Bao-An Li. Imprints of Symmetry Energy on Gravitational Waves. Collaborators: William Newton and Chang Xu,Texas A&M University-Commerce Lie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung University Che-Ming Ko and Jun Xu, Texas A&M University, College Station
Imprints of Symmetry Energy on Gravitational Waves
William Newton and Chang Xu,Texas A&M University-Commerce
Lie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung University
Che-Ming Ko and Jun Xu, Texas A&M University, College Station
De-Hua Wen, South China University of Technology
Andrew Steiner, Michigan State University
Plamen Krastev, San Diego State University
Wei-Zhou Jiang, Southeast University
Zhigang Xiao, Ming Zhang and Shengjiang Zhu, Tsinghua University
Gao-Chan Yong, Xunchao Zhang and Wei Zuo, Institute of Modern Physics
Champak B. Das, Subal Das Gupta and Charles Gale, McGill University
Partially constrained EOS of neutron-rich matter
P. Danielewicz, R. Lacey and W.G. Lynch,
Science 298, 1592 (2002))
Plamen Krastev, Bao-An Li
and Aaron Worley,
Phys. Lett. B668, 1 (2008).
Constraining the radii of neutron stars with terrestrial nuclear laboratory data
Bao-An Li and Andrew Steiner, Phys. Lett. B642, 436 (2006).
Constraining time variation of the gravitational constant G with terrestrial nuclear laboratory dataPlamenKrastev and Bao-An Li, Phys. Rev. C76, 055804 (2007).
Nuclear constraints on the moment of inertia of neutron stars
Aaron Worley, PlamenKrastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).
Constraining properties of rapidly rotating neutron stars using data from heavy-ion collisions
PlamenKrastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008)
Nuclear limit on gravitational waves from elliptically deformed pulsars
PlamenKrastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).
Locating the inner edge of neutron star crust using nuclear laboratory data,
Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, Phys. Rev. C79, 035802 (2009).
Nuclear constraints on properties of neutron star crusts
Jun Xu, Lie-Wen Chen, Bao-An Li and HongRu Ma, The Astrophysical Journal 697, 1549 (2009).
Imprints of nuclear symmetry energy on gravitational waves from the axial w-modes of neutron stars
De-HuaWen, Bao-An Li and PlamenKrastev, Phys. Rev. C80, 025801 (2009) .
Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars
De-HuaWen, Bao-An Li and Lie-Wen Chen, arXiv:0908.1922 (2009)
Constraining the gravitational binding energy of PSR J0737-3039B using terrestrial nuclear data
William Newton and Bao-An Li, arXiv:0908.1731 (2009)
Gravitational Waves of Neutron Stars
Neutron stars are formed from the gravitational collapse of massive stars undergoing a supernova.
Although somewhat rare, they are of great interest due to physics involved. Instead of being composed of normal matter, they are almost
entirely neutrons. They are very dense, but do not collapse into a black hole due to the Pauli exclusion principle.
It has been widely theorized that these objects could emit gravitational waves (GWs) due to their incredible density,
but only if they are rotating quickly. A direct consequence of the theory of general relativity, GWs are small perturbations in space-time.
Because nothing travels faster than light, changes in a gravitational field must also propagate at or below this speed. These waves are analogous
in many ways to electromagnetic waves, leading many to talk about them as the theory of gravitational radiation. GWs have not been directly
observed to date, but are a subject of intense research and debate amongst the scientific community. Many are excited because they think
we are close to detecting these GWs. Several experiments that are currently underway to accomplish this goal:
LIGO - Laser Interferometer Gravitational Wave Observatory
VIRGO - kilometer scale Michelson interferometer with Fabry-Perot arms in Italy
GEO - German/UK experiment
LISA - Laser Interferometer Space Antenna
While many sources of GWs are subject to investigation, those that are generated by rotating neutron stars are some of the most promising.
A paper by Worley, Krastev, and Li entitled Nuclear Constraints on gravitational waves from rapidly rotating neutron stars, recently submitted
to Arxiv, explores what these GWs would be like. In particular, they determine a theoretical upper limit on the strain-amplitude of GWs emitted
by rapidly rotating neutron stars. For a full explanation of strain-amplitude, see source number 2.
Their establishment of the upper limit of this property makes it easier to predict what GWs will look like in the vicinity of Earth for the
fastest pulsars currently known of. They end their paper by saying, “These predictions serve as the first direct nuclear constraint on the
gravitational waves from rapidly rotating neutron stars.” With a little luck and a lot more hard work, gravitational waves from all types of sources
will soon be directly observed.Sources:1. Worley A., Krastev P.G., Li Bao-An. Nuclear Constraints on Gravitational waves from rapidly rotating neutron stars. Arxiv December 2, 20082. Plamen G. Krastev, Bao-An Li, and Aaron Worley, Phys. Lett. B 668, 1 (2008).
Gravitational Waves = “Ripples in space-time”
Lx[1 + h(t)]
Amplitude parameterized by (tiny) dimensionless strain h: h(t) = DL/L
between two masses
The expected signal has the form (P. Jaranowski, Phys. Rev. D58, 063001 (1998) ):
Ring of test masses
responding to wave
propagating along z
Two transverse polarizations: + and X
Why do we need to study Gravitational Waves?
Michael LandryLIGO Hanford Observatoryand California Institute of Technology
LIGO, GEO, TAMA; VIRGO taking data; LISA is a ESA-NASA project
Possible sources of Gravitational Waves:
Compact binary inspiral: “chirps”
Supernovae / GRBs: “bursts”
Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993)
is the best evidence
Elliptically deformed pulsars:“periodic”
Non-radial oscillations of neutron stars
Solving linearized Einstein’s field equation of General Relativity, the leading contribution
to the GW is the mass quadrupole moment
Frequency of the pulsar
Distance to the observer
Breaking stain: fractional deformation when the crust fails
Mass quadrupole moment
Equatorial Ellipticity of pulsars
B. Abbott et al., PRL 94, 181103 (05)
B.J. Own, PRL 95, 211101 (05)
Moment of inertia
Star crust is 10 billion times stronger than steel
A NewScientist Web article by Rachel Courtland
The crust of neutron stars is 10 billion times stronger than steel, according to large scale computer simulations. That makes the surface of these ultra-dense stars tough enough to support long-lived bulges that could produce gravitational waves detectable by experiments on Earth. Because of their extreme gravity and rotational speed, neutron stars could potentially make large ripples in the fabric of space but only if their surfaces contain bumps or other imperfections that would make them asymmetrical.
See The breaking strain of neutron star crust and gravitational waves by C. J. Horowitz, and Kai Kadau, Phys Rev. Letters 102, 191102 (2009).
It predicts a breaking strain
of about 0.1
In the past, one uses
Estimate of gravitational waves from spinning-down of pulsars
Assumption: spinning-down is completely due to the GW radiation
“Standard fiducial value”
The LIGO Scientific Collaboration,
Phys. Rev. D 76, 042001 (2007)
Aaron Worley, Plamen Krastev and Bao-An Li,
The Astrophysical Journal 685, 390 (2008).
Constraining the mass-radius relation of fast pulsarsPlamen Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008)
Solving the Einstein equation in general relativity using the RNS code written by Nikolaos Stergioulas and John L. Friedman, The Astrophysics J. 444, 306 (1995)
Compare with the latest upper limits from LIGO+GEO observations
Depends on the symmetry energy and structure of NS
(completely due to general relativity)
Neutron star matter equation of state and gravitational wave emission
Authors: Omar Benhar
Mod.Phys.Lett. A20 (2005) 2335-2350
EOS of neutron-rich matter enters here:
The first w-mode
The frequency is inversely proportional to the compactness of the star
compactness of the star
Mon.Not.Roy.Astron.Soc. 299 (1998) 1059-1068
Fit calculations using 12 different EOSs
Clear imprints of the symmetry energy on the strength, frequency and damping time of various kinds of gravitational waves are observed
Why is the symmetry energy so uncertain especially at high densities?Based on the Fermi gas model (Ch. 6) and properties of nuclear matter (Ch. 8) of the textbook: Structure of the nucleus by M.A. Preston and R.K. Bhaduri (1975)
Our poor knowledge about the density and momentum dependence
of the isovector potential
Gogny-HF prediction: C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003).
Bao-An Li, C.B. Das, Subal Das Gupta and Charles Gale, NPA735, 563 (2004).
Astronomers discover the fastest-spinning neutron-star spining at 716Hz
Science 311, 1901 (2006).