K S ChengDepartment of Physics

University of Hong KongCollaborators:W.M. Suen (Wash. U)Lap-Ming Lin (CUHK)T.Harko & R. Tian (HKU)

It is proposed that strange matter is the most stable form of matter in high density (e.g. Witten 1984)

Strange matter can be formed in various astrophysical situations, e.g. early Universe (Witten 84), in the core of proto-neutron stars (e.g. Takahara et al. 85), accreting binaries (Cheng & Dai 96) etc.

However,the exact phase transition process is still an open question. It can begin with a single quark seed at the center of the star and grow to the entire star via either slow combustion or fast detonation.

Using the thermodynamics equilibrium, conservation of Baryon and conservation of charge, Glendenning (1992) shows that hybrid stars, which contain a mixture of quark droplets and normal matter, is more possible.

221. Introduction 1. Introduction

In our study we did not consider the detail formation process from normal matter to quark matter. We simply assume that a neutron star suddenly undergoes a phase-transition. We use a 3D Newtonian hydrodynamic code to study the consequences of phase-transition-induced collapse.

This code solves a set of non-viscous Newtonian fluid flow equations, which describe the motion of fluid inside the star by using a standard high-resolution shock capturing scheme with Riemann solver. The code is developed by the Washington group and has been applied to study various neutron star dynamical problems, e.g. (Gressman et al. 1999,2002; Lin & Suen 2004, Lin et al. 2006).

2. Numerical Simulation2. Numerical Simulation 33

ρ mass density of the fluid υi Cartesian components of the velocity P fluid pressure

44 2.1 Basic equations2.1 Basic equations

τ total energy density

ε internal energy per unit mass of the fluid Φ Newtonian potential

The system is completed by specifying an equation of state P = P(ρ, ε)

552.1 Basic equations2.1 Basic equations

At t=0-, the initial configuration of star is determined by hydrostatic equilibrium with an assumed neutron star EOS

At t=0+, we switch the EOS to the following form:

2. Numerical Simulation2. Numerical Simulation 66

ρtr is chosen when Pq =0 and

7

Dotted line – Glendenning 1992Solid line – our approximated model

Pressure profiles before and after phase transition

ρ =ρtr

8

Freq. is roughly scaled as ρ1/2

99

figure has no phase transition, it indicates that the oscillation is unlikely due to numerical fluctuation.

τeff effective neutrino optical depth κeff effective opacity

Janka (2001)

10103.1 Neutrinosphere3.1 Neutrinosphere

Definition of neutrinosphere

11113.2 Neutrino luminosity3.2 Neutrino luminosity

Balantekin & Yuksel (2005)

12

Temperature at the neutrinosphere

13

Density at the neutrinosphere

14143.1 Neutrinosphere3.1 Neutrinosphere

Time evolution of temperature and density profiles

Goodman et al. (1987)

15154.3 e± pair production rate4.3 e± pair production rate

1616

Annihilated e± pair energy luminosity has the same pulsation-like time evolution. The efficiency of neutrino converting into e± is very low most of the time except it increases to almost 100% at the peak of some pulses (very high neutrinosphere temperature (Tian 2008).

4.3 e± pair production rate4.3 e± pair production rate

17174.4 Mass ejection4.4 Mass ejection

Requirement

1818

Whether the absorbed energy is enough to eject mass is determined discretely at each time slice with an interval of 0.0075 ms

Suppose at T1 a layer of mass is ejected; until T2 no mass is ejected

The outer edge of the ejected mass distribution can reach the speed of light

e± pairs is created outside the star; the ejected mass will absorb e± pairs created in certain area and be accelerated

4.4 Mass ejection4.4 Mass ejection

19194.4 Mass ejection4.4 Mass ejection

(ms) (ms)

20

Profiles◦ Complicated and irregular◦ Multi-peaked or single-peaked

• Durations (T) ◦ ~ 5 ms to ~ 5 103 s, Typically ~ a few seconds

• Variabilities (T) ◦ ~ 1 ms, even ~ 0.1 ms, Typically ~ 10-2 T

Extremely intensity neutrino pulses can result from the phase-transition-induced collapse of neutron stars due to density and temperature oscillation; the temperatures of these pulse neutrinos can be as high as 10-20MeV, which is significantly higher than the non-oscillating case (~5MeV).

These high energy neutrinos can enhance the efficiency of electron/positron pair creation rate, which may blow off part of surface material from the stars and accelerate them to extremely relativistic speed, which result in gamma-ray bursts when they collide with each other or with ISM.

Summary and DiscussionSummary and Discussion 2222