Gravitational waves and neutrinos
from LGRBs
Yuichiro Sekiguchi (YITP)
Collaboration with Masaru Shibata (YITP)GRB engine
 BH + accretion disk /magnetar formed by
LGRB : Stellar core collapse Hypernova association


Talks by Della Valle, Mazzali …

SGRB : NS-NS/BH merger Timescale argument


Talks by Rosswog, Metzger,Shibata ….

Dynamics of stellar core collapse
NS formation
PNS formation
depends on
EOS & coremass

depends on
EOS & coremass

depends on B-fields& rotation profile

Magnetar GRB ??
Stellar core collapse

depends onrotation profile

Direct BH
formation

Fallback BH
formation

Collapsar GRB ?

Dynamics of stellar core collapse
NS formation
PNS formation
depends on
EOS & coremass

Neutrinos from PNS(neutrino heating)depends on
EOS & coremass

depends on B-fields& rotation profile

Magnetar GRB ??
Stellar core collapse

Neutrinos frommagnetar ?

Neutrino burst
emission

depends onrotation profile

Direct BH
formation

Fallback BH
formation

Collapsar GRB ?
Neutrinos from BH +accretion disk (NDAF)
GeV Neutrinos from GRB jet(next talk by Murase)Gravitational waves


GW Luminosity : quadrupole formulaG  LGW  5 I I5c
To be a strong emitter of GWs
Higher degree of asymmety : 𝜀 ~ (𝐼𝑥𝑥 − 𝐼𝑦𝑦 )/𝐼𝑧𝑧



General relativistic (compact)

2c 5   GM   v ~  2   G c R  cBlack hole (BH) : GM/Rc2 ~ 1

Neutron star (NS) : GM/Rc2 ~ 0.1



BH accretion disk : GM/Rc2 ~ 0.01—0.1 (for RDisk ~ RISCO)

Special relativistic (v~c)

How about in LGRBs

6

GW sources in stellar core collapse
NS formation

depends on
EOS & core
massStellar core collapse
Zwerger & Muller (1997)
Dimmelmeier et al (2002)
Shibata & YS (2003)
Ott et al. (2011)
YS et al. (2013)
Cerda-Duran et al. (2013)
Muller et al. (2004)

Instabilities
Rampp et al. (1998)
Shibata & Sekiguchi (2005)
Kobayashi & Meszaros (2003)

Magnetar GRB ??

GW from PNS g-modes

GW from rotational core bounce

GW from convection/SASI

depends on
EOS & core
PNS formation
GW from non-axisym. massdepends on B-fields& rotation profile

GW from GRB jetOtt et al. (2006)

Anisotropic neutrino emission
Muller et al. (2004)

depends onrotation profile

Direct BH
formation

Fallback BH
formation

GW from BH quasi-normal modes

Collapsar GRB ?
GW from BH+Disk system
Papaloizou-Pringle instability (Kiuchiet al. 2011)
Disk fragmentation (Piro & Pfahl 2007)
Disk precession (Romero et al. 2010)

GW from collapsar optimal @ 20Mpc
Papaloizou-Pringle instabilityof accretion disk (Kiuchi et al.)Disk fragmentation

PNS g-mode

likely to be less loud (Ott 2009)

Non-axisym. instability (high T/W)

extreme condition needed (Shibata & YS 2005)

Non-axisym instability (low T/W)

EOS dependence (Scheidegger et al. 2012)

Rot. Core bounce
PNS convection
g-mode (Cerda-Duran et al.)Anisotropic neutrino
ν-convection

Need for more studies
 Previous studies are based on ordinary supernova simulations


But see Ott+. (2011); Sekiguchi+. (2011;2013); Cerda-Duran+. (2013)

 Important physics is included incompletely(Pseudo-) Newtonian simulations with detailed microphysics
 Full GR simulations with simplified microphysics


But see Sekiguchi (2010); Kuroda+ (2012); Muller+ (2012) Cerda-Duran+ (2013)

GRNewton

Dimmelmeier et al. (2002)

Full GR Radiation-Hydrodynamics
Einstein’s equations: Puncture-BSSN/Z4c formalismGR radiation-hydrodynamics (Sekiguchi 2010; Sekiguchi + in prep.)

EOS : any tabulated EOS with 3D smooth extended connection to Timmes EOSAdvection terms : Truncated (two) Moment scheme (Shibata et al. 2011)
Fully covariant and relativistic
 gray or multi-energy but advection in energy is not included M-1 closure

Source terms : two options
Implicit treatment : Bruenn’s prescription
 Explicit treatment : trapped/streaming ν’svacuume-captures: thermal unblocking/weak magnetism; NSE rateIso-energy scattering : recoil, Coulomb, finite sizee±annihilation, plasmon decay, bremsstrahlung

diffusion rate (Rosswog & Liebendoerfer 2004)

two (beta- and non-beta) EOS method

Lepton conservation equations

absorbercorrectCode verification by 1D stellar collapse

Our implicit scheme qualitatively (or semi-quantitatively) reproduce resultsin 1D GR Boltzmann simulations !

radial velocitydensity

entropy/baryon

YeMulti-D GR RadHydro
based on Moment method

neutrino luminosity

neutrino bursts
1D GR Boltzmann
Liebendoerfer+ 2001

neutrino trappingApprox. Explicit treatment works wellReasonable agreements with full transferLν calculated from neutrino flux (not fromsource term !)Ye

Do not use Liebendorfer’s simplified prescription

Heating effects can be included

L [1053 erg/s]
e neutrino
e anti neutrino

R [km]
Entropy per baryon [kB]

R [km]
Time [ms]Application to BNS merger

Approximate solution by Thorne’s Moment scheme with a closure relation
Partial implicit treatment with an iterative time evolution / Explicit treatment
Talk by Wanajo

Application to BNS mergeree  L [1053 erg/s]

Rest-frame neutrino energy density
in the plane perpendicular to theorbital plane (x-z plane)Full GR simulation of collapsar
 Based on old version of code (Sekiguchi 2010)

Simple Eddington closure instead of M-1 closure Approximate explicit treatments for source terms
 Heating effects are not included Sekiguchi & Shibata (2011)
 Sekiguchi et al. (2013)

Dilemma in LGRB progenitor model Rapid rotation is requiredCollapsar (central engine: BH + Disk) Possible energy sources Gravitational energy of disk ⇒ neutrinosee Hot disk Rotational energy of BH⇒Poynting flux
MHDjetRotation is important in other models
 E.g. magnetar model(might be more severe due to strong B fields)
 Association of Type-Ic SNeSekiguchi & Shibata 2007

Progenitor must have been ‘lost’ H and He envelopes Angular momentum loss at the same time of mass loss ⇒ slow rotator (e.g. Yoon et al. 2005, Woosley & Heger 2006)

 How to produce energetic SNe at all when BH is formed ?

Dilemma in LGRB progenitor model Peculiar progenitor models are necessary

LGRBs are anomalous events: Progenitor cores may also be anomalous
He star merger model (Fryer & Heger 2005)
 Tidal spun up star model (van den Huevel & Yoon 2007)
 Chemically homogeneous evolution model (Woosley & Heger 2006, Yoon et al. 2006)


These models predict formation of a core different from ordinary SN
 Accompanied by strong mixing which tends to lead to high entropy core

 Suggestion: LGRB-progenitor core may have higher entropy

Massive (& compact) : BH formation
 Rapid Rotation : Disk formation / amplification of B-fields
 Evolution pass in density-temperature plane could be different fromordinary SNThree Initial Models
Evolution path is characterized by central entropy (mass)More MassiveStellar CoreRadiation pressuredominant

Gas pressure
dominant
Electron degeneratepressure dominantOrdinary SNCore

Three Initial Models

Rotational Profiles are added by hand

500 Msolar Model :Ohkubo et al. (2006)
Mcore ~20Msolar
Simplified Model
Nakazato et al, (2007)
Mcore ~ 10Msolar

100 Msolar Model :Umeda & Nomoto (2008)
Mcore ~ 3MsolarCollapse of 100Msolar presupernova model:
Umeda & Nomoto (2008) + rigid rotation Ω = 1.2 rad/s
Sekiguchi et al. (2013)~5 min animation

Neutrino luminosity
Neutrinos fromaccretion disk
Neutrino burst

Neutrinos frommassive PNS

BH
formation

Sekiguchi et al. (2013)

GWs from collapsar

Ott et al. (2011)
Sekiguchi et al. (2013)
Cerda-Duran et al. (2013)

Cerda-Duran et al. (2013)
Aloy’s talk

GWs from collapsar

Ott et al. (2011)
Sekiguchi et al. (2013)
Cerda-Duran et al. (2013)

Cerda-Duran et al. (2013)
Aloy’s talkSlower (still moderate) Rotation Case:
Spheroidal configuration, No time variability

Sekiguchi et al. (2013)

Slower (still moderate) Rotation Case:
Spheroidal configuration, No time variability

Sekiguchi et al. (2013)

Comparison of Rotational Profile Rotational profiles of Proto-Neutron Star are similar Small difference in rotational profile of outer region resultsin large difference in dynamics
rapid
moderate

PNS
RapidModerateA higher entropy coreRotational Profiles are added by hand

Simplified Model
Nakazato et al, (2007)
Mcore ~ 10Msolar

GRB without SNe ? : Collapse of Higher entropy coreeex1053 erg/sAccretion shock

entropy per baryon contour
Sekiguchi & Shibata (2011)

GRB without SNe ? : Collapse of Higher entropy coreeex1053 erg/sAccretion shock

entropy per baryon contour
Sekiguchi & Shibata (2011)Kelvin-Helmholtz instability

Infalling matterv ~ 0.3c

Convective eddy
~ 0.1cNeutrino luminosity
Just before
BH formation,
Ltot ~ 4・1054 erg/s
Thick torus emits
Ltot ~ 1054 erg/s,
time-variableThin disk emits
Ltot ~ 5・1053 erg/s

neutrinos and anti-neutrinos
are almost equally emittedNeutrino luminosity
EfficiencyJust before
Thin disk BH: ~ 0.01
formation,
Thick torus:
Ltot~~0.1
4・1054 erg/s
Thick torus emits
Ltot ~ 1054 erg/s,
time-variableThin disk emits
Ltot ~ 5・1053 erg/s

neutrinos and anti-neutrinos
are almost equally emitted

GW from disk convection

GW from Papaloizou-Pringle instability
BH + massive disk formation in collapsar
 Subject to Papaloizou-Pringle instability
Mode amplification between disk edge andcorotation point 3D Full GR simulations by Kiuchi et al. (2011)
 GWs from D ~ 100Mpc could be detected

density contour in x-y planeGW from Papaloizou-Pringle instability
BH + massive disk formation in collapsar
 Subject to Papaloizou-Pringle instabilityMode amplification between disk edge andcorotation point 3D Full GR simulations by Kiuchi et al. (2011)
 GWs from D ~ 100Mpc could be detected

density contour in x-y plane500Msolar-PopIII (Ohkubo et al. 2006) core collapse:
Outflow appears even when BH is formed directly
Matter accumulation
into the central region
due to the obliqueshock Shock wave
formation in the poleregion of the BH
 Efficient dissipation ofkinetic energy
 Inefficient advectioncooling Thermal energy isstored Outflow
Entropy per Baryon

1900km• Neutrino pair annihilation•
Zalamea & Beloborodov (2010)• Lpair ~ 1049-50 erg/s for Umeda & Nomoto (2008) model• Lpair ~ 1052-53 erg/s for higher entropy model• Strong dependence : dot(M)^(9/4) ⇒ early phase• BZ powered Jet•

McKinney (2005)• fΩ = 3 (a=0.8), 10 (a=0.9), 80 (a=1.0)• ~ 10 % can be used for GRB Jet (McKinney 2005)• LBZ ~ 1050-51 erg/s for higher entropy model• LBZ ~ 1051-52 erg/s for higher entropy model• Weaker dependence : dot(M)^(1) ⇒ later phase

How to make SN component
 Ingredients (ν-sphere + standing shock) are same, topology is different

1．There are ‘gain regions’.
 2．SASI (Standing Accretion Shock Instability) will set in.
 Simulations relaxing equatorial symmetry should be done Consequences of higher entropy

Smaller amount of heavy elements
 Less severe photo-dissociation loss Fe：~1052 erg per 1Msolar

Larger ram pressure Larger energy explosion if succeeded How important convection is ?
Milosavljevic+ 2011

gain region

Summary The first full GR simulations, incorporating microphysics, of stellar

core collapse are performed, adopting high entropy models
 PNS phase in collapsar is good source for GWs and neutrinos
Aloy’s talk

 BH formation process is quite dynamical, accompanying oblique

shock, convection, KH instability, outflows, and so onThe dynamics is sensitive to the rotational profile which is poorly known

 Massive accretion disk around BH is also dynamicalTime variability in mass accretion rate and neutrino luminosity
 Could be a strong GW emitter The resulting system has preferable features for LGRBs

appendix

GWs from PNS g-mode PNS g-mode (Burrows et al. (2006); Ott et al. (2006)):


Can not reproduce in other groups / or very weak

 Ott (2009) : g-mode amplitude strongly depends on grid

resolution and grid setting (they use a special grid)

GWs from non-axisymmetric deformation
 Strong EOS dependence (Scheidegger et al. A&A 514, A51 2010)
3D Newtonian MHD simulation without deleptonisation

 Lattimer-Swesty vs Shen (T/W@bounce ~ 9%)Amplitude: hShen is 3-10 times larger than hLS

30

100

Lattimer-Swesty

Shen et alBasic equations for (ν-)radiation field

Boltzmann (3+3+1 dim) equation for the distribution functionComputationally not feasible
to solve it directly
Some approximate treatment
is necessary

f dp a faaap

(pu)
S
[x,p, f]a
x a d p aa

Truncated moment formalism (Thorne 1981; Shibata et al. 2011)

Truncation at
2nd order,gray (for simplicity)Energy and flux conservation equations for radiation field bT ab  S a

Closure relation : Pij=Pij(E,Fk)
Tab   f ( p c , x c ) pa pb dV p  Ena nb  Fa nb  Fb na  Pab

essential for properties of radiation fields

Stiff source terms(characterized by weak interaction)
numerically cumbersome to treat

 t E   j (F j   j E )  S E
 t Fi   j (Pij   j Fi )  S F

Closure relation: M-1 closure3(1   ) ijij
 P  3  1 Pthin
Pthick22



ij



exact in optically thin and thick limits

can solve the so-called ‘shadow test’3 4 f 2F Ff  0a 0E0a25 2 43f 2
1
ab
P0 ,thick  E0 ( g ab  u au b )3vacuumabsorber

Takahashi, Ohsuga, YS, Inoue, & Tomida (2013)aab0 , thin

PbF F
 E0 0 02| F0 |

Approx. Explicit treatment
A problematic issue
 Local, weak timescale is too short in dense regionst~ Y / Y  tweakedyn

Leak-out timescale with which neutrinos leak away from the system
is much longert
 t (~ R / c) ~ tweakeleakdynRewrite the system of equation using this aTabFluid  Qb(weak) aTabFluid  Qb(leak) aTab  Qb(weak) aTab  Qb(leak)We can also include the neutrino heating in this framework

S(a -heating)   ( ) ( J  -eq  J )u a  H a

Approx. Explicit treatment


Step 1. Neutrinos are divided into ‘trapped’ and ‘streaming’ parts( )abT( , trap )abT( ,stream )abT a (Tba ( , trap)  Tba ( , stream) )  Qb(weak) aTba ( , trap)  Qb( weak )  Qb(leak)

Trapped : interact sufficiently
frequently with matter aTba ( , stream)  Qb(leak) Streaming : phenomenologicalflow of freely streaming neutrinos (characterized by leakage timescale)Step2. Trapped-ν is combined with fluid part: Tab  Tab(fluid)  Tab( ,trap ) aTba (fluid)  Qb(weak) aTba ( , trap)  Qb( weak )  Qb(leak) aTba  Qb(leak)

Solve this equation using truncated (two) momentum formalism

Summary. The equations to be solved is characterized by t,leakSee Sekiguchi et al. (2013) for further details

Importance of Rotation : Oblique Shock Torus-structured shock Infalling materials areaccumulated into the PNS
due to the oblique shock Thermal energy is efficiently
stored near the pole of PNS
 Ram pressure ↓ ⇒Outflow
 Flows hit central PNS
 NS oscillation ⇒ PdV work , Lν ↑

Importance of High Entropy/Rotation :Energy balance Compact core / Oblique shock ⇒ high mass accretion rate Energy balance may not be satisfied ……

Rotation decreases |Qadv| & |Qν| (dense disk) Additional ‘cooling’ sources requiredQ acc Q adv
 Q
 Q   Q   Q   Q acc



adv



Q
outflow/ expansion
convection

Strong dependence of Qν (ν-cooling) on T (and ρ)⇒ slight change of configuration leads to dynamically large change


Torus is partially supported by the (thermal) pressure gradient Smaller amount of heavy nuclei ⇒ more energetic SNe ?
Dissociation of 0.1 Msolar Fe costs ~ 1051 erg

Higher temperature : Less Pauli blocking in neutrino pair annihilation

Importance of Rotation: BH spin
Energy conversion efficiency can change two orders of magnitude
 Disk properties to neutrinos strongly depend on BH spin

Slow rot. BH ⇒ ISCO (disk edge) located far ⇒ low density / opacity ⇒Efficient cooling ⇒ the local valance satisfied ⇒ weak/no time variabilitytrapped

a = 0Chen & Beloborodov (2007)

a = 0.95

Similarities to ordinary SN
 Same components: ‘stalled’ shock + neutrino sphere/torus

SASI-like activities are likely to occur
 The gain (neutrino-heated) regions do exist
 Only topology is different

Smaller amount of heavy
nuclei due to high entropy⇒ more energetic SNe ?
Dissociation of 0.1 Msolar Fe
costs ~ 1051 erg

gain region

Property of the BH and the accretion disk

BH mass : 6.5 Msolar → 14 Msolar

BH spin : 0.6 → 0.9Disk mass :thin disk phase ~ 0.1 Msolar Rapid advection into BH
Thick torus phase ~ 0.8 Msolar
 High angular momentum

Mass accretion rate into BH

Thin disk phase ~ 20-40 Msolar/s
Convective torus ~ 5-10 Msolar/s
rapid time variability