Compact Stars
Lecture 11
Central engines of GRBs
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We talked about the gamma ray bursts as the
extragalactic jet sources, their
phenomenology and modeling issues.
Today I will present the GRB central engine
models, which aim to explain how the
relativistic jets are launched.
Progenitors
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Progenitors range from mergers of compact
stars to collapse of massive stars
Massive star must form a black hole: 10% of all
collapsing stars; moreover the star must have
enough rotation in its envelopee to form a disk:
another 10%. GRBs (due to collapsars) may
therefore occur in about 1% of all core-collapse
supernovae (Type I b/c)
Models must account for the energy of
explosion, collimation, rapid variability, range of
durations, statistics
Observations
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Red bump in
lightcurves and lines
in spectra: in the long
GRBs SN signatures
Variable profiles
Statistics; host
galaxies etc.
Stanek et al. (2003)
Model requirementss
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Energetics of explosion: after beaming and jet efficiency
correntions, we need to have about 1052 ergs to be released.
This is a binding energy of a compact star, E = G M 2/r (M= 10
MSun, r=10 km).
Most efficient energy extraction mechanism is accretion onto a
compact star.
Duration of event: rotation period (at the surface of star), P = 2
πr3/2/G1/2M1/2 = 0.3 ms, devided by viscosity. For small disks and
alpha~0.1 this gives about 300 ms. Short events may be
powered by accretion of remnant matter after a merger, onto a
black hole/neutron star. Long events require large disks,
fallback supply of matter from part of extended envelope, and
long-term existence of rotationally supported disks
Model requirements
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Variability of
event: size vs.
speed of light. Dt
= 2pi r /c = 0.6 ms
at the inner radius
of a disk
Some scenarios
Jet power
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Three mechanisms
proposed for jet
acceleration: thermal
expansion, radiation
pressure, magnetic field and
rotation
In GRBs, also neutrinos
may be important
(anihillation)
Collimation mechanisms:
thick disk or corona,
pressure gradient in
surrounding wall, external
(matter dominated) jet,
toroidal magnetic field
C. Fragile, 2008 (arXiv:0810.0526)
Conditions in the central engine
Pairs e+,e-
Anihillation of neutrinos
and antineutrinos
Ab
so
rpt
ion
Disk heated by viscosity
and cooled by neutrino emission
erin
t
t
a
Sc
g
Densities 1010-1012 g cm-3
Temperatures kT above 1 MeV
Annihillation efficiency
Magnetic dynamo
Hoover Dam – Arizona/Nevada (C. Fryer)
Magnetic dynamo
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Gravitation potential energy: accelerates waterfall. Water
moves the rotating magnets and electric current is
produced.
With this analogy, accretion process releases gravitational
potential energy and magnetis field is coupled with
rotation. The magnetic field lines are frozen into the disk
plasma and rotate, acting as a dynamo.
The black hole also rotates. Open field lines are formed
along the rotation axis; along these lines jets are launched.
Analogy to pulsar magnetosphere
Magnetic field lines act as
electric wires : charged particles
move along the lines towards
weaker B field and back.
In this electric loop, the Poynting
flux is driving the star's
rotational energy towards weak
B field.
Pocess proposed by Goldreich & Julian (1969) for rotating neutron
stars → pulsars
BH rotational energy extraction
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Black hole also
has
magnetosphere
The spark gaps
are formed there,
producing
electron-positron
pairs
Charged particles
move along field
lines
Blandford & Znajek 1977
See book of K. Thorne, “The
membrane paradigm” ( 1986)
Conditions in the disk
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Temperature > 1
MeV: electronpositron pairs must
be produced
Nuclear densities:
electrons partially
degenerate
Neutronisation
processes:
equilibrium p/n
established
p + e- -> n + ν
n + e+ -> p + ν-
Conditions in the disk
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Some Helium nuclei must also be formed at
such densities and temperatures (NSE)
Helium may be photodissociated.
Neutrinos: absorbed and scattered, if the
opacities are high
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Photons: totally trapped
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Advective cooling also important
Conditions in Hiperaccretion disk
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Hiperaccretion: rates
of 0.01-10 MSun/s
Chemical and
pressure balance
required by nuclear
reaction rates
These are given
under degeneracy of
species
Charge neutrality
condition; neutrino
opacities
Popham et al. 1999;
Di Matteo et al.
2002; Kohri et al.
2002, 2005; Chen &
Beloborodov 2007;
Reynoso et al. 2006;
Janiuk et al. 2004;
2007; 2010; 2013
p, n, e+, eHe,
, e, 

Hiperaccretion disk
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Model must account for coupling between
degeneracy of matter and neutrino cooling.
Cooling → lower temperature →degeneracy →
low density of positrons → lower cooling →
higher temperature
Chen & Beloborodov (2007)
Equation of state
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The total pressure must include the contributions from
gas, radiation, and degenerate electrons:
4/3
4 /3
k
1 3
11 4
c 3

P =P gas P rad P deg =  T   X nuc  a T 2  h   m p   
e
mp
4 4
12
3 8
where mass fraction of free nucleons depends nonlinearly on density and temperature (Popham et al. 1999;
Di matteo et al. 2002; Janiuk et al. 2004)
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In more advanced modeling, the equation of state
must be computed numerically by solving the balance
of nuclear reactions (Yuan 2005; Janiuk et al. 2007;
also Lattimer & Swesty 1991; Setiawan et al. 2004)
Numerical scheme for CE
structure
Janiuk, Yuan, Perna & Di Matteo (2007)
Neutrino cooling
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The photons are totally trapped in the very
opaque disk. The main cooling mechanism
is the emission of neutrinos, via the
following reactions:
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Electron and positron capture on nucleons
(URCA reactions) → electron neutrinos
Electron-positron pair anihillation (electron,
muon and tau neutrinos)
Bremsstrahlung (all neutrino flavours)
Emissivities in first two cases must be
computed numerically (Itoh et al. 1996;
Yakovlev 2005)
Neutrino luminosity
Inner disk: possibly unsttable?
Janiuk, et al., 2007, ApJ
BH rotation
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For rotating black hole,
the inner edge of the
disk moves closer to it,
depending on
a=cJ/GM2
We need to modify
also the viscous
heating, Keplerian
rotation and disk
height, accordingly to
a, in a standard alphadisk model (e.g.
Romero et al. 2009)
Riffert & Herold (1995)
BH rotation: instability region
more plausible
Collapsars?
Models with
spinning BH have
the unstable region
even for moderate
Mdot
Red: alfa = 0.1
Blue: alfa = 0.3
Mergers?
Janiuk & Yuan, 2010, A&A
Density and temperature profiles
Transfer of BH rotational energy
to the disk
–
–
Open field lines:
● Extraction of BH rotation
energy through the BlandfordZnajek process
Closed field lines:
● On the disk surface and BH
horizon the electromotive
force is induced
● Additional torque → leads to
disk extra heating
● Energy of BH rotation may be
transferred to the disk
McDonald &Thorne (1982);
van Putten (1999);
Li & Paczyński (2000); Li (2000; 2002)
Wang et al (2002)
Transfer of BH rotation to the disk
Topology of B field: assumed Bz ~ξ-n
Janiuk & Yuan, 2010
Torque is posiitive, if BH rotates faster than the differentially
rotating disk, ΩH > ΩD
Torque normalization: equipartition BH2/8πPmax = βmag ~α
Central engine
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We can model the central engine as a
differentially rotating accretion disk, with
extremely large Mdot and hence at nuclear
densities and temperatures
The disk can be magnetically coupled to the
spinning black hole
Thermal instabilities due to high neutrino
pressure and/or Helium photodissociacion may
arise in the innermost radii of this disk
The instability region may overlap with the
magnetically coupled region where extra torque
exists
Outskirts: gravitational instability
Chen & Beloborodov (2007)
Central engine
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The extra torque at inner radii due to MC
coupling with BH seems not to stabilize
the disk (Lei et al. 2009).
The gravitational instability present at
large radii.
Such instabilities are plausible to explain
the variable energy output from the
engine (hence, variable Lorentz factors
with the remote jets, internal shocks, GRB
variability etc.)
More detailed, time-dependent
simulations are needed to verify these
models. Fully GR and MHD models,
instead of alpha-disks, are necessary to
verify the role of accretion and BH spin in
GRB production.
Janiuk, Mioduszewski, Mościbrodzka 2013
Next week
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Lectures summary... cosmology, BH mergers,
gravitational waves...
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or Nature or Science. Astrophysics.
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