Radio observations of a sample of broad-lined type Ic supernovae discovered by PTF/iPTF: A search for relativistic explosions
A. Corsi, A. Gal-Yam, S.R. Kulkarni, D.A. Frail, P.A. Mazzali, S.B. Cenko, M.M. Kasliwal, Y. Cao, A. Horesh, N. Palliyaguru, D.A. Perley, R.R. Laher, F. Taddia, G. Leloudas, K. Maguire, P.E. Nugent, J. Sollerman, M. Sullivan
AApril 17, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
RADIO OBSERVATIONS OF A SAMPLE OF BROAD-LINED TYPE IC SUPERNOVAE DISCOVERED BYPTF/IPTF: A SEARCH FOR RELATIVISTIC EXPLOSIONS
A. Corsi , A. Gal-Yam , S. R. Kulkarni , D. A. Frail , P. A. Mazzali , S. B. Cenko , M. M. Kasliwal ,Y. Cao , A. Horesh , N. Palliyaguru , D. A. Perley , R. R. Laher , F. Taddia , G. Leloudas , K. Maguire ,P. E. Nugent , J. Sollerman , M. Sullivan April 17, 2018
ABSTRACTLong duration γ -ray bursts are a rare subclass of stripped-envelope core-collapse supernovae thatlaunch collimated relativistic outflows (jets). All γ -ray-burst-associated supernovae are spectroscop-ically of Type Ic with broad lines, but the fraction of broad-lined Type Ic supernovae harboringlow-luminosity γ -ray-burst remains largely unconstrained. Some supernovae should be accompaniedby off-axis γ -ray burst jets that remain invisible initially, but then emerge as strong radio sources(as the jets decelerate). However, this critical prediction of the jet model for γ -ray bursts has yetto be verified observationally. Here, we present K. G. Jansky Very Large Array observations of 15broad-lined supernovae of Type Ic discovered by the Palomar Transient Factory in an untargetedmanner. Most of the supernovae in our sample exclude radio emission observationally similar to thatof the radio-loud, relativistic SN 1998bw. We constrain the fraction of 1998bw-like broad-lined Type Icsupernovae to be (cid:46)
41% (99.865% confidence). Most of the events in our sample also exclude off-axisjets similar to GRB 031203 and GRB 030329, but we cannot rule out off-axis γ -ray-bursts expand-ing in a low-density wind environment. Three supernovae in our sample are detected in the radio.PTF11qcj and PTF14dby show late-time radio emission with average ejecta speeds of ≈ . − . (cid:46)
85% (99.865% confidence) of the broad-lined TypeIc supernovae in our sample may harbor off-axis γ -ray-bursts expanding in media with densities inthe range probed by this study. Subject headings: gamma-ray burst: general — radiation mechanisms: non-thermal — supernovae: general1.
INTRODUCTION
Long-duration ( T γ (cid:38) γ -ray bursts (GRBs) are ex-tremely energetic explosions (typically, ≈ erg re- Department of Physics, Texas Tech University, Box41051, Lubbock, TX 79409-1051, USA. E-mail: [email protected] Benoziyo Center for Astrophysics, Weizmann Institute ofScience, 76100 Rehovot, Israel. Division of Physics, Mathematics, and Astronomy, Califor-nia Institute of Technology, Pasadena, CA 91125, USA. National Radio Astronomy Observatory, P.O. Box O, So-corro, NM 87801, USA Astrophysics Research Institute, Liverpool John Moores Uni-versity, Liverpool L3 5RF, UK. Max-Planck Institut fur Astrophysik, Karl-Schwarzschildstr.1, D-85748 Garching, Germany. Astrophysics Science Division, NASA Goddard Space FlightCenter, Mail Code 661, Greenbelt, MD 20771, USA. Joint Space-Science Institute, University of Maryland, Col-lege Park, MD 20742, USA. Dark Cosmology Centre, Niels Bohr Institute, University ofCopenhagen, Juliane Maries Vej 30, 2100 Copenhagen, Den-mark. Spitzer Science Center, California Institute of Technology,M/S 314-6, Pasadena, CA 91125, USA Department of Astronomy, The Oskar Klein Center, Stock-holm University, AlbaNova, 10691 Stockholm, Sweden. Astrophysics Research Centre, School of Mathematics andPhysics, Queen’s University Belfast, Belfast BT7 1NN, UK Department of Astronomy, University of California, Berke-ley, CA 94720-3411, USA. Lawrence Berkeley National Laboratory, 1 Cyclotron Road,MS 50B-4206, Berkeley, CA 94720, USA Department of Physics and Astronomy, University ofSouthampton, Southampton, SO17 1SX, UK. leased in ≈
10 s, also referred to as collapsars) markingthe deaths of massive stars (Galama et al. 1998; Woosley& Bloom 2006). According to the popular fireball model(Piran 2004; M´esz´aros 2006), the explosion launches rel-ativistic jets in which magnetic fields are amplified andparticles accelerated (Rhoads 1999). Observers locatedwithin the initial jets’ opening angle ( θ j (cid:38) θ obs ; “on-axis” observers) see an intense flash of γ -rays. Sub-sequent emission from the decelerating jets produces a(slowly) decaying broad-band afterglow. If the fireballmodel is correct, then off-axis GRBs should exist and be ≈ /θ j times more common than the ones we see in γ -rays (Granot et al. 2002). While γ -ray emission from off-axis GRBs cannot be observed, their longer-wavelengthafterglow emission is expected to become observable atlater times, once the jet decelerates and starts spreading(Nakar et al. 2002).Off-axis GRBs have not been discovered so far, butin the light of the well-established connection betweenlong-duration GRBs and core-collapse supernovae (SNe)of spectral type Ic with broad-lines (BL-Ic; Woosley &Bloom 2006), a natural way to search for off-axis events isto observe this type of SNe and wait for the deceleratingjet to emerge. While the SN optical emission traces theslower explosion debris ( v ≈ . − . (i): the SN shock, whose radio emission is brighterand earlier-peaking the faster the SN ejecta, a r X i v : . [ a s t r o - ph . H E ] O c t Corsi et al.with expected luminosity and peak time of ≈ erg cm − s − Hz − and ≈ −
30 d since ex-plosion, respectively, for relativistic events likeSN 1998bw (Galama et al. 1998; Kulkarni et al.1998; Berger et al. 2003a); (ii): the GRB jet which, if off-axis, would be observedonly when the SN ejecta decelerate to mildly orsub-relativistic speeds, thus producing a delayedand nearly-isotropized radio emission.Radio is indeed the best wavelength range for identify-ing relativistic events such as SN 1998bw, and/or off-axisGRBs (Granot & Loeb 2003; Paczynski 2001). In thepast, hundreds of SNe Ib/c have been targeted with theKarl G. Jansky Very Large Array (VLA; Berger et al.2003a; Soderberg et al. 2006c; Bietenholz et al. 2014)and the fraction of SNe Ib/c associated with GRBs hasbeen constrained to (cid:46) − γ -rays) from GRBs observed slightly off-axis (and/or “dirty” fireballs; Section 3). We per-formed cm-wavelength follow-up observations of all theSNe in our sample with the VLA (Section 2.4), insearch for SN 1998bw-like radio emission (point (i) above)and/or later-time signatures of off-axis jets (point (ii)above). Our sample greatly enlarges the sample of radio-monitored BL-Ic SNe published over the last ≈
10 years(Berger et al. 2003a; Soderberg et al. 2006c; Ghirlandaet al. 2013; Bietenholz et al. 2014), and our observa-tional strategy allows us to probe a portion of the radioluminosity-time since explosion phase space that was leftlargely unexplored by previous studies (Section 4). Weconstrain the portion of the explosion energy-wind/ISMdensity parameter space that is excluded under the hy-pothesis that GRB jets significantly off-axis ( θ j ≈
90 deg) are associated with the SNe in our sample (Section 5),and set an upper-limit on the fraction of BL-Ic SNe inour sample that show radio emission possibly compatiblewith off-axis GRBs expanding in media with densities inthe range probed by this study (Section 6). Finally, wegive our conclusions (Section 7).Hereafter, we adopt cosmological parameter values of H = 69 . − Mpc − , Ω M = 0 . Λ = 0 . THE BL-IC SUPERNOVA SAMPLE
P48 discovery and photometry R -band (or g -band) discoveries (and follow-up) of theSNe in our sample (Table 1) were obtained using the48-inch Samuel Oschin telescope at the Palomar Obser-vatory (P48), which is routinely used by the PTF/iPTF.Processed images were downloaded from the InfraredProcessing and Analysis Center (IPAC) PTF archive(Laher et al. 2014). Photometry was performed relativeto the SDSS r -band (or g -band) magnitudes of stars inthe field (York et al. 2000). We used our custom pipelinewhich performs image subtraction, and then point spreadfunction (PSF) photometry on stacks of PTF images ex-tracted from the IPAC archive (Maguire et al. 2012; Ofeket al. 2012, 2013). The flux residuals from individualsubtracted images were binned, and converted to magni-tudes. Errors were estimated from the standard devia-tion of the photometric measurements in each bin.The R -band (or g -band) light curves of the SNe in oursample are shown in Fig. 1. PTF10bzf, PTF10qts, andPTF11qcj photometry was discussed previously in Corsiet al. (2011), Walker et al. (2014), and Corsi et al. (2014)respectively, so we do not present their photometry here(we refer the reader to these papers). The P48 discoverytime ( T P ), and the maximum R -band (or g -band) ab-solute magnitudes ( M R/g ) as measured by our P48 mon-itoring and corrected for Galactic extinction (Schlafly &Finkbeiner 2011), are reported in Table 1. Note that our M R/g is different from the SN light curve peak for casesin which the peak emission was not observed by P48. Wedo not take into account k-corrections when measuring M r/g , but refer the reader to Prentice et al. (2016) andTaddia et al. 2015 (in prep.) for a discussion of thesecorrections. Spectral classification
After the discovery with P48, we triggered a spectro-scopic follow-up campaign of all the SNe in our sample.PTF10bzf, PTF10qts, and PTF11qcj spectral propertieswere previously discussed in Corsi et al. (2011), Walkeret al. (2014), and Corsi et al. (2014) respectively, so wedo not present their spectral analysis here, but we referthe reader to these papers. For the rest of the SNe in oursample, details of the observations are reported in whatfollows. In Table 1, we also report the estimated red-shifts, and the velocities corresponding to the P-Cygni All spectra reported in this work will be made public viaWISeREP (Yaron & Gal-Yam 2012). adio emission from PTF broad-lined Type Ic supernovae 3
TABLE 1BL-Ic SNe with VLA observations in our sample. Our sample includes a total of 15 SNe, 12 of which arepresented here for the first time. PTF10bzf, PTF10qts, and PTF11qcj were previously discussed in Corsiet al. (2011), Walker et al. (2014), and Corsi et al. (2014) respectively.
PTF RA Dec T P48a z d L M R/g b v (Si) Ref.name (J2000) - - - [AB] - -- (hh:mm:ss deg:mm:ss) (MJD) (Mpc) (mag) (km s − )10bzf 11:44:02.99 +55:41:27.6 55250.504 0.0498 223 -18.3 2 . × Corsi et al. (2011)10qts 16:41:37.60 +28:58:21.1 55413.260 0.0907 418 -19.4 1 . × Walker et al. (2014)10xem 01:47:06.88 +13:56:28.8 55470.340 0.0567 255 -18.6 2 . × This paper10aavz 11:20:13.36 +03:44:45.2 55514.485 0.062 280 -19.2 1 . × This paper11cmh 13:10:21.74 +37:52:59.6 55673.336 0.1055 491 -18.6 1 . × This paper11img 17:34:36.30 +60:48:50.6 55755.408 0.158 761 -19.6 1 . × This paper11lbm 23:48:03.20 +26:44:33.5 55793.259 0.039 173 -18.0 1 . × This paper11qcj 13:13:41.51 +47:17:57.0 55866.520 c . × Corsi et al. (2014)12as 10:01:34.05 +00:26:58.4 55925.298 0.033 146 -17.5 2 . × This paper13u 15:58:51.21 +18:13:53.1 56324.481 0.10 463 -18.9 1 . × This paper13alq d . × Drake et al. (2013)13ebw 08:17:15.88 +56:34:41.6 56621.389 0.069 313 -18.2 2 . × This paper14dby 15:17:06.29 +25:21:11.4 56832.238 0.074 337 -17.9 1 . × This paper14gaq 21:32:54.08 +17:44:35.6 56924.213 0.0826 378 -18.0 1 . × This paper15dld e . × This paper/LaSilla-QUEST a Discoveries times (T
P48 ) are from P48 observations in R -band, except for the case of PTF14gaq which was discoveredand observed with P48 in g -band. b M R/g is the maximum absolute magnitude in the P48 R -band for all of the SNe but PTF14gaq, for which M R/g ismeasured in the P48 g -band. These magnitudes are corrected for galactic extinction (Schlafly & Finkbeiner 2011). c The SN was visible in a previous g -band image taken on 2011 October 23. d a.k.a. CSS130415:114802+543439/SN 2013bn: PTF13alq was also discovered by the CRTS (Drake et al. 2009) andclassified as a 1998bw-like type Ic SN by the Copernico Telescope in Asiago (Tomasella et al. 2013). e PTF15dld/LSQ15bfp was also discovered by the La Silla-QUEST variability survey (Hadjiyska et al. 2012) and classifiedby the Public ESO Spectroscopic Survey of Transient Objects (PESSTO; Smartt et al. 2015). absorption minimum of the Si II PTF10xem
On 2010 October 10 UT ( ≈ (cid:48)(cid:48) wide slit, a 600/4310grism on the blue side, and a 300/7500 grating on the redside. Exposure time and air mass were 3600 s and 1.09,respectively. The derived spectrum shows a good matchwith the Ic/BL-Ic SN 2004aw (e.g., Taubenberger et al.2006) at an epoch of about 15 d since explosion, and withthe BL-Ic SN 2002ap at 6 d since explosion (Fig. 2), sowe classify PTF10xem as a BL-Ic SN. PTF10aavz
On 2010 November 30 UT ( ≈
16 d since optical discov-ery) we observed PTF10aavz using ISIS on the WilliamHerschel Telescope (WHT), with a 1.99 (cid:48)(cid:48) wide slit, theR300B grating set at a central wavelength of ≈ ≈ PTF11cmh
We observed PTF11cmh using ISIS on the WHT on2011 May 2 UT ( ≈
10 d since optical discovery), with a 1.02 (cid:48)(cid:48) wide slit, the R300B grating set at a central wave-length of ≈ ≈ PTF11img
We observed PTF11img on 2011 August 2 UT ( ≈
20 dsince optical discovery), using the Low Resolution Imag-ing Spectrometer (LRIS; Oke et al. 1995) mounted onthe Keck-I 10 m telescope. The spectrum was taken us-ing a 1 (cid:48)(cid:48) wide slit, with the 400/8500 grating set at acentral wavelength of ≈ PTF11lbm
We observed PTF11lbm using ISIS on the WHT on2011 August 31 UT ( ≈
11 d since optical discovery), witha 1.02 (cid:48)(cid:48) wide slit, the R300B grating set at a central wave-length of ≈ ≈ Fig. 1.—
The P48 R - or g -band light curves (corrected for Galactic extinction) of the BL-Ic SNe in our sample. PTF names are reported inthe title of each panel. For comparison, we also show the r -band light curve of the GRB-associated BL-Ic SN 1998bw (solid line; Clocchiattiet al. 2011), and of the “ordinary” BL-Ic SN 2002ap (dotted line; Pandey et al. 2003). Epochs on the x-axis are measured since the time ofmaximum emission as observed by P48 (and corrected for redshift effects). Note that the time of maximum as observed by P48 is differentfrom the SN light curve peak time for cases in which the peak emission was not observed by P48. For both the blue and red side observations, the exposuretime was 900 s. The mean air mass was about 1.01. Thederived spectrum shows a good match with both the BL-Ic SN 2002ap (e.g., Gal-Yam et al. 2002; Mazzali et al.2002) at 6 d since explosion, and the type Ic hypernovaSN 1997ef (e.g., Iwamoto et al. 1998) at 35 d since explo-sion (Fig. 2). We thus classify PTF11lbm as a BL-IcSN.
PTF12as
We observed PTF12as on 2012 January 2 UT ( ≈ (cid:48)(cid:48) wide slit, with a B400/R300 grating setup. Theexposure time and airmass were 1000 s and 1.50, respec-tively. The derived spectrum shows a good match withthe GRB-associated BL-Ic SN 2002ap (e.g., Mazzali et al.2002; Gal-Yam et al. 2002) at 6 d since explosion (Fig. 2). PTF13u
On 2013 February 18 UT ( ≈
17 d since optical discov-ery) we observed PTF13u with the Double Beam Spec-trograph (DBSP; Oke & Gunn 1982) on the Palomar200-inch telescope (P200). We used the 316/7500 and600/4000 gratings for red and blue camera respectively,with a D55 dichroic, resulting in a spectral coverage of ≈ (3500 − ≈
29 d since explosion (Fig. 2).
PTF13alq
On 2013 April 13 UT ( ≈ Fig. 2.—
Spectra of the SNe BL-Ic in our sample (black) compared to the spectra of the of the hypernova SN 1997ef (Iwamoto et al.1998; Branch 1999, epoch calculated since 1997 November 15), of the GRB-associated BL-Ic SN 1998bw (epoch calculated since 1998 April25; Patat et al. 2001), of the BL-Ic SN 2002ap (epoch calculated since 2002 January 28; Gal-Yam et al. 2002; Mazzali et al. 2002), ofthe BL-Ic/hyper-energetic and asymmetric SN 2003jd (epoch calculated since 2003 October 21; Valenti et al. 2008; Mazzali et al. 2005;Soderberg et al. 2006c), of the Ic/BL-Ic SN 2004aw (epoch calculated assuming an explosion date of ≈
15 d before maximum; Taubenbergeret al. 2006), and of the relativistic BL-Ic SN 2009bb (epoch calculated since 2009 March 19; Soderberg et al. 2010; Pignata et al. 2011).(See the electronic version of this paper for colors.) gratings for red and blue camera respectively, with a D55dichroic, resulting in a spectral coverage of ≈ (3500 − PTF13ebw
We observed PTF13ebw on 2013 December 4 UT ( ≈ (cid:48)(cid:48) wide slit, with the 400/8500 grating set at a cen-tral wavelength of ≈ PTF14dby
On 2014 June 29 ( ≈ (cid:48)(cid:48) wide slit,with the 400/8500 grating set at a central wavelength of ≈ ≈
18 d since explosion (Fig.2).
PTF14gaq
We observed PTF14gaq on 2014 October 1 UT ( ≈ ≈ (3500 − ≈
18 d since explosion (Fig. 2).
PTF15dld
We observed PTF15dld on 2015 November 7 UT( ≈
15 d since the P48 optical discovery) with theDeep Extragalactic Imaging Multi-Object Spectrograph(DEIMOS) mounted on the Keck-II 10 m telescope. Thespectrum was taken using the 600ZD grating and GG455filter. The exposure time and airmass were 600 s and1.11, respectively. The derived spectrum shows a goodmatch with both the BL-Ic SN 2002ap (e.g., Gal-Yamet al. 2002; Mazzali et al. 2002) at 13 d since explosion,and with the Ic/BL-Ic SN 2004aw (e.g., Taubenbergeret al. 2006) at an epoch of about 15 d since explosion(Fig. 2).
Swift/XRT follow-up and data reduction
None of the BL-Ic SNe in our sample was found to bespatially coincident with any of the well-localized GRBin the
Swift (Gehrels et al. 2004) catalog. For some ofthe events, we triggered
Swift/XRT (Burrows et al. 2005)follow-up observations via our approved Target of Oppor-tunity Programs in order to further exclude the pres-ence of a GRB X-ray afterglow with no associated γ -rays(as would be the case for a GRB jet observed slightly off-axis, or for a so-called “dirty” fireball; see e.g. Rhoads2003).We downloaded the Swift -XRT data from thearchive . None of the SNe in our sample yielded a detec-tion with Swift/XRT , so we calculated 3 σ upper-limits onthe 0.3-10.0 keV count rate using standard analysis pro-cedures. The upper-limits are reported in Table 2, wherewe have converted the 0.3-10 keV XRT count rates intofluxes assuming a photon index of Γ X = 2 and correctingfor Galactic absorption.X-ray observations of PTF11qcj obtained with Swift /XRT and
Chandra /ACIS (Garmire et al. 2003)were previously presented in Corsi et al. (2014). We in-clude some of these observations (the most significant
Chandra /ACIS detection and the deepest
Swift /XRTupper-limit) in Table 2 for completeness.
VLA follow-up observations and data reduction
We observed all of the SNe in our sample, alongwith the necessary calibrators, with the VLA (Perleyet al. 2009) under our Target of Opportunity programs .VLA data were reduced and imaged using the CommonAstronomy Software Applications (CASA) package.The VLA flux measurements and/or upper-limits arereported in Table 3. Measurement errors are calculated Program IDs 1013248 and 1114155 (PI: Corsi). See http://heasarc.gsfc.nasa.gov/cgi-bin/W3Browse/swift.pl . The National Radio Astronomy Observatory is a facilityof the National Science Foundation operated under cooperativeagreement by Associated Universities, Inc.; VLA/11A-227, VLA/11B-034, VLA/12B-247, VLA/14A-434,and VLA/15A-314 - PI: A. Corsi; and VLA/10B-221 - PI: Kasli-wal).
Fig. 3.—
Swift /XRT upper-limits on some of the BL-Ic SNein our sample (downward pointing triangles) compared with theX-ray emission from GRB 980425 (diamonds) and with the X-rayemission expected from off-axis GRB models by van Eerten & Mac-Fadyen (2011); van Eerten et al. (2012). GRB jets opening anglesare set to θ j = (0 . − .
2) rad; the medium is a constant densityISM ( n ISM = 1 −
10 cm − ); observer’s viewing angles are in therange θ obs ≈ (2 − θ j . The fraction of energy density of the ejectagoing into electrons ( (cid:15) e ) and magnetic fields ( (cid:15) B ) are both set to0.1 in all of the above models. For PTF11qcj we plot the fluxobtained from the most significant Chandra /ACIS detection aftersubtracting the possible host galaxy contribution (asterisk), andthe deepest
Swift /XRT upper limit (dotted line). We attributethe X-ray emission from PTF11qcj to the presence of strong CSMinteraction rather than to a GRB X-ray afterglow. See Corsi et al.(2014) for a complete discussion. (See the electronic version of thispaper for colors.) by adding in quadrature the rms map error, and a basicfractional error ( ≈ X-RAY CONSTRAINTS ON ASSOCIATED GRB X-RAYAFTERGLOWS
As mentioned in the previous Section, none of the SNein our sample are spatially coincident with any well-localized GRB. For a limited number of these SNe, ourobservations with the
Swift /XRT allow us to make somecomparisons with the X-ray light curve that would beexpected from an accompanying GRB 980425-like event,or from a high-luminosity GRB observed slightly off-axis.For the last, we use the numerical model by van Eerten &MacFadyen (2011); van Eerten et al. (2012), which con-siders a relativistic GRB fireball expanding in a uniformdensity medium.As evident from Fig. 3, while
Swift /XRT upper-limits can exclude X-ray afterglows associated with high-luminosity (high-energy) GRBs observed slightly off-axis(up to θ obs (cid:46) (2 − θ j ), X-ray emission as faint as theafterglow of the low-luminosity GRB 980425 cannot beexcluded. As we discuss in Section 4, radio data col-lected with the VLA enable us to exclude 1998bw-likeemission for most of the SNe in our sample.For PTF11qcj, Chandra observations yielded a detec-tion but we attribute this X-ray emission to the presenceof strong CSM interaction rather than to a GRB X-rayadio emission from PTF broad-lined Type Ic supernovae 7
TABLE 2 σ X-ray upper-limits or detections for some of the SNe in our sample.
PTF Date ∆ T X f Instrument Band Exp. N H g Count Rate Flux (unabs) h Ref.name (MJD) (days) - (keV) (ks) (10 cm − ) (10 − s − ) (10 − erg cm − s − )10bzf 55259.290 9 Swift -XRT 0.3-10 5.0 0.88 < . < . Swift -XRT 0.3-10 5.0 ” < . < . Swift -XRT 0.3-10 4.9 2.7 < . < . Swift -XRT 0.3-10 31.4 1.0 < . < . Chandra -ACIS 0.3-8.0 9.8 ” 8 . ± . i . ± .
26 Corsi et al. (2014)12as 55932.340 7
Swift -XRT 0.3-10 4.6 2.5 < <
13 This paper” 55962.150 37
Swift -XRT 0.3-10 4.9 ” < < . Swift -XRT 0.3-10 4.8 4.6 < < . Swift -XRT 0.3-10 2.4 ” < <
20 This paper14dby 56839.043 7
Swift -XRT 0.3-10 9.5 4.2 < < . Swift -XRT 0.3-10 7.8 6.9 < < . Swift -XRT 0.3-10 9.9 3.2 < . < . f Epoch in days since P48 discovery (see Table 1), not corrected for redshift effects. g Hydrogen column densities are weighted averages from the Leiden/Argentine/Bonn (LAB) Survey of Galactic H I (Kalberla et al. 2005). h The count-rate-to-flux conversion assumes a photon index of Γ X = 2. i Chandra observations of PTF11qcj yielded detections which we attribute to the presence of strong CSM interaction rather than to a GRB X-rayafterglow. Some host galaxy contamination to the measured X-ray flux might also be present. See Corsi et al. (2014) for a complete discussion. afterglow. See Corsi et al. (2014) for a complete discus-sion. CONSTRAINING THE FRACTION OF 1998BW-LIKEEVENTS USING RADIO EMISSION
Here, we aim at observationally constraining the frac-tion of BL-Ic SNe with radio luminosities comparableto that of the GRB-associated SN 1998bw (Kulkarniet al. 1998) to ultimately constrain the fraction of BL-IcSNe harboring low-luminosity GRBs. Indeed, most ofthe GRBs with an associated and spectroscopically con-firmed SN are low-luminosity bursts ( E γ,iso (cid:46) ergs),although notable exceptions are GRB 030329 (Staneket al. 2003) and GRB 130427A (e.g., Melandri et al. 2014;Perley et al. 2014). The fraction of BL-Ic SNe harbor-ing low-luminosity GRBs was left largely unconstrainedby previous efforts (Berger et al. 2003a; Soderberg et al.2006c; Bietenholz et al. 2014) due to the very small num-ber of BL- Ic events with radio follow-up available to thecommunity.Theoretical studies have indirectly constrained thefraction of BL-Ic SNe harboring low-luminosity GRBs byconstraining the local rate of low-luminosity GRBs (vialuminosity function fitting) and then comparing this esti-mated local rate with the rate of BL-Ic SNe collected viaoptical surveys. Following this approach, Guetta & DellaValle (2007) derived that (cid:38)
10% of BL-Ic SNe are accom-panied by low-luminosity GRBs. This is consistent withthe earlier results by Podsiadlowski et al. (2004), whofound that the rates of GRBs and BL-Ic SNe are com-parable to within the uncertainties, and their ratio likely (cid:38)
30% (see Table 1 in Podsiadlowski et al. 2004). Morerecently, following a statistical approach inspired by theDrake equation, Graham & Schady (2015) estimated thatthere are 4000 ± (cid:46)
5% of the BL-IcSNe are associated with a GRB.With our PTF discoveries, we now have a sample of15 BL-Ic SNe discovered independently of a GRB trig-ger , with at least one radio follow-up observation on timescales (cid:46)
300 d since explosion (as measured in theSN rest frame; Figs. 4 and 5). Of these 15 SNe, 12 havebeen uniquely observed via our VLA programs. Our ob-servations have greatly enlarged the sample of 8 BL-IcSNe with radio follow-up at (cid:46)
300 d collected via in-dependent efforts during the last decade (Fig. 4, yel-low; Fig. 5, green, yellow, and magenta asterisks; Bergeret al. 2003a; Chomiuk & Soderberg 2010; Soderberg et al.2010; Soderberg & Chomiuk 2011; Drake et al. 2013;Kamble & Soderberg 2013; Salas et al. 2013; Chakrabortiet al. 2015; Milisavljevic et al. 2015). We are thus in a po-sition to start constraining the theoretical expectationsfor the low-luminosity GRB-to-BL-Ic SN ratio using adirect observational signature: the presence (or absence)of 1998bw-like radio emission.In Figs. 4 and 5, the 5 GHz radio light curve ofSN 1998bw is compared with the upper-limits and de-tections obtained for the SNe in our sample (4.8-6.3GHz; See Table 3). As evident from Fig. 5, we have3 SNe (PTF11cmh, PTF11qcj, and PTF14dby) thatshow bright radio emission, much brighter than theordinary BL-Ic SN 2002ap and almost at the level ofSN 1998bw, but their radio peak occurs (cid:38) × later thanfor SN 1998bw. Thus, as we explain in the following Sec-tion, we consider these SNe as observationally differentfrom SN 1998bw, likely related to events on the dividingline between ordinary SNe and GRBs, although an inter-pretation as off-axis GRB jets might also be possible. Forthe remaining 12 SNe in our sample, we detect no radioemission and set upper-limits (Fig. 4, black downward-pointing triangles). For 10 of these 12 SNe (all butPTF10xem and PTF13u), we have at least one upper-limit which constrains the radio emission to be dimmerthan the emission of SN 1998bw at a similar epoch , thusexcluding a radio light curve observationally similar tothat of the prototype relativistic BL-Ic SN 1998bw. (Wenote that 8 out of the 12 SNe also exclude radio emis-sion similar to SN 2009bb, a relativistic BL-Ic SN withno associated GRB; Soderberg et al. 2010).Based on the above results, we conclude that of the10+3 PTF SNe whose radio observations can set con-straints on SN 1998bw-like emission, none of them was Corsi et al.in fact like SN 1998bw in the radio i.e., they were all ob-servationally different. Adding to this sample the BL-IcSN 2002ap (Gal-Yam et al. 2002; Mazzali et al. 2002) andSN 2002bl (Armstrong et al. 2002; Berger et al. 2003a),and the CSM-interacting BL-Ic SN 2007bg (Salas et al.2013), we have a total of 16 BL-Ic SNe for which ra-dio emission observationally similar to SN 1998bw is ex-cluded. Because the 99.865% confidence (3 σ Gaussianequivalent for a single-sided distribution) Poisson upper-limit on zero SNe compatible with SN 1998bw is ≈ . (cid:46) . / ≈ ≈ −
30 d).Finally, only some of our upper-limits exclude radio af-terglow emission similar to that of the low-luminosityGRB 100316D (although a more quantitative compari-son with this burst is hampered by its poorly sampledradio light curve). CONSTRAINING THE FRACTION OF (LARGELY)OFF-AXIS GRBS FROM RADIO NON-DETECTIONS
Low-luminosity GRBs (such as GRB 980425 associatedwith SN 1998bw) are believed to be intrinsically less en-ergetic events (when compared to high-luminosity ones)with jet opening angles (cid:38)
30 deg (e.g., Liang et al. 2007).However, the possibility that low-luminosity GRBs arehigher-energy events observed off-axis has also been dis-cussed (e.g., Waxman 2004b; Ramirez-Ruiz et al. 2005).Indeed, most (high-luminosity) GRBs are believed tohave opening angles of the order of ∼
10 deg (e.g., Frailet al. 2001; Liang et al. 2008; Racusin et al. 2009; Zhanget al. 2015). Here, we aim at answering the questionof whether the BL-Ic SNe in our sample that do notshow evidence for radio emission observationally similarto that of SN 1998bw (Section 4) could still be accompa-nied by an off-axis ( θ obs ≈
90 deg) GRB afterglow thatwould become visible in the radio band long past the ex-plosion (at timescales of the order of ∼ t (cid:38)
500 d since explosion, not plot-ted in Figs. 4-5; see Soderberg et al. 2006c; Bietenholzet al. 2014).We model the late-time radio emission from an off-axisGRB following the works by Livio & Waxman (2000) andWaxman (2004b), modified to account for the results ofmore recent numerical simulations (Zhang & MacFadyen2009; van Eerten & MacFadyen 2012). The last haveshown that at the end of the Blandford-McKee (BM)phase, the fireball becomes non relativistic but, differ-ently from what previously thought, the transition tothe spherical Sedov-Neumann-Taylor (SNT) blast wave
Fig. 4.—
Radio (observed central frequencies of ≈ . − . t (cid:46)
300 d since discovery (as measuredin the SN rest frame), compared with: the mean radio (8.5 GHz)light curve of cosmological GRBs (blue solid line) as derived byChandra & Frail (2012), together with the 75% confidence inter-val (blue shaded region); radio ( ≈ ≈ − . t (cid:38)
300 d since ex-plosion via other studies (Soderberg et al. 2006c; Bietenholz et al.2014) are not reported here. takes a rather long time. Thus, accurate modeling ofthe fireball evolution over timescales in between the BMand SNT phases (which are relevant for this study) re-quires numerical simulations. However, Zhang & Mac-Fadyen (2009) have shown that for fireballs expanding ina medium of constant density n ,ISM (in units of cm − )and at timescales t (cid:38) (1 + z ) × t SNT / , (1)where t SNT ≈
92 d (cid:18) E n ,ISM (cid:19) / , (2)an acceptable analytical approximation to the afterglowadio emission from PTF broad-lined Type Ic supernovae 9 Fig. 5.—
BL-Ic SNe in our sample with radio detections:PTF11cmh, orange dots; PTF11qcj, purple diamonds (Corsi et al.2014); PTF14dby, blue stars. We compare these non-relativistic /CSM-interacting SNe with the light curves of the GRB-SN 1998bw(red asterisks; Kulkarni et al. 1998), of the relativistic BL-IcSN 2009bb (green asterisks; Soderberg et al. 2010), of the CSM-interacting BL-Ic SN 2007bg (magenta asterisks; Salas et al. 2013),and of the relativistic SN 2012ap (yellow asterisk; Chakraborti et al.2015). As evident from this comparison, the non-relativistic andCSM-interacting BL-Ic peak at later timescale than the relativisticones. flux is given by: F ν ( t ) ≈ . d − L, (1 + z ) (cid:16) (cid:15) e . (cid:17) (cid:16) (cid:15) B . (cid:17) / n ,ISM E × (cid:16) ν (cid:17) − / (cid:18) t
92 d(1 + z ) (cid:19) − / mJy . (3)Here E is the beaming-corrected ejecta energy in unitsof 10 erg; (cid:15) e and (cid:15) B are the fraction of ejecta energydensity going into electrons and magnetic fields, respec-tively; d L, is the luminosity distance of the source inunits of 10 cm; z is the source redshift; and the power-law index of the electron energy distribution has been setto p ≈ t SNT hasbeen eliminated by using our Eq. (2) (or, equivalently,Eq. (11) in Waxman 2004b). Using Eq. (3) to con-strain the fireball parameters by comparison with obser-vations taken at timescales t that satisfy Eq. (1), yieldsconstraints on the (beaming-corrected) energy that areaccurate to within a factor of ≈ t (cid:38) t SNT F ν ( t ) (cid:38) F obs,ν ( t ) , (4)we thus calculate, for the SNe in our sample (Table 3),the values of (beaming corrected) energy and mediumdensity that would give a radio luminosity above ourupper-limit F obs,ν ( t ), at the time t of our observation.The exclusion regions obtained in this way are shown inFig. 6. In this Figure we have set the micro-physics pa-rameters equal to their median values as estimated bySantana et al. (2014) i.e., (cid:15) e ≈ .
22 and (cid:15) B ≈ .
01. How-ever, these parameters (and especially (cid:15) B ) vary within large ranges, 0 . (cid:46) (cid:15) e (cid:46) . × − (cid:46) (cid:15) B (cid:46) . (cid:15) e (cid:15) / B , the larger theminimum E excluded for each value of n (thus, off-axis emission from lower-energy fireballs / low-luminosityGRBs is less constrained).In Fig. 7 we use our upper-limits to set similar con-straints on off-axis GRBs expanding in a wind medium.In this case, the expected radio flux is approximated as(Waxman 2004b; Soderberg et al. 2006c): F ν ( t ) ≈ . d − L, (1 + z ) / (cid:16) (cid:15) e . (cid:17) (cid:16) (cid:15) B . (cid:17) / A / ∗ E × (cid:16) ν (cid:17) − / (cid:18) t
92 d(1 + z ) (cid:19) − / mJy , (5)where A ∗ is the circumstellar density, which is relatedto progenitor mass loss-rate ˙ M and wind velocity v w as A ∗ = ( ˙ M / − M (cid:12) yr − ) / (v w / − ); and wherewe have used (Waxman 2004b; Soderberg et al. 2006c): t SNT ≈
92 d (cid:18) E A ∗ (cid:19) . (6)We note that Eq. (5) corresponds to Eq. (14) in Wax-man (2004b) where the dependence on t SNT is eliminatedby using our Eq. 6 (or, equivalently, Eq. (8) in Wax-man 2004b). Here we are assuming that the conclusionsreached by Zhang & MacFadyen (2009) for the constantdensity case are valid also for a fireball expanding in awind medium, namely, that Eq. (5) provides an esti-mate of the fireball parameters good to within a factorof ≈ t (cid:38) t SNT .We can compare the results shown in Figs. 6-7 withthe energy and density derived from the broad-bandafterglow modeling of the high-luminosity GRB 030329(for which θ j ≈ −
17 deg, E = 0 . n ,ISM ≈
3; Berger et al. 2003c; Soderberg et al. 2006c) andGRB 130427A (for which E (cid:38) . θ j (cid:38) . (cid:46) A ∗ (cid:46) .
05; Perley et al. 2014), and of thelow-luminosity GRB 980425 (for which E ≈ .
05 and A ∗ ≈ .
04; Waxman 2004a,b; Soderberg et al. 2006c) andGRB 031203 (for which E = 0 .
017 and n ,ISM = 0 . (cid:15) e (cid:15) / B , thelarger the minimum E excluded for each value of A ∗ . VLA DETECTIONS: PTF11CMH AND PTF14DBY
Non-thermal (self-absorbed) synchrotron radiation canbe emitted from SN or GRB ejecta during interaction0 Corsi et al.
Fig. 6.—
Regions of the energy ( E ) - density ( n ,ISM ) parameter space excluded by our VLA upper-limits. For each SN in our sample,red, green, and yellow colors correspond to different observations. Specifically, for each SN, we use red for the constraints derived fromthe first epoch of observations, green for the second epoch (if observed twice; see Table 3), and yellow for the third epoch (if available; seeTable 3). adio emission from PTF broad-lined Type Ic supernovae 11 Fig. 7.—
Regions of the energy ( E ) - density ( A ∗ ) parameter space excluded by our VLA upper-limits. For each SN in our sample,red, green, and yellow colors correspond to different observations. Specifically, for each SN, we use red for the constraints derived fromthe first epoch of observations, green for the second epoch (if observed twice; see Table 3), and yellow for the third epoch (if available; seeTable 3). Fig. 8.—
Best fit radio light curves of PTF11cmh in the synchrotron self-absorbed radio SN model (solid; see Section 6.2), and an off-axisGRB model light curve for a fireball expanding in a constant density ISM (dashed; see Section 6.1), compared with our VLA observations(see Table 3). See text for a discussion of the models and best fit parameters.
Fig. 9.—
PTF11cmh (LEFT) and PTF14dby (RIGHT) best fit results (diamonds) and confidence intervals for the average speed andtemporal index of the blastwave radius α r . We expect α r ≈ α r ≈ / (cid:46)
68% confidence (white),between 68% and 90% confidence (purple), between 90% and 99% confidence (light blue), and (cid:38)
99% confidence (aqua green) i.e., contourscorrespond to ∆ χ = 2 . , . , .
21 for 2 interesting parameters, respectively. The contours avoid the portions of the parameter space wherethe model’s physical assumptions break down (i.e., the index p of the electron energy distribution reaches its boundary value of p = 2). adio emission from PTF broad-lined Type Ic supernovae 13 Fig. 10.—
Best fit radio light curves of PTF14dby in the synchrotron self-absorbed radio SN model (solid; see Section 6.2), and an off-axisGRB model light curve for a fireball expanding in a constant density ISM (dashed; see Section 6.1), compared with our VLA observations(see Table 3; note that the two data points at ≈ GRB jets observed off-axis?
Three SNe in our sample, PTF11cmh, PTF11qcj, andPTF14dby, were detected during our radio follow-upwith the VLA. Interestingly, two out of these three SNe(PTF11qcj and PTF14dby) are found to be spectroscopi-cally similar to SN 1998bw. Thus, the rate of radio detec-tions for the BL-Ic SNe in our sample spectroscopically most similar to SN 1998bw is ≈ / not exclude the presence of X-ray after-glow emission comparable to that of GRB 980425, how-ever its radio emission appears different from SN 1998bwin the fact that it peaks at later times. Moreover, the ra-dio emission from PTF11cmh, PTF11qcj, and PTF14dbyis orders of magnitudes dimmer than that of an aver-age long GRB observed on-axis (blue curve shaded arein Fig. 4), and also dimmer than most low-luminosityGRBs with well-sampled radio light curves. Thus, herewe address the question of whether the radio emissionfrom these three SNe could be associated with a GRBobserved off-axis.In Figs. 8 and 10 we show a tentative comparisonof the observed radio light curves of PTF14dby andPTF11cmh with numerical model light curves of off-axislow-luminosity GRBs expanding in a constant densityenvironment of density n ISM (dashed lines; van Eerten &MacFadyen 2011; van Eerten et al. 2012). We note thatnumerical models for GRB jets expanding in a wind envi-ronment are not currently available to the community (atleast not in a format that can allow us to easily comparethese models with our observations). Thus, hereafter welimit our discussion to the case of a constant density ISM.For PTF11cmh (Fig. 8, dashed line), we have set: θ j ≈
10 deg, observer’s angle θ obs ≈
90 deg, beaming cor-rected energy E ≈ . n ISM = 10 cm − , (cid:15) B = (cid:15) e ≈ . p ≈ .
2. These values for the model parameters pro-vide a model light curve in agreement with the (limited)6 GHz data. We also point out that the limited datasetavailable for PTF11cmh does leave open the possibilityof a mildly-relativistic event (discussed in more detail inthe following Section).For PTF14dby (Fig. 10, dashed line) we have set: θ j ≈ θ obs ≈
70 deg, beaming correctedenergy E ≈ . n ISM = 10 cm − , (cid:15) B = (cid:15) e ≈ . p ≈ .
4. While the simplest off-axis GRB modelin a constant density ISM does not provide a perfectmatch, the model light curves are broadly compatiblewith the observations of PTF14dby, thus an off-axis GRBcannot be securely ruled out. We also note that in thePTF14dby radio light curve there is a hint for a late-time peak (or flattening) reminiscent of SN 1998bw, that maybe better fitted using off-axis GRB models expandingin a wind environment, and/or by invoking an energyinjection episode similar to what has been proposed byLi & Chevalier (1999) for SN 1998bw.PTF11qcj is the most difficult to interpret within thesimplest off-axis GRB models (see also Corsi et al. 2014)due to the clear late-time radio re-brightening. However,this late-time re-brightening requires modifications alsoto the simplest non-relativistic radio SN model, such asthe presence of a denser CSM shell (e.g., Salas et al.2013).Based on the tentative comparison with available mod-els described in this Section, and on the results describedin Section 5, we can attempt to constrain the fractionof BL-Ic SNe in our sample potentially harboring off-axis GRB jets. Indeed, since (cid:46) n ISM ∼
10 cm − (or A ∗ ∼
4; compare Eqs. (14) and (15) in Waxman2004b), we set a 99.865% confidence Poisson upper-limitof (cid:46) . / ≈
85% on the fraction of BL-Ic SNe pos-sibly harboring off-axis GRBs expanding in media withdensities of this order. We note, however, that a com-parison with numerical models for off-axis low-luminosityGRBs expanding in a wind environment would be neededto better determine the values of A ∗ constrained by ourdataset. Non-relativistic radio SN emission
In what follows, we model the radio emission observedfrom PTF11cmh and PTF14dby within the standard ra-dio SN model based on the interaction of non-relativisticejecta with CSM deposited via a constant mass-loss rate,constant velocity wind (i.e., ρ CSM = ˙ M w / (4 πv w r )) froma massive progenitor (Chevalier 1982). We follow the for-mulation of this standard model given in Soderberg et al.(2005), which replaces the SNT dynamics with a generalparametrization of the shock evolution which enables usto model the early SN synchrotron emission (when theejecta is very close to free expansion), while recovering(in the appropriate time limit) the correct behavior forGRBs transitioning to the sub-relativistic adiabatic ex-pansion phase (Waxman 2004b).In the standard model, synchrotron emission observedat time t is produced from an expanding spherical shell ofshock-accelerated electrons with radius r and thickness r/η . The shell interacts with a smooth CSM followinga self-similar evolution. The electrons, which are accel-erated into a power-law energy distribution N ( γ ) ∝ γ − p (with γ (cid:38) γ m ), carry a fraction (cid:15) e of the energy densityof the ejecta. Magnetic fields carry a fraction (cid:15) B of theenergy density. The temporal evolution of the shell andits properties is parametrized as (Soderberg et al. 2005,2006a): r = r (cid:18) t − t e t (cid:19) α r B = B (cid:16) t − t e t (cid:17) α B (7) γ m = γ m, (cid:18) t − t e t (cid:19) α γ (cid:15) e (cid:15) B , = F (cid:16) t − t e t (cid:17) α F . (8)In the above Equations, t is an arbitrary reference time(here set to day 10 since explosion), t e is the explosionadio emission from PTF broad-lined Type Ic supernovae 15time of the SN, α r = ( n − / ( n − s ) (Chevalier 1982,1996) with n the power-law index of the outer SN ejectadensity profile ( ρ SN ∝ ( r/t ) − n ), and s the power-lawindex of the shocked CSM electrons density profile ( n e ∝ r − s ).Following Chevalier (1996), the magnetic energy den-sity ( U B ∝ B ) and the relativistic electron energy den-sity ( U e ∝ n e γ m ) are assumed to be a fixed fraction(i.e., α F = 0) of the total post-shock energy density( U ∝ n e (cid:104) v (cid:105) , where v is the velocity). Making the addi-tional conservative assumption that the energy of the ra-dio emitting material is partitioned equally into acceler-ating electrons and amplifying magnetic fields ( (cid:15) e = (cid:15) B ,which implies F = 1 ) and assuming s = 2 (as expectedfor a wind density profile), we have (Soderberg et al.2005, 2006a): U e ∝ U ⇒ α γ = 2( α r − , (9)and U B ∝ U ⇒ α B = (2 − s )2 α r − − , (10)and, for the flux density from the uniform shell of radi-ating electrons (Soderberg et al. 2005, 2006a): f ν = C f (cid:18) t − t e t (cid:19) (4 α r +1) / (1 − exp( − τ ν )) × (cid:16) ν (cid:17) / × F ( x ) F − ( x ) mJy , (11)where C f = C f ( r , B , p ) (see Eq. (A.13) in Soderberget al. 2005), x = 2 / ν/ν m ), and ν m = γ m eB πm e c = γ m, eB πm e c (cid:18) t − t e t (cid:19) α γ + α B = ν m, (cid:18) t − t e t (cid:19) α r − (12)is the characteristic synchrotron frequency of electronswith Lorentz factor γ m . As typically assumed for radioSNe, we set ν m, ≈ γ m, is a function of B only). In Equation (11), F and F are integrals of the modified Bessel function of order2/3 (see Equation (A11) in Soderberg et al. 2005); and τ ν ( t ) = C τ (cid:18) t − t e t (cid:19) ( p − α γ +(3+ p/ α B + α r × (cid:16) ν (cid:17) − ( p +4) / F ( x ) = C τ (cid:18) t − t e t (cid:19) (2 p − α r − (5 p/ − (cid:16) ν (cid:17) − ( p +4) / F ( x ) (13)is the optical depth (Soderberg et al. 2005, 2006a), with C τ = C τ ( r , B , γ m, , p ) (see Eq. (A.14) in Soderberget al. 2005). Thus, as evident from Eqs. (11) and(13), the observed spectral and temporal evolutions ofthe radio emission ultimately depend on the parameters( r , B , t e , p, α r , η ), which we determine by comparisonwith the data. PTF11cmh radio modeling
Our VLA follow-up observations of PTF11cmh startedat an epoch of about ≈
20 d since optical discovery, andwere carried out until more than 10 d after (Table 3).Our first radio detection of PTF11cmh was more than100 d since optical discovery.Because our radio observations for PTF11cmh are verylimited, we expect any model fitting to return only tenta-tive estimates of model parameters. Within the standardsynchrotron self-absorbed scenario (Section 6.2), we canset t e = 55673 .
336 MJD (see Table 1) and η = 5 (as typ-ically assumed in radio SN studies). This leaves 4 freemodel parameters to be compared with 4 radio detectionsand 1 upper-limit (see Table 3). We thus attempt a crudefit by considering the upper-limit at epoch ≈
20 d sinceexplosion as a data point with flux value equal to themaximum radio flux detected in circular region centeredon the optical position of PTF11cmh with radius equalto half the VLA FWHP synthesized beam for the obser-vation, and error equal to the image rms i.e., 15 ± µ Jy.This way our fit returns a χ ≈ . Fromthe best fit light curves shown in Fig. 8 (solid lines),we also estimate ν p ≈ ≈
100 d since explosion,and L p, ≈ erg s − Hz − . The last is comparableto the radio spectral luminosity of the GRB-associatedSN 1998bw (Kulkarni et al. 1998).The best-fit values for the model parameters are p ≈ B ≈ R ≈ × [( t − t e ) /
10 d] . cm. The last implies an av-erage ejecta speed of R/ ∆ t ≈ . c , where c is the speedof light. This is ≈ × higher than the average speed ofordinary Ib/c SNe ( ≈ . c ), but smaller than relativisticevents such as SN 2009bb and SN 1998bw. In Fig. 9 weshow the uncertainties on the best values of the averageejecta speed ( (cid:104) v (cid:105) = r /
10 d) and power-law index α r ofthe temporal evolution of the ejecta radius, as derivedby mapping the difference ∆ χ = χ − χ , where χ isthe best fit χ value returned by our 4-parameter fit tothe data (see above); and χ is the best fit χ value ob-tained when mapping the α r - r space over a grid of pos-sible values and minimizing the χ over the remainingtwo “non-interesting” parameters (e.g, Avni 1976). Asevident from this Figure, because of the limited datasetavailable for this event, the speed of the radio emittingmaterial is very poorly constrained, with the 99% confi-dence region extending in the range (cid:104) v (cid:105) /c ≈ . − / (cid:15) e = (cid:15) B = 0 . E ≈ × ( (cid:15) e / . − [( t − t e ) /
10 d] . ergcoupled to the fastest radio-emitting outflow. This en-ergy is at the higher end of the range derived for otherradio Ib/c SNe (Margutti et al. 2014). However, we alsonote that because E ∝ r ∝ (cid:104) v (cid:105) , a factor of ≈ (cid:104) v (cid:105) (at 99% confidence) implies a factor of ≈
200 uncertainty in the estimated ejecta energy.Finally, the estimated progenitor mass-loss rate is ˙ M =10 − ( v w / − ) M (cid:12) yr − , where v w is the velocityof the stellar wind and where we have assumed a nucleon-to-proton ratio of 2 (see Eq. (13) in Soderberg et al.2005). This mass-loss rate is higher than the typical We do not expect the simplified analytical synchrotron modelto provide a perfect fit, and this value of the χ is similar to whatobtained in other analyses of radio SN light curves. M ∝ r ∝ (cid:104) v (cid:105) , a factorof ≈ (cid:104) v (cid:105) (at 99% confidence) impliesa factor of ≈
40 uncertainty in the estimated mass-lossrate.
PTF11qcj radio modeling
Our VLA follow-up observations of PTF11qcj startedabout two weeks after optical discovery, and were car-ried out until ≈
600 d after (Corsi et al. 2014). As de-scribed in Corsi et al. (2014), modeling our radio ob-servations in the standard synchrotron self-absorbed sce-nario yielded best-fit values of B ≈ . R ≈ . × [( t − t e ) /
10 d] . cm (assuming η = 5). Thelast implies an average ejecta speed of R/ ∆ t ≈ . c .This is ≈ × higher than the average speed of ordi-nary Ib/c SNe ( ≈ . c ), but smaller than relativisticevents such as SN 2009bb and SN 1998bw. For η = 5,we also estimated a minimum energy of E ≈ . × ( (cid:15) e / . − [( t − t e ) /
10 d] . erg coupled to the fastestradio-emitting outflow, and a progenitor mass-loss rateof ˙ M ≈ . × − ( v w / − ) M (cid:12) yr − , where v w isthe velocity of the stellar wind (and assuming a nucleon-to-proton ratio of 2). PTF14dby radio modeling
Our VLA follow-up observations of PTF14dby startedat an epoch of about ≈ (cid:38) σ ) VLA detection of PTF14dby at5 GHz was obtained about 20 d since optical discovery.We collected a total of 36 detections and 2 upper-limitsfor PTF14dby (see Table 3). We model our radio detec-tions in the standard synchrotron self-absorbed scenario(Section 6.2) using a χ minimization procedure wherewe set η = 5, so we are left with 5 free model parameters.The fit returns a χ ≈
115 for 31 d.o.f.. From the bestfit light curves shown in Fig. 10 (solid lines) we estimate ν p ≈ . ≈
40 d since explosion, and a spectralpeak luminosity of L p, . ≈ × erg s − Hz − .The last is ≈ × smaller than the peak radio luminos-ity of the GRB-associated SN 1998bw, but comparable tothe radio peak luminosity of the engine-drive SN 2009bb(Fig. 5; Soderberg et al. 2010).The best-fit values for the model parameters are t e ≈ p ≈ . B ≈ . R ≈ . × [( t − t e ) /
10 d] . cm. The last implies an average ejecta speedof R/ ∆ t ≈ . c . This is ≈ × higher than the averagefor ordinary Ib/c SNe ( ≈ . c ), but smaller than rela-tivistic events such as SN 2009bb and SN 1998bw.In Fig. 9 we show the uncertainties on the best valuesof the average ejecta speed ( (cid:104) v (cid:105) = r /
10 d) and power-law index α r obtained in a way similar to what describedin the previous Section. As evident from this Figure, the 99% confidence region for the average ejecta speed is (cid:104) v (cid:105) /c ≈ . − . (cid:15) e = (cid:15) B = 0 . E ≈ × ( (cid:15) e / . − [( t − t e ) /
10 d] . erg coupled to the fastest radio-emitting out-flow.Finally, the estimated progenitor mass-loss rate is˙ M ≈ × − ( v w / − ) M (cid:12) yr − (where againwe have assumed a nucleon-to-proton ratio of 2). Thismass-loss rate is in agreement with values derived forlow-luminosity GRBs (see e.g. Fig. 7), and smaller thatthe one derived for CSM-interacting BL-Ic SNe such asPTF11qcj ( ˙ M ≈ − ( v w / − ) M (cid:12) yr − ; Corsiet al. 2014). This, together with the fact that the sim-plest off-axis GRB models (dashed lines in Fig. 10) are inbroad agreement with the radio light curve of PTF14dby,calls for a more accurate numerical modeling of this SNwhich is beyond the scope of this paper, but that we hopewill get the attention of the community. SUMMARY AND CONCLUSION
We have presented the P48 photometry, spectral clas-sification, and radio/X-ray follow-up observations of 15BL-Ic SNe discovered by the PTF/iPTF. All of the SNein our sample exclude radio afterglows typical of long du-ration GRBs at cosmological distances observed on-axis.Thanks to deep VLA follow-up observations, we are ableto exclude the presence of 1998bw-like (or 2009bb-like)radio emission for most of the SNe in our sample. Be-cause radio emission traces the fastest moving ejecta, weconclude that events as relativistic as, and observation-ally similar to, SN 1998bw are (cid:46)
41% of the BL-Ic pop-ulation (99.865% confidence). None of our upper-limitsexclude radio emission similar to the radio afterglow ofGRB 060218, which faded on timescales much faster thanour VLA monitoring campaign was designed to target.Using the X-ray upper-limits collected via our pro-grams, we rule out the presence of off-axis GRB jetsobserved slightly off-axis for some of the SNe in our sam-ple. We also constrain the energy and density parame-ters of (largely) off-axis GRBs potentially harbored bythe SNe in our sample for which 1998bw-like radio emis-sion was excluded. While we can rule out the presenceof GRBs as energetic as GRB 030329 observed at largeoff-axis angles and expanding in a constant ISM withdensity n ,ISM (cid:38) .
1, we cannot rule out the presence ofoff-axis GRBs expanding in a low-density wind medium,such as the one found around GRB 130427A.Finally, we presented the detailed radio modeling oftwo radio-loud BL-Ic, PTF11cmh and PTF14dby, whichadd to our previous radio detection of PTF11qcj. Whilethe ejecta speed of PTF11cmh is very poorly constraineddue to the limited dataset, we constrained the speed ofthe radio emitting material in PTF14dby to be inter-mediate between that of non-relativistic BL-Ic SNe, andrelativistic events such as SN 2009bb. Because we can-not securely rule out off-axis GRB models for these threeevents, we set an upper-limit of (cid:46)
85% (99.865% confi-dence) on the fraction of BL-Ic SNe in our sample thatcould potentially harbor a GRB observed off-axis and ex-panding in a medium of density n ISM ∼
10 cm − . Thisestimate could be improved by comparing our data withnumerical models for off-axis GRBs expanding in a windadio emission from PTF broad-lined Type Ic supernovae 17medium.In summary, our results show that the VLA (thanks toits improved sensitivity) working in tandem with surveyslike the iPTF, can help us clarify key open questions re-garding the GRB-SN connection (such as, what fractionof purely BL-Ic SNe can host low-luminosity GRBs) andenable us to discover more events on the dividing line between ordinary BL-Ic and relativistic GRBs. Over thecourse of 5 years, we have greatly enlarged the sample ofBL-Ic SNe (discovered independently of a GRB trigger)with radio follow-up within one year since discovery. Weexpect that the Zwicky Transient Factory will be able toboost even further the rate at which we are discoveringthe rare BL-Ic events (Smith et al. 2014). REFERENCESArmstrong, M., et al. 2002, IAUC, 7845Avni, Y. 1976, ApJ, 210, 642Bennett, C. L., Larson, D., Weiland, J. 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A.C. thanks P. Chandra for graciously providing the data for the average long GRB radio light curve showing in Fig.4. A.C. acknowledges support from the NSF CAREER award http://cmsdev.ttu.edu/hpcc ) for providing HPC resources that have contributed to the research resultsreported within this paper. This research also used resources of the National Energy Research Scientific ComputingCenter, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energyunder Contract No. DE-AC02-05CH11231.adio emission from PTF broad-lined Type Ic supernovae 19
TABLE 3
VLA observations. For non-detections, the quoted UL are at 3 σ (where σ is the image rms) unless otherwise stated.PTF T VLAj ∆ T VLAk
Conf. ν BW Flux ReferenceName (MJD) (d) (GHz) (MHz) ( µ Jy)10bzf 55268.222 18 D 5.0 256 (cid:46)
33 Chomiuk & Soderberg (2010)” 55337.221 87 D 6.0 1024 (cid:46)
36 Corsi et al. (2011)” 55527.490 277 C 5.0 256 (cid:46)
35 Corsi et al. (2011)10qts 55426.028 13 D 8.5 256 (cid:46)
86 Gal-Yam et al. (2010)” 55948.524 535 DnC 6.2 2048 (cid:46)
39 This paper” 55950.435 537 DnC 6.2 2048 (cid:46)
28 This paper10xem 55767.647 297 A 5.0 256 (cid:46)
66 This paper10aavz 55566.527 52 C 4.9 256 (cid:46)
31 Soderberg & Chomiuk (2011)” 55770.969 256 A 4.9 256 (cid:46)
105 This paper11cmh 55692.145 19 B 8.4 256 (cid:46)
72 This paper” 55949.356 276 DnC 6.3 2048 159 ±
11 This paper” 56766.099 1093 A 6.2 2048 17 . ± . ±
13 This paper” 56808.981 1136 ” 2.9 ” 18 . ± . (cid:46)
48 This paper” 55950.478 199 DnC 5.0 2048 (cid:46)
66 This paper11lbm 55812.283 19 A 5.0 256 (cid:46)
78 This paper” 55948.043 155 DnC 6.2 2048 (cid:46)
28 This paper12as 55933.555 8 DnC 6.2 2048 (cid:46)
87 This paper” 55947.382 22 DnC 6.2 2048 (cid:46)
69 This paper” 56999.567 1074 C 6.2 2048 (cid:46) This paper13u 56391.376 67 D 6.2 2048 (cid:46) This paper” 56767.366 443 A 6.2 2048 (cid:46)
14 This paper” 57311.028 987 D 6.2 2048 (cid:46) This paper13alq 56401.120 7 D 4.8 2048 (cid:46)
30 Kamble & Soderberg (2013)13alq 56423.080 29 DnC 6.2 2048 (cid:46) This paper13alq 57336.833 942 D 6.3 2048 (cid:46)
33 This paper13ebw 56667.566 46 B 6.2 2048 (cid:46)
15 This paper” 57001.417 380 C 6.2 2048 (cid:46) This paper14dby 56838.197 6 D 5.2 1024 (cid:46)
33 This paper” ” ” ” 7.5 ” 40 ±
12 ”” 56853.994 22 ” 5.2 ” 40 . ± . ±
12 ”” 56879.117 47 ” 5.0 ” 194 ±
12 ”” ” ” ” 7.4 ” 279 ±
15 ”” 56889.108 57 ” 2.5 ” 164 ±
54 ”” ” ” ” 3.3 ” 125 ±
18 ”” ” ” ” 8.5 ” 176 ±
14 ”” ” ” ” 9.5 ” 159 ±
14 ”” ” ” ” 13.5 ” 107 ±
13 ”” ” ” ” 14.5 ” 105 ±
13 ”” 56902.138 70 ” 5.0 ” 72 ±
19 ”” ” ” ” 7.4 ” 73 ±
17 ”” 56903.045 71 ” 2.7 ” 121 ±
40 ”” ” ” ” 3.2 ” 79 ±
16 ”” ” ” ” 8.5 ” 108 ±
11 ”” ” ” ” 9.5 ” 102 ±
11 ”” ” ” ” 13.5 ” 56 . ± . . ± . ±
18 ”” ” ” ” 7.5 ” 60 ±
16 ”” 56914.770 83 ” 8.5 ” 61 ±
14 ”” ” ” ” 9.5 ” 80 ±
15 ”” ” ” ” 13.5 ” 38 ±
12 ”” ” ” ” 14.5 ” 41 ±
13 ”” 56946.949 115 DnC 2.5 ” 101 ±
28 ”” ” ” ” 3.5 ” 138 ±
16 ”” ” ” ” 5.0 ” 84 ±
12 ”” ” ” ” 6.0 ” 79 ±
15 ”” ” ” ” 8.5 ” 48 ±
10 ”” ” ” ” 9.5 ” 59 ±
11 ”” 56998.800 167 C 2.5 ” (cid:46)
111 ”” ” ” ” 3.4 ” 48 ±
13 ”” ” ” ” 5.0 ” 53 ±
10 ”” ” ” ” 6.0 ” 44 ±
14 ”” ” ” ” 8.5 ” 28 . ± . ±
11 ”PTF14gaq 56932.496 8 DnC 6.3 2048 (cid:46)
28 This paper” 56998.857 75 C 6.2 2048 (cid:46)
25 This paper” 57335.919 411 D 6.3 2048 (cid:46)
19 This paper σ UL corresponding to the brightness of the host galaxy. σ UL corresponding to the brightness of the host galaxy. σ UL corresponding to the brightness of the host galaxy. σ UL. σ UL corresponding to the brightness of the host galaxy.
TABLE 3
VLA observations. For non-detections, the quoted UL are at 3 σ (where σ is the image rms) unless otherwise stated.PTF T VLAj ∆ T VLAk
Conf. ν BW Flux ReferenceName (MJD) (d) (GHz) (MHz) ( µ Jy)PTF15dld 57336.049 18 D 5.0 2048 (cid:46) This paper j The VLA observation time T VLA is the time at the mid-point of the VLA observation. k VLA observation epoch in days since PTF discovery, not corrected for redshift effects. σσ