Universidad de Valencia
Departamento de Astronomía y Astrofísica
General Relativistic
hydrodynamic simulations of
post-neutron star mergers as
progenitors of short GRBs
Miguel A. Aloy
In collaboration with:
T.-H Janka and E. Müller
(find out more @ astro-ph/0408291)
UCLA Workshop III: Relativistic Astrophysics
Los Angeles, 3 – 5 - 2005
GRBs, phenomenology:
• First detected in 60s by the military satellites Vela (but 1st publication
in Klebesadel et al.1973)
• Point explosion in a r-n medium @ rate: ~ 1/day
• Energy: E ~ 1-103 FOE (isotropic, mainly in gamma-rays)

Causality ⇒ energy liberated in R~100 km on timescales of < secs.
GRBs, phenomenology:
• First detected in 60s by the military satellites Vela (but 1st publication
in Klebesadel et al.1973)
• Point explosion in a r-n medium @ rate: ~ 1/day
• Energy: E ~ 1-103 FOE (isotropic, mainly in gamma-rays)

Causality ⇒ energy liberated in R~100 km on timescales of < secs.
• Distribution: Isotropic, but inhomogeneous
Homogeneity (Euclidean space): N ~ R3
Dependence of the flux with R: P ~ R-2
N ~ P-3/2
Log N – Log P
distribution of 772
bursts in the energy and
50 – 300 keV
rd
3 BATSE GRB catalogue
(Meegan et al. 1996)
GRBs, phenomenology:
•
Non-thermal spectrum ⇒ optically thin emission region.
•
Variability of the light curves down to ~ 0.001 s.
•
Distance: z = 0.085 ... 5.0 ⇒ cosmological location!
•
Mejecta ~ 10-4 Msun, = ( 1 - v2/c2 )-1/2 ~ 100
•
Two classes:
1. Short: T90< 2 s, harder
2. Long: T90> 2 s, softer
•
Afterglows:
•
X-rays, optical, radio
•
Durations ~ days after GRB
Duration of 427 bursts
that do not display
significant gaps
3rd BATSE GRB catalogue
(Meegan et al. 1996)
GRBs, theory: Fireballs
1030
cm-3s-1
• Releasing ~
erg
implies the formation of an
fireball (Cavallo & Rees 1978).
_
+
e e ,
g
• Compactness problem: Since most of the energy detected is
_
+
>0.5 MeV, the optical depth against g g ⇒ e e is huge and
photons cannot escape!
gg =
1013 fp F-7(D / 3Gpc)2 ( t / 10ms)-2
• Relativistic expansion reduces the effective threshold energy for
pair production (Fenimore et al. 1993):
~ 100( g/10 GeV)1/2( t/MeV)1/2
gg =
•
•
1013 /
4+2
fp F-7(D / 3Gpc)2 ( t / 10ms)-2
Theoretically, a relativistic outflow results if an initial energy E0 is
imparted to a mass M0 «E0/c2 (Relativistic Sedov solution;
Blandford-McKee).
Starting from rl the expansion of the gas converts its Eint into Ekin
until ~ max~ ~ E0/M0c2 which happens at rs  rl , beyond
which the flow coasts with ~ ~ constant.
GRBs, theory: Internal vs External shocks

Some caveats of the fireball model:
1) Efficiency: Conversion of MOST of its Eint into Ekin
⇒ almost no g-luminosity, low energetic efficiency.
2) Spectrum: Quasy-thermal spectra (observed: power-law).
3) Timescales: Tg-escape ~ Tthin ~ milliseconds

⇒ cannot account for long events.
Solution:
• the energy is initially produced in another form and is only
converted in gamma-rays at large distances from the source.
• How: tenuous, collisionless, relativistic shocks that reconvert
Ekin of the baryons into nonthermal particle and g energy by,
e.g., Fermi process:
• chaotic E, B fields
• pmin ~ bulk , emin ~ (mp/me) bulk
• Diffusive shock acceleration ⇒ N( e) ∝
e
-a,
a~2-3
⇒ Gamma radiation: Synchrotron + Inverse Compton
GRBs, theory: Internal vs External shocks
Standar paradigm: fireball shocks are either external (Rees & Mészáros
1992) or internal (Rees & Mészáros 1994).


External shocks: Reff ~ 1015 – 1016 cm
 Interaction with the medium
 May explain some spectral properties of long, smooth bursts and
afterglows.
Internal shocks: Reff ~ 1013 cm
 Irregularities in the flow
-3 s).
 may explain the shortest time scale variability (~10
GRBs: Progenitors
•
Difficult to identify because of lack of observational accuracy
•
More than 200 competing models
•
Most promising: catastrophic collapse events
1) Death of massive stars/SN ⇒ Sources of long GRBs
a) Collapsars (Woosley)
b) Hypernovae (Pacynski)
This association was originally
proposed in the 1st paper on
GRBs (Klebesadel et al. 1973)!
SN-GRB association (L-GRBs!):
SN1998bw/GRB980425
SN2003dh/GRB030329
SN2003lw/GRB031203
2) Mergers of compact binaries ⇒ Sources of short GRBs &
strong GWs
(Pacynski, Goodman, Eichler et al., Mochkovitch et al., Katz &
Canel, etc.)
GRBs, progenitors: long bursts
Collapsars (Woosley 1993)
• Collapse of a massive (WR) rotating star that does not form a successful
SN to a BH (MBH ~ 3Msol ) surrounded by a thick accretion disk. The
hydrogen envelope is lost by stellar winds, interaction with a
companion, etc.
• The viscous accretion onto the BH ⇒ strong heating ⇒ thermal nñ
annihilating preferentially around the axis ⇒ fomation of a relativistic jet
( >10).
Aloy et al (2000)
Newtonian-HD
GRHD
MacFadyen & Woosley (1999)
Progenitors of short GRBs: setting the stage
Merger of a system of compact binaries (SCBs):
•
•
•
•
•
After the merger of a SCB a central BH (MBH ~ 2-3Msol) girded by a
thick accretion torus (Mtorus~ 0.05 – 0.3Msol).
Once the thick disk is formed, up to ~1051 ergs can be released above
the poles of the BH in a region that contains <10-5 Msun of baryonic
matter due to nn annihilations preferentially near axis ⇒ acceleration
to ultrarelativistic speeds.
If the observed duration Tobs
is related to the lifetime of
the system Ta this kind of
events can only belong to the
class of short GRBs because
Tdisk~ 0.05 – 0.5 s.
Local rate of NS-NS events:
~ 800 Gpc-3 y-1 (Kalogera et
al. 2004)
Local rate of short GRBs:
~ 0.8 Gpc-3 y-1 (Guetta &
Piran 2004)
Progenitors of short GRBs: our goals
1. To check the viability of the scenario of merging SCBs for
producing ultrarelativistic outflows (winds, jets, radial
outflows, canon balls?).
Sssssssssssssssssssssssss
s
2. Mechanism of collimation (if any) of the outflowing
plasma.
Sssssssssssssssssssssssss
s
3. Typical opening angles
observed rate of events.
s
and
consequences on the
Sssssssssssssssssssssssss
4. Expected durations of the GRB events generated in this
framework and their relation to the time during which the
source of energy is active (Ta).
Progenitors of short GRBs: our method
Progenitors modelled as non-selfgravitating relativistic perfect fluids:
Tmn = (r + re + p) umun + p gmn
The gravitational field is provided by central Schwarzschild BH:
ds2 = -(1-2M/r) dt2 + (1-2M/r)-1dr2 + r2dq2 + r2 sin2q df2
EoS: Boltzman gas of nucleons + e+e- + radiation (Witti, Janka &
Takahashi 1994). No degeneracy is assumed.
P = Pgas + Prad + Pe+e-
The GRHD equations are solved using the HRSC code GENESIS
(Aloy et al. 1999; num. foundations in Font´s & Rezzolas’s talk) with:
- likely initial model (BH + thick accretion disk)
- BC: rmin  BH; rmax  outflow; q = 0o, 90o reflection
- Release energy in a baryon clean environment
GENESIS: basics
It is a 1D, 2D & 3D parallelized, finite volume code, that
implements a methods of lines (e.g., LeVeque 1992) to
evolve the SRHD, GRHD or RMHD equations.
Key elements:
Coordinates: Cartesian, Cylindrical, Spherical
 Metric: Minkowski, Schwarzschild (exterior).

Riemann solver: HLLE, Marquina FF (Donat et al.
1998), Exact (Pons et al. 2000)
nd or 3rd order TVD Runge—Kutta scheme for
2
time integration (Shu & Osher 1988)

piecewise linear (MinMod)/ PPM reconstruction
 Vectorized Newton—Raphson iteration for
recovery of the primitive variables (r, p, v)

EoS: modular implementation
 Multi-species (tracer approach).
 OpenMP-parallel

GENESIS: extensions (I)
Non-thermal radiation modules: Mimica et al. (2004)







non-thermal electrons: N tracer species corresponding
to N logarithmic Lorentz factor intervals from gmin to gmax
in each energy bin the energy distribution is assumed to
be a power law, pi
Temporal evolution: analytic solution of the kinetic
equation as a piecewise power-law (generalization of
Kardaschev solution)
Radiation mechanism: Synchrotron
Two alternative parameterized shock acceleration
models: ae, z
Radiation back-reaction on the dynamics
Magnetic field energy: in a fraction of equipartition with
the internal energy of the fluid, aB (but the code is ready
for RMHD input)
GENESIS: extensions (II)
RMHD: Leisman et al. (2005)

1D, 2D Cartesian and Cylindrical

HLLE type Riemann solver





2nd or 3rd order TVD Runge—Kutta scheme for time
integration (Shu & Osher 1988)
piecewise linear (MinMod)/ PPM reconstruction
2D Newton—Raphson iteration for recovery of the
primitives (mnewt; Numerical Recipes)
contraint transport or flux central difference
scheme to keep ∇ B = 0 + O(machine precision)
EoS: ideal gas
Initial model
Two approaches:
Type-A:
Put
a
toroidal-like
distribution of matter and angular
momentum around a Schwarzschild
BH (guided by the Newtonian
simulations of, e.g., Ruffert & Janka
2001, Lee et al. 2004, Setiawan et
al. 2004) and let it relax to an
equilibrium configuration.
Ruffert & Janka (2001), A&A, 380, 544
Mtorus ~ 0.34 Msun
MBH ~ 3 Msun
Menv ~ 10- 2 Msun
Relaxed initial model
Aloy, Janka & Müller (2004), astro-ph/0408291
Initial model
Two approaches:
Type-B: Follow Font & Daigne
(2003) prescription to build up
equilibrium tori around a BH.
Outside use Michel (1972) spherical
accretion solution.
Mtorus ~ 0.34 Msun
MBH ~ 2.44 Msun
Menv ~ 10- 7 Msun
Ruffert & Janka (2001), A&A, 380, 544
Aloy, Janka & Müller (2005), astro-ph/0408291
Modelling the energy release
Guided by previous results of Janka, Ruffert et al. showing that both in NS-NS
mergers (Ruffert & Janka 1999) and in BH-NS mergers (Janka et al. 1999), can be
released up to 1051 ergs above the poles of the black hole in a region that contains
less than 10-5 Msun of baryonic matter. The dependence in z-distance is:
q(z) = q0 / z5; z = r sinq; q0 ~[30o, 75o]
z
Deposition region
(baryon clean
environment)
BH
Accretion torus
Janka et al. (1999), ApJ, 527, L39
Aloy, Janka & Müller (2005), A&A, in press
Computed Models
- Energy deposition region:
Uniform or burst like. Within a cone of 30o to 75o around the rotation axis that
extends from Rmin= 1.02 - 2.05 Rs (innermost boundary) to infinity
Type-B
Type-A
- Grids: r (log spaced) x (uniform)
Type A: 460 x 200 zones. Rmax = 3 x 109 cm
Type B: 500 x 200 zones. Rmax = 2 x 1010 cm (+resolution checks up to 2000x200 zones)
Results
- Pthr ~ 1048-49 erg/(s·sr):
* in the initial model matter falls in through the axis of rotation (vin~0.6c- 0.97c)
* might be a reason why every SBC merger DOES NOT yield a GRB
* our threshold is probably higher than in real mergers (type-A) or maybe
irrelevant in type-B models.
Collimation:
 initially the disk provides the collimation via cocoon/disk interaction, i.e., the
opening angle of the beam is set by the torus inclination.
- pure hydrodynamic collimation (no need for B- fields).
* For low dE/dt  initial opening angle set after ~ 1-3 ms ( j ~ 3-5), but
modified later by the high density halo.
* For high dE/dt  initial opening angle set after a torus scale-height lightcrossing time (~ 0.5-1 ms) with j ~ 3-5.
Collimation mechanism (in low density merger environments):
CD
CD
axis
a
P=const.
equator
r
thick accretion
torus
Aloy, Janka & Müller (2005)
Levinson & Eichler (2000)
1. A radial, baryon-rich (heavy) wind
collimates asymptotically a conical,
baryon-poor (light) jet (BPJ).
q0 z

1. The accretion torus (very heavy)
collimates along its scale hight an
almost conical, BPJ.
2. Accretion disk = slim anulus.
2. Accretion disk = thick torus.
3. Interaction reduced to a thin
shocked layer around the BPJ.
3. Interaction extended to a thick
shock.-raref. layer around the BPJ.
Results (evolution up to 100 ms)
Type A
Morphology: For P> Pthr ~
1049 erg/s the outflows are
either knotty, narrow,
relativistic jets (P < 1051
erg/s) or conical, smooth,
wide angle, ultrarelativistic
winds (P > 1051 erg/s).
1049 erg/s
Outflow open. half-angle: It
is determined by the high
density external medium
(low P) or by the inclination
angle of the side walls of
the torus (large P).
Propagation speed:
between ~ 0.6c (P < 1051
erg/s) and ~0.97c (P > 1051
erg/s).
Collimation: (dense)
external medium (+ torus).
Limit of the
deposition
region
2x1050 erg/s 1051 erg/s
5x1051 erg/s
Results (evolution up to 100 ms)
2x1050erg/s
Type B
Morphology: For P> Pthr ~ 1048 erg/(s·sr)
the outflows are always conical, wide
angle, ultrarelativistic jets.
Outflow opening half-angle: ~ 20o to 30o.
It is determined by the inclination angle
of the side walls of the torus (large P/V).
45o
1049erg/s
60o
75o
1051erg/s
Propagation speed:
larger than ~0.9999c.
Collimation: torus (no LE00)
Variability: extrinsec
 hard to disantangle it from the
engine intrinsic variability
 Imprinted via KH- or SDinstabilities (Aloy et al. 2000,
2002; Zhang et al. 2003;
Gómez & Hardee 2004)
 Qualitatively similar to L-GRBs
particularly at jet breakout.
 Quantitative differences:
r/re, G, h/he, preexisting
breakout hole
45o
45o
45o
45o
41.4o
Post-switch-off evolution
The typical time scale in which the merging of SCBs may release energy is of
some fractions of a second.
We have switched off the energy deposition after Ta=0.1s and followed the
subsequent evolution of two models: one of type-A (P =5x1051 erg/s in 0=30o)
and another of type-B (P =2x1050 erg/s in 0=45o).
A condition to produce a successful GRB is:
Gfront ultrarelativistic  Vrear  Vfront (a)
Type A
Unsuccessful GRB: Condition (a) does not hold
because the environment is too dense and the
front shock of the fireball decelerates.
T~ 300ms
Ta= 100ms
R ~ 3x109 cm
Type B
May produce a successful GRB: Condition (a) is
Vrear <Vfront in this case. Thus, the fireball
stretches radially and, it can produce events with
durations of several seconds, i.e., Ta « Tobs.
Tobs
Ta= 100ms
R ~ 1014 cm
Post-switch-off evolution. Type-A (merger in high density environment)
P = 0 (switched off)
No GRB!!!
PA09 = 5x1051erg/s
G ~ 2 in 350 ms.
Post-switch-off evolution. Type-A (merger with high density halo)
P = 0 (switched off)
No GRB, instead:
UV-flash.
Assuming adiabatic
evolution of the
cloud:
PA09 = 5x1051erg/s
Because of the small Lm, only
closeby events will be visible
Post-switch-off evolution. Type-B (merger with low density halo)
 For P = 2x1050 erg/s the Lorentz factor grows up to ~ 1000 in 500 ms.
 Switching off the energy release leads to an almost selfsimilar growth
 it is possible to produce a successful GRB!.
Pure thermal
energy is released
in this cone
Model B01:
P = 2x1050 erg/s,
o
0 = 45 ,
Pure thermal
energy is released
in this cone
Edep = 2x1049 erg, EG>100 ~ 6x1048 erg, EG>10 ~ 1.2x1049 erg
o
Mf = 7.4x1024 g
w = 24 ,
Post-switch-off evolution. Type-B
 The radially averaged variables display a
non-monotonic shape as a function of .
 The sideways expansion in the comoving
frame is subsonic.
 A part of the fireball is contracting!.
 G profile similar to that obtained in
collapsar simulations (e.g., Aloy et al 2000,
Zhang et al. 2003).
 ~ q -2
 growing?
G > 100
 relaxing?
 narrower
with time
 2-component jet?
 ~ -0.05c
Gmax ~ 70
 ~ +0.07c
T = 0.5 s
Opening angles and rates. Type-B
 qG>100 ~ 5o – 10o  f ~ 0.4 – 1.5% of the
hemisphere
 100 times more short GRBs than observed
(assuming isotropic detectability in all directions within the opening angle)
plateau
 qG>10 ~ 15o – 25o  f ~ 7 – 18% of the
hemisphere
 10 times more short GRBs than observed
Taking for granted our jet opening angles implies:
 A rate of 100 y-1observed short GRBs
yields r1 ~ 10-6 - 10-5 galaxy-1 y-1 events:
smaller but consistent with estimated
NS+NS & NS+BH merger rates
r0 ~ 10-5 -10-4 galaxy-1 y-1 (e.g., Kalogera
2004; Fryer et al. 1999; Guetta & Piran
2004)
 r1 < r0 (+lack of GRB signal produced in
type-A models) suggests that not every
merger produces a GRB.
sharp edges
(G>100)
kinetic+internal
kinetic
T = 0.5 s
Opening angles and Eiso. Type-B
Our results:
 qG>100 ~ 5o – 10o  1050  Eiso  1051 erg.
 1051  Liso  1052 erg/s
plateau
 qG>10 ~ 15o – 25o  1049  Eiso  1051 erg.
 1050  Liso  1052 erg/s
Observations/theory:
 Mao et al (1994):
Lisoshort ~ Lisolong ~ 1051-52 erg/s
 Frail et al. (1997):
Eisolong ~ 1053 erg
 Our results are consistent with the
fluence-duration proportionality
(short vs long GRBs; e.g., Balazs et al 2003)
sharp edges
(G>100)
kinetic+internal
kinetic
Burst detection. Speculative picture:
Normal s-GRB + Afterglow
Internal shocks modulate LC
Liso ~ 1050 -1052 erg/s
X-Rays/optical?
X-Rays/optical?
G > 10
only external shock,
only external shock,
q < 20o
Orphan afterglow?
Orphan afterglow?
Liso ~ 1045 -1050 erg/s
Liso ~ 1045 -1050 erg/s
2 < G < 10
2 < G < 10
20o < q < 60o
20o < q < 60o
radio??
only external shock,
Orphan afterglow?
Liso < 1045 erg/s
G<2
q > 60o
radio??
only external shock,
Orphan afterglow?
Liso < 1045 erg/s
G<2
q > 60o
Post-switch-off evolution. Type-B
 Efficiency: 10% - 30% of Edep within the ultrarelativistic outflow (q ~ 5o – 10o)
Post-switch-off evolution. Type-B
 Efficiency: 10% - 30% of Edep within the ultrarelativistic outflow (q ~ 5o – 10o)
G=2
 After 0.5 s only ~0.5% of Edep is converted to Ekin but
the trend is to increase with time.
Extrapolation of the results to ~ 1000 s very difficult
but the trend seems to be:
A large fraction of the energy will be kinetic before
transparency sets in.
G = 10
G = 50
G = 100
Post-switch-off evolution. Type-B
 Efficiency: 10% - 30% of Edep within the ultrarelativistic outflow (q ~ 5o – 10o)
 The jet opening angles are much larger than for long GRBs (note, however, that
Guetta & Piran (2004) predict much smaller opening angles for short GRBs on the
basis that every merger yield a GRB):
Long GRBs (Frail et al. 2001): <qw> ~ 3.6o, with 2.5o < qw < 17o
Short GRBs:
Aloy et al. (2005): <qw> ~ 20o, with 15o < qw < 25o
Rosswog & Ramirez-Ruiz (2003): <qw> ~ 8o, with 1o < qw < 21o
Afterglow or not afterglow?
A) If every merger event yiels a short GRB, Guetta & Piran (2004) conclude that their
afterglows will be produced just minutes after the GRB because of the narrower
angles they predict.
B) If SCBs are ejected from the host galaxy into an external medium much less
dense than the assumed ISM (next ~ 0.1 – 1 cm-3), an external blast wave will
occur
at much larger distances and on much longer timescales than in usual afterglows
(e.g., Lee & Ramirez-Ruiz 2002).
Our (rough) estimates assuming uniform external medium density:
Raft ~ 4·1016 cm (next ~ 1 cm-3)
Raft ~ 2·1017 cm (next ~ 0.01 cm-3)
We favour B) because:
1.- high density environments the outflow does not produce a GRB signature
2.- our outflow opening angles are larger than assumed in A).
 The afterglow will be dimmer than those of Long GRBs because we have an
intrinsic energy 2 orders of magnitude smaller and, thus, below present day
observational limits (Panaitescu, Kumar & Narayan 2001).
Concluding remarks:
Releasing energy over the poles at rates above our Pthr and with a functional
depencence suggested by Janka et al (1999) relativistic (Gmax ~ 1000), collimated
conical/jet-like, outflows are produced.
Collimation: via interaction with the external medium and/or the accretion torus.
Aplication of the analytic Levinson & Eichler’s collimation mechanism yields wrong
results. Typical opening angles: qG>100 ~ 5o – 10o (qG>10 ~ 20o – 30o).
 An observed rate of 100 y-1 short GRBs needs of 10-5 galaxy-1 y-1 s-GRB
events, which is consistent with estimated NS+NS & NS+BH merger rates.
While mergers in low-density environments successful GRBs can be produced, in
high-density media the observational signature may be a thermal UV-flash
(T~5x104 K) with very low luminosity (L~1043 erg/s) and durations of ~1000 s.
 continuous transition between UV-flashes and GRBs??
The fireball stretches radially and, it can produce events with durations of few
seconds (although the central engine may survive only for a few 0.1 s).
Our results are consitent with the fluence-duration proportionallity (short vs long
GRBs; e.g., Balazs et al 2003): Eiso ~ 1051 erg while Edep = 1049 erg (in 0.1 s).
The fireball structure is inhomogeneous both in radial and angular directions (KHinstab.) and has a contractive, ultrarelativistic core + relativistic, expanding layer
Open questions:
What is the dependence of the
outflow on the assumed energy
deposition law?
Some hints to find answers:

Other forms of the energy release
needed. Optimally, a detailed neutrino
transport has to be used.
What is the role of the magnetic field
in the acceleration, collimation and
energy conversion?

3D-effects: will the outflow survive to
hydromagnetic instabilities?
3D GRMHD simulations.
Which part of the radially-stretched
fireball stretches is responsible for
the observed emission?
Extend current models x 1000 radially.
 Call for AMR and/or massively
parallel simulations.

Are there observational signatures
that allow us to unambiguously

differentiate between progenitors of
short and of long GRBs (in addition to
GW-signal)?
Neutrinos?, afterglows?, baryonic
winds from the merger?