Etoile_rot Class Reference
[Stars and black holes]

Class for isolated rotating stars *** DEPRECATED : use class Star_rot instead ***. More...

#include <etoile.h>

Inheritance diagram for Etoile_rot:

Public Member Functions
	Etoile_rot (Map &mp_i, int nzet_i, bool relat, const Eos &eos_i)
	Standard constructor.
	Etoile_rot (const Etoile_rot &)
	Copy constructor.
	Etoile_rot (Map &mp_i, const Eos &eos_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Etoile_rot ()
	Destructor.
void	operator= (const Etoile_rot &)
	Assignment to another `Etoile_rot`.
virtual double	get_omega_c () const
	Returns the central value of the rotation angular velocity ([f_unit] ).
const Tenseur &	get_bbb () const
	Returns the metric factor B.
const Tenseur &	get_b_car () const
	Returns the square of the metric factor B.
const Tenseur &	get_nphi () const
	Returns the metric coefficient $N^\varphi$ .
const Tenseur &	get_tnphi () const
	Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
const Tenseur &	get_uuu () const
	Returns the norm of `u_euler`.
const Tenseur &	get_logn () const
	Returns the metric potential $\nu = \ln N$ = `logn_auto`.
const Tenseur &	get_nuf () const
	Returns the part of the Metric potential $\nu = \ln N$ = `logn` generated by the matter terms.
const Tenseur &	get_nuq () const
	Returns the Part of the Metric potential $\nu = \ln N$ = `logn` generated by the quadratic terms.
const Tenseur &	get_dzeta () const
	Returns the Metric potential $\zeta = \ln(AN)$ = `beta_auto`.
const Tenseur &	get_tggg () const
	Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$ .
const Tenseur &	get_w_shift () const
	Returns the vector used in the decomposition of `shift` , following Shibata's prescription [Prog.
const Tenseur &	get_khi_shift () const
	Returns the scalar $\chi$ used in the decomposition of `shift` following Shibata's prescription [Prog.
const Tenseur_sym &	get_tkij () const
	Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$ .
const Tenseur &	get_ak_car () const
	Returns the scalar $A^2 K_{ij} K^{ij}$ .
virtual void	sauve (FILE *) const
	Save in a file.
virtual void	display_poly (ostream &) const
	Display in polytropic units.
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 $(\theta', \phi')$ .
virtual double	mass_b () const
	Baryon mass.
virtual double	mass_g () const
	Gravitational mass.
virtual double	angu_mom () const
	Angular momentum.
virtual double	tsw () const
	Ratio T/W.
virtual double	grv2 () const
	Error on the virial identity GRV2.
virtual double	grv3 (ostream *ost=0x0) const
	Error on the virial identity GRV3.
virtual double	r_circ () const
	Circumferential radius.
virtual double	aplat () const
	Flatening r_pole/r_eq.
virtual double	z_eqf () const
	Forward redshift factor at equator.
virtual double	z_eqb () const
	Backward redshift factor at equator.
virtual double	z_pole () const
	Redshift factor at North pole.
virtual double	mom_quad () const
	Quadrupole moment.
virtual double	r_isco (ostream *ost=0x0) const
	Circumferential radius of the innermost stable circular orbit (ISCO).
virtual double	f_isco () const
	Orbital frequency at the innermost stable circular orbit (ISCO).
virtual double	espec_isco () const
	Energy of a particle on the ISCO.
virtual double	lspec_isco () const
	Angular momentum of a particle on the ISCO.
virtual double	f_eccentric (double ecc, double periast, ostream *ost=0x0) const
	Computation of frequency of eccentric orbits.
virtual double	f_eq () const
	Orbital frequency at the equator.
virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
void	update_metric ()
	Computes metric coefficients from known potentials.
void	fait_shift ()
	Computes `shift` from `w_shift` and `khi_shift` according to Shibata's prescription [Prog.
void	fait_nphi ()
	Computes `tnphi` and `nphi` from the Cartesian components of the shift, stored in `shift` .
void	extrinsic_curvature ()
	Computes `tkij` and `ak_car` from `shift` , `nnn` and `b_car` .
virtual void	equilibrium (double ent_c, double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, double mbar_wanted, double aexp_mass, Tbl &diff, Param *=0x0)
	Computes an equilibrium configuration.
Map &	set_mp ()
	Read/write of the mapping.
void	set_enthalpy (const Cmp &)
	Assignment of the enthalpy field.
virtual 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 *ent_limit=0x0)
	Computes a spherical static configuration.
void	equil_spher_regular (double ent_c, double precis=1.e-14)
	Computes a spherical static configuration.
virtual void	equil_spher_falloff (double ent_c, double precis=1.e-14)
	Computes a spherical static configuration with the outer boundary condition at a finite radius.
const Map &	get_mp () const
	Returns the mapping.
int	get_nzet () const
	Returns the number of domains occupied by the star.
bool	is_relativistic () const
	Returns `true` for a relativistic star, `false` for a Newtonian one.
const Eos &	get_eos () const
	Returns the equation of state.
const Tenseur &	get_ent () const
	Returns the enthalpy field.
const Tenseur &	get_nbar () const
	Returns the proper baryon density.
const Tenseur &	get_ener () const
	Returns the proper total energy density.
const Tenseur &	get_press () const
	Returns the fluid pressure.
const Tenseur &	get_ener_euler () const
	Returns the total energy density with respect to the Eulerian observer.
const Tenseur &	get_s_euler () const
	Returns the trace of the stress tensor in the Eulerian frame.
const Tenseur &	get_gam_euler () const
	Returns the Lorentz factor between the fluid and Eulerian observers.
const Tenseur &	get_u_euler () const
	Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tenseur &	get_logn_auto () const
	Returns the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur &	get_logn_auto_regu () const
	Returns the regular part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur &	get_logn_auto_div () const
	Returns the divergent part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur &	get_d_logn_auto_div () const
	Returns the gradient of `logn_auto_div`.
const Tenseur &	get_beta_auto () const
	Returns the logarithm of the part of the product AN generated principaly by the star.
const Tenseur &	get_nnn () const
	Returns the total lapse function N.
const Tenseur &	get_shift () const
	Returns the total shift vector .
const Tenseur &	get_a_car () const
	Returns the total conformal factor .
double	ray_eq () const
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ [r_unit].
double	ray_eq (int kk) const
	Coordinate radius at $\phi=2k\pi/np$ , $\theta=\pi/2$ [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].
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 $(\theta', \phi')$ .
Static Public Member Functions
static double	lambda_grv2 (const Cmp &sou_m, const Cmp &sou_q)
	Computes the coefficient $\lambda$ which ensures that the GRV2 virial identity is satisfied.
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 <<).
virtual void	partial_display (ostream &) const
	Printing of some informations, excluding all global quantities.
Protected Attributes
double	omega
	Rotation angular velocity ([f_unit] ).
Tenseur	bbb
	Metric factor B.
Tenseur	b_car
	Square of the metric factor B.
Tenseur	nphi
	Metric coefficient $N^\varphi$ .
Tenseur	tnphi
	Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
Tenseur	uuu
	Norm of `u_euler`.
Tenseur &	logn
	Metric potential $\nu = \ln N$ = `logn_auto`.
Tenseur	nuf
	Part of the Metric potential $\nu = \ln N$ = `logn` generated by the matter terms.
Tenseur	nuq
	Part of the Metric potential $\nu = \ln N$ = `logn` generated by the quadratic terms.
Tenseur &	dzeta
	Metric potential $\zeta = \ln(AN)$ = `beta_auto`.
Tenseur	tggg
	Metric potential $\tilde G = (NB-1) r\sin\theta$ .
Tenseur	w_shift
	Vector used in the decomposition of `shift` , following Shibata's prescription [Prog.
Tenseur	khi_shift
	Scalar $\chi$ used in the decomposition of `shift` , following Shibata's prescription [Prog.
Tenseur_sym	tkij
	Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$ .
Tenseur	ak_car
	Scalar $A^2 K_{ij} K^{ij}$ .
Cmp	ssjm1_nuf
	Effective source at the previous step for the resolution of the Poisson equation for `nuf` by means of `Map_et::poisson` .
Cmp	ssjm1_nuq
	Effective source at the previous step for the resolution of the Poisson equation for `nuq` by means of `Map_et::poisson` .
Cmp	ssjm1_dzeta
	Effective source at the previous step for the resolution of the Poisson equation for `dzeta` .
Cmp	ssjm1_tggg
	Effective source at the previous step for the resolution of the Poisson equation for `tggg` .
Cmp	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` .
Tenseur	ssjm1_wshift
	Effective source at the previous step for the resolution of the vector Poisson equation for .
double *	p_angu_mom
	Angular momentum.
double *	p_tsw
	Ratio T/W.
double *	p_grv2
	Error on the virial identity GRV2.
double *	p_grv3
	Error on the virial identity GRV3.
double *	p_r_circ
	Circumferential radius.
double *	p_aplat
	Flatening r_pole/r_eq.
double *	p_z_eqf
	Forward redshift factor at equator.
double *	p_z_eqb
	Backward redshift factor at equator.
double *	p_z_pole
	Redshift factor at North pole.
double *	p_mom_quad
	Quadrupole moment.
double *	p_r_isco
	Circumferential radius of the ISCO.
double *	p_f_isco
	Orbital frequency of the ISCO.
double *	p_espec_isco
	Specific energy of a particle on the ISCO.
double *	p_lspec_isco
	Specific angular momentum of a particle on the ISCO.
double *	p_f_eq
	Orbital frequency at the equator.
Map &	mp
	Mapping associated with the star.
int	nzet
	Number of domains of `*mp` occupied by the star.
bool	relativistic
	Indicator of relativity: `true` for a relativistic star, `false` for a Newtonian one.
double	unsurc2
	: `unsurc2=1` for a relativistic star, 0 for a Newtonian one.
int	k_div
	Index of regularity of the gravitational potential `logn_auto` .
const Eos &	eos
	Equation of state of the stellar matter.
Tenseur	ent
	Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).
Tenseur	nbar
	Baryon density in the fluid frame.
Tenseur	ener
	Total energy density in the fluid frame.
Tenseur	press
	Fluid pressure.
Tenseur	ener_euler
	Total energy density in the Eulerian frame.
Tenseur	s_euler
	Trace of the stress tensor in the Eulerian frame.
Tenseur	gam_euler
	Lorentz factor between the fluid and Eulerian observers.
Tenseur	u_euler
	Fluid 3-velocity with respect to the Eulerian observer.
Tenseur	logn_auto
	Total of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur	logn_auto_regu
	Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur	logn_auto_div
	Divergent part (if `k_div!=0` ) of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur	d_logn_auto_div
	Gradient of `logn_auto_div` (if `k_div!=0` ).
Tenseur	beta_auto
	Logarithm of the part of the product AN generated principaly by by the star.
Tenseur	nnn
	Total lapse function.
Tenseur	shift
	Total shift vector.
Tenseur	a_car
	Total conformal factor .
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
ostream &	operator<< (ostream &, const Etoile &)
	Display.

Detailed Description

Class for isolated rotating stars *** DEPRECATED : use class Star_rot instead ***.

()

The metric is

$ds^2 = - N^2 dt^2 + A^2 (dr^2 + r^2 d\theta^2) + B^2 r^2 \sin^2\theta (d\varphi - N^\varphi dt)^2$

Definition at line 1482 of file etoile.h.

Constructor & Destructor Documentation

Etoile_rot::Etoile_rot	(	Map &	mp_i,
		int	nzet_i,
		bool	relat,
		const Eos &	eos_i
	)

Standard constructor.

Parameters:

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

Definition at line 127 of file etoile_rot.C.

References ak_car, b_car, bbb, khi_shift, nphi, nuf, nuq, omega, Tenseur::set(), set_der_0x0(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_std_base(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tkij, tnphi, uuu, and w_shift.

Etoile_rot::Etoile_rot ( const Etoile_rot & et )

Copy constructor.

Definition at line 197 of file etoile_rot.C.

References omega, and set_der_0x0().

Etoile_rot::Etoile_rot	(	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 229 of file etoile_rot.C.

References b_car, bbb, fait_nphi(), fait_shift(), fread_be(), Map::get_bvect_cart(), Map::get_mg(), khi_shift, Etoile::mp, nuf, nuq, omega, set_der_0x0(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, uuu, and w_shift.

Etoile_rot::~Etoile_rot ( ) [virtual]

Destructor.

Definition at line 315 of file etoile_rot.C.

References del_deriv().

Member Function Documentation

double Etoile_rot::angu_mom ( ) const [virtual]

Angular momentum.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 178 of file et_rot_global.C.

References Etoile::a_car, b_car, Etoile::ener_euler, Cmp::integrale(), Cmp::mult_r(), Etoile::nbar, p_angu_mom, Etoile::press, Etoile::relativistic, Cmp::std_base_scal(), uuu, and Cmp::va.

double Etoile_rot::aplat ( ) const [virtual]

Flatening r_pole/r_eq.

Definition at line 411 of file et_rot_global.C.

References p_aplat, Etoile::ray_eq(), and Etoile::ray_pole().

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

Deletes all the derived quantities.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 325 of file etoile_rot.C.

References p_angu_mom, p_aplat, p_espec_isco, p_f_eq, p_f_isco, p_grv2, p_grv3, p_lspec_isco, p_mom_quad, p_r_circ, p_r_isco, p_tsw, p_z_eqb, p_z_eqf, p_z_pole, and set_der_0x0().

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

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

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 373 of file etoile_rot.C.

References del_deriv().

void Etoile_rot::display_poly ( ostream & ost ) const [virtual]

Display in polytropic units.

Reimplemented in Et_rot_diff.

Definition at line 665 of file etoile_rot.C.

References angu_mom(), Etoile::ener, Etoile::eos, Eos_poly::get_gam(), Eos_poly::get_kap(), get_omega_c(), mass_b(), mass_g(), Etoile::nbar, pow(), r_circ(), Etoile::ray_eq(), and sqrt().

void Etoile::equation_of_state ( ) [virtual, inherited]

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

Reimplemented in Et_rot_bifluid, and Et_magnetisation.

Definition at line 562 of file etoile.C.

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

void Etoile::equil_spher_falloff	(	double	ent_c,
		double	precis = `1.e-14`
	)			`[virtual, inherited]`

Computes a spherical static configuration with the outer boundary condition at a finite radius.

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)

Definition at line 53 of file etoile_eqsph_falloff.C.

References Etoile::a_car, Tenseur::annule(), Etoile::beta_auto, diffrel(), Cmp::dsdr(), Map_af::dsdr(), Etoile::ener, Etoile::ener_euler, Etoile::ent, Etoile::equation_of_state(), exp(), Etoile::gam_euler, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map_af::homothetie(), Etoile::logn_auto, Etoile::mass_b(), Etoile::mass_g(), Etoile::mp, Etoile::nbar, Etoile::nnn, norme(), Etoile::nzet, Etoile::press, Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), Etoile::shift, sqrt(), Etoile::u_euler, Etoile::unsurc2, and Map::val_r().

void Etoile::equil_spher_regular	(	double	ent_c,
		double	precis = `1.e-14`
	)			`[inherited]`

Computes a spherical static configuration.

The sources for Poisson equations are regularized by extracting analytical diverging parts.

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)

Definition at line 110 of file et_equil_spher_regu.C.

References Etoile::a_car, Tenseur::annule(), Etoile::beta_auto, Etoile::d_logn_auto_div, Eos::der_ener_ent_p(), Eos::der_nbar_ent_p(), diffrel(), Map_af::dsdr(), Etoile::ener, Etoile::ener_euler, Etoile::ent, Etoile::eos, Etoile::equation_of_state(), exp(), Etoile::gam_euler, Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tenseur::gradient_spher(), Map_af::homothetie(), Etoile::k_div, Etoile::logn_auto, Etoile::logn_auto_div, Etoile::logn_auto_regu, Etoile::mass_b(), Etoile::mass_g(), Etoile::mp, Etoile::nbar, Etoile::nnn, norme(), Etoile::nzet, Map_af::poisson(), Map_af::poisson_regular(), Etoile::press, Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), Etoile::shift, sqrt(), Cmp::std_base_scal(), Etoile::u_euler, Etoile::unsurc2, and Map::val_r().

void Etoile_rot::equilibrium	(	double	ent_c,
		double	omega0,
		double	fact_omega,
		int	nzadapt,
		const Tbl &	ent_limit,
		const Itbl &	icontrol,
		const Tbl &	control,
		double	mbar_wanted,
		double	aexp_mass,
		Tbl &	diff,
		Param *	= `0x0`
	)			`[virtual]`

Computes an equilibrium configuration.

Parameters:

	ent_c	[input] Central enthalpy
	omega0	[input] Requested angular velocity (if `fact_omega=1`. )
	fact_omega	[input] 1.01 = search for the Keplerian frequency, 1. = otherwise.
	nzadapt	[input] Number of (inner) domains where the mapping adaptation to an iso-enthalpy surface should be performed
	ent_limit	[input] 1-D `Tbl` of dimension `nzet` which defines the enthalpy at the outer boundary of each domain
	icontrol	[input] Set of integer parameters (stored as a 1-D `Itbl` of size 8) to control the iteration: `icontrol(0)` = mer_max : maximum number of steps `icontrol(1)` = mer_rot : step at which the rotation is switched on `icontrol(2)` = mer_change_omega : step at which the rotation velocity is changed to reach the final one `icontrol(3)` = mer_fix_omega : step at which the final rotation velocity must have been reached `icontrol(4)` = mer_mass : the absolute value of `mer_mass` is the step from which the baryon mass is forced to converge, by varying the central enthalpy (`mer_mass>0` ) or the angular velocity (`mer_mass<0` ) `icontrol(5)` = mermax_poisson : maximum number of steps in `Map_et::poisson` `icontrol(6)` = mer_triax : step at which the 3-D perturbation is switched on `icontrol(7)` = delta_mer_kep : number of steps after `mer_fix_omega` when `omega` starts to be increased by `fact_omega` to search for the Keplerian velocity
	control	[input] Set of parameters (stored as a 1-D `Tbl` of size 7) to control the iteration: `control(0)` = precis : threshold on the enthalpy relative change for ending the computation `control(1)` = omega_ini : initial angular velocity, switched on only if `mer_rot<0` , otherwise 0 is used `control(2)` = relax : relaxation factor in the main iteration `control(3)` = relax_poisson : relaxation factor in `Map_et::poisson` `control(4)` = thres_adapt : threshold on dH/dr for freezing the adaptation of the mapping `control(5)` = ampli_triax : relative amplitude of the 3-D perturbation `control(6)` = precis_adapt : precision for `Map_et::adapt`
	mbar_wanted	[input] Requested baryon mass (effective only if `mer_mass` > `mer_max` )
	aexp_mass	[input] Exponent for the increase factor of the central enthalpy to converge to the requested baryon mass
	diff	[output] 1-D `Tbl` of size 7 for the storage of some error indicators : `diff(0)` : Relative change in the enthalpy field between two successive steps `diff(1)` : Relative error in the resolution of the Poisson equation for `nuf` `diff(2)` : Relative error in the resolution of the Poisson equation for `nuq` `diff(3)` : Relative error in the resolution of the Poisson equation for `dzeta` `diff(4)` : Relative error in the resolution of the Poisson equation for `tggg` `diff(5)` : Relative error in the resolution of the equation for `shift` (x comp.) `diff(6)` : Relative error in the resolution of the equation for `shift` (y comp.)

Reimplemented in Et_rot_diff.

Definition at line 143 of file et_rot_equilibrium.C.

References Etoile::a_car, abs(), Map::adapt(), Param::add_cmp_mod(), Param::add_double(), Param::add_double_mod(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Param::add_tenseur_mod(), ak_car, Cmp::annule(), bbb, Valeur::c_cf, Tenseur::change_triad(), Map::cmp_zero(), Valeur::coef(), cos(), diffrel(), dzeta, Etoile::ener_euler, Etoile::ent, Etoile::equation_of_state(), fait_nphi(), flat_scalar_prod(), Etoile::gam_euler, Map::get_bvect_cart(), Tenseur::get_etat(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_t(), Tenseur::gradient_spher(), grv2(), Map_et::homothetie(), hydro_euler(), khi_shift, log(), log10(), logn, mass_b(), mass_g(), Etoile::mp, Cmp::mult_rsint(), Etoile::nbar, Etoile::nnn, nphi, nuf, nuq, Etoile::nzet, omega, partial_display(), Map::phi, Map::poisson2d(), pow(), Etoile::press, Etoile::ray_eq(), Etoile::ray_pole(), Map::reevaluate(), Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Tbl::set(), Tenseur::set_etat_qcq(), Tbl::set_etat_qcq(), Tenseur::set_std_base(), Etoile::shift, Map::sint, sqrt(), ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, Cmp::std_base_scal(), tggg, tkij, Etoile::u_euler, update_metric(), uuu, Cmp::va, and w_shift.

void Etoile::equilibrium_spher	(	double	ent_c,
		double	precis = `1.e-14`,
		const Tbl *	ent_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 83 of file etoile_equil_spher.C.

References Etoile::a_car, Map_et::adapt(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Tenseur::annule(), Etoile::beta_auto, diffrel(), Cmp::dsdr(), Map_af::dsdr(), Etoile::ener, Etoile::ener_euler, Etoile::ent, Etoile::equation_of_state(), exp(), Etoile::gam_euler, Map_et::get_alpha(), Map_af::get_alpha(), Map_et::get_beta(), Map_af::get_beta(), Etoile::get_ent(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Etoile::get_press(), Map_af::homothetie(), Etoile::logn_auto, Etoile::mass_b(), Etoile::mass_g(), Etoile::mp, Etoile::nbar, Etoile::nnn, norme(), Etoile::nzet, Map_af::poisson(), Etoile::press, Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Map_af::set_alpha(), Map_af::set_beta(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), Etoile::shift, sqrt(), Etoile::u_euler, Etoile::unsurc2, and Map::val_r().

double Etoile_rot::espec_isco ( ) const [virtual]

Energy of a particle on the ISCO.

Definition at line 297 of file et_rot_isco.C.

References p_espec_isco, and r_isco().

void Etoile_rot::extrinsic_curvature ( )

Computes tkij and ak_car from shift , nnn and b_car .

Definition at line 53 of file et_rot_extr_curv.C.

References ak_car, b_car, contract(), Tenseur::get_etat(), Cmp::get_etat(), Map::get_mg(), Tenseur::gradient(), Etoile::mp, Cmp::mult_rsint(), Etoile::nnn, nphi, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Etoile::shift, tkij, and Cmp::va.

double Etoile_rot::f_eccentric	(	double	ecc,
		double	periast,
		ostream *	ost = `0x0`
	)			const `[virtual]`

Computation of frequency of eccentric orbits.

Parameters:

	ecc	eccentricity of the orbit
	periasrt	periastron of the orbit
	ost	output stream to give details of the computation; if set to 0x0 [default value], no details will be given.

Returns:: orbital frequency

Definition at line 74 of file et_rot_f_eccentric.C.

References Param::add_cmp(), Param::add_int(), Cmp::annule(), bbb, Cmp::dsdr(), Map::get_mg(), Mg3d::get_nzone(), Etoile::mp, Etoile::nnn, nphi, Etoile::nzet, p_f_isco, p_r_isco, Map::r, Etoile::ray_eq(), sqrt(), Cmp::std_base_scal(), Cmp::va, Valeur::val_point(), and Map::val_r().

double Etoile_rot::f_eq ( ) const [virtual]

Orbital frequency at the equator.

Definition at line 315 of file et_rot_isco.C.

References p_f_eq, and r_isco().

double Etoile_rot::f_isco ( ) const [virtual]

Orbital frequency at the innermost stable circular orbit (ISCO).

Definition at line 263 of file et_rot_isco.C.

References p_f_isco, and r_isco().

void Etoile_rot::fait_nphi ( )

Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .

Definition at line 756 of file etoile_rot.C.

References Map::comp_p_from_cartesian(), Tenseur::get_etat(), Etoile::mp, nphi, Tenseur::set(), Tenseur::set_etat_qcq(), Etoile::shift, and tnphi.

void Etoile_rot::fait_shift ( )

Computes shift from w_shift and khi_shift according to Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

$N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right)$

Definition at line 723 of file etoile_rot.C.

References Tenseur::dec2_dzpuis(), Tenseur::dec_dzpuis(), Tenseur::get_etat(), Tenseur::get_triad(), Tenseur::gradient(), khi_shift, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_triad(), Etoile::shift, skxk(), and w_shift.

const Tenseur& Etoile::get_a_car ( ) const [inline, inherited]

Returns the total conformal factor $A^2$ .

Definition at line 718 of file etoile.h.

References Etoile::a_car.

const Tenseur& Etoile_rot::get_ak_car ( ) const [inline]

Returns the scalar $A^2 K_{ij} K^{ij}$ .

For axisymmetric stars, this quantity is related to the derivatives of $N^\varphi$ by

$A^2 K_{ij} K^{ij} = {B^2 \over 2 N^2} \, r^2\sin^2\theta \, \left[ \left( {\partial N^\varphi \over \partial r} \right) ^2 + {1\over r^2} \left( {\partial N^\varphi \over \partial \theta} \right) ^2 \right] \ .$

In particular it is related to the quantities $k_1$ and $k_2$ introduced by Eqs.~(3.7) and (3.8) of Bonazzola et al. Astron. Astrophys. 278 , 421 (1993) by

$A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ .$

Definition at line 1782 of file etoile.h.

References ak_car.

const Tenseur& Etoile_rot::get_b_car ( ) const [inline]

Returns the square of the metric factor B.

Definition at line 1698 of file etoile.h.

References b_car.

const Tenseur& Etoile_rot::get_bbb ( ) const [inline]

Returns the metric factor B.

Definition at line 1695 of file etoile.h.

References bbb.

const Tenseur& Etoile::get_beta_auto ( ) const [inline, inherited]

Returns the logarithm of the part of the product AN generated principaly by the star.

Definition at line 709 of file etoile.h.

References Etoile::beta_auto.

const Tenseur& Etoile::get_d_logn_auto_div ( ) const [inline, inherited]

Returns the gradient of logn_auto_div.

Definition at line 704 of file etoile.h.

References Etoile::d_logn_auto_div.

const Tenseur& Etoile_rot::get_dzeta ( ) const [inline]

Returns the Metric potential $\zeta = \ln(AN)$ = beta_auto.

Definition at line 1725 of file etoile.h.

References dzeta.

const Tenseur& Etoile::get_ener ( ) const [inline, inherited]

Returns the proper total energy density.

Definition at line 664 of file etoile.h.

References Etoile::ener.

const Tenseur& Etoile::get_ener_euler ( ) const [inline, inherited]

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

Definition at line 670 of file etoile.h.

References Etoile::ener_euler.

const Tenseur& Etoile::get_ent ( ) const [inline, inherited]

Returns the enthalpy field.

Definition at line 658 of file etoile.h.

References Etoile::ent.

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

Returns the equation of state.

Reimplemented in Et_rot_bifluid.

Definition at line 655 of file etoile.h.

References Etoile::eos.

const Tenseur& Etoile::get_gam_euler ( ) const [inline, inherited]

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 676 of file etoile.h.

References Etoile::gam_euler.

const Tenseur& Etoile_rot::get_khi_shift ( ) const [inline]

Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

$N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right)$

NB: w_shift contains the components of $W^i$ with respect to the Cartesian triad associated with the mapping mp .

Definition at line 1756 of file etoile.h.

References khi_shift.

const Tenseur& Etoile_rot::get_logn ( ) const [inline]

Returns the metric potential $\nu = \ln N$ = logn_auto.

Definition at line 1712 of file etoile.h.

References logn.

const Tenseur& Etoile::get_logn_auto ( ) const [inline, inherited]

Returns the logarithm of the part of the lapse N generated principaly by the star.

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

Definition at line 686 of file etoile.h.

References Etoile::logn_auto.

const Tenseur& Etoile::get_logn_auto_div ( ) const [inline, inherited]

Returns the divergent part of the logarithm of the part of the lapse N generated principaly by the star.

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

Definition at line 700 of file etoile.h.

References Etoile::logn_auto_div.

const Tenseur& Etoile::get_logn_auto_regu ( ) const [inline, inherited]

Returns the regular part of the logarithm of the part of the lapse N generated principaly by the star.

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

Definition at line 693 of file etoile.h.

References Etoile::logn_auto_regu.

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

Returns the mapping.

Definition at line 644 of file etoile.h.

References Etoile::mp.

const Tenseur& Etoile::get_nbar ( ) const [inline, inherited]

Returns the proper baryon density.

Definition at line 661 of file etoile.h.

References Etoile::nbar.

const Tenseur& Etoile::get_nnn ( ) const [inline, inherited]

Returns the total lapse function N.

Definition at line 712 of file etoile.h.

References Etoile::nnn.

const Tenseur& Etoile_rot::get_nphi ( ) const [inline]

Returns the metric coefficient $N^\varphi$ .

Definition at line 1701 of file etoile.h.

References nphi.

const Tenseur& Etoile_rot::get_nuf ( ) const [inline]

Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.

Definition at line 1717 of file etoile.h.

References nuf.

const Tenseur& Etoile_rot::get_nuq ( ) const [inline]

Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.

Definition at line 1722 of file etoile.h.

References nuq.

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

Returns the number of domains occupied by the star.

Definition at line 647 of file etoile.h.

References Etoile::nzet.

double Etoile_rot::get_omega_c ( ) const [virtual]

Returns the central value of the rotation angular velocity ([f_unit] ).

Reimplemented in Et_rot_diff.

Definition at line 655 of file etoile_rot.C.

References omega.

const Tenseur& Etoile::get_press ( ) const [inline, inherited]

Returns the fluid pressure.

Definition at line 667 of file etoile.h.

References Etoile::press.

const Tenseur& Etoile::get_s_euler ( ) const [inline, inherited]

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

Definition at line 673 of file etoile.h.

References Etoile::s_euler.

const Tenseur& Etoile::get_shift ( ) const [inline, inherited]

Returns the total shift vector $N^i$ .

Definition at line 715 of file etoile.h.

References Etoile::shift.

const Tenseur& Etoile_rot::get_tggg ( ) const [inline]

Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$ .

Definition at line 1728 of file etoile.h.

References tggg.

const Tenseur_sym& Etoile_rot::get_tkij ( ) const [inline]

Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$ .

tkij contains the Cartesian components of ${\tilde K_{ij}}$ .

Definition at line 1763 of file etoile.h.

References tkij.

const Tenseur& Etoile_rot::get_tnphi ( ) const [inline]

Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.

Definition at line 1706 of file etoile.h.

References tnphi.

const Tenseur& Etoile::get_u_euler ( ) const [inline, inherited]

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

Definition at line 679 of file etoile.h.

References Etoile::u_euler.

const Tenseur& Etoile_rot::get_uuu ( ) const [inline]

Returns the norm of u_euler.

Definition at line 1709 of file etoile.h.

References uuu.

const Tenseur& Etoile_rot::get_w_shift ( ) const [inline]

Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

$N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right)$

NB: w_shift contains the components of $W^i$ with respect to the Cartesian triad associated with the mapping mp .

Definition at line 1742 of file etoile.h.

References w_shift.

double Etoile_rot::grv2 ( ) const [virtual]

Error on the virial identity GRV2.

This indicator is only valid for relativistic computations.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 244 of file et_rot_global.C.

References Etoile::a_car, ak_car, Etoile::ener_euler, flat_scalar_prod(), Tenseur::gradient_spher(), lambda_grv2(), logn, Etoile::mp, Etoile::nbar, p_grv2, Etoile::press, Etoile::relativistic, and uuu.

double Etoile_rot::grv3 ( ostream * ost = 0x0 ) const [virtual]

Error on the virial identity GRV3.

The error is computed as the integral defined by Eq. (43) of [Gourgoulhon and Bonazzola, Class. Quantum Grav. 11, 443 (1994)] divided by the integral of the matter terms.

Parameters:

ost

output stream to give details of the computation; if set to 0x0 [default value], no details will be given.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 275 of file et_rot_global.C.

References Etoile::a_car, ak_car, bbb, dzeta, flat_scalar_prod(), Cmp::get_dzpuis(), Cmp::get_etat(), Tenseur::gradient_spher(), log(), logn, Etoile::mp, Valeur::mult_ct(), Etoile::nbar, p_grv3, Etoile::press, Etoile::relativistic, Etoile::s_euler, Cmp::set_dzpuis(), Tenseur::set_std_base(), Valeur::ssint(), Cmp::std_base_scal(), Valeur::sx(), uuu, Cmp::va, and Map_radial::xsr.

void Etoile_rot::hydro_euler ( ) [virtual]

Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.

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

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, and Et_rot_diff.

Definition at line 79 of file et_rot_hydro.C.

References Etoile::a_car, Tenseur::annule(), b_car, Tenseur::change_triad(), del_deriv(), Etoile::ener, Etoile::ener_euler, Etoile::gam_euler, Map::get_bvect_cart(), Map::get_bvect_spher(), Tenseur::get_etat(), Map::get_mg(), Mg3d::get_nzone(), Etoile::mp, Etoile::nnn, omega, Etoile::press, Etoile::s_euler, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), Tenseur::set_triad(), Etoile::shift, sqrt(), Etoile::u_euler, Etoile::unsurc2, uuu, Map::x, and Map::y.

bool Etoile::is_relativistic ( ) const [inline, inherited]

Returns true for a relativistic star, false for a Newtonian one.

Definition at line 652 of file etoile.h.

References Etoile::relativistic.

const Itbl & Etoile_rot::l_surf ( ) const [virtual]

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 from Etoile.

Reimplemented in Et_rot_bifluid.

Definition at line 85 of file et_rot_global.C.

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

double Etoile_rot::lambda_grv2	(	const Cmp &	sou_m,
		const Cmp &	sou_q
	)			`[static]`

Computes the coefficient $\lambda$ which ensures that the GRV2 virial identity is satisfied.

$\lambda$ is the coefficient by which one must multiply the quadratic source term $\sigma_q$ of the 2-D Poisson equation

$\Delta_2 u = \sigma_m + \sigma_q$

in order that the total source does not contain any monopolar term, i.e. in order that

$\int_0^{2\pi} \int_0^{+\infty} \sigma(r, \theta) \, r \, dr \, d\theta = 0 \ ,$

where $\sigma = \sigma_m + \sigma_q$ . $\lambda$ is computed according to the formula

$\lambda = - { \int_0^{2\pi} \int_0^{+\infty} \sigma_m(r, \theta) \, r \, dr \, d\theta \over \int_0^{2\pi} \int_0^{+\infty} \sigma_q(r, \theta) \, r \, dr \, d\theta } \ .$

Then, by construction, the new source $\sigma' = \sigma_m + \lambda \sigma_q$ has a vanishing monopolar term.

Parameters:

	sou_m	[input] matter source term $\sigma_m$
	sou_q	[input] quadratic source term $\sigma_q$

Returns:: value of $\lambda$

Definition at line 75 of file et_rot_lambda_grv2.C.

References Valeur::c, Cmp::check_dzpuis(), Valeur::coef_i(), Map_radial::dxdr, Map_af::get_alpha(), Map_af::get_beta(), Valeur::get_etat(), Cmp::get_etat(), Tbl::get_etat(), Mg3d::get_grille3d(), Map::get_mg(), Cmp::get_mp(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_r(), Map_af::set_alpha(), Map_af::set_beta(), Tbl::t, Mtbl::t, Cmp::va, Map::val_r(), Grille3d::x, and Map_radial::xsr.

double Etoile_rot::lspec_isco ( ) const [virtual]

Angular momentum of a particle on the ISCO.

Definition at line 280 of file et_rot_isco.C.

References p_lspec_isco, and r_isco().

double Etoile_rot::mass_b ( ) const [virtual]

Baryon mass.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid.

Definition at line 115 of file et_rot_global.C.

References Etoile::a_car, bbb, Etoile::gam_euler, Tenseur::get_etat(), Cmp::integrale(), Etoile::nbar, Etoile::p_mass_b, Etoile::relativistic, and Cmp::std_base_scal().

double Etoile_rot::mass_g ( ) const [virtual]

Gravitational mass.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 147 of file et_rot_global.C.

References Etoile::a_car, bbb, Etoile::ener_euler, mass_b(), Etoile::nnn, Etoile::p_mass_g, Etoile::press, Etoile::relativistic, Etoile::s_euler, Tenseur::set_std_base(), tnphi, and uuu.

double Etoile_rot::mom_quad ( ) const [virtual]

Quadrupole moment.

The quadrupole moment Q is defined according to Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)]. At the Newtonian limit it is related to the component ${\bar I}_{zz}$ of the MTW (1973) reduced quadrupole moment ${\bar I}_{ij}$ by: $Q = -3/2 {\bar I}_{zz}$ . Note that Q is the negative of the quadrupole moment defined by Laarakkers and Poisson, Astrophys. J. 512 , 282 (1999).

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 514 of file et_rot_global.C.

References Etoile::a_car, ak_car, bbb, Cmp::check_dzpuis(), Etoile::ener_euler, flat_scalar_prod(), Cmp::get_etat(), Tenseur::gradient_spher(), Cmp::inc2_dzpuis(), log(), logn, Etoile::mp, Valeur::mult_ct(), Cmp::mult_r(), Etoile::nbar, p_mom_quad, Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Tenseur::set_std_base(), and Cmp::va.

void Etoile_rot::operator= ( const Etoile_rot & et )

Assignment to another Etoile_rot.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, Et_rot_diff, Et_rot_mag, and Et_magnetisation.

Definition at line 388 of file etoile_rot.C.

References ak_car, b_car, bbb, del_deriv(), khi_shift, nphi, nuf, nuq, omega, ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tkij, tnphi, uuu, and w_shift.

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

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

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, Et_rot_diff, Et_rot_mag, and Et_magnetisation.

Definition at line 450 of file etoile_rot.C.

References Etoile::a_car, angu_mom(), aplat(), b_car, diffrel(), dzeta, f_isco(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), get_omega_c(), grv2(), grv3(), khi_shift, logn, mass_g(), mom_quad(), Etoile::mp, nphi, Etoile::nzet, omega, pow(), r_circ(), r_isco(), Etoile::ray_eq(), sqrt(), tsw(), uuu, w_shift, z_eqb(), z_eqf(), and z_pole().

void Etoile_rot::partial_display ( ostream & ost ) const [protected, virtual]

Printing of some informations, excluding all global quantities.

Reimplemented in Et_rot_bifluid.

Definition at line 605 of file etoile_rot.C.

References Etoile::a_car, aplat(), b_car, dzeta, Etoile::ener, Etoile::ent, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), get_omega_c(), logn, Etoile::mp, Etoile::nbar, Etoile::nnn, nphi, Etoile::nzet, Etoile::press, Etoile::ray_eq(), and uuu.

double Etoile_rot::r_circ ( ) const [virtual]

Circumferential radius.

Definition at line 380 of file et_rot_global.C.

References bbb, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Etoile::mp, Etoile::nzet, p_r_circ, and Etoile::ray_eq().

double Etoile_rot::r_isco ( ostream * ost = 0x0 ) const [virtual]

Circumferential radius of the innermost stable circular orbit (ISCO).

Parameters:

ost

output stream to give details of the computation; if set to 0x0 [default value], no details will be given.

Definition at line 80 of file et_rot_isco.C.

References Param::add_cmp(), Param::add_int(), Cmp::annule(), bbb, Cmp::dsdr(), Map::get_mg(), Mg3d::get_nzone(), Etoile::mp, Etoile::nnn, nphi, Etoile::nzet, p_espec_isco, p_f_eq, p_f_isco, p_lspec_isco, p_r_isco, Map::r, Etoile::ray_eq(), sqrt(), Cmp::std_base_scal(), Cmp::va, Valeur::val_point(), Map::val_r(), and zerosec().

double Etoile::ray_eq ( int kk ) const [inherited]

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

Definition at line 436 of file etoile_global.C.

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

double Etoile::ray_eq ( ) const [inherited]

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

Definition at line 116 of file etoile_global.C.

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

double Etoile::ray_eq_3pis2 ( ) const [inherited]

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

Definition at line 331 of file etoile_global.C.

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

double Etoile::ray_eq_pi ( ) const [inherited]

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

Definition at line 252 of file etoile_global.C.

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

double Etoile::ray_eq_pis2 ( ) const [inherited]

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

Definition at line 165 of file etoile_global.C.

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

double Etoile::ray_pole ( ) const [inherited]

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

Definition at line 411 of file etoile_global.C.

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

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

Save in a file.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, Et_rot_diff, Et_rot_mag, and Et_magnetisation.

Definition at line 425 of file etoile_rot.C.

References fwrite_be(), khi_shift, nuf, nuq, omega, Cmp::sauve(), Tenseur::sauve(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, and w_shift.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Etoile.

Reimplemented in Et_rot_bifluid, and Et_rot_mag.

Definition at line 351 of file etoile_rot.C.

References p_angu_mom, p_aplat, p_espec_isco, p_f_eq, p_f_isco, p_grv2, p_grv3, p_lspec_isco, p_mom_quad, p_r_circ, p_r_isco, p_tsw, p_z_eqb, p_z_eqf, and p_z_pole.

void Etoile::set_enthalpy ( const Cmp & ent_i ) [inherited]

Assignment of the enthalpy field.

Definition at line 461 of file etoile.C.

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

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

Read/write of the mapping.

Definition at line 591 of file etoile.h.

References Etoile::mp.

double Etoile_rot::tsw ( ) const [virtual]

Ratio T/W.

Reimplemented in Et_rot_diff, and Et_rot_mag.

Definition at line 210 of file et_rot_global.C.

References Etoile::a_car, angu_mom(), bbb, Etoile::ener, Etoile::gam_euler, Cmp::integrale(), logn, mass_g(), Etoile::nbar, omega, p_tsw, Etoile::relativistic, and Cmp::std_base_scal().

void Etoile_rot::update_metric ( )

Computes metric coefficients from known potentials.

The calculation is performed starting from the quantities logn , dzeta , tggg and shift , which are supposed to be up to date. From these, the following fields are updated: nnn , a_car , bbb and b_car .

Definition at line 65 of file et_rot_upmetr.C.

References Etoile::a_car, b_car, bbb, del_deriv(), Cmp::div_rsint(), dzeta, exp(), extrinsic_curvature(), logn, Etoile::nnn, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), tggg, and Etoile::unsurc2.

const Tbl & Etoile::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 97 of file etoile_global.C.

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

double Etoile_rot::z_eqb ( ) const [virtual]

Backward redshift factor at equator.

Definition at line 460 of file et_rot_global.C.

References Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Etoile::mp, Etoile::nnn, nphi, Etoile::nzet, p_z_eqb, r_circ(), sqrt(), and uuu.

double Etoile_rot::z_eqf ( ) const [virtual]

Forward redshift factor at equator.

Definition at line 428 of file et_rot_global.C.

References Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Etoile::mp, Etoile::nnn, nphi, Etoile::nzet, p_z_eqf, r_circ(), sqrt(), and uuu.

double Etoile_rot::z_pole ( ) const [virtual]

Redshift factor at North pole.

Definition at line 495 of file et_rot_global.C.

References Etoile::nnn, p_z_pole, and Etoile::ray_pole().

Friends And Related Function Documentation

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

Display.

Member Data Documentation

Tenseur Etoile::a_car [protected, inherited]

Total conformal factor $A^2$ .

Definition at line 503 of file etoile.h.

Tenseur Etoile_rot::ak_car [protected]

Scalar $A^2 K_{ij} K^{ij}$ .

For axisymmetric stars, this quantity is related to the derivatives of $N^\varphi$ by

$A^2 K_{ij} K^{ij} = {B^2 \over 2 N^2} \, r^2\sin^2\theta \, \left[ \left( {\partial N^\varphi \over \partial r} \right) ^2 + {1\over r^2} \left( {\partial N^\varphi \over \partial \theta} \right) ^2 \right] \ .$

In particular it is related to the quantities $k_1$ and $k_2$ introduced by Eqs.~(3.7) and (3.8) of Bonazzola et al. Astron. Astrophys. 278 , 421 (1993) by

$A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ .$

Definition at line 1572 of file etoile.h.

Tenseur Etoile_rot::b_car [protected]

Square of the metric factor B.

Definition at line 1493 of file etoile.h.

Tenseur Etoile_rot::bbb [protected]

Metric factor B.

Definition at line 1490 of file etoile.h.

Tenseur Etoile::beta_auto [protected, inherited]

Logarithm of the part of the product AN generated principaly by by the star.

Definition at line 494 of file etoile.h.

Tenseur Etoile::d_logn_auto_div [protected, inherited]

Gradient of logn_auto_div (if k_div!=0 ).

Definition at line 489 of file etoile.h.

Tenseur& Etoile_rot::dzeta [protected]

Metric potential $\zeta = \ln(AN)$ = beta_auto.

Definition at line 1520 of file etoile.h.

Tenseur Etoile::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 448 of file etoile.h.

Tenseur Etoile::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 453 of file etoile.h.

Tenseur Etoile::ent [protected, inherited]

Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).

Definition at line 445 of file etoile.h.

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

Equation of state of the stellar matter.

Reimplemented in Et_rot_bifluid.

Definition at line 440 of file etoile.h.

Tenseur Etoile::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 459 of file etoile.h.

int Etoile::k_div [protected, inherited]

Index of regularity of the gravitational potential logn_auto .

If k_div=0 , logn_auto contains the total potential generated principaly by the star, otherwise it should be supplemented by logn_auto_div .

Definition at line 438 of file etoile.h.

Tenseur Etoile_rot::khi_shift [protected]

Scalar $\chi$ used in the decomposition of shift , following Shibata's prescription [Prog.

Theor. Phys. 101 , 1199 (1999)] :

$N^i = {7\over 8} W^i - {1\over 8} \left(\nabla^i\chi+\nabla^iW^kx_k\right)$

Definition at line 1546 of file etoile.h.

Tenseur& Etoile_rot::logn [protected]

Metric potential $\nu = \ln N$ = logn_auto.

Definition at line 1507 of file etoile.h.

Tenseur Etoile::logn_auto [protected, inherited]

Total of the logarithm of the part of the lapse N generated principaly by the star.

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

Definition at line 472 of file etoile.h.

Tenseur Etoile::logn_auto_div [protected, inherited]

Divergent part (if k_div!=0 ) of the logarithm of the part of the lapse N generated principaly by the star.

Definition at line 485 of file etoile.h.

Tenseur Etoile::logn_auto_regu [protected, inherited]

Regular part of the logarithm of the part of the lapse N generated principaly by the star.

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

Definition at line 479 of file etoile.h.

Map& Etoile::mp [protected, inherited]

Mapping associated with the star.

Definition at line 416 of file etoile.h.

Tenseur Etoile::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 447 of file etoile.h.

Tenseur Etoile::nnn [protected, inherited]

Total lapse function.

Definition at line 497 of file etoile.h.

Tenseur Etoile_rot::nphi [protected]

Metric coefficient $N^\varphi$ .

Definition at line 1496 of file etoile.h.

Tenseur Etoile_rot::nuf [protected]

Part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.

Definition at line 1512 of file etoile.h.

Tenseur Etoile_rot::nuq [protected]

Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.

Definition at line 1517 of file etoile.h.

int Etoile::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 421 of file etoile.h.

double Etoile_rot::omega [protected]

Rotation angular velocity ([f_unit] ).

Definition at line 1487 of file etoile.h.

double* Etoile_rot::p_angu_mom [mutable, protected]

Angular momentum.

Definition at line 1617 of file etoile.h.

double* Etoile_rot::p_aplat [mutable, protected]

Flatening r_pole/r_eq.

Definition at line 1622 of file etoile.h.

double* Etoile_rot::p_espec_isco [mutable, protected]

Specific energy of a particle on the ISCO.

Definition at line 1630 of file etoile.h.

double* Etoile_rot::p_f_eq [mutable, protected]

Orbital frequency at the equator.

Definition at line 1633 of file etoile.h.

double* Etoile_rot::p_f_isco [mutable, protected]

Orbital frequency of the ISCO.

Definition at line 1628 of file etoile.h.

double* Etoile_rot::p_grv2 [mutable, protected]

Error on the virial identity GRV2.

Definition at line 1619 of file etoile.h.

double* Etoile_rot::p_grv3 [mutable, protected]

Error on the virial identity GRV3.

Definition at line 1620 of file etoile.h.

Itbl* Etoile::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 527 of file etoile.h.

double* Etoile_rot::p_lspec_isco [mutable, protected]

Specific angular momentum of a particle on the ISCO.

Definition at line 1632 of file etoile.h.

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

Baryon mass.

Definition at line 535 of file etoile.h.

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

Gravitational mass.

Definition at line 536 of file etoile.h.

double* Etoile_rot::p_mom_quad [mutable, protected]

Quadrupole moment.

Definition at line 1626 of file etoile.h.

double* Etoile_rot::p_r_circ [mutable, protected]

Circumferential radius.

Definition at line 1621 of file etoile.h.

double* Etoile_rot::p_r_isco [mutable, protected]

Circumferential radius of the ISCO.

Definition at line 1627 of file etoile.h.

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

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

Definition at line 509 of file etoile.h.

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

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

Definition at line 518 of file etoile.h.

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

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

Definition at line 515 of file etoile.h.

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

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

Definition at line 512 of file etoile.h.

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

Coordinate radius at $\theta=0$ .

Definition at line 521 of file etoile.h.

double* Etoile_rot::p_tsw [mutable, protected]

Ratio T/W.

Definition at line 1618 of file etoile.h.

Tbl* Etoile::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 533 of file etoile.h.

double* Etoile_rot::p_z_eqb [mutable, protected]

Backward redshift factor at equator.

Definition at line 1624 of file etoile.h.

double* Etoile_rot::p_z_eqf [mutable, protected]

Forward redshift factor at equator.

Definition at line 1623 of file etoile.h.

double* Etoile_rot::p_z_pole [mutable, protected]

Redshift factor at North pole.

Definition at line 1625 of file etoile.h.

Tenseur Etoile::press [protected, inherited]

Fluid pressure.

Definition at line 449 of file etoile.h.

bool Etoile::relativistic [protected, inherited]

Indicator of relativity: true for a relativistic star, false for a Newtonian one.

Definition at line 426 of file etoile.h.

Tenseur Etoile::s_euler [protected, inherited]

Trace of the stress tensor in the Eulerian frame.

Definition at line 456 of file etoile.h.

Tenseur Etoile::shift [protected, inherited]

Total shift vector.

Definition at line 500 of file etoile.h.

Cmp Etoile_rot::ssjm1_dzeta [protected]

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

Definition at line 1589 of file etoile.h.

Cmp Etoile_rot::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 1602 of file etoile.h.

Cmp Etoile_rot::ssjm1_nuf [protected]

Effective source at the previous step for the resolution of the Poisson equation for nuf by means of Map_et::poisson .

Definition at line 1578 of file etoile.h.

Cmp Etoile_rot::ssjm1_nuq [protected]

Effective source at the previous step for the resolution of the Poisson equation for nuq by means of Map_et::poisson .

Definition at line 1584 of file etoile.h.

Cmp Etoile_rot::ssjm1_tggg [protected]

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

Definition at line 1594 of file etoile.h.

Tenseur Etoile_rot::ssjm1_wshift [protected]

Effective source at the previous step for the resolution of the vector Poisson equation for $W^i$ .

$W^i$ 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 1611 of file etoile.h.

Tenseur Etoile_rot::tggg [protected]

Metric potential $\tilde G = (NB-1) r\sin\theta$ .

Definition at line 1523 of file etoile.h.

Tenseur_sym Etoile_rot::tkij [protected]

Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$ .

tkij contains the Cartesian components of ${\tilde K_{ij}}$ .

Definition at line 1553 of file etoile.h.

Tenseur Etoile_rot::tnphi [protected]

Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.

Definition at line 1501 of file etoile.h.

Tenseur Etoile::u_euler [protected, inherited]