Magnetized Binary Neutron Stars with Whisky

Transcription

1 Magnetized Binary Neutron Stars with Whisky Bruno Giacomazzo (AEI, Potsdam, Germany) in collaboration with Luca Baiotti (Tokyo) and Luciano Rezzolla (AEI)

2 Plan of the Talk Introduction The Whisky(MHD) code Binary Neutron Star Mergers The Role of Magnetic Fields in the gws Magnetic Fields amplification Summary and Conclusions

3 Due to their duration and dynamics, Binary Neutron Stars are very good sources for gravitational wave detectors such as Virgo (Italy) and Ligo (USA) Virgo (Pisa, Italy) Binary neutron stars mergers are also possible sources for short gamma-ray bursts

4 The Whisky(MHD) code Full GR Magneto-Hydro-Dynamical Code Based on the Cactus framework Solves the HD and MHD equations on dynamical curved background Uses HRSC (High Resolution Shock Capturing) methods Can handle BH formation with or without Excision Implements the Method of Lines Adopts Adaptive Mesh Refinement techniques (Carpet) Implements the Constrained Transport and the Hyperbolic Divergence Cleaning schemes It s meant as an astrophysical laboratory to study several different sources of gws

5 Matter fields evolution The evolution equations of the matter are given as usual by the conservation of the baryon number and energymomentum: µ T µν = 0 µ J µ = 0 J µ ρu µ T µν = (ρ + ρɛ + p + b 2 )u µ u ν + plus an Equation of State P=P(ρ,ε) For the simulations presented here we have used during the evolution an ideal-fluid EoS P = ρɛ(γ 1) or a polytropic EoS P = κρ Γ (p + 12 ) b2 g µν b µ b ν

6 GRMHD equations The evolution of the magnetic field obeys Maxwell s equations: ν F µν = 0 that give the divergence free condition: ( ) γ B = 0 and the equations for the evolution of the magnetic field: t ( γ B ) = [( α v β ) ( γ B )]

7 Binary Neutron Stars Mergers with Magnetic Fields

8 Previous Works In Newtonian Physics (SPH) Price and Rosswog 2006, SCIENCE 312, 719 studied the mf amplification after the merger initial mf B~10 12 Gauss Fully General Relativistic Simulations: Anderson et al., PRL 100, (2008) adaptive mesh refinement used initial data built by hand not able to follow the BH formation initial mf B~10 16 Gauss (strong effects in the waves) Liu et al 2008, PRD 78, no mesh refinement ( fish-eye coords) consistent (irrotational) initial data only one orbit but follow the BH formation second order reconstruction and low resolution initial mf B~10 16 Gauss (weak effects in the waves)

9 Initial Model All the initial models are computed using the Lorene code for unmagnetized binary NSs (Bonazzola et al. 1999): Model M1,M2 d (km) low-mass high-mass Technical data for the simulations: polytropic or ideal fluid EOS outer boundary: ~370 km 5 refinement levels; res. on finest level: ~0.36km minmod or PPM for the reconstruction HLLE flux Runge Kutta (3rd-order)

10 Adding Magnetic Fields We have considered the same models also when an initially poloidal magnetic field of ~10 12 or ~10 17 Gauss is introduced The magnetic field is added by hand using the following vector potential: A φ = A b r 2 [max(p P cut, 0)] n A b P cut = 0.04 max(p ) where and are two constants defining respectively the strength and the extension of the mf inside the star. n=2 defines the profile of the initial mf. The initial magnetic field is contained inside the star

11 Starting Up... We started using HLLE+minmod (2nd order) and a Polytropic EOS Here we consider the high-mass model with B~10 12 Gauss

12 Starting Up... We started using HLLE+minmod (2nd order) and a Polytropic EOS Here we consider the high-mass model with B~10 12 Gauss

13 Waveforms Waveforms obtained using HLLE+minmod and a Polytropic EOS

14 Waveforms Waveforms obtained using HLLE+minmod and a Polytropic EOS High-mass

15 Waveforms Waveforms obtained using HLLE+minmod and a Polytropic EOS Low-mass High-mass

16 Waveforms Waveforms obtained using HLLE+minmod and an Ideal FLuid EOS

17 Waveforms Waveforms obtained using HLLE+minmod and an Ideal FLuid EOS No differences in the waves even for large magnetic fields!?!

18 Waveforms Minmod is known to be dissipative. We moved to HLLE+PPM (3 rd order) Here we consider the highmass model with B=0 and B~10 17 Gauss and an Ideal Fluid EOS

19 Waveforms Minmod is known to be dissipative. We moved to HLLE+PPM (3 rd order) Here we consider the highmass model with B=0 and B~10 17 Gauss and an Ideal Fluid EOS Strong differences in the waves also during the inspiral!!!

20 MHD effects during the inspiral Here we consider the high-mass model with B=0 and B~10 17 Gauss and a Ideal Fluid EOS evolved with HLLE+PPM (3rd order) high-mass IF B=0 high-mass IF B~10 17

21 MHD effects during the inspiral Here we consider the high-mass model with B=0 and B~10 17 Gauss and a Ideal Fluid EOS evolved with HLLE+PPM (3rd order) high-mass IF B=0 high-mass IF B~10 17

22 MHD effects during the inspiral High-mass model with B=0 and B~10 17 Gauss and Ideal Fluid EOS ~1.5 ms of difference in the time of the merger

23 MHD effects during the inspiral high-mass IF B=0 high-mass IF B~10 17 The mf has an effect on the tidal deformations and then on the inspiral

24 Magnetic field amplification High-mass model with B~10 17 Gauss and an Ideal Fluid EOS After the merger the magnetic field is amplified of one order of magnitude

25 Hydrodynamics Instabilities During the merger a shear interface forms across which the velocities are discontinuous. This leads to the formation of vortices (Kelvin- Helmholtz instability). In the presence of a poloidal magnetic field, this determines the generation of a large toroidal magnetic field even if the poloidal one is small This can have an important role in the formation of magnetars and short gamma-ray bursts

26 KH instability: high-mass BNS Visualization by Giacomazzo, Rezzolla

27 KH instability: high-mass BNS Visualization by Giacomazzo, Rezzolla

28 KH instability: high-mass binary Note the development of vortices in the shear boundary layer produced at the time of the merger More evident in terms of the weighted vorticity. in corotating frame

29 KH instability: high-mass binary Evolution of the weighted vorticity for high-mass ideal-fluid without mf

30 KH instability: high-mass binary Evolution of the weighted vorticity for high-mass ideal-fluid without mf

31 Conclusions We were able to perform the inspiral and merger of BNSs with different magnetic fields since some time; we now believe the results are robust Crucial to use high-order reconstruction (at least 3rd order) Effects of high-magnetic fields are clearly visible in the gws both during the inspiral and after the merger We are able to extract the full gravitational wave signal We are extending the picture to include a larger set of possible magnetic field strengths the amplification of the magnetic field at the merger and after BH formation is particularly challenging; great care is needed to obtain convincing results