Star_bin Class Reference
[Stars and black holes]

Class for stars in binary system. More...

#include <star.h>

Inheritance diagram for Star_bin:

Public Member Functions
	Star_bin (Map &mp_i, int nzet_i, const Eos &eos_i, bool irrot, bool conf_flat)
	Standard constructor.
	Star_bin (const Star_bin &)
	Copy constructor.
	Star_bin (Map &mp_i, const Eos &eos_i, FILE *fich)
	Constructor from a file (see `sauve(FILE* )`).
virtual	~Star_bin ()
	Destructor.
void	operator= (const Star_bin &)
	Assignment to another `Star_bin`.
Scalar &	set_pot_centri ()
	Read/write the centrifugal potential.
Scalar &	set_logn_comp ()
	Read/write of the logarithm of the lapse generated principally by the companion.
void	set_logn_auto (const Scalar &logn_auto_new)
	Assignment of a new logn_auto.
void	set_lnq_auto (const Scalar &lnq_auto_new)
	Assignment of a new lnq_auto.
Vector &	set_beta_auto ()
	Read/write of .
Vector &	set_beta ()
	Read/write of .
void	set_conf_flat (bool confflat)
	Write if conformally flat.
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_pot_centri () const
	Returns the centrifugal potential.
const Scalar &	get_logn_auto () const
	Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the star.
const Scalar &	get_logn_comp () const
	Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the companion star.
const Vector &	get_beta_auto () const
	Returns the part of the shift vector $\beta^i$ generated principally by the star.
const Vector &	get_beta_comp () const
	Returns the part of the shift vector $\beta^i$ generated principally by the star.
const Scalar &	get_lnq_auto () const
	Returns the part of the vector field generated principally by the star.
const Scalar &	get_lnq_comp () const
	Returns the part of the vector field generated principally by the companion star.
const Vector &	get_dcov_logn () const
	Returns the covariant derivative of .
const Vector &	get_dcon_logn () const
	Returns the contravariant derivative of .
const Vector &	get_dcov_phi () const
	Returns the covariant derivative of $\Phi$ (logarithm of the conformal factor).
const Vector &	get_dcon_phi () const
	Returns the contravariant derivative of $\Phi$ (logarithm of the conformal factor).
const Scalar &	get_psi4 () const
	Return the conformal factor $\psi^4$ .
const Metric &	get_flat () const
	Return the flat metric defined on the mapping (Spherical components with respect to the mapping of the star).
const Metric &	get_gtilde () const
	Return the conformal 3-metric $\tilde \gamma$ .
const Sym_tensor &	get_hij () const
	Return the total deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric.
const Sym_tensor &	get_hij_auto () const
	Return the deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric principally generated by the star.
const Sym_tensor &	get_hij_comp () const
	Return the deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the companion star.
const Sym_tensor &	get_tkij_auto () const
	Returns the part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by `beta_auto`.
const Sym_tensor &	get_tkij_comp () const
	Returns the part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by `beta_comp`.
const Scalar &	get_kcar_auto () const
	Returns the part of $\tilde K^{ij} \tilde K_{ij}$ generated by `beta_auto`.
const Scalar &	get_kcar_comp () const
	Returns the part of $\tilde K^{ij} \tilde K_{ij}$ generated by `beta_comp`.
const Scalar	get_decouple () const
	Returns the function used to construct `beta_auto` from `beta`.
bool	is_conf_flat () const
virtual void	sauve (FILE *) const
	Save in a file.
virtual double	mass_b () const
	Baryon mass.
virtual double	mass_g () const
	Gravitational mass.
virtual double	xa_barycenter () const
	Absolute coordinate X of the barycenter of the baryon density,.
virtual void	hydro_euler ()
	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 (const Star_bin &comp, double omega)
	Computes metric coefficients from known potentials, when the companion is another star.
void	update_metric (const Star_bin &comp, const Star_bin &star_prev, double relax, double omega)
	Same as `update_metric`(const Star_bin& ) but with relaxation.
void	update_metric_der_comp (const Star_bin &comp, double omega)
	Computes the derivative of metric functions related to the companion star.
void	kinematics (double omega, double x_axe)
	Computes the quantities `bsn` and `pot_centri`.
void	fait_d_psi ()
	Computes the gradient of the total velocity potential $\psi$ .
void	extrinsic_curvature (double omega)
	Computes `tkij_auto` and `akcar_auto` from `beta_auto`, `nn` and `Q`.
void	equilibrium (double ent_c, int mermax, int mermax_potvit, int mermax_poisson, double relax_poisson, double relax_potvit, double thres_adapt, Tbl &diff, double om)
	Computes an equilibrium configuration.
double	velocity_potential (int mermax, double precis, double relax)
	Computes the non-translational part of the velocity scalar potential $\psi0$ by solving the continuity equation.
void	relaxation (const Star_bin &star_prev, double relax_ent, double relax_met, int mer, int fmer_met)
	Performs a relaxation on `ent`, `logn_auto`, `lnq_auto`, `beta_auto` and `hij_auto`.
void	test_K_Hi () const
	Test if the gauge conditions we impose are well satisfied.
void	helical (double omega) const
	Test of the helical symmetry.
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	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.
virtual void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.
virtual void	del_hydro_euler ()
	Sets to `ETATNONDEF` (undefined state) the hydrodynamical quantities relative to the Eulerian observer.
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<).
Protected Attributes
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	pot_centri
	Centrifugal potential.
Scalar	logn_auto
	Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the star.
Scalar	logn_comp
	Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the companion star.
Vector	dcov_logn
	Covariant derivative of the total logarithm of the lapse.
Vector	dcon_logn
	Contravariant derivative of the total logarithm of the lapse.
Scalar	lnq_auto
	Scalar field $Q = \psi^2 N$ generated principally by the star.
Scalar	lnq_comp
	Scalar field $Q = \psi^2 N$ generated principally by the companion star.
Scalar	psi4
	Conformal factor $\psi^4$ .
Vector	dcov_phi
	Covariant derivative of the logarithm of the conformal factor.
Vector	dcon_phi
	Contravariant derivative of the logarithm of the conformal factor.
Metric_flat	flat
	Flat metric defined on the mapping (Spherical components with respect to the mapping of the star) .
Metric	gtilde
	Conformal metric $\tilde \gamma_{ij}$ .
Vector	beta_auto
	Part of the shift vector generated principally by the star (Spherical components with respect to the mapping of the star).
Vector	beta_comp
	Part of the shift vector generated principally by the star (Spherical components with respect to the mapping of the star).
Sym_tensor	hij
	Total deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric.
Sym_tensor	hij_auto
	Deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the star.
Sym_tensor	hij_comp
	Deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the companion star.
Sym_tensor	tkij_auto
	Part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by `beta_auto`.
Sym_tensor	tkij_comp
	Part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by `beta_comp`.
Scalar	kcar_auto
	Part of the scalar $K_{ij} K^{ij}$ generated by `beta_auto`, i.e.
Scalar	kcar_comp
	Part of the scalar $K_{ij} K^{ij}$ generated by `beta_auto` and `beta_comp`, i.e.
Scalar	ssjm1_logn
	Effective source at the previous step for the resolution of the Poisson equation for `logn_auto`.
Scalar	ssjm1_lnq
	Effective source at the previous step for the resolution of the Poisson equation for `lnq_auto`.
Scalar	ssjm1_khi
	Effective source at the previous step for the resolution of the Poisson equation for `khi`.
Vector	ssjm1_wbeta
Scalar	ssjm1_h11
	Effective source at the previous step for the resolution of the Poisson equation for `h00_auto`.
Scalar	ssjm1_h21
	Effective source at the previous step for the resolution of the Poisson equation for `h10_auto`.
Scalar	ssjm1_h31
	Effective source at the previous step for the resolution of the Poisson equation for `h20_auto`.
Scalar	ssjm1_h22
	Effective source at the previous step for the resolution of the Poisson equation for `h11_auto`.
Scalar	ssjm1_h32
	Effective source at the previous step for the resolution of the Poisson equation for `h21_auto`.
Scalar	ssjm1_h33
	Effective source at the previous step for the resolution of the Poisson equation for `h22_auto`.
Scalar	decouple
	Function used to construct the part generated by the star from the total .
bool	conf_flat
	`true` if the 3-metric is conformally flat, `false` for a more general metric.
double *	p_xa_barycenter
	Absolute coordinate X of the barycenter of the baryon density.
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	Binary
ostream &	operator<< (ostream &, const Star &)
	Display.

Detailed Description

Class for stars in binary system.

*** UNDER DEEVELOPMENT *** ()

A Star_bin can be construted in two states, represented by the bool member irrotational: (i) irrotational (i.e. the fluid motion is irrotational) or (ii) rigidly corotating with respect to the orbital motion (synchronized binary).

Version:: $Id: star.h,v 1.31 2010/12/09 10:36:42 m_bejger Exp $#

Definition at line 479 of file star.h.

Constructor & Destructor Documentation

Star_bin::Star_bin	(	Map &	mp_i,
		int	nzet_i,
		const Eos &	eos_i,
		bool	irrot,
		bool	conf_flat
	)

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	should be `true` for an irrotational star, `false` for a corotating one
	conf_flat	should be `true` for a conformally flat metric `false` for a general one

Definition at line 111 of file star_bin.C.

References Star::beta, beta_auto, beta_comp, bsn, Tensor::change_triad(), Vector::change_triad(), d_psi, dcon_logn, dcon_phi, dcov_logn, dcov_phi, Map::flat_met_cart(), Star::gamma, Map::get_bvect_cart(), hij, hij_auto, hij_comp, kcar_auto, kcar_comp, lnq_auto, lnq_comp, loggam, logn_auto, logn_comp, Star::mp, pot_centri, psi0, psi4, set_der_0x0(), Tensor::set_etat_zero(), ssjm1_h11, ssjm1_h21, ssjm1_h22, ssjm1_h31, ssjm1_h32, ssjm1_h33, ssjm1_khi, ssjm1_lnq, ssjm1_logn, Star::stress_euler, tkij_auto, tkij_comp, Star::u_euler, and wit_w.

Star_bin::Star_bin ( const Star_bin & star )

Copy constructor.

Definition at line 206 of file star_bin.C.

References set_der_0x0().

Star_bin::Star_bin	(	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 254 of file star_bin.C.

References Star::beta, beta_comp, bsn, Tensor::change_triad(), Vector::change_triad(), conf_flat, d_psi, dcon_logn, dcon_phi, dcov_logn, dcov_phi, Map::flat_met_cart(), Star::gam_euler, Star::gamma, Map::get_bvect_cart(), Map::get_mg(), hij, hij_comp, irrotational, kcar_auto, kcar_comp, lnq_comp, loggam, logn_comp, Star::mp, pot_centri, psi0, psi4, set_der_0x0(), Tensor::set_etat_zero(), Star::stress_euler, tkij_auto, tkij_comp, Star::u_euler, and wit_w.

Star_bin::~Star_bin ( ) [virtual]

Destructor.

Definition at line 355 of file star_bin.C.

References del_deriv().

Member Function Documentation

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

Deletes all the derived quantities.

Reimplemented from Star.

Definition at line 365 of file star_bin.C.

References p_xa_barycenter, and set_der_0x0().

void Star_bin::del_hydro_euler ( ) [protected, virtual]

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

Reimplemented from Star.

Definition at line 385 of file star_bin.C.

References del_deriv().

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_bin::equilibrium	(	double	ent_c,
		int	mermax,
		int	mermax_potvit,
		int	mermax_poisson,
		double	relax_poisson,
		double	relax_potvit,
		double	thres_adapt,
		Tbl &	diff,
		double	om
	)

Computes an equilibrium configuration.

Parameters:

	ent_c	[input] Central enthalpy
	mermax	[input] Maximum number of steps
	mermax_poisson	[input] Maximum number of steps in poisson scalar
	relax_poisson	[input] Relaxation factor in poisson scalar
	mermax_potvit	[input] Maximum number of steps in Map_radial::poisson_compact
	relax_potvit	[input] Relaxation factor in Map_radial::poisson_compact
	thres_adapt	[input] Threshold on dH/dr for the adaptation of the mapping
	diff	[output] 1-D `Tbl` for the storage of some error indicators

Definition at line 139 of file star_bin_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_hard(), Cmp::annule_hard(), Star::beta, beta_auto, Metric_flat::con(), Metric::con(), conf_flat, contract(), Metric::cov(), dcon_logn, dcon_phi, dcov_logn, dcov_phi, Scalar::dec_dzpuis(), Tensor::dec_dzpuis(), Scalar::derive_con(), Tensor::derive_con(), Tensor_sym::derive_con(), Tensor_sym::derive_cov(), Tensor::derive_cov(), Scalar::derive_cov(), Sym_tensor::derive_lie(), diffrel(), Sym_tensor::divergence(), Vector::divergence(), Scalar::dsdr(), Star::ener_euler, Star::ent, Star::equation_of_state(), exp(), flat, Map::get_bvect_cart(), Connection::get_delta(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map::get_ori_x(), Map::get_rot_phi(), gtilde, hij, hij_auto, Map_et::homothetie(), hydro_euler(), Tenseur::inc_dzpuis(), Tensor::inc_dzpuis(), irrotational, kcar_auto, kcar_comp, Scalar::laplacian(), lnq_auto, loggam, Star::logn, logn_auto, logn_comp, max(), Star::mp, Star::nn, norme(), Star::nzet, Scalar::poisson(), pot_centri, pow(), Star::press, psi4, Map::r, Star::ray_eq(), Star::ray_eq_pi(), Star::ray_pole(), Map::reevaluate_symy(), Map::resize(), Star::s_euler, Coord::set(), Tensor::set(), Itbl::set(), Vector::set(), Tenseur::set(), Tbl::set(), Scalar::set_domain(), Tenseur::set_etat_qcq(), Tbl::set_etat_qcq(), Cmp::set_etat_qcq(), Scalar::set_outer_boundary(), Scalar::set_spectral_va(), Tenseur::set_std_base(), sqrt(), ssjm1_h11, ssjm1_h21, ssjm1_h22, ssjm1_h31, ssjm1_h32, ssjm1_h33, ssjm1_khi, ssjm1_lnq, ssjm1_logn, Scalar::std_spectral_base(), Star::stress_euler, tkij_auto, tkij_comp, Star::u_euler, Scalar::val_grid_point(), Scalar::val_point(), Map::val_r(), velocity_potential(), Map::xa, Map::ya, and Map::za.

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_bin::extrinsic_curvature ( double omega )

Computes tkij_auto and akcar_auto from beta_auto, nn and Q.

Parameters:

omega

angular velocity with respect to an asymptotically inertial observer

Definition at line 71 of file star_bin_extr_curv.C.

References Scalar::annule_hard(), beta_auto, Metric::con(), contract(), del_deriv(), Tensor::derive_con(), Sym_tensor::derive_lie(), Vector::divergence(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), Map::get_rot_phi(), gtilde, hij_auto, kcar_auto, Star::mp, Star::nn, Tensor::set(), Coord::set(), Mg3d::std_base_vect_cart(), tkij_auto, Tensor::up_down(), Map::xa, and Map::ya.

void Star_bin::fait_d_psi ( )

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

Definition at line 641 of file star_bin.C.

References Tensor::annule(), Scalar::annule_hard(), bsn, Vector::change_triad(), d_psi, Scalar::derive_cov(), Star::ent, exp(), flat, 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(), Vector::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_bin::get_beta_auto ( ) const [inline]

Returns the part of the shift vector $\beta^i$ generated principally by the star.

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

Definition at line 813 of file star.h.

References beta_auto.

const Vector& Star_bin::get_beta_comp ( ) const [inline]

Returns the part of the shift vector $\beta^i$ generated principally by the star.

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

Definition at line 819 of file star.h.

References beta_comp.

const Vector& Star_bin::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 794 of file star.h.

References bsn.

const Vector& Star_bin::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 777 of file star.h.

References d_psi.

const Vector& Star_bin::get_dcon_logn ( ) const [inline]

Returns the contravariant derivative of $logn$ .

Definition at line 837 of file star.h.

References dcon_logn.

const Vector& Star_bin::get_dcon_phi ( ) const [inline]

Returns the contravariant derivative of $\Phi$ (logarithm of the conformal factor).

Definition at line 847 of file star.h.

References dcon_phi.

const Vector& Star_bin::get_dcov_logn ( ) const [inline]

Returns the covariant derivative of $logn$ .

Definition at line 833 of file star.h.

References dcov_logn.

const Vector& Star_bin::get_dcov_phi ( ) const [inline]

Returns the covariant derivative of $\Phi$ (logarithm of the conformal factor).

Definition at line 842 of file star.h.

References dcov_phi.

const Scalar Star_bin::get_decouple ( ) const [inline]

Returns the function used to construct beta_auto from beta.

Definition at line 904 of file star.h.

References decouple.

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 Metric& Star_bin::get_flat ( ) const [inline]

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

Definition at line 855 of file star.h.

References flat.

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 Metric& Star_bin::get_gtilde ( ) const [inline]

Return the conformal 3-metric $\tilde \gamma$ .

Definition at line 858 of file star.h.

References gtilde.

const Sym_tensor& Star_bin::get_hij ( ) const [inline]

Return the total deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric.

Definition at line 863 of file star.h.

References hij.

const Sym_tensor& Star_bin::get_hij_auto ( ) const [inline]

Return the deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric principally generated by the star.

Definition at line 869 of file star.h.

References hij_auto.

const Sym_tensor& Star_bin::get_hij_comp ( ) const [inline]

Return the deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the companion star.

Definition at line 875 of file star.h.

References hij_comp.

const Scalar& Star_bin::get_kcar_auto ( ) const [inline]

Returns the part of $\tilde K^{ij} \tilde K_{ij}$ generated by beta_auto.

Definition at line 893 of file star.h.

References kcar_auto.

const Scalar& Star_bin::get_kcar_comp ( ) const [inline]

Returns the part of $\tilde K^{ij} \tilde K_{ij}$ generated by beta_comp.

Definition at line 898 of file star.h.

References kcar_comp.

const Scalar& Star_bin::get_lnq_auto ( ) const [inline]

Returns the part of the vector field $Q$ generated principally by the star.

Definition at line 824 of file star.h.

References lnq_auto.

const Scalar& Star_bin::get_lnq_comp ( ) const [inline]

Returns the part of the vector field $Q$ generated principally by the companion star.

Definition at line 829 of file star.h.

References lnq_comp.

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

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

Definition at line 788 of file star.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 Scalar& Star_bin::get_logn_auto ( ) const [inline]

Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the star.

Definition at line 802 of file star.h.

References logn_auto.

const Scalar& Star_bin::get_logn_comp ( ) const [inline]

Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the companion star.

Definition at line 807 of file star.h.

References logn_comp.

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_bin::get_pot_centri ( ) const [inline]

Returns the centrifugal potential.

Definition at line 797 of file star.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_bin::get_psi0 ( ) const [inline]

Returns the non-translational part of the velocity potential.

Definition at line 772 of file star.h.

References psi0.

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

Return the conformal factor $\psi^4$ .

Definition at line 850 of file star.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 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_bin::get_tkij_auto ( ) const [inline]

Returns the part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by beta_auto.

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

Definition at line 882 of file star.h.

References tkij_auto.

const Sym_tensor& Star_bin::get_tkij_comp ( ) const [inline]

Returns the part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by beta_comp.

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

Definition at line 888 of file star.h.

References tkij_comp.

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_bin::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 783 of file star.h.

References wit_w.

void Star_bin::helical ( double omega ) const

Test of the helical symmetry.

void Star_bin::hydro_euler ( ) [virtual]

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 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.

Reimplemented from Star.

Definition at line 62 of file star_bin_hydro.C.

References Tensor::annule_domain(), bsn, Metric::con(), contract(), Metric::cov(), d_psi, del_deriv(), Star::ener, Star::ener_euler, Star::ent, exp(), Star::gam_euler, Star::gamma, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), irrotational, log(), loggam, Star::mp, norme(), Star::press, Star::s_euler, Tensor::set(), Scalar::set_dzpuis(), Tensor::set_etat_zero(), sqrt(), Vector::std_spectral_base(), Scalar::std_spectral_base(), Star::stress_euler, Star::u_euler, and wit_w.

bool Star_bin::is_irrotational ( ) const [inline]

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

Definition at line 769 of file star.h.

References irrotational.

void Star_bin::kinematics	(	double	omega,
		double	x_axe
	)

Computes the quantities bsn and pot_centri.

The calculation is performed starting from the quantities nn, beta, Q, which are supposed to be up to date.

Parameters:

	omega	angular velocity with respect to an asymptotically inertial observer
	x_axe	absolute X coordinate of the rotation axis

Definition at line 71 of file star_bin_kinema.C.

References Scalar::annule(), Tensor::annule(), Star::beta, bsn, Vector::change_triad(), contract(), Metric::cov(), del_deriv(), Star::gamma, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), Map::get_rot_phi(), log(), Star::mp, Star::nn, pot_centri, Vector::set(), sqrt(), Scalar::std_spectral_base(), Vector::std_spectral_base(), Map::xa, and Map::ya.

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_bin::mass_b ( ) const [virtual]

Baryon mass.

Implements Star.

Definition at line 63 of file star_bin_global.C.

References Metric::determinant(), Star::gam_euler, Star::gamma, Scalar::integrale(), Star::nbar, Star::p_mass_b, sqrt(), and Scalar::std_spectral_base().

double Star_bin::mass_g ( ) const [virtual]

Gravitational mass.

Implements Star.

Definition at line 89 of file star_bin_global.C.

References Metric::determinant(), Star::ener_euler, Star::gamma, Scalar::integrale(), Star::nn, Star::p_mass_g, Star::s_euler, sqrt(), and Scalar::std_spectral_base().

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

Assignment to another Star_bin.

Reimplemented from Star.

Definition at line 400 of file star_bin.C.

References beta_auto, beta_comp, bsn, conf_flat, d_psi, dcon_logn, dcon_phi, dcov_logn, dcov_phi, decouple, del_deriv(), flat, gtilde, hij, hij_auto, hij_comp, irrotational, kcar_auto, kcar_comp, lnq_auto, lnq_comp, loggam, logn_auto, logn_comp, pot_centri, psi0, psi4, ssjm1_h11, ssjm1_h21, ssjm1_h22, ssjm1_h31, ssjm1_h32, ssjm1_h33, ssjm1_khi, ssjm1_lnq, ssjm1_logn, tkij_auto, tkij_comp, and wit_w.

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

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

Reimplemented from Star.

Definition at line 518 of file star_bin.C.

References Star::beta, beta_auto, bsn, d_psi, Star::gam_euler, Map::get_ori_x(), irrotational, kcar_auto, kcar_comp, loggam, logn_auto, logn_comp, max(), min(), Star::mp, Star::ray_eq(), Star::ray_eq_pi(), tkij_auto, tkij_comp, Star::u_euler, Scalar::val_grid_point(), Map::val_r(), wit_w, and xa_barycenter().

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_bin::relaxation	(	const Star_bin &	star_prev,
		double	relax_ent,
		double	relax_met,
		int	mer,
		int	fmer_met
	)

Performs a relaxation on ent, logn_auto, lnq_auto, beta_auto and hij_auto.

Parameters:

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

Definition at line 697 of file star_bin.C.

References beta_auto, del_deriv(), Star::ent, Star::equation_of_state(), hij_auto, lnq_auto, and logn_auto.

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

Save in a file.

Reimplemented from Star.

Definition at line 485 of file star_bin.C.

References beta_auto, conf_flat, Star::gam_euler, hij_auto, irrotational, lnq_auto, logn_auto, psi0, Tensor_sym::sauve(), Tensor::sauve(), Scalar::sauve(), ssjm1_h11, ssjm1_h21, ssjm1_h22, ssjm1_h31, ssjm1_h32, ssjm1_h33, ssjm1_khi, ssjm1_lnq, and ssjm1_logn.

Vector & Star_bin::set_beta ( )

Read/write of $beta$ .

Definition at line 471 of file star_bin.C.

References Star::beta, and del_deriv().

Vector & Star_bin::set_beta_auto ( )

Read/write of $beta_auto$ .

Definition at line 464 of file star_bin.C.

References beta_auto, and del_deriv().

void Star_bin::set_conf_flat ( bool confflat ) [inline]

Write if conformally flat.

Definition at line 761 of file star.h.

References conf_flat.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Star.

Definition at line 377 of file star_bin.C.

References p_xa_barycenter.

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().

void Star_bin::set_lnq_auto ( const Scalar & lnq_auto_new ) [inline]

Assignment of a new lnq_auto.

Definition at line 751 of file star.h.

References lnq_auto.

void Star_bin::set_logn_auto ( const Scalar & logn_auto_new ) [inline]

Assignment of a new logn_auto.

Definition at line 747 of file star.h.

References logn_auto.

Scalar & Star_bin::set_logn_comp ( )

Read/write of the logarithm of the lapse generated principally by the companion.

Definition at line 457 of file star_bin.C.

References del_deriv(), and logn_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_bin::set_pot_centri ( )

Read/write the centrifugal potential.

Definition at line 450 of file star_bin.C.

References del_deriv(), and pot_centri.

void Star_bin::test_K_Hi ( ) const

Test if the gauge conditions we impose are well satisfied.

Definition at line 723 of file star_bin.C.

References Metric::con(), Tensor_sym::derive_cov(), Sym_tensor::divergence(), flat, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), gtilde, Star::mp, and norme().

void Star_bin::update_metric	(	const Star_bin &	comp,
		const Star_bin &	star_prev,
		double	relax,
		double	omega
	)

Same as update_metric(const Star_bin& ) but with relaxation.

Parameters:

	comp	companion star.
	star_prev	previous value of the star.
	relax	relaxation parameter.
	omega	angular velocity with respect to an asymptotically inertial observer

Definition at line 272 of file star_bin_upmetr.C.

References Star::beta, beta_auto, beta_comp, Tensor::change_triad(), Vector::change_triad(), Metric_flat::con(), conf_flat, del_deriv(), Metric::determinant(), exp(), extrinsic_curvature(), flat, Star::gamma, Map::get_bvect_cart(), Map::get_mg(), Star::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::get_triad(), gtilde, hij, hij_auto, hij_comp, Scalar::import(), lnq_auto, lnq_comp, Star::logn, logn_auto, logn_comp, Star::mp, Star::nn, psi4, Tensor::set(), Vector::set(), Tensor::set_etat_qcq(), Scalar::set_etat_qcq(), Tensor::set_etat_zero(), Scalar::set_etat_zero(), Tensor::set_triad(), Tensor::std_spectral_base(), Vector::std_spectral_base(), and Scalar::std_spectral_base().

void Star_bin::update_metric	(	const Star_bin &	comp,
		double	omega
	)

Computes metric coefficients from known potentials, when the companion is another star.

The calculation is performed starting from the quantities logn_auto, lnq_auto, beta_auto, hij_auto, comp.logn_auto, comp.lnq_auto, comp.beta_auto, comp.hij_auto which are supposed to be up to date. From these, the following fields are updated: logn_comp, lnq_comp, beta_comp, hij_comp, nn, psi4, beta,

Parameters:

	comp	companion star.
	omega	angular velocity with respect to an asymptotically inertial observer

Definition at line 89 of file star_bin_upmetr.C.

References Star::beta, beta_auto, beta_comp, Tensor::change_triad(), Vector::change_triad(), Metric_flat::con(), conf_flat, del_deriv(), Metric::determinant(), exp(), extrinsic_curvature(), flat, Star::gamma, Map::get_bvect_cart(), Map::get_mg(), Star::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tensor::get_triad(), gtilde, hij, hij_auto, hij_comp, Scalar::import(), lnq_auto, lnq_comp, Star::logn, logn_auto, logn_comp, Star::mp, Star::nn, psi4, Tensor::set(), Vector::set(), Tensor::set_etat_qcq(), Scalar::set_etat_qcq(), Tensor::set_etat_zero(), Scalar::set_etat_zero(), Tensor::set_triad(), Tensor::std_spectral_base(), Vector::std_spectral_base(), and Scalar::std_spectral_base().

void Star_bin::update_metric_der_comp	(	const Star_bin &	comp,
		double	omega
	)

Computes the derivative of metric functions related to the companion star.

Parameters:

omega

angular velocity with respect to an asymptotically inertial observer

Definition at line 97 of file star_bin_upmetr_der.C.

References Scalar::annule_hard(), beta_comp, Vector::change_triad(), Metric::con(), contract(), dcon_logn, dcon_phi, dcov_logn, dcov_phi, Tensor::dec_dzpuis(), del_deriv(), Tensor::derive_con(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Sym_tensor::derive_lie(), Vector::divergence(), flat, Map::get_bvect_cart(), get_flat(), Map::get_mg(), Tensor::get_mp(), Mg3d::get_nzone(), Map::get_rot_phi(), Tensor::get_triad(), gtilde, hij_comp, Scalar::import(), Tensor::inc_dzpuis(), kcar_comp, lnq_auto, logn_auto, Star::mp, Star::nn, Tensor::set(), Coord::set(), Vector::set(), Valeur::set_base(), Scalar::set_spectral_va(), Mg3d::std_base_vect_cart(), tkij_auto, tkij_comp, Tensor::up_down(), Map::xa, and Map::ya.

double Star_bin::velocity_potential	(	int	mermax,
		double	precis,
		double	relax
	)

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

Parameters:

	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 72 of file star_bin_vel_pot.C.

References Param::add_double(), Param::add_int(), Param::add_int_mod(), Tensor::annule(), Scalar::annule(), bsn, Vector::change_triad(), contract(), d_psi, Eos::der_nbar_ent(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), diffrel(), Tensor::down(), 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(), hij, Tensor::inc_dzpuis(), Scalar::laplacian(), Star::mp, norme(), Star::nzet, Map::poisson_compact(), psi0, psi4, Vector::set(), Cmp::set(), Scalar::set_domain(), Scalar::set_spectral_va(), Tensor::set_triad(), Scalar::std_spectral_base(), Cmp::va, Valeur::ylm(), and Valeur::ylm_i().

double Star_bin::xa_barycenter ( ) const [virtual]

Absolute coordinate X of the barycenter of the baryon density,.

Definition at line 114 of file star_bin_global.C.

References Tensor::annule_domain(), Metric::determinant(), Star::gam_euler, Star::gamma, Map::get_mg(), Mg3d::get_nzone(), Scalar::integrale(), mass_b(), Star::mp, Star::nbar, p_xa_barycenter, sqrt(), Scalar::std_spectral_base(), and Map::xa.

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]`

Display.

Member Data Documentation

Vector Star::beta [protected, inherited]

Shift vector.

Definition at line 224 of file star.h.

Vector Star_bin::beta_auto [protected]

Part of the shift vector generated principally by the star (Spherical components with respect to the mapping of the star).

Definition at line 566 of file star.h.

Vector Star_bin::beta_comp [protected]

Part of the shift vector generated principally by the star (Spherical components with respect to the mapping of the star).

Definition at line 571 of file star.h.

Vector Star_bin::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 514 of file star.h.

bool Star_bin::conf_flat [protected]

true if the 3-metric is conformally flat, false for a more general metric.

Definition at line 677 of file star.h.

Vector Star_bin::d_psi [protected]

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

Definition at line 497 of file star.h.

Vector Star_bin::dcon_logn [protected]

Contravariant derivative of the total logarithm of the lapse.

Definition at line 534 of file star.h.

Vector Star_bin::dcon_phi [protected]

Contravariant derivative of the logarithm of the conformal factor.

Definition at line 553 of file star.h.

Vector Star_bin::dcov_logn [protected]

Covariant derivative of the total logarithm of the lapse.

Definition at line 531 of file star.h.

Vector Star_bin::dcov_phi [protected]

Covariant derivative of the logarithm of the conformal factor.

Definition at line 551 of file star.h.

Scalar Star_bin::decouple [protected]

Function used to construct the part $lnq_auto$ generated by the star from the total $lnq$ .

Mainly this Scalar is 1 around the star and 0 around the companion and the sum of decouple for the star and his companion is 1 everywhere.

Definition at line 672 of file star.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_bin::flat [protected]

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

Definition at line 558 of file star.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.

Metric Star_bin::gtilde [protected]

Conformal metric $\tilde \gamma_{ij}$ .

Definition at line 561 of file star.h.

Sym_tensor Star_bin::hij [protected]

Total deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric.

Definition at line 577 of file star.h.

Sym_tensor Star_bin::hij_auto [protected]

Deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the star.

Definition at line 584 of file star.h.

Sym_tensor Star_bin::hij_comp [protected]

Deviation of the inverse conformal metric $\tilde \gamma^{ij}$ from the inverse flat metric generated principally by the companion star.

Definition at line 590 of file star.h.

bool Star_bin::irrotational [protected]

true for an irrotational star, false for a corotating one

Definition at line 487 of file star.h.

Scalar Star_bin::kcar_auto [protected]

Part of the scalar $K_{ij} K^{ij}$ generated by beta_auto, i.e.

$K_{ij}^{\rm auto} K^{ij}_{\rm auto}$

Definition at line 608 of file star.h.

Scalar Star_bin::kcar_comp [protected]

Part of the scalar $K_{ij} K^{ij}$ generated by beta_auto and beta_comp, i.e.

$K_{ij}^{\rm auto} K^{ij}_{\rm comp}$

Definition at line 614 of file star.h.

Scalar Star_bin::lnq_auto [protected]

Scalar field $Q = \psi^2 N$ generated principally by the star.

Definition at line 539 of file star.h.

Scalar Star_bin::lnq_comp [protected]

Scalar field $Q = \psi^2 N$ generated principally by the companion star.

Definition at line 544 of file star.h.

Scalar Star_bin::loggam [protected]

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

Definition at line 508 of file star.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.

Scalar Star_bin::logn_auto [protected]

Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the star.

Definition at line 523 of file star.h.

Scalar Star_bin::logn_comp [protected]

Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principally by the companion star.

Definition at line 528 of file star.h.

Map& Star::mp [protected, inherited]

Mapping associated with the star.

Definition at line 176 of file star.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::p_mass_g [mutable, protected, inherited]

Gravitational mass.

Definition at line 265 of file star.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.

double* Star_bin::p_xa_barycenter [mutable, protected]

Absolute coordinate X of the barycenter of the baryon density.

Definition at line 683 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_bin::pot_centri [protected]

Centrifugal potential.

Definition at line 517 of file star.h.

Scalar Star::press [protected, inherited]

Fluid pressure.

Definition at line 190 of file star.h.

Scalar Star_bin::psi0 [protected]

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

Definition at line 492 of file star.h.

Scalar Star_bin::psi4 [protected]

Conformal factor $\psi^4$ .

Definition at line 548 of file star.h.

Scalar Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 197 of file star.h.

Scalar Star_bin::ssjm1_h11 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h00_auto.

Definition at line 637 of file star.h.

Scalar Star_bin::ssjm1_h21 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h10_auto.

Definition at line 642 of file star.h.

Scalar Star_bin::ssjm1_h22 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h11_auto.

Definition at line 652 of file star.h.

Scalar Star_bin::ssjm1_h31 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h20_auto.

Definition at line 647 of file star.h.

Scalar Star_bin::ssjm1_h32 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h21_auto.

Definition at line 657 of file star.h.

Scalar Star_bin::ssjm1_h33 [protected]

Effective source at the previous step for the resolution of the Poisson equation for h22_auto.

Definition at line 662 of file star.h.

Scalar Star_bin::ssjm1_khi [protected]

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

(second scalar equation for the resolution of the vectorial poisson equation for the shift)

Definition at line 630 of file star.h.

Scalar Star_bin::ssjm1_lnq [protected]

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

Definition at line 624 of file star.h.

Scalar Star_bin::ssjm1_logn [protected]

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

Definition at line 619 of file star.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_bin::tkij_auto [protected]

Part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by beta_auto.

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

Definition at line 596 of file star.h.

Sym_tensor Star_bin::tkij_comp [protected]

Part of the extrinsic curvature tensor $\tilde K^{ij}$ generated by beta_comp.

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

Definition at line 602 of file star.h.

Vector Star::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 203 of file star.h.

Vector Star_bin::wit_w [protected]

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 503 of file star.h.

The documentation for this class was generated from the following files:

Star_bin Class Reference [Stars and black holes]

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

Star_bin Class Reference
[Stars and black holes]