Y TP YUKAWA INSTITUTE FOR THEORETICAL PHYSICS NPCSM 2016, - - PowerPoint PPT Presentation

Neutrino-driven Mass Ejection from the Remnant of Binary Neutron Star Merger

Sho Fujibayashi (Kyoto U), Yuichiro Sekiguchi (Toho U),

Kenta Kiuchi (YITP), and Masaru Shibata (YITP)

Y TP

YUKAWA INSTITUTE FOR THEORETICAL PHYSICS

NPCSM 2016, 11.9.2016, YITP, Kyoto, Japan

Evolution After Remnant of Binary NS Merger

(Demorest et al. 10; Antoniadis et al. 13)

Neutrino-driven Outflow in MNS Phase

MNS Torus

ν

ν¯ ν

¯ ν

◎ MNS phase

• Large neutrino luminosity from the

MNS and torus (~1053 erg/s)

• The effect of neutrinos would be significant.

GRB?

Neutrino-driven Outflow in MNS Phase

MNS Torus

ν

ν¯ ν

¯ ν

Due to neutrino pair-annihilation heating ◎ Relativistic jet for short GRBs?

GRB?

Neutrino-driven Outflow in MNS Phase

MNS Torus

Just et al. 16

Recent studies : Monte-Carlo method using Newtonian simulation

ν

ν¯ ν

¯ ν

RHD simulations for BH-torus using equilibrium torus as initial conditions

Richers et al. 15,

Due to neutrino pair-annihilation heating ◎ Relativistic jet for short GRBs?

Kilonova/ Macronova?

GRB?

Neutrino-driven Outflow in MNS Phase

MNS Torus

ν

ν¯ ν

¯ ν

Fernandez & Metzger 13, Perego et al. 14 Metzger & Fernandez 14, Just et al. 15 Fernandez et al. 15

◎ Neutrino-driven winds

This component would contributes to heavy element nucleosynthesis and electromagnetic signals

Just et al. 16

Due to neutrino pair-annihilation heating ◎ Relativistic jet for short GRBs?

Recent studies : Monte-Carlo method using Newtonian simulation RHD simulations for BH-torus using equilibrium torus as initial conditions

Richers et al. 15,

Heavy element synthesis?

Viscosity-driven wind : Fernandez’s talk

Kilonova/ Macronova?

GRB?

Neutrino-driven Outflow in MNS Phase

MNS Torus

ν

ν¯ ν

¯ ν

Fernandez & Metzger 13, Perego et al. 14 Metzger & Fernandez 14, Just et al. 15 Fernandez et al. 15

◎ Neutrino-driven winds

This component would contributes to heavy element nucleosynthesis and electromagnetic signals

Just et al. 16

Due to neutrino pair-annihilation heating ◎ Relativistic jet for short GRBs?

Recent studies : Monte-Carlo method using Newtonian simulation RHD simulations for BH-torus using equilibrium torus as initial conditions

Richers et al. 15,

Heavy element synthesis?

Viscosity-driven wind : Fernandez’s talk

We simulate the MNS-torus system in fully general relativistic manner in order to investigate the properties of neutrino-driven

• utflow from the NS−NS merger remnant.

We consider reaction and investigate the effects.

ν¯ ν → e−e+

◎ Strategy

(Sekiguchi et al. 15)

x-y plane

i) Merger of NS−NS and MNS formation by 3-D full GR simulation

Equation of state : DD2 ( → The remnant is long-lived MNS)

Method

◎ Strategy

(Sekiguchi et al. 15)

x-y plane

i) Merger of NS−NS and MNS formation by 3-D full GR simulation

Equation of state : DD2 ( → The remnant is long-lived MNS)

x-z plane

Angle-averaged configuration

Average over azimuthal angles around the rotational axis after ~50 ms after the merger, when the system settles into quasi-axisymmetic configuration.

ii) Long-term Axisymmetric 2-D simulation using angle-averaged configuration as a initial condition

Method

MNS & innermost part of the torus have large neutrino emissivity !

◎ Basic Equations

Method

• Full GR axisymmetric neutrino radiation hydrodynamics simulation

Thorne 81 Shibata et al. 11

• Einstein’s equation : BSSN formalism
• General relativistic radiation hydrodynamics :
• Lepton fraction equations

We use Cartoon method to impose axially symmetric conditions.

rαT α

β = Q(leak)β

rαT(S,ν)

α β = Q(leak)β

baryons, electrons, trapped neutrinos streaming neutrinos † We solve neutrino radiation transfer using Moment formalism with M1-closure. ††We do not consider the viscosity in this simulation. Thus we focus only on purely radiation-hydrodynamical effects on the system.

Leakage+ scheme incorporating Moment formalism

= 1c

Results : Dynamics of Fluid

The density around the rotational axis falls rapidly. Outflow with ~0.5 c. Relativistic outflow is not seen.

Density color map of meridional plane

100 ms 10 ms 300 ms

Results : Dynamics of Fluid

• First ~50 ms

Strong outflow due to Pair-annihilation heating

Log Pair-annihilation heating rate density [erg/s/cm3]

• ~100 ms later

Heating rate decrease → outflow becomes weak

~ 0.2 c

Relativistic outflow is not observed in this setup

100 ms 10 ms 300 ms

Results : Dynamics of Fluid

• First ~50 ms

Strong outflow due to Pair-annihilation heating

Result w/o Pair-heating

• ~100 ms later

Heating rate decrease → outflow becomes weak

~ 0.2 c

※ Effect of Pair-heating is large. Strong outflow is not seen in the result without ν ν pair-annihilation.

−

Results : Luminosity & Pair-annihilation heating rates

1051 1052 1053 50 100 150 200 250 300 350 400 Luminosity [erg/s] time [ms] electron anti-electron

• ther

Neutrino Luminosities ( νe νe νx )

− t = 0 ms t = 300 ms

1048 1049 1050 1051 50 100 150 200 250 300 350 400 0.0001 0.001 0.01 0.1 Total heating rate (>1010g/cc) [erg/s] Efficiency time [ms]

Time [ms] Efficiency Total Heating Rate (ρ<1010g/cc)

◎ Luminosity decreases to ~1052 erg/s in ~300ms. and get quasi-stationary.

◎ Total pair-annihilation heating rate is >1050 erg/s in first 50 ms, but decreases to ~1049 erg/s in ~300 ms

˙ Epair ∝ Lν

2

efficiency ∝ Lν

→

Efficiency :

η = ˙ Epair Lν,tot ~ 0.3% → 0.03 %

1051 1052 1053 50 100 150 200 250 300 350 400 Luminosity [erg/s] time [ms] electron anti-electron

• ther

Neutrino Luminosities ( νe νe νx )

−

1048 1049 1050 1051 50 100 150 200 250 300 350 400 0.0001 0.001 0.01 0.1 Total heating rate (>1010g/cc) [erg/s] Efficiency time [ms]

Time [ms] Efficiency Total Heating Rate (ρ<1010g/cc)

◎ Luminosity decreases to ~1052 erg/s in ~300ms. and get quasi-stationary.

Results : Luminosity & Pair-annihilation heating rates

˙ Epair = Z

ρ<1010g/cm3 d3x ˙

Qpair

Results: The Properties of the Ejecta

• Unbound mass ~ 3×10-4 M☉
• Kinetic energy ~ 5×1048 erg

Subdominant compared to dynamical ejecta

(~10-3 M☉, 2×1049 erg for DD2 EOS)

(Sekiguchi et al. 15)

0×100 1×10-4 2×10-4 3×10-4 Mej [Msun] w/ pair w/o pair 0×100 2×1048 4×1048 6×1048 Ekin [erg] 0.1 0.2 50 100 150 200 250 300 350 400 Vej [c] Time [ms]

Time [ms]

~ 0.1− 0.2 c

• Average velocity

ejected mass kinetic energy Typical velocity w/ pair-heating w/o pair-heating

※ Effect of Pair-heating is large. Without pair-heating process, we underestimate the amount and kinetic energy of the neutrino-driven outflow.

Results : Electron fraction & Entropy distribution

10-6 10-5 10-4 0.1 0.2 0.3 0.4 0.5 mass per bin [Msun] Ye 400.28 ms w/o pair 10 100 1000 s [kB/baryon]

◎ Mass histogram of ejected material @ t=400 ms

• Material of Ye>0.25 is mainly ejected. Typical value : ~0.4.
• A small amount (~10-6M☉) of material has very large specific entropy.

Pair-annihilation process ( ) can inject energy regardless of baryon density.

ν + ¯ ν → e− + e+

Histogram with pair-heating without pair-heating

electron fraction specific entropy

r-process in ν-driven outflow

◎ Estimate following Hoffman et al. 97. In the most of the neutrino-driven outflow, heavy nuclei of A>130 are hardly produced via r-process. Detailed nucleosynthesis study → Next work

275.02 ms 10 100 1000 s [kB/baryon] 0.1 0.2 0.3 0.4 0.5 Ye

• 7
• 6
• 5

Mass per bin [Msun]

A>200 A>130

(assuming τexp ~ 50 ms)

A>130 A>200 nuclei are produced via the r-process

Mass distribution in Entropy – Electron fraction plane

Pair-annihilation Heating by Ray-tracing Method

Current treatment of neutrino transfer: Moment formalism with M1-closure relation (Shibata et al. 11)

This method cannot treat the crossing of two beams. Pair-annihilation heating rate should be compared to more Ab initio calculation.

Calculate the pair-annihilation heating rate by ray-tracing method using snapshots of the simulation.

Qν¯

ν = 1

4 c(mec2)2 C1 + C2 3 Z dΩIν Z dΩ0I¯

ν[h✏iν + h✏i¯ ν](1 cos ✓ν¯ ν)2

dΩIν = Qeff

ν

d3x0 π|x − x0|2

*We ignore general relativistic effects. (Ruffert et al. 97)

Log Total neutrino emissivity [erg/s/cm3]

Pair-annihilation Heating Rate by Ray-tracing method

Cooling

24 25 26 27 28 29 30 31 32 33 10 15 20 25 30 35 40 log heating/cooling rate [erg/s/cc] z [km] t = 100.000 ms Qpair(M1) (ray-tracing) total cooling

Pair-annihilation heating rate along z-axis using snapshot at t = 100ms

Moment formalism Ray-tracing Heating rate estimated with (simple) ray-tracing method ~10 times larger that that with moment formalism. Heating rate would be underestimated.

Summary

Long-term simulations for MNS-torus system to investigate the neutrino- driven mass ejection from the system.

• Neutrinos

– Luminosity ~1053 → 1052 erg/s in ~100ms. – Pair-annihilation heating > 1050 erg/s at first (η~0.3%), but decreases to ~ 1049 erg/s (η~ 0.03%). – heating rate would be underestimated.

• Ejected mass

– Unbound mass : Mej ~ (10-4−10-3) M☉. – The kinetic energy : Ekin ~ 1048 − 1049 erg. – Subdominant compared to dynamical component.

† Investigating viscosity-driven wind : near future!

( 3+1 decomposition of )

Moment Formalism

n Evolution Eqs.

M αβ = Z dVppαpβf(p, x) = Enαnβ + F αnβ + F βnα + P αβ

(Energy-momentum tensor of neutrino) nα : normal of the time slice

Thorne 81, Shibata et al. 11

n Variables n Closure relation (M1-closure)

• pt. thin →

P ij = E 2w2 + 1 ⇥ (2w2 − 1)γij − 4V iV j⇤ + 1 w ⇥ F iV j + F jV i⇤ + 2F kuk w(2w2 + 1) ⇥ −w2γij + V iV j⇤ P ij = E F iF j γklF kF l

= 1 3Eγij (if ui = 0)

• pt. thick→

rβM αβ = (Source Terms)α

Qeff = (1 − e−τ)Qleak + e−τQreac

✏leak = Qleak/Rleak ✏reac = Qreac/Rreac

✏ = (1 − e−τ)✏leak + e−τ✏reac

τdiff(E) = τ 2(E) c lmfp(E)

diffusion time

Qleak = Z dE En(E) τdiff(E)

• due to diffusion (opt-thick limit)

Qreac = Qreac(ρ, Ye, T) =

(electron, positron-capture of nuclei) + (pair-production)

• Energy loss rate due to reaction (opt-thin limit)
• Effective energy loss rate

Solving this Eq. → obtain ε