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, 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 ~ g / cm 3 ) 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 Artist view A few simple facts: Energy ~ M solar c 2 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

Gamma Ray Burst Overachievers In γ’s, the current record holder for most distant burst (or astrophysical source) is the long GRB , 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 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 Suspected of being merger of two neutron stars or a neutron star and a black hole Associated with death of massive stars

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 ) Gravitational field: G / c 4 (8 x )

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

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 or an absolute length of 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) Fireball Collimation from neutrino driven baryonic wind

The Setting: Numerical Simulations A humbling experience is that this gentleman, Jim Wilson ( ), 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 [check]

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 [check]

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 (<~ 10 9 Kelvin), neutrinos freely stream out (leak out) and provide optically thin cooling of the matter. For the higher expected temperatures of ~10 11 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 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

HD MHD High ResMed Res Results: Double Neutron Star Binaries Resolution Effects and K-H Instability

Results: Double Neutron Star Binaries Magnetic Buoyancy

Results: Double Neutron Star Binaries Gravitational Wave Signature

Results: Double Neutron Star Binaries

Results: Neutron Star – Black Hole Binaries

Initial Setup Lorene initial data Neutron Star: Irrotational, Γ = 2 R = 15 [km] M = 1.4 M solar Initial dipole field of strength [Gauss] Black Hole: M = 7 M Solar 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

Simulations Explore the parameter space of initial separation {90, 100, 150 [km]} black hole spin {0, 0.5} initial magnetic field {0, [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 Ψ 4 a = 0, B = a = 0.5, B = 0 and a = 0.5, B = 10 12

Evolution with a = 0, B = 10 12

Evolution with a = 0.5, B = 10 12

Evolution with a = 0.5, B = 0

Results: Neutron Star – Black Hole Binaries Rayleigh-Taylor Instability

Vertical Structure with a = 0.5 UnmagnetizedB = initially M Disk = 1.6%M Disk = 1.7%

Results: Neutron Star – Black Hole Binaries Remnant Mass Total Mass Disk Mass

Results: Neutron Star – Black Hole Binaries Magnetic Field Structure

Results: Neutron Star – Black Hole Binaries Magnetic Field Structure

Summary 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, ?)

Summary This work was supported by the NSF through grants PHY and PHY 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).