Supernovae associated with a Gamma-Ray Bursts:
disk wind in the collapsar model
Tomoyasu Hayakawa*, Keiichi Maeda** Department of Astronomy, Kyoto Uni

1Levan +2014

Gamma-Ray Bursts (GRBs)
L ,iso ⇠ 1051 54 erg · s 1

tduration ⇠ a few ⇥ 1

10sec

Bipolar like ejecta

Supernovae (SNe)
Lbol ⇠ 1042 erg · s 1
Ek ⇠ 1051 erg

A death of massive stars

NASA's Goddard Space Flight Center2

Moriya + 2016

Discovery of SNe associated with a GRB
In 1998, SN1998bw was found in the error box of GRB980425(Galama +1998, Iwamato +1999)

About 20 events have been detected
All of them are type Ic SNe (broad-lined Ic, Core Collapse SNe) w/

Ek ' 2 ⇥ 1052 erg ' 10 ⇥ Ek,canonicalEnergy by the GRBs are widely ranged
Toy +20163

Collapsar model(Woosley 1993, MacFadyen & Woosley 1999, Popham+1999)

Collapse of rapidly rotating massive stars with formingBlack Hole (BH) accretion disk (hyper accreting BH)

T.Totaniʼs HP, University of Tokyo4

Strong outﬂows in hyper accreting BH

16,000 [km](MacFayden & Woosley1999)

X like shape
Disk wind(~0.1c)→ supernova?
Rotational axisJet(~c)→ GRB?

BH + disk

16,000 [km]1822

color:log (energy density) [erg/g]5

Problems
Only the core region is calculated without envelope in the collapsar model
Envelope would play an important role to GRB jet and SN explosion
The relation between GRBs and SNe is not clear

Our study

Motivation & Goal

外層envelope

We have to construct self-consistent model.
→ Are GRB-SNe really explainedby the collapsar model ?
Can we explain the diversity of GRB-SNe
by adopting the diﬀerent progenitors ?

calculated region in the previous work

~ 108 9 cm

~ 1010 11 cm

6Method: evolution of the BH, disk & envelope(Bardeen + 1972, Kohri + 2005, Woosley & Heger 2006, Kumar + 2008)

Mg,Ne,O,CSiFe
Wolf Rayet starex) mass evolution

Initial condition
density structure (Woosley & Heger 2006)

10.7, 13.8, 21.1, 27.9M
0.2/rangular velocity

19 modelsnearly breaking up to whole collapse

free fall rate from the envelope to the diskmshellṁfb 't↵

accretion rate from the disk to BH

mdiskṁacc 'tacc

mass loss rate by the disk windṁwindṁdisk = ṁfbṁBH = ṁaccṁacc ṁwind7

Method: estimate of the jet energy & the disk wind energy(Blandford & Begelman 1999, Piran 2004, Kohri + 2005, McKinney 2005, Kumar + 2008,
Zalamea + 2011)

Jet luminosity
BZ process:ﬁtting formula w/ accretion rate & BH spin based on GRMHD (McKinney 2005)

Disk wind
the parameterized way( Piran 2004, Kohri + 2005, Kumar +2008)

Ėwind 'Z routerrin2Ṁwind vesc
dr8

Method: Judgment of succession of GRB jet and SN(Maeda & Tominaga 2008)

We regard that the explosion succeed only when the pressure
overwhelm the ram pressure from the infalling material

GRB jetPram

Pjet > Pram

SN explosion

Pwind > Pram

Pjet
Pwind

9Quasi spherical wind cannot expel the envelopepressure at outer disk
GRB jet:pressure [dyn]1030
102810261024
10

easily penetrate the envelope
because of the collimation

Pram
Pwind
Pjet

GRB jetジェット Disk wind:envelopecannot expel the envelope
if we assume the spherical wind2210201018
1016

Disk wind
100

1000

time [s]Mprogenitor ' 14M
Jstandard = 3 ⇥ 1051 [g · cm2 · s 1 ]10Collimated disk wind can expel the envelope
Collimated wind which does not prevent infalling in thesame time

✓wind = 30

Spherical

pressure [dyn]

1030

Pram
Pwind
Pjet

1028
1026
1024

envelope

1022
1020

1030
1028
1026

envelope

1024
1022

disk wind1020

18101016

1016
1000

10

Pram
Pwind

100

disk wind

18time [s]

102

103
11

Dependence on the progenitor
Our results mainly depends on the angular momentumof the progenitor rather than the mass

Jstandard = 3 ⇥ 1051 [g · cm2 · s 1 ] 12

Expected counterparts by Collapsar model
Nearly breaking up progenitors

5 ⇥ Jstandard

SNe with energetic GRB

Ejet1052 erg

Standard progenitors in theprevious⇠ Jstandard
Weak or canonical SNe w/ GRB
Nearly whole collapse  0.3 ⇥ Jstandard
low luminosity GRBs w/o SNe13

Summary
GRB-SNe have been found since 1998.
One of the candidate is collapsar model (collapse of massive star)
Only the core region is calculated in the previous

We constructed self-consistent collapsar model

We found that there need to be two conditions→ collimated disk wind
→ still active engine by infalling envelope

Nearly breaking up progenitors canexplain a part of observations
Expected counterparts mainly depends on
the progenitorsʼ angular momentum
14

Appendix

15

103

101010108614200.1-5 -4 -3 -2 -1 0 1 2 3101010101010101010
Mejecta [Msolar]

1024⇥Jstandard

Mejecta [Msolar]

102

NisolarDisk wind energy(10M [M]50erg)

Collimated wind case, our model can reveal therelation between kinetic energy and ejected massby changing angular momentum.

1
12TI [10.7Msolar]
16TI [13.8Msolar]
35OB [21.1Msolar]
35OC [27.9Msolar]
GRB980425/SN1998bw
GRB030329/SN2003dh
GRB031203/SN2003lw
GRB060218/SN2006aj
GRB091127/SN2009bz
GRB100316/SN2010bh
GRB120422A/SN2012bz
GRB130427A/SN2013cq
GRB130702A/SN2013dx
GRB140606B/iPTF14bfu

68ejected Mmass(solarejecta [Msolar] mass)

0.1

10Jstandard = 3 ⇥ 1051 [g · cm2 · s 1 ]16

Dependence on the progenitors
The results mainly depending on the angular momentum
Some correlations found by the observations are explained by ourmodel17

18

Method: nucleosynthesis in the disk and the envelope(Surman + 2006, 2011, Maeda & Tominaga 2008)

Estimate the temperature and entropy
in both of the wind and the envelope→ rough estimate of 56Ni
9Twind < 5 ⇥ 10 K
no production

Twind > 5 ⇥ 109 K
Ni production depending on entropy
high: He rich
low: Ni rich
19

What model is suitable for GRB-SNe ?
It is needed for the disk to be fed by the falling from envelop toexplain the GRB-SNe.

20

Discussion:
How to explain SNe w/ weak GRB like GRB980425/SN1998bw ?

Ejet ! Ewind

21

Discussion:
How to explain SNe w/ weak GRB like GRB980425/SN1998bw ?
We have to treat the jet carefully
The cocoon would spread inside theColle + 2017
envelope.

Ejet ! Ewind

22