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Can the Merger of a Compact Binary Power a Short-Hard Gamma Ray Burst?. Patrick M. Motl (IUK). Ball State University Department of Physics & Astronomy Colloquium, Thursday February 11 th 2010. Anderson et al . 2008, Physical Review Letters, 100 , 191101. In Collaboration with:

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Can the Merger of a Compact Binary Power a Short-Hard Gamma Ray Burst?

Patrick M. Motl (IUK)

Ball State University Department of Physics & Astronomy Colloquium, Thursday February 11th 2010


Anderson et al. 2008, Physical Review Letters, 100, 191101

In Collaboration with:

David Neilsen, Eric Hirschmann and Michael Besselman (BYU)

Joel E. Tohline, Matt Anderson, Sarvnipun Chawla (LSU)

Steve Liebling (LIU), Carlos Palenzuela (CITA), Luis Lehner (PI)


The Story

The Cast of Characters

Compact Objects (Neutron Stars and Black Holes)

Gamma Ray Bursts

Gravitational Radiation

The Setting

Cartoon Model for Short-Hard GRBs

Numerical Simulations, astrophysics in silico

Recent Results

Double Neutron Star Binaries

Neutron Star – Black Hole Binaries


Compact Objects: Neutron Stars

Shortly after the discovery of the neutron by Chadwick, Zwicky and Baade hypothesized that stellar explosions (supernovae) may result in a dense star made almost entirely of neutrons.

Oppenheimer and collaborators worked out what the structure of such an object would be – they are horrendously small for a star.

Pulsars were discovered accidently by Jocelyn Bell-Burnell (while she was a graduate student working with Anthony Hewish) some thirty years later and it was quickly realized that pulsars must be rapidly rotating, magnetized neutron stars.


Compact Objects: Neutron Stars

A stellar remnant so dense it is just shy of a black hole – gravity is so strong we must use Einstein’s general theory of relativity to describe these objects

Like a single nucleus with a mass about the mass of the sun but in a sphere with a radius of only about 10 kilometers ( density of ~ 1015 g / cm3 )

On occasion, a binary pair of massive stars give rise to a neutron star binary after each has exploded as a supernova


Compact Objects: Neutron Stars

Relatively little is known about matter in the core of a neutron star – can’t study similar regime on Earth

Lattimer & Prakash 2004, Science


Compact Objects: Neutron Stars

Our relatively poor understanding of the underlying nuclear physics governing matter introduces a wide range of uncertainty – a great opportunity to learn something new!

Lattimer & Prakash 2004, Science


Compact Objects: Black Holes

No physical surface for a black hole but there is an event horizon*, to escape from the event horizon you must have a velocity equal to the speed of light (impossible for any material body).

The region inside the event horizon is fundamentally isolated (causally disconnected) from the outside Universe

From a certain point of view, astrophysical black holes are far simpler objects than even atoms. A black hole has only three possible parameters to describe its structure: mass, spin angular momentum, electrical charge

* Naked singularities are possible, theoretically speaking, but not observed


Gamma Ray Bursts

General Considerations:

At cosmological distances (invoke beaming)

Non-thermal spectra

Burst in γ’s with afterglow from X-ray to radio

A few simple facts:

Energy ~ Msolar c2

Size ~ kilometers

Duration ~ seconds

Lead to the current party line that the central engine is an accreting black hole and the photons come from a shocked, relativistic fireball

Artist view


Gamma Ray Burst Overachievers

In γ’s, the current record holder for most distant burst (or astrophysical source) is the long GRB 090423, discovered by NASA’s Swift mission. Redshift of 8.2 meaning it resulted from a stellar death about 600 million years after the big bang.

The current record for the most distant naked-eye object is the afterglow in visible light from GRB 080319.

Despite being about 7.5 billion light years distant from Earth (redshift ~ 0.94), it was bright enough to have been visible to the naked eye for about 30 seconds.


Gamma Ray Bursts

Associated with death of massive stars

Suspected of being merger of two neutron stars or a neutron star and a black hole


Short Duration Gamma Ray Bursts

Suspected to arise form the merger of two neutron stars or a neutron star falling into a black hole. Again, will have interaction of material with a rapidly rotating black hole.


Gravitational Radiation

But why would these compact objects merge?

The compact objects, orbiting about one another in a binary, lose energy and angular momentum to gravitational radiation. As their orbit decays, they must eventually merge.

From electricity and magnetism, any time an electrical charge accelerates, this creates a disturbance in the charge’s electric and magnetic fields.

A part of this kink (disturbance) propagates as electromagnetic radiation and carries away energy, momentum and angular momentum from the charge to infinity.


Gravitational Radiation

Einstein’s General Theory of Relativity makes a similar prediction for gravitational fields.

Any time a mass accelerates (with a sufficient degree of asymmetry in its motion), this creates a propagating gravitational disturbance that carries energy, angular momentum and momentum to infinity.


Gravitational Radiation

Gravity is a horrendously weak force compared to electrical and magnetic forces (think of a refrigerator magnet) and so gravitational radiation is not detectable from motions of masses in our daily lives.

For radiation

Electric field: unity

Magnetic field: 1/c (3 x 10-9)

Gravitational field: G / c4 (8 x 10-45)


Gravitational Radiation

As a gravitational wave passes, it alternately stretches and compresses space itself (by a minute amount).

Everything changes so you can’t just measure the length of a standard object with a ruler.


Gravitational Radiation

Hulse and Taylor won the 1993 Nobel prize for indirectly measuring gravitational radiation through the changes in the orbit of PSR 1923+16


Gravitational Radiation

The LIGO observatory and other experiments are attempting to measure the ripples of gravitational radiation directly

4 km arm length for the LIGO interferometer

A passing gravitational wave changes the arm lengths relative to one another. LIGO can currently measure a relative change of 10-21 or an absolute length of 10-18 m


The Setting: Cartoon Model

My collaborators and I write code and run simulations to, as an example, test the following theoretical cartoon for short-hard GRBs (Rosswog, Ramirez-Ruiz, Davis 2003)

Collimation from neutrino driven baryonic wind



The Setting: Numerical Simulations

A humbling experience is that this gentleman, Jim Wilson (1922-2007), started writing and running these codes 20 years before anyone else could.


The Setting: Numerical Simulations

Studying neutron stars involves all four fundamental forces directly

Gravity: Must solve Einstein’s equations of general relativity to describe the space-time the neutron star or black hole creates

6 hyperbolic partial differential equations to evolve

4 equations of constraint that the initial data must satisfy



The Setting: Numerical Simulations

Electromagnetic: Treat the matter in the ideal magnetohydrodynamic limit (conducting, magnetized fluid without viscosity or electrical resistance)

5 hyperbolic partial differential equations that describe mass, energy and momentum conservation

3 hyperbolic equations for the magnetic field components

1 equation of constraint – no such thing as a magnetic monopole



The Setting: Numerical Simulations

Strong Nuclear Force: Use tabular equations of state to encapsulate the microphysics of strong nuclear interactions. Best guess at pressure and entropy of the fluid as a function of density, temperature and composition. For example, hyperons (strange quark matter) will be more tightly bound to itself – this reduces the pressure for a given density

Split the internal energy density of the fluid into a part that depends on temperature like an ideal gas does and a part that depends on interactions

[in progress]


The Setting: Numerical Simulations

Weak Nuclear Force:

At “cool” temperatures (<~ 109 Kelvin), neutrinos freely stream out (leak out) and provide optically thin cooling of the matter.

For the higher expected temperatures of ~1011 Kelvin, matter optically thick to neutrinos.

Introduce radiation transport in the code – radically different partial differential equations to deal with now. A radiation field evolves with time in six dimensional phase space - you must keep track of three spatial coordinates and three momentum coordinates.

[in progress]


The Setting: Numerical Simulations

Can’t discretize a six dimensional problem on a current computer. Instead sample the solution with a bias towards the most important contributions with Monte Carlo technique.

Use Graphical Processor Units (GPUs) to accelerate the very expensive Monte-Carlo sampling of the radiation field.

[in progress]


Results: Double Neutron Star Binaries

Equal mass neutron star binaries with an initial magnetar scale magnetic field of 1015 Gauss. Initial data is simply superposition of spherical polytrope solutions. Simulations did not extend past gravitational collapse.


Results: Double Neutron Star Binaries

High end simulations of GRMHD (general relativity + a magnetized fluid) take about two months on 200 – 500 computing cores

Saving the state of the computation takes 300 – 500 GB


Results: Double Neutron Star Binaries

Merger Phase, Kelvin-Helmholtz Instability

4.4 ms

9.9 ms


Results: Double Neutron Star Binaries

Resolution Effects and K-H Instability

Med Res

High Res




Results: Double Neutron Star Binaries

Gravitational Wave Signature


Initial Setup

Lorene initial data

Neutron Star:

Irrotational, Γ = 2

R = 15 [km]

M = 1.4 Msolar

Initial dipole field of strength 1012 [Gauss]

Black Hole:

M = 7 MSolar

a = 0, 0.5

Initial separation of 100 [km]

Grid extends to ± 443 [km]

Peak resolution of 0.73 [km] or 40 points across initial neutron star



Explore the parameter space of

initial separation {90, 100, 150 [km]}

black hole spin {0, 0.5}

initial magnetic field {0, 1012 [Gauss]}

Adaptive Mesh Refinement with the had package to couple

Einstein solver: generalized harmonic formalism with excision

MHD solver: High resolution shock-capturing code using PPM reconstruction and HLLE flux

Information about had and the application codes available at


Gravitational Radiation measured from Ψ4

a = 0.5, B = 0 and

a = 0.5, B = 1012

a = 0, B = 1012


Vertical Structure with a = 0.5


B = 1012 initially

MDisk = 1.7%

MDisk = 1.6%


Results: Neutron Star – Black Hole Binaries

Remnant Mass

Total Mass

Disk Mass



NS-NS binaries:

promising sites for SHGRBS

rapid magnetic field amplification, possibly leading to a magnetic dynamo

work ongoing with other magnetic field configurations and a realistic equation of state carrying the evolutions beyond formation of a singularity

BH-NS binaries:

Obviously will do something but initial exploration of the parameter space shows that the remnant object is short lived (caveats: numerical resolution, explored only one mass ratio, ?)



This work was supported by the NSF through grants PHY-0803629 and PHY-0653375 to LSU. Thanks also to the College of Arts and Sciences at IU Kokomo for their support.

The computations presented here were performed on resources from the Teragrid and the Louisiana Optical Network Initiative (LONI).