NASA Technical Reports Server (NTRS) 20120008468: SN 2010ay is a Luminous and Broad-lined Type Ic Supernova within a Low-metallicity Host Galaxy

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Draftversion October 19,2011
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
SN2010AY IS A LUMINOUS AND BROAD-LINED TYPE IC SUPERNOVA WITHIN A LOW-METALLICITY
HOST GALAXY
N. E. Sanders1, A. M. Soderberg1, S. Valenti2, L. Chomiuk1,3, E. Berger1, S. Smartt2, K. Hurley4, S. D.
Barthelmy5, R. Chornock1, R. J. Foley1, E. M. Levesque6, G. Narayan7, M.T. Botticella2, M. S. Briggs8, V.
Connaughton8, Y. Terada9, N. Gehrels5, S. Golenetskii10, E. Mazets10, T. Cline11, A. von Kienlin12, W.
Boynton13, K. C. Chambers14, T. Grav15, J. N. Heasley14, K. W. Hodapp14, R. Jedicke14, N. Kaiser14, R. P.
Kirshner1, R.-P. Kudritzki14, G. A. Luppino14, R. H. Lupton16, E. A. Magnier14, D. G. Monet17, J. S. Morgan14,
1 P. M. Onaka14, P. A. Price16, C. W. Stubbs7, J. L. Tonry14, R. J. Wainscoat14, M. F. Waterson18.
1 Draft versionOctober 19, 2011
0
2 ABSTRACT
t We report on our serendipitous pre-discovery detection and detailed follow-up of the broad-lined
c Type Ic supernova SN2010ay at z ≈ 0.067 imaged by the Pan-STARRS1 3π survey just ∼ 4 days
O
after explosion. Combining our photometric observations with those available in the literature, we
estimate the explosion date and the peak luminosity of the SN, M ≈ −20.2 mag, significantly
8 R
brighter than known GRB-SNe and one of the most luminous SNe Ibc ever discovered. We measure
1
the photospheric expansion velocity of the explosion from our spectroscopic follow-up observations,

] vph ≈19.2×103 km s−1 at ∼ 40 days after explosion. In comparison with other broad-lined SNe, the
E characteristic velocity of SN2010ay is 2−5× higher and similar to the measurements for GRB-SNe
H at comparable epochs. Moreover the velocity declines two times slower than other SNe Ic-BL and
GRB-SNe. Assuming that the optical emission is powered by radioactive decay, the peak magnitude
.
h implies the synthesis of an unusually large mass of 56Ni, M = 0.9+0.1 M . Our modeling of the
p light-curve points to a total ejecta mass, M ≈ 4.7M , andNtiotal kin−e0t.i1c en⊙ergy, E ≈ 11. Thus
ej ⊙ K,51
-
the ratioofM to M isatleasttwice aslargeforSN2010aythaninGRB-SNe andmayindicatean
o Ni ej
r additional energy reservoir. We also measure the metallicity (log(O/H)+12=8.19) of the explosion
t site within the host galaxy using a high S/N optical spectrum. Our abundance measurement places
s
a this SN in the low-metallicity regime populated by GRB-SNe, and ∼ 0.2(0.5) dex lower than that
[ typically measured for the hostenvironments of normal(broad-lined) Ic supernovae. Despite striking

similaritiestotherecentGRB-SN100316D/2010bh,weshowthatgamma-rayobservationsruleoutan
2
associatedGRBwithE .6×1048erg(25-150keV).Similarly,ourdeepradiofollow-upobservations
v γ
3 with the Expanded Very Large Array rule out relativistic ejecta with energy, E & 1048 erg. These
6 observations challenge the importance of progenitor metallicity for the production of a GRB, and
3 suggest that other parameters also play a key role.
2 Subject headings: Surveys:Pan-STARRS1 — gamma-rays: bursts — supernovae: individual (2010ay)
.
0
1
1
1 [email protected]
: 1Harvard-Smithsonian Center for Astrophysics, 60 Garden
v Street, Cambridge,MA02138USA
i 2Astrophysics Research Centre, School of Maths and
X
Physics,Queens University,BT71NN,Belfast,UK
r 3NationalRadioAstronomyObservatory,Socorro,NM87801,
a USA
4Space Sciences Laboratory, University of California Berke-
ley,7GaussWay,Berkeley,CA94720, USA
5NASAGoddardSpaceFlightCenter,Greenbelt,MD20771,
USA
6CASA,DepartmentofAstrophysicalandPlanetarySciences,
UniversityofColorado,389-UCB,Boulder,CO80309,USA
7DepartmentofPhysics,HarvardUniversity,Cambridge,MA
02138, USA
8CSPAR,UniversityofAlabamainHuntsville,Huntsville,Al-
abama,USA.
9Department of Physics, Saitama University, Shimo-Okubo,
Sakura-ku,Saitama-shi,Saitama338-8570 14Institute for Astronomy, University of Hawaii at Manoa,
10Ioffe Physico-Technical Institute, Laboratory for Experi- Honolulu,HI96822, USA
mental Astrophysics, 26 Polytekhnicheskaya, St. Petersburg 15DepartmentofPhysicsandAstronomy,JohnsHopkinsUni-
194021, Russia versity,3400NorthCharlesStreet, Baltimore,MD21218,USA
11Emeritus, NASAGoddard Space FlightCenter, Code 661, 16Department of Astrophysical Sciences, Princeton Univer-
Greenbelt, MD20771, USA sity,Princeton,NJ08544, USA
12Max-Planck Institut fu¨r extraterrestrische Physik, 85748 17US Naval Observatory, Flagstaff Station, Flagstaff, AZ
Garching,Germany 86001, USA
13Lunar and Planetary Laboratory, University of Arizona, 18International Center for Radio Astronomy Research, The
Tucson, AZ85721, USA UniversityofWesternAustralia,Crawley,Perth,Australia
2 Sanders et al.
1. INTRODUCTION ronment was characterized by a super-solar metallicity,
Z ∼1−2Z (Levesque et al.2010c). Togetherwiththe
Recent observations have shown that long-duration ⊙
growinglack of evidence for massive progenitor stars for
gamma-ray bursts are accompanied by Type Ic super-
SNe Ic in pre-explosion Hubble Space Telescope images
novae (SNe) with broad absorption features (hereafter,
(Smartt 2009), a lower mass (M ∼ 10−20 M ) binary
“broad-lined” (BL)), indicative of high photospheric ex- ⊙
progenitor system model (with a gentler metallicity de-
pansion velocities (see Woosley & Bloom 2006, for a re-
pendence) is gaining increasing popularity (Yoon et al.
view). This GRB-SN connection is popularly explained
2010). Multi-wavelength studies of SNe Ic-BL in metal-
by the favored “collapsar model” (MacFadyen et al.
poor environments may shed further light on the role of
2001) in which the gravitational collapse of massive
metallicityonnatureofthe progenitorandtheexplosion
(M & 20 M ) progenitor star gives birth to a central
⊙
properties,includingtheproductionofrelativisticejecta.
engine – a rapidly rotating and accreting compact ob-
Fortunately, with the recent advent of wide-field opti-
ject – that powers a relativistic outflow. At the same
cal transient surveys (e.g., Catalina Real-time Transient
time, not all SNe Ic-BL show evidence for a central en-
Survey(CRTS);Drake et al.2009,PanchromaticSurvey
gine. Radio observations constrain the fraction of SNe
TelescopeandRapidResponseSystem; (Pan-STARRS1,
Ic-BL harboring relativistic outflows to be less than a
abbreviated PS1) Kaiser et al. 2002, Palomar Transient
third (Soderberg et al. 2006a, 2010).
Factory; Law et al. 2009) SNe Ic-BL are now being
The physical parameter(s) that distinguish the pro-
discovered in metal-poor environments, Z ∼ 0.5 Z
genitors of GRB-associated SNe from other SNe Ic-BL ⊙
(Arcavi et al.2010;Modjaz et al.2011)thankstoanun-
remains debated, while theoretical considerations indi-
biased search technique. In this paper, we present pre-
cate that progenitor metallicity may play a key role
discovery Pan-STARRS1 imaging and multi-wavelength
(Woosley & Heger2006). Inthecollapsarscenario,mas-
follow-up observations for the SN Ic-BL 2010ay discov-
sive progenitor stars with metallicity above a thresh-
ered by CRTS (Drake et al. 2010). In §2, we report our
old, Z & 0.3 Z , lose angular momentum to metal
⊙
optical (Pan-STARRS1, Gemini, William Herschel Tele-
line-driven winds, preventing the formation of a rapidly
scope) and radio (Expanded Very Large Array; EVLA)
rotating compact remnant, and in turn, a relativistic
observations. In§3,wemodeltheopticallight-curveand
outflow. At the same time, the hydrogen-free spec-
analyze the spectra to derive the explosion properties of
tra of SNe Ic-BL indicate that their stellar envelopes
SN2010ay. In §5, we use our observations of SN2010ay
have been stripped prior to explosion, requiring higher
with the EVLA to place strict limits on the presence
metallicities (e.g., Z ≈ Z ) if due to radiation driven-
⊙ of relativistic outflow. In §5, we draw from gamma-ray
winds (Woosley et al. 1995). Alternatively, short-period
satellitecoveragetoruleoutadetectedgamma-rayburst
(∼0.1days)binaryinteractionmaybeinvokedtospinup
in association with SN2010ay. In §6, we derive the ex-
starsviatidalforcesaswellascausemasslossviaRoche
plosionsitemetallicityandfindittobesignificantlysub-
lobe overflow (Podsiadlowskiet al. 2004; Fryer & Heger
solar and typical of most GRB-SNe host environments.
2005). However, even in the binary scenario, GRB for-
In§7,wediscussthe implicationsofthesefindingsinthe
mation is predicted to occur at higher rates in lower-
context of the explosion and progenitor properties and
metallicityenvironments,wheretheradiusandmassloss
conclude in §8.
rates of stars should be smaller (Izzard et al. 2004).
Observationally, most GRB-SNe are discoveredwithin
2. OBSERVATIONS
dwarf star-forming galaxies (Fruchter et al. 2006) char-
acterized by sub-solar metallicities, Z . 0.5 Z 2.1. Discovery by CRTS
⊙
(Levesque et al. 2010a). This has been interpreted as SN2010ay was discovered by the Catalina Real-
observational support for the metallicity-dependent col- time Transient Survey (Drake et al. 2009) on 2010
lapsarmodel. Meanwhile, SNe Ic-BL without associated March 17.38 UT (Drake et al. 2010) and designated
GRBs have historically been found in more enriched en- CSS100317:123527+270403, with an unfiltered magni-
vironments (Modjaz et al. 2008), motivating the sugges- tude of m ≈ 17.5 mag and located . 1” of the cen-
tion of an observationally determined “cut-off metallic- ter of a compact galaxy, SDSS J123527.19+270402.7 at
ity”abovewhichGRB-SNe do notform(Kocevski et al. z = 0.067 (Table 1). We adopt a distance, D = 297.9
L
2009). However, this difference may be partly at- Mpc, to the host galaxy19, and note that the Galac-
tributable to the different survey strategies: SNe have
tic extinction toward this galaxy is E(B −V) = 0.017
been found in large numbers by galaxy-targeted sur-
(Schlegel et al. 1998). Pre-discovery unfiltered images
veysbiasedtowardsmoreluminous(andthereforehigher
from CRTS revealed an earlier detection of the SN on
metallicity) environments, while GRB host galaxies are
Mar5.45UTatm≈18.2magandanon-detectionfrom
foundinanuntargetedmannerthroughtheirgamma-ray
Feb 17.45 UT at m&18.3 mag (Drake et al. 2010).
emission.
AspectrumobtainedonMar22UTrevealedtheSNto
Against this backdropof progress,recent observations
be of Type Ic with broad features, similar to the GRB-
have begun to call into question some aspects of this
associatedSN1998bwspectrumobtainednearmaximum
scenario. First, several long-duration GRBs have now
light (Filippenko et al. 2010). This classification was
been identified in solar or super-solar metallicity en-
confirmed by Prieto (2010) who additionally reported
vironments (e.g., GRB020819; Levesque et al. 2010b).
photometry for the SN (see Table 2). After numerically
Similarly, the luminous radio emission seen from SN
subtracting the host galaxy emission, they estimate an
Ic-BL 2009bb pointed unequivocally to the production
unusually brightabsolute magnitude of V ≈−19.4 mag.
of copious relativistic ejecta resembling a GRB after-
glow (Soderberg et al. 2010) while the explosion envi-
19 WeassumeH0=71kms−1 Mpc−1,ΩΛ=0.73,ΩM =0.27
SN2010ay: a luminous broad-lined SN Ic 3
TABLE 1 TABLE 2
SN2010ayhostgalaxySDSS SN2010aylight-curve photometry
J123527.19+270402.7
MJD tpeaka Filter mb MRc Source
Parameter Value
55244.4 -29 ··· <18.3 <−19.2±0.2 d
RA 12h35m27s.2(J2000) 55248.6 -25 rP1 <22.0±0.1 <−16.0±0.1 e
DEC +27◦04′03′′ (J2000) 55252.2 -21 iP1 21.1±0.3 −16.8±0.3 e
Redshift(z) 0.0671 55260.4 -13 ··· 18.2 −19.3±0.2 d
Petrosianradius 1.355′′ 55272.4 -1 ··· 17.5 −20.4±0.2 d
55277.2 4 B 18.39±0.05 ··· f
Photometrya 55277.2 4 V 17.61±0.05 ··· f
u′ 19.56±0.03mag 55277.2 4 R 17.44±0.05 −20.22±0.07 f
g′ 19.02±0.01mag 55287.0 14 R 18.2±0.2 −19.2±0.2 g
r′ 19.02±0.01mag 55297.0 24 g 18.9±0.1 ··· h
i′ 18.69±0.01mag 55297.0 24 r 18.3±0.1 −19.0±0.1 h
z′ 18.87±0.04mag 55297.0 24 i 18.0±0.1 ··· h
U 19.50±0.06mag 55645.0 372 iP1 <22.2±0.2 <−16.22±0.1 e
B 19.02±0.05mag 55649.0 376 rP1 <21.9±0.1 <−15.7±0.1 e
V 19.13±0.05mag
R 18.94±0.05mag
I 18.90±0.06mag aTimesincepeakindays,relativetothefittedvalue: 2010March18.1±1.9.
b Themeasuredapparentmagnitudeofthesource,inthefilternotedand
Extinction withoutextinctioncorrection. ForthePan-STARRS1photometry,atem-
plateimagewassubtracted;fortheotherpoints,thehostgalaxyfluxhas
E(B-V)MWb 0.017mag notbeensubtractednumerically.
E(B-V)hostc 0.2mag c The absolute R magnitude of the SN. Filter conversion, host flux sub-
traction, and extinction correction have been performed as described in
§exp:lcmodel.
Note. — SDSS host galaxy properties d Drakeetal.(2010),unfiltered(syntheticV-band).
aandMuogdreizl pmhoatgonmiteutdreys. from SDSS DR8 ef PPrhioettoom(2e0tr1y0)f.romthePan-STARRS13π survey.
(Aiharaetal. 2011). Host galaxy photom- g SyntheticphotometryobtainedfromourWHTspectrumasdescribedin
etry has not been corrected for extinction.
§2.3.
UBVRI photometry has been converted h PhotometryfromourGemini/GMOSobservationsdescribedin§2.2.
from the SDSS ugriz measurements us-
ingthetransformationofBlanton&Roweis (Alard 2000). No residual flux was found in the differ-
(2007).
b TheMilkyWayextinctionasdetermined ence rP1-bandimagefrom2010February21with anup-
by Schlegeletal. (1998), assuming RV = per limit of r > 22.0 mag. However, we detect residual
3.1. flux at the position of SN2010ay in the i -band resid-
c The host galaxy extinction determined ual image from 2010 February 25 with aPm1 agnitude of
from the SDSS spectrum centered on the
i=21.1±0.3 mag.
galaxy nucleus, via the Balmer decrement
asdescribedin§2.3.1. The field was again observed in the iP1band on 2011
March 25 and the r -band on 2011 March 29, but no
2.2. Pre-Discovery Detection With Pan-STARRS1 3π P1
residual flux was detected in the subtractions at the SN
The field of SN2010ay was serendipitously observed position to limits of i′ &22.2 and r′ &21.9.
with the PS1 3π survey in the weeks preceding its In Table 2 and Figure 2, we compile photometry from
discovery. Pan-STARRS1 is a wide-field imaging sys- thePS1detections,ouropticalobservations,andthecir-
tem at Haleakala, Hawaii dedicated to survey obser- culars to construct a light-curve for SN2010ay.
vations (Kaiser et al. 2002). The PS1 optical design
(Hodapp et al. 2004) uses a 1.8 meter diameter f/4.4 2.3. Optical observations
primarymirror,anda0.9msecondary. Thetelescopeil-
Weobtainedanopticalspectrum(∼3000−11000˚A)of
luminatesadiameterof3.3degrees. ThePan-STARRS1
SN2010ayonApril1UT,fromtheISISbluearminstru-
imager (Tonry & Onaka 2009) comprises a total of 60
ment of the 4.2 m William Herschel Telescope (WHT)
4800×4800pixel detectors, with 10 µm pixels that sub-
at the Roque de Los MuchachosObservatory. The spec-
tend 0.258 arcsec. The PS1 observations are obtained
trum was taken at the parallactic angle and the expo-
throughasetoffivebroadbandfilters designatedasg ,
P1 sure time was 1800 sec. We obtained a second 1800 sec
r , i , z , and y . These filters are similar to those
P1 P1 P1 P1 optical spectrum (∼ 3600−9600 ˚A) using the Gemini
used in previous surveys, such as SDSS (Fukugita et al.
Multi-Object Spectrograph(GMOS) on the 8.1 m Gem-
1996). However, The g filter extends 20 nm redward
P1 iniNorthtelescopeon2010April11.4UT.Weemployed
of g′, the z filter is cut off at 930 nm, and SDSS has
P1 standard two-dimensional long-slit image reduction and
no corresponding y filter (Stubbs et al. 2010).
P1 spectralextractionroutinesinIRAF20.We donotapply
The field of SN2010ay was observed on 2010 Febru-
a correction for atmospheric differential refraction, be-
ary 21st (r -band) and February 25th (i -band, Fig-
P1 P1 cause the displacement should be . 0.5′ at the airmass
ure 1). On each night, four exposures were collected fol-
of the observations, ≈1.0.
lowing the strategy of the PS1-3pi survey (Chambers et
al., in preparation). Following the CRTS discovery and
20 IRAFisdistributedbytheNational Optical AstronomyOb-
announcementof SN2010ay,we geometrically registered
servatory, whichisoperated bytheAssociationofUniversitiesfor
SDSS pre-explosion images to the PS1 images and per- ResearchinAstronomy(AURA)undercooperativeagreementwith
formed digital image subtraction using the ISIS package theNationalScienceFoundation.
4 Sanders et al.
Fig. 1.— Images illustrating the Pan-STARRS1 pre-discovery detection of SN2010ay. a) Pre-explosion i-band image from the SDSS
DR7 (Abazajianetal. 2009), observed 2004 December 21, b) iP1-band image from the 3π survey of PS1, observed 2010 February 25, c)
thedifferenceoftheSDSSi′ andPS1iP1 images. ThetransientemissioncanbeseenintheNEcorneroftheframe.
and blueshift of the feature near 6355 ˚A are similar for
−21 SN2010ay and SN2010bh, and are broader and more
blueshifted than in SN1998bw at a comparable epoch.
We discuss the comparison between these two SN fur-
−20
ther in §3.3 and §6.2.
Additionally, we obtained 60 s gri-band images of
−19 SN2010ay on 2010 April 11.4 UT using GMOS. The
data were reduced using the gemini package in IRAF,
1998bw
MR −18 aGnMdOpShozteormo-eptoryintws2a1s. peWrfoermmeedasuurseingthathte[gs,tra,nid]ar=d
Circular [18.90,18.32,18.04]±0.1 mag.
−17 PS1 Imagingphotometryisnotavailableattheepochofour
WHT spectrum. We perform synthetic photometry on
WHT
thespectrumtoextracttheflux atthe centralfrequency
−16 Gemini oftheR-band(6527˚A)andfindR=18.2±0.2mag. We
then subtract the host galaxy flux numerically.
55240 55255 55270 55285 55300
MJD
2.3.1. Host galaxy features
Fig.2.— The optical R-band light curve of SN2010ay, as com-
We measure fluxes of the narrow emission lines from
piledinTable2fromCBET2224(redsquares),thePS13πsurvey
(blue),ourGeminiimages(black,andsyntheticphotometry(§2.3) the host galaxy in our Gemini spectrum, as reported in
basedonourWHTspectrum(gold). Trianglesdenoteupperlimits. Table 3. We fit a Gaussian profile to each narrow emis-
The thick dashed line represents the luminosity of an expanding sion line; for nearby lines such as [N II] and Hα, we fit
fireball fit to our early-time photometry (§3.1). The thin dashed
multiple Gaussians simultaneously. We model the local
line is the SN Ibc light-curve template of Droutetal. (2010) and
the gray field represents the standard deviation among its con- continuumwithalinearfitto20˚Aregionsoneitherside
stituentphotometry. Thetemplateisstretchedby(1+z)=1.067 of each line.
withthebestfitparameterstRpeak=March18±2(MJD55273±2), The host galaxy is significantly reddened as evidenced
MRpeak=−20.2±0.2mag,andreducedχ2=0.5. Thesolidlineis by the flux ratio of H to H , ≈ 3.44. We infer E(B-
thelight-curveof theSN-GRB 1998bw (Galamaetal.1998), red- α β
shifted to match SN2010ay. The vertical dotted lines mark the V)= 0.2 mag (AV = 0.6 mag), as measured from the
epochs ofourGeminiandWHTspectroscopy. Balmer decrement in our Gemini spectrum, assuming
R =3.1, Case B recombination(Osterbrock & Ferland
V
2006), and the reddening law of Cardelli et al. (1989).
In both our Gemini and WHT spectra, broad absorp-
This is similar to the value derived from the SDSS DR8
tionfeatures associatedwith the SN are clearlydetected
nuclear fiber spectroscopy line fluxes for the host galaxy
inadditionto narrowemissionlines typicalofstar form-
(E(B-V)=0.2mag). ThevaluereportedinModjaz et al.
ing galaxies. We distinguish the host galaxy emission
(2010)wasalsosimilar: E(B-V)=0.3mag. Furthermore,
from the continuum dominated by the highly broadened
we note that the color (B−V =0.78±0.07 mag) as re-
SN emission by subtracting a high-order spline fit to
ported by Prieto (2010) at 4 d after R−band peak is
the continuum. Both SN and host galaxy spectral com-
significantly redder than SN Ibc color curve templates
ponents are shown in Figure 3. As illustrated in the
Drout et al. (2010), further supporting a non-negligible
Figure, the broad, highly-blended spectral features of
host galaxy extinction.
SN2010ay resemble those of the Type Ic-BL SN2010bh
(associatedwithGRB100316D)atasimilarsimilarepoch
(Chornock et al. 2010). In particular, the broadening 21 http://www.gemini.edu/?q=node/10445
SN2010ay: a luminous broad-lined SN Ic 5
SN2010ay
(+14d)
SN2010ay
(+24d)
⊕
SN2010bh
(+10.0d)
SN1998bw
1) (+19d)
−
A˚
1
−
s
2−m 727869HǫHδ Hγ Hβ959 007 875 548Hα584731
1610−ergc 20 [OII]3[NeIII]3 [OIII]4 [OIII]5 HeI5 [NII]6 [NII]6[SII]6717,6 Hγ [OIII]4363
(
x
u
Fl
10
0
4000 5000 6000 7000 8000 9000
Restwavelength(A˚)
Fig.3.— Optical spectra of SN2010ay from Gemini (24 days after R-band peak) and the WHT (14 days). The spectrum is plotted
decomposed into SN (above, with narrow lines clipped) and host galaxy (below, fromGemini, withspline-fitsubtracted) components for
clarity. The spectrum of SN2010bh from Chornocketal. (2010) is given in black for comparison, at 21.2 days after the GRB 100316D
trigger (∼ 10.0 days after R-band peak, Canoetal. 2011a). The spectrum of SN 1998bw at +19 days from Patatetal. (2001) is also
plotted. BotharetransformedtotheredshiftofSN2010ay. TheSNeareshiftedinfluxforclarity. Inthelowerplot,relevanthostgalaxy
emissionlinesaremarkedwitharedlineandlabeled.
2.4. Radio Observations Chevalier & Fransson 2006; Soderberg et al. 2010 and
referenceswithin)andafactorof102to103lessluminous
We observed SN2010ay with the EVLA (Perley et al.
than the radio afterglows associatedwith GRBs 020903,
2009) on three epochs, 2010 March 26, 2010 April 29,
030329,and031203atearlyepochs(Berger et al.2003b;
and 2011 May 7. All EVLA observations were obtained
Soderberg et al. 2004a,b; Frail et al. 2005). In compar-
with a bandwidth of 256 MHz centered at 4.9 GHz. We
ison with the radio luminosities observed for the rela-
used calibrator J1221+2813 to monitor the phase and
tivistic SNe 1998bw (Kulkarni et al. 1998) and 2009bb
3C286 for flux calibration. Data were reduced using the
(Soderberg et al. 2010), SN2010ay is a factor of & 10
standardpackagesoftheAstronomicalImageProcessing
less luminous. The only relativistic explosion with de-
System(AIPS). We do notdetecta radiocounterpartto
tectedradioemissionbelowourEVLAlimitsistheweak
SN2010ay in these observations and place upper limits
and fast fading XRF060218 (Soderberg et al. 2006a).
of F .46, 42, 30 µJy (3σ) for each epoch respectively
ν
correspondingto upper limits onthe spectralluminosity 3. INITIALCONSTRAINTS
spanning Lν .(3.6−5.5)×1027 erg cm−2 s−1. 3.1. Light Curve Modeling
As shown in Figure 4, these limits are compa-
rable to the peak luminosities observed for ordi- We construct an R-band lightcurve for SN2010ay us-
nary SNe Ibc (Berger et al. 2003a; Soderberg 2007; ingtheobservationsdescribedin§2.3(Table2). Wecon-
vert the i band data points to the R−band assuming
P1
6 Sanders et al.
Fig.4.—EVLAupperlimitsforSN2010ay(blackarrows)arecomparedwiththeobservedradiolight-curvesforordinarySNeIbc(grey;
Soderberg 2007 and references within) and the radioafterglows of allGRB-SNe withinz ≤0.25. SN2010ay is afactor of 102 to 103 less
luminous than XRF020903 (orange; Soderbergetal. 2004a), GRB030329 (blue; Bergeretal. 2003b; Frailetal. 2005), and GRB031203
(Soderbergetal.2004b). Relativistic,engine-drivenSNe1998bw(red;Kulkarnietal.1998)and2009bb(darkblue;Soderbergetal.2010)
areafactorof 10moreluminousthantheSN2010ay limitsonacomparabletimescale,whileXRF060218 liesafactor ofafewbelowthe
limits. WeconstraintheradiocounterparttobenomoreluminousthanXRF060218andcomparabletothepeakluminositiesofordinary
SNeIbc.
1998). Photometry for the unfiltered CRTS images was
TABLE 3 reported by Drake et al. (2010) after transformation to
Emission linefluxesmeasuredforthe
the synthetic V-band (A.J. Drake, private communica-
host galaxyofSN2010ay
tion);wethereforeassumetheV −RcolorofSN1998bw
EmissionLine Flux at the appropriate epoch. For the Pan-STARRS1 pho-
(10−16erg s−1cm−2) tometry, the host galaxy flux was subtracted using a
template image. For all other photometry, we have sub-
[OII]λ3726,3729 52±2
Hδ 4.5±0.2 tractedthe flux ofthe hostgalaxynumerically assuming
Hγ 9.9±0.1 the magnitude reported in Table 1. A total (Galactic +
[OIII]λ4363 0.7±0.1 host) reddening of E(B-V)= 0.2 mag has been assumed
Hβ 24.5±0.1
(see §2.3.1).
[OIII]λ4959 30.4±0.1
[OIII]λ5007 90.1±0.2 To estimate the explosion date of SN2010ay we have
[NII]λ6548 2.2±0.1 fit an expanding fireball model to the optical light curve
Hα 84.5±0.1 (Figure2),followingConley et al.(2006). Inthis model,
[NII]λ6584 6.33±0.06
the luminosity increases as
[SII]λ6717 7.46±0.06
[SII]λ6731 5.59±0.06
n
froNmootue.rG—emAinlilsflpuecxtersumha.vNeobreeedndemneinagsucroerd- L∝ t−t0 (1)
1+z
rection has been applied. There is an addi- !
tionalsystematicuncertaintyinthefluxmea-
surementsof∼10%duetofluxcalibration. We derive an explosion date t of 2010 February
0
21.2±1.5. Here we have assumed an index n = 2. This
the unextincted i′ −R color observed for the Type Ic- suggests that the PS1 3π i band pre-discovery detec-
P1
BL SN1998bw at the appropriate epoch (Galama et al. tion image of SN2010ay was taken ∼ 4 days after the
SN2010ay: a luminous broad-lined SN Ic 7
explosion. This early observation provides a valuable peak, Chornock et al. 2010). In particular, the blueshift
datapoint for estimating the explosion date and also for of the feature near 6355 ˚A is larger than in SN 1998bw
constraining the rise-time of the SN. and more similar to SN2010bh. This feature is com-
In Figure 2, we compare the light curve of SN2010ay monly associated with Si II λ6355˚A (e.g. Patat et al.
tothe SNIbc light-curvetemplate ofDrout et al.(2010) 2001). However, this feature has two clearly-detectable
afterstretchingbyafactorof(1+z). Thetemplate pro- absorption minima in SN2010ay, but not in SN2010bh.
vides a reasonable fit to optical evolution of SN2010ay. This could be due to increased blending in SN2010bh
Fitting the template to our photometry we derive (re- or the absence of contaminating lines. The red ends of
duced χ2 = 0.5) a date of R-band peak of 2010 March the SN2010ay and SN2010bh spectra (rest wavelength
18±2UT(MJD55273±2)andaR-bandpeakmagnitude > 7500 ˚A) have similar P-Cygni features, but the emis-
ofMR ≈−19.7magbeforeextinctioncorrection. Asdis- sion and absorption components in SN 2010bh are each
cussedin§2.3.1,basedontheBalmerdecrementobserved blueshifted by ∼ 200 ˚A more than in the spectrum of
for the host galaxy emission lines, we assume an extinc-
SN2010ay. Chornock et al. (2010) attribute this feature
tion of E(B −V) = 0.2 mag. Applying this correction, to the Ca II NIR triplet, with a gf-weighted line cen-
the peak absolute magnitude is MR ≈−20.2±0.2 mag. troid of 8479 ˚A, and find a velocity that is high, but
We note that this fitted value is ≈ 0.2 mag fainter than
consistent with the early-time velocity of Si II λ6355˚A
that estimatedfromthe data point nearpeak. Here, the
(30−35× 103 km s−1).
uncertainty is dominated by the template fitting.
Weestimatethephotosphericexpansionvelocity(v )
Regardless of the extinction correction, SN2010ay ph
is brighter than all the 25 SNe Ibc in the sample from the minimum of the Si II λ6355˚A absorption
of Drout et al. (2010), except for SN 2007D (M ≈ feature. We smooth the spectrum using an inverse-
R
−20.65 mag, which was also significantly extincted: variance-weighted Gaussian filter (Blondin et al. 2006,
A ∼ 1.0 mag). Assuming an intrinsic V-R color with dλ/λ = 0.005) and measure the minimum position
V
ofthe redmostcomponentofthe absorptionprofile. The
of zero at peak (e.g. 1998bw: Galama et al. 1998;
Patat et al. 2001), SN2010ay is also brighter than any blue componentofthe absorptionprofileshifts blueward
of the 22 GRB and XRF-producing SNe in the compila- over time, suggesting that it is produced by a combina-
tion of ions separated by several 103 km s−1, such as
tion of Cano et al. (2011b), all corrected for extinction,
and is 1.5 standard deviations from the mean bright- He I λ5876˚A and Na I D, whose relative optical depth
ness. The peak magnitude is only ∼ 1 mag below that changes with time.
of the Type Ic SN2007bi (M = −21.3 ± 0.1 mag), The photospheric velocity inferred from the
R
which Gal-Yam et al. (2009) report as a candidate pair- Si II λ6355˚A feature is ∼ 2× faster than that of SN
instability supernova. 1998bwat similar times, and more similar to that of SN
2010bh (Figure 3). For SN 1998bw, Patat et al. (2001)
3.2. Large Nickel Mass for SN2010ay measured∼10×103kms−1at+13days. ForSN2010bh,
Chornock et al. (2010) measured v ≈26×103 km s−1
We use the available photometry for SN2010ay dis- ph
cussedabovetoderivethemassof56Nirequiredtopower at +10.0 days after explosion. Prieto (2010) re-
the optical light-curve under the assumption that the ported a velocity of vph ≈22.6×103 km s−1 from the
emission is powered by radioactive decay. Using the Si II λ6355˚A feature in a spectrum of SN2010ay taken
relation between M and M found by Drout et al. at +4 days. From our [WHT,Gemeni] spectra taken
Ni R
(2010), log(M ) = (−0.41 M − 8.3) M , we esti- [+14,+24] days after R-band peak (see §3.1), we
Ni R ⊙
matethatSN2010aysynthesizedanickelmassofM = estimate v ≈[19.2,18.3]×103 km s−1.
Ni ph
0.9+0.1 M . We have estimated the uncertainty in the In addition to the broadening of the spectral fea-
−0.1 ⊙
M estimate by propagation of the uncertainty in the tures and the blueshift of the Si II λ6355˚A line, ad-
Ni
template fitted peak magnitude — systematic uncer- ditional lines of evidence suggest a high photospheric
tanties are not included. If we instead adopt the most expansion velocity for SN2010ay. We measure v ≈
ph
luminous individual data point in the light curve as the [21.7,20.1]×103kms−1fromtheCaIINIRtripletonthe
peakvalue,ratherthanthesmallerpeakvaluefromtem- smoothed [WHT,Gemini] spectra, relative to a line cen-
plate fitting, we find MNi ≈1.2 M⊙. terat8479˚A. Thisiswithinafew103 kms−1 ofthev
ph
The M estimate for SN2010ay is larger than that
Ni we measure from SiII λ6355˚A at these epochs. Further-
of all but one (SN2007D) of the 25 SNe Ibc in the
more,we do not detect the broademission“bump” near
Drout et al. (2010) compilation and significantly larger
4500 ˚A in either of our spectra. This feature was also
than the estimate for GRB-SN2010bh, M = 0.12 ±
Ni absent in SN2010bh, but was identified in SN2003dh,
0.01M , as estimated by Cano et al. (2011a). On the
⊙
SN2006aj,and severalIc-BLs not associatedwith GRBs
otherhand,M ofSN2010ayisatleast3×smallerthan
Ni and normal SNe Ic; Chornock et al. (2010) suggest that
for SN2007bi (M ≈3.5−4.5 M , Young et al. 2010).
Ni ⊙ theabsenceofthisfeatureindicatesahighexpansionve-
ApairinstabilitysupernovashouldproduceM &3M
Ni ⊙ locity if it is due to blending of the ironlines to the blue
(Gal-Yam et al. 2009).
and red of 4500 ˚A.
3.3. Unusually high photospheric expansion velocity We compare the late-time expansion velocity of
SN2010ay to other SNe Ic-BL and GRB-SNe with de-
As illustrated in Figure 3, the broad, highly-blended
tailed time-dependent velocity measurements from the
spectral features of SN2010ay at the time of the WHT
literatureinFigure5. Inthisfigure,wealsofitpower-law
observations (14 days after R-band peak, see §3.1) re-
gradients to the time-evolution of the velocity of these
semblethoseofSN2010bhatasimilartime(10.0dafter
8 Sanders et al.
alsoconsiderthevelocityofthecandidatepair-instability
TABLE 4 SN2007bi. VelocitymeasurementsforSN2007biareonly
Velocity Evolution of
available at late times (> 50 d, Young et al. 2010). Fit-
SNe Ic-BL
ting to these late-time Si II λ6355˚A velocity measure-
SN v30 α ments,we findthatSN2007bihasa characteristicveloc-
ph
ity∼3×smallerthan2010ay: v30 =8andthe late-time
ph
SNeIc-BL velocity gradient is ∼4× slower: α=−0.1.
1997ef 6 -0.8
2002ap 4 -1.1 3.4. Ejecta Mass and Energy
2003jd 10 -0.5
We use the scaling relations provided by Drout et al.
2007bg 7 -0.2
2007ru 10 -0.5 (2010), basedon the originalformalismofArnett (1982)
2010ay 22 -0.4 andmodified by Valenti et al.(2008), to derivethe total
mass of the ejecta and the kinetic energy.
Engine-drivenSNeIc-BL
1998bw 10 -0.9
2003dh 12 -0.9 2
τ v
2003lw 10 -0.8 M =0.8 c ph M (2)
2006aj 15 -0.3 ej 8d 10,000 km s−1 ⊙
! !
2009bb 11 -0.8
2010bh 24 -0.2 2 3
τ v
E =0.5 c ph ×1051 erg (3)
Note. — To the velocity K 8d! 10,000 km s−1!
measurements for each SN,
we have fit a power law of
We assume the fitted peak magnitude for SN2010ay
wthheerfeortmisvtphhe=timvep30hs(itn/c3e0)eαx-, (MR = −20.2±0.2, §3.1), the photospheric expansion
plosionindaysandv30 isthe velocitywemeasurefromourWHT spectrumat14days
ph
v10el3ockimtyas−t13.0dTahyesipnaruanmitesteorf after maximum light (vph = 19.2×103 km s−1, §3.3),
α then represents the expo- and a characteristic time (light-curve width) consistent
nential velocity gradient and with the data and the mean value from the Drout et al.
ivtp3y0h. iTshaescehpaorawcetrerliaswticfivtselaorce- (2010) sample of SNe Ic-BL (τc =14 d).
illustratedinFigure5. Using these values, the total mass ejected was Mej ≈
4.7 M , and the total kinetic energy of the explosion
⊙
SNe with the formv =v30(t/30)α, where t is the time was EK ≈ 10.8×1051 ergs. Hereafter we refer to the
ph ph definition E =E /1051 ergs.
since explosionindaysandv30 is the velocityat30days K,51 K
ph Thesystematicuncertaintiesassociatedwiththismod-
in units of 103 km s−1. These parameters are listed in eling dominate the statistical uncertainties. In particu-
Table 4. Figure 5 illustrates that most SNe are well de- lar, the models rely on the assumptions of homologous
scribed by a single power law.22 Contamination from expansion,sphericalsymmetry,all56Nicentralizedatthe
different ions or detached features will add uncertainty center of the ejecta, optically thick ejecta and constant
to velocities measured from the SiII λ6355˚A feature. opacity.
SN2010ay and 2010bh share high characteristic ve- We note that an earlier measurement of the photo-
locities at 30 days after explosion and velocity gradi- spheric velocity is preferred for optical modeling. Since
ents that are slow relative to other broad-lined Ic SNe wehavearguedthatSN2010ayandSN2010bhhavesim-
with and without associated GRBs. For SN 2010ay, ilar characteristic velocities (v30), if we instead adopt
ph
vp3h0 = 22 is 2 − 5× larger than for other SNe Ic-BL a higher velocity of 25,000 km s−1 as measured for
without associated GRBs (6 for 1997ef, 4 for 2002ap, SN2010bh by Cano et al. (2011a), we estimate M ≈
ej
10 for 2003jd, 7 for 2007bg, and 10 for 2007ru) and is 6.1 M and E ≈23.9 for SN2010ay.
⊙ K,51
similar to the GRB-SN 2010bh (v30 = 24). No other The M and E of SN2010ay are consistent with
ph ej K,51
GRB-SN or SN Ic-BL has v30 > 15. The SNe Ic-BL the mean for SNe Ic-BL in the Drout et al. (2010) sam-
and GRB-SNe with the mostphshallow velocity gradients ple(4.7+−21..38 M⊙ and11+−64,respectively),becausethe au-
among these twelve objects have α < −0.5; they are thors assumed a velocity (vph =2×104 km s−1) similar
SN2006aj(α=−0.3),SN2007bg(α=−0.2),SN2010ay to the late-time velocity we measure. For comparison,
(α = −0.4), and SN2010bh (α = −0.2). Two of these SN2010bh had a total ejecta mass of ∼ 2 M⊙ and a
objects are GRB-SNe, one is SN2007bg (whose small total kinetic energy of EK,51 ≈13 (Cano et al. 2011a).
velocity at early times distinguishes it from other SNe The ratio of Ni to total ejecta mass is ∼ 0.2 for SN
Ic-BL), and the other is SN2010ay. The velocity of SNe 2010ay,significantlyhigherthanthevaluestypicalofSNe
2010ay and 2010bh, respectively, declines about 2 and Ic-BL and GRB-SNe. For comparison, the ratio is just
4× more slowly than the other SNe Ic-BL (mean and ∼0.05forSN2010bh. Adoptingthe valuesderivedfrom
standard deviation: α = −0.8±0.3) and about 1.5 and bolometric light curve modeling by Cano et al. (2011a),
3× more slowly the GRB-SNe (α=−0.6±0.3). the MNi and MNi/Mej ratios for other GRB-SNe are: ∼
GiventhehighpeakluminosityofSN2010ay(§3.1),we 0.5M⊙and∼0.06−0.22(1998bw),∼0.4M⊙and∼0.08
(2003dh), ∼ 0.15 M and ∼ 0.07−0.1 (2006aj), and ∼
⊙
22 Abreakat∼2×104 kms−1 appearstoexistforSN1998bw 0.2M⊙ and∼0.06(2009bb). ThisratioforSN2010ayis
at∼16days. largerthanthatofallbut4ofthe25SNeofDrout et al.
SN2010ay: a luminous broad-lined SN Ic 9
40
30
1997ef
20 1998bw
)
1
− 2002ap
s
m
2003dh
k
3
0 2003jd
1
(
ph 10 2003lw
v
2006aj
2007bg
2007ru
5 2009bb
2010ay
2010bh
100 101
Timesinceexplosion(days)
Fig.5.—Acomparisonofthetime-evolvingphotosphericexpansionvelocityofSN2010ayandotherSNeIc-BL(red)andGRB-SNe(blue)
from the literature. Typical uncertainties in velocity estimates are 10%. For each SN, we fit a power law of the form vph =vp30h(t/30)α,
wheretisthetimeindays,v30 isthevelocityat30dayssinceexplosion(dashedverticalline),andαisthevelocitygradient. Thevelocities
ph
for SNe 1997ef, 2003dh, 2003lw are from Mazzalietal. (2006), as determined by spectral modeling. The velocities for all other SNe are
measured from the Si II λ6355˚A feature as follows: SN2007ru are from Sahuetal. (2009); SNe 1998bw, 2006aj, and 2010bh are from
Chornocketal. (2010), from spectra in references therein; SN2007bg are from Youngetal. (2010); SNe 2002ap, 2009bb, and 2003jd are
fromPignataetal.(2011)andreferencestherein.
(2010): the Type Ic SNe 2004ge (M /M ∼ 0.4) ans (Chomiuk et al. 2011; Quimby et al. 2011).
Ni ej
2005eo(M /M ∼0.2),theTypeIbSN2005hg(∼0.4),
Ni ej
and the Type Ic-BL SN2007D (∼0.6). 4. CONSTRAINTSONRELATIVISTIC EJECTA
ThelargevalueofM weestimateforSN2010ayraises
Ni WeuseourEVLAupperlimitsforSN2010ayspanning
the question of whether a process other than Ni decay
∆t ≈ 29−433 days to constrain the properties of the
may be powering its light-curve. An independent test
shockwave and those of the local circumstellar environ-
of the physical process powering the light-curve is the
ment. TheradioemissionfromSNeIbcandGRBsispro-
decay rate of the late-time light curve which should be
duced by the dynamical interaction of the fastest ejecta
≈ 0.01 mag day−1 for SNe powered by radioactive de-
with the surrounding material(Chevalier 1982). The ki-
cayof56Co. ForSN2007bi,Gal-Yam et al.(2009)derive
neticenergyoftheejectaisconverted,inpart,tointernal
M = 3.5 M from the measured peak magnitude and
Ni ⊙ energyoftheshockedmaterialwhichitselfispartitioned
find that the late-time light curve is consistent with the
betweenrelativisticelectrons(ǫ )andamplifiedmagnetic
decay rate of 56Co. While the Pan-STARRS1 3π sur- e
fields(ǫ ). Followingthebreakoutoftheshockwavefrom
vey also observed the field in 2011 March, the SN was B
the stellar surface, electrons in the environment of the
notdetected in our subtractedimages andthe limits are
explosion are shock-accelerated to relativistic velocities
not constraining in the context of 56Co decay (see §2.2
with Lorentz factor, γ and distributed in a power-law
and Table 2). Another possible process is a radiation- distributioncharacterizeedbyN(γ )∝γ−p. Here,pchar-
dominatedshockthatemergesduetointeractionwithan e e
acterizesthe electronenergy index. The particles gyrate
opaque circumstellar medium, as has recently been pro-
inamplified magnetic fields andgive rise to non-thermal
posedbyChevalier & Irwin(2011)fortheultra-luminous
synchrotron emission that peaks in the radio and mm-
SNe SN2006gy and SN2010gx (Pastorello et al. 2010;
bands in the days to weeks following explosion with ob-
Quimby et al. 2011). However, while this class of
servedspectralindex, F ∝ν−(p−1)/2. Atlowerfrequen-
ultra-luminous objects shares some spectroscopic sim- ν
cies the emission is suppressed due to synchrotron self-
ilarities to SNe Ic (Pastorello et al. 2010), they show
absorption which defines a spectral peak, ν (Chevalier
peak luminosities ∼ 4 − 100× higher than SN2010ay p
1998).
10 Sanders et al.
The dynamics of the shockwave determine the evo-
lution of the synchrotron spectrum, and in turn, the
−4/19 −2/19
ǫ L
properties of the observed radio light-curves. In the B≈0.43 e ν,p
case of SNe Ibc, there are three primary scenarios for ǫ 1028 erg s−1 Hz−1
(cid:18) B(cid:19) (cid:18) (cid:19)
the dynamical regime of the ejecta depending on the ν
shock velocity, v = βc (associated Lorentz factor, Γ): × p G. (6)
5 GHz
(i) non-relativistic (v ≈ 0.2c) free-expansion as in the (cid:16) (cid:17)
case of ordinary SNe Ibc (Chevalier 1998), (ii) a de- Finally, the mass loss rate of the progenitor star,
coupled and relativistic (Γ ∼ 10) shell of ejecta that M˙ , may be derived from the number density of emit-
evolves according to the Blandford-McKee solution for ting electrons. Here we normalize the wind profile ac-
several months (Sari et al. 1998) before transitioning to cording to ρ ∝ Ar−2 and A∗ = A/5 × 1011 g cm−.
the Sedov-Taylor regime (Frail et al. 2000). This is the This normalization of A∗ implies that an A∗ of 1 corre-
standard scenario for typical GRBs. And (iii) a sub- spondsto typicalWolf-Rayetprogenitorwind properties
energetic GRB with trans-relativistic velocity (βΓ . 3) ofM˙ =10−5 M yr−1 anda progenitorwindvelocity of
⊙
that bridges the free-expansion and Blandford McKee v =103 km s−1.
w
dynamicalregimes(e.g.SN1998bw;Kulkarni et al.1998,
Li & Chevalier 1999).
We consider our EVLA upper limits in the context A ≈0.15 ǫB −1 ǫe −8/19 Lν,p −4/19
of these three models below. For shock velocities of ∗ 0.1 ǫ 1028 erg s−1 Hz−1
v & 0.2c, ǫ ≈ 0.1 is reasonable (Soderberg et al. 2005; (cid:16) (cid:17) (cid:18) B(cid:19) (cid:18) (cid:19)
e ν 2 ∆t 2
Chevalier & Fransson2006). Wefurtherassumeequipar- × p cm−1 (7)
tition, ǫ = ǫ = 0.1. We adopt a free expansion model 5 GHz 10 days
forbothethenBon-relativisticordinarySNIbccaseandthe (cid:16) (cid:17) (cid:18) (cid:19)
where we assume a shock compression factor of ∼4 and
sub-energetic,trans-relativisticGRBscenario. Asshown
an nucleon-to-electronratio of two.
by Li & Chevalier (1999) a free-expansion model is still
We builtatwo-dimensionalgridoffiducialradiolight-
reasonableinthetrans-relativisticregime(casesiandiii,
curves according to Eqn. 4 in which we vary the pa-
see above).
rameters L and ν over a reasonable range of pa-
νp p
rameters space, bounded by t ≈ [1,3000] days and
4.1. Freely-expanding shockwave p
F ≈ 0.04−1000 mJy. We identify the fiducial light-
ν,p
In the free-expansion scenario, a shock discontinuity curves associated with a radio luminosity higher than
separates the forward and reverse shocks, located at the the EVLA upper limits for SN2010ay at each epoch as
outer edge of the stellar envelope. The bulk ejecta is in these are excluded by our observations. We extract the
freeexpansionwhilethethinlayerofpostshockmaterial physicalparametersassociatedwiththeseexcludedlight-
is slightly decelerated, R ∝ t0.9 (Chevalier & Fransson curves (R, B, E, A ) to define the parameter space ex-
∗
2006). Atagivenfrequency,the bell-shapedlight-curves cluded by our radio observations. The parameter space
of the SN synchrotron emission may be described as for ν and F are bounded by the respective values for
p ν,p
(Chevalier 1998) whichthemodelexceedsrelativisticvelocities,βΓ∼few.
AsshowninFigure6,ourdeepEVLAlimitsenableus
L ≈1.582×L ∆t a 1−e−(∆t/tp)−(a+b) (4) tEo &rul1e0o48uterag,scceonuaprlieodintowahircehlatthiveirsetiicsocuotpflioouws,einnetrhgyis,
ν ν,p
t
(cid:18) p (cid:19) h i two-dimensional E −v parameter space. The excluded
region includes GRB-SNe 1998bw and 060218 as well as
where L is the flux density at the spectral peak at
ν,p
the relativistic SN2009bb. It does not exclude the stan-
epoch, t . Assuming an electron index of p ≈ 3, consis-
p
dard scenario in which a small percent of the energy is
tentwithradiospectraofSNeIbc(Chevalier & Fransson
coupled to fast moving material within the homologous
2006), the exponents are a ≈ 2.3 and b ≈ 1.3. The time
outflow, as is typically observed for ordinary SNe Ibc
averagedshockwavevelocity is v ≈R/∆t whereR is the
(E ≈1047 and v ≈0.2c; Soderberg et al. 2010).
shockwave radius defined as
Next we consider the effects of circumstellar density
since lower mass loss rates produce fainter radio coun-
ǫ −1/19 L 9/19 terparts. As shown in Figure 7, the EVLA limits for
R≈2.9×1016 ǫe 1028 ergνs,p−1 Hz−1 SN2010ay exclude the region of parameter space popu-
(cid:18) B(cid:19) (cid:18) (cid:19) lated by SNe 1998bw and 2009bb with mass loss rates
ν −1
× p cm. (5) of A∗ ∼ 0.1, however, the low density environment of
5 GHz GRB060218 lies outside of our excluded region due to
(cid:16) (cid:17) its lower CSM density, A ∼ 0.01 that gives rise to a
Here we make the assumption that the radio emitting ∗
lower luminosity radio counterpart.
region is half of the total volume enclosed by a spheri-
cal blastwave. Next, we estimate the internal energy, E,
4.2. Relativistic Ejecta
of the radio emitting material from the post-shock mag-
neticenergydensity,E ≈B2R3/12ǫ wherewemaintain In the case of relativistic deceleration the ejecta are
B
the assumption of equipartition. As shown by Chevalier confined to a thin jet and are physically separated from
(1998), the amplified magnetic field at peak luminosity the homologous SN component. Deceleration of the jet
isalsodirectlydeterminedfromtheobservedradioprop- occurs on a timescale of ∆t ≈ (E /A ) years in a
51 ∗
erties, wind-stratified medium (Waxman 2004). On this same