School of Physics and Astronomy

Modeling the central engine of relativistic jets ‐ application to GRBs outﬂows
Noemie Globus & Amir Levinson

A. Levinson and N. Globus, ApJ 770, 159 (2013)
N. Globus and A. Levinson, Phys. Rev. D, 88, 084046 (2013)

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

The double ﬂow structure of a black hole magnetosphere

RotaGng black hole

GRBs: energy deposiGon by νν → e‐e+
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

The double ﬂow structure of a black hole magnetospherestagnaGon
up=0

RotaGng black hole
The posiGon of the stagnaGon surface depends on the energy injecGon rate (Levinson & Globus 2013)

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

The double ﬂow structure of a black hole magnetosphere

RotaGng black hole

GRBs: energy deposiGon by νν → e‐e+Zalamea & Beloborodov 2011

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

The double ﬂow structure of a black hole magnetosphere

Blandford Znajek activated:energy ﬂux along magnetic ﬁeld linesRotaGng black hole + magneGc ﬁeld (B~1015G)
CondiGons
1) ωH>ΩF>0
Takahashi+ 1990

2) Alfvén surface of the inﬂow inside the ergoregion

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

3) Loading ?

Loaded GRMHD ﬂows
Levinson, 2006; Globus & Levinson, 2013

• staGonary + axi‐symmetric MHD• mass and energy injecGon included

source terms: parGcle qn; energy‐momentum qα• split‐monopole geometry invoked

Stream funcGon (magneGc ﬂux) : Ψ(r,θ) (assumed)
Constants of moGon along a given streamline (qn= qα=0)‐‐‐‐‐

angular velocity: Ω (a free parameter)parGcle ﬂux per unit B ﬂux: ηspeciﬁc energy (per baryon ): εspeciﬁc angular momentum : L
speciﬁc entropy : s

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto Universityoudlow
oudlow

TYPE Ineutrino
powered by black holeenergy ﬂux
BZ ac+vated! ηε(inﬂow: η < 0)
εH<0 ⇒ εr > 0 (extracGon)

powered by external source

accre+on diskblackholea>0a>0

oudlow
oudlow

TYPE IIB! (rst ) ! 0

inﬂow
inﬂow

heaGngenergy ﬂux on horizon: εrenergy ﬂux

rst

rst

inﬂow
inﬂow

black hole

< <a1< 1
0 <0 aergosphereenergy ﬂux

rstst

B! (rst ) = 0
hea+ngenergy ﬂux

accre+on disk

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

oudlow
oudlow

rst

rst

TYPE I

neutrino
powered by black holeenergy ﬂux
BZ ac+vatedaccre+on disk

blackholea>0a>0oudlow
oudlow

powered by external source

B! (rst ) ! 0

inﬂow
inﬂowheaGng

TYPE II

energy ﬂux

plasma load

inﬂow
inﬂow

black hole

< <a1< 10 <0 aergosphereenergy ﬂux

rstst

B! (rst ) = 0hea+ng
energy ﬂux

accre+on disk

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

Loaded GRMHD ﬂows
Levinson, 2006; Globus & Levinson, 2013

• staGonary + axi‐symmetric MHD• mass and energy injecGon included

source terms: parGcle qn; energy‐momentum qα• split‐monopole geometry invoked
Loading :Energy deposiGon

1"r!g(qt (r) = qt 0! (r ! rst ))adiabaGc (ε is conserved)!g! r = !qt

εr = ρur ε energy ﬂux
ParGcle deposiGon

qn (r) = qn0! (r ! rst )qt (r) = f (r) (ε not cst)

(η is conserved along ﬁeld lines)

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

TYPE I

Loaded MHD ﬂows in Kerr geometry
Example : cold adiabatic case

Globus & Levinson, 2013

BZ result

Assump+ons
sta+onnarity
axisymmetry
ideal MHD
Split monopole geometryeach diamond = an inﬂow solution that crosses all the MHD criticalpoints and for which rotational energy is extracted from the BH
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

TYPE I

Loaded MHD ﬂows in Kerr geometry
Example : cold adiabatic case

BZ result

criGcal loading:for η > ηc
BZ is shut‐down !
Assump+ons
sta+onnarity
axisymmetry
ideal MHD
Split monopole geometry

spin dependance
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

ηc ∝a21+ 1− a2

TYPE I

Assump+ons
sta+onnarity
axisymmetry
ideal MHDSplit monopole geometry

Loaded MHD ﬂows in Kerr geometry
Example : cold adiabatic caseangular dependance η c ∝ sin 2 θ
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

oudlow
oudlow

TYPE I

neutrino
powered by black holeenergy ﬂux
BZ ac+vatedaccre+on disk

blackholea>0
a>0

oudlow
oudlow

powered by external source

B! (rst ) ! 0

inﬂow
inﬂow

heaGngTYPE II

energy ﬂux

rst

rst

inﬂow
inﬂow

black hole

< <a1< 10 <0 aergosphereenergy ﬂux

rstst

B! (rst ) = 0
hea+ngenergy ﬂux

accre+on disk

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

TYPE II

Double transonic ﬂow in Schwarzschild geometry
Levinson & Globus, 2013

a=L=0soluGons with a realisGc energy injecGon!bproﬁle : !qt (r) = Q! 0 r
outer sonic line

Inner sonic line

Q! 0 : neutrino annihilaGon rates from Zalamea& Beloborodov 2011

Sonic points

3rc2 (−q tc ) = ±4(rc − 3m H )pc• powered by neutrino source• fracGon of injected energy that emerges at inﬁnity > 0.5• high speciﬁc entropy
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto Universityoudlow
oudlow

TYPE I

neutrino
powered by black holeenergy ﬂux

rstrstη < ηcεH < 0B! (rst ) ! 0

inﬂow
inﬂow

energy ﬂux

heaGngBZ ac+vatedaccre+on disk

blackholea>0a>0ergosphere

Loading

oudlow
oudlow

TYPE IIpowered by external source

inﬂow
inﬂow

black hole

< <a1< 1
0 <0 aenergy ﬂux

rstst

B! (rst ) = 0
hea+ngenergy ﬂux

accre+on disk

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

η > ηcεH > 0To conclude...
GRB case :oudlow
oudlow

TYPE I

energy ﬂux

heaGng)2/9#M &! acc < 0.1 % H (! m$ 3M " 'B! (rst ) ! 0

inﬂow
inﬂow

neutrino
powered by black holeif

E! !! < PBZ

energy ﬂux

rstrstη < ηcεH < 0BZ ac+vated
8/9#& blackhole*> 0 M .s)1% 27 B 2 ( aF(a)"$ 10 G cm ' a > 0accre+on diskergosphere(both BZ and pressure driven jets currently under invesGgaGon)

oudlow
oudlow

Otherwise:

TYPE IIdriven by neutrino annihilaGon

inﬂow
inﬂow

νν → e‐e+black hole

< <a1< 10 <0 aenergy ﬂux

rstst

B! (rst ) = 0hea+ng
energy ﬂux

accre+on disk

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

η > ηcεH > 0BACK‐UP

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

Energy source for GRBs relativistic winds...From the accretion disk ?
• Neutrino dominated accreGon ﬂows are candidates to be the central engine of GRB oudlows.
⇒ DerivaGon of disk structure and neutrino annihilaGon rates: Popham et al. 1999, Zalamea &Beloborodov 2011 (calculaGons in the Kerr spaceGme)• Levinson, 2006 : Loaded (i.e. non adiabaGc) relaGvisGc MHD wind in the Schwarzschild spaceGme.

…From the black hole polar region ?

(this talk)• Plasma injecGon in the magnetosphere : νν → e+e‐ in GRBs (the baryonic component from the disk
can be neglected)• The energy source is the rotaGonal energy of the black hole⇒ Pioneering work of Blandford & Znajek 1977
⇒ Many semi‐analyGc studies and numerical simulaGons support this scenario (Takahashi et al. 1990,Komissarov 2004, Barkov & Komissarov 2008..)• The energy source is neutrino annihilaGon (neutrinos are emimed from the accreGon disk)⇒ SoluGons for the double‐ﬂow structure in the Schwarzschild geometry : pressure‐driven winds(Jaroszynski, 1996; Levinson & Globus 2013)

Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University

TYPE II

Loaded MHD ﬂows in Kerr geometry
Example : hot caseh= w/ρ ≈ 4p/ρ >> 1
w = speciﬁc enthalpy

Assump+ons
sta+onnarity
axisymmetry
ideal MHD
Split monopole geometry
Conference on Gamma‐Ray Bursts Nov.11 ‐ Nov. 15, 2013 Kyoto University