Neutron star coalescences A good microphysics laboratory

Transcription

1 Neutron star coalescences A good microphysics laboratory Rubén M. Cabezón Grup d Astronomia i Astrofísica Dept. de Física i Enginyeria Nuclear UPC (Barcelona)

2 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

3 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

4 Motivation Nuclear EOS is not well known: log(p) A AU B C F FPS G L N O UU WS SH M (M Ÿ ) 6 4 A AU B C F FPS G L N O UU WS SH ρ c = g cm -3 N L 20 O SH 32 2 C log(ρ) 0 FPS F AU B A G UU WS R/(10 Km)

5 Motivation General scheme: Nuclear EOS? affects NS structure relate ed constrain Observable affects NS merger hydrodynamics produces Gravitational waves

6 Motivation General scheme: Nuclear EOS? affects NS structure relate ed constrain Observable affects NS merger hydrodynamics produces Gravitational waves

7 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

8 Neutron stars At first order a star is an accumulation of gas (H and He mainly) that it is in a delicate equilibrium between gravitational force (that tends to collapse the star) and internal pressure (that tries to make it expand). MASS Gravitational force EQUILIBRIUM NUCLEAR REACTIONS Internal pressure

9 Neutron stars The variation of the abundances of chemical spices due to the nuclear reactions produces an evolution. Life and death of a star are strongly determined by its initial mass and chemical composition.

10 Neutron stars Progenit tor mass AGB star Planetary Nebulae White dwarfs Neutron stars M 0 8 M M n 3 M? Black holes Supernova

11 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

12 Gravitational waves GW are a metric perturbation due to the rapid movement of mass charges. g + [ ] ( ) 2 µν = ηµν + hµν O hµν Transverse-Traceless gauge simplifies things: h µ 0 = 0, pure spatial tensor hlml, = 0, divergence - free hll = 0, trace -free Two independent modes of polarization: Einstein online e e + e e x x e e x y e + e y y e e y z

13 Gravitational waves GW have a quadrupolar nature because of the conservation of linear and angular momentum. Trace-free part of the second moment of the mass distribution (i.e. reduced quadrupole moment) (slow-motion wake-field Newtonian quadrupole approx.): I lm 1 = ρ xlxm δ 3 lm r 2 d 3 x h TT lm = 2G 4 c r I& TT lm h h + = = G 4 c r 2G 4 c r ( I&& I&& ) I&& θθ θφ φφ I I I θθ φφ θφ = = = ( Ixx cos φ + Iyy sin φ + Ixy sin 2φ ) 2 I sin θ ( I cosφ + I sinφ) I ( Iyy Ixx ) cosθ sin 2φ + I ( I sinφ I cosφ ) sinθ. 1 2 xx zz sin xz 2 φ + I yy yz xz cos 2 φ I yz xy sin 2φ, xy cos 2 sin 2θ, θ cosθ cos 2φ

14 Gravitational waves Currently working interferometric detectors: NAME (COUNTRY) LOCATION ARM SENS. PEAK LIGO (USA) Livingston 4 km a 180 Hz COST (M ) 580 (los tres) LIGO (USA) Hanford 4 km Id Id LIGO (USA) Hanford 2 km Id Id TAMA 300 (JAPAN) GEO 600 (GERMANY) VIRGO (ITALY) Tokyo 300 m (0.7-1 khz) 11 Hannover 600 m a 600 Hz 11 Pisa 3 km a 500 Hz 72

15 Gravitational waves Currently working interferometric detectors NAME (COUNTRY) LOCATION ARM SENS. PEAK COST (M ) LIGO (USA) Livingston 4 km a 180 Hz 580 (los tres) LIGO (USA) LIGO (USA) Hanford Hanford 4 km 2 km Id Id Id Id TAMA 300 (JAPAN) Tokyo 300 m (0.7-1 khz) 11 Hannover 600 m a 600 Hz 11 Pisa 3 km a 500 Hz 72 GEO 600 (GERMANY) VIRGO (ITALY)

16 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

17 NS-NS mergers D.R.Lorimer Statistics of Compact Objects and Coalescence Rates

18 NS-NS mergers 7 known DNS systems (2006). 3 of them will merge within Hubble time: PSR B B J merging timescale = 85 Myr! NS-NS merger rate ~ yr -1 (Kim et al. 2006) NS-NS mergers are powerful sources of GW. Det. rate (ini. LIGO) ~ 1 event per yr Det. rate (adv. LIGO) ~ events per yr

19 NS-NS mergers Dip: onset of dynamical instability Peak: Barlike structure GW spectra of 2 NS of 1.4 M and 10 Km Sec. Peak: Transient oscillations Point-mass inspiral trajectory LIGO Zhuge et al (1994)

20 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

21 Smooth Particle Hydrodynamics SPH is a fully lagrangian hydrocode. The system is discretized in particles. Physical properties, in every particle position, are retrieved through interpolation over close neighbours. ~ Particles Interpolation points evolve with the fluid, following the HD equations. Weighting function (Kernel) 2h 2h 2h 2h h: smoothing length

22 Smooth Particle Hydrodynamics We can make SPH versions of the equations of fluid dynamics: Continuity eq.: Acceleration eq.: Energy eq.: Red. quadrupole: (Sec. derivative) dρi = dt r dvi = dt du dt i j j m j m ( r r v v ) j i j W P P i + 2 ρi ρ i j 2 j 1 P P i j = m j j ρi ρj ij + ij + iw ij i i i i i i 2 2vlvm + xmal + xlam δ 3 ij ( r r v v ) W + S& 2 I& i, lm = mi lm i i i j i ij r r r ( v + a ) i i EOS: P = ( ρ ) i P i

23 Numerical simulations System starts in the point-mass inspiral regime. When stars are close dynamical effects appear (tidal torque), leading an accelerated inspiral, merger and coalescence. A temporary barlike structure is formed. Spiral arms transport angular momentum outwards. The resulting core axial symmetry depends on the EOS stiffness.

24 Numerical simulations 60 km Gravitational waves as tracers of nuclear equation of state Rubén M. Cabezón XXIII Trob. Cient. de la Mediterrània 2007

25 Numerical simulations 120 km Gravitational waves as tracers of nuclear equation of state Rubén M. Cabezón XXIII Trob. Cient. de la Mediterrània 2007

26 Numerical simulations 11 realistic EOS 1.4 M NS SH UU WS FPS L O N A AU B F

27 Numerical simulations A AU B F FPS L UU N O SH WS

28 Numerical simulations L L / L t / t d

29 Numerical simulations Polytropic EOS vs. realistic EOS P = K ρ Γ log (P) 34 Γ log (P) log (ρ) log (ρ)

30 Numerical simulations Polytropic EOS vs. realistic EOS Polytropic EOS have been widely used to simulate this scenario but it is not straightforward to do a correspondence between polytropic and realistic EOS Linear adjustment of the realistic EOS 8x10 14 Range of adjustment not well defined (ρ 95 - ρ c ) log ρ (P) (g/cm 3 ) 36 6x x10 14 Γ adj ρ 95 32x x10 0 0x10 0 1x x10 M 33 3x M (g) log (ρ)

31 Numerical simulations Polytropic EOS vs. realistic EOS Polytropic EOS have been widely used to simulate this scenario but it is not straightforward to do a correspondence between polytropic and realistic EOS. Linear adjustment of the realistic EOS 38 3x10 33 Mass-weighted average of local Γ. log M (P) (M Ÿ ) 36 2x Γ i+2 Γ i Γ i+1 1x Γ wgt = miγi shells 0x10 0 0x10 0 4x10 5 8x10 5 1x R/(10 Km) log (ρ) M

32 Numerical simulations Polytropic EOS vs. realistic EOS Polytropic EOS have been widely used to simulate this scenario but it is not straightforward to do a correspondence between polytropic and realistic EOS. Linear adjustment of the realistic EOS Mass-weighted average of local Γ. Log R Adjust. of NS structure from realistic EOS Input parameters: M, R and ρ c Find best Γ

33 Numerical simulations AB Arnett & Bowers (1977), APJS 33, 415 WFF Wiringa, Fiks & Fabrocini (1988), Phys. Rev. C 38, 1010 LRP Lorenz, Ravenhall & Pethick (1993), PRL 70, 379 S Shen, et al. (1998), Prog. Theor. Phys, 100, 1013

34 In this talk: o Motivation o What is a neutron star and how is it formed? o Gravitational waves o Coalescence of neutron stars o Hydrodynamical simulations o Conclusions

35 Conclusions o GW signals depend very sensitively on the nuclear matter EOS. Therefore they can impose strong constraints and help us to understand the behavior of matter at high densities and impose a criteria to differentiate between NS and black holes. o NS-NS mergers are a good laboratory to test EOS. They are strong GW emiters and very susceptible of being detected by ground based interferometers (LIGO, GEO, TAMA ) o Numerical calculations are a useful tool to explore the parameter space. They can provide a useful set of luminosity and waveform templates that helps to understand not only the hydrodynamics but the microphysics involved. o It is important to use realistic equations of state in numerical simulations since there is not a clear relation between realistic and polytropical EOS.

36 Neutron star coalescences A good microphysics laboratory Rubén M. Cabezón Grup d Astronomia i Astrofísica Dept. de Física i Enginyeria Nuclear UPC (Barcelona)