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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

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

- Outline:
- Who cares whether the symmetry energy is important for astrophysics or not?
- A brief introduction to gravitational waves
- Imprints of the symmetry energy on gravitational waves

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).

Astrophysical Impacts of the Partially Constrained EOS of Neutron-Rich Matter

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

http://dailyphysics.com/

Daily Physics

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”What are Gravitational Waves?

Traveling GW

Gravity

J.B. Hartle

Lx

Lx[1 + h(t)]

Amplitude parameterized by (tiny) dimensionless strain h: h(t) = DL/L

proper separation

between two masses

The expected signal has the form (P. Jaranowski, Phys. Rev. D58, 063001 (1998) ):

- F+ and Fx : plus and cross polarization, bounded between -1 and 1
- h0 – amplitude of the gravitational wave signal, y – polarization angle of signal
- i – inclination angle of source with respect to line of sight, F(t)-phase of pulsar

Example:

Ring of test masses

responding to wave

propagating along z

Interaction of Gravitational Waves with matterTwo transverse polarizations: + and X

Why do we need to study Gravitational Waves?

Michael LandryLIGO Hanford Observatoryand California Institute of Technology

- Test General Relativity:
- Quadrupolar radiation? Travels at speed of light?
- Unique probe of strong-field gravity
- Gain different view of Universe:
- Sources cannot be obscured by dust / stellar envelopes
- Detectable sources are some of the most interesting,
- least understood in the Universe
- Opens up entirely new non-electromagnetic spectrum

Gravitational Wave Interferometer Projects

LISA

GEO

LIGO

VIRGO

TAMA

ACIGA

Michelson-Morley IFO

LIGO, GEO, TAMA; VIRGO taking data; LISA is a ESA-NASA project

8

Gravitational Waves

Possible sources of Gravitational Waves:

Compact binary inspiral: “chirps”

Examples

Supernovae / GRBs: “bursts”

Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993)

is the best evidence

so far.

Elliptically deformed pulsars:“periodic”

Non-radial oscillations of neutron stars

Gravitational waves from elliptically deformed pulsars

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

EOS

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”

- Solid black lines: LIGO and GEO science requirement, for T=1 year
- Circles: upper limits on gravitational waves from known EM pulsars, obtained from measured spin-down
- Only known, isolated targets shown here

GEO

LIGO

The LIGO Scientific Collaboration,

Phys. Rev. D 76, 042001 (2007)

Testing the standard fudicial value of the moment of inertia

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)

Constraining the strength of gravitational wavesPlamen Krastev, Bao-An Li and Aaron Worley, Phys. Lett. B668, 1 (2008).

Compare with the latest upper limits from LIGO+GEO observations

ӿ

or 0.1

Depends on the symmetry energy and structure of NS

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

The f-mode

Fit calculations using 12 different EOSs

Summary

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)

Kinetic

Isovector

Isoscalar

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).

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