Imprints of Symmetry Energy on Gravitational Waves

Collaborators:William Newton and Chang Xu,Texas A&M University-CommerceLie-Wen Chen and Hongru Ma, Shanghai Jiao-Tung UniversityChe-Ming Ko and Jun Xu, Texas A&M University, College StationDe-Hua Wen, South China University of TechnologyAndrew Steiner, Michigan State UniversityPlamen Krastev, San Diego State UniversityWei-Zhou Jiang, Southeast UniversityZhigang Xiao, Ming Zhang and Shengjiang Zhu, Tsinghua UniversityGao-Chan Yong, Xunchao Zhang and Wei Zuo, Institute of Modern PhysicsChampak B. Das, Subal Das Gupta and Charles Gale, McGill University

Bao-An Li

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 data Plamen Krastev and Bao-An Li, Phys. Rev. C76, 055804 (2007).

• Nuclear constraints on the moment of inertia of neutron stars Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).• Constraining properties of rapidly rotating neutron stars using data from heavy-ion

collisions Plamen Krastev, Bao-An Li and Aaron Worley, The Astrophysical Journal, 676, 1170 (2008)• Nuclear limit on gravitational waves from elliptically deformed pulsars Plamen Krastev, 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-Hua Wen, Bao-An Li and Plamen Krastev, Phys. Rev. C80, 025801 (2009) .

• Super-soft symmetry energy encountering non-Newtonian gravity in neutron stars

De-Hua Wen, 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 ObservatoryVIRGO - kilometer scale Michelson interferometer with Fabry-Perot arms in ItalyGEO - German/UK experimentLISA - Laser Interferometer Space AntennaWhile 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).

http://dailyphysics.com/

Daily Physics

• Gravitational Waves = “Ripples in space-time”What are Gravitational Waves?

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

Lx Lx[1 + h(t)]

Traveling GW

2

0 0

1 cost F t; h cos ( ) F t; h cos sin ( )

2h t t

F+ and Fx : plus and cross polarization, bounded between -1 and 1

h0 – amplitude of the gravitational wave signal, – polarization angle of signal

– inclination angle of source with respect to line of sight, (t)- phase of pulsar

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

proper separation between two masses

GravityJ.B. Hartle

Example:

Ring of test masses

responding to wave

propagating along z

Two transverse polarizations: + and X

Interaction of Gravitational Waves with matter

• 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

Why do we need to study Gravitational Waves?

Michael LandryLIGO Hanford Observatoryand California Institute of Technology

8 Gravitational Waves

LIGO

VIRGO

GEO

TAMA

ACIGA

LISAGravitational

Wave Interferometer

Projects

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

Michelson-Morley IFO

Compact binary inspiral: “chirps”

Possible sources of Gravitational Waves:

Supernovae / GRBs: “bursts”

Elliptically deformed pulsars: “periodic”

Examples

Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993)is the best evidence so far.

Non-radial oscillations of neutron stars

Gravitational waves from elliptically deformed

pulsars

xx yy

zz

I I

I

Equatorial Ellipticity of pulsars

Mass quadrupole moment

Breaking stain: fractional deformation when the crust fails

EOS

B. Abbott et al., PRL 94, 181103 (05)B.J. Own, PRL 95, 211101 (05)

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

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

• 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

LIGO

GEO

The LIGO Scientific Collaboration, Phys. Rev. D 76, 042001 (2007)

Estimate of gravitational waves from spinning-down of pulsarsAssumption: spinning-down is completely due to the GW radiation

“Standard fiducial value”

Testing the standard fudicial value of the moment of inertia

Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).

1/ 2

k 3

Assuming the observed frequency is the Kepler frequency

1f

2eq

GM

R

Constraining the mass-radius relation of fast pulsars

Plamen 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

Depends on the symmetry energy and structure of NS

or 0.1

ӿ

(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

Mon.Not.Roy.Astron.Soc. 299 (1998) 1059-1068

The first w-mode The frequency is inversely proportional to the compactness of the star

compactness of the star

EOS of neutron-rich matter enters here:

The f-mode1/ 2

fBased on the Newtonian gravity:

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 Isoscalar Isovector

Gogny-HF prediction: C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003).

Our poor knowledge about the density and momentum dependence of the isovector potential

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).