Department of Physics, South China Univ. of Tech. Properties of Neutron Star and its oscillations collaborators Bao-An Li, William Newton, Plamen Krastev Department of Physics and astronomy, Texas A&M University-Commerce Institute of Theoretical Physics, Shanghai Jiao Tong University

Outline I. Research history and observations II. EOS constrained by terrestrial data and non-Newtonian gravity in neutron star III. Gravitational radiations from oscillations of neutron star

I. Research History and Observations

A year following Chadwicks 1932 discovery of neutron, Baade and Zwicky conceived the notion of neutron star in the course of their investigation of supernovae. But no searches for neutron stars were mounted immediately following their work. No one knew what to look for, as the neutron star was believed to be cold and much smaller than white dwarfs. In 1939 (about 30 years before the discovery of pulsars), Oppenheimer, Volkoff and Tolman first estimated its radius and maximum based on the general relativity. Theory prediction

First observation of NS In 1967 at Cambridge University, Jocelyn Bell observed a strange radio pulse that had a regular period of seconds, which is believed to be a neutron star formed from a supernova.

Nature, 17(1968)709

1054

Science, 304(2004) A. Hewish R. A. Hulse & J. H. Taylor × 1.4 g/cm 3 6x10 -5 T 25

Distribution of known galactic disk pulsars in the period–period-derivative plane. Pulsars detected only at x-ray and higher energies are indicated by open stars; pulsars in binary systems are indicated by a circle around the point. Assuming spin-down due to magnetic dipole radiation, we can derive a characteristic age for the pulsar t=p/(2dp/dt), and the strength of the magnetic field at the neutron star surface, Bs= 3.2*10 19 (P*dp/dt) 0.5 G. Lines of constant characteristic age and surface magnetic field are shown. All MSPs lie below the spin-up line. The group of x-ray pulsars in the upper right corner are known as magnetars. R. N. Manchester, et al. Science 304, 542 (2004) Observations: (1) Period and its derivation

Phys.Rev.Lett. 94 (2005) (2) Observation of pulsar masses. Demorest, P., Pennucci, T., Ransom, S., Roberts, M., & Hessels, J. 2010, Nature, 467, 1081

(3) The ten fastest-spinning known radio pulsars. Science, 311(2006)190

(5) Distribution of the Ms NS v1 (4) Distribution of the millisecond NS

(5) Constraints on the Equation-of-State of neutron stars from nearby neutron star observations arXiv: v1 Radius Determinations for NSs, namely for RXJ1856 and RXJ0720, provide strong constraints for the EoS, as they exclude quark stars, but are consistent with a very stiff EoS.

(7) Observational Constraints for Neutron Stars

II. EOS constrained by terrestrial data and non-Newtonian gravity in neutron star

TOV equation From Lattimer 2008 talk 1.

M-R constraint from observation

2006NuPhA Equation of state of neutron star matter Stiffest and softest EOS

Possible EOSs of NS APJ, 550(2001)426

Physics Reports, 442(2007) 109 Mass-Radius of neutron star

symmetry energy Energy per nucleon in symmetric matter Energy per nucleon in asymmetric matter δ Isospin asymmetry (1) Symmetry energy and equation of state of nuclear matter constrained by the terrestrial nuclear data B. A. Li et al., Phys. Rep. 464, 113 (2008)

Constrain by the flow data of relativistic heavy-ion reactions P. Danielewicz, R. Lacey and W.G. Lynch, Science 298 (2002) 1592

Promising Probes of the E sym (ρ) in Nuclear Reactions (NSCL) (GSI) FAIR B. A. Li et al., Phys. Rep. 464, 113 (2008)

1. R. B. Wiringa et al., Phys. Rev. C 38, 1010 (1988). 2. M. Kutschera, Phys. Lett. B 340, 1 (1994). 3. B. A. Brown, Phys. Rev. Lett. 85, 5296 (2000). 4. S. Kubis et al, Nucl. Phys. A720, 189 (2003). 5. J. R. Stone et al., Phys. Rev. C 68, (2003). 6. A. Szmaglinski et al., Acta Phys. Pol. B 37, 277(2006). 7. B. A. Li et al., Phys. Rep. 464, 113 (2008). 8. Z. G. Xiao et al., Phys. Rev. Lett. 102, (2009). Many models predict that the symmetry energy first increases and then decreases above certain supra-saturation densities. The symmetry energy may even become negative at high densities. According to Xiao et al. (Phys. Rev. Lett. 102, (2009)), constrained by the recent terrestrial nuclear laboratory data, the nuclear matter could be described by a super softer EOS MDIx1.

Can not support the observations of neutron stars!

1.E. G. Adelberger et al., Annu. Rev. Nucl. Part. Sci. 53, 77(2003). 2.M.I. Krivoruchenko, et al., hep-ph/ v1 and references there in. The inverse square-law (ISL) of gravity is expected to be violated, especially at less length scales. The deviation from the ISL can be characterized effectively by adding a Yukawa term to the normal gravitational potential In the scalar/vector boson (U-boson ) exchange picture, and Within the mean-field approximation, the extra energy density and the pressure due to the Yukawa term is (2). Super-soft symmetry energy encountering non- Newtonian gravity in neutron stars

Hep-ph\ v3 PRL-2005,94,e Hep-ph\ Constraints on the coupling strength with nucleons g 2 /(4 ) and the mass μ (equivalently and ) of hypothetical weakly interacting light bosons.

EOS of MDIx1+WILB D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

M-R relation of neutron star with MDIx1+WILB D.H.Wen, B.A.Li and L.W. Chen, Phys. Rev. Lett., 103(2009)211102

Conclusion 1.It is shown that the super-soft nuclear symmetry energy preferred by the FOPI/GSI experimental data can support neutron stars stably if the non-Newtonian gravity is considered; 2.Observations of pulsars constrain the g 2 / 2 in a rough range of 50~150 GeV -2.

V. Gravitational Radiation from oscillations of neutron star

Why do We Need to Study Gravitational Waves? 1. Test General Relativity: probe of strong-field gravity 2. Gain different view of Universe: (1) Sources cannot be obscured by dust / stellar envelopes (2) Detectable sources are some of the most interesting, least understood in the Universe Gravitational Waves = Ripples in space-time (I). Gravitational Radiation and detection

Compact binary Orbital decay of the Hulse-Taylor binary neutron star system (Nobel prize in 1993) is the best evidence so far. Supernovae Mountain on neutron star Oscillating neutron star Possible Sources of Gravitational Waves From Neutron star

Hanford Washington Livingston, Louisiana (Laser Interferometer Gravitational-Wave Observatory ) LIGO From v2

LIGOs International Partners VIRGO: Pisa, Italy [Italy/France] GEO600, Hanover Germany [UK, Germany] TAMA300, Tokyo [Japan] AIGO, Jin-Jin West Australia

A network of large-scale ground-based laser- interferometer detectors (LIGO, VIRGO, GEO600, TAMA300) is on-line in detecting the gravitational waves (GW). Theorists are presently try their best to think of various sources of GWs that may be observable once the new ultra-sensitive detectors operate at their optimum level. MNRAS(2001)320,307 The importance for astrophysics GWs from non-radial neutron star oscillations are considered as one of the most important sources. (II). Oscillation modes

Axial mode: under the angular transformation θ π θ, ϕ π + ϕ, a spherical harmonic function with index transforms as (1)+1 for the expanding metric functions. Axial w-mode : not accompanied by any matter motions and only the perturbation of the space-time. The non-radial neutron star oscillations could be triggered by various mechanisms such as gravitational collapse, a pulsar glitch or a phase transition of matter in the inner core. Polar mode: transforms as (1) 1. Axial w-modes of static neutron stars

Key equation of axial w-mode Inner the star (l=2) Outer the star The equation for oscillation of the axial w-mode is give by 1 where or 1 S.Chandrasekhar and V. Ferrari, Proc. R. Soc. London A, 432, 247(1991) Nobel prize in 1983

Eigen-frequency of the w I -mode scaled by the gravitational energy Wen D.H. et al., Physical Review C 80, (2009) the minimum compactness for the existence of the w II -mode to be M/R

In Newtonian theory, the fundamental dynamical equation (Euler equations) that governs the fluid motion in the co-rotating frame is Acceleration = Coriolis force centrifugal force external force where is the fluid velocity and represents the gravitational potential. Euler equations in the rotating frame 2. R-modes (1). Background

For the rotating stars, the Coriolis force provides a restoring force for the toroidal modes, which leads to the so-called r-modes. Its eigen-frequency is It is shown that the structure parameters (M and R) make sense for the through the second order of. Definition of r-mode Class. Quantum Grav. 20 (2003) R105P111/p113 or

CFS instability and canonical energy APJ,222(1978)281 The function E c govern the stability to nonaxisymmetric perturbations as: (1) if, stable; (2) if, unstable. For the r-mode, The condition E c < 0 is equivalent to a change of sign in the pattern speed as viewed in the inertial frame, which is always satisfied for r-mode. gr-qc/ v1 canonical energy (conserved in absence of radiation and viscosity):

Seen by a non-rotating observer (star is rotating faster than the r-mode pattern speed) seen by a co-rotating observer. Looks like it's moving backwards The fluid motion has no radial component, and is the same inside the star although smaller by a factor of the square of the distance from the center. Fluid elements (red buoys) move in ellipses around their unperturbed locations. Note: The CFS instability is not only existed in GR, but also existed in Newtonian theory. Images of the motion of r-modes

Viscous damping instability The r-modes ought to grow fast enough that they are not completely damped out by viscosity. Two kinds of viscosity, bulk and shear viscosity, are normally considered. At low temperatures (below a few times 10 9 K) the main viscous dissipation mechanism is the shear viscosity arises from momentum transport due to particle scattering.. At high temperature (above a few times 10 9 K) bulk viscosity is the dominant dissipation mechanism. Bulk viscosity arises because the pressure and density variations associated with the mode oscillation drive the fluid away from beta equilibrium.

The r-mode instability window Condition : To have an instability we need t gw to be smaller than both t sv and t bv. For l = m = 2 r-mode of a canonical neutron star (R = 10 km and M = 1.4M and Kepler period P K 0.8 ms (n=1 polytrope)). Int.J.Mod.Phys. D10 (2001) 381

(2). Motivations (a) Old neutron stars (having crust) in LMXBs with rapid rotating frequency (such as EXO ) may have high core temperature (arXiv: v1.) ; which hints that there may exist r-mode instability in the core. (b) The discovery of massive neutron star ( PRS J , Nature 467, 1081(2010) and EXO , Nature 441, 1115(2006) ) reminds us restudy the r-mode instability of massive NS, as most of the previous work focused on the 1.4M sun neutron star. (c) The constraint on the symmetric energy at sub-saturation density range and the core-crust transition density by the terrestrial nuclear laboratory data could provide constraints on the r-mode instability.

PhysRevD Here only considers l=2, I 2 = And the viscosity c is density and temperature dependent: The subscript c denotes the quantities at the outer edge of the core. T<10 9 K: T>10 9 K: The viscous timescale for dissipation in the boundary layer: (3). Basic equations for calculating r-mode instability window of neutron star with rigid crust

The gravitational radiation timescale: According to, the critical rotation frequency is obtained: Based on the Kepler frequency, the critical temperature defined as: PhysRevD

Equation of states W. G. Newton, M. Gearheart, and Bao-An Li, v1

The mass-radius relation and the core radius Wen, et al, v1

Comparing the time scale The gravitational radiation timescale The viscous timescale Wen, et al, v1

Constraints of the symmetric energy and the core- crust transition density on the r-mode instability Windows Wen, et al, v1

The location of the LMXBs in the r-mode instability windows The temperatures are derived from their observed accretion luminosity and assuming the cooling is dominant by the modified Urca neutrino emission process for normal nucleons or by the modified Urca neutrino emission process for neutrons being super-fluid and protons being super-conduction. Phys. Rev. Lett. 107, (2011) Wen, et al, v1

The critical temperature under the Kepler frequency varies with transition density for 1.4M sun (except for ploy2.0) neutron star The critical temperatures should be constrained in the shaded area by the constrained symmetric energy. Wen, et al, v1

Conclusion (1)Obtained the constraint on the r-mode instability windows by the symmetric energy and the core-crust transition, which are constrained by the terrestrial nuclear laboratory data; (2) A massive neutron star has a wider instability window; (3)Giving the constraint on the critical temperature.

Thanks