xx SeedMagneticFieldsBNS: An Einstein Toolkit thorn for seeding magnetic fields to binary neutron star systems

SeedxMagneticxFieldsxBNS: An Einstein Toolkit thorn for seeding magnetic fields to binary neutron star systems

Zachariah B.xEtienne <zachetie *at* gmail *dot* com >

Documentation by Leonardo R.xWerneck <wernecklr *at* gmail *dot* com >

Feb 2, 2022

Abstract

SeedxMagneticxFieldsxBNS is designed to seed a poloidal magnetic field to binary neutron star (BNS) initial data.

1 Overview We provide a basic overview of the mathematical expressions implemented by this thorn, as well as key references.

1.1 Poloidal : Axfieldxtype = poloidalxAxinterior.

We seed a poloidal magnetic field in the interior of the two neutron stars (NSs) following the prescription described in AppendixxC ofx[1], namely

It is recommended to set to about 4% of the initial maximum pressure. Furthermore, should be adjusted in order to obtain the desired initial magnetic-to-gas pressure ratio.

1.2 Dipolar : Axfieldxtype = dipolarxAxeverywhere

We seed a dipolar magnetic field onto the BNS system by extending the prescription ofx[2] from one to two NSs. Namely, we consider that each neutron star contributes the following term to the vector potential in spherical basis: where identifies the neutron star, , where are the NS radii and the radii of the current loops, , is the position of each neutron star (assumed to be in the -axis), and .

We then set the vector potential in the Cartesian basis using the standard formulae

Note that the behavior described above is valid when using staggered vector potentials (see Table 1 for details).

11 Variable 11Storage location
11Non-staggered11

11            11
11            11
11            11

11

Tablex1: Storage location on grid of vector potential .

2 Basic usage

The following lines provide an example of how to use this thorn to use this thorn to seed a poloidal magnetic field to the interior of two stars located at (in code units). The star radii are not specified explicitly, and we use the default radius as a good enough estimate.

ActiveThornsx=x"Seed_Magnetic_Fields_BNS"
Seed_Magnetic_Fields_BNS::enable_IllinoisGRMHD_staggered_A_fieldsx=x"yes"
Seed_Magnetic_Fields_BNS::A_field_typex=x"poloidal_A_interior"
Seed_Magnetic_Fields_BNS::have_two_NSs_along_x_axisx=x"yes"
Seed_Magnetic_Fields_BNS::x_c1x=x+15
Seed_Magnetic_Fields_BNS::x_c2x=x-15
Seed_Magnetic_Fields_BNS::A_bx=x49529.954
Seed_Magnetic_Fields_BNS::n_sx=x2.0
#xSetxtox4%xinitialxmaxxpressure,xwhichxisx0.000113824867150113*0.04x=x.00000455299468600452
Seed_Magnetic_Fields_BNS::P_cutx=x0.00000455299468600452

References

[1]xxxZ.xB.xEtienne, V.xPaschalidis, R.xHaas, P.xMxsta, & S.xL.xShapiro, IllinoisGRMHD: an open-source, user-friendly GRMHD code for dynamical spacetimes, Classical and Quantum Gravity, 32(17), 175009 (2015).

[2]xxxV.xPaschalidis, Z.xB.xEtienne, & S.xL.xShapiro, General-relativistic simulations of binary black hole-neutron stars: precursor electromagnetic signals, Physical Review D, 88(2), 021504 (2013).

3 Parameters

11axb  10Scope: restrictedx01  REAL

11Description: Magnetic field strength parameter.

11 Range 10 x01 Default: 1e-3
11*:*  10Any real

11

11axfieldxtype  10Scope: restrictedx01  KEYWORD

11Description: Which field structure to use.

11 Range 10 x01 Default: poloidalxAxinterior
11see [1] below  10Dipole magnetic field, interior to the star
11see [1] below  10Dipole magnetic field everywhere

11

poloidal\_A\_interior

[1]

dipolar\_A\_everywhere

11enablexillinoisgrmhdxstaggeredxaxfields 10Scope: restrictedx01  BOOLEAN

11Description: Define A fields on an IllinoisGRMHD staggered grid

11                              10  x01  Default: no

11

11havextwoxnssxalongxxxaxis  10Scope: restrictedx01  BOOLEAN

11Description: Do we have two NSs centered along x-axis?

11                              10  x01  Default: no

11

11ixzeroxns1  10Scope: restrictedx01  REAL

11Description: Magnetic field loop current of NS1.

11 Range 10 x01 Default: 0.0
110.0:*)  10

11

11ixzeroxns2  10Scope: restrictedx01  REAL

11Description: Magnetic field loop current of NS2.

11 Range 10 x01 Default: 0.0
110.0:*)  10

11

11nxs  10Scope: restrictedx01  REAL

11Description: Magnetic field strength pressure exponent.

11 Range 10 x01 Default: 1.0
11*:*  10Any real

11

11pxcut  10Scope: restrictedx01  REAL

11Description: Cutoff pressure, below which vector potential is set to zero. Typically set to 4% of the maximum initial pressure.

11  Range  10  x01  Default: 1e-5
110:*  10Positive

11

11rxns1  10Scope: restrictedx01  REAL

11Description: Radius of NS1. Does not have to be perfect, but must not overlap other star.

11 Range 10 x01 Default: 13.5
110:*  10Any positive

11

11rxns2  10Scope: restrictedx01  REAL

11Description: Radius of NS2. Does not have to be perfect, but must not overlap other star.

11 Range 10 x01 Default: 13.5
110:*  10Any positive

11

11rxzeroxns1  10Scope: restrictedx01  REAL

11Description: Current loop radius of NS1.

11 Range 10 x01 Default: 1.0
110.0:*)  10

11

11rxzeroxns2  10Scope: restrictedx01  REAL

11Description: Current loop radius of NS2.

11 Range 10 x01 Default: 1.0
110.0:*)  10

11xxc1  10Scope: restrictedx01  REAL

11Description: x coordinate of NS1 center

11 Range 10 x01 Default: -15.2
11*:*  10Any real

11

11xxc2  10Scope: restrictedx01  REAL

11Description: x coordinate of NS2 center

11 Range 10 x01 Default: 15.2
11*:*  10Any real

11

4 Interfaces

General Implements: seedxmagneticxfieldsxprivt

Inherits: grid admbase hydrobase

5 Schedule This section lists all the variables which are assigned storage by thorn WVUThornsxDiagnostics/SeedxMagneticxFieldsxBNS. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage x

11Always:  11x
11HydroBase::rho[1] HydroBase::press[1] HydroBase::eps[1] HydroBase::vel[1] HydroBase::Bvec[1] HydroBase::Avec[1] HydroBase::Aphi[1]11x

11x  11x

11

Scheduled Functions

HydroBasexInitial x seedxmagneticxfieldsxprivt x set up binary neutron star seed magnetic fields. x

11x11After: 11meudonxbinxnsxinitialise
11 x 11Before: 11illinoisgrmhdxidxconverter
11 x 11Language:11c
11 x 11Type: 11function