Transcript motl_bsu_021210

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 BellBurnell (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
Compact Objects: 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
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
Artist view
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 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
Fireball
neutrino driven
 
baryonic wind
e ,e
 i i
i

 
 
i
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
[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 (<~ 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
MHD
HD
Med Res
High Res
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
http://www.lorene.obspm.fr
Black Hole:
M = 7 MSolar
a = 0, 0.5
Neutron Star:
Irrotational, Γ = 2
R = 15 [km]
M = 1.4 Msolar
Initial dipole field of
strength 1012 [Gauss]
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, 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 http://had.liu.edu
Gravitational Radiation measured from Ψ4
a = 0, B = 1012
a = 0.5, B = 0 and
a = 0.5, B = 1012
Evolution with a = 0, B = 1012
Evolution with a = 0.5, B = 1012
Evolution with a = 0.5, B = 0
Results: Neutron Star – Black Hole Binaries
Rayleigh-Taylor Instability
Vertical Structure with a = 0.5
Unmagnetized
B = 1012 initially
MDisk = 1.7%
MDisk = 1.6%
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-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).