Class for differentially rotating stars. More...

#include <et_rot_diff.h>

Inheritance diagram for Lorene::Et_rot_diff:

Public Member Functions
	Et_rot_diff (Map &mp_i, int nzet_i, bool relat, const Eos &eos_i, double(frot_i)(double, const Tbl &), double(primfrot_i)(double, const Tbl &), const Tbl &par_frot_i)
	Standard constructor. More...

	Et_rot_diff (const Et_rot_diff &)
	Copy constructor. More...

	Et_rot_diff (Map &mp_i, const Eos &eos_i, FILE fich, double(frot_i)(double, const Tbl &), double(*primfrot_i)(double, const Tbl &))
	Constructor from a file (see `sauve(FILE*)` ). More...

virtual	~Et_rot_diff ()
	Destructor. More...

void	operator= (const Et_rot_diff &)
	Assignment to another `Et_rot_diff`. More...

const Tenseur &	get_omega_field () const
	Returns the angular velocity field $\Omega$ . More...

virtual double	get_omega_c () const
	Returns the central value of the rotation angular velocity ([f_unit] ) More...

virtual void	sauve (FILE *) const
	Save in a file. More...

virtual void	display_poly (ostream &) const
	Display in polytropic units. More...

virtual double	tsw () const
	Ratio T/W. More...

virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame. More...

void	fait_omega_field (double omeg_min, double omeg_max, double precis, int nitermax)
	Computes $\Omega(r,\theta)$ (member `omega_field` ). More...

void	fait_prim_field ()
	Computes the member `prim_field` from `omega_field` . More...

double	funct_omega (double omeg) const
	Evaluates $F(\Omega)$ , where F is the function defining the rotation profile. More...

double	prim_funct_omega (double omeg) const
	Evaluates the primitive of $F(\Omega)$ , where F is the function defining the rotation profile. More...

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. More...

const Tenseur &	get_bbb () const
	Returns the metric factor B. More...

const Tenseur &	get_b_car () const
	Returns the square of the metric factor B. More...

const Tenseur &	get_nphi () const
	Returns the metric coefficient $N^\varphi$ . More...

const Tenseur &	get_tnphi () const
	Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector. More...

const Tenseur &	get_uuu () const
	Returns the norm of `u_euler`. More...

const Tenseur &	get_logn () const
	Returns the metric potential $\nu = \ln N$ = `logn_auto`. More...

const Tenseur &	get_nuf () const
	Returns the part of the Metric potential $\nu = \ln N$ = `logn` generated by the matter terms. More...

const Tenseur &	get_nuq () const
	Returns the Part of the Metric potential $\nu = \ln N$ = `logn` generated by the quadratic terms. More...

const Tenseur &	get_dzeta () const
	Returns the Metric potential $\zeta = \ln(AN)$ = `beta_auto`. More...

const Tenseur &	get_tggg () const
	Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$ . More...

const Tenseur &	get_w_shift () const
	Returns the vector used in the decomposition of `shift` , following Shibata's prescription [Prog. More...

const Tenseur &	get_khi_shift () const
	Returns the scalar $\chi$ used in the decomposition of `shift` following Shibata's prescription [Prog. More...

const Tenseur_sym &	get_tkij () const
	Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$ . More...

const Tenseur &	get_ak_car () const
	Returns the scalar $A^2 K_{ij} K^{ij}$ . More...

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 $(\theta', \phi')$ . More...

virtual double	mass_b () const
	Baryon mass. More...

virtual double	mass_g () const
	Gravitational mass. More...

virtual double	angu_mom () const
	Angular momentum. More...

virtual double	grv2 () const
	Error on the virial identity GRV2. More...

virtual double	grv3 (ostream *ost=0x0) const
	Error on the virial identity GRV3. More...

virtual double	r_circ () const
	Circumferential equatorial radius. More...

virtual double	r_circ_merid () const
	Circumferential meridional radius. More...

virtual double	area () const
	Surface area. More...

virtual double	mean_radius () const
	Mean radius. More...

virtual double	aplat () const
	Flatening r_pole/r_eq. More...

virtual double	z_eqf () const
	Forward redshift factor at equator. More...

virtual double	z_eqb () const
	Backward redshift factor at equator. More...

virtual double	z_pole () const
	Redshift factor at North pole. More...

virtual double	mom_quad () const
	Quadrupole moment. More...

virtual double	mom_quad_old () const
	Part of the quadrupole moment. More...

virtual double	mom_quad_Bo () const
	Part of the quadrupole moment. More...

virtual double	r_isco (ostream *ost=0x0) const
	Circumferential radius of the innermost stable circular orbit (ISCO). More...

virtual double	f_isco () const
	Orbital frequency at the innermost stable circular orbit (ISCO). More...

virtual double	espec_isco () const
	Energy of a particle on the ISCO. More...

virtual double	lspec_isco () const
	Angular momentum of a particle on the ISCO. More...

virtual double	f_eccentric (double ecc, double periast, ostream *ost=0x0) const
	Computation of frequency of eccentric orbits. More...

virtual double	f_eq () const
	Orbital frequency at the equator. More...

void	update_metric ()
	Computes metric coefficients from known potentials. More...

void	fait_shift ()
	Computes `shift` from `w_shift` and `khi_shift` according to Shibata's prescription [Prog. More...

void	fait_nphi ()
	Computes `tnphi` and `nphi` from the Cartesian components of the shift, stored in `shift` . More...

void	extrinsic_curvature ()
	Computes `tkij` and `ak_car` from `shift` , `nnn` and `b_car` . More...

Map &	set_mp ()
	Read/write of the mapping. More...

void	set_enthalpy (const Cmp &)
	Assignment of the enthalpy field. More...

virtual void	equation_of_state ()
	Computes the proper baryon and energy density, as well as pressure from the enthalpy. More...

virtual void	equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *ent_limit=0x0)
	Computes a spherical static configuration. More...

void	equil_spher_regular (double ent_c, double precis=1.e-14)
	Computes a spherical static configuration. More...

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. More...

const Map &	get_mp () const
	Returns the mapping. More...

int	get_nzet () const
	Returns the number of domains occupied by the star. More...

bool	is_relativistic () const
	Returns `true` for a relativistic star, `false` for a Newtonian one. More...

const Eos &	get_eos () const
	Returns the equation of state. More...

const Tenseur &	get_ent () const
	Returns the enthalpy field. More...

const Tenseur &	get_nbar () const
	Returns the proper baryon density. More...

const Tenseur &	get_ener () const
	Returns the proper total energy density. More...

const Tenseur &	get_press () const
	Returns the fluid pressure. More...

const Tenseur &	get_ener_euler () const
	Returns the total energy density with respect to the Eulerian observer. More...

const Tenseur &	get_s_euler () const
	Returns the trace of the stress tensor in the Eulerian frame. More...

const Tenseur &	get_gam_euler () const
	Returns the Lorentz factor between the fluid and Eulerian observers. More...

const Tenseur &	get_u_euler () const
	Returns the fluid 3-velocity with respect to the Eulerian observer. More...

const Tenseur &	get_logn_auto () const
	Returns the logarithm of the part of the lapse N generated principaly by the star. More...

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. More...

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. More...

const Tenseur &	get_d_logn_auto_div () const
	Returns the gradient of `logn_auto_div`. More...

const Tenseur &	get_beta_auto () const
	Returns the logarithm of the part of the product AN generated principaly by the star. More...

const Tenseur &	get_nnn () const
	Returns the total lapse function N. More...

const Tenseur &	get_shift () const
	Returns the total shift vector . More...

const Tenseur &	get_a_car () const
	Returns the total conformal factor . More...

double	ray_eq () const
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq (int kk) const
	Coordinate radius at $\phi=2k\pi/np$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_pis2 () const
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_pi () const
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_eq_3pis2 () const
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ [r_unit]. More...

double	ray_pole () const
	Coordinate radius at $\theta=0$ [r_unit]. More...

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 $(\theta', \phi')$ . More...

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. More...

Protected Member Functions
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<). More...

virtual void	del_deriv () const
	Deletes all the derived quantities. More...

virtual void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

virtual void	del_hydro_euler ()
	Sets to `ETATNONDEF` (undefined state) the hydrodynamical quantities relative to the Eulerian observer. More...

virtual void	partial_display (ostream &) const
	Printing of some informations, excluding all global quantities. More...

Protected Attributes
double(*	frot )(double, const Tbl &)
	Function $F(\Omega)$ defining the rotation profile. More...

double(*	primfrot )(double, const Tbl &)
	Primitive of the function $F(\Omega)$ , which vanishes at the stellar center. More...

Tbl	par_frot
	Parameters of the function $F(\Omega)$ . More...

Tenseur	omega_field
	Field $\Omega(r,\theta)$ . More...

double	omega_min
	Minimum value of $\Omega$ . More...

double	omega_max
	Maximum value of $\Omega$ . More...

Tenseur	prim_field
	Field $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$ . More...

double	omega
	Rotation angular velocity ([f_unit] ) More...

Tenseur	bbb
	Metric factor B. More...

Tenseur	b_car
	Square of the metric factor B. More...

Tenseur	nphi
	Metric coefficient $N^\varphi$ . More...

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

Tenseur	uuu
	Norm of `u_euler`. More...

Tenseur &	logn
	Metric potential $\nu = \ln N$ = `logn_auto`. More...

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

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

Tenseur &	dzeta
	Metric potential $\zeta = \ln(AN)$ = `beta_auto`. More...

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

Tenseur	w_shift
	Vector used in the decomposition of `shift` , following Shibata's prescription [Prog. More...

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

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

Tenseur	ak_car
	Scalar $A^2 K_{ij} K^{ij}$ . More...

Cmp	ssjm1_nuf
	Effective source at the previous step for the resolution of the Poisson equation for `nuf` by means of `Map_et::poisson` . More...

Cmp	ssjm1_nuq
	Effective source at the previous step for the resolution of the Poisson equation for `nuq` by means of `Map_et::poisson` . More...

Cmp	ssjm1_dzeta
	Effective source at the previous step for the resolution of the Poisson equation for `dzeta` . More...

Cmp	ssjm1_tggg
	Effective source at the previous step for the resolution of the Poisson equation for `tggg` . More...

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` . More...

Tenseur	ssjm1_wshift
	Effective source at the previous step for the resolution of the vector Poisson equation for . More...

double *	p_angu_mom
	Angular momentum. More...

double *	p_tsw
	Ratio T/W. More...

double *	p_grv2
	Error on the virial identity GRV2. More...

double *	p_grv3
	Error on the virial identity GRV3. More...

double *	p_r_circ
	Circumferential equatorial radius. More...

double *	p_r_circ_merid
	Circumferential meridional radius. More...

double *	p_area
	Surface area. More...

double *	p_aplat
	Flatening r_pole/r_eq. More...

double *	p_z_eqf
	Forward redshift factor at equator. More...

double *	p_z_eqb
	Backward redshift factor at equator. More...

double *	p_z_pole
	Redshift factor at North pole. More...

double *	p_mom_quad
	Quadrupole moment. More...

double *	p_mom_quad_old
	Part of the quadrupole moment. More...

double *	p_mom_quad_Bo
	Part of the quadrupole moment. More...

double *	p_r_isco
	Circumferential radius of the ISCO. More...

double *	p_f_isco
	Orbital frequency of the ISCO. More...

double *	p_espec_isco
	Specific energy of a particle on the ISCO. More...

double *	p_lspec_isco
	Specific angular momentum of a particle on the ISCO. More...

double *	p_f_eq
	Orbital frequency at the equator. More...

Map &	mp
	Mapping associated with the star. More...

int	nzet
	Number of domains of `*mp` occupied by the star. More...

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

double	unsurc2
	: `unsurc2=1` for a relativistic star, 0 for a Newtonian one. More...

int	k_div
	Index of regularity of the gravitational potential `logn_auto` . More...

const Eos &	eos
	Equation of state of the stellar matter. More...

Tenseur	ent
	Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case) More...

Tenseur	nbar
	Baryon density in the fluid frame. More...

Tenseur	ener
	Total energy density in the fluid frame. More...

Tenseur	press
	Fluid pressure. More...

Tenseur	ener_euler
	Total energy density in the Eulerian frame. More...

Tenseur	s_euler
	Trace of the stress tensor in the Eulerian frame. More...

Tenseur	gam_euler
	Lorentz factor between the fluid and Eulerian observers. More...

Tenseur	u_euler
	Fluid 3-velocity with respect to the Eulerian observer. More...

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

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

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. More...

Tenseur	d_logn_auto_div
	Gradient of `logn_auto_div` (if `k_div!=0` ) More...

Tenseur	beta_auto
	Logarithm of the part of the product AN generated principaly by by the star. More...

Tenseur	nnn
	Total lapse function. More...

Tenseur	shift
	Total shift vector. More...

Tenseur	a_car
	Total conformal factor . More...

double *	p_ray_eq
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_pis2
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_pi
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ . More...

double *	p_ray_eq_3pis2
	Coordinate radius at $\phi=3\pi/2$ , $\theta=\pi/2$ . More...

double *	p_ray_pole
	Coordinate radius at $\theta=0$ . More...

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 $(\theta', \phi')$ . More...

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 $(\theta', \phi')$ . More...

double *	p_mass_b
	Baryon mass. More...

double *	p_mass_g
	Gravitational mass. More...

Detailed Description

Class for differentially rotating stars.

()

Definition at line 73 of file et_rot_diff.h.

Constructor & Destructor Documentation

◆ Et_rot_diff() [1/3]

Lorene::Et_rot_diff::Et_rot_diff	(	Map &	mp_i,
		int	nzet_i,
		bool	relat,
		const Eos &	eos_i,
		double(*)(double, const Tbl &)	frot_i,
		double(*)(double, const Tbl &)	primfrot_i,
		const Tbl &	par_frot_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
frot_i	Function $F(\Omega)$ defining the rotation profile.
primfrot_i	Primitive of $F(\Omega)$ which vanishes at the stellar center
par_frot_i	Parameters of functions `frot_i` and `primfrot_i` , `par_frot_i(0)` being the central value of $\Omega$ .

Definition at line 85 of file et_rot_diff.C.

References Lorene::Etoile_rot::omega, omega_field, omega_max, omega_min, and prim_field.

◆ Et_rot_diff() [2/3]

Lorene::Et_rot_diff::Et_rot_diff ( const Et_rot_diff & et )

Copy constructor.

Definition at line 110 of file et_rot_diff.C.

◆ Et_rot_diff() [3/3]

Lorene::Et_rot_diff::Et_rot_diff	(	Map &	mp_i,
		const Eos &	eos_i,
		FILE *	fich,
		double(*)(double, const Tbl &)	frot_i,
		double(*)(double, const Tbl &)	primfrot_i
	)

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` )
frot_i	Function $F(\Omega)$ defining the rotation profile.
primfrot_i	Primitive of $F(\Omega)$ which vanishes at the stellar center

Definition at line 124 of file et_rot_diff.C.

References fait_prim_field(), Lorene::fread_be(), Lorene::Etoile::mp, omega_field, omega_max, and omega_min.

◆ ~Et_rot_diff()

Lorene::Et_rot_diff::~Et_rot_diff ( )

virtual

Destructor.

Definition at line 150 of file et_rot_diff.C.

Member Function Documentation

◆ angu_mom()

double Lorene::Etoile_rot::angu_mom ( ) const

virtualinherited

Angular momentum.

Reimplemented in Lorene::Et_magnetisation, Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 197 of file et_rot_global.C.

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

◆ aplat()

double Lorene::Etoile_rot::aplat ( ) const

virtualinherited

Flatening r_pole/r_eq.

Definition at line 554 of file et_rot_global.C.

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

◆ area()

double Lorene::Etoile_rot::area ( ) const

virtualinherited

◆ del_deriv()

void Lorene::Etoile_rot::del_deriv ( ) const

protectedvirtualinherited

Deletes all the derived quantities.

Reimplemented from Lorene::Etoile.

Reimplemented in Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 344 of file etoile_rot.C.

◆ del_hydro_euler()

void Lorene::Etoile_rot::del_hydro_euler ( )

protectedvirtualinherited

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

Reimplemented from Lorene::Etoile.

Reimplemented in Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 400 of file etoile_rot.C.

References Lorene::Etoile_rot::del_deriv(), and Lorene::Etoile::del_hydro_euler().

◆ display_poly()

void Lorene::Et_rot_diff::display_poly ( ostream & ost ) const

virtual

Display in polytropic units.

Reimplemented from Lorene::Etoile_rot.

Definition at line 271 of file et_rot_diff.C.

References Lorene::Etoile_rot::display_poly(), Lorene::Etoile::ener, Lorene::Etoile::eos, Lorene::Eos_poly::get_gam(), Lorene::Eos_poly::get_kap(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::max(), Lorene::Etoile::mp, Lorene::Etoile::nbar, Lorene::Etoile::nzet, omega_field, omega_max, omega_min, Lorene::pow(), and Lorene::sqrt().

◆ equation_of_state()

void Lorene::Etoile::equation_of_state ( )

virtualinherited

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

Reimplemented in Lorene::Et_magnetisation, and Lorene::Et_rot_bifluid.

Definition at line 569 of file etoile.C.

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

◆ equil_spher_falloff()

void Lorene::Etoile::equil_spher_falloff	(	double	ent_c,
		double	precis = `1.e-14`
	)

virtualinherited

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 60 of file etoile_eqsph_falloff.C.

◆ equil_spher_regular()

void Lorene::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 118 of file et_equil_spher_regu.C.

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

◆ equilibrium()

void Lorene::Et_rot_diff::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 central angular velocity (if `fact_omega=1`. )
fact_omega	[input] 1.01 = search for the Keplerian frequency, = 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 central 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 from Lorene::Etoile_rot.

Definition at line 91 of file et_rot_diff_equil.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_t(), and Lorene::Etoile::mp.

◆ equilibrium_spher()

void Lorene::Etoile::equilibrium_spher	(	double	ent_c,
		double	precis = `1.e-14`,
		const Tbl *	ent_limit = `0x0`
	)

virtualinherited

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 90 of file etoile_equil_spher.C.

◆ espec_isco()

double Lorene::Etoile_rot::espec_isco ( ) const

virtualinherited

Energy of a particle on the ISCO.

Definition at line 304 of file et_rot_isco.C.

References Lorene::Etoile_rot::p_espec_isco, and Lorene::Etoile_rot::r_isco().

◆ extrinsic_curvature()

void Lorene::Etoile_rot::extrinsic_curvature ( )

inherited

Computes tkij and ak_car from shift , nnn and b_car .

Definition at line 60 of file et_rot_extr_curv.C.

References Lorene::Cmp::get_etat(), Lorene::Map::get_mg(), Lorene::Etoile::mp, Lorene::Etoile_rot::nphi, Lorene::Tenseur::set_etat_zero(), and Lorene::Etoile_rot::tkij.

◆ f_eccentric()

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

virtualinherited

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 81 of file et_rot_f_eccentric.C.

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

◆ f_eq()

double Lorene::Etoile_rot::f_eq ( ) const

virtualinherited

Orbital frequency at the equator.

Definition at line 322 of file et_rot_isco.C.

References Lorene::Etoile_rot::p_f_eq, and Lorene::Etoile_rot::r_isco().

◆ f_isco()

double Lorene::Etoile_rot::f_isco ( ) const

virtualinherited

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

Definition at line 270 of file et_rot_isco.C.

References Lorene::Etoile_rot::p_f_isco, and Lorene::Etoile_rot::r_isco().

◆ fait_nphi()

void Lorene::Etoile_rot::fait_nphi ( )

inherited

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

Definition at line 803 of file etoile_rot.C.

References Lorene::Tenseur::get_etat(), and Lorene::Etoile::shift.

◆ fait_omega_field()

void Lorene::Et_rot_diff::fait_omega_field	(	double	omeg_min,
		double	omeg_max,
		double	precis,
		int	nitermax
	)

Computes $\Omega(r,\theta)$ (member omega_field ).

The computation amounts to solving the equation

$F(\Omega) - {B^2 r^2\sin^2\theta (\Omega - N^\varphi) \over N^2 - B^2 r^2 \sin^2(\Omega-N^\varphi)^2} = 0$

for $\Omega$ .

Parameters

omeg_min	[input] Lower bound of the interval for searching omega
omeg_max	[input] Higher bound of the interval for searching omega
precis	[input] Required precision in the determination of the zero by the secant method
nitermax	[input] Maximum number of iterations in the secant method to compute the zero.

Definition at line 76 of file et_rot_diff_faitomeg.C.

References Lorene::Param::add_cmp(), Lorene::Param::add_etoile(), Lorene::Param::add_int(), Lorene::Cmp::annule(), Lorene::Etoile_rot::bbb, Lorene::Tenseur::get_etat(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile::nnn, Lorene::Etoile_rot::nphi, omega_field, and Lorene::Cmp::std_base_scal().

◆ fait_prim_field()

void Lorene::Et_rot_diff::fait_prim_field ( )

Computes the member prim_field from omega_field .

Definition at line 202 of file et_rot_diff_faitomeg.C.

References Lorene::Tenseur::allocate_all(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Etoile::mp, Lorene::Etoile::nzet, omega_field, par_frot, prim_field, primfrot, Lorene::Tbl::set(), Lorene::Tenseur::set(), Lorene::Cmp::set(), and Lorene::Tenseur::set_std_base().

◆ fait_shift()

void Lorene::Etoile_rot::fait_shift ( )

inherited

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 766 of file etoile_rot.C.

References Lorene::Tenseur::get_etat(), Lorene::Tenseur::gradient(), and Lorene::Etoile_rot::khi_shift.

◆ funct_omega()

double Lorene::Et_rot_diff::funct_omega ( double omeg ) const

Evaluates $F(\Omega)$ , where F is the function defining the rotation profile.

This function is linked to the components of the fluid 4-velocity by

$F(\Omega) = u^t u_\varphi \ .$

funct_omega calls frot with the parameters par_frot .

Parameters

omeg	[input] value of $\Omega$

Returns: value of $F(\Omega)$

Definition at line 318 of file et_rot_diff.C.

References frot, and par_frot.

◆ get_a_car()

const Tenseur& Lorene::Etoile::get_a_car ( ) const

inlineinherited

Returns the total conformal factor $A^2$ .

Definition at line 736 of file etoile.h.

References Lorene::Etoile::a_car.

◆ get_ak_car()

const Tenseur& Lorene::Etoile_rot::get_ak_car ( ) const

inlineinherited

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 1803 of file etoile.h.

References Lorene::Etoile_rot::ak_car.

◆ get_b_car()

const Tenseur& Lorene::Etoile_rot::get_b_car ( ) const

inlineinherited

Returns the square of the metric factor B.

Definition at line 1719 of file etoile.h.

References Lorene::Etoile_rot::b_car.

◆ get_bbb()

const Tenseur& Lorene::Etoile_rot::get_bbb ( ) const

inlineinherited

Returns the metric factor B.

Definition at line 1716 of file etoile.h.

References Lorene::Etoile_rot::bbb.

◆ get_beta_auto()

const Tenseur& Lorene::Etoile::get_beta_auto ( ) const

inlineinherited

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

Definition at line 727 of file etoile.h.

References Lorene::Etoile::beta_auto.

◆ get_d_logn_auto_div()

const Tenseur& Lorene::Etoile::get_d_logn_auto_div ( ) const

inlineinherited

Returns the gradient of logn_auto_div.

Definition at line 722 of file etoile.h.

References Lorene::Etoile::d_logn_auto_div.

◆ get_dzeta()

const Tenseur& Lorene::Etoile_rot::get_dzeta ( ) const

inlineinherited

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

Definition at line 1746 of file etoile.h.

References Lorene::Etoile_rot::dzeta.

◆ get_ener()

const Tenseur& Lorene::Etoile::get_ener ( ) const

inlineinherited

Returns the proper total energy density.

Definition at line 682 of file etoile.h.

References Lorene::Etoile::ener.

◆ get_ener_euler()

const Tenseur& Lorene::Etoile::get_ener_euler ( ) const

inlineinherited

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

Definition at line 688 of file etoile.h.

References Lorene::Etoile::ener_euler.

◆ get_ent()

const Tenseur& Lorene::Etoile::get_ent ( ) const

inlineinherited

Returns the enthalpy field.

Definition at line 676 of file etoile.h.

References Lorene::Etoile::ent.

◆ get_eos()

const Eos& Lorene::Etoile::get_eos ( ) const

inlineinherited

Returns the equation of state.

Definition at line 673 of file etoile.h.

References Lorene::Etoile::eos.

◆ get_gam_euler()

const Tenseur& Lorene::Etoile::get_gam_euler ( ) const

inlineinherited

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 694 of file etoile.h.

References Lorene::Etoile::gam_euler.

◆ get_khi_shift()

const Tenseur& Lorene::Etoile_rot::get_khi_shift ( ) const

inlineinherited

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 1777 of file etoile.h.

References Lorene::Etoile_rot::khi_shift.

◆ get_logn()

const Tenseur& Lorene::Etoile_rot::get_logn ( ) const

inlineinherited

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

Definition at line 1733 of file etoile.h.

References Lorene::Etoile_rot::logn.

◆ get_logn_auto()

const Tenseur& Lorene::Etoile::get_logn_auto ( ) const

inlineinherited

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 704 of file etoile.h.

References Lorene::Etoile::logn_auto.

◆ get_logn_auto_div()

const Tenseur& Lorene::Etoile::get_logn_auto_div ( ) const

inlineinherited

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 718 of file etoile.h.

References Lorene::Etoile::logn_auto_div.

◆ get_logn_auto_regu()

const Tenseur& Lorene::Etoile::get_logn_auto_regu ( ) const

inlineinherited

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 711 of file etoile.h.

References Lorene::Etoile::logn_auto_regu.

◆ get_mp()

const Map& Lorene::Etoile::get_mp ( ) const

inlineinherited

Returns the mapping.

Definition at line 662 of file etoile.h.

References Lorene::Etoile::mp.

◆ get_nbar()

const Tenseur& Lorene::Etoile::get_nbar ( ) const

inlineinherited

Returns the proper baryon density.

Definition at line 679 of file etoile.h.

References Lorene::Etoile::nbar.

◆ get_nnn()

const Tenseur& Lorene::Etoile::get_nnn ( ) const

inlineinherited

Returns the total lapse function N.

Definition at line 730 of file etoile.h.

References Lorene::Etoile::nnn.

◆ get_nphi()

const Tenseur& Lorene::Etoile_rot::get_nphi ( ) const

inlineinherited

Returns the metric coefficient $N^\varphi$ .

Definition at line 1722 of file etoile.h.

References Lorene::Etoile_rot::nphi.

◆ get_nuf()

const Tenseur& Lorene::Etoile_rot::get_nuf ( ) const

inlineinherited

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

Definition at line 1738 of file etoile.h.

References Lorene::Etoile_rot::nuf.

◆ get_nuq()

const Tenseur& Lorene::Etoile_rot::get_nuq ( ) const

inlineinherited

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

Definition at line 1743 of file etoile.h.

References Lorene::Etoile_rot::nuq.

◆ get_nzet()

int Lorene::Etoile::get_nzet ( ) const

inlineinherited

Returns the number of domains occupied by the star.

Definition at line 665 of file etoile.h.

References Lorene::Etoile::nzet.

◆ get_omega_c()

double Lorene::Et_rot_diff::get_omega_c ( ) const

virtual

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 330 of file et_rot_diff.C.

References omega_field.

◆ get_omega_field()

const Tenseur& Lorene::Et_rot_diff::get_omega_field ( ) const

inline

Returns the angular velocity field $\Omega$ .

Definition at line 173 of file et_rot_diff.h.

References omega_field.

◆ get_press()

const Tenseur& Lorene::Etoile::get_press ( ) const

inlineinherited

Returns the fluid pressure.

Definition at line 685 of file etoile.h.

References Lorene::Etoile::press.

◆ get_s_euler()

const Tenseur& Lorene::Etoile::get_s_euler ( ) const

inlineinherited

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

Definition at line 691 of file etoile.h.

References Lorene::Etoile::s_euler.

◆ get_shift()

const Tenseur& Lorene::Etoile::get_shift ( ) const

inlineinherited

Returns the total shift vector $N^i$ .

Definition at line 733 of file etoile.h.

References Lorene::Etoile::shift.

◆ get_tggg()

const Tenseur& Lorene::Etoile_rot::get_tggg ( ) const

inlineinherited

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

Definition at line 1749 of file etoile.h.

References Lorene::Etoile_rot::tggg.

◆ get_tkij()

const Tenseur_sym& Lorene::Etoile_rot::get_tkij ( ) const

inlineinherited

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 1784 of file etoile.h.

References Lorene::Etoile_rot::tkij.

◆ get_tnphi()

const Tenseur& Lorene::Etoile_rot::get_tnphi ( ) const

inlineinherited

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

Definition at line 1727 of file etoile.h.

References Lorene::Etoile_rot::tnphi.

◆ get_u_euler()

const Tenseur& Lorene::Etoile::get_u_euler ( ) const

inlineinherited

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

Definition at line 697 of file etoile.h.

References Lorene::Etoile::u_euler.

◆ get_uuu()

const Tenseur& Lorene::Etoile_rot::get_uuu ( ) const

inlineinherited

Returns the norm of u_euler.

Definition at line 1730 of file etoile.h.

References Lorene::Etoile_rot::uuu.

◆ get_w_shift()

const Tenseur& Lorene::Etoile_rot::get_w_shift ( ) const

inlineinherited

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 1763 of file etoile.h.

References Lorene::Etoile_rot::w_shift.

◆ grv2()

double Lorene::Etoile_rot::grv2 ( ) const

virtualinherited

Error on the virial identity GRV2.

This indicator is only valid for relativistic computations.

Reimplemented in Lorene::Et_magnetisation, Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 263 of file et_rot_global.C.

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

◆ grv3()

double Lorene::Etoile_rot::grv3 ( ostream * ost = 0x0 ) const

virtualinherited

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 Lorene::Et_magnetisation, Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 294 of file et_rot_global.C.

References Lorene::Etoile_rot::ak_car, Lorene::Etoile_rot::bbb, Lorene::Etoile_rot::dzeta, Lorene::flat_scalar_prod(), Lorene::Cmp::get_etat(), Lorene::Tenseur::gradient_spher(), Lorene::log(), Lorene::Etoile_rot::logn, Lorene::Etoile::mp, Lorene::Etoile_rot::p_grv3, Lorene::Etoile::relativistic, Lorene::Tenseur::set_std_base(), and Lorene::Cmp::srdsdt().

◆ hydro_euler()

void Lorene::Et_rot_diff::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 omega_field , 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 Lorene::Etoile_rot.

Definition at line 64 of file et_rot_diff_hydro.C.

References Lorene::Tenseur::annule(), Lorene::Cmp::annule(), Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Valeur::get_etat(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Etoile::mp, Lorene::Etoile::nnn, Lorene::Etoile_rot::nphi, omega_field, Lorene::Valeur::set(), Lorene::Tenseur::set(), Lorene::Tenseur::set_etat_qcq(), Lorene::Tenseur::set_std_base(), Lorene::Tenseur::set_triad(), Lorene::Etoile::shift, Lorene::Etoile::u_euler, Lorene::Cmp::va, Lorene::Map::x, and Lorene::Map::y.

◆ is_relativistic()

bool Lorene::Etoile::is_relativistic ( ) const

inlineinherited

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

Definition at line 670 of file etoile.h.

References Lorene::Etoile::relativistic.

◆ l_surf()

const Itbl & Lorene::Etoile_rot::l_surf ( ) const

virtualinherited

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 Lorene::Etoile.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 104 of file et_rot_global.C.

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

◆ lambda_grv2()

double Lorene::Etoile_rot::lambda_grv2	(	const Cmp &	sou_m,
		const Cmp &	sou_q
	)

staticinherited

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 82 of file et_rot_lambda_grv2.C.

References Lorene::Cmp::check_dzpuis(), Lorene::Map::get_mg(), Lorene::Cmp::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::val_r().

◆ lspec_isco()

double Lorene::Etoile_rot::lspec_isco ( ) const

virtualinherited

Angular momentum of a particle on the ISCO.

Definition at line 287 of file et_rot_isco.C.

References Lorene::Etoile_rot::p_lspec_isco, and Lorene::Etoile_rot::r_isco().

◆ mass_b()

double Lorene::Etoile_rot::mass_b ( ) const

virtualinherited

Baryon mass.

Reimplemented from Lorene::Etoile.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 134 of file et_rot_global.C.

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

◆ mass_g()

double Lorene::Etoile_rot::mass_g ( ) const

virtualinherited

Gravitational mass.

Reimplemented from Lorene::Etoile.

Reimplemented in Lorene::Et_magnetisation, Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 166 of file et_rot_global.C.

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

◆ mean_radius()

double Lorene::Etoile_rot::mean_radius ( ) const

virtualinherited

Mean radius.

Definition at line 530 of file et_rot_global.C.

References Lorene::Etoile_rot::area(), and Lorene::sqrt().

◆ mom_quad()

double Lorene::Etoile_rot::mom_quad ( ) const

virtualinherited

Quadrupole moment.

The quadrupole moment Q is defined according to Eq. (11) of [Pappas and Apostolatos, Physical Review Letters 108, 231104 (2012)]. This is a corrected version of the quadrupole moment defined by [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)]. Following this definition, $Q = {\bar Q } - 4/3 (1/4 + b) M^3$ , where ${\bar Q }$ is defined as the negative of the (wrong) quadrupole moment defined in Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)], b is defined by Eq. (3.37) of [Friedman and Stergioulas, Rotating Relativistic Stars, Cambridge Monograph on mathematical physics] and M is the gravitational mass of the star.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 658 of file et_rot_global.C.

References Lorene::Etoile_rot::mass_g(), Lorene::Etoile_rot::mom_quad_Bo(), Lorene::Etoile_rot::mom_quad_old(), Lorene::Etoile_rot::p_mom_quad, Lorene::pow(), and Lorene::Etoile::relativistic.

◆ mom_quad_Bo()

double Lorene::Etoile_rot::mom_quad_Bo ( ) const

virtualinherited

Part of the quadrupole moment.

$B_o$ is defined as $bM^2$ , where b is given by Eq. (3.37) of [Friedman and Stergioulas, Rotating Relativistic Stars, Cambridge Monograph on mathematical physics] and M is the the gravitational mass of the star.

Reimplemented in Lorene::Et_magnetisation, and Lorene::Et_rot_bifluid.

Definition at line 676 of file et_rot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::bbb, Lorene::Cmp::integrale(), Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile::nnn, Lorene::Etoile_rot::p_mom_quad_Bo, Lorene::Etoile::press, and Lorene::Cmp::std_base_scal().

◆ mom_quad_old()

double Lorene::Etoile_rot::mom_quad_old ( ) const

virtualinherited

Part of the quadrupole moment.

This term ${\bar Q }$ is defined by Laarakkers and Poisson, Astrophys. J. 512 , 282 (1999). Note that ${\bar Q }$ is the negative of the (wrong) quadrupole moment defined in Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)].

Reimplemented in Lorene::Et_magnetisation, Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 699 of file et_rot_global.C.

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

◆ operator=()

void Lorene::Et_rot_diff::operator= ( const Et_rot_diff & et )

Assignment to another Et_rot_diff.

Definition at line 159 of file et_rot_diff.C.

References frot, omega_field, omega_max, omega_min, Lorene::Etoile_rot::operator=(), par_frot, prim_field, and primfrot.

◆ operator>>()

ostream & Lorene::Et_rot_diff::operator>> ( ostream & ost ) const

protectedvirtual

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 199 of file et_rot_diff.C.

References Lorene::Etoile_rot::angu_mom(), Lorene::Etoile_rot::aplat(), display_poly(), Lorene::Etoile::ener, Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), get_omega_c(), Lorene::Etoile_rot::mass_b(), Lorene::Etoile_rot::mass_g(), Lorene::max(), Lorene::Etoile::mp, Lorene::Etoile::nbar, Lorene::Etoile::nzet, omega_field, omega_max, omega_min, Lorene::Etoile_rot::operator>>(), par_frot, Lorene::pow(), Lorene::Etoile::press, Lorene::Etoile::ray_eq(), Lorene::sqrt(), and tsw().

◆ partial_display()

void Lorene::Etoile_rot::partial_display ( ostream & ost ) const

protectedvirtualinherited

Printing of some informations, excluding all global quantities.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 645 of file etoile_rot.C.

◆ prim_funct_omega()

double Lorene::Et_rot_diff::prim_funct_omega ( double omeg ) const

Evaluates the primitive of $F(\Omega)$ , where F is the function defining the rotation profile.

Parameters

omeg	[input] value of $\Omega$

Returns: value of $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$

Definition at line 324 of file et_rot_diff.C.

References par_frot, and primfrot.

◆ r_circ()

double Lorene::Etoile_rot::r_circ ( ) const

virtualinherited

Circumferential equatorial radius.

Definition at line 399 of file et_rot_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nzet, and Lorene::Etoile_rot::p_r_circ.

◆ r_circ_merid()

double Lorene::Etoile_rot::r_circ_merid ( ) const

virtualinherited

Circumferential meridional radius.

Definition at line 425 of file et_rot_global.C.

References Lorene::Valeur::annule_hard(), Lorene::Valeur::dsdt(), Lorene::Etoile::get_a_car(), Lorene::Mg3d::get_angu(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Etoile_rot::l_surf(), Lorene::Etoile::mp, Lorene::Etoile_rot::p_r_circ_merid, Lorene::sqrt(), Lorene::Valeur::std_base_scal(), Lorene::Cmp::std_base_scal(), Lorene::Cmp::va, Lorene::Valeur::val_point_jk(), Lorene::Map_radial::val_r_jk(), and Lorene::Etoile::xi_surf().

◆ r_isco()

double Lorene::Etoile_rot::r_isco ( ostream * ost = 0x0 ) const

virtualinherited

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 87 of file et_rot_isco.C.

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

◆ ray_eq() [1/2]

double Lorene::Etoile::ray_eq ( ) const

inherited

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

Definition at line 123 of file etoile_global.C.

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

◆ ray_eq() [2/2]

double Lorene::Etoile::ray_eq ( int kk ) const

inherited

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

Definition at line 443 of file etoile_global.C.

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

◆ ray_eq_3pis2()

double Lorene::Etoile::ray_eq_3pis2 ( ) const

inherited

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

Definition at line 338 of file etoile_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, and Lorene::Etoile::p_ray_eq_3pis2.

◆ ray_eq_pi()

double Lorene::Etoile::ray_eq_pi ( ) const

inherited

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

Definition at line 259 of file etoile_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, and Lorene::Etoile::p_ray_eq_pi.

◆ ray_eq_pis2()

double Lorene::Etoile::ray_eq_pis2 ( ) const

inherited

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

Definition at line 172 of file etoile_global.C.

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

◆ ray_pole()

double Lorene::Etoile::ray_pole ( ) const

inherited

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

Definition at line 418 of file etoile_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, and Lorene::Etoile::p_ray_pole.

◆ sauve()

void Lorene::Et_rot_diff::sauve ( FILE * fich ) const

virtual

Save in a file.

Reimplemented from Lorene::Etoile_rot.

Definition at line 182 of file et_rot_diff.C.

References Lorene::fwrite_be(), omega_field, omega_max, omega_min, par_frot, Lorene::Tbl::sauve(), Lorene::Tenseur::sauve(), and Lorene::Etoile_rot::sauve().

◆ set_der_0x0()

void Lorene::Etoile_rot::set_der_0x0 ( ) const

protectedvirtualinherited

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Etoile.

Reimplemented in Lorene::Et_rot_bifluid, and Lorene::Et_rot_mag.

Definition at line 374 of file etoile_rot.C.

◆ set_enthalpy()

void Lorene::Etoile::set_enthalpy ( const Cmp & ent_i )

inherited

Assignment of the enthalpy field.

Definition at line 468 of file etoile.C.

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

◆ set_mp()

Map& Lorene::Etoile::set_mp ( )

inlineinherited

Read/write of the mapping.

Definition at line 604 of file etoile.h.

References Lorene::Etoile::mp.

◆ tsw()

double Lorene::Et_rot_diff::tsw ( ) const

virtual

Ratio T/W.

Reimplemented from Lorene::Etoile_rot.

Definition at line 70 of file et_rot_diff_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Etoile::ener, Lorene::Etoile::ener_euler, Lorene::Etoile::gam_euler, Lorene::Cmp::integrale(), Lorene::Etoile_rot::logn, Lorene::Etoile_rot::mass_g(), Lorene::Cmp::mult_r(), Lorene::Etoile::nbar, omega_field, Lorene::Etoile_rot::p_tsw, Lorene::Etoile::press, Lorene::Etoile::relativistic, Lorene::Cmp::std_base_scal(), Lorene::Etoile_rot::uuu, and Lorene::Cmp::va.

◆ update_metric()

void Lorene::Etoile_rot::update_metric ( )

inherited

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 72 of file et_rot_upmetr.C.

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

◆ xi_surf()

const Tbl & Lorene::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 104 of file etoile_global.C.

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

◆ z_eqb()

double Lorene::Etoile_rot::z_eqb ( ) const

virtualinherited

Backward redshift factor at equator.

Definition at line 603 of file et_rot_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nzet, and Lorene::Etoile_rot::p_z_eqb.

◆ z_eqf()

double Lorene::Etoile_rot::z_eqf ( ) const

virtualinherited

Forward redshift factor at equator.

Definition at line 571 of file et_rot_global.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nzet, and Lorene::Etoile_rot::p_z_eqf.

◆ z_pole()

double Lorene::Etoile_rot::z_pole ( ) const

virtualinherited

Redshift factor at North pole.

Definition at line 638 of file et_rot_global.C.

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

Member Data Documentation

◆ a_car

Tenseur Lorene::Etoile::a_car

protectedinherited

Total conformal factor $A^2$ .

Definition at line 518 of file etoile.h.

◆ ak_car

Tenseur Lorene::Etoile_rot::ak_car

protectedinherited

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 1589 of file etoile.h.

◆ b_car

Tenseur Lorene::Etoile_rot::b_car

protectedinherited

Square of the metric factor B.

Definition at line 1510 of file etoile.h.

◆ bbb

Tenseur Lorene::Etoile_rot::bbb

protectedinherited

Metric factor B.

Definition at line 1507 of file etoile.h.

◆ beta_auto

Tenseur Lorene::Etoile::beta_auto

protectedinherited

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

Definition at line 509 of file etoile.h.

◆ d_logn_auto_div

Tenseur Lorene::Etoile::d_logn_auto_div

protectedinherited

Gradient of logn_auto_div (if k_div!=0 )

Definition at line 504 of file etoile.h.

◆ dzeta

Tenseur& Lorene::Etoile_rot::dzeta

protectedinherited

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

Definition at line 1537 of file etoile.h.

◆ ener

Tenseur Lorene::Etoile::ener

protectedinherited

Total energy density in the fluid frame.

Definition at line 463 of file etoile.h.

◆ ener_euler

Tenseur Lorene::Etoile::ener_euler

protectedinherited

Total energy density in the Eulerian frame.

Definition at line 468 of file etoile.h.

◆ ent

Tenseur Lorene::Etoile::ent

protectedinherited

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

Definition at line 460 of file etoile.h.

◆ eos

const Eos& Lorene::Etoile::eos

protectedinherited

Equation of state of the stellar matter.

Definition at line 454 of file etoile.h.

◆ frot

double(* Lorene::Et_rot_diff::frot) (double, const Tbl &)

protected

Function $F(\Omega)$ defining the rotation profile.

This function is linked to the components of the fluid 4-velocity by

$F(\Omega) = u^t u_\varphi \ .$

The first argument of frot must be $\Omega$ ; the second argument contains the parameters, the first of which being necessarily the central value of $\Omega$ .

Definition at line 88 of file et_rot_diff.h.

◆ gam_euler

Tenseur Lorene::Etoile::gam_euler

protectedinherited

Lorentz factor between the fluid and Eulerian observers.

Definition at line 474 of file etoile.h.

◆ k_div

int Lorene::Etoile::k_div

protectedinherited

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 452 of file etoile.h.

◆ khi_shift

Tenseur Lorene::Etoile_rot::khi_shift

protectedinherited

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 1563 of file etoile.h.

◆ logn

Tenseur& Lorene::Etoile_rot::logn

protectedinherited

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

Definition at line 1524 of file etoile.h.

◆ logn_auto

Tenseur Lorene::Etoile::logn_auto

protectedinherited

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 487 of file etoile.h.

◆ logn_auto_div

Tenseur Lorene::Etoile::logn_auto_div

protectedinherited

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

Definition at line 500 of file etoile.h.

◆ logn_auto_regu

Tenseur Lorene::Etoile::logn_auto_regu

protectedinherited

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 494 of file etoile.h.

◆ mp

Map& Lorene::Etoile::mp

protectedinherited

Mapping associated with the star.

Definition at line 432 of file etoile.h.

◆ nbar

Tenseur Lorene::Etoile::nbar

protectedinherited

Baryon density in the fluid frame.

Definition at line 462 of file etoile.h.

◆ nnn

Tenseur Lorene::Etoile::nnn

protectedinherited

Total lapse function.

Definition at line 512 of file etoile.h.

◆ nphi

Tenseur Lorene::Etoile_rot::nphi

protectedinherited

Metric coefficient $N^\varphi$ .

Definition at line 1513 of file etoile.h.

◆ nuf

Tenseur Lorene::Etoile_rot::nuf

protectedinherited

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

Definition at line 1529 of file etoile.h.

◆ nuq

Tenseur Lorene::Etoile_rot::nuq

protectedinherited

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

Definition at line 1534 of file etoile.h.

◆ nzet

int Lorene::Etoile::nzet

protectedinherited

Number of domains of *mp occupied by the star.

Definition at line 435 of file etoile.h.

◆ omega

double Lorene::Etoile_rot::omega

protectedinherited

Rotation angular velocity ([f_unit] )

Definition at line 1504 of file etoile.h.

◆ omega_field

Tenseur Lorene::Et_rot_diff::omega_field

protected

Field $\Omega(r,\theta)$ .

Definition at line 108 of file et_rot_diff.h.

◆ omega_max

double Lorene::Et_rot_diff::omega_max

protected

Maximum value of $\Omega$ .

Definition at line 111 of file et_rot_diff.h.

◆ omega_min

double Lorene::Et_rot_diff::omega_min

protected

Minimum value of $\Omega$ .

Definition at line 110 of file et_rot_diff.h.

◆ p_angu_mom

double* Lorene::Etoile_rot::p_angu_mom

mutableprotectedinherited

Angular momentum.

Definition at line 1634 of file etoile.h.

◆ p_aplat

double* Lorene::Etoile_rot::p_aplat

mutableprotectedinherited

Flatening r_pole/r_eq.

Definition at line 1641 of file etoile.h.

◆ p_area

double* Lorene::Etoile_rot::p_area

mutableprotectedinherited

Surface area.

Definition at line 1640 of file etoile.h.

◆ p_espec_isco

double* Lorene::Etoile_rot::p_espec_isco

mutableprotectedinherited

Specific energy of a particle on the ISCO.

Definition at line 1651 of file etoile.h.

◆ p_f_eq

double* Lorene::Etoile_rot::p_f_eq

mutableprotectedinherited

Orbital frequency at the equator.

Definition at line 1654 of file etoile.h.

◆ p_f_isco

double* Lorene::Etoile_rot::p_f_isco

mutableprotectedinherited

Orbital frequency of the ISCO.

Definition at line 1649 of file etoile.h.

◆ p_grv2

double* Lorene::Etoile_rot::p_grv2

mutableprotectedinherited

Error on the virial identity GRV2.

Definition at line 1636 of file etoile.h.

◆ p_grv3

double* Lorene::Etoile_rot::p_grv3

mutableprotectedinherited

Error on the virial identity GRV3.

Definition at line 1637 of file etoile.h.

◆ p_l_surf

Itbl* Lorene::Etoile::p_l_surf

mutableprotectedinherited

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 542 of file etoile.h.

◆ p_lspec_isco

double* Lorene::Etoile_rot::p_lspec_isco

mutableprotectedinherited

Specific angular momentum of a particle on the ISCO.

Definition at line 1653 of file etoile.h.

◆ p_mass_b

double* Lorene::Etoile::p_mass_b

mutableprotectedinherited

Baryon mass.

Definition at line 550 of file etoile.h.

◆ p_mass_g

double* Lorene::Etoile::p_mass_g

mutableprotectedinherited

Gravitational mass.

Definition at line 551 of file etoile.h.

◆ p_mom_quad

double* Lorene::Etoile_rot::p_mom_quad

mutableprotectedinherited

Quadrupole moment.

Definition at line 1645 of file etoile.h.

◆ p_mom_quad_Bo

double* Lorene::Etoile_rot::p_mom_quad_Bo

mutableprotectedinherited

Part of the quadrupole moment.

Definition at line 1647 of file etoile.h.

◆ p_mom_quad_old

double* Lorene::Etoile_rot::p_mom_quad_old

mutableprotectedinherited

Part of the quadrupole moment.

Definition at line 1646 of file etoile.h.

◆ p_r_circ

double* Lorene::Etoile_rot::p_r_circ

mutableprotectedinherited

Circumferential equatorial radius.

Definition at line 1638 of file etoile.h.

◆ p_r_circ_merid

double* Lorene::Etoile_rot::p_r_circ_merid

mutableprotectedinherited

Circumferential meridional radius.

Definition at line 1639 of file etoile.h.

◆ p_r_isco

double* Lorene::Etoile_rot::p_r_isco

mutableprotectedinherited

Circumferential radius of the ISCO.

Definition at line 1648 of file etoile.h.

◆ p_ray_eq

double* Lorene::Etoile::p_ray_eq

mutableprotectedinherited

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

Definition at line 524 of file etoile.h.

◆ p_ray_eq_3pis2

double* Lorene::Etoile::p_ray_eq_3pis2

mutableprotectedinherited

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

Definition at line 533 of file etoile.h.

◆ p_ray_eq_pi

double* Lorene::Etoile::p_ray_eq_pi

mutableprotectedinherited

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

Definition at line 530 of file etoile.h.

◆ p_ray_eq_pis2

double* Lorene::Etoile::p_ray_eq_pis2

mutableprotectedinherited

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

Definition at line 527 of file etoile.h.

◆ p_ray_pole

double* Lorene::Etoile::p_ray_pole

mutableprotectedinherited

Coordinate radius at $\theta=0$ .

Definition at line 536 of file etoile.h.

◆ p_tsw

double* Lorene::Etoile_rot::p_tsw

mutableprotectedinherited

Ratio T/W.

Definition at line 1635 of file etoile.h.

◆ p_xi_surf

Tbl* Lorene::Etoile::p_xi_surf

mutableprotectedinherited

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 548 of file etoile.h.

◆ p_z_eqb

double* Lorene::Etoile_rot::p_z_eqb

mutableprotectedinherited

Backward redshift factor at equator.

Definition at line 1643 of file etoile.h.

◆ p_z_eqf

double* Lorene::Etoile_rot::p_z_eqf

mutableprotectedinherited

Forward redshift factor at equator.

Definition at line 1642 of file etoile.h.

◆ p_z_pole

double* Lorene::Etoile_rot::p_z_pole

mutableprotectedinherited

Redshift factor at North pole.

Definition at line 1644 of file etoile.h.

◆ par_frot

Tbl Lorene::Et_rot_diff::par_frot

protected

Parameters of the function $F(\Omega)$ .

To be used as the second argument of functions frot and primfrot . The parameter par_frot(0) must always be the central angular velocity.

Definition at line 105 of file et_rot_diff.h.

◆ press

Tenseur Lorene::Etoile::press

protectedinherited

Fluid pressure.

Definition at line 464 of file etoile.h.

◆ prim_field

Tenseur Lorene::Et_rot_diff::prim_field

protected

Field $\int_{\Omega_{\rm c}}^\Omega F(\Omega') \, d\Omega'$ .

Definition at line 114 of file et_rot_diff.h.

◆ primfrot

double(* Lorene::Et_rot_diff::primfrot) (double, const Tbl &)

protected

Primitive of the function $F(\Omega)$ , which vanishes at the stellar center.

The first argument of primfrot must be $\Omega$ ; the second argument contains the parameters, the first of which being necessarily the central value of $\Omega$ .

Definition at line 96 of file et_rot_diff.h.

◆ relativistic

bool Lorene::Etoile::relativistic

protectedinherited

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

Definition at line 440 of file etoile.h.

◆ s_euler

Tenseur Lorene::Etoile::s_euler

protectedinherited

Trace of the stress tensor in the Eulerian frame.

Definition at line 471 of file etoile.h.

◆ shift

Tenseur Lorene::Etoile::shift

protectedinherited

Total shift vector.

Definition at line 515 of file etoile.h.

◆ ssjm1_dzeta

Cmp Lorene::Etoile_rot::ssjm1_dzeta

protectedinherited

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

Definition at line 1606 of file etoile.h.

◆ ssjm1_khi

Cmp Lorene::Etoile_rot::ssjm1_khi

protectedinherited

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 1619 of file etoile.h.

◆ ssjm1_nuf

Cmp Lorene::Etoile_rot::ssjm1_nuf

protectedinherited

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

Definition at line 1595 of file etoile.h.

◆ ssjm1_nuq

Cmp Lorene::Etoile_rot::ssjm1_nuq

protectedinherited

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

Definition at line 1601 of file etoile.h.

◆ ssjm1_tggg

Cmp Lorene::Etoile_rot::ssjm1_tggg

protectedinherited

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

Definition at line 1611 of file etoile.h.

◆ ssjm1_wshift

Tenseur Lorene::Etoile_rot::ssjm1_wshift

protectedinherited

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 1628 of file etoile.h.

◆ tggg

Tenseur Lorene::Etoile_rot::tggg

protectedinherited

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

Definition at line 1540 of file etoile.h.

◆ tkij

Tenseur_sym Lorene::Etoile_rot::tkij

protectedinherited

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 1570 of file etoile.h.

◆ tnphi

Tenseur Lorene::Etoile_rot::tnphi

protectedinherited

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

Definition at line 1518 of file etoile.h.

◆ u_euler

Tenseur Lorene::Etoile::u_euler

protectedinherited

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 477 of file etoile.h.

◆ unsurc2

double Lorene::Etoile::unsurc2

protectedinherited

$1/c^2$ : unsurc2=1 for a relativistic star, 0 for a Newtonian one.

Definition at line 445 of file etoile.h.

◆ uuu

Tenseur Lorene::Etoile_rot::uuu

protectedinherited

Norm of u_euler.

Definition at line 1521 of file etoile.h.

◆ w_shift

Tenseur Lorene::Etoile_rot::w_shift

protectedinherited

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 1553 of file etoile.h.

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Et_rot_diff() [1/3]

◆ Et_rot_diff() [2/3]

◆ Et_rot_diff() [3/3]

◆ ~Et_rot_diff()

Member Function Documentation

◆ angu_mom()

◆ aplat()

◆ area()

◆ del_deriv()

◆ del_hydro_euler()

◆ display_poly()

◆ equation_of_state()

◆ equil_spher_falloff()

◆ equil_spher_regular()

◆ equilibrium()

◆ equilibrium_spher()

◆ espec_isco()

◆ extrinsic_curvature()

◆ f_eccentric()

◆ f_eq()

◆ f_isco()

◆ fait_nphi()

◆ fait_omega_field()

◆ fait_prim_field()

◆ fait_shift()

◆ funct_omega()

◆ get_a_car()

◆ get_ak_car()

◆ get_b_car()

◆ get_bbb()

◆ get_beta_auto()

◆ get_d_logn_auto_div()

◆ get_dzeta()

◆ get_ener()

◆ get_ener_euler()

◆ get_ent()

◆ get_eos()

◆ get_gam_euler()

◆ get_khi_shift()

◆ get_logn()

◆ get_logn_auto()

◆ get_logn_auto_div()

◆ get_logn_auto_regu()

◆ get_mp()

◆ get_nbar()

◆ get_nnn()

◆ get_nphi()

◆ get_nuf()

◆ get_nuq()

◆ get_nzet()

◆ get_omega_c()

◆ get_omega_field()

◆ get_press()

◆ get_s_euler()

◆ get_shift()

◆ get_tggg()

◆ get_tkij()

◆ get_tnphi()

◆ get_u_euler()

◆ get_uuu()

◆ get_w_shift()

◆ grv2()

◆ grv3()

◆ hydro_euler()

◆ is_relativistic()

◆ l_surf()

◆ lambda_grv2()

◆ lspec_isco()

◆ mass_b()

◆ mass_g()

◆ mean_radius()

◆ mom_quad()

◆ mom_quad_Bo()

◆ mom_quad_old()