iso as ν_γ,peak=97  keV(E_γ,iso/10^52  erg s^-1)^0.49<cit.>, we derive E_ iso≳ 5×10^50 erg may be expected. Incidentally we note that our fit of the second radio peak within the off-axis GRB model implied E_ iso∼ 7×10^52 erg, so the two results are not in contrast with each other if one assumes a kinetic-energy-to-γ-ray-energy conversion efficiency of ≳ 1%.
    
    We finally note that within the SSA scenario, the expected angular diameter of PTF11qcj would reach the ∼ 1 mas level at ∼ 2500 d post explosion, or around 6.8 yr since explosion. A larger angular diameter may be realized if higher ejecta speeds (such as those associated with a GRB jet) would have occurred at any time during the evolution of this explosion. Thus, late-time VLBI observations could potentially probe directly the size of PTF11qcj, and may help distinguish between the standard SSA and off-axis hypothesis.
     A.C. and N.T.P. acknowledge support from the NSF CAREER award #1455090. J.V. is supported by the GINOP-2.3.2-15-2016-00033 project which is funded by the
    Hungarian National Research, Development and Innovation Fund and the European Union.
    JCW is supported in part by the Samuel T. and Fern Yanagisawa Regents Professorship. A.G.-Y. is supported by the EU via ERC grant No. 725161, 
    the Quantum Universe I-Core program, the ISF, the BSF Transformative program and by a Kimmel award.
    The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
    
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