Magneto rotational explosion of a massive star
supported by neutrino heating in full 3DGR simulationand its nucleosynthesis• Takami Kuroda (TU Darmstadt)• Moritz Reichert (TU Darmstadt)• Marius Eichler (TU Darmstadt)• Almudena Arcones (TU Darmstadt)• Tomoya Takiwaki (NAOJ)• Kei Kotake (Fukuoka Univ.)
理論懇, 国立天文台, 25-27/12/2019

(1)The standard explosion mechanism
Neutrino driven explosion,
Colgate&White’66, Bethe&Wilson’85
For reviews, Janka’12, Kotake+,’12, Burrows+,’13~99% of internal energy
is radiated away
via neutrinos (~1053ergs)—> ~10% energy depositionis enough to explain
Eexp~1051ergs
Takiwaki+, ‘16

O’Connor & Couch, ‘18

Numerical simulations
can’t fully explain
canonical explosion energies• neutrino-matter interactions?
• resolution problem?
• too short simulation time?
Vartanyan+, ‘19
Müller+, ‘17

(1)The standard explosion mechanism
Neutrino driven explosion,
Colgate&White’66, Bethe&Wilson’85
For reviews, Janka’12, Kotake+,’12, Burrows+,’13(2)If the magnetic field is strong enough
MHD explosion, • Angular momentum transfer• Mass ejection by B pressure• efficient neutrino heating
2D: Ardeljan+,’00, Kotake+,’04, Obergaulinger+,’06,’17, Burrows+,’07, Takiwaki+,’09,
3D: Mikami+, ’08;
Mösta+,’14;
Obergaulinger+,’19;

Newtonian, no neutrino, Polytropic EOS
full GR but very simplified neutrino transport
SR with M1 neutrino transport (preliminary result)

PNS

Obergaulinger+,’17

Things still to be explored• resolution problem->MRI?
• 2D artefacts ->3D non-axisymmeties• microphysics->neutrino effects
Mösta+,’14

Can the MHD explosion be the r-process site?
3D:Mösta+,’18
color: different Lnu

2D:Nishimura+,’15

Strong MHD jet can potentially produce the 3rd peak(due to low-Ye ejeta)
Neutrino radiation significantly influences on the ejecta Ye

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andtheirtheir
anti-particles),ε represents
3
Since,
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untilthethe neutrino-driven
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termevolutionForindex
ν isν omitted
below.
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energy),(e)),
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forthe BSSNradiation
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introducing
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The AstrophysicalSupplement
Series,2016toFebruary
Kuroda,Takiwaki,mmn
2009;Marek
Marek&&Janka
Janka 2009)2009) oror ∼500∼500 ms
ms inin 2D-GRet etal.al.2009;
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2
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4
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ini g (becomputedinthe(e) nm , (13)e)ò, and! previous(7) 1D
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checkthethevalidity
validityofnewcodeα(Rinijthe
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Ãij new= ecode
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Ãmijnmn−+
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ik(eγ̃) n
results
in
early
(
e
)
e
)
(
T((ea) F=i E-(eb) niE n ) +F(ge)an¶ (+F(en) n) +e)P,(mn,˜e)
postbounce
phase.
¶
g
E
+
¶
g
+
e
M
t
(e)
i
(e)
e
(e)
(e) m
where
postbounce
phase.
(13)mn
m un + H un + H um + L mn .
This paper is organized as follows. In Section 2, after we = - g aS m nm=
J
u
(3 )
m n
.
() 14mn) .
(e)
mijun + (H(eH
) n um +(eLµνe) µνThis paper is organizedh as
follows.
In
Section
2,
after
we
e)
m− Ln )K = −∆α + α(Ã Ãij + K 2 /3) + 4πα(n (n
=
J
u
u
+
(3 )
(∂
T
+
γ
γ
γ
T
)
(14)
(
e
)
(e)
µ ν (total)iµ jν (total)(e)(e)
shortly introduce theformulation
mn Ht(e) H(eβof) the GR transport ijscheme,
2formulation¯
shortly
introduce
the
of
the
GR
transport
scheme,F(e) º. i of hydrodynamics(8µν) andm =readily
k a
ij
2 k
we describe the governing
equations
From theabove
two equations,
onencan
see
that
the
total
(
1
a
,
b
In
the
above
equations,is a unit vector
(∂
−
β
∂
)
Γ̃
=
16πγ̃
γ
n
T
J
t
iµ
ν
k
m
k)a
(
e
)
(total)weneutrino
describetransport
the governing
equationsofhydrodynamics
and
n
=
(
1
a
,
b
)themis a unit vector
In
the
above
equations,in detail. Some practical implementationenergy(sumofmatterandneutrinos)
contained
inorthogonal
tothespace-like
hypersurface
andu ism the four
2 ij
neutrinotransportindetail.
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i orthogonal
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to
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−2α(
γ̃
K
−
6
Ã
φ
−
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Ã
)
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quantities
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In Equation (8), hmn º gmn + um un is the projection operator.
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computational
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Enm º Indx theg (ttruncated+ ò deE(e) )moment
velocity
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schemes
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leptonandconservative
momentumare given
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velocity
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formalism
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as In
long
as
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Aswill discusslater, by the deﬁnitionof F̄(e) in Equation(8),
1
2ouri basic
j 1981;
Shibataetal.
2011),
evolves
jk
i
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k
j
i
j
i
ij
as Section
lepton 3.number,energy,momentum+γ̃
βare+ givenγ̃ βwith− Γ̃ β,j + Γ̃ β,j + β Γ̃,j − 2Ã α,j ,(15),jk,kj inThe mainresultsand
anddetailed
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1981;
Shibataetal.
2011),
evolves radiation
ﬂux throughthenumerical
andmomentumspace
one can appropriately
reproduce
severalimportantneutrino
3
3
energy (Em(e)) and radiation ﬂux (F(e) )a inboundaries
aone
conservative
form
Section3.
The
main
results
anddetailed
comparisons
withprevious studies
are presented
in Section
5. rapidly
Note that(i.e., ò denergy
˜ibehaviors,for example,
neutrino
trapping
in
the
e
[
¶
(
e
M
n
)]
=
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).
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denotes
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and
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P
previous
studiesarepresented
inSection
5.
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(
e
)
geometrizedunit
systemisusedinSections
2
and
3,
i.e.,
the
mn
The vector
leptonnumberconservationneeds
toanalyticbesatisﬁedwith relation
collapsing opaque core.
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solve
the(−α,simultaneoustrace-free
operator,nµ2nd=0) is 3,thei.e.,time-likeunit
normaltothe t = constanttime
slices.
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P
GRMHD(9variables):
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and
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GR-Rad
(4x3xNvariables):3rdand 2ndene(e)
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systemisusedinSections
2
and
the
E
Equation(6)).
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evolution
equationsfor
speed of (7)–(8)light, tothe
gravitational
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andthePlanck(ethe) and F(e) are
good
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becauseit
determines
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Equation (13),constantthe explicit
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Equation(6)).
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for
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speed
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postbounce
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here
explain
how
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treat
c
=
G
=
h
=
1
,
and
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units
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aresettounity:
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equationsarewritteninaconservative
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code.
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equations
¶
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E
+
¶
g
b
g a¶e (eM˜ (e) nm )indicesfrom
1 to 3.
areusedin Section
5. Greek indices
run
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0
to
3
and
t
(
e
)
i
(e)
(
e
)
k
k
k
kl
i
m
= ∂i ∂j α −(9Γ̃γ̃ij γ̃ ∂l φ ∂k α. i
) ij + 2 δj ∂i φ + δ¶i ∂j φg −iE (16)
˜
E
+
¶
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(
a
F
b
)
+
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a
¶
(
e
M
ij
m
i
indicesfrom 1 to 3.¶t r* + ¶i (r*v ) = 0,
t⎛
)
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e
(e) nm )(4)
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Pdij )(4 )⎝=m u g⎠(aP(e⎝) Km
ij u- ⎠F(e) ¶i a - aS(e) nm ) ,and
2.
FORMALISM
This
starts= -section
g [S 0 ¶Sk ¶i ba kbrief- 2asummary
Skk ¶i f of the basic equationsde m
i a -withga(S(ne, e) - S(¯mne, e) ) um ,(15) m
=
and
ò
and
the
numerical
schemesofGRradiationhydrodynamics.
jjThis section-4starts
with
a
brief
summary
of
the
basic
equations⎤emf (S - Pg ) ¶ g jk 2 + a¶t g F(e)i + ¶j g (aP(e)i - b F(e)i ) - g a¶e (eM˜ (e) gim )+ ae our
d
e
S
g
,
(
10
)
m
jkprevious
jk work
i˜
i
⎥
(
)
e
Following(Kurodaetal.
2012),
ourcodeò
⎦and the numerical schemes of GR radiationhydrodynamics.
mjjFab ) - jkg a¶ (eM
˜
0¶
i
g
F
+
¶
g
(
a
P
b
j
(
e
)
(
e
)
t
j
im )
(
e
)
e
consistsofthefollowing
threeparts,
wheretheevolution
¶
(
q
g
a
)
+
¶
(
q
g
a
)
g
a
¶
(
e
q
)
u
(
e)mgg
i iE(e(e))¶i a + F(e) ij ¶i b e + ((eat (e) =g [) i 2b) Pa(e) ¶i g jk + aS
Following our previous i work (Kurodaetal.
2012),
ourcode(e) im ] ,equations
neutrinotheradiationaregtmetric,(tv +threeP (v i +b i )) where¶t of+following¶i ghydrodynamics,andg a gm[ - E(e) ¶i a + F(e) ¶i b j + (a 2) P jk ¶i g jk + aS m(5gconsistsoftheparts,
evolution=(e() 16)(e) ) im ] ,j=S(e) um ,solved.
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of
them
in
an
operator-splittingmanner,k is solved
˜f4
ij
equations of=metric,hydrodynamics,andradiation are
g [aKS(Sij - Pgijneutrino)Aek 3 + aebut the system evolves
self-consistently
as a whole, satisfying Inrespectively.
(5 )GRMRHDone
solvesthese
Here code,
γ is the determinantof the three
metric3
solved. Each of themissolvedinanoperator-splittingmanner,⎤m
the Hamiltonian
momentum
Regardinga+adeS(e) nm ⎥⎦constraints.
,(11) thewhere g º det (g ) and S m is the source term for neutrino matter- Si D iandòbutmetric
the systemevolves
self-consistentlyasawhole,
satisfying(e) γ (26+12*N
ij
systemswithrespectively.
Hereis the determinant
the three metricene)ofvariables
evolution, the spatial metric gij (in the standard (3+1)aaba the currently implementeda1
the Hamiltonian
andmomentumconstraints.
Regardingtheinteractions(see
AppendixAform ("(e) u + (e) ) ,qººe ) Tand(17neutrino)(e) ubS=
2 = - a 2dt 2 +g (dx i + b idt )(dx j + b jdt ) , with α(e) detisthesourceterm
formatter
g
(
g
m
form:
m
ds
d
e
(
e
)
ij
mab
mab
m
m
satisfying
theHamiltonian,i spatial
ija
˜
(in
the
standard(3+1)
metricthemetricgprocesses).
isdeﬁnedby,where
M̃
M
º
M
u
M
¶t (revolution,
Y
)
+
¶
(
r
Y
v
)
=
g
m
(
S
S
)
u
,
b a
i
e
u ò
ij (ne, e)(e )(e)for the(e) currently(e )(¯ne, e) minteractions
implemented*i ebeing*2 lapseab
gb a Appendix
a b A ab
-1T(seeeitheandshift,
respectively)
andits
extrinsic
and
b
i
j
j
2
2
q
º
e
h
=
(
u
+
$
)
,
(
18
)
e) & no-monopole(e)m g rank (moment(eofdenotes
the third
distribution mab(e)momentum,
form: ds = -a dt +gij (dx + b dt )(dx + b dt ),(12withαm) theneutrinomab
˜)
processes).
isdeﬁned
by
M̃
M
º
M
u
are
evolved
using
the
BSSN
formulation(Shibata
curvatureKb a ,where M(e)ij(e )(e) the explicit
(e )
i
k i
i k
i
function(seeShibata
et
al.
2011
for
expression).
a , $ab ) º e-1 (J , H a, Lab ). The conservation equabeing ∂thelapse
and its extrinsic
and&bNakamura= ∂Baumgarte(B shift,v − respectively)
B& vShapiro)
1995;
1999;see
Kurodawith (",denotes
tB
kand
the
third
rank
momentoftheneutrino
distribution
constraints
By adopting the M1 closure scheme, the radiation pressurer evolved
g W , using
Si = rhWu
where Krij =, Sij =,
rhui uj + Pg(Shibata
iBSSN
are
the
formulation
curvatureijtion for neutrinos(16) corresponds to Equation (3.22) (divided
et al. 2012,* 2014 for more details).

BSSN equa)ons (17 variables): 4th order accuracy in space and )me

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io
n

t
de

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in

m

m

at
ur
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m

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rv

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ur
at

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io
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es

cr

neutrino cooling/heating

The basic equations for neutrino transport
neutrinoTμν
= Enμnν + Fμnν + Fνnμ + Pμν

advection

gravitational source

Shibata+’11, TK+’16(E, F, P: 0th, 1st, 2nd momenta (in Euler))

gravitational redshift/Doppler

neutrino-matter interaction

TK+,’16

Numerical setups• 20Msun model (WHW07)• dx~458m@center, ~3.2km@R=100km• Basic neutrino opacities based on Bruennʼ85 (same as TK+,ʼ18)• Nene=12 bins (1<ε<300MeV)• 3 models(R0B00, R1B00, R1B12)• SFHo (Steiner+ʼ13)• Cylindrical2 rotational law
R0Ω = Ω0 2
ϖ + R02Ω0 = 1(rad/s)(βb ∼ 1%)

• Dipole-like B

B0 R03
Aϕ =
Rsinθ
3
3
2 R + R0

B0 = 1012G (βmag,b ∼ 1%)• CT method for divB=0• XC40 @ NAOJ

TK, Kei Kotake, T. Takiwaki, & F.-K. Thielemann2018, MNRAS Letterlog(Pmag/Pgas)

Entropy

Rotating magnetized model (R1B12)
Tpb=55ms
100ms
250ms

2D-3D comparison
Entropy

Takiwaki+,’09

log(Pmag/Pgas)

Obergaulinger+,’17

Mösta+,’14

Rotating model

Non-rotating model

Non-magnetized models

Energetics

Shock evolution

Diagnostic energy

Rotation and Magnetic fields facilitate the explosion

TITLE

5

TITLE

Neutrino heated? or magneto-driven?

60°
EquatorialPole• Rotation & B increase Mgain and Qdot
• For MHD model• Equatorial
expansion
is supported by ν-heating
Fig. 5.—In each set ofpanels,• Prompt bipolar outflow is due to magnetic field• Later by ν-heating τadv /τheat > 1

τadv /τheat > 1
τadv /τheat < 1

Neutrino emission (angle dependence)νebar-νeνx

Neutrino emission (angle dependence)
x-z

y-z

R1B00
equatorial(m=1) Spiral SASI leads tomodulated Lnu/Enu reflecting
the SASI mode frequency

Takiwaki+,’18Ejecta structure

PNS

low Ye (Pmag supported)Ejecta structure

PNShigh Ye (neutrino heating)−νen → e p

Selection rule
(1)Ye and entropy unchanged (and low peak temperature),such that the progenitor composition does not change much

(2) Ye unchanged, but high peak temperature, with explosive nucleosynthesis(3) Ye once <0.45 and at the end >0.38(4) Ye always <0.45 and entropy<15(5) Ye always <0.45 and entropy>15(6)T9lt8: final temperature (averaged in time of ~10ms) decreases below 8GK.

Entropy

Scattering in S-Ye planeYeEntropy

Scattering in S-Ye plane

ta
s
Mö

8
1
+,’

Ye

Due to the interaction νen → e −p
Ye & S tend to become higher

Mösta+,’18Ejecta distributionEjecta distribution

Cat2,3

Cat4

Cat5

Cat1

Nucleosynthesis (1st peak)Cat2,3Cat4Cat5Reichert, Eichler, TK+, in prep.

Cat1

Nucleosynthesis (weak 2nd peak)Cat2,3Cat4Cat5Reichert, Eichler, TK+, in prep.

Cat1

Nucleosynthesis (2nd + weak 3rd peak)Cat2,3Cat4Cat5Reichert, Eichler, TK+, in prep.

Cat1

Nucleosynthesis

Cat2,3Cat4Cat5Reichert, Eichler, TK+, in prep.

Cat1

Nucleosynthesis (1st peak)

Reichert, Eichler, TK+, in prep.

Not enough to produce 3rd peakconsistent with Mösta+, ’18

1.

2.
3.
4.

Summary
SN simulations are becoming more realistic(full GR, 3D effects, sophisticated neutrino opacities)—> more reliable messages from SNe———(GWs, neutrinos, and heavy elements)
In MHD model, the polar/equatorial explosion is boosted
mainly by B/neutrinos.
2nd & weak 3rd peak elements can be produced withsignificant B/neutrino effects depending on the trajectory
Temporal modulation in neutrinos reflecting the SASI
motions.