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Imprints of Symmetry Energy on Gravitational Waves

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

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Imprints of Symmetry Energy on Gravitational Waves

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  1. 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

  2. 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).

  3. 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)

  4. 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).

  5. 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

  6. Example: Ring of test masses responding to wave propagating along z Interaction of Gravitational Waves with matter Two transverse polarizations: + and X

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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)

  13. Testing the standard fudicial value of the moment of inertia Aaron Worley, Plamen Krastev and Bao-An Li, The Astrophysical Journal 685, 390 (2008).

  14. 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)

  15. 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

  16. (completely due to general relativity)

  17. Neutron star matter equation of state and gravitational wave emission Authors: Omar Benhar Mod.Phys.Lett. A20 (2005) 2335-2350

  18. 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

  19. The f-mode Fit calculations using 12 different EOSs

  20. Summary Clear imprints of the symmetry energy on the strength, frequency and damping time of various kinds of gravitational waves are observed

  21. 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).

  22. Bao-An Li, C.B. Das, Subal Das Gupta and Charles Gale, NPA735, 563 (2004).

  23. Astronomers discover the fastest-spinning neutron-star spining at 716Hz Science 311, 1901 (2006).

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