ガンマ線バーストの長期放射に伴う高エネルギーニュートリノ放射
松井理輝, 木村成生 (東北大学)
日本天文学会2023年秋季年会

Gamma-Ray Burst (GRB)
The most luminous transient (in EM wave).
Mechanism ? Central object ? (Progenitor ?)[NSF/LIGO/Sonoma State University/A. Simonn

Pe’er +152

Relativistic Jets with v ∼ c, Γ ∼ 100
Canonical Theory of GRB• Prompt emission : Jet internal dissipation• Afterglow : Jet-ISM dissipation
CocoonEngineJetlog L

PromptDissipation,

Afterglow

Acceleration
Star/EjectaΓ ∼ 100

PromptAfterglowt

0.1 - 10 slog t3

Late-time Emission of Gamma-Ray BurstTheory of GRB
log L

Short GRBLong GRB

PromptAfterglow

0.1 - 1 shour year

log t
Kisaka +17“Extended Emission”(~ 2/3 of SGRBs)

100 s 1000 s

Yi +16“X-ray Flare”(~ 1/3 of LGRBs)

Prolonged central enigine activity

log LStandard Scenario for late-time emission :Prolonged engine activity & Jet dissipation

PromptAfterglow(e.g. Ioka et al. 2005, Perna et al. 2006)

Tobs ∼ 100 − 1000 s
~ 2s

log t

Tobs ∼ 100 − 1000 s

EngineDissipation(Kisaka +17)

Afterglow
EngineProblem :(Yi +16)

Properties of the late-time jet are unknown.

Prolonged central enigine activity
Standard Scenario for late-time emission :Prolonged engine activity & Jet dissipation

Theory of GRB
log L

Prompt

Question

Afterglow(e.g. Ioka et al. 2005, Perna et al. 2006)

Can we characterize
it byT ∼ 100 − 1000
obs

~ 2ss

log t

other
observations？
T ∼ 100 − 1000
Engineobss

Dissipation(Kisaka +17)

Afterglow
EngineA. Yes. (Neutrino)
Problem :Properties of the late-time jet are unknown.

Prolonged Engine and Cocoon Scenario
See also, Kimura+19 (γ), Hamid+21, 23 (simu), Mei+22 (γ, obs)

Break out t < ∼ 1 s

Jet launch t = 0 s
EngineCocoon

BH

BH Cocoon

Ejecta/star

Prompt emission Tobs ∼ 0 s
CocoonLate-time emission Tobs ∼ 100 − 1000 s
Cocoonγ

Jet

BH

P
Dissipation

Dissipationν

Based on Prolonged jet model

7

Prolonged Engine and Cocoon Scenario
See also, Kimura+19 (γ), Hamid+21, 23 (simu), Mei+22 (γ, obs)

Break out t < ∼ 1 s

Jet launch t = 0 s
EngineEjecta/starThis Work

Prompt emission Tobs ∼ 0 s
CocoonCocoonBH

BH Cocoon

Jet

Late-time emission Tobs ∼ 100 − 1000 s
Cocoon γBHDissipation

PDissipation

ν8Results 1 : Neutrino Spectra
Extended Emission
2.5dL = 300Mpc tdur = 10 s rdis = 1012X-ray Flare
32.5cm, Γj = 200

dL = 300Mpc, t are = 10 tdur = 10 s rdis = 10

RM + 23

Preliminary

12cm, Γj = 100

Without Cocoon

flfl

Cocoon increase the νux by 1000 times at ~PeV. 9

Results 2 : Expected Number of Detection
Neutrino Spectra
2.5

dL = 300Mpc tdur = 10 s rdis = 1012IceCube E ective Areacm, Γj = 200NorthHighSouthLow

Upper limit (Abbasi+22)
Gen2 sensitivity limit(Aartsen+21)N̄νμ = dενμϕνμ+ν̄μ(ενμ)Ae (δ, ενμ)∫Number of the Detection

ffff

1ν/10 GRBs by IceCube ※ Fixed dL = 300 Mpc, tdur ∼ 300 se.t.c.

10Results 3 : Operation time
Extended Emission

X-ray Flare

Undetectable

IceCubeRM+ 23Preliminary※ For local GRBs

90 %2σGen23σHighlyDetectable

flNeutrinos are 90% detectable in 10 years (Gen2, E.E of local sGRB ).
※ X-ray ares take more than 30 years.

11Cosmological GRB
Typical distance : z ∼ 0.5 (SGRB) / z ∼ 2 (LGRB)

Rough estimation
Flux ∝−2dL ,Event rate ∝3dL → Neutrino signal∝ dLExactly,• Flux : Comparable with the atomospheric BG ?
• Event rate ∝34dL f(z)/ (1 + z)
12

Model Parameters
γ number density∘θj = 5

ξp = Up /Uγ,
ξB = UB /Uγϵp = Up /Uk ∼ 0.3,
ϵB = UB /Uk ∼ 0.01

Proton number13

Discussion : Constraints on physics of sGRB
Extended Emission

Preliminary

X-ray FlarePreliminary

Propaty of late-time Jet>> 1 event/10 yr
or<< 1event/10yr•• How jets dissipated ?
• How many CRs ?
How jets launched ?

Mechanisim of the
prolonged central
engine activity ?
14

Summary• We calculated the neutrino emission associated with thelate-time emission of Gamma-Ray Bursts, considering theprolonged engine activity model and cocoon photons.
1neutrino
will
bedetectedwith
10localGRBs()
d∼
300
MpcL
•

• Neutrinos should be detected from GRBs in 10 years.
( Gen2 : 90%)

• The dissipation radius and the Lorentz factor of late-time jet
will be constrained by the high energy observation in the future.
15

Take-home message

ガンマ線バーストの100 -1000 s 後に100 TeV - 1 PeV のニュートリノがX線と相関して見つかるかも(特に重力波も相関する、SGRBのExtended emission に注目)
16

Back Up

Method 1 : Neutrino emission
Neutrino Spectrum (One-Zone approx.)γdNνμdNp
122ενμ≈ fpγ εpdενμ8dεp

BHDissipation

Prdis ∼ 1012ν,
εp=ενμ/0.05cmwhere fpγ = t′cool /t′pγ ,+p+γ→π+ X → 3ν +X′t′pγ+ Adiabatic cooling+ Bethe Heitler process+ Synchrotron coolingdn′γc′−2dε̄σκε̄dε′εγ pγ pγ γγ γ′2∫∫2γp ε̄thdε′γε̄γ /2γp∞∼ nγσct′acc Spectra of Photon and Proton are required.

￼￼+ di usive accelerationt′cool′−1tpγ =∞ff￼

￼

￼

￼

￼

￼

￼

￼

￼

￼

18

Method 2 : Photons in Dissipation Region
Photon Spectrumγ• Internal photons (Kimura +17 )BHPrdis ∼ 1012′inDissipation

νcmInternaldn′−0.5∝ εγdε′γ(ε′γ ≥ ε′γ,pk)

′−2
∝ εγ

(ε′γ < ε′γ,pk)• Cocoon photons (←New )￼38π(ε′γ /Γj)dn1ε′γ= Γjdε′γ
h 3c 3 exp(ε′γ /ΓjkBTcoc) − 1′ex￼

￼￼￼
￼

￼￼￼

￼

￼

￼

￼

CocoonkBTcoc ∼ 20 eV

19Method 3 : Protons in Dissipation Region
γProton (Cosmic-Ray) Spectrum

BHDissipation

Prdis ∼ 1012dNp

ν

dεpcm

= Nεp,nor

εp−2( εp,cut )εpexp −,( εp,cut )( assuming Fermi accelelation)

where￼￼￼

￼

εp,cut※co-moving′−1′−1tacc (ε′p) = tcool(ε′p)→ εp,cut20

Cocoon model for Extended emission
Tcoc : Cocoon temperature (Kimura+19)
vcoc, Ekin,coc, Eint,coc

31/4Tcoc = (3ℰcoc /4πRcocarad)(at break out time)from Hamidani +20

122.5

Rcoc = 3 × 10 (tdur /10 s) cm (Constant velocity)
44

2.5ℰcoc = 8.8 × 10 (tdur /10 s)−1

Part of initialinternal energy44

2.5−0.3erg + 9.3 × 10 (tdur /10 s)
Injected byradioactive decay

21erg

Emprical relation for Extended emission
logtDuration,:
Gaussian
byObservational
datadur••−2.5
LX ∝ tdur( Emprical Low , Kisaka +17)

• Location：homogenous, dL < 300Mpc−3−1• Event rate : RsGRB ∼ 8 Gpc yr(Kisaka +17)

22

Cocoon model for X-ray
4
Internal energy density : aTcoc =areEi,coc,brr*
3 /3 ct
4πrdissareInternal E. at break out : Ei,coc,br = Ljtb × (1 − βh)(Hamidani & Ioka 2022)

2Jet (kinetic) luminosity : Lj = Lk,isoθj /4

Jet isotropic-equivalent luminnosity : Lk,iso = 30 Lprompt,iso2 41/3
break out time : tb = 0.9 (r* θj M* /Lj)

(Hamidani & Ioka 2022)

Jet velocity before break out : βh = r* /ctb
flwhere Prompt emission Luminosity : Lprompt,iso, Dissipation radis : rdiss,
Steller mass, radius : M*, r* ,Jet opening angle θj,

fl23

Emprical relation and distribution for X-ray
Prompt emission (radiation) luminonsity : Lprompt,iso ∼ 30 Lx, are48−1.02

X-ray are luminosity : Lx,iso = 1.3 × 10 × (t are,3 (1 + z))
1.12

Duration of X-ray are : tdur = 450 × (t are,3 (1 + z))−1.72
Distribution of t are : F(t are) dt are ∝ t are dt areserg/sare(Liu & Mao 19)(Yi+16)(Yi+16)(Yi+16)

where X-ray are peak time : t are, t are,3 = t are /(1000 s)

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Yi+1624