The Unusual Super-Luminous Supernovae SN 2011kl and ASASSN-15lh

0.23 MB·

by  Melina C. Bersten

Submittedto ApJLon November12,2015. Accepted on December 27,2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
THE UNUSUAL SUPER-LUMINOUS SUPERNOVAE SN 2011klAND ASASSN-15lh
Melina C. Bersten1,2,6, Omar G. Benvenuto1,2,3, Mariana Orellana4,5 and Ken’ichi Nomoto6,7
Submitted toApJL on November 12, 2015. Accepted on December 27, 2015
ABSTRACT
Two recently discovered very luminous supernovae (SNe) present stimulating cases to explore the
extents of the available theoretical models. SN 2011kl represents the first detection of a supernova
6
explosionassociatedwithanultra-longdurationgammarayburst. ASASSN-15lhwasevenclaimedas
1
themostluminousSNeverdiscovered,challengingthescenariossofarproposedforstellarexplosions.
0
Here we use ourradiationhydrodynamicscode in orderto simulate magnetarpoweredSNe. Toavoid
2
explicitlyassumingneutronstarpropertiesweadoptthemagnetarluminosityandspin-downtimescale

n as free parameters of the model. We find that the light curve (LC) of SN 2011kl is consistent with a
a magnetarpowersource,aspreviouslyproposed,butwenotethatsomeamountof56Ni(&0.08M⊙)is
J
necessaryto explainthe lowcontrastbetweenthe LCpeak andtail. Forthe caseofASASSN-15lhwe

6 findphysicallyplausiblemagnetarparametersthatreproducetheoverallshapeoftheLCprovidedthe
progenitormassisrelativelylarge(anejectamassof≈6M⊙). Theejectahydrodynamicsofthisevent
] is dominated by the magnetar input, while the effect is more moderate for SN 2011kl. We conclude
E
thatamagnetarmodelmaybeusedfortheinterpretationoftheseeventsandthatthehydrodynamical
H
modeling is necessary to derive the properties of powerful magnetars and their progenitors.
h. Subject headings: stars: evolution — supernovae: general — supernovae: individual (SN 2011kl)
p — supernovae: individual (ASASSN-15lh) — gamma-ray burst: individual (GRB
- 111209A)
o
r
st 1. INTRODUCTION Moriya et al. 2010), so competing, so competing alter-
a natives have been proposed. One possible mechanism
Superluminous supernovae (SLSNe) have been dis-
[
invoked to explain SLSNe is the energy injection by an
covered almost a decade ago (Quimby et al. 2007;
accretingblackholethatlaunchesrelativisticjets,orfall-
1 Smith et al. 2007). They show a factor 10 to 100 times
v brighterthannormalcore-collapsesupernovae(SNe), of- backscenario(e.g.,Dexter & Kasen2013,andreferences
1 ten well above −22 absolute magnitude. It is believed therein). The interaction of the SN ejecta with dense
2 thattheyaretheexplosionofmassivestarswhichusually circumstellarmaterial(CSM) is anotherproposedmech-
0 are found in low luminosity, star forming dwarf galax- anism (see e.g. Sorokina et al. 2015). Another popular
1 explanation is that a magnetar is formed by the col-
ies (Neill et al. 2011; Lunnan et al. 2014; Leloudas et al.
0 lapse of a massive star. The magnetar is a strongly-
2015). But the physical origin of the extreme luminos-
. magnetized, rapidly-rotating neutron star that loses ro-
1 ityemittedremainsspeculative(see,e.g.,Gal-Yam2012,
tational energy via magnetic dipole radiation. Although
0 forareview). ThehighluminosityofSLSNemakesthem
someprogressintheareawererecentlyreported(seee.g.
6 ideal to get information from the early universe and to
1 explore the capability to use them as cosmological stan- Timokhin & Harding 2015), other important aspects of
: dard candles at much further distance than normal SNe the scenario are still unclear.
v In this work we study two peculiar SLSNe of Type
(Quimby et al. 2011; Inserra & Smartt 2014).
i
X In order to be radioactively powered, as normal Ic (lacking hydrogen), SN 2011kl and for ASASSN-
15lh. SN 2011kl has been associated with the ultra-
r SNe, SLSNe would require a too large nickel mass ex-
a cept for pair instability SNe and hypernovae (see, e.g., long-durationgammarayburstGRB 111209A,ata red-
shiftz of0.677(Greiner et al.2015). Itslightcurve(LC)
wassignificantlyover-luminouscomparedtootherGRB-
[email protected] associated SNe, suggesting for the first time a link be-
1Facultad de Ciencias Astron´omicas y Geof´ısicas, Universi- tween SN-GRB and SLSNe-ultra long GRB (ULGRB).
dad Nacional de La Plata, Paseo del Bosque S/N, B1900FWA
The precise explosion time estimation makes this SN
LaPlata,Argentina
2InstitutodeAstrof´ısicadeLaPlata(IALP),CONICET,Ar- ideal for numerical modeling.
gentina Morerecently,ASASSN-15lhatz =0.2326wasdiscov-
3Member of the Carrera del Investigador Cient´ıfico de la
ered by the All-Sky Automated Survey for SuperNovae
Comisi´on de Investigaciones Cient´ıficas de la Provincia de
(Dong et al. 2015). It showed an hydrogen-poor spec-
Buenos Aires(CIC), Argentina
4SedeAndina,UniversidadNacionaldeR´ıoNegro,Mitre630 trum,andthe maximumluminositywas∼2.2×1045 erg
(8400) Bariloche,Argentina s−1, i.e. more luminous than any previously known SN.
5Member of the Carrera del Investigador Cient´ıfico y Tec- Contrary to SN 2011kl, the explosion date of ASASSN-
nol´ogicodelCONICET,Argentina
6Kavli Institute for the Physics and Mathematics of the 15lh is unknown, and data before the luminous peak
Universe, The University of Tokyo Institutes for Advanced were less reliable than later. The optical emission was
Study (UTIAS), The University of Tokyo, 5-1-5 Kashiwanoha, continuously detected for more than 100 days after the
Kashiwa,Chiba277-8583, Japan explosion. The spectrum lacked the broad Hα emission
7HamamatsuProfessor
2 Bersten, Benvenuto, Orellana and Nomoto
feature that would have evidenced interaction between The values of B and P can be found later from t , L ,
0 p p
the supernova and an H-rich circumstellar environment assuming an NS mass. Then, the radius and momen-
(Milisavljevic et al. 2015). tum of inertia are found for a given EOS. In this way,
Magnetar models have been proposed for the two one avoids to assume from beforehand explicit values of
SLSNe of this work (Greiner et al. 2015; Metzger et al. theNSsproperties. Thismethodopensthepossibilityto
2015), even for the extremely luminous ASASSN-15lh. accommodate a variety of NS structures, which is rele-
However, the analysis was based on simplistic assump- vant because of our poor knowledge of the EOS at these
tions that neglected the dynamic effects on the ejecta. extreme conditions.
Here we shall study the magnetar scenario using hydro- Along the calculation, if the photosphere recedes deep
dynamic calculations which incorporate the dynamical enough so that part of the magnetar energy is directly
effect and considering the limit imposed by the neutron depositedoutsidethephotosphere,weaddthisenergyto
star (NS) matter equation of state (EOS). the bolometric luminosity. The same treatment is used
for 56Ni deposition (Swartz et al. 1991; Bersten et al.
2. MAGNETARMODELS 2011). We implicitly assume that the magnetar (or the
We include an extra source of energy due to a rapidly 56Ni decay)produces hard photons than can be trapped
rotating and strongly magnetized NS (or “magnetar”) even if the ejecta is optically thin to optical photons.
in our one-dimensional LTE radiation hydrodynamic During these epochs, usually after about 60 days (al-
code (Bersten et al. 2011). A spherical young mag- thoughthisdependsontheprogenitormassandenergy),
netar releases its rotational energy at a well known theemitted luminosityisalmostthe sameasthe magne-
rate described by the radiating magnetic dipole (e.g. tar luminosity.
Shapiro & Teukolsky 1983). We assume that this en- 3. RESULTS
ergy is fully deposited and thermalized in the innermost
3.1. Models for SN 2011kl
layers of our pre-supernova model. This assumption as
well as a large inclination i = 45◦ is the same used in Greiner et al. (2015) (hereafter G15), recently ana-
previous numerical works of magnetar powered SN light lyzed the LC and spectrum of SN 2011kl. A low ejecta
curves (Woosley 2010; Kasen & Bildsten 2010). Power- mass ≈ 2.4 M⊙ and high explosion energy ≈ 5.5 ×1051
ful enough magnetars may force the envelope to expand ergwereobtainedfromtheiranalysis. Theradiativeout-
at velocities comparable to the speed of light (see be- putofSN2011kl locatesitinbetweentheGRB-SNeand
low, particularly Fig. 5). Therefore, we have modified SLSNe. A large 56Ni mass ≈ 1 M⊙ was found necessary
our code to properly include relativistic velocities. A inordertoreproducethe highobservedluminosity. This
detailed description of our treatment of relativistic radi- largeamountofradioactivematerialseems tobe neither
ating hydrodynamics will be presented in a forthcoming compatible with the spectrum properties nor with the
paper. low mass ejecta, as pointed by G15. A magnetar source
Our hydrodynamical calculations simulate the explo- was then proposed by the authors to explain the LC.
sion of an evolved star, followed consistently until core We used the code describe in §2 to study SN 2011kl.
collapse condition. The pre-SN He star models of dif- Oneadvantageofthehydrodynamicscalculationsisthat
ferent masses used in this paper were calculated by the explosion time (t ) is fully determined from the
exp
Nomoto & Hashimoto (1988). The explosion itself is assumed physical parameters. The GRB detection of
simulated as usual by the injection of a certain energy SN2011kl establishesa tightvalue oft 9 then, itisan
exp
(a few ×1051 erg) at the innermost layers of our pre-SN ideal target of study. Motivated by the values proposed
models. In addition to the explosion energy, the rota- byG15weassumedapre-SNHestarof4M⊙ withacut
tional energy lost by newly born magnetar is included. mass(Mcut)of1.5M⊙ correspondingtoanejected mass
Once the NS momentum of inertia and radius R are (Mej) of 2.5 M⊙ and an explosion energy of 5.5×1051
fixed, this energy source essentially depends on two pa- erg. While the LC of SN 2011kl is unlikely to be pow-
rameters, the strength of the dipole magnetic field8, B, ered only by 56Nisome amount of radioactive material
and the initial rotational period, P0 (see, e.g., equations is usually expectedto be producedduring the explosion.
1 and 2 of Kasen & Bildsten (2010)). It is equally pos- We assume a 56Ni mass of 0.2 M⊙ consistent with ra-
sible to use the spin-down timescale (tp) and magnetar dioactive yield of energetic SN (Nomoto et al. 2013).
energy loss rate (Lp) as the free parameters to be deter- Weextensivelyexploredthemagnetarparameterspace
minedbyfittingtheobservedlightcurve(LC).Therefore and found a reasonable agreement with the data for
the magnetar luminosity can be written as P = 3.5 ms and magnetic field B = 1.95 × 1015 G.
0
Figure1 showsthis modelwiththick solidline. Ourval-
t −2 ues lie out of the ranges given by G15 whose analysis
L=L 1+ , (1)
p(cid:18) tp(cid:19) gave P0 = 12.2±0.3 ms and B = 7.5±1.5×1014 G.
The thin line of Figure 1 show the result of our hydro-
with dynamicalcalculationsassumingthesameparametersas
4π4R6B2 in G15. We found a poor match to the data as opposed
L = , (2)
p 3c3 P4 to G15 (see their Fig. 2). We note that we have used
OPAL opacity tables with an opacity floor of 0.2 cm2
and g−1 corresponding to the electron scattering opacity for
3c3I P2
t = NS . (3)
p π2R6 B2 9 Here we assume that the GRB precursor indicated the ex-
plosion itself. But see Vietri&Stella (1999) for other possible
8 Consideredfixedduringtheevolution scenarios.
SLSNe SN 2011kland ASASSN-15lh 3
hydrogen free material. This value is usually assumed 3.2. Models for ASASSN-15lh
as gray opacity in LC magnetar models in the literature
Dong et al.(2015)reportedthediscoveryofthebright-
(Kasen & Bildsten 2010; Inserra et al. 2013). However,
est known SN, ASASSN-15lh with a peak luminosity of
with a lower and constant value of κ = 0.07 cm2 g−1, ≈2×1045 ergs−1,almosttwomagnitudesbrighterthan
presumablyusedinG15,werecoveredareasonablefitto theaverageobservedSLSNe,andwithtotalradiateden-
thedataforthemagnetarparametersofG15(seedotted ergyof≈1052 erg. The spectra presentedsome similari-
line of Figure 1). ties to SLSNe-Ic. Magnetar models seem to be the most
In addition, we present our results for a model pow- plausible explanation for this class of SLSNe. However,
ered only by 56Ni. A model with M(56Ni)= 1 M⊙ is Dong et al. (2015) emphasized the difficulty to explain
shown with a dashed line in Figure 1. Even with this this object in the magnetar context. The short initial
large amount of 56Ni we could not reach the high lumi- period≈1msrequiredtomatchtheLCpropertiescould
nosity needed to explain SN 2011kl using our opacity be incontradictionwith the maximumrotationalenergy
prescription. While an non-standard source of energy is (E ) available that in turn is limited by the emission
max
necessary to explain the peak luminosity, some amount of gravitational waves. However, Metzger et al. (2015)
of 56Ni (& 0.08 M⊙) is also needed to explain the tail lately suggested that E could be up to one order of
max
luminosity. Magnetar models without nickel produce a magnitude larger than previous estimations, depending
largercontrastbetweenpeakandtailandthusapoorfit ontheNSproperties,butavoidingtheproblemraisedby
to the data. Dong et al. (2015).
Wecalculatedasetofmagnetarmodelstoanalyzethe
LC of ASASSN-15lh. Here we use L and t as free
p p
parametersforthefitting(see§2). Inthisway,weavoid
including explicitly the properties of the NS. Once the
LC fit is admissible, we derived B and P as a function
0
of the magnetar mass (see bellow). Figure 3 shows our
resultsforapre-SNHestarof4M⊙ withMcut=1.5M⊙
andMej =2.5M⊙ (thinredline)andforamoremassive
model of He star 8 M⊙ with Mcut= 2 M⊙ and Mej = 6
M⊙ (thick blue line). We assumed an initial explosion
energy of 5.5×1051 erg although this has a minor effect
on the results. Also, we assumed that the SN exploded
a week before the discovery.
ThemagnetarparametersareinthiscaseL =9×1045
p
erg s−1 and t = 40 days. For the less massive model
p
we could not reproduce the overall LC shape. A more
massive pre-SN model with 8 M⊙ or more is therefore
neededtoreproducethetemporalwidthoftheLC.At∼
100 days, there is a slight change on the LC slope in co-
Fig.1.— Bolometric LC of SN 2011kl compared with several incidencewiththemomentthatthephotospherereaches
LC models. Thick red solid line shows our preferred model with
P0 = 3.5 ms, and magnetic field B = 1.95×1015 G (see text for
moredetails). Amodel withP0 =12.2msand B=7.5×1014 G
assuggestedbyG15computedwithourhydrodynamicalmodeling
andouropacityprescriptionisshowninthinbluelineandindotted 2255
linefor κ=0.07 cm2 g−1. A 56Ni power model with a56Ni mass 95.6 d
of1M⊙ isshownwithdashedline. 3.3 d
4.8 h
2200 2.2 m
Figure 2 shows the velocity profile at different times
since the explosion for our preferred model (solid thick
s) 1155 1.3 m
line of Fig. 1). Initially, the shock wave propagates as m/
k
in a standard explosion. Later the dynamic effect is no- 30
ticeablealthoughnotasextremeasthecaseofASASSN- v (1 1100
15lh (see below). The extra heating source due to the
magnetar swell the inner zones and produces larger ve-
locities and a flat profile that raise steeply only at the 55 1122..88 ss 23.3 s 48.0 s
outermost layers. The high ejecta velocity is consistent
with the analysisby G15 who inferredthat a largevalue
of v would explain the rather featureless spectrum by
ph
11..55 22..00 22..55 33..00 33..55 44..00
Doppler line blending. We remark that here the opacity
prescription is probably responsible for the differences M r / MO •
found between our calculation and the analytic models Fig.2.— Velocity profile for the explosion that reproduce the
presentedbyG15. Thehydrodynamiceffectsofthemag- LCofSN2011kl. Theinteriordynamicsisaffected incomparison
netar on the luminosity are not as important as in the toastandardexplosionwithoutanymagnetar. Adayafterexplo-
sion the bulk of the stellar mass expands at ≈ 13×103 km s−1,
case of ASASSN-15lh, although as shown in Figure 2, it
or higher, whereas the outermost layers (not shown in the figure)
is evident in the velocity evolution. reachvelocitiesevenhigher(upto0.21c).
4 Bersten, Benvenuto, Orellana and Nomoto
the inner regions where the magnetar energy is directly
deposited. The observable effect of this fact should po-
tentiallymodifythespectralenergydistribution,andde-
serve further investigation.
Figure4 showsthe values ofB andP asa functionof
0
theNSmassderivedfromL andt . Forthestructureof
p p
themagnetarwehaveassumedthedatapresentedinTa-
ble 12 of Arnett & Bowers (1977). This corresponds to
the structure ofaNS assumingthe nuclearmatter equa-
tion of state of Bowers et al. (1975) that gives a mass
radius relation similar to those currently favored by re-
cent observations (see Fig. 11b of Lattimer 2012). We
haveneglectedrotationalandmagneticeffectsontheNS
structure. Forcomparison,weincludedthe curveforthe
case of SN 2011kl whichrepresents the locationof other
possible solutions (i.e. the degeneracy of the parameters
B and P ). Physically possible solutions correspond to
0
rotation periods larger than the critical breakup value.
Fig.3.— Observed bolometric LC of ASASSN-15lh (dots;
For the complete NSs mass range, we found solutions
Dongetal. 2015) compared with models of 4 M⊙ (dashed line)
that fulfill this condition. For the pre-SN model a spe- and 8 M⊙ (solid line) pre-SN mass for magnetar parameters of
cific value of Mcut was assumed, but we have corrob- Lp=9×1045 andtp=40daysandtexp=JD2457143.
orated that changing this value in the range shown in
Figure 4 produces a minor effect on the LC model.
Weconcludethatinitialperiodsranging∼1−2msand
magneticfieldsof∼(0.3−1)×1014Grelatedbythecurve
ofFigure4provideareasonablefittotheLC.Thesemag-
netar values are in good agreement with those proposed
by Metzger et al. (2015) although they assumed a lower
ejecta mass of 3 M⊙. However, we could not reproduce
the data with such low mass progenitor.
Here we should note that the uncertainty regarding
t could modify the exact value of the parameters. In
exp
any case, the scope of this analysis is to show that the
magnetar scenario is plausible for this object and not to
provide definitive values of the physical parameters.
Figure 5 shows the velocity profiles for our preferred
model of 8 M⊙. In this case the magnetar is extremely
powerfulandthedynamicaleffectismorenoticeablethan
for the case of SN 2011kl. The energy permanently sup-
plied by the magnetar impulses all the envelope at high
velocities and particularly the outermost layers. As re-
sult, a few days after the explosion most of the material
movesatconstantvelocity,whichincreaseswithtimedue
tothe permanentinjectionofmagnetarenergy. Thisdy-
namic behavior should have a clear effect on the spec-
Fig. 4.— Magnetic fields (in units of 1014 Gauss, represented
trum. Broad line features at 4100 and 4400 ˚A were ob- withdottedlines)andinitialspinperiods(inmilliseconds,denoted
servedinthe opticalspectrumofASASSN-15lh between with solidlines) of the magnetar as a function of its mass. Black
13 and 20 days after maximum implying very high ve- linescorrespondtotheparametersforSN2011kl whereasredlines
locities of ≈ 20.000 km s−1 (Metzger et al. 2015). This denotethecaseofASSASN-15lh. Forcomparison,thecriticalspin
periodisgiven witha dashed line. Notice that for both cases the
timing and velocity are fully consistent with the model NScanrotateattherequiredrate.
showninFigure5. We notethatthe photosphereatthis
epoch is located in the flat part of the velocity profile.
which in turn depend on the properties of the nuclear
4. DISCUSSIONANDCONCLUSIONS matter EOS which is poorly known.
We were able to reproduce the LC of SN 2011kl and For SN 2011kl we found L ≈ 1.2×1045 erg s−1 and
p
ASASSN-15lh inthe contextofmagnetar-poweredmod- t ∼15days. AfamilyofvaluesofP andBwerederived
p 0
els with physically allowed parameters (the NS rotating that lie outside the ranges proposedby G15. We ascribe
below breakup point). the differences to the opacity values adopted and not to
By adopting the magnetar luminosity and spin-down the hydrodynamic effects. We note that in addition to
timescale as free parameters we could separate the LC the extrasourceofenergydue to a magnetar,somenon-
fit from any assumption on the NS structure. The usual negligibleamountof56Ni(&0.08M⊙)wasalsonecessary
parameters(B andP )couldbe recoveredafterwardsby in our calculation to produce the LC peak and tail.
0
assumingtheNSconfigurationforagivenEOS.Wehave Regarding the extreme luminosity of ASASSN-15lh
shownthatthis leadsto adegeneracybetweenB andP the overall shape of the LC was reproduced for L ≈
0 p
SLSNe SN 2011kland ASASSN-15lh 5
M⊙ (see Tanaka et al. 2009, for a relation between pre-
SN mass and M ). On the other hand, if no He is
5500 ZAMS
present, then the pre-SN star could be a C+O star of
84.2 d
28.0 d 8 M⊙, which corresponds to a MZAMS ∼ 30 M⊙. In
4400 13.7 d both cases, the progenitor mass is close to the bound-
6.1 d ary mass between BH and NS formation (Nomoto et al.
2013). We emphasize that hydrodynamical modeling of
s) 3300 the LC can provide better constraints on the highly un-
m/ certainprogenitormassesofmagnetarsthantheanalytic
k
30 prescription.
1
v ( 2200 Our treatment of the SN evolution illustrates the im-
portance of the dynamical effects on the ejecta, espe-
1.1 m - 6.0 d cially in cases of powerful magnetars. The homologous
1100 expansion,usuallyassumedinSNstudies,canbebroken
5.3 s 20.9 s 49.5 s becauseoftheadditionalenergysource. Thiscouldhave
animportanteffect onthe line formationandthe photo-
sphericvelocityevolution. ForASASSN-15lh wefounda
33 44 55 66 77 88
M r / MO • totalenergyreleasebythemagnetarofE ∼3×1052erg,
which is one order of magnitude larger than the initial
Fig.5.—VelocityprofileforASASSN-15lh magnetarmodelwith explosion energy. For the more moderate SN 2011kl we
Lexpte=rna9l×ra1d0i4a5lzaonndestpup=to400.d1a5ycs.. This extreme case inflates the obtained E ∼ 1.6×1051 erg. In general, the dynamical
effects on the expansion of the ejecta become significant
whenthemagnetarenergyiscomparablewiththeexplo-
sion energy.
9×1045 erg s−1 and t ∼40 days. The resulting ranges
p
of B and P were compatible with those proposed by
0
Metzger et al. (2015). However, we note that our nu- We are grateful to Sergei Blinnikov and Gasto´n Fo-
merical models require a massive progenitor with M ≈ latelli for the helpful conversations and to Jose Prieto
ej
6 M⊙, i.e. a factor of 2 larger than the value adopted for sending the data of ASASSN-15lh. This research
by Metzger et al. (2015). Translating M into a zero- is supported by the World Premier International Re-
ej
age main-sequence mass, M , of the progenitor in- searchCenter Initiative (WPI Initiative), MEXT, Japan
ZAMS
volves several uncertainties. It is particularly important andtheGrant-in-AidforScientific ResearchoftheJSPS
whetherthe He featurescanbe hiddeninthe earlyspec- (23224004,26400222),Japan. M.O. would like to thank
traofSLSNe(Hachinger et al.2012;Dessart et al.2012). KavliIPMUforthesupportforhervisittoKavliIPMU.
Assuming that this is the case, the pre-SN star could be M.O. also acknowledges UNRN partial support through
a He star of 8 M⊙, which corresponds to MZAMS ∼ 25 grant 2014PI 40B364.
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