Class for two-fluid rotating relativistic stars. More...

#include <et_rot_bifluid.h>

Inheritance diagram for Lorene::Et_rot_bifluid:

Public Member Functions
	Et_rot_bifluid (Map &mp_i, int nzet_i, bool relat, const Eos_bifluid &eos_i)
	Standard constructor.
	Et_rot_bifluid (const Et_rot_bifluid &)
	Copy constructor.
	Et_rot_bifluid (Map &mp_i, const Eos_bifluid &eos_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ) Works only for relativistic stars.
virtual	~Et_rot_bifluid ()
	Destructor.
void	operator= (const Et_rot_bifluid &)
	Assignment to another Et_rot_bifluid.
void	set_enthalpies (const Cmp &, const Cmp &)
	Sets both enthalpy profiles.
void	equilibrium_spher_bi (double ent_c, double ent_c2, double precis=1.e-14)
	Computes a spherical static configuration.
void	equil_spher_regular (double ent_c, double ent_c2, double precis=1.e-14)
	Computes a spherical static configuration.
const Eos_bifluid &	get_eos () const
	Returns the equation of state.
const Tenseur &	get_ent2 () const
	Returns the enthalpy field for fluid 2.
const Tenseur &	get_nbar2 () const
	Returns the proper baryon density for fluid 2.
const Tenseur &	get_K_nn () const
	Returns the coefficient $K_{nn}$ .
const Tenseur &	get_K_np () const
	Returns the coefficient $K_{np}$ .
const Tenseur &	get_K_pp () const
	Returns the coefficient $K_{pp}$ .
const Tenseur &	get_alpha_eos () const
	Returns the coefficient $\alpha$ (entrainment parameter).
const Tenseur &	get_delta_car () const
	Returns the "relative velocity" (squared) $\Delta^2$ of the two fluids.
const Tenseur &	get_gam_euler2 () const
	Returns the Lorentz factor between the fluid 2 and Eulerian observers.
double	get_omega2 () const
	Returns the rotation angular velocity of fluid 2([f_unit] ).
const Tenseur &	get_uuu2 () const
	Returns the norm of the fluid 2 3-velocity with respect to the eulerian frame.
virtual void	sauve (FILE *) const
	Save in a file.
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.
virtual const Itbl &	l_surf () const
	Description of the surface of fluid 1: returns a 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
const Itbl &	l_surf2 () const
	Description of the surface of fluid 2: returns a 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
const Tbl &	xi_surf2 () const
	Description of the surface of fluid 2: returns a 2-D `Tbl` containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .
double	ray_eq2 () const
	Coordinate radius for fluid 2 at $\phi=0$ , $\theta=\pi/2$ [r_unit].
double	ray_eq2_pis2 () const
	Coordinate radius for fluid 2 at $\phi=\pi/2$ , $\theta=\pi/2$ [r_unit].
double	ray_eq2_pi () const
	Coordinate radius for fluid 2 at $\phi=\pi$ , $\theta=\pi/2$ [r_unit].
double	ray_pole2 () const
	Coordinate radius for fluid 2 at $\theta=0$ [r_unit].
double	mass_b1 () const
	Baryon mass of fluid 1.
double	mass_b2 () const
	Baryon mass of fluid 2.
virtual double	mass_b () const
	Total Baryon mass.
virtual double	mass_g () const
	Gravitational mass.
virtual double	angu_mom () const
	Angular momentum.
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_circ2 () const
	Circumferential radius for fluid 2.
virtual double	area2 () const
	Surface area for fluid 2.
virtual double	mean_radius2 () const
	Mean radius for fluid 2.
virtual double	aplat2 () const
	Flatening r_pole/r_eq for fluid 2.
virtual double	mom_quad () const
	Quadrupole moment.
virtual double	mom_quad_old () const
	Part of the quadrupole moment.
virtual double	mom_quad_Bo () const
	Part of the quadrupole moment.
virtual double	angu_mom_1 () const
	Angular momentum of fluid 1.
virtual double	angu_mom_2 () const
	Angular momentum of fluid 2.
virtual double	coupling_mominert_1 () const
	Quantities used to study the different fluid couplings: $\tilde{I}_X$ , $\tilde{\varepsilon}_X\tilde{I}_X$ and $\tilde{\omega}_X\tilde{I}_X$ .
virtual double	coupling_mominert_2 () const
virtual double	coupling_entr () const
virtual double	coupling_LT_1 () const
virtual double	coupling_LT_2 () const
virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
virtual void	equation_of_state ()
	Computes the proper baryon and energy densities, as well as pressure and the coefficients Knn, Knp and Kpp, from the enthalpies and both velocities.
void	equilibrium_bi (double ent_c, double ent_c2, double omega0, double omega20, const Tbl &ent_limit, const Tbl &ent2_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, int mer_mass, double mbar1_wanted, double mbar2_wanted, double aexp_mass)
	Computes an equilibrium configuration.
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	display_poly (ostream &) const
	Display in polytropic units.
virtual double	tsw () const
	Ratio T/W.
virtual double	r_circ () const
	Circumferential equatorial radius.
virtual double	r_circ_merid () const
	Circumferential meridional radius.
virtual double	area () const
	Surface area.
virtual double	mean_radius () const
	Mean 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	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.
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	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 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.

Protected Attributes
const Eos_bifluid &	eos
	Equation of state for two-fluids model.
double	omega2
	Rotation angular velocity for fluid 2 ([f_unit] ).
Tenseur	ent2
	Log-enthalpy for the second fluid.
Tenseur	nbar2
	Baryon density in the fluid frame, for fluid 2.
Tenseur	K_nn
	Coefficient $K_{nn}$ .
Tenseur	K_np
	Coefficient $K_{np}$ .
Tenseur	K_pp
	Coefficient $K_{pp}$ .
Tenseur	alpha_eos
	Coefficient $\alpha$ relative to entrainment effects.
Tenseur	sphph_euler
	The component $S^\varphi_\varphi$ of the stress tensor ${S^i}_j$ .
Tenseur	j_euler
	Total angular momentum (flat-space!) 3-vector $J_\mathrm{euler}$ , which is related to of the "3+1" decomposition, but expressed in a flat-space triad.
Tenseur	j_euler1
	To compute .
Tenseur	j_euler2
	To compute .
Tenseur	enerps_euler
	the combination : useful because in the Newtonian limit $\rightarrow \rho$ .
Tenseur	uuu2
	Norm of the (fluid no.2) 3-velocity with respect to the eulerian observer.
Tenseur	gam_euler2
	Lorentz factor between the fluid 2 and Eulerian observers.
Tenseur	delta_car
	The "relative velocity" (squared) $\Delta^2$ of the two fluids.
double *	p_ray_eq2
	Coordinate radius at $\phi=0$ , $\theta=\pi/2$ .
double *	p_ray_eq2_pis2
	Coordinate radius at $\phi=\pi/2$ , $\theta=\pi/2$ .
double *	p_ray_eq2_pi
	Coordinate radius at $\phi=\pi$ , $\theta=\pi/2$ .
double *	p_ray_pole2
	Coordinate radius at $\theta=0$ .
Itbl *	p_l_surf2
	Description of the surface of fluid 2: 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
Tbl *	p_xi_surf2
	Description of the surface of fluid 2: 2-D `Tbl` containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .
double *	p_r_circ2
	Circumferential radius of fluid no.2.
double *	p_area2
	Surface area of fluid no.2.
double *	p_aplat2
	Flatening r_pole/r_eq of fluid no.2.
double *	p_mass_b1
	Baryon mass of fluid 1.
double *	p_mass_b2
	Baryon mass of fluid 2.
double *	p_angu_mom_1
	Angular momentum of fluid 1.
double *	p_angu_mom_2
	Angular momentum of fluid 2.
double *	p_coupling_mominert_1
	Quantities used to describe the different couplings between the fluids.
double *	p_coupling_mominert_2
	$\tilde{I}_p$
double *	p_coupling_entr
	$\tilde{\varepsilon}_n\tilde{I}_n = \tilde{\varepsilon}_p\tilde{I}_p$
double *	p_coupling_LT_1
	$\tilde{\omega}_n\tilde{I}_n$
double *	p_coupling_LT_2
	$\tilde{\omega}_p\tilde{I}_p$
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 equatorial radius.
double *	p_r_circ_merid
	Circumferential meridional radius.
double *	p_area
	Surface area.
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_mom_quad_old
	Part of the quadrupole moment.
double *	p_mom_quad_Bo
	Part of the 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` .
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.

Detailed Description

Class for two-fluid rotating relativistic stars.

()

This is a child class of Etoile_rot , with the same metric and overloaded member functions.

There are two number-density fields nbar and nbar2
(and 2 log-enthalpies, see class Eos_bifluid ), as well as two velocity fields, with phi-components (with respect to the Eulerian observer) uuu and uuu2 .

Fluid 1 can be considered to correspond to the (superfluid) neutrons, whereas fluid 2 would consist of the protons (and electrons) The quantity u_euler of the class Etoile is not used in this class! Only the "3+1" components of ${T^\mu}_\nu$ should be used outside of hydro_euler() , namely s_euler, sphph_euler, j_euler and ener_euler.

Definition at line 150 of file et_rot_bifluid.h.

Constructor & Destructor Documentation

◆ Et_rot_bifluid() [1/3]

Lorene::Et_rot_bifluid::Et_rot_bifluid	(	Map &	mp_i,
		int	nzet_i,
		bool	relat,
		const Eos_bifluid &	eos_i )

Standard constructor.

Definition at line 128 of file et_rot_bifluid.C.

References alpha_eos, delta_car, enerps_euler, ent2, eos, Lorene::Etoile_rot::Etoile_rot(), Lorene::Etoile::gam_euler, gam_euler2, Lorene::get_bvect_cart(), j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, Lorene::Map(), Lorene::Etoile::mp, nbar2, omega2, set_der_0x0(), sphph_euler, and uuu2.

◆ Et_rot_bifluid() [2/3]

Lorene::Et_rot_bifluid::Et_rot_bifluid ( const Et_rot_bifluid & et )

Copy constructor.

Definition at line 174 of file et_rot_bifluid.C.

References alpha_eos, delta_car, enerps_euler, ent2, eos, Et_rot_bifluid(), Lorene::Etoile_rot::Etoile_rot(), gam_euler2, j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, nbar2, omega2, set_der_0x0(), sphph_euler, and uuu2.

◆ Et_rot_bifluid() [3/3]

Lorene::Et_rot_bifluid::Et_rot_bifluid	(	Map &	mp_i,
		const Eos_bifluid &	eos_i,
		FILE *	fich )

Constructor from a file (see sauve(FILE*) ) Works only for relativistic stars.

This has to be improved....

Definition at line 201 of file et_rot_bifluid.C.

References alpha_eos, delta_car, enerps_euler, ent2, eos, Lorene::Etoile_rot::Etoile_rot(), Lorene::fread_be(), gam_euler2, Lorene::get_bvect_cart(), j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, Lorene::Map(), Lorene::Etoile::mp, nbar2, omega2, set_der_0x0(), sphph_euler, and uuu2.

◆ ~Et_rot_bifluid()

Lorene::Et_rot_bifluid::~Et_rot_bifluid ( )

virtual

Destructor.

Definition at line 247 of file et_rot_bifluid.C.

References del_deriv().

Member Function Documentation

◆ angu_mom()

double Lorene::Et_rot_bifluid::angu_mom ( ) const

virtual

Angular momentum.

Reimplemented from Lorene::Etoile_rot.

Definition at line 196 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Tenseur::change_triad(), Lorene::Cmp::integrale(), j_euler, Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile_rot::p_angu_mom, and Lorene::Cmp::std_base_scal().

◆ angu_mom_1()

double Lorene::Et_rot_bifluid::angu_mom_1 ( ) const

virtual

Angular momentum of fluid 1.

Definition at line 222 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Tenseur::change_triad(), Lorene::Cmp::integrale(), j_euler1, Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), p_angu_mom_1, and Lorene::Cmp::std_base_scal().

◆ angu_mom_2()

double Lorene::Et_rot_bifluid::angu_mom_2 ( ) const

virtual

Angular momentum of fluid 2.

Definition at line 247 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Tenseur::change_triad(), Lorene::Cmp::integrale(), j_euler2, Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), p_angu_mom_2, and Lorene::Cmp::std_base_scal().

◆ aplat()

double Lorene::Etoile_rot::aplat ( ) const

virtualinherited

Flatening r_pole/r_eq.

Definition at line 554 of file et_rot_global.C.

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

◆ aplat2()

double Lorene::Et_rot_bifluid::aplat2 ( ) const

virtual

Flatening r_pole/r_eq for fluid 2.

Definition at line 559 of file et_bfrot_global.C.

References p_aplat2, ray_eq2(), and ray_pole2().

◆ area()

double Lorene::Etoile_rot::area ( ) const

virtualinherited

◆ area2()

double Lorene::Et_rot_bifluid::area2 ( ) const

virtual

Surface area for fluid 2.

Definition at line 577 of file et_bfrot_global.C.

References Lorene::Valeur::annule_hard(), Lorene::Valeur::c_cf, Lorene::Valeur::dsdt(), Lorene::Etoile::get_a_car(), Lorene::Mg3d::get_angu(), Lorene::Etoile_rot::get_bbb(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), l_surf2(), Lorene::Etoile::mp, Lorene::Valeur::mult_st(), p_area2, Lorene::Valeur::set(), Lorene::sqrt(), Lorene::Valeur::std_base_scal(), Lorene::Cmp::va, Lorene::Valeur::val_point_jk(), Lorene::Map_radial::val_r_jk(), and xi_surf2().

◆ coupling_entr()

double Lorene::Et_rot_bifluid::coupling_entr ( ) const

virtual

Definition at line 334 of file et_bfrot_global.C.

◆ coupling_LT_1()

double Lorene::Et_rot_bifluid::coupling_LT_1 ( ) const

virtual

Definition at line 357 of file et_bfrot_global.C.

◆ coupling_LT_2()

double Lorene::Et_rot_bifluid::coupling_LT_2 ( ) const

virtual

Definition at line 383 of file et_bfrot_global.C.

◆ coupling_mominert_1()

double Lorene::Et_rot_bifluid::coupling_mominert_1 ( ) const

virtual

Quantities used to study the different fluid couplings: $\tilde{I}_X$ , $\tilde{\varepsilon}_X\tilde{I}_X$ and $\tilde{\omega}_X\tilde{I}_X$ .

These terms are defined in Eqs. (C5) - (C7) of Sourie et al., MNRAS 464 , 4641-4657 (2017). Note that these quantities only make sense in the slow-rotation approximation and to first order in the lag.

Definition at line 282 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Etoile::ent, eos, Lorene::exp(), Lorene::Cmp::integrale(), Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile::nbar, Lorene::Etoile::nnn, p_coupling_mominert_1, Lorene::Tenseur::set_std_base(), Lorene::Cmp::std_base_scal(), and Lorene::Etoile::unsurc2.

◆ coupling_mominert_2()

double Lorene::Et_rot_bifluid::coupling_mominert_2 ( ) const

virtual

Definition at line 308 of file et_bfrot_global.C.

◆ del_deriv()

void Lorene::Et_rot_bifluid::del_deriv ( ) const

protectedvirtual

Deletes all the derived quantities.

Reimplemented from Lorene::Etoile_rot.

Definition at line 257 of file et_rot_bifluid.C.

References Lorene::Etoile_rot::del_deriv(), p_angu_mom_1, p_angu_mom_2, p_aplat2, p_area2, p_coupling_entr, p_coupling_LT_1, p_coupling_LT_2, p_coupling_mominert_1, p_coupling_mominert_2, p_l_surf2, p_mass_b1, p_mass_b2, p_r_circ2, p_ray_eq2, p_ray_eq2_pi, p_ray_eq2_pis2, p_ray_pole2, p_xi_surf2, and set_der_0x0().

◆ del_hydro_euler()

void Lorene::Et_rot_bifluid::del_hydro_euler ( )

protectedvirtual

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 311 of file et_rot_bifluid.C.

References alpha_eos, del_deriv(), Lorene::Etoile_rot::del_hydro_euler(), delta_car, enerps_euler, gam_euler2, j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, sphph_euler, and uuu2.

◆ display_poly()

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

virtualinherited

Display in polytropic units.

Reimplemented in Lorene::Et_rot_diff.

Definition at line 708 of file etoile_rot.C.

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

◆ equation_of_state()

void Lorene::Et_rot_bifluid::equation_of_state ( )

virtual

Computes the proper baryon and energy densities, as well as pressure and the coefficients Knn, Knp and Kpp, from the enthalpies and both velocities.

Reimplemented from Lorene::Etoile.

Definition at line 639 of file et_rot_bifluid.C.

References Lorene::Cmp::allocate_all(), alpha_eos, Lorene::Eos_bf_tabul::calcule_interpol(), del_deriv(), delta_car, Lorene::Etoile::ener, Lorene::Etoile::ent, ent2, eos, Lorene::Mg3d::get_grille3d(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), K_nn, K_np, K_pp, Lorene::Etoile::mp, Lorene::Etoile::nbar, nbar2, Lorene::Etoile::nzet, Lorene::pow(), Lorene::Etoile::press, Lorene::Cmp::set(), Lorene::Mtbl::set(), Lorene::Mtbl::set_etat_qcq(), Lorene::Tbl::set_etat_qcq(), Lorene::Cmp::std_base_scal(), Lorene::Mtbl::t, Lorene::Etoile::unsurc2, 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.

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

◆ equil_spher_regular() [1/2]

void Lorene::Et_rot_bifluid::equil_spher_regular	(	double	ent_c,
		double	ent_c2,
		double	precis = 1.e-14 )

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 1
ent_c2	[input] central value of the enthalpy 2
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)

◆ equil_spher_regular() [2/2]

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

◆ equilibrium()

void Lorene::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 )

virtualinherited

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, = 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 Lorene::Et_rot_diff.

Definition at line 150 of file et_rot_equilibrium.C.

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

◆ equilibrium_bi()

void Lorene::Et_rot_bifluid::equilibrium_bi	(	double	ent_c,
		double	ent_c2,
		double	omega0,
		double	omega20,
		const Tbl &	ent_limit,
		const Tbl &	ent2_limit,
		const Itbl &	icontrol,
		const Tbl &	control,
		Tbl &	diff,
		int	mer_mass,
		double	mbar1_wanted,
		double	mbar2_wanted,
		double	aexp_mass )

Computes an equilibrium configuration.

Parameters

ent_c	[input] Central enthalpy for fluid 1
ent_c2	[input] Central enthalpy for fluid 2
omega0	[input] Requested angular velocity for fluid 1
omega20	[input] Requested angular velocity for fluid 2
ent_limit	[input] 1-D `Tbl` of dimension `nzet` which defines the enthalpy for fluid 1 at the outer boundary of each domain
ent2_limit	[input] 1-D `Tbl` of dimension `nzet` which defines the enthalpy for fluid 2 at the outer boundary of each domain
icontrol	[input] Set of integer parameters (stored as a 1-D `Itbl` of size 5) 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)` = mermax_poisson : maximum number of steps in `Map_et::poisson`
control	[input] Set of parameters (stored as a 1-D `Tbl` of size 5) 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)` = omega2_ini : initial angular velocity, switched on only if `mer_rot` < 0 , otherwise 0 is used `control(3)` = relax : relaxation factor in the main iteration `control(4)` = relax_poisson : relaxation factor in `Map_et::poisson`
diff	[output] 1-D `Tbl` of size 8 for the storage of some error indicators : `diff(0)` : Relative change in the enthalpy field 1 between two successive steps `diff(1)` : Relative change in the enthalpy field 2 between two successive steps `diff(2)` : Relative error in the resolution of the Poisson equation for `nuf` `diff(3)` : Relative error in the resolution of the Poisson equation for `nuq` `diff(4)` : Relative error in the resolution of the Poisson equation for `dzeta` `diff(5)` : Relative error in the resolution of the Poisson equation for `tggg` `diff(6)` : Relative error in the resolution of the equation for `shift` (x comp.) `diff(7)` : Relative error in the resolution of the equation for `shift` (y comp.)

Definition at line 140 of file et_bfrot_equilibre.C.

◆ 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.

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

◆ equilibrium_spher_bi()

void Lorene::Et_rot_bifluid::equilibrium_spher_bi	(	double	ent_c,
		double	ent_c2,
		double	precis = 1.e-14 )

Computes a spherical static configuration.

Parameters

ent_c	[input] central value of the enthalpy 1
ent_c2	[input] central value of the enthalpy 2
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)

◆ 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 p_espec_isco, and 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 ak_car, b_car, Lorene::contract(), Lorene::Cmp::get_etat(), Lorene::Tenseur::get_etat(), Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile::nnn, nphi, Lorene::Etoile::shift, tkij, and Lorene::Cmp::va.

◆ 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(), bbb, Lorene::Cmp::dsdr(), Lorene::Etoile::mp, Lorene::Etoile::nnn, nphi, Lorene::Etoile::nzet, p_f_isco, p_r_isco, Lorene::r, Lorene::Etoile::ray_eq(), Lorene::sqrt(), Lorene::Cmp::std_base_scal(), Lorene::Cmp::va, and Lorene::Valeur::val_point().

◆ 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 p_f_eq, and 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 p_f_isco, and 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::Etoile::mp, nphi, Lorene::Etoile::shift, and tnphi.

◆ 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::dec2_dzpuis(), Lorene::Tenseur::dec_dzpuis(), Lorene::Tenseur::get_etat(), khi_shift, Lorene::Etoile::mp, Lorene::Etoile::shift, Lorene::skxk(), and w_shift.

◆ 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 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 ak_car.

◆ get_alpha_eos()

const Tenseur & Lorene::Et_rot_bifluid::get_alpha_eos ( ) const

inline

Returns the coefficient $\alpha$ (entrainment parameter).

Definition at line 340 of file et_rot_bifluid.h.

References alpha_eos.

◆ 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 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 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 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 d_logn_auto_div.

◆ get_delta_car()

const Tenseur & Lorene::Et_rot_bifluid::get_delta_car ( ) const

inline

Returns the "relative velocity" (squared) $\Delta^2$ of the two fluids.

Definition at line 343 of file et_rot_bifluid.h.

References delta_car.

◆ 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 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 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 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 ent.

◆ get_ent2()

const Tenseur & Lorene::Et_rot_bifluid::get_ent2 ( ) const

inline

Returns the enthalpy field for fluid 2.

Definition at line 325 of file et_rot_bifluid.h.

References ent2.

◆ get_eos()

const Eos_bifluid & Lorene::Et_rot_bifluid::get_eos ( ) const

inline

Returns the equation of state.

Definition at line 322 of file et_rot_bifluid.h.

References 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 gam_euler.

◆ get_gam_euler2()

const Tenseur & Lorene::Et_rot_bifluid::get_gam_euler2 ( ) const

inline

Returns the Lorentz factor between the fluid 2 and Eulerian observers.

Definition at line 346 of file et_rot_bifluid.h.

References gam_euler2.

◆ get_K_nn()

const Tenseur & Lorene::Et_rot_bifluid::get_K_nn ( ) const

inline

Returns the coefficient $K_{nn}$ .

Definition at line 331 of file et_rot_bifluid.h.

References K_nn.

◆ get_K_np()

const Tenseur & Lorene::Et_rot_bifluid::get_K_np ( ) const

inline

Returns the coefficient $K_{np}$ .

Definition at line 334 of file et_rot_bifluid.h.

References K_np.

◆ get_K_pp()

const Tenseur & Lorene::Et_rot_bifluid::get_K_pp ( ) const

inline

Returns the coefficient $K_{pp}$ .

Definition at line 337 of file et_rot_bifluid.h.

References K_pp.

◆ 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 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 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 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 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 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::Map(), and 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 nbar.

◆ get_nbar2()

const Tenseur & Lorene::Et_rot_bifluid::get_nbar2 ( ) const

inline

Returns the proper baryon density for fluid 2.

Definition at line 328 of file et_rot_bifluid.h.

References nbar2.

◆ 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 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 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 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 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 nzet.

◆ get_omega2()

double Lorene::Et_rot_bifluid::get_omega2 ( ) const

inline

Returns the rotation angular velocity of fluid 2([f_unit] ).

Definition at line 349 of file et_rot_bifluid.h.

References omega2.

◆ get_omega_c()

double Lorene::Etoile_rot::get_omega_c ( ) const

virtualinherited

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

Reimplemented in Lorene::Et_rot_diff.

Definition at line 698 of file etoile_rot.C.

References omega.

◆ get_press()

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

inlineinherited

Returns the fluid pressure.

Definition at line 685 of file etoile.h.

References 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 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 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 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 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 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 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 uuu.

◆ get_uuu2()

const Tenseur & Lorene::Et_rot_bifluid::get_uuu2 ( ) const

inline

Returns the norm of the fluid 2 3-velocity with respect to the eulerian frame.

Definition at line 352 of file et_rot_bifluid.h.

References uuu2.

◆ 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 w_shift.

◆ grv2()

double Lorene::Et_rot_bifluid::grv2 ( ) const

virtual

Error on the virial identity GRV2.

Given by the integral Eq. (4.6) in [Bonazzola, Gougoulhon, Salgado, Marck, A&A 278 , 421 (1993)].

Reimplemented from Lorene::Etoile_rot.

Definition at line 412 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::ak_car, Lorene::flat_scalar_prod(), Lorene::Etoile_rot::lambda_grv2(), Lorene::Etoile_rot::logn, Lorene::Etoile::mp, Lorene::Etoile_rot::p_grv2, and sphph_euler.

◆ grv3()

double Lorene::Et_rot_bifluid::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 from Lorene::Etoile_rot.

Definition at line 437 of file et_bfrot_global.C.

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

◆ hydro_euler()

void Lorene::Et_rot_bifluid::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 , ent2 , ener , press , K_nn , K_np , K_pp and a_car, which are supposed to be up to date. From these,
the following fields are updated: delta_car , gam_euler , gam_euler2 , ener_euler , s_euler , sphph_euler and j_euler .

Reimplemented from Lorene::Etoile_rot.

Definition at line 735 of file et_rot_bifluid.C.

References Lorene::Etoile_rot::bbb, del_deriv(), delta_car, Lorene::Etoile::ener_euler, enerps_euler, Lorene::Etoile::ent, eos, Lorene::Etoile::gam_euler, gam_euler2, Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, Lorene::Etoile::mp, Lorene::Etoile::nbar, nbar2, Lorene::Etoile::nnn, Lorene::Etoile_rot::nphi, Lorene::Etoile::nzet, Lorene::Etoile_rot::omega, omega2, Lorene::Etoile::press, Lorene::Etoile::relativistic, Lorene::Etoile::s_euler, Lorene::Tenseur::set_std_base(), sphph_euler, Lorene::sqrt(), Lorene::Etoile::u_euler, Lorene::Etoile::unsurc2, Lorene::Etoile_rot::uuu, and uuu2.

◆ 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 relativistic.

◆ l_surf()

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

virtual

Description of the surface of fluid 1: returns a 2-D Itbl
containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .

This surface is defined as the location where the density 1 (member nbar ) vanishes.

Reimplemented from Lorene::Etoile_rot.

Definition at line 752 of file et_bfrot_global.C.

References Lorene::Cmp::annule(), Lorene::Etoile::mp, Lorene::Etoile::nbar, Lorene::Etoile::nzet, Lorene::Etoile::p_l_surf, Lorene::Etoile::p_xi_surf, and Lorene::Cmp::va.

◆ l_surf2()

const Itbl & Lorene::Et_rot_bifluid::l_surf2 ( ) const

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

This surface is defined as the location where the density 2 (member nbar2 ) vanishes.

Definition at line 785 of file et_bfrot_global.C.

References Lorene::Cmp::annule(), Lorene::Etoile::mp, nbar2, Lorene::Etoile::nzet, p_l_surf2, p_xi_surf2, and Lorene::Cmp::va.

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

◆ 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 p_lspec_isco, and r_isco().

◆ mass_b()

double Lorene::Et_rot_bifluid::mass_b ( ) const

virtual

Total Baryon mass.

Reimplemented from Lorene::Etoile_rot.

Definition at line 154 of file et_bfrot_global.C.

References mass_b1(), mass_b2(), and Lorene::Etoile::p_mass_b.

◆ mass_b1()

double Lorene::Et_rot_bifluid::mass_b1 ( ) const

Baryon mass of fluid 1.

Definition at line 122 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::bbb, eos, Lorene::Etoile::gam_euler, Lorene::Cmp::integrale(), Lorene::Etoile::nbar, p_mass_b1, and Lorene::Cmp::std_base_scal().

◆ mass_b2()

double Lorene::Et_rot_bifluid::mass_b2 ( ) const

Baryon mass of fluid 2.

Definition at line 138 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::bbb, eos, gam_euler2, Lorene::Cmp::integrale(), nbar2, p_mass_b2, and Lorene::Cmp::std_base_scal().

◆ mass_g()

double Lorene::Et_rot_bifluid::mass_g ( ) const

virtual

Gravitational mass.

Reimplemented from Lorene::Etoile_rot.

Definition at line 168 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Tenseur::change_triad(), enerps_euler, Lorene::integrale(), j_euler, Lorene::Etoile::mp, Lorene::Etoile::nnn, Lorene::Etoile::p_mass_g, Lorene::Tenseur::set_std_base(), and Lorene::Etoile_rot::tnphi.

◆ mean_radius()

double Lorene::Etoile_rot::mean_radius ( ) const

virtualinherited

Mean radius.

Definition at line 530 of file et_rot_global.C.

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

◆ mean_radius2()

double Lorene::Et_rot_bifluid::mean_radius2 ( ) const

virtual

Mean radius for fluid 2.

Definition at line 631 of file et_bfrot_global.C.

References area2(), and Lorene::sqrt().

◆ mom_quad()

double Lorene::Et_rot_bifluid::mom_quad ( ) const

virtual

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 from Lorene::Etoile_rot.

Definition at line 644 of file et_bfrot_global.C.

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

◆ mom_quad_Bo()

double Lorene::Et_rot_bifluid::mom_quad_Bo ( ) const

virtual

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 from Lorene::Etoile_rot.

Definition at line 660 of file et_bfrot_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::Et_rot_bifluid::mom_quad_old ( ) const

virtual

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 from Lorene::Etoile_rot.

Definition at line 683 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::ak_car, Lorene::Etoile_rot::bbb, Lorene::Cmp::check_dzpuis(), enerps_euler, Lorene::flat_scalar_prod(), Lorene::Cmp::get_etat(), Lorene::Tenseur::gradient_spher(), Lorene::Cmp::inc2_dzpuis(), Lorene::integrale(), Lorene::log(), Lorene::Etoile_rot::logn, Lorene::Etoile::mp, Lorene::Valeur::mult_ct(), Lorene::Cmp::mult_r(), Lorene::Etoile::nbar, nbar2, Lorene::Etoile_rot::p_mom_quad_old, Lorene::Etoile::relativistic, Lorene::Tenseur::set(), Lorene::Tenseur::set_std_base(), and Lorene::Cmp::va.

◆ operator=()

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

Assignment to another Et_rot_bifluid.

Definition at line 352 of file et_rot_bifluid.C.

References alpha_eos, del_deriv(), delta_car, enerps_euler, ent2, eos, Et_rot_bifluid(), gam_euler2, j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, nbar2, omega2, Lorene::Etoile_rot::operator=(), sphph_euler, and uuu2.

◆ operator>>()

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

virtual

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 400 of file et_rot_bifluid.C.

◆ partial_display()

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

virtual

Printing of some informations, excluding all global quantities.

Reimplemented from Lorene::Etoile_rot.

Definition at line 573 of file et_rot_bifluid.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::aplat(), aplat2(), Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::dzeta, Lorene::Etoile::ener, Lorene::Etoile::ent, ent2, Lorene::Etoile_rot::logn, Lorene::Etoile::mp, Lorene::Etoile::nbar, nbar2, Lorene::Etoile::nnn, Lorene::Etoile_rot::nphi, Lorene::Etoile::nzet, Lorene::Etoile_rot::omega, omega2, Lorene::Etoile::press, Lorene::Etoile::ray_eq(), ray_eq2(), Lorene::Etoile_rot::uuu, and uuu2.

◆ r_circ()

double Lorene::Etoile_rot::r_circ ( ) const

virtualinherited

Circumferential equatorial radius.

Definition at line 399 of file et_rot_global.C.

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

◆ r_circ2()

double Lorene::Et_rot_bifluid::r_circ2 ( ) const

virtual

Circumferential radius for fluid 2.

Definition at line 534 of file et_bfrot_global.C.

References Lorene::Etoile_rot::bbb, Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nzet, p_r_circ2, and ray_eq2().

◆ 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::c_cf, Lorene::Valeur::coef(), Lorene::Valeur::dsdt(), Lorene::Etoile::get_a_car(), Lorene::Mg3d::get_angu(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), l_surf(), Lorene::Etoile::mp, p_r_circ_merid, Lorene::Valeur::set(), Lorene::sqrt(), Lorene::Valeur::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(), bbb, Lorene::Cmp::dsdr(), Lorene::Etoile::mp, Lorene::Etoile::nnn, nphi, Lorene::Etoile::nzet, p_espec_isco, p_f_eq, p_f_isco, p_lspec_isco, p_r_isco, Lorene::r, Lorene::Etoile::ray_eq(), Lorene::sqrt(), Lorene::Cmp::std_base_scal(), Lorene::Cmp::va, Lorene::Valeur::val_point(), 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::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf(), mp, p_ray_eq, Lorene::phi, and xi_surf().

◆ 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::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf(), mp, Lorene::phi, and xi_surf().

◆ ray_eq2()

double Lorene::Et_rot_bifluid::ray_eq2 ( ) const

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

Definition at line 837 of file et_bfrot_global.C.

References Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf2(), Lorene::Etoile::mp, p_ray_eq2, Lorene::phi, and xi_surf2().

◆ ray_eq2_pi()

double Lorene::Et_rot_bifluid::ray_eq2_pi ( ) const

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

Definition at line 928 of file et_bfrot_global.C.

References Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf2(), Lorene::Etoile::mp, p_ray_eq2_pi, Lorene::phi, ray_eq2(), and xi_surf2().

◆ ray_eq2_pis2()

double Lorene::Et_rot_bifluid::ray_eq2_pis2 ( ) const

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

Definition at line 871 of file et_bfrot_global.C.

References Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf2(), Lorene::Etoile::mp, p_ray_eq2_pis2, Lorene::phi, and xi_surf2().

◆ 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::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf(), mp, p_ray_eq_3pis2, Lorene::phi, ray_eq_pis2(), and xi_surf().

◆ 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::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf(), mp, p_ray_eq_pi, Lorene::phi, ray_eq(), and xi_surf().

◆ 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::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_p(), Lorene::Mg3d::get_type_t(), l_surf(), mp, p_ray_eq_pis2, Lorene::phi, and xi_surf().

◆ 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::Mg3d::get_type_t(), l_surf(), mp, p_ray_pole, Lorene::phi, and xi_surf().

◆ ray_pole2()

double Lorene::Et_rot_bifluid::ray_pole2 ( ) const

Coordinate radius for fluid 2 at $\theta=0$ [r_unit].

Definition at line 977 of file et_bfrot_global.C.

References l_surf2(), Lorene::Etoile::mp, p_ray_pole2, Lorene::phi, and xi_surf2().

◆ sauve()

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

virtual

Save in a file.

Reimplemented from Lorene::Etoile_rot.

Definition at line 386 of file et_rot_bifluid.C.

References ent2, Lorene::fwrite_be(), omega2, and Lorene::Etoile_rot::sauve().

◆ set_der_0x0()

void Lorene::Et_rot_bifluid::set_der_0x0 ( ) const

protectedvirtual

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Etoile_rot.

Definition at line 286 of file et_rot_bifluid.C.

References p_angu_mom_1, p_angu_mom_2, p_aplat2, p_area2, p_coupling_entr, p_coupling_LT_1, p_coupling_LT_2, p_coupling_mominert_1, p_coupling_mominert_2, p_l_surf2, p_mass_b1, p_mass_b2, p_r_circ2, p_ray_eq2, p_ray_eq2_pi, p_ray_eq2_pis2, p_ray_pole2, p_xi_surf2, and Lorene::Etoile_rot::set_der_0x0().

◆ set_enthalpies()

void Lorene::Et_rot_bifluid::set_enthalpies	(	const Cmp &	ent_i,
		const Cmp &	ent2_i )

Sets both enthalpy profiles.

Definition at line 332 of file et_rot_bifluid.C.

References del_deriv(), Lorene::Etoile::ent, ent2, and equation_of_state().

◆ 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 del_deriv(), ent, and 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::Map(), and mp.

◆ tsw()

double Lorene::Etoile_rot::tsw ( ) const

virtualinherited

Ratio T/W.

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

Definition at line 229 of file et_rot_global.C.

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

◆ 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, b_car, bbb, del_deriv(), Lorene::Cmp::div_rsint(), dzeta, Lorene::exp(), extrinsic_curvature(), logn, Lorene::Etoile::nnn, 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 l_surf(), p_l_surf, and p_xi_surf.

◆ xi_surf2()

const Tbl & Lorene::Et_rot_bifluid::xi_surf2 ( ) const

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

This surface is defined as the location where the density 2 (member nbar2 ) vanishes.

Definition at line 819 of file et_bfrot_global.C.

References l_surf2(), p_l_surf2, and p_xi_surf2.

◆ 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::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nnn, nphi, Lorene::Etoile::nzet, p_z_eqb, r_circ(), Lorene::sqrt(), and uuu.

◆ 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::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_type_t(), Lorene::Etoile::mp, Lorene::Etoile::nnn, nphi, Lorene::Etoile::nzet, p_z_eqf, r_circ(), Lorene::sqrt(), and uuu.

◆ 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, 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.

◆ alpha_eos

Tenseur Lorene::Et_rot_bifluid::alpha_eos

protected

Coefficient $\alpha$ relative to entrainment effects.

Definition at line 170 of file et_rot_bifluid.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.

◆ delta_car

Tenseur Lorene::Et_rot_bifluid::delta_car

protected

The "relative velocity" (squared) $\Delta^2$ of the two fluids.

See Prix et al.(2003) and see also Eos_bifluid .

Definition at line 204 of file et_rot_bifluid.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.

◆ enerps_euler

Tenseur Lorene::Et_rot_bifluid::enerps_euler

protected

the combination $E+S_i^i$ : useful because in the Newtonian limit $\rightarrow \rho$ .

Definition at line 192 of file et_rot_bifluid.h.

◆ ent

Tenseur Lorene::Etoile::ent

protectedinherited

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

Definition at line 460 of file etoile.h.

◆ ent2

Tenseur Lorene::Et_rot_bifluid::ent2

protected

Log-enthalpy for the second fluid.

Definition at line 163 of file et_rot_bifluid.h.

◆ eos

const Eos_bifluid& Lorene::Et_rot_bifluid::eos

protected

Equation of state for two-fluids model.

Definition at line 155 of file et_rot_bifluid.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.

◆ gam_euler2

Tenseur Lorene::Et_rot_bifluid::gam_euler2

protected

Lorentz factor between the fluid 2 and Eulerian observers.

Definition at line 198 of file et_rot_bifluid.h.

◆ j_euler

Tenseur Lorene::Et_rot_bifluid::j_euler

protected

Total angular momentum (flat-space!) 3-vector $J_\mathrm{euler}$ , which is related to $J^i$ of the "3+1" decomposition, but expressed in a flat-space triad.

In axisymmetric circular cases, only $J_\mathrm{euler}(\varphi)=r \sin\theta\, J^\varphi$ is nonzero.

Definition at line 186 of file et_rot_bifluid.h.

◆ j_euler1

Tenseur Lorene::Et_rot_bifluid::j_euler1

protected

To compute $J_n$ .

Definition at line 188 of file et_rot_bifluid.h.

◆ j_euler2

Tenseur Lorene::Et_rot_bifluid::j_euler2

protected

To compute $J_p$ .

Definition at line 189 of file et_rot_bifluid.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.

◆ K_nn

Tenseur Lorene::Et_rot_bifluid::K_nn

protected

Coefficient $K_{nn}$ .

Definition at line 167 of file et_rot_bifluid.h.

◆ K_np

Tenseur Lorene::Et_rot_bifluid::K_np

protected

Coefficient $K_{np}$ .

Definition at line 168 of file et_rot_bifluid.h.

◆ K_pp

Tenseur Lorene::Et_rot_bifluid::K_pp

protected

Coefficient $K_{pp}$ .

Definition at line 169 of file et_rot_bifluid.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.

◆ nbar2

Tenseur Lorene::Et_rot_bifluid::nbar2

protected

Baryon density in the fluid frame, for fluid 2.

Definition at line 165 of file et_rot_bifluid.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.

◆ omega2

double Lorene::Et_rot_bifluid::omega2

protected

Rotation angular velocity for fluid 2 ([f_unit] ).

Definition at line 157 of file et_rot_bifluid.h.

◆ p_angu_mom

double* Lorene::Etoile_rot::p_angu_mom

mutableprotectedinherited

Angular momentum.

Definition at line 1634 of file etoile.h.

◆ p_angu_mom_1

double* Lorene::Et_rot_bifluid::p_angu_mom_1

mutableprotected

Angular momentum of fluid 1.

Definition at line 240 of file et_rot_bifluid.h.

◆ p_angu_mom_2

double* Lorene::Et_rot_bifluid::p_angu_mom_2

mutableprotected

Angular momentum of fluid 2.

Definition at line 241 of file et_rot_bifluid.h.

◆ p_aplat

double* Lorene::Etoile_rot::p_aplat

mutableprotectedinherited

Flatening r_pole/r_eq.

Definition at line 1641 of file etoile.h.

◆ p_aplat2

double* Lorene::Et_rot_bifluid::p_aplat2

mutableprotected

Flatening r_pole/r_eq of fluid no.2.

Definition at line 235 of file et_rot_bifluid.h.

◆ p_area

double* Lorene::Etoile_rot::p_area

mutableprotectedinherited

Surface area.

Definition at line 1640 of file etoile.h.

◆ p_area2

double* Lorene::Et_rot_bifluid::p_area2

mutableprotected

Surface area of fluid no.2.

Definition at line 234 of file et_rot_bifluid.h.

◆ p_coupling_entr

double* Lorene::Et_rot_bifluid::p_coupling_entr

mutableprotected

$\tilde{\varepsilon}_n\tilde{I}_n = \tilde{\varepsilon}_p\tilde{I}_p$

Definition at line 246 of file et_rot_bifluid.h.

◆ p_coupling_LT_1

double* Lorene::Et_rot_bifluid::p_coupling_LT_1

mutableprotected

$\tilde{\omega}_n\tilde{I}_n$

Definition at line 247 of file et_rot_bifluid.h.

◆ p_coupling_LT_2

double* Lorene::Et_rot_bifluid::p_coupling_LT_2

mutableprotected

$\tilde{\omega}_p\tilde{I}_p$

Definition at line 248 of file et_rot_bifluid.h.

◆ p_coupling_mominert_1

double* Lorene::Et_rot_bifluid::p_coupling_mominert_1

mutableprotected

Quantities used to describe the different couplings between the fluids.

$\tilde{I}_n$

Definition at line 244 of file et_rot_bifluid.h.

◆ p_coupling_mominert_2

double* Lorene::Et_rot_bifluid::p_coupling_mominert_2

mutableprotected

$\tilde{I}_p$

Definition at line 245 of file et_rot_bifluid.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_l_surf2

Itbl* Lorene::Et_rot_bifluid::p_l_surf2

mutableprotected

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

Definition at line 225 of file et_rot_bifluid.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_b1

double* Lorene::Et_rot_bifluid::p_mass_b1

mutableprotected

Baryon mass of fluid 1.

Definition at line 237 of file et_rot_bifluid.h.

◆ p_mass_b2

double* Lorene::Et_rot_bifluid::p_mass_b2

mutableprotected

Baryon mass of fluid 2.

Definition at line 238 of file et_rot_bifluid.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_circ2

double* Lorene::Et_rot_bifluid::p_r_circ2

mutableprotected

Circumferential radius of fluid no.2.

Definition at line 233 of file et_rot_bifluid.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_eq2

double* Lorene::Et_rot_bifluid::p_ray_eq2

mutableprotected

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

Definition at line 210 of file et_rot_bifluid.h.

◆ p_ray_eq2_pi

double* Lorene::Et_rot_bifluid::p_ray_eq2_pi

mutableprotected

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

Definition at line 216 of file et_rot_bifluid.h.

◆ p_ray_eq2_pis2

double* Lorene::Et_rot_bifluid::p_ray_eq2_pis2

mutableprotected

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

Definition at line 213 of file et_rot_bifluid.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_ray_pole2

double* Lorene::Et_rot_bifluid::p_ray_pole2

mutableprotected

Coordinate radius at $\theta=0$ .

Definition at line 219 of file et_rot_bifluid.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_xi_surf2

Tbl* Lorene::Et_rot_bifluid::p_xi_surf2

mutableprotected

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

Definition at line 231 of file et_rot_bifluid.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.

◆ press

Tenseur Lorene::Etoile::press

protectedinherited

Fluid pressure.

Definition at line 464 of file etoile.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.

◆ sphph_euler

Tenseur Lorene::Et_rot_bifluid::sphph_euler

protected

The component $S^\varphi_\varphi$ of the stress tensor ${S^i}_j$ .

Definition at line 179 of file et_rot_bifluid.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.

◆ uuu2

Tenseur Lorene::Et_rot_bifluid::uuu2

protected

Norm of the (fluid no.2) 3-velocity with respect to the eulerian observer.

Definition at line 195 of file et_rot_bifluid.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_bifluid() [1/3]

◆ Et_rot_bifluid() [2/3]

◆ Et_rot_bifluid() [3/3]

◆ ~Et_rot_bifluid()

Member Function Documentation

◆ angu_mom()

◆ angu_mom_1()

◆ angu_mom_2()

◆ aplat()

◆ aplat2()

◆ area()

◆ area2()

◆ coupling_entr()

◆ coupling_LT_1()

◆ coupling_LT_2()

◆ coupling_mominert_1()

◆ coupling_mominert_2()

◆ del_deriv()

◆ del_hydro_euler()

◆ display_poly()

◆ equation_of_state()

◆ equil_spher_falloff()

◆ equil_spher_regular() [1/2]

◆ equil_spher_regular() [2/2]

◆ equilibrium()

◆ equilibrium_bi()

◆ equilibrium_spher()

◆ equilibrium_spher_bi()

◆ espec_isco()

◆ extrinsic_curvature()

◆ f_eccentric()

◆ f_eq()

◆ f_isco()

◆ fait_nphi()

◆ fait_shift()

◆ get_a_car()

◆ get_ak_car()

◆ get_alpha_eos()

◆ get_b_car()

◆ get_bbb()

◆ get_beta_auto()

◆ get_d_logn_auto_div()

◆ get_delta_car()

◆ get_dzeta()

◆ get_ener()

◆ get_ener_euler()

◆ get_ent()

◆ get_ent2()

◆ get_eos()

◆ get_gam_euler()

◆ get_gam_euler2()

◆ get_K_nn()

◆ get_K_np()

◆ get_K_pp()

◆ get_khi_shift()

◆ get_logn()

◆ get_logn_auto()

◆ get_logn_auto_div()

◆ get_logn_auto_regu()

◆ get_mp()

◆ get_nbar()

◆ get_nbar2()

◆ get_nnn()

◆ get_nphi()

◆ get_nuf()

◆ get_nuq()

◆ get_nzet()

◆ get_omega2()

◆ get_omega_c()

◆ get_press()

◆ get_s_euler()

◆ get_shift()

◆ get_tggg()

◆ get_tkij()