c ESO 2014

Astronomy & Astrophysics manuscript no. pisnLC5
March 21, 2014

Observational properties of low redshift pair instability supernovae
A. Kozyreva1 , S. Blinnikov2,3 , N. Langer1 , and S.-C. Yoon4

arXiv:1403.5212v1 [astro-ph.HE] 20 Mar 2014

1

Argelander-Institut für Astronomie, Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
e-mail: kozyreva@astro.uni-bonn.de2
Institute for Theoretical and Experimental Physics, Bolshaya Cheremushkinskaya Str. 25, 117218 Moscow, Russia
3
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa,
Chiba 277-8583, Japan
4
Department of Physics & Astronomy, Seoul National University, Gwanak-ro 1, Gwanak-gu, 151-742, Seoul, South Korea
Preprint online version: March 21, 2014
ABSTRACT

Context. So called superluminous supernovae have been recently discovered in the local Universe. It appears possible that some ofthem originate from stellar explosions induced by the pair instability mechanism. Recent stellar evolution models also predict pairinstability supernovae from very massive stars at fairly high metallicities (i.e., Z ∼ 0.004).
Aims. We provide supernova models and synthetic light curves for two progenitor models, a 150 M⊙ red-supergiant and a 250 M⊙
yellow-supergiant at a metallicity of Z = 0.001, for which the evolution from the main sequence to collapse, and the initiation of thepair instability supernova (PISN) itself, has been previously computed in a realistic and self-consistent way.
Methods. We are using the radiation hydrodynamics code STELLA to describe the supernova evolution of both models over a timeframe of about 500 days.
Results. We describe the shock-breakout phases of both supernovae which are characterized by a higher luminosity, a longer duration
and a lower effective temperature than those of ordinary Type IIP supernovae. We derive the bolometric as well as the U, B, V, R and
I light curves of our pair instability supernova models, which show a long-lasting plateau phase with maxima at Mbol ≃ −19.3 magand −21.3 mag for our lower and higher mass model, respectively. While we do not produce synthetic spectra, we also describe thephotospheric composition and velocity as function of time.
Conclusions. We conclude that the light curve of the explosion of our initially 150 M⊙ star resembles those of relatively brighttype IIP supernovae, whereas its photospheric velocity at early times is somewhat smaller. Its 56 Ni mass of 0.04 M⊙ also falls wellinto the range found in ordinary core collapse supernovae. The light curve and photospheric velocity of our 250 M⊙ models has
a striking resemblance with that of the superluminous SN 2007bi, strengthening its interpretation as pair instability supernova. We
conclude that pair instability supernovae may occur more frequently in the local universe than previously assumed.
Key words. stars: massive – stars: evolution – stars: supernovae: super-luminous supernovae – supernovae: pair instability supernovae– supernovae: general

1. Introduction
The final fate of very massive stars with initial masses between
approximately 140 M⊙ and 260 M⊙ has been studied in many
papers (Fowler & Hoyle 1964; Bisnovatyi-Kogan & Kazhdan
1967; Rakavy & Shaviv 1967; Barkat et al. 1967; Fraley 1968;
El Eid & Langer 1986; Heger et al. 2003). Such massive stars
undergo the dynamical instability caused by the creation ofelectron-positron pairs in oxygen cores, if they can retain theiroxygen core masses high enough (& 60 M⊙ ) until carbon exhaustion at the center (Heger et al. 2003). This leads to explosive oxygen burning that eventually causes complete disruptionof the star without leaving a compact remnant behind.
Theoretical models predict that these pair instability supernovae (PISNe) can be much more energetic and luminous thanordinary SNe. Explosion energies of up to 10 53 erg and massesof radioactive nickel up to 40 M⊙ (e.g., Heger & Woosley 2002)
are found to be achieved depending on the progenitor mass.
The corresponding light curves are characterized by a longduration of several hundreds of days and luminosities of up to
10 43 − 10 44 erg s−1 (Scannapieco et al. 2005; Kasen et al. 2011;
Dessart et al. 2013; Whalen et al. 2013a,c).

It is believed that PISNe are particularly relevant to thefirst generations of stars in the early Universe. Theoreticalstudies indicate that a significant fraction of the first stars
would be massive enough to be potential progenitors of PISNe,
mainly because of the lack of efficient coolants in the starforming regions in the early Universe (e.g., Bromm et al. 1999;
Nakamura & Umemura 2001; Abel et al. 2002; Omukai & Palla
2003; O’Shea & Norman 2006; Ohkubo et al. 2009). Such very
massive stars in the early Universe would not lose much
mass during the pre-supernova evolutionary stages in favor of
PISN production, because metal-free massive stars are not supposed to have strong line-driven winds (Krtička & Kubát 2006)
and because they are expected to be stable against pulsations(Baraffe et al. 2001). Several numerical studies have been therefore presented to discuss the nature and detectability of PISNe in
the early Universe (Scannapieco et al. 2005; Kasen et al. 2011;
Dessart et al. 2013; Whalen et al. 2013a). These studies considered a variety of PISN progenitors including red supergiants(RSG), blue supergiants (BSG) and pure helium stars, but theconsidered metallicities of these progenitor models were limited
to zero or very small values (Z ≤ 10 −4 ).
However, several recent studies indicate that PISNe arelikely to occur not only in the early Universe, but also in the local
1

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

Table 1: Characteristics of the PISN models: name of the model, initial metallicity Z, initial/final mass (Mini /Mf ) in solar masses,
radius of the star at the onset of the radiative calculation R in solar radii, explosion (Eexpl ) and kinetic (Ekin ) energy in foe (=10 51 erg), specific energy (E/M) in units [10 50 erg/M⊙], the velocity at the outer edge of the 56 Ni-rich layer in km s−1 (vni,max ), bulk
yields of the isotopes in the ejecta in solar masses (hydrogen 1 H, helium 4 He, carbon 12 C, oxygen 16 O, silicon 28 Si, nickel 56 Ni). The
names of the models starting with ’R’ indicate red supergiants. The names starting with ‘B’ are blue supergiants. Models labeled‘.D’ (Dessart et al. 2013) and labeled ‘.K’ (Kasen et al. 2011) are given for comparison.
Name

Z

150M
R150.K
R190.D
R250.K
B190.D
B210.D
250M
B250.K

10 −3
2 × 10 −6
2 × 10 −6
2 × 10 −6
2 × 10 −6
2 × 10 −6
10 −3
0Min /Mf(M⊙ )150/94150/143
190/164250/236
190/134
210/147
250/169
250/250

R
(R⊙ )
3394
2314
4044
3214
186
146
745
187

Eexpl
(foe)
12
9
44
69
∼44
75
70
63

Ekin
(foe)
8
33
34
66
44

E/M
1.3
0.6
2.7
2.9
3.3
5.1
4.1
2.5

Universe where metallicity is systematically higher than in theenvironments at high redshift. Crowther et al. (2010) found several very massive stars (VMS) with initial masses of 150 M⊙ .
M . 320 M⊙ in the Large Magellanic Clouds (LMC), which
are potential PISN progenitors. The final fate of such VMS stars
is critically determined by mass loss (e.g., Vink et al. 2011).
Given the strong metallicity dependence of the stellar winds
mass loss rate (e.g., Mokiem et al. 2007), it is generally believedthat VMSs can not retain enough mass to produce PISNe forhigh metallicity. However, Langer et al. (2007) point out thatthe production of PISNe does not necessarily require extremely
metal poor environments, although low metallicity is still preferred. Using stellar evolution models, they argue that the metallicity threshold below which PISNe may occur (ZPISN ) can be as
high as Z⊙ /3 (Langer 2009). More recently Yusof et al. (2013)
drew a similar conclusion.
The recent discovery of several superluminous SNe (SLSNe)that cannot be easily explained by usual core-collapse and/or interaction supernovae (see Gal-Yam 2012a, for a recent review)also provides evidence for PISN in the local Universe. In particular, the observed properties of SN 2007bi and SN 22131745 seem to imply a large amount of radioactive nickel inthese supernovae (i.e, more than 3 M⊙ of 56 Ni), for which PISN
explosion gives one of the best explanations (Gal-Yam et al.
2009; Young et al. 2010; Cooke et al. 2012). Given that someother possibilities like very energetic core-collapse explosion ormagnetar-driven SN have also been suggested to explain SLSNe(Moriya et al. 2010; Woosley 2010; Kasen & Bildsten 2010) andthat future observational SN surveys will discover more diverse
SLSN events in nearby galaxies, detailed studies on the observable properties of PISNe in the local Universe are still needed tohave a solid conclusion on the association of SLSNe and PISNe(e.g., Dessart et al. 2012b).
Langer et al. (2007) presented PISN progenitor models withinitial masses of 150 M⊙ and 250 M⊙ , which roughly represent
the low- and high-mass ends of PISN progenitors, at a metallicity of Z=0.001 to discuss the possible event rate of PISNe in
the local Universe. Kozyreva et al. (2014) investigated the explosions and consequent nucleosynthesis of these models to discuss the implications of PISNe for the chemical evolution. In
this paper, we explore these models further to investigate theirobservable properties using the radiation hydrodynamics code
STELLA (Blinnikov et al. 2006). These models together withthose from Herzig et al. (1990) and Whalen et al. (2013b) are
2

vni,max(km/s)
500
no data
1800
5000
1200
4400
5000
3200

1

H
(M⊙ )
5
50
24
73
6
4
10
86

4

He
(M⊙ )
24
21
46
39
34
31
48
40

12

C
(M⊙ )
2

16

O
(M⊙ )
47

28

Si
(M⊙ )
6

5

78

0.05

5
6
1

78
93
42

0.05
0.06
23

56

Ni
(M⊙ )
0.04
0.07
2.63
37.9
2.99
21.3
19.3
23.1

among the highest metallicity PISN light curve models available
in the literature, and therefore useful to identify PISN events at
low redshift.
We explain the method of calculations in Section 2 and discuss the produced light curves in Section 3. In Section 4, wecompare our results with other synthetic light curves for PISNe
and with observational light curves of usual and unusual corecollapse SNe (CCSNe). We conclude our work in Section 5.

2. Evolutionary models and light curves modeling2.1. Description of the evolutionary models

For simulating the light curves of PISNe we use the results ofevolutionary calculations produced with the Binary Evolution
Code (BEC, Langer et al. 2007; Kozyreva et al. 2014). These
are initially 150 M⊙ and 250 M⊙ models at a metallicity of
Z = 10 −3, with an initial rotation velocity of 10 km s−1 . The
evolution of the stars was calculated all the way from the zeroage main sequence to the thermonuclear explosion caused by thepair instability. To follow the nucleosynthesis, Kozyreva et al.
(2014) used the Torch nuclear network developed by Timmes(1998, 1999) using 200 isotopes. Our progenitor models are redand yellow supergiants for the 150 M⊙ and 250 M⊙ models, respectively (Langer et al. 2007; Kozyreva et al. 2014). The main
characteristics of the models are summarized in Table 1.
Our stellar models lose a large fraction of their initial
mass during core hydrogen and core helium burning due
to line-driven winds (Langer et al. see 2007, for details andKudritzki et al. 1989; Vink et al. 2001; Vink & de Koter 2005;
Yoon et al. 2010). The average mass-loss rate is about 2 ×
10 −5 M⊙ yr −1 . By the onset of the pair instability our 150 M⊙
star has lost 56 M⊙ and our 250 M⊙ star 81 M⊙ . We show the
pre-supernova evolution of stellar mass in Figure 3.
The stellar evolutionary models were calculated with the assumption of semi-convection using a large semi-convective mixing parameter (αSEM = 1), and without convective core overshooting. The mixing length parameter was chosen to be 1.5(Yoon et al. 2006). Note that we neglected any convective mixing during the pair instability phase (Kozyreva et al. 2014).
The input models for the STELLA calculations already contain the shock wave generated at the boundary between the oxygen and helium shells emerging from the interaction between
the rapidly expanding inner core and the nearly static outerA. Kozyreva et al.: Observational properties of low redshift pair instability supernovae
6

260

4

240

log ρ , g cm −3

Stellar mass,solar masses

250M

2
0
−2
−4

150M

−6
−8
−10
−12
0

200

Hydrogenburning

250M

180

Heliumburning

160
140
120

150M

100
20

40

60
80
100 120
Mass, solar masses

140

160

180

Fig. 1: The density structure of the 150 M⊙ and 250 M⊙ PISN
progenitor models at the onset of the STELLA calculations.
helium-hydrogen envelope (Kozyreva et al. 2014). The physics
of the pair instability explosion mechanism is well understoodand smoothly reproduced by evolutionary simulations without
the need of invoking artificial assumptions. This is contrasted toother SN types that often need free parameters for supernova
modeling, such as the critical density for the transition fromdeflagration to detonation for type Ia supernovae and the masscut, degree of chemical mixing, and explosion energy for corecollapse supernovae.
In Figures 1 and 2, we show the density and the chemical
structure of our progenitor models at the onset of the STELLA
calculations. At this moment the matter below the helium shell
expands nearly homologously (v ∝ r). In Figure 2, we truncatedthe outer hydrogen-helium envelope which moves at very low
velocity compared to the fast moving inner ejecta. We also do
not show in this figure the bottom of the hydrogen-helium envelope where the shock is located and causes a strong discontinuities. The ejecta in the 150 M⊙ model contain 0.04 M⊙ of56
Ni in the innermost region, moving at a velocity of less than
500 km s−1 . The 250 M⊙ model contains 19 M⊙ of nickel overan extended region with 0 km s−1 ≤ v ≤ 5000 km s−1 , whichcorresponds to 0 M⊙ ≤ Mr ≤ 50 M⊙ . We do not apply any mixing in our models. Later we discuss the impact of this chemical
structure on light curves. There is a small amount of helium in
the innermost region of the 250 M⊙ star as seen in Figure 2. This
helium was produced by photo-disintegration of heavy elements
during the explosive burning. We summarize the main propertiesof the PISNe in Table 1 along with other PISN models that we
use for comparison.
2.2. Simulation of theoretical light curves and SEDs1

For simulating the hydrodynamic evolution during the pair instability explosion we use the one-dimensional (1D) multigroupradiation Lagrangian implicit hydrodynamics code STELLA(Blinnikov et al. 2006 and references therein). The code solves
the hydrodynamic equations coupled with the radiative transfer
equations without assuming radiative equilibrium. The STELLA
code uses one temperature for the matter and has no specific1

220

SED — spectral energy distribution.

80

6

10

5

4

10
10
Time before the explosion

3

10

Fig. 3: The pre-supernova evolution of the stellar mass of ourmodels due to stellar wind mass loss.

temperature for radiation. The non-steady radiative transfer issolved for each of the one hundred frequency groups in all radialzones. The energy groups are uniformly distributed in logarithmic scale (i.e. in geometric progression) between the maximum
wavelength of 50,000 Å and the minimum wavelength of 1 Å.
The light curves are computed by integration of fluxes calculated with the STELLA code with UBVRI Bessel filter function
using logarithmic interpolation.
The opacity is calculated for each frequency group taking
about 160000 spectral lines into account according to Kurucz
data (Kurucz 1991). The opacity also includes photoionization, free-free absorption and electron scattering assuming local thermodynamical equilibrium. Because of the large velocity gradient the opacity is calculated accounting for the effectof an expanding medium following Friend & Castor (1983) andEastman & Pinto (1993). Local thermodynamic equilibrium isassumed in the plasma allowing to use the Boltzmann-Saha’s
distribution for ionization and level populations. This is neededfor determining absorption, scattering and emission coefficients.
Gamma-ray transfer is calculated using the one-group approximation for the non-local deposition of energy from the radioactive decay (Ambwani & Sutherland 1988). The code treatsstrong discontinuities (shock propagation) with an artificial viscosity term. The STELLA code does not follow any nuclear reactions.
To map the BEC models into the STELLA code weremeshed the models. The original number of zones was reduced
from 1931 BEC zones to 242 STELLA zones for the 150 M⊙
model and from 2202 BEC zones to 276 STELLA zones forthe 250 M⊙ model. We reduce the number of isotopes from 200(from hydrogen to germanium) to 16 (H, He, C, N, O, Ne, Na,
Mg, Al, Si, S, Ar, Ca, Fe, Co, Ni).
The envelopes of the progenitor models are optically thickand photons are not able to leave them on a short time scale.
Therefore, STELLA radiation transport calculations are computationally very expensive for an input model in which a shock
is located far from the photosphere. On the other hand, using amore evolved input model in which the shock front is closer tothe photosphere causes more numerical instabilities just behindthe shock because the BEC code does not include artificial vis3

1

1

0.9

0.9

0.8

0.8
O

Isotope Mass fraction

Isotope Mass fraction

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

He

0.7
Si

0.6

150M

0.5

Ni

0.4 S
Ne

0.3

Mg

C

He
Ni
O

0.7
Si

0.6

250M

0.5
0.4
Ar Ca

0.3

Ne

0.2

0.2 ArCa
0.1

0.1

H

0
0

1

2
3
4
Velocity, 1000 km/s

5

C
H

He

0
0

6

Mg

S

2

4
6
Velocity, 1000 km/s

810Fig. 2: The chemical structure of the exploding 150 M⊙ and 250 M⊙ stars at metallicity Z = 10 −3 at the onset of the STELLA
calculations.
−26

Mbol

−22

150M

−25

Mbol

−24

R−2

−18
−16
−14

Mbol
−12

Absolute magnitude

Absolute magnitude

−20

250M

R−2

−23
−22

I−1

−21

B+1

−20
−19

U+2

−18
−17

−10

U+2
0

50

100

150

B+1

V

200 250
Time, days

300

I−1
350

400

450

−16
−15

V
0

100

200

300
400
Time, days

Mbol
500

600

700

Fig. 4: Bolometric and multiband (U, B, V, I, R) light curves for 150 M⊙ and 250 M⊙ PISNe at metallicity Z = 10 −3 . U, B, V, I, R
magnitudes are plotted with a shift of +2, +1, 0, -1, -2 magnitudes, respectively.
cosity. We therefore compared two different cases to test how
the choice of the starting model affects the final outcome: one inwhich the shock front is located at the bottom of the helium shelland the other in which the shock is propagating in the middle ofthe helium envelope. We find that the final solutions differ only
by less than 10% in the terms of bolometric luminosity. In thefollowing we use the model in which the shock reached the bottom of hydrogen-helium envelope. This defines the point t = 0
for all the figures.
Note that the zero point in time (t = 0) is not the same as thetime of the explosion. Nevertheless, the time between the onsetof the pair instability explosion (namely the highest central density) and the beginning of the light curve calculations is 1 hourfor 150 M⊙ model and 44 seconds for 250 M⊙ model. These
are the time intervals that the shock takes to propagate throughthe shallow pure helium layer to reach the bottom of hydrogenhelium envelope. These intervals are relatively small compared4

to the light curve evolution (months), therefore, one can consider
the time in all figures as approximate time since the onset of thepair instability explosion.

3. Results
In Figure 4, we plot the bolometric and U, B, V, R, I band light
curves for the 150 M⊙ and 250 M⊙ models. Hereafter, in figures and tables we designate the models as Model 150M andModel 250M respectively. The U, B, V, R, I magnitudes are plotted with a shift of +2, +1, 0, -1, -2 magnitudes, respectively. The
bolometric curves follow closely the V-band light curves, except for early time where it needs ultraviolet bolometric corrections, and for late time where it needs infrared bolometric corrections (Bersten & Hamuy 2009). We summarize the details about
shock breakout events (duration, maximum luminosity, effective and color temperatures, spectral wavelength peak, spectral

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

−1

O

He

Ne

H

0
log Mass fraction at photospherelog Mass fraction at photosphere

0

Mg

C

Si

−2

150M

O

He

Ne
−1

H

Si

S

Ca
Ar

C
−2

Mg

Fe−Co−Ni

S
−3
0

50

100

150
200
Time, days

250

300

250M
−3
150

350

200

250

300

Time, days

Fig. 5: Evolution of the composition at the receding electron-scattering photosphere for the 150 M⊙ and 250 M⊙ PISN models.
whole envelope is optically thick it takes a long time for photons generated during the explosive burning to reach the surface(optically transparent medium). Therefore, firstly, during about
6 days for Model 150M and 12 hours for Model 250M the shock
passes through the entire envelope (see e.g. Shigeyama et al.
1987; Blinnikov et al. 2000). The shock wave reaches the surface, and the envelope matter behind the shock is heated and15 ionized. When the shock emerges at the surface the energetic
shock breakout flash of ultraviolet and X-ray emission appears
with a duration of a few hours. The shock breakout is shownin the Figure 6. We draw some important conclusions about theshock breakout in Section 4.

−25

Bolometric magnitude

−20

150M

−15
−10
0

5

10
Time, days

−30
−25
−20

250M
3.1. The 150 M⊙ model

−15
−10
0

5

10

15
Time, hours

20

25

30

Fig. 6: Shock breakout events for 150 M⊙ and 250 M⊙ PISN explosions.

energy peak) and light curves in comparison to other radiative
simulations of PISN explosion (Kasen et al. 2011; Dessart et al.
2013) in Table 2.
For the discussion on the light curves below, we also show
the evolution of the chemical composition at the photospherewhich recedes along the decreasing Lagrangian mass coordinate,
in Figure 5. The photosphere is defined as the mass zone where
the electron-scattering optical depth in B-band turns above 2/3.
This consideration is valid while matter and radiation temperatures are comparable at an accuracy better than 10%. The estimated period during which such conditions are present is approximately the first 350 days for Model 150M and 250 days for
Model 250M. At later times, the opacity is dominated by line
opacity and non-local thermodynamical equilibrium consideration is required.
Soon after the explosion, the shock wave forms when thefast expanding inner part of the star encounters the slowly moving helium layer and the hydrogen-helium envelope. Because theSoon after the shock breakout, the temperature drops rapidly
due to adiabatic cooling. Later the recombination losses become comparable to adiabatic cooling (Grasberg et al. 1971).
The recession of the photosphere along the Lagrangian mass
coordinate is compensated by an overall expansion of the envelope. The combination of expansion and cooling provides
the condition for only slight variations of the luminosity forsome time (Grasberg & Nadezhin 1976; Imshennik & Nadezhin1989). This emerges as a plateau phase in the light curve.
The plateau phase lasts for about 100 days for Model 150M.
The light curve shape of Model 150M looks similar to thatof ordinary type IIP supernovae. This fact is also noticed by
Scannapieco et al. (2005) and Kasen et al. (2011). The absolute
V-band magnitude becomes about MV = −19 mag at the visual maximum, which is about 10 times brighter than an average
SN IIP. However, the peak luminosities of type IIP SNe vary bya factor of 100, and that of our model is still contained in thisrange. Its high luminosity results from the relatively high supernova energy (about 10 foe) and the large radius (3394 R⊙ ) of theprogenitor. Once the photosphere recedes to the region below thehydrogen-rich envelope, the luminosity decreases rapidly andthen becomes governed by the radioactive decay of 56 Co.
It is interesting to consider the effective temperature evolution which we present in Figure 7. Note that the recombination effectively slows the adiabatic cooling during the expansion.
The recombination starts playing a role when recombination
5

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

Temperature, K

in U, B, V-bands at magnitude M ≃ −18.5 mag. Such precursor
could be perceived as a separate hydrogen-rich SN being discovered long before reaching the maximum luminosity.
A rebrightening occurs thereafter, as the energy from the5radioactive
decay of nickel and cobalt in the ejecta diffuses10
out (Dessart et al. 2010). The photosphere recedes below thehydrogen-rich envelope starting at about day 175 (Figure 5), but
unlike in the case of Model 150M, the luminosity keeps increas150M Tcolor
ing until about 220 days, reaching MV = −21 mag at the visualmaximum. At later times, the light curve is largely governed by
250M Tcolor
4
the radioactive decay of 56 Co. A hump-like feature on top of the10
main maximum phase is shown around day 220. At this time
the photosphere leaves the oxygen-rich layer and moves down
250M Teff
to the silicon-rich layers. The receding front gradually encounters a bubble of diffusing photons generated by the radioactive
decay.
150M Teff
3
10
It is interesting to note that the photosphere is located in the
0
50
100
150
200
250
300
350
400
inner
layers where there is no hydrogen and helium well before
Time, days
the luminosity reaches its peak, as mentioned above (Figures 4
Fig. 7: Evolution of the effective and color temperature of and 5). Based on our results we can not predict whether hydro150 M⊙ and 250 M⊙ PISN models. The solid and dashed curves gen and helium lines are expected in the spectrum at the timepresent effective and color temperatures correspondingly. The of maximum luminosity due to excitation by radiation above
thin line is located at 5000 K and approximately corresponds to the photosphere. However, Dessart & Hillier (2011) showed thatthe Balmer lines disappear after the photosphere leaves thehydrogen recombination temperature.
hydrogen-rich shell of ejecta in the case of type II plateau SN and
there are no Balmer-continuum photons at later time. The spectral models for PISNe by Dessart et al. (2013) also indicate thatradiation becomes comparable to adiabatic cooling. This hap- hydrogen lines do not appear once the photosphere moves downpens when the effective temperature is approximately 10000 K to the hydrogen-free core. Non-thermal excitation of hydrogen(Imshenik & Nadezhin 1965), i.e. well before the establishment can happen if there is some degree of mixing of cobalt andof a recombination cooling wave. The effective temperature of nickel into layers containing hydrogen (Li et al. 2012). However
an ordinary SN II remains nearly constant (∼ 5500 K) after the it is expected that PISNe do not experience such mixing durestablishment of a recombination cooling wave. This phase be- ing the explosion according to the recent numerical simulations
gins about 20 days after the explosion for an ordinary SN II of Joggerst & Whalen (2011). Therefore, we expect that PISNe(Bersten & Hamuy 2009; Dessart & Hillier 2011). This delay of like Model 250M will not have any hydrogen lines once the pho20 days depends mostly on the progenitor radius (Grasberg et al. tosphere recedes to the hydrogen-free core. For the same reason,
1971; Imshennik & Utrobin 1977).
we do not expect helium lines in the optical bands either, because
Due to the very large progenitor radius of 150 M⊙ PISN strong mixing of helium and radioactive nickel is needed to ex(3400 R⊙ ) the onset of the recombination cooling wave is de- cite helium lines as shown in Dessart et al. (2012a). This means
layed up to day 100 in this case. For about 20 days thereafter, that the Model 250M would appear as a type II SN initially but
when the photosphere is still inside the hydrogen-helium layer look like a SN Ic from about day 175, well before the luminosity(Figure 5), the recombination cooling wave is established for reaches its peak value.
a while and the effective temperature is kept at the hydrogen
recombination level. Although the mass fraction ratio betweenhydrogen and helium is 4:1, the number of hydrogen atoms is 4. Discussion
about equal to the number of helium atoms and the relative contribution to the electron density from hydrogen stays high. The 4.1. Comparison with other theoretical PISN light curves
plateau phase of this model mostly corresponds to the phase of In this section we compare our results with other PISN modrapidly evolving photospheric temperature. This is different from els from red or blue supergiant progenitors. These include PISN
the case of ordinary SN IIP (see e.g. Bersten & Hamuy 2009). In models carried out with the Monte Carlo radiation transport
Section 4.3 we provide the comparison of the color temperature code SEDONA (labeled ‘.K’ in figures, tables; Kasen et al.
with those of typical and bright SNe IIP, and with SN 2009kf 2006, 2011) and with the non-LTE radiative-transfer code
which was bright in the near-ultraviolet (NUV) range at early CMFGEN (labeled ‘.D’; Dessart et al. 2013). Light curves fromtime.
the SEDONA simulations are integrated from spectra provided
by D. Kasen and artificially smoothed. The noisy appearance is aconsequence of the statistical approach of Monte Carlo transport
3.2. The 250 M⊙ model
calculations. The advantage of the STELLA calculations overThe light curve looks very different for our Model 250M the SEDONA and the non-LTE CMFGEN codes is the capabil(Figure 4). After the shock breakout, the bolometric magnitude ity to simulate the radiation-hydrodynamical evolution from thedrops to about M ≃ −18 mag during the first 50 days. The lu- onset of the explosion. Hence we reproduce the emergence of theminosity decreases due to the adiabatic expansion more rapidly shock breakout event and the hydrodynamical evolution during
than in Model 150M, because the progenitor of Model 250M the pair instability explosion. Both, SEDONA and CMFGEN,
is more compact (i.e., R = 745 R⊙ , compared to 3394 R⊙ in carry out the radiative transfer calculations once the homoloModel 150M). A precursor-like event happens at around day 20 gous expansion is reached. The codes have their advantages
6

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae
45

46
45.5

R250.K

44

log Bolometric luminosity

log Bolometric luminosity

44.5

43.5
43
42.5

R190.D

42
41.5

R150.K

41

40

0

100

200
300
Time, Days

400

500

Photospheric Velocity, 1000 km/s,

16

12

R250.K

10
8

R150.K

R190.D

4

0

150M
0

50

100

43.5
43
42.5

B190.D150
200
250
Time, Days

300

41

0

100

200
300
Time, Days

400

500

Fig. 10: Bolometric luminosity for the Model 250M (blue curve),
Model B190.D (green curve), Model B210.D (red curve), andModel B250.K (cyan curve).
As already discussed by Kasen et al. (2011) and Dessart et al.
(2013), more massive progenitors result in higher luminosities and broader light curves. In particular, heating due to radioactive decay of nickel and cobalt leads to a rebrightening
in Model R190.D and Model R250.K which produced large
amounts of 56 Ni (2.63 M⊙ and 37.9 M⊙ , respectively), while itis not seen in Model R150.K and Model 150M which have only
0.07 M⊙ and 0.04 M⊙ of 56 Ni, respectively. The tail of each light
curve is powered by cobalt decay and its luminosity is directly
proportional to the amount of radioactive nickel generated during the explosion. This dependence is clearly visible in Figure 8.
Our Model 150M is directly comparable to Model R150.K,
because it has the same initial progenitor mass, a similar explosion energy and a similar nickel mass (Table 1). Compared toModel 150M, Model R150.K has a 500 times lower metallicity,which results in several important differences in the progenitor
properties:

142

B250.K

44

41.5

Fig. 8: Bolometric luminosity for the red supergiant models
150M (blue curve), R150.K (green curve), R190.D (red curve),
and R250.K (cyan curve).

6

B210.D

44.5

42

150M

40.5

250M

45

350

400

Fig. 9: The photospheric velocities for the same models as shownin Figure 8. Labels and colours have identical meanings.

for spectral computations well described in a number of papers(Kasen et al. 2006; Woosley et al. 2007; Dessart & Hillier 2010,2011).
4.1.1. Red supergiants

Red supergiant (RSG) progenitors are common for producing
SNe IIP (Grasberg et al. 1971; Smartt 2009). Typically the light
curve from the explosion of a red supergiant is characterized bya pronounced plateau phase lasting for about 100 days, followed
by a radioactive tail (Barbon et al. 1979). In this section we compare our lower mass PISN Model 150M with other PISNe produced by RSG progenitors.
In Figure 8, we plot the theoretical light curves for different RSG PISN models: Model 150M, Model R150.K,
Model R150.D, and Model R250.K (see Table 1 for details).

1. The ejecta mass is much lower for Model 150M (94 M⊙ )than that of Model R150.K (143 M⊙ ).
2. The hydrogen-helium envelope masses are 29 M⊙ in
Model 150M and 71 M⊙ in Model R150.K, respectively.
3. Because of stronger mass loss, the hydrogen mass fraction in
the envelope of Model 150M is much lower (XH ≈ 0.2) thanthat of Model R150.K (XH ≈ 0.7).
4. The radius at the pre-supernova stage is significantly larger
for Model 150M (R = 3394 R⊙ ) than for Model R150.K(R = 2314 R⊙ ).
As a consequence the overall plateau duration is shorter inModel 150M than in Model R150.K, because of the smaller hydrogen envelope mass and lower mass fraction of hydrogen in
the envelope. Moreover, nickel was additionally mixed into outerlayers in Model R150.K which in turn caused extra nickel heating during plateau phase.
Figure 9 plots the photospheric velocities of the RSG models. The Model 150M and Model R150.K have a phase where
the photospheric velocity remains nearly constant, which resultsfrom the interplay between the recession of the photosphericfront and the expansion of the ejecta. For the models with higher
E/M ratio, i.e. Model R190.D and Model R250.K, the photo7

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

radioactive decay. These photons ionize the just recombined
medium and push the photospheric front to outer shells. A larger
envelope mass leads to a broader phase of this reverse photosphere motion.
20
The sudden drop in the velocity of Model 250M occurs around day 175. At this time the photosphere leaves thehydrogen-helium envelope (Figure 5) and moves rapidly through15hotter layers of oxygen, neon, carbon and magnesium heatedby diffusing nickel photons. There is a lack of such a sharp
250M
drop in other calculations because their input chemical struc10
ture was smeared (Kasen et al. 2011; Dessart et al. 2013) toB250.K
mimic hydrodynamical mixing happened during the explosion.
However, it was shown by a number of studies that the degreeof mixing for the inner regions containing radioactive nickel is5
not so prominent (Joggerst & Whalen 2011; Chen et al. 2012;
B210.D
Chatzopoulos et al. 2013; Chen et al. 2014). Mixing is more efB190.D
ficient in the oxygen layer where the shock emerges and above it
0
0
50
100
150
200
250
300
350
400 due to the propagation of the reverse shock. Red supergiants exhibit a higher degree of mixing compared to more compact blue
Time, Days
supergiants, similar to red and blue supergiant core collapse SNeFig. 11: The photospheric velocities for the same models as (Joggerst et al. 2009).
shown in Figure 10. Labels and colours have identical meanings.
Photospheric Velocity, 1000 km/s,

25

4.2. The chemical structure during the coasting phasespheric velocities stay at a high level for a longer time. This is theresult of a stronger explosion and hence a more powerful shock.
More energetic photons keep the medium ionised for longer
and the photosphere remains in hydrogen-rich regions (larger
Lagrangian mass coordinate) for a longer time (up to aroundday 250 and day 300 for Model R190.D and Model R250.K,
respectively).
The photospheric velocity in Model 150M is very low
at the moment of shock breakout (4000 km/s) because theshock spends a large fraction of its energy on ionizing the
medium while traveling along the extremely extended envelope. As showed in Grasberg et al. (1971), Falk & Arnett (1977),
Blinnikov & Tolstov (2011) and Tolstov et al. (2013), extended
progenitors result in lower photospheric velocities than morecompact ones.
4.1.2. Yellow and blue supergiants

In Figure 10, we plot light curves for PISNe from more compact progenitors than RSGs: Model 250M, Model B190.D2 ,Model B210.D, and Model B250.K. These PISNe produce light
curves reminiscent to that of SN 1987A: the luminosity decreases rapidly in the beginning, but the supernova rebrightenes
as the thermalized photons from the radioactive decay of nickel
and cobalt diffuse out. The bolometric luminosity of our yellow
supergiant Model 250M is higher than that of the other blue supergiant models during the initial phase (t . 50 days), becauseof the larger radius of the progenitor (e.g. Popov 1993).
In Figure 11, we show the evolution of the photosphericvelocity for the compact progenitor models. In all of thesemodels, the photosphere recedes very rapidly through the outerhydrogen-helium layer after shock breakout. In Model 250M,
Model B210.D and Model B250.K, where the amounts of nickel
exceed 19 M⊙ , the reversion of the photospheric velocity occurs when the recombination and cooling wave encounters the
expanding “bubble” of diffusing photons generated by nickel
2

Blue supergiant B190.D is the same evolutionary model as red supergiant R190.D but with truncated hydrogen atmosphere (about 30 M⊙
of outer hydrogen layer is cut; Dessart et al. 2013).
8

Figure 12 shows the ejecta structure of Model 150M andModel 250M at coasting phase. In fact, the coasting phase begins around day 10 for both our models. In Figure 12, we plot
the chemical composition of the ejecta at day 950 and day 1200,
respectively. The plots demonstrate what would be the degree of
Doppler broadening for the spectral lines of the given elements
10 days after the explosion and later.
The oxygen shell in Model 150M, which contains small
amounts of carbon, neon, magnesium and silicon, expands at avelocity of 1000 – 2200 km s−1 . The inner silicon-sulfur shell
moves at velocities below 2000 km s−1 . Model 250M shows
systematically higher velocities. The oxygen-rich layers travelat 4000 – 5000 km s−1 , the silicon-sulfur shell — at about
4000 km s−1 , and the nickel-rich layer moves at 0 – 3900 km s−1 .
In the Model 250M the structure has some peculiarity at thesulfur-silicon layer moving at velocity around 4000 km s−1 . The
reason is the hydrodynamical effect of nickel heating (Arnett
1988; Woosley 1988; Arnett et al. 1989; Pinto & Eastman 2000;
Woosley et al. 2007). The additional radiation pressure producedby nickel heating provides an acceleration of the innermost
30 M⊙ of ejecta. The effect increases the velocity field in the
inner part of the ejecta by a few hundred km s−1 and decreases
the density. The overall changes in density and velocity do not
exceed 10% on a relative scale. This effect has no influence on
the light curve shape around the luminosity peak (Woosley et al.
2007) because the photosphere retains far from the innermost
region at this time.
4.3. Comparison with observed SNe
4.3.1. Relatively low-mass PISNe and type IIP SNe

Our Model 150M is particularly relevant for the identificationof PISNe in the local Universe. This is because SNe from thelow-mass end of the PISN regime like Model 150M are expected to be more abundant than those from the high-mass end
like our Model 250M. In Figure 13, therefore, we show the
first 170 days of light curves for our synthetic PISN models
and compare it to several observed plateau SNe. The data forthese particular SNe are taken from the Sternberg Astronomical

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

Table 2: Shock breakout and plateau-maximum phase characteristics. Shock breakout duration (defined as a full width at halfmaximum), bolometric peak luminosity, effective and color temperature, spectral wavelength peak in Å, spectral energy peak in
keV. The photospheric phase begins after relaxation from the shock breakout and is limited by the transition to the radioactive
decay tail. Model 150M and Model 250M are those of 150 M⊙ and 250 M⊙ PISNe simulated in the frame of present study. Labeled‘R190.D’, ‘B190.D’ and ‘B210.D’ are models from (Dessart et al. 2013) and ‘R150.K’ and ‘R250.K’ are models simulated by(Kasen et al. 2011).

duration,(hours)
6
2
—
1.6
—
—
1.4
0.3

150M
R150.K
R190.D
R250.K
B190.D
B210.D
250M
B250.Kshock breakoutL,
T eff /T color ,(erg/s)(10 3 K)
5.4 × 10 44
60/160
1.2 × 10 45
90/170——
9.6 × 10 45
130/350————
6.2 × 10 45
230/570
1.4 × 10 45
330/630

λmax ,
(Å)
170
169
—
83
—
—
51
46

Ep,
(keV)
0.07
0.07
—
0.15
—
—
0.24
0.27

photospheric phaseduration,L,(days)(erg/s)110
1.6 × 10 43
200
3 × 10 42 − 10 43
260
3 × 10 43
410
6 × 10 43 − 10 44300
1.6 × 10 43
280
2 × 10 42 − 10 44
280
10 43 − 6 × 10 43
440
2 × 10 42 − 5 × 10 43−21
1

2009kf

−20

150M

0.9
O

0.7
Mass fraction

Absolute V−magnitude

−19

0.8

He

0.6 Si
0.5
0.4

Ar Ca

0.3
S

Fe−Co−Ni

0.2

0
0

Ne C

2

H

3
4
Velocity, 1000 km/s

56Fe−Co−NiO

Mass fraction

0.7

250M

0

20

40

60

80
100
Time, days

120

140

160

He

S
Ne

0.3

Ar Ca

Mg

C

0.2

H

0.1
0
0

7

150M

Si

0.6

0.4

1999emFig. 13: The absolute V-band light curve for 150 M⊙ PISN (bluesolid line) is shown together with the absolute V-band magnitudes for typical plateau SN 1999em (green circles) and threebright plateau SNe 1992H (magenta circles), 1992am (cyansquares), 2009kf (red squares).

0.9

0.5

−15

−13

1

0.8

1992H

−16

−12
1

1992am

−17

−14

Mg

0.1

−18

2

4
6
Velocity, 1000 km/s

8Fig. 12: The chemical structure of ejecta of 150 M⊙ and 250 M⊙
PISNe at day 950 and day 1200 correspondingly.

Institute Supernova Light Curve Catalogue (Tsvetkov et al.
2010; Tsvetkov & Pavlyuk 2013) and are compiled from theoriginal data (Tsvetkov 1994; Clocchiatti et al. 1996; Hamuy
2001; Botticella et al. 2010).
Model 150M has a plateau phase during the first 115 days
which is not unusual for SNe IIP. Although this model has ahigher envelope mass (29 M⊙ ) than those of typical SNe IIP progenitors (< 10 M⊙ ), the helium mass fraction is very high (about80%). At the same time it is expected that the envelopes of typical SN IIP progenitors have helium mass fractions of 35% – 50%
depending on their initial masses (Woosley et al. 2002; Langer2012). Helium recombines at higher temperatures to reduce theelectron scattering opacity and the hydrogen recombination front
recedes more rapidly with a higher fraction of helium in the envelope (Kasen & Woosley 2009). This makes our Model 150M
to have a fairly short duration of the plateau phase compared9

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae
12
Photospheric Velocity, 1000 km/s,

4

Color Temperature, 10 K

1.6

150M
1.4
1.2

2009kf1
0.8
0.6

SN IIP: 1999br
1999em
1999gi
2003bn2003hn

10

8

6

150M
4

2

1999em
0.4

0

20

40

60
80
Time, days

100

120

140

0

0

50

100

150
200
Time, days

250

300

350

Fig. 14: Color temperature evolution of 150 M⊙ PISN isshown together with those of typical SN IIP SN 1999em and
NUV-bright SN 2009kf. SN 1999em and SN 2009kf data aretaken from Bersten & Hamuy (2009); Botticella et al. (2010).
SN 2009kf data are shifted in time by 15 days.

Fig. 15: The photospheric velocity for our 150 M⊙ PISN model(blue solid line) is shown together with observational data forseveral SNe IIP (Jones 2008). The zero point for the observed
data is the first spectroscopic observation.

to high redshift RSG PISN models (cf. Figure 8). The plateau
duration of the light curve for our Model 150M is comparable
to those of typical SNe IIP, despite the relatively high envelopemass.
During the plateau phase, the V-band magnitude varies by 12 magnitudes (Barbon et al. 1979; Hamuy 2003). Compared tothe typical plateau supernova SN 1999em, the plateau luminosityof the Model 150M is higher by 2-3 magnitudes, but comparable to those of the three bright SNe IIP (SN 1992H, 1992am and2009kf, cf. Figure 13). The estimated nickel masses for theseSNe IIP are comparable or higher than that in Model 150M:
MNi = 0.058 M⊙ , 0.075M⊙ , 0.36M⊙ for 1999em, 1992H,
1992am (Clocchiatti et al. 1996; Hamuy 2003; Nadyozhin 2003;
Bersten et al. 2011), respectively, and limited by 0.4 M⊙ for2009kf (Botticella et al. 2010).
Our Model 150M has a very large initial radius of 3394 R⊙(see Table 1), while those of ordinary SNe IIP progenitors haveradii of less than 1000 R⊙ . Due to this difference our PISN explosion and SN IIP explosions have a different appearance ofthe shock breakout event. The shock breakout duration is longer
for a larger progenitor (Tominaga et al. 2011). The color temperature is higher for a SN IIP shock breakout than that for our
PISN (T col ∼ R −1/2 ) while the peak luminosity is similar depending mostly on the explosion energy (Tolstov et al. 2013). Since
our PISN shock breakout is redder the spectral maximum occurs
at a longer wavelength (see Table 2). Unfortunately the shock
breakout of local SNe II is very difficult to detect because it appears as a ultraviolet/X-ray burst lasting only minutes to hours(Calzavara & Matzner 2004).
The large progenitor radius of our 150 M⊙ PISN model
has consequences for the photospheric temperature evolution. In Figure 14, we compare the color temperature of our
150 M⊙ PISN with those of the typical SN IIP SN 1999em andthe near UV-bright SN 2009kf. The color temperature evolutionof our model is very different to that of SN IIP 1999em, but similar to that of SN IIP SN 2009kf, which had a high NUV excess at early time. Nevertheless, the NUV light curve of ourmodel does not show such a high luminosity as SN 2009kf. The

maximum NUV luminosity reaches −20.5 mag and −22 magfor our 150 M⊙ PISN model and for SN 2009kf, respectively(Botticella et al. 2010). The high NUV luminosity of 2009kf is
explained by the interaction of the SN shock with a dense stellar wind preceding the SN explosion (Moriya et al. 2011). The
higher temperature is the direct consequence of the ultraviolet
excess. However, in case of our low mass PISN model the shock
breakout event occurs and the high temperature is related to therelaxation of the highly excited medium. Any interaction of the
SN ejecta with the progenitor wind is neglected in our model.
Another possible way to distinguish a SN IIP from a PISN
explosion is to check the photospheric velocities. In Figure 15
we show the photospheric velocity for our 150 M⊙ PISN model
along with those of a few ordinary plateau SNe taken from Jones(2008). The estimate for the photospheric velocity is based on
the Hβ absorption line (Jones et al. 2009). The distinct propertyof our model is the low photospheric velocity at earlier timecompared to the maximum photospheric velocities of SNe IIP(cf., Grasberg et al. 1971; Young 2004). The photospheric velocities at later time are similar for both SNe IIP and our low
mass PISN model.

10

4.3.2. SLSNe linked to type Ic SNe

As discussed in Section 3 the photosphere of our 250 M⊙ PISN
model during its peak luminosity phase recedes to the bottom of the hydrogen-rich envelope (see also Kasen et al. 2011;
Dessart et al. 2013). Therefore, one could classify it as a SN Ic,
like SN 2007bi, if it was discovered during the maximum or
post-maximum phase. In Figure 16, therefore, we compare thesynthetic bolometric light curve of our 250 M⊙ model with thequasi-bolometric light curves of some superluminous type Ic
SNe: SN 2010gx, PS1-10awh, PS1-10ky PS1-10bzj, SN 2007bi,
and PTF10nmn.
From Figure 16 (left panel) it is clear that Model 250M cannot explain several of the unusually luminous SNe Ic, becauseof the very broad light curve of our model. Unambiguous evidence for a pair instability explosion of an initially high mass

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae−2245

PS1−10awh
slsn Ic
PS1−10ky
slsn Ic
PS1−10bzj
slsn Ic

44−21
Absolute magnitudelog Bolometric Luminosity

250M

SN2007bi
slsn Ic

43

SN2010gx
slsn Ic

42

250M
Mbol

SN2007bi
R−band−20−19

PTF10nmn
R−band−18

250M
R−band

−17

41
0

100

200

300
Time, days

400

500

600

−16
0

100

200

300
400
Time, days

500

600

700

Fig. 16: Left panel: The absolute bolometric light curve for our 250 M⊙ PISN model (blue solid curve) is shown together withquasi-bolometric and bolometric light curves of superluminous type Ic SN 2010gx (red, Inserra et al. 2013), PS1-10awh and PS110ky (green and black, Chomiuk et al. 2011) PS1-10bzj (magenta, Lunnan et al. 2013), and PISN candidate SN 2007bi (yellow,
Young et al. 2010).
Right panel: The absolute R-band and bolometric light curve for our 250 M⊙ PISN model (green and blue) with superimposed
R-band data for SLSN 2007bi (cyan) and PTF-10nmn (red). Data are taken from Gal-Yam (2012b).
For both plots the observed curves are shifted in time by 200 days to coincide with the maximum phase of the theoretical curve.
progenitor would be the observation of an extremely long riseto the maximum phase (Benetti et al. 2013). Therefore, some attempts are made to complete the light curves with retrospective
detection of data points before the maximum phase(Nicholl et al.
2013). The synthetic light curve of our 250 M⊙ PISN modelshows 200 days of rise while many SNe Ibc and SLSNe demonstrate significantly shorter rise time less than 40 days (see e.g.
Modjaz et al. 2009; Drout et al. 2011; Chomiuk et al. 2011). A
good example of a SLSN with a reliable long-lasting rise is
PTF10nmn. The data for this particular SLSN and for SN 2007bi
are shown in the right panel of Figure 16. Our Model 250Magrees well with the broad light curves of PTF10nmn andSN 2007bi.
The photospheric velocity of our high mass PISN modelaround the luminosity peak is smaller than typical velocities
of luminous SNe Ibc (Figure 17). The reason for the low velocity is the high ejecta mass of our model. This may be another criterion for distinguishing luminous PISNe powered bylarge amounts of nickel from superluminous CCSNe. However,the photospheric velocities measured for SN 2007bi demonstratethat the ejecta of this particular SLSN moves at a lower velocity
than those of other SLSNe, which is in good agreement with ourmodel. This renders precise spectroscopic observations important to shed light on this question.
Being discovered around or after its maximum, SN 2007bi
resembles some other SLSNe which show a short rise to theirpeak luminosity (Nicholl et al. 2013). Particularly, this rulesout the pair instability origin of these SNe. Nevertheless, weconclude that our Model 250M agrees with observed properties (light curve, photospheric velocity) of SLSN 2007bi well.
Therefore, SN 2007bi might emerge from pair instability explosion of very massive star with initial mass above 200 M⊙ .

5. Conclusions
We carried out simulations of shock breakouts and light curvesof pair instability supernovae using two evolutionary models of
150 M⊙ and 250 M⊙ at metallicity Z = 10 −3 (Langer et al.
2007; Kozyreva et al. 2014). We used the radiation hydrodynamics code STELLA for this purpose (Blinnikov et al. 2006).
The considered metallicity (Z = 10 −3 ) is among the highest of
PISN models that have been so far presented in the literature(Herzig et al. 1990; Whalen et al. 2013b). Therefore, our models may serve as useful references for future studies on PISNe
observed in the local Universe, as well as in the early Universe.
From our qualitative comparison to ordinary core collapse
SNe we conclude that it is difficult to distinguish low masspair instability explosions from hydrogen-rich core collapse explosions. The photometric and spectroscopic observations, including X-ray and ultraviolet (for detection of shock breakout
events), should be very detailed from the earliest epoch to help
shedding light on this. The increasing number of SN surveys allows to increase the number of discovered SNe and detailed datafrom the very early epoch after explosion, especially those missions which have the short cadences (e.g. PTF).
Given the low-mass preference of the stellar initial massfunction, a large fraction of PISNe that will be observed in thelocal Universe could resemble our 150 M⊙ model, which represents PISNe from the low-mass end of the PISN regime. ThesePISNe are predicted to have the following characteristics:
1. The progenitors are likely to be red-supergiants having very
extended envelopes (R ∼ 3000 R⊙ ), if they can retain somefraction of the hydrogen envelopes by the time of explosion.
Our 150 M⊙ model has the final mass of 94 M⊙ and the envelope mass is 29 M⊙ , which is significantly smaller than in
the corresponding case of zero or extremely low metallicity(∼ 70 M⊙ ). The hydrogen mass fraction in the envelope is
only about 0.25.
11

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae

to our high mass PISN Model 250M. This concerns the light
curve shape, the peak luminosity, the photospheric velocity andthe bulk ejecta masses.
We suggest the following criteria to distinguish high mass
PISN from CCSN:

25
Photospheric Velocity, 1000 km/s,

slsn Ic PS1−10ky
20slsn Ic PS1−10awh
slsn Ic SN2010gx

15

slsn Ic PTF09cnd

10

slsn Ic SN2007bi
5

250M
0
0

100

200
300
Time, days

400

500

Fig. 17: The photospheric velocity of our 250 M⊙ PISN modeland of several SLSN Ic. The observed data are taken from
Young et al. (2010); Chomiuk et al. (2011). SN 2007bi points
show the lower velocity limit measured from O I λ 7774 which
we use as a best estimate for the photospheric velocity. The observed data are shifted to the maximum phase of the theoreticalcurve (day 175). The bold part of the theoretical curve (green)
covers the maximum phase (from day 175) and the successive
decline phase.
2. The resulting PISN would appear to be a bright type IIP supernova like SN 2009kf. Its luminosity at the visual maximum would be typically higher by 2-3 magnitudes than average SNe IIP, although the total amount of radioactive nickel
would be more or less similar to those from usual hydrogenrich core-collapse supernovae (∼ 0.05 M⊙ ), depending on
the final mass of the progenitor.
3. The plateau duration would be similar to those of ordinary
SNe IIP, but much shorter than in the corresponding case at
extremely low metallicity because of the relatively low massof the envelope and the low hydrogen mass fraction.
4. The shock breakout duration would be somewhat longer (∼6 hrs) and redder (0.07 keV) than those of ordinary SNe IIP.
5. The photospheric color temperature would be systematicallyhigher than those of ordinary SNe IIP, and its evolution
would look quite similar to that of SN 2009kf, which is anunusually bright SN IIP with a NUV-excess.
6. Because of the very large radius of the progenitor, the photospheric velocity at early times would be systematically lower
than those of ordinary SNe IIP (Figure 15).
We also conclude that some observed luminous SNe Ic could
have emerged from a pair instability explosion. Careful and deep
photometric and spectroscopic observations would help to differentiate a pair instability explosion from SN Ic, in particular forthe rise epoch and the tail. A general property of PISN explosions from the high mass regime is a slow light curve evolution
due to massive ejecta. This causes a long rise to the peak luminosity and a long transition to the radioactive tail.
It was previously noted (Scannapieco et al. 2005;
Kasen et al. 2011; Whalen et al. 2013a; Dessart et al. 2013) thata PISN from the high mass end of the PISN regime does notresemble any of the observed supernovae so far. However, wedemonstrated that SLSNe 2007bi and PTF10mnm may fit well12

1. A short precursor in U, B, V-bands at about −19 mag lasting
less than 40 days which can appear itself as a SN long before(e.g. half a year – a year before) the main maximum.
2. The pronounced rise time is larger than 200 days, which issignificantly longer than for ordinary SN Ic.
3. A PISN may evolve from hydrogen-rich to hydrogen-poor
type.
4. The nebular luminosity is powered by radioactive nickel decay and determined by the amount of produced nickel. Largeamounts of radioactive nickel, tens of solar masses, producedin PISN significantly exceed typical 0.05 – 0.5 M⊙ of nickel
left by ordinary SNe Ic.
5. The photospheric velocity is lower than the velocities of
SNe Ic during the whole evolution. On top of that the PISN
photospheric velocity has a peculiar evolution during the rise
to maximum light.
Increasing SN statistics allows to discover the brightest
SNe together with others (Kaiser et al. 2002; Ivezic et al. 2008;
Law et al. 2009). According to Langer et al. (2007) one pairinstability explosion in the local Universe occurs among one
thousand core collapse SNe. At present the number of discovered SNe per year surpasses one thousand, therefore, we expect several PISNe among the large number of discovered SNe.
However, their unambiguous identification may be challenging,which we hope to facilitate with our present study.
Acknowledgements. We thank Stephen Smartt, Matt Nicholl, Luc Dessart, andTakashi Moriya for fruitful and useful discussions, Nikolay Pavlyuk for providing observed light curves, Matı́as Jones, Cosimo Inserra, Maria-Teresa Botticellafor providing the observed data, Daniel Kasen and Luc Dessart who provided
the data from their simulations. SB acknowledges the support by the grant of
the Russian Federation government 11.G34.31.0047 and also partial support by
grants for Scientific Schools 5440.2012.2, 3205.2012.2, and joint RFBR-JSPS
grant 13–02–92119.

References
Abel, T., Bryan, G. L., & Norman, M. L. 2002, Science, 295, 93
Ambwani, K. & Sutherland, P. 1988, ApJ, 325, 820
Arnett, D., Fryxell, B., & Mueller, E. 1989, ApJ, 341, L63
Arnett, W. D. 1988, ApJ, 331, 377
Baraffe, I., Heger, A., & Woosley, S. E. 2001, ApJ, 550, 890
Barbon, R., Ciatti, F., & Rosino, L. 1979, A&A, 72, 287
Barkat, Z., Rakavy, G., & Sack, N. 1967, Physical Review Letters, 18, 379
Benetti, S., Nicholl, M., Cappellaro, E., et al. 2013, ArXiv e-prints, 1310.1311,
submitted to MNRAS
Bersten, M. C., Benvenuto, O., & Hamuy, M. 2011, ApJ, 729, 61
Bersten, M. C. & Hamuy, M. 2009, ApJ, 701, 200
Bisnovatyi-Kogan, G. S. & Kazhdan, Y. M. 1967, Soviet Ast., 10, 604
Blinnikov, S., Lundqvist, P., Bartunov, O., Nomoto, K., & Iwamoto, K. 2000,
ApJ, 532, 1132
Blinnikov, S. I., Röpke, F. K., Sorokina, E. I., et al. 2006, A&A, 453, 229
Blinnikov, S. I. & Tolstov, A. G. 2011, Astronomy Letters, 37, 194
Botticella, M. T., Trundle, C., Pastorello, A., et al. 2010, ApJ, 717, L52
Bromm, V., Coppi, P. S., & Larson, R. B. 1999, ApJ, 527, L5
Calzavara, A. J. & Matzner, C. D. 2004, MNRAS, 351, 694
Chatzopoulos, E., Wheeler, J. C., & Couch, S. M. 2013, ApJ, 776, 129
Chen, K. J., Heger, A., & Almgren, A. 2012, in Astronomical Societyof the Pacific Conference Series, Vol. 453, Advances in Computational
Astrophysics: Methods, Tools, and Outcome, ed. R. Capuzzo-Dolcetta,
M. Limongi, & Tornambe
Chen, K.-J., Heger, A., Woosley, S., Almgren, A., & Whalen, D. 2014, ArXiv
e-prints, 1402.5960, submitted to ApJ
Chomiuk, L., Chornock, R., Soderberg, A. M., et al. 2011, ApJ, 743, 114

A. Kozyreva et al.: Observational properties of low redshift pair instability supernovae
Clocchiatti, A., Benetti, S., Wheeler, J. C., et al. 1996, AJ, 111, 1286
Cooke, J., Sullivan, M., Gal-Yam, A., et al. 2012, Nature, 491, 228
Crowther, P. A., Schnurr, O., Hirschi, R., et al. 2010, MNRAS, 408, 731
Dessart, L. & Hillier, D. J. 2010, MNRAS, 405, 2141
Dessart, L. & Hillier, D. J. 2011, MNRAS, 410, 1739
Dessart, L., Hillier, D. J., Li, C., & Woosley, S. 2012a, MNRAS, 424, 2139
Dessart, L., Hillier, D. J., Waldman, R., Livne, E., & Blondin, S. 2012b,
MNRAS, 426, L76
Dessart, L., Livne, E., & Waldman, R. 2010, MNRAS, 405, 2113
Dessart, L., Waldman, R., Livne, E., Hillier, D. J., & Blondin, S. 2013, MNRAS,
428, 3227
Drout, M. R., Soderberg, A. M., Gal-Yam, A., et al. 2011, ApJ, 741, 97
Eastman, R. G. & Pinto, P. A. 1993, ApJ, 412, 731
El Eid, M. F. & Langer, N. 1986, A&A, 167, 274
Falk, S. W. & Arnett, W. D. 1977, ApJS, 33, 515
Fowler, W. A. & Hoyle, F. 1964, ApJS, 9, 201
Fraley, G. S. 1968, Ap&SS, 2, 96
Friend, D. B. & Castor, J. I. 1983, ApJ, 272, 259
Gal-Yam, A. 2012a, Science, 337, 927
Gal-Yam, A. 2012b, in IAU Symposium, Vol. 279, Death of Massive Stars:
Supernovae and Gamma-Ray Bursts, 253–260
Gal-Yam, A., Mazzali, P., Ofek, E. O., et al. 2009, Nature, 462, 624
Grasberg, E. K., Imshenik, V. S., & Nadyozhin, D. K. 1971, Ap&SS, 10, 3
Grasberg, E. K. & Nadezhin, D. K. 1976, Ap&SS, 44, 409
Hamuy, M. 2001, PhD thesis, The University of Arizona
Hamuy, M. 2003, ApJ, 582, 905
Heger, A., Fryer, C. L., Woosley, S. E., Langer, N., & Hartmann, D. H. 2003,
ApJ, 591, 288
Heger, A. & Woosley, S. E. 2002, ApJ, 567, 532
Herzig, K., El Eid, M. F., Fricke, K. J., & Langer, N. 1990, A&A, 233, 462
Imshenik, V. S. & Nadezhin, D. K. 1965, Soviet Ast., 8, 664
Imshennik, V. S. & Nadezhin, D. K. 1989, Astrophysics and Space Physics
Reviews, 8, 1
Imshennik, V. S. & Utrobin, V. P. 1977, Soviet Astronomy Letters, 3, 34
Inserra, C., Smartt, S. J., Jerkstrand, A., et al. 2013, ApJ, 770, 128
Ivezic, Z., Tyson, J. A., Acosta, E., et al. 2008, ArXiv e-prints
Joggerst, C. C. & Whalen, D. J. 2011, ApJ, 728, 129
Joggerst, C. C., Woosley, S. E., & Heger, A. 2009, ApJ, 693, 1780
Jones, M. I. 2008, PhD Thesis, ArXiv e-prints, 0810.5538, 104 pp.
Jones, M. I., Hamuy, M., Lira, P., et al. 2009, ApJ, 696, 1176
Kaiser, N., Aussel, H., Burke, B. E., et al. 2002, in Society of Photo-Optical
Instrumentation Engineers (SPIE) Conference Series, Vol. 4836, Survey andOther Telescope Technologies and Discoveries, ed. J. A. Tyson & S. Wolff,
154–164
Kasen, D. & Bildsten, L. 2010, ApJ, 717, 245
Kasen, D., Thomas, R. C., & Nugent, P. 2006, ApJ, 651, 366
Kasen, D. & Woosley, S. E. 2009, ApJ, 703, 2205
Kasen, D., Woosley, S. E., & Heger, A. 2011, ApJ, 734, 102
Kozyreva, A., Yoon, S.-C., & Langer, N. 2014, submitted to A & A
Krtička, J. & Kubát, J. 2006, A&A, 446, 1039
Kudritzki, R. P., Pauldrach, A., Puls, J., & Abbott, D. C. 1989, A&A, 219, 205
Kurucz, R. L. 1991, in NATO ASIC Proc. 341: Stellar Atmospheres - Beyond
Classical Models, ed. L. Crivellari, I. Hubeny, & D. G. Hummer, 441
Langer, N. 2009, Nature, 462, 579
Langer, N. 2012, ARA&A, 50, 107
Langer, N., Norman, C. A., de Koter, A., et al. 2007, A&A, 475, L19
Law, N. M., Kulkarni, S. R., Dekany, R. G., et al. 2009, PASP, 121, 1395
Li, C., Hillier, D. J., & Dessart, L. 2012, MNRAS, 426, 1671
Lunnan, R., Chornock, R., Berger, E., et al. 2013, ApJ, 771, 97
Modjaz, M., Li, W., Butler, N., et al. 2009, ApJ, 702, 226
Mokiem, M. R., de Koter, A., Vink, J. S., et al. 2007, A&A, 473, 603
Moriya, T., Tominaga, N., Blinnikov, S. I., Baklanov, P. V., & Sorokina, E. I.
2011, MNRAS, 415, 199
Moriya, T., Tominaga, N., Tanaka, M., Maeda, K., & Nomoto, K. 2010, ApJ,
717, L83
Nadyozhin, D. K. 2003, MNRAS, 346, 97
Nakamura, F. & Umemura, M. 2001, ApJ, 548, 19
Nicholl, M., Smartt, S. J., Jerkstrand, A., et al. 2013, Nature, 502, 346
Ohkubo, T., Nomoto, K., Umeda, H., Yoshida, N., & Tsuruta, S. 2009, ApJ, 706,
1184
Omukai, K. & Palla, F. 2003, ApJ, 589, 677
O’Shea, B. W. & Norman, M. L. 2006, ApJ, 648, 31
Pinto, P. A. & Eastman, R. G. 2000, ApJ, 530, 744
Popov, D. V. 1993, ApJ, 414, 712
Rakavy, G. & Shaviv, G. 1967, ApJ, 148, 803
Scannapieco, E., Madau, P., Woosley, S., Heger, A., & Ferrara, A. 2005, ApJ,
633, 1031

Shigeyama, T., Nomoto, K., Hashimoto, M., & Sugimoto, D. 1987, Nature, 328,
320
Smartt, S. J. 2009, ARA&A, 47, 63
Timmes, F. X. 1998, http://cococubed.asu.edu/code_pages/net_torch.shtml
Timmes, F. X. 1999, ApJS, 124, 241
Tolstov, A. G., Blinnikov, S. I., & Nadyozhin, D. K. 2013, MNRAS, 429, 3181
Tominaga, N., Morokuma, T., Blinnikov, S. I., et al. 2011, ApJS, 193, 20
Tsvetkov, D. Y. 1994, Astronomy Letters, 20, 374
Tsvetkov, D. Y. & Pavlyuk, N. N. 2013, http://dau.itep.ru/sn/node/72
Tsvetkov, D. Y., Pavlyuk, N. N., Bartunov, O. S., & Pskovskii, Yu, P. 2010,
http://stella.sai.msu.su/˜pavlyuk/snlcurve/
Vink, J. S. & de Koter, A. 2005, A&A, 442, 587
Vink, J. S., de Koter, A., & Lamers, H. J. G. L. M. 2001, A&A, 369, 574
Vink, J. S., Muijres, L. E., Anthonisse, B., et al. 2011, A&A, 531, A132
Whalen, D. J., Even, W., Frey, L. H., et al. 2013a, ApJ, 777, 110
Whalen, D. J., Even, W., Smidt, J., et al. 2013b, ArXiv e-prints, 1312.5360,
submitted to ApJ
Whalen, D. J., Fryer, C. L., Holz, D. E., et al. 2013c, ApJ, 762, L6
Woosley, S. E. 1988, ApJ, 330, 218
Woosley, S. E. 2010, ApJ, 719, L204
Woosley, S. E., Heger, A., & Weaver, T. A. 2002, Reviews of Modern Physics,
74, 1015
Woosley, S. E., Kasen, D., Blinnikov, S., & Sorokina, E. 2007, ApJ, 662, 487
Yoon, S.-C., Langer, N., & Norman, C. 2006, A&A, 460, 199
Yoon, S.-C., Woosley, S. E., & Langer, N. 2010, ApJ, 725, 940
Young, D. R., Smartt, S. J., Valenti, S., et al. 2010, A&A, 512, A70
Young, T. R. 2004, ApJ, 617, 1233
Yusof, N., Hirschi, R., Meynet, G., et al. 2013, MNRAS, 433, 1114

13