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連星中性子星合体からの電磁波
仏坂健太 (京都大学)
共同： 大川博督(CENTRA)、久徳浩太郎(UWM)、 谷口敬介(東大)、田中雅臣、和南城伸也(国立天文台)、 木内建太、柴田大、関口雄一郎、長倉洋樹(京大基研)、 井岡邦仁(KEK)
重力波天文学に向けて
Advanced LIGO Advanced Virgo KAGRA
GW コンパクト連星合体 （中性子星やブラックホール）
2017〜 2016〜 2015, 16〜
GW
予想イベントレート(連星中性子星)
第一世代 (IniDal LIGO, Virgo) 第二世代 (Advanced LIGO, Virgo, KAGRA)
0.0002 〜 0.02 /yr 0.2 〜 400 /yr
Abadie et al (2010)
(これまで) (数年後)
重力波ー電磁波観測
• 第二世代重力波望遠鏡時代の宇宙物理学
ü 多数の銀河(〜数100Mpc)までカバーする。
検出閾値付近のイベントが多い➡電磁波で確認➡発見の手助け
重力波源の電磁波による追観測が重要！！
電磁波で母銀河、距離を決定➡ GW-‐photon伝播の物理
ü 波源の位置決定が苦手。
波源は中性子星？ブラックホール？または？➡電磁波から示唆
ü 重力波から合体時刻、天体の質量はわかるだろう。
重力波から粗い位置情報 ➡電磁波の観測戦略が必要
ü 有望な電磁波対応天体の予想
1. 連星中性子星合体に付随する確率が高い。
2. 現在、または将来の望遠鏡で観測可能。
3. 他の天体現象と区別可能。
ü いつ、どの波長で観測すべきか？
30
28 26
-‐2 0 2 4 6 8 10
log(L) [e
rg/s]
Log
Luminosity
(erg/s/Hz)
log(t) [s]
Merger remnant (radio)
Kilonova /Macronova (NIR)
Extended Emission (X)
GRB A[erglow (X)
Merger Breakout (X)
GRB A[erglow (visible)
GRB a[erglow (radio)
GRB (X~γ) 52
50
48
46
44
42
log(Lν) [erg/s/Hz
]
Merger Breakout (radio)
予想光度曲線 Refs: Nakar (2007)
Norris & Bonnell (2006) Sari, Piran, Narayan (1998)
Li & Paczynski (1998) Nakar & Piran (2012)
Kyutoku, Ioka, Shibata (2012) Kelley, Mandel, Ramirez-‐Ruiz (2012)
Nakamura et al (2013)
明るさ
時間
30
28 26
-‐2 0 2 4 6 8 10
log(L) [e
rg/s]
Log
Luminosity
(erg/s/Hz)
log(t) [s]
Merger remnant (radio)
Kilonova /Macronova (NIR)
Extended Emission? (X)
GRB A[erglow (X)
Merger Breakout (X)
GRB A[erglow (visible)
GRB a[erglow (radio)
GRB (X~γ) 52
50
48
46
44
42
log(Lν) [erg/s/Hz
]
Merger Breakout (radio)
予想光度曲線(4π)
時間
明るさ
30
28 26
-‐2 0 2 4 6 8 10
log(L) [e
rg/s]
Log
Luminosity
(erg/s/Hz)
log(t) [s]
Merger remnant (radio)
Kilonova /Macronova (NIR)
Extended Emission?? (X)
GRB A[erglow (X)
Merger Breakout (X)
GRB A[erglow (visible)
GRB a[erglow (radio)
GRB (X~γ) 52
50
48
46
44
42
log(Lν) [erg/s/Hz
]
Merger Breakout (radio)
予想光度曲線(4π，環境非依存)
時間
明るさ
At peak luminosity (diffusion Dme = expansion Dme)
Kilonova(理論的に予言)
ü Kilonovaとは？ Li & Paczynsky (1998) 連星中性子星合体 => 質量の数%が放射性元素として宇宙空間に放出される。 ⇒ 放射性元素の崩壊により、等方に明るく輝く。
⇒ 有望な電磁波対応天体
Nova < Kilonova < Supernova
t ~ 5days M0.01Msun
!
"#
$
%&
12 v0.1c!
"#
$
%&−12 κ10cm2g−1!
"#
$
%&
12
L ~ 5×1040erg / s f10−6#
$%
&
'(
M0.01Msun
#
$%
&
'(
12 v0.1c#
$%
&
'(−12 κ10cm2g−1#
$%
&
'(
−12
Hydrodynamics Microphysics
Kilonovaはどんな風に光るか？
エジェクタ中の光の伝播を解く。 ※放射性崩壊による加熱を取り入れる。
NS-‐NS 合体 BH-‐NS 合体 質量放出を計算
Kilonovaの光度曲線とスペクトルを求める
数値相対論 シミュレーション
輻射輸送 シミュレーション
2010 年まではとても単純なモデルしかなかった。 ➡電磁波対応天体として観測するためには、もっと詳細な計算が必要
数値相対論シミュレーション：赤道面の質量放出
300 km x 300 km 2400 km x 2400 km
Model : 1.2Msun – 1.5Msun, EOS=APR
log(density g/cc)
Hotokezaka et al. (2013)
300 km x 300 km 2400 km x 2400 km
Model : 1.2Msun – 1.5Msun, EOS=APR
log(density g/cc)
質量放出 : Mej 〜 0.01Msun, v 〜 0.2c
数値相対論シミュレーション：赤道面の質量放出 Hotokezaka et al. (2013)
300 km x 150 km 2400 km x 1200 km
Model : 1.2Msun – 1.5Msun, EOS=APR
log(density g/cc)
(x-‐z plane) 数値相対論シミュレーション：子午面の質量放出
300 km x 150 km 2400 km x 1200 km
Model : 1.2Msun – 1.5Msun, EOS=APR
log(density g/cc)
(x-‐z plane)
NS-‐NS Ejecta は比較的球に近い
数値相対論シミュレーション：子午面の質量放出
2
4
6
8
10
11 12 13 14 15
Mes
c/10-3
Msu
n
R1.35 [km]
結果：エジェクタの質量と中性子星状態方程式
中性子星半径
エジェクタ質量
Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals 9
10 11 12 13 14 15 160
0.002
0.004
0.006
0.008
0.01
0.012
Mej
ecta
[Msu
n]
R1.35 [km]11 12 13 14 15
0.005
0.01
0.015
0.02
Mej
ecta
[Msu
n]
R1.35 [km]
10 11 12 13 14 15 160.31
0.32
0.33
0.34
0.35
0.36
|v1|+
|v2| [
c]
R1.35 [km]11 12 13 14 15
0.315
0.32
0.325
0.33
0.335
0.34
0.345
|v1|+
|v2| [
c]
R1.35 [km]
Fig. 3.— Amount of unbound material for 1.35-1.35 M! mergers (top left) and 1.2-1.5 M! mergers (top right) for different EoSscharacterized by the corresponding radius R1.35 of a nonrotating NS. Red crosses denote EoSs which include thermal effects consistently,while black (blue) symbols indicate zero-temperature EoSs that are supplemented by a thermal ideal-gas component with Γth = 2 (Γth = 1.5)(see main text). Small symbols represent EoSs which are incompatible with current NS mass measurements (Demorest et al. 2010). Circlesdisplay EoSs which lead to the prompt collapse to a black hole. The lower panels display the sum of the maxima of the coordinate velocitiesof the mass centers of the two binary components as a function of R1.35 for symmetric (bottom left) and asymmetric (bottom right)binaries.
ima of the coordinate velocities of the mass centers ofthe two asymmetric binary components. As in the sym-metric case the two stars collide with a higher impactvelocity if the initial radii of the NSs are smaller.Due to the asymmetry the dynamics of the merger pro-
ceeds differently from the symmetric case (see Fig. 4).Prior to the merging the less massive binary componentis deformed to a drop-like structure with the cusp point-ing to the 1.5 M! NS (top panels). After the stars beginto touch each other, the lighter companion is stretchedand a massive tidal tail forms (middle left panel). Thedeformed 1.2 M! component is wound around the moremassive companion (middle panels). Also in the case ofasymmetric mergers the majority of the ejecta originatesfrom the contact interface of the collision, i.e. from thecusp of the “tear drop” and from the equatorial surfaceof the more massive companion, where the impact ab-lates matter (see top panels). Some matter at the tipof the cusp directly fulfills the ejecta criterion (top rightpanel), while the majority obtains an additional pushby the interaction with the asymmetric, mass-shedding
central remnant and the developing spiral arms (middleright and bottom panels). A smaller amount of ejecta ofroughly 25 per cent originates from the outer end of theprimary tidal tail (particles in the lower part of the topright panel). A part of this matter becomes unbound bytidal forces (at the tip of the tidal tail in the middle leftpanel) and the other fraction by an interaction with thecentral remnant (middle left panel).Figure 5 displays the distribution of the ejecta in a
plane perpendicular to the binary orbit for the symmetricmerger (left panel) compared to the asymmetric merger(right panel) for the last timesteps shown in Fig. 2 andFig. 4, respectively. A considerable fraction of the ejectedmatter is expelled with large direction angles relative tothe orbital plane. For a timestep about 5 ms later theejecta geometry is visualized (azimuthally averaged) inFig. 6 excluding the bound matter. For both mergersthe outflows exhibit a (torus or donut-like) anisotropywith an axis ratio of about 2:3. The velocity fields alsoshow a slight dependence on the direction.
Hotokezaka + (2013)
Bauswain + (2013)
Mtot = 2.7Msun
If HMNS is formed
ü エジェクタ質量：0.001 – 0.01Msun ü 状態方程式によって桁で異なる。
多核種の崩壊のHeaDng rate
This value of the effective temperature implys that the kilonova emission can be observed
in near-infrared band. Note that the above description of the compact binary merger
ejecta is so simple. In order to obtain more realisitic ejecta structure, ejecta mass, and
velocity profile, we need to perform numerical-relaticvity simulations of NS–NS and BH–
NS mergers. Furthermore, the microphysics play crucial role to understand kilonova
emissions such as the heating rate of the radioactive decays and the opacity of the ejecta.
In the next subsection, we briefly discuss the heating rate and opacity. In Chap. 7,
we focus on the ejecta properties for NS–NS mergers based on the results of numerical
relativity simulations.
3.3.2 Microphysics in NS–NS Merger Ejecta
r-process nucleaosysnthesis
The lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q, Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matirx elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays. The heating
rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
19
ベータ崩壊：原子核＝＞原子核＋電子＋ニュートリノ
終状態数の足し上げ
rate of the radioactive decays and the opacity of the ejecta. In the next subsection, we
briefly discuss the heating rate and opacity. In Chap. 7, we focus on the ejecta properties
for NS–NS mergers based on the results of numerical relativity simulations.
3.2.2 Microphysics in NS–NS Merger Ejecta
Decay of r-process elements
The β-decay lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q, Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matrix elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q5
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays (Colgate and
White 1966). The heating rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
where β0 is a constant. For the case that the number of radioactive nuclei is uniformly
distributed in each energy scale, the power of the heating rate is −1.2 (see e.g. Colgate
and McKee 1969). Although the above argument is quite simplified, the behavior of the
heating rate due to the β-decays of r-process elements can be understood as shown in
Fig. 3.3.
24
rate of the radioactive decays and the opacity of the ejecta. In the next subsection, we
briefly discuss the heating rate and opacity. In Chap. 7, we focus on the ejecta properties
for NS–NS mergers based on the results of numerical relativity simulations.
3.2.2 Microphysics in NS–NS Merger Ejecta
Decay of r-process elements
The β-decay lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q, Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matrix elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q5
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays (Colgate and
White 1966). The heating rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
where β0 is a constant. For the case that the number of radioactive nuclei is uniformly
distributed in each energy scale, the power of the heating rate is −1.2 (see e.g. Colgate
and McKee 1969). Although the above argument is quite simplified, the behavior of the
heating rate due to the β-decays of r-process elements can be understood as shown in
Fig. 3.3.
24
rate of the radioactive decays and the opacity of the ejecta. In the next subsection, we
briefly discuss the heating rate and opacity. In Chap. 7, we focus on the ejecta properties
for NS–NS mergers based on the results of numerical relativity simulations.
3.2.2 Microphysics in NS–NS Merger Ejecta
Decay of r-process elements
The β-decay lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q,Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matrix elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q5
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays (Colgate and
White 1966). The heating rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
where β0 is a constant. For the case that the number of radioactive nuclei is uniformly
distributed in each energy scale, the power of the heating rate is −1.2 (see e.g. Colgate
and McKee 1969). Although the above argument is quite simplified, the behavior of the
heating rate due to the β-decays of r-process elements can be understood as shown in
Fig. 3.3.
24
Sargent’ law
rate of the radioactive decays and the opacity of the ejecta. In the next subsection, we
briefly discuss the heating rate and opacity. In Chap. 7, we focus on the ejecta properties
for NS–NS mergers based on the results of numerical relativity simulations.
3.2.2 Microphysics in NS–NS Merger Ejecta
Decay of r-process elements
The β-decay lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q, Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matrix elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q5
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays (Colgate and
White 1966). The heating rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
where β0 is a constant. For the case that the number of radioactive nuclei is uniformly
distributed in each energy scale, the power of the heating rate is −1.2 (see e.g. Colgate
and McKee 1969). Although the above argument is quite simplified, the behavior of the
heating rate due to the β-decays of r-process elements can be understood as shown in
Fig. 3.3.
24
rate of the radioactive decays and the opacity of the ejecta. In the next subsection, we
briefly discuss the heating rate and opacity. In Chap. 7, we focus on the ejecta properties
for NS–NS mergers based on the results of numerical relativity simulations.
3.2.2 Microphysics in NS–NS Merger Ejecta
Decay of r-process elements
The β-decay lifetime τ of a radioactive particle can be obtained by
1
τ(Q)=
∫ Q
mec2
2π
! |Mfi|2dρf (Q, Ee)
dEedEe, (3.16)
where Q is the total energy of the decay, Mfi is the matrix elements of the decay, Ee is
the energy of the electron, and ρf is the density of state of released particles. Here, we
suppose that the matrix elemets do not depend on the energy and their form |Mfi|2 =
(g2V + 3g2
A)/V 2, where V is the volume, and gV and gA. Because an electron and neutrino
are ejected at the β-decay, the density of state can be written in the form
dρf (Q,Ee) =4πp2
e
(2π!)3
dpe
dEe
4πp2ν
(2π!)3
dpν
dQV 2dEe, (3.17)
where pe and pν are the momentum of an electron and neutrino, respectively. Note that
the factor V 2 is cancelled out with the same factor in the matrix elements. Assuming
Q ! mec2, the lifetime of the particle with Q can be described as
1
τ(Q)≈ 1
!7c6
(g2
V + 3g2A
) Q5
60π3≈ 1
1600s−1
(Q
1MeV
)5
(3.18)
This dependence of the lifetime of the β-decay energy is called the Sargent’s law.
Now we consider the heating rate of a statistical ensemble of β-decays (Colgate and
White 1966). The heating rate per unit mass is given by
ε(t) =
∫ ∞
0
Qf(Q)
τ(Q)exp(−t/τ(Q))dQ, (3.19)
where f(Q) is the distribution function. One supposes that flat distribution function
f(Q) ≈ f0 for Q ≤ Qmax, where Qmax is the upper limit of the distribution. Substituting
τ(Q) = t0Q−5 into Eq. (3.19), one can obtain the heating rate as
ε(t) =β0
t0
(t
t0
)−1.4
, (3.20)
where β0 is a constant. For the case that the number of radioactive nuclei is uniformly
distributed in each energy scale, the power of the heating rate is −1.2 (see e.g. Colgate
and McKee 1969). Although the above argument is quite simplified, the behavior of the
heating rate due to the β-decays of r-process elements can be understood as shown in
Fig. 3.3.
24
ε(t)∝ t−1.2仮定：Qが各スケールに一様に分布
核反応計算：和南城さんのトーク
Colgate and White (1966)
輻射輸送計算：重力波源としてのKilonova
（1）可視(赤)〜近赤外で一週間ほど増光する （2）４〜10m クラスの望遠鏡が必要
可視光
近赤外
Radiative Transfer Simulations for NS Merger Ejecta 9
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
Radiative Transfer Simulations for NS Merger Ejecta 9
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
Radiative Transfer Simulations for NS Merger Ejecta 9
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erve
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Days after the merger
K band200 Mpc
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
短波長 長波長
Tanaka & KH 2013 Kasen et al, 2013 Barnes & Kasen 2013 Grossman et al 2013
2013年、夏、Kilonovaの発見
ショートガンマ線バースト GRB 130603Bの後に、 “Kilonova”の初めての観測に成功。
Tanvir et al.,Nature,2013 Berger et al., ApJ, 2013 de Ugarte PosDgo et al, 2013
ü ショートガンマ線バーストがコンパクト連星合体起源である傍証 ü R-‐process の起源に迫る (地球質量の数１０倍の金が生産) ü 重力波源の電磁波対応天体の最有力候補 ü 初めて数値相対論の結果と観測を比べれるようになった
和南城さんトーク、関口さんポスター
観測： short GRB 130603B
Figure 9: Light curves of GRB 130603B, indicated detections with dots and upper limits (3-�) with arrows. V -band photometry has been scaled and plotted together with the g-band. The vertical lines indicate the times whenspectra were obtained. Dotted lines indicate the light curve fits to a power law temporal decay from 0.3 to 3 daysafter the burst. We include data from the literature [21, 22]. The dashed blue line is the expected r-band lightcurve of a supernova like SN1998bw, the most common template for long GRBs after including an extinction ofAV = 0.9 magnitude. The most constraining limits indicate that any supernova contribution would be at least 100times dimmer than SN 1998bw in the r-band, once corrected of extinction (blue dashed-dotted line).
2.2 Spectral energy distribution of the afterglow and extinction
In this section we aim to fit the X-ray to optical/NIR SED using the method followed in [23, 24] to derive the
extinction in the line of sight of the GRB and determine some spectral parameters. The procedure is briefly
explained below.
The flux calibrated spectrum has been analysed after removing wavelength intervals affected by telluric lines
and strong absorption lines. We then rebinned the spectrum in bins of approximately 8 A by a sigma-clipping
algorithm. To check the flux calibration of the X-shooter spectrum, we compare the continuum with the flux
densities obtained from the extrapolation of the photometry at the time of the spectrum (mid time around 8.56 hr).
We include the X-ray spectrum from the X-ray telescope (XRT) on board Swift. We used XSELECT (v2.4) to
26
de Ugarte PosDgo et al 2013
光度
時間
ガンマ線バースト残光(X-‐ray)
Swi[ XRT
赤外増光 ハッブル宇宙望遠鏡
Page 8 of 16
Figure 1 HST imaging of the location of SGRB 130603B. The host is well resolved
and displays a disturbed, late-type morphology. The position (coordinates RAJ2000 = 11
28 48.16, DecJ2000 = +17 04 18.2) at which the SGRB occurred (determined from
ground-based imaging) is marked as a red circle, lying slightly off a tidally distorted
spiral arm. The left-hand panel shows the host and surrounding field from the higher
resolution optical image. The next panels show in sequence the first epoch and second
epoch imaging, and difference (upper row F606W/optical and lower row F160W/nIR).
The difference images have been smoothed with a Gaussian of width similar to the psf,
to enhance any point-source emission. Although the resolution of the nIR image is
inferior to the optical, we clearly detect a transient point source, which is absent in the
optical.
u Hubble Space Telescope imaging
可視 (r-‐band)
近赤外 (H-‐band)
9 days a[er the burst 30 days
The host galaxy
Tanvir et al.,Nature,2013 Berger et al., ApJ, 2013
GRB 130603Bに付随した赤外増光
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Days after the merger
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
Radiative Transfer Simulations for NS Merger Ejecta 9
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Fig. 8.— Expected observed ugrizJHK-band light curves (in AB magnitude) for model NSM-all and 4 realistic models. The distanceto the NS merger event is set to be 200 Mpc. K correction is taken into account with z = 0.05. Horizontal lines show typical limitingmagnitudes for wide-field telescopes (5σ with 10 min exposure). For optical wavelengths (ugriz bands), “1 m”, “4 m”, and “8 m” limitsare taken or deduced from those of PTF (Law et al. 2009), CFHT/Megacam, and Subaru/HSC (Miyazaki et al. 2006), respectively. ForNIR wavelengths (JHK bands), “4 m” and “space” limits are taken or deduced from those of Vista/VIRCAM and the planned limits ofWFIRST (Green et al. 2012) and WISH (Yamada et al. 2012), respectively.
ハッブル宇宙望遠鏡の観測日
結果： 数値相対論＋輻射輸送 vs 観測データ
The Astrophysical Journal Letters, 777:L1 (5pp), 2013 ??? Hotokezaka et al.
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Rest-frame days after GRB 130603B
SLy(Mej=0.02)H4(Mej=0.004)
rH
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APR4(Mej=0.01)r
H
Figure 3. Predicted light curves for NS–NS and BH–NS models. Left panel: NS–NS models. The dashed, solid, and dot-dashed curves show the H-band light curvesfor the models: SLy (Q = 1.0,Mej = 0.02 M!), H4 (Q = 1.25,Mej = 4 × 10−3 M!), respectively. The total mass of the progenitor is fixed to be 2.7 M!. The upper,middle, and lower curves for each model correspond to the high-, fiducial- and low-heating models. Right panel: BH–NS models. The dashed, solid, and dot-dashedcurves show the models MS1 (Mej = 0.07 M!), H4 (Mej = 0.05 M!), and APR4 (Mej = 0.01 M!), respectively. Here only the fiducial-heating models are shown.The thin and thick lines denote the r and H-band light curves. Here we set (Q,χ ) = (3, 0.75). The observed data (filled circles), upper limits (triangles), and the lightcurves (dashed lines) of the afterglow model of GRB 130603B in r and H-band are plotted (Tanvir et al. 2013; de Ugarte Postigo et al. 2013). The observed pointin the r-band at 1 days after the GRB is consistent with the afterglow model. The key observations for an electromagnetic transient are the observed H-band data at7 days after the GRB, which exceed the H-band light curve of the afterglow model, and the upper limit in H-band at 22 days after the GRB. These data suggest theexistence of an electromagnetic transient associated with GRB 130603B.(A color version of this figure is available in the online journal.)
(Q = 1.0, Mej = 0.02 M!) and H4 (Q = 1.25, Mej =4 × 10−3 M!) for reference. Here the total mass of the progen-itor is chosen to be Mtot = 2.7 M!. We plot three light curvesderived with the fiducial- (the middle curves), high- (the uppercurves), and low-heating models (the lower curves). We expectthat the realistic light curves may lie within the shaded regions.For the NS–NS models, the computed r-band light curves arefainter than 30 mag. The right panel of Figure 3 shows the lightcurves of the BH–NS merger models, MS1 (Mej = 0.07 M!),H4 (Mej = 0.05 M!), and APR4 (Mej = 0.01 M!) with(Q,χ) = (3, 0.75). For these cases, we employ the fiducial-heating model. Note that the r-band light curves of the BH–NSmodels reach ∼27 mag, which implies that the light curves ofthe BH–NS models are bluer than those of the NS–NS models.This is because the energy from radioactive decay is depositedinto a small volume for the BH–NS models (see Tanaka et al.2013 in details). As shown in Figure 6 of Kasen et al. (2013, seealso Figure 15 of Tanaka & Hotokezaka 2013), the opacity ofr-process elements depends strongly on the temperature, andthus the time after the merger. The small bumps in theH-band light curves of BH–NS models are caused by this time-dependent opacity.
Uncertainties are expected to be associated with the differencein the morphology between the models of the same progenitortype but different masses and spins. Moreover, the light curvesmay depend on the viewing angle. However, these uncertaintiesare not large enough to significantly affect our results (seeTanaka & Hotokezaka 2013; Tanaka et al. 2013 for details).
We now translate these results into the progenitor models asQ, χ , and EOS.
Q1 NS–NS models. The NS–NS models for GRB 130603B shouldhave ejecta of mass !0.02 M!. This is consistent with thatderived by Berger et al. (2013). This value strongly constrainsthe NS–NS models because the amount of ejecta is at most∼0.02 M! for an NS–NS merger within the plausible mass rangeof the observed NS–NS systems (Ozel et al. 2012). Specifically,as shown in Figure 2, such a large amount of ejecta can be
obtained only for the soft EOS models in which a hypermassiveneutron star with a lifetime of !10 ms is formed after themerger. For the stiff EOS models, the amount of ejecta is atmost 4 × 10−3 M!. Thus we conclude that the ejecta of theNS–NS models with soft EOSs (R1.35 " 12 km) are favored asthe progenitor of GRB 130603B.
BH–NS models. The observed data in the H-band is consistentwith the BH–NS models which produce the ejecta of ∼0.05 M!in our fiducial-heating model. Such a large amount of ejectacan only be obtained with the stiff EOSs (R1.35 ! 13.5 km) forthe case of χ = 0.75 and 3 # Q # 7 as shown in Figure 2.For the soft EOS models, the total amount of ejecta reachesonly 0.01 M! as long as χ # 0.75, which hardly reproducesthe observed near-infrared excess. Thus the models with stiffEOSs are favored for the BH–NS merger models as long as0.5 # χ # 0.75 and 3 # Q # 7 is the progenitor model ofGRB 130603B. It is worth noting that any BH–NS models with
Q2χ # 0.5 and Q $ 7 are unlikely to reproduce the observednear-infrared excess.
5. DISCUSSION AND CONCLUSION
We explored possible progenitor models of the electromag-netic transient associated with the Swift short GRB 130603B.This electromagnetic transient may have been powered by theradioactive decay of r-process elements, a so called kilonova/macronova. We analyzed the dynamic ejecta of NS–NS andBH–NS mergers for the progenitor models of this event. Tocompute the expected light curves, we carried out radiativetransfer simulations using density and velocity structures ob-tained from numerical-relativity simulations with several totalmasses, mass ratios, and EOSs. Depending on these quantities,the total amount of ejecta mass varies by orders of magnitude10−4 M! to 10−2 M! for the NS–NS models and 10−5 M! to10−1 M! for the BH–NS models.
For both NS–NS and BH–NS models, we found that there areprogenitor models that can reproduce the observed near-infrared
4
NS-‐NS merger BH-‐NS merger
Ejecta x-‐z plane
Hotokezaka et al., ApJL, (2013)
Kilonova Kilonova
観測に合うモデル NS-‐NS merger (So[ EOS) BH-‐NS merger (SDff EOS)
まとめと今後
ü 重力波源の電磁波対応天体の同定が重要
ü ショートガンマ線バーストGRB 130603Bに赤外線増光が付随
ü 今後、kilonovaの確定のため、より詳細なスペクトルが必要
ü 重力波源の電磁波対応天体としてのKilonova
数値相対論＋輻射輸送から予想された“Kilonova”と極めて類似
ショートガンマ線バーストのコンパクト連星合体起源の証拠 状態方程式がわかれば、NS-‐NS or BH-‐NSを区別できる可能性あり
r-‐process elementの吸収係数が必須
4m-‐ 10mクラスの追観測できる望遠鏡が必要
GRB130603B：NS-‐NS合体 or BH-‐NS合体？
The Astrophysical Journal Letters, 777:L1 (5pp), 2013 ??? Hotokezaka et al.
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Figure 2. Ejecta masses as a function of the compactness of the neutron star, which is defined by GMtot/2R1.35c2 and GMNS/R1.35c
2 for NS–NS and BH–NS models,respectively. Left panel: NS–NS models. Each point shows the ejecta mass for the equal mass cases. Error bars denote the dispersion of the ejecta masses due tothe various Q. Right panel: BH–NS models. The filled and open symbols correspond to the models with (Q, χ ) = (3–7, 0.75) and (7, 0.5), respectively. The blueshaded region in each panel shows the ejecta masses allowed in order to reproduce the observed near-infrared excess of GRB 130603B, 0.02 ! Mej/M! ! 0.07 and0.02 ! Mej/M! ! 0.1 for the NS–NS and BH–NS models, respectively. The lower and upper bounds are imposed by hypothetical high- and low-heating models,respectively.(A color version of this figure is available in the online journal.)
as a hypermassive neutron star with a lifetime of !10 ms isformed after the merger. More massive NS–NS mergers resultin hypermassive neutron stars with a lifetime of "10 ms or inblack holes. For such a case, the ejecta mass decreases withincreasing Mtot because of the shorter duration of mass ejection.
BH–NS ejecta. Tidal disruption of a neutron star results inanisotropic mass ejection for a BH–NS merger (Kyutoku et al.2013). As a result, the ejecta is concentrated near the binaryorbital plane as shown in Figure 1, and it is shaped like a diskor crescent.
The amount of ejecta for the BH–NS models is smaller formore compact neutron star models with fixed values of χ and Qas shown in Figure 2. This is because tidal disruption occurs ina less significant manner. This dependence of the BH–NS ejectaon the compactness of neutron stars is opposite to the case ofthe NS–NS ejecta.
More specifically, the amount of ejecta is
5 × 10−4 " Mej/M! " 10−2 (soft EOSs),
4 × 10−2 " Mej/M! " 7 × 10−2 (stiff EOSs), (2)
for χ = 0.75 and 3 # Q # 7. For χ = 0.5, the ejecta mass issmaller than that for χ = 0.75. Only the stiff EOS models canproduce large amounts of ejecta more than 0.01 M! for χ = 0.5and Q = 7.
For both NS–NS and BH–NS merger models, winds drivenby neutrino/viscous/nuclear-recombination heating or the mag-netic field from the central object might provide ejecta in addi-tion to the dynamic ejecta (Dessart et al. 2009; Wanajo & Janka2012; Kiuchi et al. 2012; Fernandez & Metzger 2013). However,it is not easy to estimate the amount of wind ejecta, because itdepends strongly on the condition of the remnant formed afterthe merger. In this Letter, we focus only on the dynamic ejecta.
3. RADIATIVE TRANSFER SIMULATIONSFOR THE EJECTA
For the NS–NS and BH–NS merger models described inSection 2, we perform radiative transfer simulations to obtain
the light curves of the radioactively powered emission fromthe ejecta using the three-dimensional, time-dependent, multi-frequency Monte Carlo radiative transfer code (Tanaka &Hotokezaka 2013). For a given density structure of the ejectaand elemental abundances, this code computes the emissionin the ultraviolet, optical, and near-infrared wavelength rangesby taking into account the detailed r-process opacities. In thisLetter, we include r-process elements with Z $ 40 assuming thesolar abundance ratios by Simmerer et al. (2004). More detailsof the radiation transfer simulations are described in Tanaka &Hotokezaka (2013); Tanaka et al. (2013).
The heating rate from the radioactive decay of r-processelements is one of the important ingredients of radiative transfersimulations. As a fiducial-heating model, we employ the heatingrate computed with the abundance distribution that reproducesthe solar r-process pattern (see Tanaka et al. 2013 for moredetail). Heating is due to β-decays only, which increase atomicnumbers from the neutron-rich region toward the β-stabilityline without changing the mass number A. This heating rate is inreasonable agreement with those from previous nucleosynthesiscalculations (Metzger et al. 2010; Goriely et al. 2011; Grossmanet al. 2013) except for the first several seconds.
We note that quantitative uncertainties could exist in theheating rate as well as in the opacities. As an example, theheating rate would be about a factor 2 higher if the r-processabundances of A ∼ 130 (or those produced with the electronfraction of Ye ∼ 0.2) were dominant in the ejecta (Metzgeret al. 2010; Grossman et al. 2013). To take into account suchuncertainties, we also consider the cases in which the lightcurves of mergers are twice and half as luminous (high- and low-heating models; only explicitly shown for the NS–NS modelsin Figure 3) as those computed with the fiducial-heating model.
4. LIGHT CURVES AND POSSIBLEPROGENITOR MODELS
The computed light curves and observed data in r andH-band are compared in Figure 3. The left panel of Figure 3shows the light curves of the NS–NS merger models SLy
3
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NS-‐NS BH-‐NS 観測点を 説明できる領域
Hotokezaka et al (2013)
Kilonova研究の進展 流体計算 核反応 opacity (cm^2/g) Li & Paczynski (1998) 0.01Msun, 0.3c f ~ 10^-‐3 grey κ = 0.2 Metzger + (2010) -‐ network cal. f~10^-‐6 grey κ = 0.1 Roberts + (2011) Goriely + (2011) Hydro. (Newton) network cal. grey κ=0.1 Korobkin + (2012) Hotokezaka + (2013) Hydro. (GR) + EOSs -‐ -‐ Bauswein + (2013) Hydro. (CF) + EOSs network cal. -‐ Kasen + (2013) -‐ -‐ 単一元素 Nd κ~10 Tanaka & KH (2013) Hydro. (GR) -‐ 多元素(低イオン化状態) κ~10 Grossman + (2013) Hydro. (Newton) network cal. κ=10 & κ=1
Tanvir + (2013) & Berger + (2013) “Kilonova”発見、Short GRB13603B (z = 0.356)
ニュートリノ効果 Wind 成分
今後 核分裂 R-‐process元素 オパシティーの計算
