Type II supernova energetics and comparison of light curves to shock-cooling models

29 Pages·2015·3.24 MB·English

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Title
TYPE II SUPERNOVA ENERGETICS and COMPARISON of LIGHT CURVES to SHOCK-COOLING
MODELS
Permalink
https://escholarship.org/uc/item/0xt5267g
Journal
Astrophysical Journal, 820(1)
ISSN
0004-637X
Authors
Rubin, A
Gal-Yam, A
De Cia, A
et al.
Publication Date
2016-03-20
DOI
10.3847/0004-637X/820/1/33

Peer reviewed
eScholarship.org Powered by the California Digital Library
University of California
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
TYPE II SUPERNOVA ENERGETICS AND COMPARISON OF LIGHT CURVES TO SHOCK-COOLING
MODELS
Adam Rubin,1 Avishay Gal-Yam,1 Annalisa De Cia,1 Assaf Horesh,1 Danny Khazov,1 Eran O. Ofek,1 S. R.
Kulkarni,2,3 Iair Arcavi,4,5 Ilan Manulis,1 Ofer Yaron,1 Paul Vreeswijk,1 Mansi M. Kasliwal,6 Sagi Ben-Ami,7
Daniel A. Perley,2,8 Yi Cao,2 S. Bradley Cenko,9,10 Umaa D. Rebbapragada,11 P. R. Wo´zniak,12 Alexei V.
Filippenko,13 K. I. Clubb,13 Peter E. Nugent,13,14 Y.-C. Pan,15 C. Badenes,16 D. Andrew Howell,4,17 Stefano
Valenti,4 David Sand,18 J. Sollerman,19 Joel Johansson,20 Douglas C. Leonard,21 J. Chuck Horst,21 Stephen F.
Armen,21 Joseph M. Fedrow,21,22 Robert M. Quimby,21,23 Paulo Mazzali,24,25 Elena Pian,26,27 Assaf Sternberg,25,28
Thomas Matheson,29 M. Sullivan,30 K. Maguire,31 and Sanja Lazarevic32
5
1
ABSTRACT
0
2 During the first few days after explosion, Type II supernovae (SNe) are dominated by relatively
simple physics. Theoretical predictions regarding early-time SN light curves in the ultraviolet (UV)
v
and optical bands are thus quite robust. We present, for the first time, a sample of 57 R-band Type
o
II SN light curves that are well monitored during their rise, having > 5 detections during the first
N
10 days after discovery, and a well-constrained time of explosion to within 1–3 days. We show that
0 the energy per unit mass (E/M) can be deduced to roughly a factor of five by comparing early-
3 time optical data to the model of Rabinak & Waxman (2011), while the progenitor radius cannot be
determined based on R-band data alone. We find that Type II SN explosion energies span a range of

] E/M =(0.2−20)×1051 erg/(10M ),andhaveameanenergyperunitmassof(cid:104)E/M(cid:105)=0.85×1051
(cid:12)
E
erg/(10 M ), corrected for Malmquist bias. Assuming a small spread in progenitor masses, this
(cid:12)
H indicates a large intrinsic diversity in explosion energy. Moreover, E/M is positively correlated with
. the amount of 56Ni produced in the explosion, as predicted by some recent models of core-collapse
h
SNe. We further present several empirical correlations. The peak magnitude is correlated with the
p
decline rate (∆m ), the decline rate is weakly correlated with the rise time, and the rise time is not
- 15
o significantly correlated with the peak magnitude. Faster declining SNe are more luminous and have
r longer rise times. This limits the possible power sources for such events.
t
s
a
[

1Department of Particle Physics and Astrophysics, Weiz-
1
mann Institute of Science, 234 Herzl St., Rehovot, Israel;
v [email protected]
3 2Astronomy Department, California Institute of Technology,
3 Pasadena,CA91125,USA
7 3Caltech Optical Observatories, California Institute of Tech- Barbara, Broida Hall, Mail Code 9530, Santa Barbara, CA
nology,Pasadena,CA91125,USA 93106-9530,USA
0 4Las Cumbres Observatory Global Telescope Network, 6740 18Physics Department, Texas Tech University, Lubbock, TX
0 CortonaDr.,Suite102,Goleta,CA93117,USA 79409,USA
. 5Kavli Institute for Theoretical Physics, University of Cali- 19The Oskar Klein Centre, Department of Astronomy,
2 fornia,SantaBarbara,CA93106,USA StockholmUniversity,SE-10691Stockholm,Sweden
1 6Observatories of the Carnegie Institution for Science, 813 20TheOskarKleinCentre,DepartmentofPhysics,Stockholm
5 SantaBarbaraStreet,Pasadena,CA91101,USA University,SE-10691Stockholm,Sweden
1 7Smithsonian Astrophysical Observatory, Harvard- 21DepartmentofAstronomy,SanDiegoStateUniversity,San
SmithsonianCenterforAstrophysics,60GardenSt.,Cambridge, Diego,CA92182-1221,USA
:
v MA02138,USA 22YukawaInstituteforTheoreticalPhysics,KyotoUniversity,
i 8DarkCosmologyCentre,NielsBohrInstitute,Universityof Kyoto606-8502,Japan
X Copenhagen, Juliane Maries Vej 30, DK-2100 København Ø, 23Kavli IPMU (WPI), UTIAS, The University of Tokyo,
Denmark Kashiwa,Chiba,277-8583,Japan
r 9AstrophysicsScienceDivision,NASAGoddardSpaceFlight 24Astrophysics Research Institute, Liverpool John Moores
a
Center,MailCode661,Greenbelt,MD20771,USA University, IC2, Liverpool Science Park, 146 Browlow Hill,
10Joint Space Science Institute, University of Maryland, LiverpoolL35RF,UK
CollegePark,MD20742,USA 25Max-Planck-Institut fu¨r Astrophysik, Karl-Schwarzschild-
11JetPropulsionLaboratory,CaliforniaInstituteofTechnol- Strasse1,D-85748Garching,Germany
ogy,Pasadena,CA91109,USA 26INAF,InstituteofSpaceAstrophysicsandCosmicPhysics,
12Los Alamos National Laboratory, Los Alamos, NM 87545, viaP.Gobetti101,40129Bologna,Italy
USA 27Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126
13DepartmentofAstronomy,UniversityofCalifornia,Berke- Pisa,Italy
ley,CA94720-3411,USA 28Excellence Cluster Universe, Technische Universitat
14Lawrence Berkeley National Laboratory, Berkeley, CA Mu¨nchen,Boltzmannstr. 2,D-85748Garching,Germany
94720,USA 29National Optical Astronomy Observatory, 950 N. Cherry
15Astronomy Department, University of Illinois at Urbana- Avenue,Tucson,AZ85719,USA
Champaign,1002W.GreenStreet,Urbana,IL61801,USA 30SchoolofPhysicsandAstronomy,UniversityofSouthamp-
16Department of Physics and Astronomy, and Pittsburgh ton,SouthamptonSO171BJ,UK
Particle Physics, Astrophysics, and Cosmology Center (PITT- 31ESO, Karl-Schwarzschild-Str. 2, D-85748 Garching, Ger-
PACC), University of Pittsburgh, 3941 O’Hara St., Pittsburgh, many
PA15260,USA 32Department of Astronomy, Faculty of Mathematics,
17Department of Physics, University of California, Santa UniversityofBelgrade,Serbia
2
1. INTRODUCTION 2. THESAMPLE
DespitetherecentavailabilityoflargesamplesofType Oursampleconsistsof57SNefromthePalomarTran-
IISNlightcurves(e.g.,Arcavietal.2012;Andersonetal. sient Factory (PTF; Law et al. 2009; Rau et al. 2009)
2014;Faranetal.2014a,b;Sandersetal.2015;Gonz´alez- and the intermediate Palomar Transient Factory (iPTF;
Gait´anetal.2015),thereislittlehigh-qualitydatainthe Kulkarni 2013) surveys. Data were routinely collected
literature against which to test predictions (e.g., Nakar by the Palomar 48-inch survey telescope in the Mould R
& Sari 2010; Rabinak & Waxman 2011, NS10, RW11) band(Lawetal.2009). Follow-upobservationswerecon-
regarding early-time light-curve behavior in the ultravi- ductedmainlywiththerobotic60-inchtelescope(Cenko
olet(UV)andopticalbands. Rabinak&Waxman(2011) et al. 2006) using an SDSS r-band filter, with addi-
showed that it is possible to deduce the progenitor star tional telescopes providing supplementary photometry
radius (R ) and energy per unit mass (E/M) from the and spectroscopy (see Gal-Yam et al. 2011). We chose
∗
early UV light curve. This is because at early times SNe that show hydrogen lines in their spectra (Type II),
(in the first 3–4 days after explosion), the light curve is butdonotshownarrowemissionlinesatlatetimes(Type
dominated by shock cooling; the photosphere is at the IIn; Schlegel 1990; Filippenko 1997; Kiewe et al. 2012).
outer edge of the ejecta, and no recombination has set This was done primarily because the optical emission
in. RW11 models describe well the handful of available frominteractingSNeIInisdominatedbytheirsurround-
early UV SN light curves (Soderberg et al. 2008; Gezari ing medium, and we are interested in the physics of the
et al. 2008; Schawinski et al. 2008), and can fit the rate exploding star itself. We rejected transitional Type IIb
ofUVdetectionsbyaGALEX/PTFsurvey(Ganotetal. SNe that develop strong He I lines and resemble SNe Ib.
2014). We also selected only SNe that had (1) at least five de-
Recently,Galletal.(2015)andGonz´alez-Gait´anetal. tections within ten days of the first detection, (2) well-
(2015) compared large samples of SN II light curves to sampled peaks/plateaus, and (3) an estimated date of
RW11/NS10 shock-cooling models. Both papers com- explosion determined to within 3 days.
pared SN rise times to rise times derived from shock- ThefulllistofSNe,theircoordinates,andclassification
coolingmodels: Galletal.(2015)usedr-banddata,while spectraispresentedinTable1. Mostofthespectrawere
Gonz´alez-Gait´anetal.(2015)comparedmulti-bandpho- obtained with the Double Spectrograph (Oke & Gunn
tometry. Both papers concluded that only models with 1982) on the 5-m Hale telescope at Palomar Observa-
small radii are consistent with the data — a conclusion tory,theKastspectrograph(Miller&Stone1993)onthe
thatisintensionwiththeknownassociationofredsuper- Shane 3-m telescope at Lick Observatory, the Low Reso-
giants (RSGs) with Type II-P SNe (Smartt et al. 2009). lution Imaging Spectrometer (LRIS; Oke et al. 1995) on
However, as we show in Section 5, comparing to models theKeck-110-mtelescope,andtheDEepImagingMulti-
based on their rise time requires the application of the Object Spectrograph (DEIMOS; Faber et al. 2003) on
models beyond their validity and leads to rejection of the Keck-2 10-m telescope. Spectral reductions followed
modelswithlargerradiithatfittheearly-timedatawell. standard techniques (e.g., Matheson et al. 2000; Silver-
Valenti et al. (2014) and Bose et al. (2015) compared man et al. 2012). All spectra are publicly available via
multi-band photometry of SN 2013ej and SN 2013ab to the Weizmann Interactive Supernova Data Repository
RW11models,butlimitedtheiranalysistothefirstweek (WISeREP, Yaron & Gal-Yam 2012).
after explosion. They found their data to be consistent The redshift (z) range is 0.0026–0.093, with a median
with RW11 models with radii of 400–600 R and 450– value of 0.03. The distribution of redshifts is given in
(cid:12)
1500 R , respectively. Figure 1. Note that this is a flux-limited survey, and
(cid:12)
Basic empirical relations involving the time scales of is unbiased with respect to host galaxy. Some of the
the rising light curve have yet to be established. This is eventsinoursamplebrieflyshowednarrowemissionlines
duetothefactthatmostofthepublishedSNphotometry whichvanishedafterafewdays. Theseareinterpretedas
begins shortly prior to the peak (if at all); light curves “flash-ionizationevents”(Gal-Yametal.2014;Khazovet
thatarewellsampledduringthefirstdaysafterexplosion al. 2015, submitted). All of the photometry is available
arestillrare. Basedonthreesuchevents,Gal-Yametal. in the online material.
(2011) suggested that there may be a trend where more Arcavi et al. (2014) identified PTF10iam and
luminous SNe II-P also rise more slowly. More recently, PTF10nuj as abnormal transients. They were therefore
Faran et al. (2014a) suggested that the rise time and lu- discardedfromthesample,leaving57events. Allremain-
minosity are uncorrelated, but did not perform a quan- ing objects had typical SN II spectra. Three objects in
titative analysis owing to their small sample size. Gall the sample were difficult to classify but were ultimately
et al. (2015) studied the rise times of 19 well-monitored retained. We compared the spectrum of PTF10uls and
SNe, and concluded that there is a qualitative trend be- PTF12krf to templates using SNID (Blondin & Tonry
tweenrisetimeandpeakmagnitude,withbrighterevents 2007). We found that PTF10uls is consistent with a
havinglongerrisetimes. Hereweuseasampleof57spec- SN II-P spectrum (Figure 2), while PTF12krf is con-
troscopically confirmed SN II R-band light curves that sistent with a SN II-P, though we cannot rule out that
were well monitored during their rise to test and estab- it is a SN IIb (Figure 3). The spectrum of iPTF14ajq
lish such correlations, and we quantitatively compare 33 hadsignificantgalaxycontamination. Figure4showsthe
of these to shock-cooling models. spectrum after subtraction of an Sb1 template (Kinney
et al. 1996); it is that of a reddened SN II.
3
Mpc 2.5
0 100 200 300 400
16
14 2
12
ber of SNe180 ux [arbitrary]1.15
m Fl
Nu 6
4 0.5
12krf
2 SN 1993J -2
SN 2004et +20
0
00 4000 5000 6000 7000 8000 9000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Observed wavelength
Redshift
Figure 3. SpectrumofPTF12krf. Superimposedarethespectra
Figure 1. RedshiftdistributionoftheSNeinthesample.
of Type IIb SN 1993J (2 days before peak) and Type II-P SN
2004et (20 days after peak). Note the weaker He I line compared
3 toSNIIb1993J.
×10-16
3
2.5
14ajq orig
Sb1
2.5 14ajq - Sb1
2
y] 2
ar
arbitr1.5 1.5
x [
u x
Fl 1 Flu 1
0.5
0.5
0
10uls
SN 2004et +12
-0.5
0
4000 4500 5000 5500 6000 6500 7000 7500 8000
Observed wavelength -1
3000 4000 5000 6000 7000 8000 9000 10000
Figure 2. SpectrumofPTF10uls. Superimposedisthespectrum
Rest frame wavelength (Angstrom)
ofSN2004et(12daysafterpeak).
Figure 4. Subtraction of an Sb1 template from the spectrum of
iPTF14ajq. ThehydrogenBalmerseriesisshownoffsetby12,000
3. ANALYSIS kms−1.
3.1. Photometry
published by Zhang et al. (2014).
The photometry was extracted using a point-spread The light curves are presented in Appendix Figures
function(PSF)fittingroutine(Sullivanetal.2006;Firth B1—B4. We found that small additive constants (indi-
et al. 2015) applied after image subtraction. Photom- cated in the figures) are needed to bring the supplemen-
etry for iPTF13dkk, iPTF13dqy (Yaron et al. 2015; tary and the 60-inch data in line with the PTF 48-inch
submitted to Nature Physics), and iPTF13dzb was sup- observations; this is due most likely to the different r/R
plemented with data from the Las Cumbres Observa- filter responses of the 48-inch, 60-inch, and other data
tory Global Telescope Network (LCOGT; Brown et al. sources. The photometry was corrected for Galactic ex-
2013). This was obtained by PSF fitting, and fitting tinction using the Schlegel et al. (1998) maps.33 The
a low-order polynomial to the background. Photome- distance moduli were calculated from the spectroscopic
try for PTF12cod was supplemented with data from the redshifts of the host galaxies using a cosmological model
40-inchtelescopeatMountLagunaObservatory(MLO), with H = 70 km s−1 Mpc−1, Ω = 0.3, and Ω = 0.7.
0 m Λ
whichwasalsoobtainedwithPSFfitting;seeSmithetal. TheanalysispresentedmadeuseoftheMATLAB(cid:114)pack-
(2015)fordetailsontheMLOreductionprocedure. Pho- age for astronomy and astrophysics (Ofek 2014).
tometry for PTF10vdl (SN 2010id) was supplemented The sample was not corrected for local host-galaxy
with that published by Gal-Yam et al. (2011), photome- extinction. Faran et al. (2014a) explored various dust-
try for PTF12bvh (SN 2012aw) was supplemented with
that published by Munari et al. (2013), and photometry 33 Derived using the sky ebv routine in MATLAB, with RV =
forPTF13aaz(SN2013am)wassupplementedwiththat 3.08.
4
extinction correction techniques including photometric of the fits presented in Appendix Figures B13—B15.
methods based on comparison to low-extinction SNe, as Extending the fit to t > 4 days forces the naturally
well as spectroscopic methods using the Na D doublet overshootingregiontocoincidewiththepeakdata. This
equivalent width. They found that none of the pro- has two effects: first, the t < 4 day data get undershot;
cedures increased the uniformity of their sample, and second, this procedure effectively shortens the rise time
in some cases even increased the scatter. Thus, we inthemodel,whichreducestheprobabilityoflargeradii.
wouldbeintroducingmoreuncertaintybycorrectingac- An example of the RW11 fit, and the effect of extending
cording to the classical prescriptions. However, we in- the fit beyond four days, is shown in Figure 5.
spected the sample and found only five questionable ob- As in Gonz´alez-Gait´an et al. (2015) and Gall et al.
jects. PTF09cjq has a red continuum, Na D absorption (2015), RSG models were compared to the sample with-
lines, and likely suffers from extinction. PTF10bgl and outdistinguishingbetweenTypeII-PandII-LSNe. This
iPTF14ajq have a red continuum, but no Na D absorp- is justified for the following two reasons: first, there
tion lines, and may suffer from extinction. PTF10uqn, is evidence that Type II-P and II-L SNe may form a
iPTF13bld, and iPTF13akg have a blue continuum, but continuum in both their photometric and spectroscopic
showclearNaDabsorptionlines,andmaypossiblysuffer properties (see Anderson et al. 2014; Guti´errez et al.
from extinction — but this is unlikely to be significant, 2014, this work), making it unlikely that they originate
anditmaybecausedbyhostcontaminationinthespec- from different progenitors. Second, blue supergiants are
tra. unlikely progenitors primarily because their small radii
The time of explosion for most objects was esti- (Kudritzki et al. 2008) will cause severe adiabatic losses,
mated as the midpoint between the last non-detection and they will not have the energy budget to reach the
and the first detection. For PTF09ecm, PTF10bgl, peak luminosity of Type II-L SNe which can peak above
PTF10umz, PTF11iqb, PTF12efk, PTF12hsx, -18 (Figure 9). Yellow hypergiants are extremely rare
iPTF13cly, iPTF14adz, and iPTF14aoi — where (Oudmaijer et al. 2009), and they are known to be as-
the limits were poorer, but the rise was well sampled sociated with Type IIb SNe (Maund et al. 2011). This
— we estimated the time of explosion with an expo- leaves RSGs as a reasonable default for the progenitors
nential fit described in Section A. The fits are shown in of Type II-P and II-L SNe.
Appendix Figure B5. In order to compare with RW11 models, we selected
Theobservedlightcurvesweresmoothedwithalinear onlythoseeventswithatleastfivedetectionsinthefirst
regression using a Gaussian kernel described in Section four days from explosion; this left 33 events. We then
A. The full set of light-curve fits is shown in Appendix generated bolometric light curves using Equation 14 of
Figures B6—B9. We determined the time of maximum RW11 (appropriate for RSGs, n=3/2):
luminositybyamethodsimilartothatusedbyGalletal.
(2015). We fit a first-order polynomial to a three-day L=8.5×1042 E501.92R∗,13 t−0.16 ergs−1, (1)
window of our smoothed light curve, and then shifted f0.27(M/M )0.84κ0.92 5
ρ (cid:12) 0.34
the window along the light curve. The algorithm was
terminated when the slope of the polynomial surpassed where the explosion energy E51 = E/1051 erg, the pro-
−0.01 mag day−1. The termination position of the algo- genitor radius R = R/1013 cm, the opacity κ =
∗,13 0.34
rithm was determined as the time of maximum luminos- κ/0.34 g−1 cm2, the ejecta mass M, and the time from
ity. The change in magnitude between peak and 15 days explosion t = t/105 s. Also, f ≡ ρ /ρ¯, where ρ¯ is
5 ρ 1/2
post-peak, ∆m15 (Phillips 1993), was determined by in- the mean density of the ejecta and ρ1/2 is the density at
terpolatingthesmoothedlightcurveto15daysafterthe
r =R /2. Note that n is the index of the density at the
time of maximum and subtracting the peak magnitude. edgeo∗ftheejectagivenbyρ(r )=ρ δn. Theapparent
These values are listed in Table 2. 0 1/2
R-bandmagnitudewascalculatedwiththephotospheric
3.2. Comparison to RW11 temperature given in Equation 13 of RW11,
Care should be taken when comparing observations
in the optical bands with RW11 or other models such E0.027R1/4
as those of Nakar & Sari (2010), which converge at Tph =1.6fρ−0.037(M/M51 )0.0∗5,41κ30.28t5−0.45 eV, (2)
t ≈ 1 day (note that all times given in this paper, un- (cid:12) 0.34
less stated otherwise, are relative to the estimated date corrected to the color temperature with the factor T =
c
of explosion and are given in the rest frame). The ap- 1.2T (see discussion in RW11, their Section 3.2 and
ph
propriatemodelhastwostrongrequirementsforvalidity: Figure 1). Then the modeled R-band magnitudes were
first, the emitting region must have originated in layers calculated with the synphot routine (Ofek 2014).
δm that were initially close to the surface of the star, WegeneratedlightcurvesforagridofRSGprogenitors
δm ≡ (R∗ −r)/R∗ (cid:28) 1; second, the temperature must withradiiR∗ =102–103 R(cid:12) (200pointslogarithmically
begreaterthan1eV,whereThomsonscatteringisdom- spaced), explosion energies E ≡ E/1051 erg = 10−2–
51
inant and recombination is negligible (see the beginning 102 (250 points logarithmically spaced), a fixed ejected
of Section 3 in RW11). Breakdown of the first assump-
mass M ≡M/(10M )=1,34 f =0.1, κ =1, and
tion causes the dominant divergence of the solution by 10 (cid:12) ρ 0.34
varioustimesofexplosionwithinouruncertaintyonthis
changing the final velocity of each element (f ) from the
ν
asymptoticvalueused, f =2. Thisinducesanunderes-
ν 34 The early-time light curve depends on the energy per unit
timation of the temperature (discussed in Section 3.1 of
mass;therefore,thepossiblediversityinM iscoveredbyourrange
RW11), causing an overestimation of the luminosity, as ofE51. ForfurtherdiscussionseeRabinak&Waxman(2011)and
canbeseeninthemodelovershootatlatertimesofmost Ganotetal.(2014).
5
date (50 points linearly spaced between t ±∆t ). For eight events which had good late-time coverage, we
0 0
Withthemodellightcurvesinhand,wecalculatedthe fitforthesynthesizedradioactivenickelmass. Thelumi-
χ2 values for the observed flux (in the first 4 days from nosityperunitmassreleasedbyradioactive56Niisgiven
explosion) for all combinations of the radius, explosion by
energyperunitmass,andallpossibledatesofexplosion.
Finally, we scaled the flux errors until the minimal χ2
reached 1.35 The energy per unit mass was estimated l=3.9×1010e−t/τNi + (7)
at the minimum χ2 of the grid, and the 95% confidence 7×109(cid:16)e−t/τCo −e−t/τNi(cid:17) ergg−1 s−1,
interval was estimated using a profile likelihood: find-
ing optimal t and R for each energy, and then finding
0 ∗ where τ and τ are 8.8, and 111.09 days, respectively.
valuesofE wherethecumulativedistributionfunction Ni Co
51 ForeachoftherelevantSNe,wefittheinitialnickelmass
CDF(χ2) ≤ 0.95. The E/M values we determined are
by minimizing the linear least-squares equation
listed in Table 2, and are shown in Figure 6.
To calculate the mean value of E/M, we have to cor-
rect for Malmquist bias. We used an effective distance L(ti)=MNil(ti), (8)
modulus DM∗ such that all SNe would have the same
where L(t ) and l(t ) are (respectively) the observed
peak apparent magnitude as the faintest SN in our sam- i i
luminosity and expected luminosity per unit mass at
ple with the formula
time t , and M is the initial nickel mass. We also fit
i Ni
three events from the literature for which the authors
Max{mpeak}=Mipeak+DMi∗, (3) derived 56Ni masses using multi-band quasi-bolometric
lightcurves(SN2005cs,SN2012aw,andSN2013ab;Fig-
where Max{mpeak} is the faintest peak apparent magni-
ure8),andfoundthatourvaluesforM aresufficiently
tude in the sample, DM∗ is the effective distance mod- Ni
i close to justify no bolometric correction. However, to be
ulus that sets the peak absolute magnitude Mipeak equal conservative,weassumea50%uncertaintyinourderived
tothefaintestpeakapparentmagnitude. Thenthemean 56Ni mass. These values are reported in Table 2.
SN E/M value in the sample was calculated as
4. RESULTS
(cid:28)E (cid:29) Σ (E/M) /D∗3
= i i i , (4) Figure5showsanexampleofthefittoaRW11model.
M Σj1/Dj∗3 WefoundthatRW11modelsdescribetheearly-timelight
curveswellinmostcases(AppendixFiguresB13—B15).
where D∗ is theluminosity distancetakenfrom therela-
For each combination of E/M and R the time of explo-
tion ∗
sion was selected that minimizes the χ2. The contours
(cid:18) D∗ (cid:19) represent the 68%, 95%, and 99.7% χ2 confidence inter-
DM∗ =5log . (5) vals. Figure 5 is typical, and demonstrates that while
10 10pc theradiusoftheprogenitorcannotbeconstrainedbased
on the early-time R-band light curve, E/M can be esti-
Thisprocedureaccountsfortheoverrepresentationoflu-
mated to better than a factor of five.
minous events in our flux-limited sample. By weight-
The energies derived for each SN and the cumulative
ing according to their equivalent volume, less-luminous
fractionofeventsbelowagivenE/M areshowninFigure
events — which naturally have a small volume — get
6. WefindthatE/M spansarangeof∼(0.2−20)×1051
put on equal footing with more-luminous events. The
erg/(10 M ). Moreover, the E/M values deduced from
correctedhistogramofE/M valuesisshowninFigure6. (cid:12)
the fit to RW11 models are significantly (P-value <<
0.05) correlated with the observed photospheric velocity
3.3. Spectroscopy
(Figure 7).36 Taking the confidence interval as symmet-
WeestimatetheexpansionvelocityofeachSNbymea- ric, a power-law fit gives
suringtheminimumoftheHαP-Cygniprofile. Thiswas
accomplishedbyfittingasecond-orderpolynomialtothe
Hα absorption. In order to normalize the velocities to a E /M =(2.1±4.8)×10−4 (9)
51 10
uniformepoch,therelationfromFaranetal.(2014a)was ×(v /103 km s−1)4.5±1.1,
used, relating the velocities measured to the velocity on 50
day 50 for SNe II-P. The relation is given by wheretheuncertaintiesare95%confidenceintervals. We
findthatE/M fromthefitisalsosignificantlycorrelated
(cid:18) t (cid:19)0.412±0.02 withthepeakmagnitude(Figure7),andisrelatedtothe
v =v (t) . (6)
50 Hα 50 peak luminosity by
The measured velocities are presented in Table 2.
E /M =(1.71±0.17)L /1042 erg (10)
51 10 peak
3.4. 56Ni Mass Estimation −(8.4±6.2)×10−2,
where L is the peak luminosity.
35 Thefluxerrorsfromourpipelineareunderestimated,leading peak
tohighχ2formodelswhichfitthedatawell. Theerrorswerescaled
toallowforthecomparisonofdifferentmodelstoeachother. The 36 AllcorrelationsreportedwerecalculatedusingtheSpearman
scalingvaluesarepresentedinAppendixFiguresB13—B15. correlationtest.
6
17 103
18
g
a
M
19
R R⊙
ed R∗=100 /
erv20 E /M =3.9 R
s 51 10
b
O CE=2.1
21
22 102
-2 0 2 4 6 8 10 12 14 10-2 10-1 100 101 102
MJD - 56000.854 E / M
51 10
17 103
18
g
a
M
19
R R⊙
ed R∗=100 /
serv20 E51/M10=2.8 R
b
O CE=3
21
22 102
-2 0 2 4 6 8 10 12 14 10-2 10-1 100 101 102
MJD - 56000.854 E / M
51 10
Figure 5. Topleft: ExampleRW11bestfittoPTF12bro. ThevaluesoftheprogenitorradiusR,explosionenergyperunitmassE51/M10,
and error scaling factor CE are displayed. Only filled symbols were included in the fit. Top right: The projection of χ2 onto the R−E
plane (at optimal explosion date t0 for each point). The contours of 68%, 95%, and 99.7% confidence intervals are shown. Bottom left,
right: Best fit to PTF12bro and χ2 contours including data where t ≤ 10. Notice that including later data reduces the probability for
higherradii.
We added to our sample several events from the lit- Inaddition,wefindseveralempiricalcorrelations(Fig-
erature which have determined parameters from hydro- ure 9). The peak luminosity is significantly and strongly
dynamic light-curve modeling (see Table 3). Three SNe correlated with ∆m — brighter events decline faster.
15
(SN2005cs,SN2012aw,andSN2013ab)weresufficiently This is the opposite of well-established trends in SNe Ia
wellsampledduringtheirrisetoallowustoperformour and Ib/c (Phillips 1993) that are powered by 56Ni dur-
RW11 analysis, although it was necessary to slightly re- ing their rise, and is in agreement with the findings of
laxourcriteriaandincludeR-banddatauptoday6from Anderson et al. (2014) for Type II V-band light curves.
explosion. Wefoundourresultstobeconsistentwiththe Thepeakluminosityisalsocorrelatedwithv : brighter
50
estimatedexplosionparametersfromtheliterature(Fig- eventshavehighervelocitiesatday50. Thisrelationhas
ure 8); however, we derive a higher E/M value for SN already been established for Type II-P SNe (Hamuy &
2013abthandoBoseetal.(2015). Boseetal.(2015)esti- Pinto2002;Nugentetal.2006),althoughithasnotbeen
matedE/M fromhydrodynamicmodeling,makingitdif- demonstrated until now for SNe II generally. The rise
ficult to assess the source of this discrepancy. Note that time is more weakly correlated with ∆m , and with a
15
our derived 56Ni mass of ∼5×10−3 M for iPTF13aaz largerscatter,althoughitsignificantlyshowsthatslower
(cid:12)
(SN 2013am) is lower than the 1.5×10−2 M reported risers are also faster decliners. We do not observe a sig-
(cid:12)
by Zhang et al. (2014), but the source of this discrep- nificant correlation between the rise time and the peak
ancy is unclear. We find that the 56Ni mass is strongly luminosity,contrarytothesuggestionsofGal-Yametal.
correlated with E/M (ρ = 0.76, P-value << 0.05; Fig- (2011) and Gall et al. (2015).
ure 8). This result has been observed in Type Ib/c SNe
5. DISCUSSION
(Mazzali et al. 2013), and is in line with models such as
that of Kushnir (2015), which predict that more 56Ni is We have performed the first direct fitting of analyti-
produced by more-energetic SN II explosions. cal early light-curve models (RW11) to a large sample
of Type II SNe with a well-sampled rise. Our results
7
Total number of events 33
102 1
s
ent 0.8
v
e
101 of
0 n 0.6
1 o
E / M51 e fracti 0.4
100 ativ
ul
m 0.2
u Uncorrected
C
Corrected
10-1 0
0 5 10 15 20 25 30 35 100 101
Event # E / M
51 10
Figure 6. Left: E/M derivedfromRW11with95%profilelikelihoodconfidenceintervals. Right: Cumulativefractionofeventsbelowa
givenE/M,correctedanduncorrectedforMalmquistbias.
ρ =0.67, P-Value =3.4e-04 ρ =-0.86, P-Value =1.1e-10
1.5 1.5
E /M =(2.1±4.8)×10−4 E /M =(1.71±0.17)L /1042erg
51 10 51 10 peak
×(v /103kms−1)4.5±1.1 −(8.4±6.2)×10−2
50
1 1
M10 0.5 M10 0.5
E/51 E / 51
log10 0 log 10 0
-0.5 -0.5
-1 -1
4 6 8 10 12 -19 -18 -17 -16 -15 -14
v50 Hα / 103 kms−1 Peak R absolute magnitude
Figure 7. Left: E/M fromthefittoRW11asafunctionofthevelocitynormalizedtov50 ofHα. Right: E/M fromRW11asafunction
ofpeakmagnitude. Redlinesarethebestfitsdescribedinthetext.
show that, assuming a RSG progenitor, we can deduce begin to break down. As was explained in Section 3, the
the value of E/M to within roughly a factor of five from breakdownoftheseassumptionsleadstoanovershootof
early-time optical light curves. Progenitor radii are not the data at later times (t > 4 days). By comparing to
constrained by R-band data alone, and require UV ob- rise times from the models, these works rejected models
servations (Ganot et al. 2014). which fit the early photometric data well.
Gall et al. (2015) and Gonza´lez-Gait´an et al. (2015) Figure 10 demonstrates this using LSQ13cuw, a well-
recently compared light curves to RW11/NS10 shock- sampledeventfromGalletal.(2015). Wefittwoextreme
coolingmodelsandfoundthatonlysmallradii(R<400 cases,withradiiof100and1000R ,tothefirstsixdays
(cid:12)
R ) appeared to be consistent with observations, in ofdata. Bothmodelsfittheearly-timedataequallywell.
(cid:12)
strong tension with direct measurements of Type II-P While the 100 R model has a consistent rise time with
(cid:12)
SNe(Smarttetal.2009;Smartt2015). However,Valenti LSQ13cuw, it does not agree at all with the photometry
et al. (2014) and Bose et al. (2015) compared single ob- near peak. We suspect that this explains the apparent
jects and found no such discrepancy. discrepancy between the radii inferred from the models
It appears that the Gall et al. (2015) and Gonz´alez- by Gall et al. (2015) and Gonz´alez-Gait´an et al. (2015),
Gait´an et al. (2015) method of extracting a rise time and the measured RSG radii (Smartt et al. 2009) of the
from the models and comparing it to the rise time of progenitors of SNe II-P.
their light curves is inaccurate. The models are valid for We find a strong correlation between the RW11 E/M
abrief(t≈4days)periodbeforeimportantassumptions valuesandtheSNexpansionvelocityatday50. Because
suchastheemissioncomingfromathinshellattheedge v is an independent estimate of E/M, this provides
50
of the star, and the temperature being well above 1 eV, support for the deduced E/M values. We find that our
8
ρ=0.76,P-Value=4.43e-04 models, longer-rising SNe also decline more slowly. We
-0.8
interpret this as evidence that Type II SNe are not pow-
-1 ered by any of these potential sources during their early
phase.
-1.2
2013ab 2012aw 6. SUMMARY
-1.4
⊙ OurmainconclusionsregardingSNeIIcanbesumma-
M-1.6 rized as follows.
/
Ni-1.8
56 • The progenitor radius cannot be inferred by com-
g10 -2 parison to shock-cooling models based on R-band
o
l photometry alone. The value of E/M can be in-
-2.2
ferred to within a factor of five.
-2.4
• ThemeanSNIIenergyperunitmass,correctedfor
-2.6 2005cs Malmquist bias, is (cid:104)E/M(cid:105) = 0.85×1051 erg/(10
M ), and has a range of (0.2–20) ×1051 erg/(10
-2.8 (cid:12)
-1.5 -1 -0.5 0 0.5 1 1.5 M(cid:12)).
log E / M
10 51 10
• The derived value of E/M from RW11 models is
Figure 8. E/M from the fit to RW11 vs. 56Ni mass. Empty strongly correlated with the photospheric velocity
symbols are taken from the literature (Table 3) with parameters
at day 50, peak magnitude, and 56Ni mass pro-
estimated from hydrodynamic modeling. The blue, red, and ma-
gentafilled(empty)symbolsrepresentour(literature)estimatesof duced in the explosion.
the parameters of SN 2005cs, SN 2012aw, and SN 2013ab. Note
thegoodagreementin56Nimassbetweenouranalysisandthelit- • ∆m is correlated with the rise time — slower
15
erature. ThesourceofthediscrepancybetweenourE/M estimate
risers are also faster decliners. This indicates that
for SN 2013ab and that of Bose et al. (2015) is unclear, due to
the different methods used. Diamonds represent events from the TypeIISNeareunlikelytobepoweredbyradioac-
literature which did not have sufficient early-time data on which tive decay or other central-engine models at early
toperformouranalysis. times.
sample has a mean energy per unit mass, corrected for
While it was not possible to infer the radius from R-
Malmquist bias, of (cid:104)E /M (cid:105) = 0.85, with a range of
51 10 banddataalone,thepathforfutureworkisclear. Multi-
E /M ≈ 0.2–20. Because the progenitor mass of a
51 10 band light curves, which will be acquired by future sur-
SN II-P is suggested to be confined to a relatively nar-
veys such as the Zwicky Transient Facility (ZTF; Bellm
row range (8–16 M ; Smartt et al. 2009), our results
(cid:12) 2014; Smith et al. 2014) and the Large Synoptic Survey
lead to the conclusion that there is a significant intrinsic
Telescope(LSST;Ivezicetal.2008),aswellasearly-time
diversity in explosion energies. The correlation between
UVphotometryfromsatellitessuchasULTRASAT(Sa-
peak magnitude and E/M indicates that more energetic
giv et al. 2014), will drastically reduce the uncertainties
explosions also have higher peak luminosity. In addi-
in determining the progenitor radius. The benefit will
tion, the strong positive correlation between E/M and
be twofold: these facilities will reduce uncertainties in
56Nimassimpliesthatstrongerexplosionsproducemore
the time of first light, and there will be more useful pho-
56Ni. This result is consistent with the predictions of
tometrywithinthewindowofvalidityofavailableshock-
some models, including those of Kushnir & Katz (2015)
cooling models, because the rise time is much shorter in
and Kushnir (2015), claiming that the explosion mecha-
blue and UV bands.
nism of CC SNe is thermonuclear detonation of the in-
falling outer shells.
In our sample, we do not find that the rise time and We are grateful to the staffs at the many observato-
peak magnitude of SNe II are correlated (Figure 9). Al- ries where data for this study were collected (Palomar,
thoughitwassuggestedinthepastthatbrighterSNeII- Lick, Keck, etc.). We thank J. Silverman, G. Duggan,
P may have longer rise times (Gal-Yam et al. 2011), our A. Miller, A. Waszczak, E. Bellm, K. Mooley, J. Van
sample of well-monitored light curves disfavors this hy- Roestel, A. Cucchiara, R. J. Foley, M. T. Kandrashoff,
pothesis. Our correlation between ∆m15 and the peak B. Sesar, I. Shivvers, J. S. Bloom, D. Xu, J. Surace, and
magnitude recovers a relation previously shown by An- L. Magill for helping with some of the observations and
dersonetal.(2014)intheV band. Wealsofind,however, datareduction. SpecificallyforassistancewiththeMLO
that∆m15 iscorrelatedwiththerisetime,althoughwith observations, we acknowledge N. Duong, T. Fetherolf, S.
a large scatter. SNe with longer rise times also decline Brunker, R. Dixon, and A. Rachubo.
faster. A.G.Y. is supported by the EU/FP7 via ERC grant
Nicholl et al. (2015) have recently explored various no. 307260,theQuantumUniverseI-COREProgramby
mechanisms to explain hydrogen-poor superluminous the Israeli Committee for Planning and Budgeting and
SNe(SLSNe,Gal-Yam2012). Theirmodelsincludemag- theIsraelScienceFoundation(ISF);byMinervaandISF
netars (Kasen & Bildsten 2010; Woosley 2010), circum- grants;bytheWeizmann-UK“makingconnections”pro-
stellar interaction (Woosley et al. 2007; Ofek et al. 2010; gram; and by Kimmel and ARCHES awards. E.O.O. is
Chevalier & Irwin 2011), and 56Ni radioactive decay. incumbent of the Arye Dissentshik career development
They find an opposing correlation to ours: in hydrogen- chairandisgratefulforsupportbygrantsfromtheWill-
poor SLSNe, as well as in all of the above-mentioned nerFamilyLeadershipInstituteIlanGluzman(Secaucus,
9
ρ =-0.61, P-Value =1.1e-06 ρ =0.32, P-Value =1.6e-02
10 10
5 5
0 0
0.4 0.4
5 5
1 1
m 0.2 m 0.2
∆ ∆
0 0
-0.2 -0.2
-19 -18 -17 -16 -15 0 5 10 2 4 6 8 10 12 14 16 0 5 10
Peak R absolute magnitude Rest frame rise time in days
ρ =-0.22, P-Value =0.11 ρ =-0.65, P-Value =7.7e-04
10 5
5
0 0
e e
d d
u u
nit-15 nit-15
g g
a a
m m
-16 -16
e e
ut ut
sol-17 sol-17
b b
a a
R R
k -18 k -18
a a
e e
P P
-19 -19
2 4 6 8 10 12 14 16 0 5 10 2 4 6 8 10 0 2 4
Rest frame rise time in days v50 Hα / 103 kms−1
Figure 9. Topleft: ∆m15asafunctionofthepeakmagnitude. Topright: ∆m15asafunctionofrisetime. Bottomleft: Peakmagnitude
asafunctionofrisetime,derivedfromthesmoothedlightcurves(AppendixFiguresB6—B9). Bottomright: Peakmagnitudeasafunction
ofv50.
NJ),ISF,Minerva,Weizmann-UK,andtheI-COREPro- chos of the Instituto de Astrof´ısica de Canarias. This
gramofthePlanningandBudgetingCommitteeandthe research has made use of the APASS database, located
ISF. M.S. acknowledges support from the Royal Soci- at the AAVSO web site. Funding for APASS has been
ety and EU/FP7-ERC grant no [615929]. K.M. is grate- provided by the Robert Martin Ayers Sciences Fund. A
ful for a Marie Curie Intra-European Fellowship, within portionofthisworkwascarriedoutattheJetPropulsion
the 7th European Community Framework Programme Laboratory under a Research and Technology Develop-
(FP7). D.C.L., S.F.A., J.C.H., and J.M.F. are sup- ment Grant, under contract with the National Aeronau-
ported by NSF grants AST-1009571 and AST-1210311, tics and Space Administration. Copyright 2015 Califor-
under which part of this research (photometry data col- nia Institute of Technology. All Rights Reserved. US
lectedatMLO)wascarriedout. Thesupernovaresearch Government Support Acknowledged. LANL participa-
of A.V.F.’s group at U.C. Berkeley presented herein is tion in iPTF is supported by the US Department of En-
supported by Gary & Cynthia Bengier, the Christopher ergy as part of the Laboratory Directed Research and
R. Redlich Fund, the TABASGO Foundation, and NSF Development program.
grant AST-1211916.
ResearchatLickObservatoryispartiallysupportedby
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