Star_bhns Class Reference
[Stars and black holes]

Class for stars in black hole-neutron star binaries. More...

#include <star_bhns.h>

Inheritance diagram for Star_bhns:

Public Member Functions
	Star_bhns (Map &mp_i, int nzet_i, const Eos &eos_i, bool irrot_i)
	Standard constructor.
	Star_bhns (const Star_bhns &)
	Copy constructor.
	Star_bhns (Map &mp_i, const Eos &eos_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Star_bhns ()
	Destructor.
void	operator= (const Star_bhns &)
	Assignment to another Star_bhns.
Scalar &	set_pot_centri ()
	Read/write the centrifugal potential.
Scalar &	set_lapconf_auto ()
	Read/write of the lapconf function generated by the neutron star.
Scalar &	set_lapconf_comp ()
	Read/write of the lapconf function generated by the companion black hole.
Vector &	set_shift_auto ()
	Read/write of the shift vector generated by the neutron star.
Vector &	set_shift_comp ()
	Read/write of the shift vector generated by the companion black hole.
Scalar &	set_confo_auto ()
	Read/write of the conformal factor generated by the neutron star.
Scalar &	set_confo_comp ()
	Read/write of the conformal factor generated by the companion black hole.
bool	is_irrotational () const
	Returns `true` for an irrotational motion, `false` for a corotating one.
const Scalar &	get_psi0 () const
	Returns the non-translational part of the velocity potential.
const Vector &	get_d_psi () const
	Returns the covariant derivative of the velocity potential (Spherical components with respect to the mapping of the star).
const Vector &	get_wit_w () const
	Returns the spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
const Scalar &	get_loggam () const
	Returns the logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
const Vector &	get_bsn () const
	Returns the shift vector, divided by N , of the rotating coordinates, $\beta^i/N$ .
const Scalar &	get_gam () const
	Returns the Lorentz factor gam.
const Scalar &	get_gam0 () const
	Returns the Lorentz factor gam0.
const Scalar &	get_pot_centri () const
	Returns the centrifugal potential.
const Scalar &	get_lapconf_auto () const
	Returns the part of the lapconf function generated by the star.
const Scalar &	get_lapconf_comp () const
	Returns the part of the lapconf function generated by the companion black hole.
const Scalar &	get_lapconf_tot () const
	Returns the total lapconf function.
const Scalar &	get_lapse_auto () const
const Scalar &	get_lapse_tot () const
	Returns the total lapse function.
const Vector &	get_d_lapconf_auto () const
	Returns the derivative of the lapse function generated by the star.
const Vector &	get_d_lapconf_comp () const
	Returns the derivative of the lapse function generated by the companion black hole.
const Vector &	get_shift_auto () const
	Returns the part of the shift vector generated by the star.
const Vector &	get_shift_comp () const
	Returns the part of the shift vector generated by the companion black hole.
const Vector &	get_shift_tot () const
	Returns the part total shift vector.
const Tensor &	get_d_shift_auto () const
	Returns the derivative of the shift vector generated by the star.
const Tensor &	get_d_shift_comp () const
	Returns the derivative of the shift vector generated by the companion black hole.
const Scalar &	get_confo_auto () const
	Returns the part of the conformal factor generated by the star.
const Scalar &	get_confo_comp () const
	Returns the part of the conformal factor generated by the companion black hole.
const Scalar &	get_confo_tot () const
	Returns the total conformal factor.
const Vector &	get_d_confo_auto () const
	Returns the derivative of the conformal factor generated by the star.
const Vector &	get_d_confo_comp () const
	Returns the derivative of the conformal factor generated by the companion black hole.
const Scalar &	get_psi4 () const
	Returns the fourth power of the total conformal factor.
const Sym_tensor &	get_taij_auto () const
	Returns the part of the extrinsic curvature tensor $\tilde A^{ij}$ generated by the neutron star part.
const Scalar &	get_taij_quad_auto () const
	Returns the part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}^{\rm auto}$ .
virtual void	sauve (FILE *) const
	Save in a file.
virtual double	mass_b () const
	Baryon mass.
virtual double	mass_b_bhns (bool kerrschild, const double &mass_bh, const double &sepa) const
virtual double	mass_g () const
	Gravitational mass.
virtual double	mass_g_bhns () const
void	hydro_euler_bhns (bool kerrschild, const double &mass_bh, const double &sepa)
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame, as well as `wit_w` and `loggam` .
void	update_metric_bhns (const Hole_bhns &hole, const Star_bhns &star_prev, double relax)
	Computes metric coefficients from known potentials with relaxation when the companion is a black hole.
void	update_met_der_comp_bhns (const Hole_bhns &hole)
	Computes derivative of metric quantities from the companion black hole.
void	kinema_bhns (bool kerrschild, const double &mass_bh, const double &sepa, double omega, double x_rot, double y_rot)
	Computes the quantities `bsn` and `pot_centri` .
void	fait_d_psi_bhns ()
	Computes the gradient of the total velocity potential $\psi$ .
void	extr_curv_bhns ()
	Computes `taij_auto` , `taij_quad_auto` from `shift_auto` , `lapse_auto` , `confo_auto` .
void	equilibrium_bhns (double ent_c, const double &mass_bh, const double &sepa, bool kerrschild, int mer, int mermax_ns, int mermax_potvit, int mermax_poisson, int filter_r, int filter_r_s, int filter_p_s, double relax_poisson, double relax_potvit, double thres_adapt, double resize_ns, const Tbl &fact_resize, Tbl &diff)
	Computes an equilibrium configuration.
double	velo_pot_bhns (const double &mass_bh, const double &sepa, bool kerrschild, int mermax, double precis, double relax)
	Computes the non-translational part of the velocity scalar potential $\psi0$ by solving the continuity equation.
double	chi_rp (double radius, double phi)
	Sensitive indicator of the mass-shedding to the direction of , $\theta=\pi/2$ , $\phi$ .
double	radius_p (double phi)
	Radius of the star to the direction of $\theta=\pi/2$ and $\phi$ .
double	phi_min ()
	Azimuthal angle when the indicator of the mass-shedding takes its minimum chi_min.
double	phi_local_min (double phi_ini)
	Azimuthal angle when the indicator of the mass-shedding takes its local minimum.
void	relax_bhns (const Star_bhns &star_prev, double relax_ent, double relax_met, int mer, int fmer_met)
	Performs a relaxation on `ent` , `lapse_auto` , `shift_auto` , `confo_auto` .
void	equil_spher_bhns (double ent_c, double precis)
	Computes a spherical configuration.
Map &	set_mp ()
	Read/write of the mapping.
void	set_enthalpy (const Scalar &)
	Assignment of the enthalpy field.
void	equation_of_state ()
	Computes the proper baryon and energy density, as well as pressure from the enthalpy.
virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame (`nbar`, `ener` and `press`).
virtual void	equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *pent_limit=0x0)
	Computes a spherical static configuration.
const Map &	get_mp () const
	Returns the mapping.
int	get_nzet () const
	Returns the number of domains occupied by the star.
const Eos &	get_eos () const
	Returns the equation of state.
const Scalar &	get_ent () const
	Returns the enthalpy field.
const Scalar &	get_nbar () const
	Returns the proper baryon density.
const Scalar &	get_ener () const
	Returns the proper total energy density.
const Scalar &	get_press () const
	Returns the fluid pressure.
const Scalar &	get_ener_euler () const
	Returns the total energy density with respect to the Eulerian observer.
const Scalar &	get_s_euler () const
	Returns the trace of the stress tensor in the Eulerian frame.
const Scalar &	get_gam_euler () const
	Returns the Lorentz factor between the fluid and Eulerian observers.
const Vector &	get_u_euler () const
	Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tensor &	get_stress_euler () const
	Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.
const Scalar &	get_logn () const
	Returns the logarithm of the lapse N.
const Scalar &	get_nn () const
	Returns the lapse function N.
const Vector &	get_beta () const
	Returns the shift vector $\beta^i$ .
const Scalar &	get_lnq () const
const Metric &	get_gamma () const
	Returns the 3-metric $\gamma$ .
double	ray_eq () const
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ [r_unit].
double	ray_eq_pis2 () const
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ [r_unit].
double	ray_eq_pi () const
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ [r_unit].
double	ray_eq_3pis2 () const
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ [r_unit].
double	ray_pole () const
	Coordinate radius at $\theta=0$ [r_unit].
virtual const Itbl &	l_surf () const
	Description of the stellar surface: returns a 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
const Tbl &	xi_surf () const
	Description of the stellar surface: returns a 2-D `Tbl` containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .
Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities.
void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<).
virtual void	del_hydro_euler ()
	Sets to `ETATNONDEF` (undefined state) the hydrodynamical quantities relative to the Eulerian observer.
Protected Attributes
Map_af	mp_aff
	Affine mapping for solving poisson's equations of metric quantities.
bool	irrotational
	`true` for an irrotational star, `false` for a corotating one
Scalar	psi0
	Scalar potential $\Psi_0$ of the non-translational part of fluid 4-velocity (in the irrotational case).
Vector	d_psi
	Gradient of $\Psi$ (in the irrotational case) (Spherical components with respect to the mapping of the star).
Vector	wit_w
	Spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
Scalar	loggam
	Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Vector	bsn
	3-vector shift, divided by N , of the rotating coordinates, $\beta^i/N$ .
Scalar	gam
	Lorentz factor between the fluid and the co-orbiting observer.
Scalar	gam0
	Lorentz factor between the co-orbiting observer and the Eulerian one.
Scalar	pot_centri
	Centrifugal potential.
Scalar	lapconf_auto
	Lapconf function generated by the star.
Scalar	lapconf_comp
	Lapconf function generated by the companion black hole.
Scalar	lapconf_tot
	Total lapconf function.
Scalar	lapse_auto
	Lapse function generated by the "star".
Scalar	lapse_tot
	Total lapse function.
Vector	d_lapconf_auto
	Derivative of the lapconf function generated by the star $\partial_j \alpha$ .
Vector	d_lapconf_comp
	Derivative of the lapconf function generated by the companion black hole.
Vector	shift_auto
	Shift vector generated by the star.
Vector	shift_comp
	Shift vector generated by the companion black hole.
Vector	shift_tot
	Total shift vector.
Tensor	d_shift_auto
	Derivative of the shift vector generated by the star $\eta^{ik} \partial_k \beta^j$ .
Tensor	d_shift_comp
	Derivative of the shift vector generated by the companion black hole.
Scalar	confo_auto
	Conformal factor generated by the star.
Scalar	confo_comp
	Conformal factor generated by the companion black hole.
Scalar	confo_tot
	Total conformal factor.
Vector	d_confo_auto
	Derivative of the conformal factor generated by the star $\partial_j \psi$ .
Vector	d_confo_comp
	Derivative of the conformal factor generated by the companion black hole.
Scalar	psi4
	Fourth power of the total conformal factor.
Sym_tensor	taij_auto
	Part of the extrinsic curvature tensor $A^{ij}$ generated by `shift_auto` , `lapse_auto` , and `confo_auto` .
Scalar	taij_quad_auto
	Part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}^{\rm auto}$ .
Metric_flat	flat
	Flat metric defined on the mapping (Spherical components with respect to the mapping of the star ).
Scalar	ssjm1_lapconf
	Effective source at the previous step for the resolution of the Poisson equation for `lapconf_auto` .
Scalar	ssjm1_confo
	Effective source at the previous step for the resolution of the Poisson equation for `confo_auto` .
Scalar	ssjm1_khi
	Effective source at the previous step for the resolution of the Poisson equation for the scalar $\chi$ by means of `Map_et::poisson` .
Vector	ssjm1_wshift
	Effective source at the previous step for the resolution of the vector Poisson equation for by means of `Map_et::poisson` .
double *	p_mass_b_bhns
	Baryon mass.
double *	p_mass_g_bhns
	Gravitational mass.
Map &	mp
	Mapping associated with the star.
int	nzet
	Number of domains of `*mp` occupied by the star.
const Eos &	eos
	Equation of state of the stellar matter.
Scalar	ent
	Log-enthalpy.
Scalar	nbar
	Baryon density in the fluid frame.
Scalar	ener
	Total energy density in the fluid frame.
Scalar	press
	Fluid pressure.
Scalar	ener_euler
	Total energy density in the Eulerian frame.
Scalar	s_euler
	Trace of the stress scalar in the Eulerian frame.
Scalar	gam_euler
	Lorentz factor between the fluid and Eulerian observers.
Vector	u_euler
	Fluid 3-velocity with respect to the Eulerian observer.
Sym_tensor	stress_euler
	Spatial part of the stress-energy tensor with respect to the Eulerian observer.
Scalar	logn
	Logarithm of the lapse N .
Scalar	nn
	Lapse function N .
Vector	beta
	Shift vector.
Scalar	lnq
Metric	gamma
	3-metric
double *	p_ray_eq
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ .
double *	p_ray_eq_pis2
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ .
double *	p_ray_eq_pi
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ .
double *	p_ray_eq_3pis2
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ .
double *	p_ray_pole
	Coordinate radius at $\theta=0$ .
Itbl *	p_l_surf
	Description of the stellar surface: 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
Tbl *	p_xi_surf
	Description of the stellar surface: 2-D `Tbl` containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .
double *	p_mass_b
	Baryon mass.
double *	p_mass_g
	Gravitational mass.
Friends
class	Bin_bhns
ostream &	operator<< (ostream &, const Star &)
	Display.

Detailed Description

Class for stars in black hole-neutron star binaries.

()

Definition at line 54 of file star_bhns.h.

Constructor & Destructor Documentation

Star_bhns::Star_bhns	(	Map &	mp_i,
		int	nzet_i,
		const Eos &	eos_i,
		bool	irrot_i
	)

Standard constructor.

Parameters:

	mp_i	Mapping on which the star will be defined
	nzet_i	Number of domains occupied by the star
	eos_i	Equation of state of the stellar matter
	irrot_i	should be `true` for an irrotational star, `false` for a corotating one

Definition at line 69 of file star_bhns.C.

References bsn, Vector::change_triad(), confo_auto, confo_comp, confo_tot, d_confo_auto, d_confo_comp, d_lapconf_auto, d_lapconf_comp, d_psi, d_shift_auto, d_shift_comp, gam, gam0, Map::get_bvect_cart(), lapconf_auto, lapconf_comp, lapconf_tot, lapse_auto, lapse_tot, loggam, pot_centri, psi0, psi4, set_der_0x0(), Tensor::set_etat_zero(), shift_auto, shift_comp, shift_tot, ssjm1_confo, ssjm1_khi, ssjm1_lapconf, ssjm1_wshift, Scalar::std_spectral_base(), taij_auto, taij_quad_auto, Star::u_euler, and wit_w.

Star_bhns::Star_bhns ( const Star_bhns & star )

Copy constructor.

Definition at line 174 of file star_bhns.C.

References set_der_0x0().

Star_bhns::Star_bhns	(	Map &	mp_i,
		const Eos &	eos_i,
		FILE *	fich
	)

Constructor from a file (see sauve(FILE*) ).

Parameters:

	mp_i	Mapping on which the star will be defined
	eos_i	Equation of state of the stellar matter
	fich	input file (must have been created by the function `sauve` )

Definition at line 217 of file star_bhns.C.

References bsn, Vector::change_triad(), confo_comp, confo_tot, d_confo_auto, d_confo_comp, d_lapconf_auto, d_lapconf_comp, d_psi, d_shift_auto, d_shift_comp, gam, gam0, Star::gam_euler, Map::get_bvect_cart(), Map::get_mg(), irrotational, lapconf_comp, lapconf_tot, lapse_auto, lapse_tot, loggam, Star::mp, pot_centri, psi0, psi4, set_der_0x0(), Tensor::set_etat_zero(), shift_comp, shift_tot, Scalar::std_spectral_base(), taij_auto, taij_quad_auto, Star::u_euler, and wit_w.

Star_bhns::~Star_bhns ( ) [virtual]

Destructor.

Definition at line 325 of file star_bhns.C.

References del_deriv().

Member Function Documentation

double Star_bhns::chi_rp	(	double	radius,
		double	phi
	)

Sensitive indicator of the mass-shedding to the direction of $r$ , $\theta=\pi/2$ , $\phi$ .

Parameters:

	radius	[input] Radial coordinate
	phi	[input] Azimuthal angle

Definition at line 57 of file star_bhns_chi.C.

References Scalar::dsdr(), Star::ent, Star::ray_pole(), and Scalar::val_point().

void Star_bhns::del_deriv ( ) const [protected, virtual]

Deletes all the derived quantities.

Reimplemented from Star.

Definition at line 337 of file star_bhns.C.

References p_mass_b_bhns, p_mass_g_bhns, and set_der_0x0().

void Star::del_hydro_euler ( ) [protected, virtual, inherited]

Sets to ETATNONDEF (undefined state) the hydrodynamical quantities relative to the Eulerian observer.

Reimplemented in Star_bin, Star_bin_xcts, Star_rot, and Star_rot_Dirac.

Definition at line 326 of file star.C.

References Star::del_deriv(), Star::ener_euler, Star::gam_euler, Star::s_euler, Tensor::set_etat_nondef(), Scalar::set_etat_nondef(), Star::stress_euler, and Star::u_euler.

void Star::equation_of_state ( ) [inherited]

Computes the proper baryon and energy density, as well as pressure from the enthalpy.

Reimplemented in Gravastar.

Definition at line 458 of file star.C.

References Param::add_int(), Scalar::allocate_all(), Star::del_deriv(), Star::ener, Eos::ener_ent(), Star::ent, Star::eos, Mg3d::get_grille3d(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Star::mp, Star::nbar, Eos::nbar_ent(), Star::nzet, Star::press, Eos::press_ent(), Mtbl::set(), Scalar::set_domain(), Scalar::set_etat_qcq(), Tbl::set_etat_qcq(), Mtbl::set_etat_qcq(), Scalar::std_spectral_base(), Mtbl::t, and Grille3d::x.

void Star_bhns::equil_spher_bhns	(	double	ent_c,
		double	precis
	)

Computes a spherical configuration.

Parameters:

	ent_c	[input] Central enthalpy
	precis	[input] precision

Definition at line 60 of file star_bhns_spher.C.

References Scalar::annule(), confo_auto, confo_tot, diffrel(), Scalar::dsdr(), Star::ener, Star::ener_euler, Star::ent, Star::equation_of_state(), exp(), Star::gam_euler, Scalar::get_dzpuis(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map_af::homothetie(), Scalar::inc_dzpuis(), Scalar::integrale(), lapconf_auto, lapconf_tot, lapse_auto, lapse_tot, log(), Star::mp, norme(), Star::nzet, Map_af::poisson(), pow(), Star::press, psi4, Star::s_euler, Vector::set(), Cmp::set_etat_qcq(), shift_auto, sqrt(), Scalar::std_spectral_base(), Star::u_euler, Scalar::val_grid_point(), and Map::val_r().

void Star_bhns::equilibrium_bhns	(	double	ent_c,
		const double &	mass_bh,
		const double &	sepa,
		bool	kerrschild,
		int	mer,
		int	mermax_ns,
		int	mermax_potvit,
		int	mermax_poisson,
		int	filter_r,
		int	filter_r_s,
		int	filter_p_s,
		double	relax_poisson,
		double	relax_potvit,
		double	thres_adapt,
		double	resize_ns,
		const Tbl &	fact_resize,
		Tbl &	diff
	)

Computes an equilibrium configuration.

Parameters:

	ent_c	[input] Central enthalpy
	mass_bh	[input] BH mass in the background metric
	sepa	[input] Separation between NS and BH
	kerrschild	should be `true` for a Kerr-Schild background, `false` for a Conformally flat one
	mer	[input] Number of iteration
	mermax_ns	[input] Maximum number of iteration steps
	mermax_potvit	[input] Maximum number of steps in Map_radial::poisson_compact
	mermax_poisson	[input] Maximum number of steps in poisson scalar
	filter_r	[input] No. points to be deleted for (r): lap,conf
	filter_r_s	[input] No. points to be deleted for (r): shift
	filter_p_s	[input] No. points to be deleted for (phi): shift
	relax_poisson	[input] Relaxation factor in poisson scalar
	relax_potvit	[input] Relaxation factor in Map_radial::poisson_compact
	thres_adapt	[input] Threshold on dH/dr for the adaptation of the mapping
	resize_ns	[input] Resize factor for the first shell
	fact_resize	[input] 1-D `Tbl` for the input of some factors : \ `fact(0)` : A resizing factor for the first shell
	diff	[output] 1-D `Tbl` for the storage of some error indicators :

Definition at line 63 of file star_bhns_equilibrium.C.

References abs(), Map::adapt(), Param::add_cmp_mod(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Param::add_tenseur_mod(), Scalar::annule(), Cmp::annule_hard(), chi_rp(), confo_auto, confo_tot, d_confo_auto, d_lapconf_auto, Tensor::dec_dzpuis(), Scalar::derive_con(), Tensor::derive_con(), diffrel(), Vector::divergence(), Tensor::divergence(), Scalar::dsdr(), Scalar::dsdx(), Scalar::dsdy(), Star::ener_euler, Star::ent, Star::equation_of_state(), exp(), Scalar::filtre(), flat, gam, gam0, Map::get_bvect_cart(), Scalar::get_dzpuis(), Scalar::get_etat(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map_et::homothetie(), hydro_euler_bhns(), Scalar::inc_dzpuis(), irrotational, lapconf_auto, lapconf_comp, Scalar::laplacian(), log(), loggam, max(), Star::mp, Star::nzet, phi_min(), Scalar::poisson(), pot_centri, pow(), Star::press, radius_p(), Star::ray_eq_pi(), Star::ray_pole(), Map::reevaluate(), Map::resize(), Star::s_euler, Vector::set(), Tenseur::set(), Tbl::set(), Tenseur::set_etat_qcq(), Tbl::set_etat_qcq(), Scalar::set_etat_qcq(), Cmp::set_etat_qcq(), Scalar::set_spectral_va(), Tenseur::set_std_base(), shift_auto, Valeur::smooth(), sqrt(), ssjm1_confo, ssjm1_khi, ssjm1_lapconf, ssjm1_wshift, Vector::std_spectral_base(), Scalar::std_spectral_base(), taij_auto, taij_quad_auto, Star::u_euler, Scalar::val_grid_point(), Scalar::val_point(), Map::val_r(), velo_pot_bhns(), Map::x, and Map::y.

void Star::equilibrium_spher	(	double	ent_c,
		double	precis = `1.e-14`,
		const Tbl *	pent_limit = `0x0`
	)			`[virtual, inherited]`

Computes a spherical static configuration.

Parameters:

	ent_c	[input] central value of the enthalpy
	precis	[input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)
	ent_limit	[input] : array of enthalpy values to be set at the boundaries between the domains; if set to 0x0 (default), the initial values will be kept.

Definition at line 91 of file star_equil_spher.C.

References Map_et::adapt(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Scalar::annule(), diffrel(), Scalar::dsdr(), Map_af::dsdr(), Star::ener, Star::ener_euler, Star::ent, Star::equation_of_state(), exp(), Star::gam_euler, Star::gamma, Map_et::get_alpha(), Map_af::get_alpha(), Map_et::get_beta(), Map_af::get_beta(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map_af::homothetie(), Scalar::integrale(), Star::logn, Star::mass_b(), Star::mass_g(), Star::mp, Star::nn, norme(), Star::nzet, Map_af::poisson(), Star::press, Star::s_euler, Vector::set(), Map_af::set_alpha(), Map_af::set_beta(), Scalar::set_dzpuis(), Cmp::set_etat_qcq(), Scalar::set_etat_zero(), sqrt(), Scalar::std_spectral_base(), Star::u_euler, Scalar::val_grid_point(), and Map::val_r().

void Star_bhns::extr_curv_bhns ( )

Computes taij_auto , taij_quad_auto from shift_auto , lapse_auto , confo_auto .

Definition at line 56 of file star_bhns_extr_curv.C.

References Metric_flat::con(), confo_auto, Metric_flat::cov(), d_shift_auto, flat, Map::get_bvect_cart(), lapconf_auto, Star::mp, pow(), Tensor::std_spectral_base(), Scalar::std_spectral_base(), taij_auto, and taij_quad_auto.

void Star_bhns::fait_d_psi_bhns ( )

Computes the gradient of the total velocity potential $\psi$ .

Definition at line 531 of file star_bhns.C.

References Tensor::annule(), Scalar::annule_hard(), bsn, d_psi, Scalar::deriv(), Star::ent, exp(), Star::gam_euler, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), irrotational, Star::mp, Star::nzet, psi0, psi4, Vector::set(), Tensor::set(), Valeur::set_base(), Tensor::set_etat_nondef(), Tensor::set_etat_qcq(), Scalar::std_spectral_base(), and Cmp::va.

const Vector& Star::get_beta ( ) const [inline, inherited]

Returns the shift vector $\beta^i$ .

Definition at line 398 of file star.h.

References Star::beta.

const Vector& Star_bhns::get_bsn ( ) const [inline]

Returns the shift vector, divided by N , of the rotating coordinates, $\beta^i/N$ .

(Spherical components with respect to the mapping of the star)

Definition at line 322 of file star_bhns.h.

References bsn.

const Scalar& Star_bhns::get_confo_auto ( ) const [inline]

Returns the part of the conformal factor generated by the star.

Definition at line 378 of file star_bhns.h.

References confo_auto.

const Scalar& Star_bhns::get_confo_comp ( ) const [inline]

Returns the part of the conformal factor generated by the companion black hole.

Definition at line 383 of file star_bhns.h.

References confo_comp.

const Scalar& Star_bhns::get_confo_tot ( ) const [inline]

Returns the total conformal factor.

Definition at line 386 of file star_bhns.h.

References confo_tot.

const Vector& Star_bhns::get_d_confo_auto ( ) const [inline]

Returns the derivative of the conformal factor generated by the star.

Definition at line 391 of file star_bhns.h.

References d_confo_auto.

const Vector& Star_bhns::get_d_confo_comp ( ) const [inline]

Returns the derivative of the conformal factor generated by the companion black hole.

Definition at line 396 of file star_bhns.h.

References d_confo_comp.

const Vector& Star_bhns::get_d_lapconf_auto ( ) const [inline]

Returns the derivative of the lapse function generated by the star.

Definition at line 351 of file star_bhns.h.

References d_lapconf_auto.

const Vector& Star_bhns::get_d_lapconf_comp ( ) const [inline]

Returns the derivative of the lapse function generated by the companion black hole.

Definition at line 356 of file star_bhns.h.

References d_lapconf_comp.

const Vector& Star_bhns::get_d_psi ( ) const [inline]

Returns the covariant derivative of the velocity potential (Spherical components with respect to the mapping of the star).

Definition at line 305 of file star_bhns.h.

References d_psi.

const Tensor& Star_bhns::get_d_shift_auto ( ) const [inline]

Returns the derivative of the shift vector generated by the star.

Definition at line 370 of file star_bhns.h.

References d_shift_auto.

const Tensor& Star_bhns::get_d_shift_comp ( ) const [inline]

Returns the derivative of the shift vector generated by the companion black hole.

Definition at line 375 of file star_bhns.h.

References d_shift_comp.

const Scalar& Star::get_ener ( ) const [inline, inherited]

Returns the proper total energy density.

Definition at line 366 of file star.h.

References Star::ener.

const Scalar& Star::get_ener_euler ( ) const [inline, inherited]

Returns the total energy density with respect to the Eulerian observer.

Definition at line 372 of file star.h.

References Star::ener_euler.

const Scalar& Star::get_ent ( ) const [inline, inherited]

Returns the enthalpy field.

Definition at line 360 of file star.h.

References Star::ent.

const Eos& Star::get_eos ( ) const [inline, inherited]

Returns the equation of state.

Definition at line 357 of file star.h.

References Star::eos.

const Scalar& Star_bhns::get_gam ( ) const [inline]

Returns the Lorentz factor gam.

Definition at line 325 of file star_bhns.h.

References gam.

const Scalar& Star_bhns::get_gam0 ( ) const [inline]

Returns the Lorentz factor gam0.

Definition at line 328 of file star_bhns.h.

References gam0.

const Scalar& Star::get_gam_euler ( ) const [inline, inherited]

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 378 of file star.h.

References Star::gam_euler.

const Metric& Star::get_gamma ( ) const [inline, inherited]

Returns the 3-metric $\gamma$ .

Definition at line 405 of file star.h.

References Star::gamma.

const Scalar& Star_bhns::get_lapconf_auto ( ) const [inline]

Returns the part of the lapconf function generated by the star.

Definition at line 334 of file star_bhns.h.

References lapconf_auto.

const Scalar& Star_bhns::get_lapconf_comp ( ) const [inline]

Returns the part of the lapconf function generated by the companion black hole.

Definition at line 339 of file star_bhns.h.

References lapconf_comp.

const Scalar& Star_bhns::get_lapconf_tot ( ) const [inline]

Returns the total lapconf function.

Definition at line 342 of file star_bhns.h.

References lapconf_tot.

const Scalar& Star_bhns::get_lapse_tot ( ) const [inline]

Returns the total lapse function.

Definition at line 348 of file star_bhns.h.

References lapse_tot.

const Scalar& Star_bhns::get_loggam ( ) const [inline]

Returns the logarithm of the Lorentz factor between the fluid and the co-orbiting observer.

Definition at line 316 of file star_bhns.h.

References loggam.

const Scalar& Star::get_logn ( ) const [inline, inherited]

Returns the logarithm of the lapse N.

In the Newtonian case, this is the Newtonian gravitational potential (in units of $c^2$ ).

Definition at line 392 of file star.h.

References Star::logn.

const Map& Star::get_mp ( ) const [inline, inherited]

Returns the mapping.

Definition at line 351 of file star.h.

References Star::mp.

const Scalar& Star::get_nbar ( ) const [inline, inherited]

Returns the proper baryon density.

Definition at line 363 of file star.h.

References Star::nbar.

const Scalar& Star::get_nn ( ) const [inline, inherited]

Returns the lapse function N.

Definition at line 395 of file star.h.

References Star::nn.

int Star::get_nzet ( ) const [inline, inherited]

Returns the number of domains occupied by the star.

Definition at line 354 of file star.h.

References Star::nzet.

const Scalar& Star_bhns::get_pot_centri ( ) const [inline]

Returns the centrifugal potential.

Definition at line 331 of file star_bhns.h.

References pot_centri.

const Scalar& Star::get_press ( ) const [inline, inherited]

Returns the fluid pressure.

Definition at line 369 of file star.h.

References Star::press.

const Scalar& Star_bhns::get_psi0 ( ) const [inline]

Returns the non-translational part of the velocity potential.

Definition at line 300 of file star_bhns.h.

References psi0.

const Scalar& Star_bhns::get_psi4 ( ) const [inline]

Returns the fourth power of the total conformal factor.

Definition at line 399 of file star_bhns.h.

References psi4.

const Scalar& Star::get_s_euler ( ) const [inline, inherited]

Returns the trace of the stress tensor in the Eulerian frame.

Definition at line 375 of file star.h.

References Star::s_euler.

const Vector& Star_bhns::get_shift_auto ( ) const [inline]

Returns the part of the shift vector generated by the star.

Definition at line 359 of file star_bhns.h.

References shift_auto.

const Vector& Star_bhns::get_shift_comp ( ) const [inline]

Returns the part of the shift vector generated by the companion black hole.

Definition at line 364 of file star_bhns.h.

References shift_comp.

const Vector& Star_bhns::get_shift_tot ( ) const [inline]

Returns the part total shift vector.

Definition at line 367 of file star_bhns.h.

References shift_tot.

const Tensor& Star::get_stress_euler ( ) const [inline, inherited]

Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 386 of file star.h.

References Star::stress_euler.

const Sym_tensor& Star_bhns::get_taij_auto ( ) const [inline]

Returns the part of the extrinsic curvature tensor $\tilde A^{ij}$ generated by the neutron star part.

Definition at line 404 of file star_bhns.h.

References taij_auto.

const Scalar& Star_bhns::get_taij_quad_auto ( ) const [inline]

Returns the part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}^{\rm auto}$ .

Definition at line 410 of file star_bhns.h.

References taij_quad_auto.

const Vector& Star::get_u_euler ( ) const [inline, inherited]

Returns the fluid 3-velocity with respect to the Eulerian observer.

Definition at line 381 of file star.h.

References Star::u_euler.

const Vector& Star_bhns::get_wit_w ( ) const [inline]

Returns the spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.

(Spherical components with respect to the mapping of the star)

Definition at line 311 of file star_bhns.h.

References wit_w.

void Star::hydro_euler ( ) [virtual, inherited]

Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame (nbar, ener and press).

Reimplemented in Star_bin, Star_bin_xcts, Star_rot, Star_rot_Dirac, and Star_rot_Dirac_diff.

Definition at line 573 of file star.C.

void Star_bhns::hydro_euler_bhns	(	bool	kerrschild,
		const double &	mass_bh,
		const double &	sepa
	)

Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame, as well as wit_w and loggam .

The calculation is performed starting from the quantities ent , ener , press , a_car and bsn , which are supposed to be up to date. From these, the following fields are updated: gam_euler , u_euler , ener_euler , s_euler , stress_euler , wit_w and loggam .

Parameters:

	kerrschild	should be `true` for a Kerr-Schild background, `false` for a Conformally flat one
	mass_bh	BH mass in the background metric
	sepa	Separation between NS and BH

Definition at line 55 of file star_bhns_hydro.C.

References Tensor::annule_domain(), bsn, d_psi, del_deriv(), Star::ener, Star::ener_euler, Star::ent, exp(), gam, gam0, Star::gam_euler, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), Map::get_ori_y(), Tensor::get_triad(), irrotational, log(), loggam, Star::mp, Star::press, psi4, Star::s_euler, Vector::set(), Tensor::set(), Scalar::set_dzpuis(), Tensor::set_etat_qcq(), Tensor::set_etat_zero(), sqrt(), Vector::std_spectral_base(), Scalar::std_spectral_base(), Star::u_euler, wit_w, Map::x, Map::y, and Map::z.

bool Star_bhns::is_irrotational ( ) const [inline]

Returns true for an irrotational motion, false for a corotating one.

Definition at line 297 of file star_bhns.h.

References irrotational.

void Star_bhns::kinema_bhns	(	bool	kerrschild,
		const double &	mass_bh,
		const double &	sepa,
		double	omega,
		double	x_rot,
		double	y_rot
	)

Computes the quantities bsn and pot_centri .

The calculation is performed starting from the quantities lapse_tot , shift_tot , which are supposed to be up to date.

Parameters:

	kerrschild	should be `true` for a Kerr-Schild background, `false` for a Conformally flat one
	mass_bh	BH mass in the background metric
	sepa	Separation between NS and BH
	omega	angular velocity with respect to an asymptotically inertial observer
	x_rot	absolute X coordinate of the rotation axis
	y_rot	absolute Y coordinate of the rotation axis

Definition at line 57 of file star_bhns_kinema.C.

References Tensor::annule_domain(), bsn, confo_tot, del_deriv(), gam0, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), Map::get_ori_y(), Map::get_rot_phi(), lapconf_tot, log(), Star::mp, pot_centri, psi4, Tensor::set(), Vector::set(), shift_tot, sqrt(), Scalar::std_spectral_base(), Vector::std_spectral_base(), Map::x, Map::xa, Map::y, Map::ya, and Map::z.

const Itbl & Star::l_surf ( ) const [virtual, inherited]

Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .

The stellar surface is defined as the location where the enthalpy (member ent) vanishes.

Reimplemented in Star_rot.

Definition at line 59 of file star_global.C.

References Star::ent, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Scalar::get_spectral_va(), Star::mp, Star::nzet, Star::p_l_surf, and Star::p_xi_surf.

double Star_bhns::mass_b ( ) const [virtual]

Baryon mass.

Implements Star.

Definition at line 59 of file star_bhns_global.C.

References confo_tot, Star::gam_euler, Scalar::integrale(), Star::nbar, Star::p_mass_b, pow(), and Scalar::std_spectral_base().

double Star_bhns::mass_g ( ) const [virtual]

Gravitational mass.

Implements Star.

Definition at line 134 of file star_bhns_global.C.

void Star_bhns::operator= ( const Star_bhns & star )

Assignment to another Star_bhns.

Reimplemented from Star.

Definition at line 364 of file star_bhns.C.

References bsn, confo_auto, confo_comp, confo_tot, d_confo_auto, d_confo_comp, d_lapconf_auto, d_lapconf_comp, d_psi, d_shift_auto, d_shift_comp, del_deriv(), flat, gam, gam0, irrotational, lapconf_auto, lapconf_comp, lapconf_tot, lapse_auto, lapse_tot, loggam, mp_aff, pot_centri, psi0, psi4, shift_auto, shift_comp, shift_tot, ssjm1_confo, ssjm1_khi, ssjm1_lapconf, ssjm1_wshift, taij_auto, taij_quad_auto, and wit_w.

ostream & Star_bhns::operator>> ( ostream & ost ) const [protected, virtual]

Operator >> (virtual function called by the operator <<).

Reimplemented from Star.

Definition at line 491 of file star_bhns.C.

References confo_tot, Star::ent, lapse_tot, Star::ray_eq(), Star::ray_eq_pi(), Star::ray_eq_pis2(), Star::ray_pole(), shift_tot, and Scalar::val_grid_point().

double Star_bhns::phi_local_min ( double phi_ini )

Azimuthal angle when the indicator of the mass-shedding takes its local minimum.

Parameters:

phi_ini

[input] Initial azumuthal angle to search minimum

Definition at line 141 of file star_bhns_chi.C.

References chi_rp(), and radius_p().

double Star_bhns::phi_min ( )

Azimuthal angle when the indicator of the mass-shedding takes its minimum chi_min.

Definition at line 79 of file star_bhns_chi.C.

References chi_rp(), Map::get_mg(), Mg3d::get_np(), Star::mp, phi_local_min(), radius_p(), Tbl::set(), and Tbl::set_etat_qcq().

double Star_bhns::radius_p ( double phi )

Radius of the star to the direction of $\theta=\pi/2$ and $\phi$ .

Parameters:

phi

[input] Azimuthal angle

Definition at line 70 of file star_bhns_chi.C.

References Star::mp, Star::nzet, and Map::val_r().

double Star::ray_eq ( ) const [inherited]

Coordinate radius at $\phi=0$ , $\theta=\pi/2$ [r_unit].

Definition at line 104 of file star_global.C.

References Map::get_mg(), Mg3d::get_nt(), Mg3d::get_type_p(), Mg3d::get_type_t(), Star::l_surf(), Star::mp, Star::p_ray_eq, Map::val_r(), and Star::xi_surf().

double Star::ray_eq_3pis2 ( ) const [inherited]

Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ [r_unit].

Definition at line 229 of file star_global.C.

References Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_type_p(), Mg3d::get_type_t(), Star::l_surf(), Star::mp, Star::p_ray_eq_3pis2, Star::ray_eq_pis2(), Map::val_r(), and Star::xi_surf().

double Star::ray_eq_pi ( ) const [inherited]

Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ [r_unit].

Definition at line 182 of file star_global.C.

References Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_type_p(), Mg3d::get_type_t(), Star::l_surf(), Star::mp, Star::p_ray_eq_pi, Star::ray_eq(), Map::val_r(), and Star::xi_surf().

double Star::ray_eq_pis2 ( ) const [inherited]

Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ [r_unit].

Definition at line 134 of file star_global.C.

References Map::get_mg(), Mg3d::get_np(), Mg3d::get_nt(), Mg3d::get_type_p(), Mg3d::get_type_t(), Star::l_surf(), Star::mp, Star::p_ray_eq_pis2, Map::val_r(), and Star::xi_surf().

double Star::ray_pole ( ) const [inherited]

Coordinate radius at $\theta=0$ [r_unit].

Definition at line 274 of file star_global.C.

References Map::get_mg(), Mg3d::get_type_t(), Star::l_surf(), Star::mp, Star::p_ray_pole, Map::val_r(), and Star::xi_surf().

void Star_bhns::relax_bhns	(	const Star_bhns &	star_prev,
		double	relax_ent,
		double	relax_met,
		int	mer,
		int	fmer_met
	)

Performs a relaxation on ent , lapse_auto , shift_auto , confo_auto .

Parameters:

	star_prev	[input] star at the previous step
	relax_ent	[input] Relaxation factor for `ent`
	relax_met	[input] Relaxation factor for `lapse_auto` , `shift_auto` , `confo_auto` , only if (merfmer_met=0) .
	mer	[input] Step number
	fmer_met	[input] Step interval between metric updates

Definition at line 590 of file star_bhns.C.

References confo_auto, del_deriv(), Star::ent, Star::equation_of_state(), lapconf_auto, and shift_auto.

void Star_bhns::sauve ( FILE * fich ) const [virtual]

Save in a file.

Reimplemented from Star.

Definition at line 466 of file star_bhns.C.

References confo_auto, Star::gam_euler, irrotational, lapconf_auto, psi0, Tensor::sauve(), Scalar::sauve(), shift_auto, ssjm1_confo, ssjm1_khi, ssjm1_lapconf, and ssjm1_wshift.

Scalar & Star_bhns::set_confo_auto ( )

Read/write of the conformal factor generated by the neutron star.

Definition at line 445 of file star_bhns.C.

References confo_auto, and del_deriv().

Scalar & Star_bhns::set_confo_comp ( )

Read/write of the conformal factor generated by the companion black hole.

Definition at line 452 of file star_bhns.C.

References confo_comp, and del_deriv().

void Star_bhns::set_der_0x0 ( ) const [protected, virtual]

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Star.

Definition at line 348 of file star_bhns.C.

References p_mass_b_bhns, and p_mass_g_bhns.

void Star::set_enthalpy ( const Scalar & ent_i ) [inherited]

Assignment of the enthalpy field.

Definition at line 375 of file star.C.

References Star::del_deriv(), Star::ent, and Star::equation_of_state().

Scalar & Star_bhns::set_lapconf_auto ( )

Read/write of the lapconf function generated by the neutron star.

Definition at line 417 of file star_bhns.C.

References del_deriv(), and lapconf_auto.

Scalar & Star_bhns::set_lapconf_comp ( )

Read/write of the lapconf function generated by the companion black hole.

Definition at line 424 of file star_bhns.C.

References del_deriv(), and lapconf_comp.

Map& Star::set_mp ( ) [inline, inherited]

Read/write of the mapping.

Definition at line 318 of file star.h.

References Star::mp.

Scalar & Star_bhns::set_pot_centri ( )

Read/write the centrifugal potential.

Definition at line 410 of file star_bhns.C.

References del_deriv(), and pot_centri.

Vector & Star_bhns::set_shift_auto ( )

Read/write of the shift vector generated by the neutron star.

Definition at line 431 of file star_bhns.C.

References del_deriv(), and shift_auto.

Vector & Star_bhns::set_shift_comp ( )

Read/write of the shift vector generated by the companion black hole.

Definition at line 438 of file star_bhns.C.

References del_deriv(), and shift_comp.

void Star_bhns::update_met_der_comp_bhns ( const Hole_bhns & hole )

Computes derivative of metric quantities from the companion black hole.

Parameters:

hole

companion black hole

Definition at line 56 of file star_bhns_upmetr_der.C.

References d_confo_comp, d_lapconf_comp, d_shift_comp, del_deriv(), Hole_bhns::get_d_confo_auto(), Hole_bhns::get_d_lapconf_auto(), Hole_bhns::get_d_shift_auto(), Tensor::inc_dzpuis(), Tensor::set(), Vector::set(), Tensor::set_etat_qcq(), Tensor::set_etat_zero(), Tensor::std_spectral_base(), and Vector::std_spectral_base().

void Star_bhns::update_metric_bhns	(	const Hole_bhns &	hole,
		const Star_bhns &	star_prev,
		double	relax
	)

Computes metric coefficients from known potentials with relaxation when the companion is a black hole.

The calculation is performed starting from the quantities lapse_auto , shift_auto , confo_auto , comp.lapse_auto , comp.confo_auto which are supposed to be up to date. From these, the following fields are updated: lapse_comp , lapse_tot, confo_comp, confo_tot , psi4 ,

Parameters:

	hole	companion black hole
	star_prev	previous value of the star
	relax	relaxation parameter

Definition at line 56 of file star_bhns_upmetr.C.

References confo_auto, confo_comp, confo_tot, d_confo_auto, d_lapconf_auto, d_shift_auto, del_deriv(), Scalar::deriv(), Map::get_bvect_cart(), Hole_bhns::get_confo_auto(), Hole_bhns::get_lapconf_auto(), Black_hole::get_mp(), Hole_bhns::get_shift_auto(), Tensor::get_triad(), Scalar::import(), lapconf_auto, lapconf_comp, lapconf_tot, lapse_auto, lapse_tot, Star::mp, pow(), psi4, Tensor::set(), Vector::set(), Tensor::set_etat_qcq(), Scalar::set_etat_qcq(), Tensor::set_etat_zero(), Scalar::set_etat_zero(), Tensor::set_triad(), shift_auto, shift_comp, shift_tot, Tensor::std_spectral_base(), Vector::std_spectral_base(), and Scalar::std_spectral_base().

double Star_bhns::velo_pot_bhns	(	const double &	mass_bh,
		const double &	sepa,
		bool	kerrschild,
		int	mermax,
		double	precis,
		double	relax
	)

Computes the non-translational part of the velocity scalar potential $\psi0$ by solving the continuity equation.

Parameters:

	mass_bh	[input] BH mass in the background metric
	sepa	[input] Separation between NS and BH
	kerrschild	should be `true` for a Kerr-Schild background, `false` for a Conformally flat one
	mermax	[input] Maximum number of steps in the iteration
	precis	[input] Required precision: the iteration will be stopped when the relative difference on $\psi0$ between two successive steps is lower than `precis` .
	relax	[input] Relaxation factor.

Returns:: Relative error of the resolution obtained by comparing the operator acting on the solution with the source.

Definition at line 63 of file star_bhns_vel_pot.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Tensor::annule(), Scalar::annule(), bsn, Vector::change_triad(), confo_tot, contract(), d_confo_auto, d_confo_comp, d_lapconf_auto, d_lapconf_comp, d_psi, Eos::der_nbar_ent(), Scalar::deriv(), Scalar::derive_con(), Scalar::derive_cov(), diffrel(), Star::ent, Star::eos, exp(), flat, Map::flat_met_spher(), Star::gam_euler, Map::get_bvect_cart(), Map::get_bvect_spher(), Scalar::get_etat(), Map::get_mg(), Mg3d::get_nzone(), Tensor::get_triad(), lapconf_tot, Scalar::laplacian(), log(), Star::mp, norme(), Star::nzet, Map::poisson_compact(), psi0, psi4, Vector::set(), Cmp::set(), Scalar::set_domain(), Tensor::set_etat_qcq(), Scalar::set_spectral_va(), Tensor::set_triad(), Scalar::std_spectral_base(), Cmp::va, Valeur::ylm(), and Valeur::ylm_i().

const Tbl & Star::xi_surf ( ) const [inherited]

Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .

The stellar surface is defined as the location where the enthalpy (member ent) vanishes.

Definition at line 85 of file star_global.C.

References Star::l_surf(), Star::p_l_surf, and Star::p_xi_surf.

Friends And Related Function Documentation

ostream& operator<<	(	ostream &	,
		const Star &
	)			`[friend, inherited]`

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Member Data Documentation

Vector Star::beta [protected, inherited]

Shift vector.

Definition at line 224 of file star.h.

Vector Star_bhns::bsn [protected]

3-vector shift, divided by N , of the rotating coordinates, $\beta^i/N$ .

(Spherical components with respect to the mapping of the star)

Definition at line 94 of file star_bhns.h.

Scalar Star_bhns::confo_auto [protected]

Conformal factor generated by the star.

Definition at line 152 of file star_bhns.h.

Scalar Star_bhns::confo_comp [protected]

Conformal factor generated by the companion black hole.

Definition at line 155 of file star_bhns.h.

Scalar Star_bhns::confo_tot [protected]

Total conformal factor.

Definition at line 158 of file star_bhns.h.

Vector Star_bhns::d_confo_auto [protected]

Derivative of the conformal factor generated by the star $\partial_j \psi$ .

Definition at line 163 of file star_bhns.h.

Vector Star_bhns::d_confo_comp [protected]

Derivative of the conformal factor generated by the companion black hole.

Definition at line 168 of file star_bhns.h.

Vector Star_bhns::d_lapconf_auto [protected]

Derivative of the lapconf function generated by the star $\partial_j \alpha$ .

Definition at line 125 of file star_bhns.h.

Vector Star_bhns::d_lapconf_comp [protected]

Derivative of the lapconf function generated by the companion black hole.

Definition at line 130 of file star_bhns.h.

Vector Star_bhns::d_psi [protected]

Gradient of $\Psi$ (in the irrotational case) (Spherical components with respect to the mapping of the star).

Definition at line 77 of file star_bhns.h.

Tensor Star_bhns::d_shift_auto [protected]

Derivative of the shift vector generated by the star $\eta^{ik} \partial_k \beta^j$ .

Definition at line 144 of file star_bhns.h.

Tensor Star_bhns::d_shift_comp [protected]

Derivative of the shift vector generated by the companion black hole.

Definition at line 149 of file star_bhns.h.

Scalar Star::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 189 of file star.h.

Scalar Star::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 194 of file star.h.

Scalar Star::ent [protected, inherited]

Log-enthalpy.

Definition at line 186 of file star.h.

const Eos& Star::eos [protected, inherited]

Equation of state of the stellar matter.

Definition at line 181 of file star.h.

Metric_flat Star_bhns::flat [protected]

Flat metric defined on the mapping (Spherical components with respect to the mapping of the star ).

Definition at line 187 of file star_bhns.h.

Scalar Star_bhns::gam [protected]

Lorentz factor between the fluid and the co-orbiting observer.

Definition at line 97 of file star_bhns.h.

Scalar Star_bhns::gam0 [protected]

Lorentz factor between the co-orbiting observer and the Eulerian one.

Definition at line 102 of file star_bhns.h.

Scalar Star::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 200 of file star.h.

Metric Star::gamma [protected, inherited]

3-metric

Definition at line 231 of file star.h.

bool Star_bhns::irrotational [protected]

true for an irrotational star, false for a corotating one

Definition at line 67 of file star_bhns.h.

Scalar Star_bhns::lapconf_auto [protected]

Lapconf function generated by the star.

Definition at line 108 of file star_bhns.h.

Scalar Star_bhns::lapconf_comp [protected]

Lapconf function generated by the companion black hole.

Definition at line 111 of file star_bhns.h.

Scalar Star_bhns::lapconf_tot [protected]

Total lapconf function.

Definition at line 114 of file star_bhns.h.

Scalar Star_bhns::lapse_auto [protected]

Lapse function generated by the "star".

Definition at line 117 of file star_bhns.h.

Scalar Star_bhns::lapse_tot [protected]

Total lapse function.

Definition at line 120 of file star_bhns.h.

Scalar Star_bhns::loggam [protected]

Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.

Definition at line 88 of file star_bhns.h.

Scalar Star::logn [protected, inherited]

Logarithm of the lapse N .

In the Newtonian case, this is the Newtonian gravitational potential (in units of $c^2$ ).

Definition at line 218 of file star.h.

Map& Star::mp [protected, inherited]

Mapping associated with the star.

Definition at line 176 of file star.h.

Map_af Star_bhns::mp_aff [protected]

Affine mapping for solving poisson's equations of metric quantities.

Definition at line 62 of file star_bhns.h.

Scalar Star::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 188 of file star.h.

Scalar Star::nn [protected, inherited]

Lapse function N .

Definition at line 221 of file star.h.

int Star::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 179 of file star.h.

Itbl* Star::p_l_surf [mutable, protected, inherited]

Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .

Definition at line 256 of file star.h.

double* Star::p_mass_b [mutable, protected, inherited]

Baryon mass.

Definition at line 264 of file star.h.

double* Star_bhns::p_mass_b_bhns [mutable, protected]

Baryon mass.

Definition at line 220 of file star_bhns.h.

double* Star::p_mass_g [mutable, protected, inherited]

Gravitational mass.

Definition at line 265 of file star.h.

double* Star_bhns::p_mass_g_bhns [mutable, protected]

Gravitational mass.

Definition at line 221 of file star_bhns.h.

double* Star::p_ray_eq [mutable, protected, inherited]

Coordinate radius at $\phi=0$ , $\theta=\pi/2$ .

Definition at line 238 of file star.h.

double* Star::p_ray_eq_3pis2 [mutable, protected, inherited]

Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ .

Definition at line 247 of file star.h.

double* Star::p_ray_eq_pi [mutable, protected, inherited]

Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ .

Definition at line 244 of file star.h.

double* Star::p_ray_eq_pis2 [mutable, protected, inherited]

Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ .

Definition at line 241 of file star.h.

double* Star::p_ray_pole [mutable, protected, inherited]

Coordinate radius at $\theta=0$ .

Definition at line 250 of file star.h.

Tbl* Star::p_xi_surf [mutable, protected, inherited]

Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .

Definition at line 262 of file star.h.

Scalar Star_bhns::pot_centri [protected]

Centrifugal potential.

Definition at line 105 of file star_bhns.h.

Scalar Star::press [protected, inherited]

Fluid pressure.

Definition at line 190 of file star.h.

Scalar Star_bhns::psi0 [protected]

Scalar potential $\Psi_0$ of the non-translational part of fluid 4-velocity (in the irrotational case).

Definition at line 72 of file star_bhns.h.

Scalar Star_bhns::psi4 [protected]

Fourth power of the total conformal factor.

Definition at line 171 of file star_bhns.h.

Scalar Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 197 of file star.h.

Vector Star_bhns::shift_auto [protected]

Shift vector generated by the star.

Definition at line 133 of file star_bhns.h.

Vector Star_bhns::shift_comp [protected]

Shift vector generated by the companion black hole.

Definition at line 136 of file star_bhns.h.

Vector Star_bhns::shift_tot [protected]

Total shift vector.

Definition at line 139 of file star_bhns.h.

Scalar Star_bhns::ssjm1_confo [protected]

Effective source at the previous step for the resolution of the Poisson equation for confo_auto .

Definition at line 197 of file star_bhns.h.

Scalar Star_bhns::ssjm1_khi [protected]

Effective source at the previous step for the resolution of the Poisson equation for the scalar $\chi$ by means of Map_et::poisson .

$\chi$ is an intermediate quantity for the resolution of the elliptic equation for the shift vector $N^i$

Definition at line 205 of file star_bhns.h.

Scalar Star_bhns::ssjm1_lapconf [protected]

Effective source at the previous step for the resolution of the Poisson equation for lapconf_auto .

Definition at line 192 of file star_bhns.h.

Vector Star_bhns::ssjm1_wshift [protected]

Effective source at the previous step for the resolution of the vector Poisson equation for $W^i$ by means of Map_et::poisson .

$W^i$ is an intermediate quantity for the resolution of the elliptic equation for the shift vector $N^i$ (Components with respect to the Cartesian triad associated with the mapping mp )

Definition at line 215 of file star_bhns.h.

Sym_tensor Star::stress_euler [protected, inherited]

Spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 208 of file star.h.

Sym_tensor Star_bhns::taij_auto [protected]

Part of the extrinsic curvature tensor $A^{ij}$ generated by shift_auto , lapse_auto , and confo_auto .

Definition at line 177 of file star_bhns.h.

Scalar Star_bhns::taij_quad_auto [protected]

Part of the scalar $\eta_{ik} \eta_{jl} A^{ij} A^{kl}$ generated by $A_{ij}^{\rm auto}$ .

Definition at line 182 of file star_bhns.h.

Vector Star::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.