Etoile_bin Class Reference
[Stars and black holes]

Class for stars in binary system. More...

#include <etoile.h>

Inheritance diagram for Etoile_bin:
Etoile Et_bin_bhns_extr Et_bin_nsbh

List of all members.

Public Member Functions

 Etoile_bin (Map &mp_i, int nzet_i, bool relat, const Eos &eos_i, bool irrot, const Base_vect &ref_triad_i)
 Standard constructor.
 Etoile_bin (const Etoile_bin &)
 Copy constructor.
 Etoile_bin (Map &mp_i, const Eos &eos_i, const Base_vect &ref_triad_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) ).
virtual ~Etoile_bin ()
 Destructor.
void operator= (const Etoile_bin &)
 Assignment to another Etoile_bin.
Tenseur & set_logn_comp ()
 Read/write the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.
Tenseur & set_pot_centri ()
 Read/write the centrifugal potential.
Tenseur & set_w_shift ()
 Read/write of w_shift.
Tenseur & set_khi_shift ()
 Read/write of khi_shift.
bool is_irrotational () const
 Returns true for an irrotational motion, false for a corotating one.
const Tenseur & get_psi0 () const
 Returns the non-translational part of the velocity potential.
const Tenseur & get_d_psi () const
 Returns the gradient of the velocity potential (Cartesian components with respect to ref_triad ).
const Tenseur & get_wit_w () const
 Returns the spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
const Tenseur & get_loggam () const
 Returns the logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
const Tenseur & get_logn_comp () const
 Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.
const Tenseur & get_d_logn_auto () const
 Returns the gradient of logn_auto (Cartesian components with respect to ref_triad ).
const Tenseur & get_d_logn_auto_regu () const
 Returns the gradient of logn_auto_regu (Cartesian components with respect to ref_triad ).
const Tenseur & get_d_logn_comp () const
 Returns the gradient of logn_comp (Cartesian components with respect to ref_triad ).
const Tenseur & get_beta_comp () const
 Returns the part of the logarithm of AN generated principaly by the companion star.
const Tenseur & get_d_beta_auto () const
 Returns the gradient of beta_auto (Cartesian components with respect to ref_triad ).
const Tenseur & get_d_beta_comp () const
 Returns the gradient of beta_comp (Cartesian components with respect to ref_triad ).
const Tenseur & get_shift_auto () const
 Returns the part of the shift vector $N^i$ generated principaly by the star.
const Tenseur & get_shift_comp () const
 Returns the part of the shift vector $N^i$ generated principaly by the companion star.
const Tenseur & get_w_shift () const
 Returns the vector $W^i$ used in the decomposition of shift_auto , following Shibata's prescription [Prog.
const Tenseur & get_khi_shift () const
 Returns the scalar $\chi$ used in the decomposition of shift_auto following Shibata's prescription [Prog.
const Tenseur_sym & get_tkij_auto () const
 Returns the part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_auto .
const Tenseur_sym & get_tkij_comp () const
 Returns the part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_comp .
const Tenseur & get_akcar_auto () const
 Returns the part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto , i.e.
const Tenseur & get_akcar_comp () const
 Returns the part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto and shift_comp , i.e.
const Tenseur & get_bsn () const
 Returns the shift vector, divided by N , of the rotating coordinates, $B^i/N$.
const Tenseur & get_pot_centri () const
 Returns the centrifugal potential.
const Cmp get_decouple () const
 Returns the function used to construct tkij_auto from tkij_tot .
virtual void sauve (FILE *) const
 Save in a file.
virtual double mass_b () const
 Baryon mass.
virtual double mass_g () const
 Gravitational mass.
virtual double xa_barycenter () const
 Absolute coordinate X of the barycenter of the baryon density, defined according to the formula

\[ X_G := \int A^3 \Gamma_{\rm n} \, n \, X \, d^3x \ , \]

where $\Gamma_{\rm n}$ is the Lorentz factor between the fluid and Eulerian observers.

virtual Tenseur sprod (const Tenseur &t1, const Tenseur &t2) const
 Performs the scalar product of two tensors by contracting the last index of t1 with the first index of t2 .
virtual void hydro_euler ()
 Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame, as well as wit_w and loggam .
void update_metric (const Etoile_bin &comp)
 Computes metric coefficients from known potentials, when the companion is another star.
void update_metric (const Etoile_bin &comp, const Etoile_bin &star_prev, double relax)
 Same as update_metric(const Etoile_bin& ) but with relaxation.
void update_metric_der_comp (const Etoile_bin &comp)
 Computes the derivative of metric functions related to the companion star.
virtual void kinematics (double omega, double x_axe)
 Computes the quantities bsn and pot_centri .
void fait_d_psi ()
 Computes the gradient of the total velocity potential $\psi$.
void fait_shift_auto ()
 Computes shift_auto from w_shift and khi_shift according to Shibata's prescription [Prog.
virtual void extrinsic_curvature ()
 Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .
void equilibrium (double ent_c, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, double thres_adapt, const Tbl &fact, Tbl &diff, const Tbl *ent_limit=0x0)
 Computes an equilibrium configuration.
void equil_regular (double ent_c, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, double thres_adapt, const Tbl &fact, Tbl &diff)
 Computes an equilibrium configuration by regularizing the diverging source.
double velocity_potential (int mermax, double precis, double relax)
 Computes the non-translational part of the velocity scalar potential $\psi0$ by solving the continuity equation.
void relaxation (const Etoile_bin &star_prev, double relax_ent, double relax_met, int mer, int fmer_met)
 Performs a relaxation on ent , logn_auto , beta_auto and shift_auto .
Map & set_mp ()
 Read/write of the mapping.
void set_enthalpy (const Cmp &)
 Assignment of the enthalpy field.
virtual void equation_of_state ()
 Computes the proper baryon and energy density, as well as pressure from the enthalpy.
virtual void equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *ent_limit=0x0)
 Computes a spherical static configuration.
void equil_spher_regular (double ent_c, double precis=1.e-14)
 Computes a spherical static configuration.
virtual void equil_spher_falloff (double ent_c, double precis=1.e-14)
 Computes a spherical static configuration with the outer boundary condition at a finite radius.
const Map & get_mp () const
 Returns the mapping.
int get_nzet () const
 Returns the number of domains occupied by the star.
bool is_relativistic () const
 Returns true for a relativistic star, false for a Newtonian one.
const Eos & get_eos () const
 Returns the equation of state.
const Tenseur & get_ent () const
 Returns the enthalpy field.
const Tenseur & get_nbar () const
 Returns the proper baryon density.
const Tenseur & get_ener () const
 Returns the proper total energy density.
const Tenseur & get_press () const
 Returns the fluid pressure.
const Tenseur & get_ener_euler () const
 Returns the total energy density with respect to the Eulerian observer.
const Tenseur & get_s_euler () const
 Returns the trace of the stress tensor in the Eulerian frame.
const Tenseur & get_gam_euler () const
 Returns the Lorentz factor between the fluid and Eulerian observers.
const Tenseur & get_u_euler () const
 Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tenseur & get_logn_auto () const
 Returns the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur & get_logn_auto_regu () const
 Returns the regular part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur & get_logn_auto_div () const
 Returns the divergent part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseur & get_d_logn_auto_div () const
 Returns the gradient of logn_auto_div.
const Tenseur & get_beta_auto () const
 Returns the logarithm of the part of the product AN generated principaly by the star.
const Tenseur & get_nnn () const
 Returns the total lapse function N.
const Tenseur & get_shift () const
 Returns the total shift vector $N^i$.
const Tenseur & get_a_car () const
 Returns the total conformal factor $A^2$.
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].
virtual const Itbl & l_surf () const
 Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
const Tbl & xi_surf () const
 Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Protected Member Functions

virtual void del_deriv () const
 Deletes all the derived quantities.
virtual void set_der_0x0 () const
 Sets to 0x0 all the pointers on derived quantities.
virtual void del_hydro_euler ()
 Sets to ETATNONDEF (undefined state) the hydrodynamical quantities relative to the Eulerian observer.
virtual ostream & operator>> (ostream &) const
 Operator >> (virtual function called by the operator <<).

Protected Attributes

bool irrotational
 true for an irrotational star, false for a corotating one
const Base_vect & ref_triad
 Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's are defined, except for w_shift and ssjm1_wshift .
Tenseur psi0
 Scalar potential $\Psi_0$ of the non-translational part of fluid 4-velocity (in the irrotational case).
Tenseur d_psi
 Gradient of $\Psi$ (in the irrotational case) (Cartesian components with respect to ref_triad ).
Tenseur wit_w
 Spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
Tenseur loggam
 Logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Tenseur logn_comp
 Part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.
Tenseur d_logn_auto
 Gradient of logn_auto (Cartesian components with respect to ref_triad ).
Tenseur d_logn_auto_regu
 Gradient of logn_auto_regu (Cartesian components with respect to ref_triad ).
Tenseur d_logn_comp
 Gradient of logn_comp (Cartesian components with respect to ref_triad ).
Tenseur beta_comp
 Part of the logarithm of AN generated principaly by the companion star.
Tenseur d_beta_auto
 Gradient of beta_auto (Cartesian components with respect to ref_triad ).
Tenseur d_beta_comp
 Gradient of beta_comp (Cartesian components with respect to ref_triad ).
Tenseur shift_auto
 Part of the shift vector $N^i$ generated principaly by the star.
Tenseur shift_comp
 Part of the shift vector $N^i$ generated principaly by the companion star.
Tenseur w_shift
 Vector $W^i$ used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Tenseur khi_shift
 Scalar $\chi$ used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Tenseur_sym tkij_auto
 Part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_auto .
Tenseur_sym tkij_comp
 Part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_comp .
Tenseur akcar_auto
 Part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto , i.e.
Tenseur akcar_comp
 Part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto and shift_comp , i.e.
Tenseur bsn
 3-vector shift, divided by N , of the rotating coordinates, $B^i/N$.
Tenseur pot_centri
 Centrifugal potential.
Cmp ssjm1_logn
 Effective source at the previous step for the resolution of the Poisson equation for logn_auto by means of Map_et::poisson .
Cmp ssjm1_beta
 Effective source at the previous step for the resolution of the Poisson equation for beta_auto by means of Map_et::poisson .
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 $W^i$ by means of Map_et::poisson .
Cmp ssjm1_psi
 Effective source at the previous step for the resolution of the Poisson equation for the scalar $\psi$ by means of Map_et::poisson_interne .
Cmp decouple
 Function used to construct the part of $K^{ij}$ generated by the star from the total $K^{ij}$.
double * p_xa_barycenter
 Absolute coordinate X of the barycenter of the baryon density.
Map & mp
 Mapping associated with the star.
int nzet
 Number of domains of *mp occupied by the star.
bool relativistic
 Indicator of relativity: true for a relativistic star, false for a Newtonian one.
double unsurc2
 $1/c^2$ : unsurc2=1 for a relativistic star, 0 for a Newtonian one.
int k_div
 Index of regularity of the gravitational potential logn_auto .
const Eos & eos
 Equation of state of the stellar matter.
Tenseur ent
 Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).
Tenseur nbar
 Baryon density in the fluid frame.
Tenseur ener
 Total energy density in the fluid frame.
Tenseur press
 Fluid pressure.
Tenseur ener_euler
 Total energy density in the Eulerian frame.
Tenseur s_euler
 Trace of the stress tensor in the Eulerian frame.
Tenseur gam_euler
 Lorentz factor between the fluid and Eulerian observers.
Tenseur u_euler
 Fluid 3-velocity with respect to the Eulerian observer.
Tenseur logn_auto
 Total of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur logn_auto_regu
 Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur logn_auto_div
 Divergent part (if k_div!=0 ) of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur d_logn_auto_div
 Gradient of logn_auto_div (if k_div!=0 ).
Tenseur beta_auto
 Logarithm of the part of the product AN generated principaly by by the star.
Tenseur nnn
 Total lapse function.
Tenseur shift
 Total shift vector.
Tenseur a_car
 Total conformal factor $A^2$.
double * p_ray_eq
 Coordinate radius at $\phi=0$, $\theta=\pi/2$.
double * p_ray_eq_pis2
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$.
double * p_ray_eq_pi
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$.
double * p_ray_eq_3pis2
 Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$.
double * p_ray_pole
 Coordinate radius at $\theta=0$.
Itbl * p_l_surf
 Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
Tbl * p_xi_surf
 Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double * p_mass_b
 Baryon mass.
double * p_mass_g
 Gravitational mass.

Friends

class Bin_ns_bh
 Friend class Bin_ns_bh.
ostream & operator<< (ostream &, const Etoile &)
 Display.

Detailed Description

Class for stars in binary system.

()

This class implements the formalism for corotating or irrotational systems presented in Bonazzola, Gourgoulhon & Marck Phys. Rev. Lett. 82 , 892 (1999). In particular, the conformal 3-metric $\tilde h_{ij}$ introduced in Eq.~(eetoilemetrique}) is flat.

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

Definition at line 799 of file etoile.h.

Constructor & Destructor Documentation

Etoile_bin::Etoile_bin ( Map &  mp_i,
int  nzet_i,
bool  relat,
const Eos &  eos_i,
bool  irrot,
const Base_vect &  ref_triad_i 
)

Standard constructor.

Parameters:
mp_i Mapping on which the star will be defined
nzet_i Number of domains occupied by the star
relat should be true for a relativistic star, false for a Newtonian one
eos_i Equation of state of the stellar matter
irrot should be true for an irrotational star, false for a corotating one
ref_triad_i Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's are defined, except for w_shift and ssjm1_wshift whose components are defined with respect to the mapping mp Cartesian triad.

Definition at line 203 of file etoile_bin.C.

References akcar_auto, akcar_comp, beta_comp, bsn, d_beta_auto, d_beta_comp, d_logn_auto, d_logn_auto_regu, d_logn_comp, d_psi, khi_shift, loggam, logn_comp, pot_centri, psi0, ref_triad, Tenseur::set(), set_der_0x0(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_triad(), Etoile::shift, shift_auto, shift_comp, ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_psi, ssjm1_wshift, tkij_auto, tkij_comp, Etoile::u_euler, w_shift, and wit_w.

Etoile_bin::Etoile_bin ( const Etoile_bin &  et  ) 

Copy constructor.

Definition at line 287 of file etoile_bin.C.

References set_der_0x0().

Etoile_bin::Etoile_bin ( Map &  mp_i,
const Eos &  eos_i,
const Base_vect &  ref_triad_i,
FILE *  fich 
)

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

Parameters:
mp_i Mapping on which the star will be defined
eos_i Equation of state of the stellar matter
ref_triad_i Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's are defined, except for w_shift and ssjm1_wshift whose components are defined with respect to the mapping mp Cartesian triad.
fich input file (must have been created by the function sauve )

Definition at line 325 of file etoile_bin.C.

References akcar_auto, akcar_comp, beta_comp, bsn, d_beta_auto, d_beta_comp, d_logn_auto, d_logn_auto_regu, d_logn_comp, d_psi, fait_shift_auto(), Etoile::gam_euler, Map::get_bvect_cart(), Map::get_mg(), irrotational, khi_shift, loggam, logn_comp, Etoile::mp, pot_centri, psi0, ref_triad, set_der_0x0(), Tenseur::set_etat_zero(), Tenseur::set_triad(), Etoile::shift, shift_comp, ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_psi, ssjm1_wshift, tkij_auto, tkij_comp, Etoile::u_euler, w_shift, and wit_w.

Etoile_bin::~Etoile_bin (  )  [virtual]

Destructor.

Definition at line 433 of file etoile_bin.C.

References del_deriv().

Member Function Documentation

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

Deletes all the derived quantities.

Reimplemented from Etoile.

Definition at line 443 of file etoile_bin.C.

References p_xa_barycenter, and set_der_0x0().

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

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

Reimplemented from Etoile.

Definition at line 463 of file etoile_bin.C.

References del_deriv().

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

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

Reimplemented in Et_rot_bifluid, and Et_magnetisation.

Definition at line 562 of file etoile.C.

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

void Etoile_bin::equil_regular ( double  ent_c,
int  mermax,
int  mermax_poisson,
double  relax_poisson,
int  mermax_potvit,
double  relax_potvit,
double  thres_adapt,
const Tbl &  fact,
Tbl &  diff 
)

Computes an equilibrium configuration by regularizing the diverging source.

The values of logn_comp , beta_comp , pot_centri are held fixed during the iteration.

Parameters:
ent_c [input] Central enthalpy
ent_limit is the table of enthalpy values on the domain borders
mermax [input] Maximum number of steps
mermax_poisson [input] Maximum number of steps in Map_et::poisson
relax_poisson [input] Relaxation factor in Map_et::poisson
mermax_potvit [input] Maximum number of steps in Map_radial::poisson_compact
relax_potvit [input] Relaxation factor in Map_radial::poisson_compact
thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping
fact [input] 1-D Tbl for the input of some factors :

  • fact(0) : A resizing factor for the first shell
diff [output] 1-D Tbl for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field between two successive steps
  • diff(1) : Relative error returned by the routine Etoile_bin::velocity_potential
  • diff(2) : Relative error in the resolution of the Poisson equation for logn_auto
  • diff(3) : Relative error in the resolution of the Poisson equation for beta_auto
  • diff(4) : Relative error in the resolution of the equation for shift_auto (x comp.)
  • diff(5) : Relative error in the resolution of the equation for shift_auto (y comp.)
  • diff(6) : Relative error in the resolution of the equation for shift_auto (z comp.)

Definition at line 139 of file et_bin_equil_regu.C.

References Etoile::a_car, abs(), Map::adapt(), Param::add_cmp_mod(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Param::add_tenseur_mod(), akcar_auto, akcar_comp, Etoile::beta_auto, Tenseur::change_triad(), contract(), d_beta_auto, d_beta_comp, d_logn_auto, Etoile::d_logn_auto_div, d_logn_comp, Tenseur::dec2_dzpuis(), Eos::der_ener_ent_p(), Eos::der_nbar_ent_p(), diffrel(), Etoile::ener_euler, Etoile::ent, Etoile::eos, Etoile::equation_of_state(), Cmp::filtre(), flat_scalar_prod_desal(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tenseur::gradient(), Map_et::homothetie(), hydro_euler(), Tenseur::inc2_dzpuis(), irrotational, Etoile::k_div, khi_shift, loggam, Etoile::logn_auto, Etoile::logn_auto_div, Etoile::logn_auto_regu, logn_comp, max(), Etoile::mp, Etoile::nbar, Etoile::nnn, Etoile::nzet, Tenseur::poisson_vect_regu(), pot_centri, Etoile::press, Etoile::ray_eq(), Etoile::ray_pole(), Map::reevaluate_symy(), ref_triad, Etoile::relativistic, Map::resize(), Etoile::s_euler, Tenseur::set(), Tbl::set(), Tenseur::set_etat_qcq(), Tbl::set_etat_qcq(), Tenseur::set_std_base(), shift_auto, sqrt(), ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_wshift, Cmp::std_base_scal(), tkij_auto, Etoile::u_euler, Map::val_r(), velocity_potential(), and w_shift.

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

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

Parameters:
ent_c [input] central value of the enthalpy
precis [input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)

Definition at line 53 of file etoile_eqsph_falloff.C.

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

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

Computes a spherical static configuration.

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

Parameters:
ent_c [input] central value of the enthalpy
precis [input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)

Definition at line 110 of file et_equil_spher_regu.C.

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

void Etoile_bin::equilibrium ( double  ent_c,
int  mermax,
int  mermax_poisson,
double  relax_poisson,
int  mermax_potvit,
double  relax_potvit,
double  thres_adapt,
const Tbl &  fact,
Tbl &  diff,
const Tbl *  ent_limit = 0x0 
)

Computes an equilibrium configuration.

The values of logn_comp , beta_comp , pot_centri are held fixed during the iteration.

Parameters:
ent_c [input] Central enthalpy
mermax [input] Maximum number of steps
mermax_poisson [input] Maximum number of steps in Map_et::poisson
relax_poisson [input] Relaxation factor in Map_et::poisson
mermax_potvit [input] Maximum number of steps in Map_radial::poisson_compact
relax_potvit [input] Relaxation factor in Map_radial::poisson_compact
thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping
fact [input] 1-D Tbl for the input of some factors :

  • fact(0) : A resizing factor for the first shell
diff [output] 1-D Tbl for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field between two successive steps
  • diff(1) : Relative error returned by the routine Etoile_bin::velocity_potential
  • diff(2) : Relative error in the resolution of the Poisson equation for logn_auto
  • diff(3) : Relative error in the resolution of the Poisson equation for beta_auto
  • diff(4) : Relative error in the resolution of the equation for shift_auto (x comp.)
  • diff(5) : Relative error in the resolution of the equation for shift_auto (y comp.)
  • diff(6) : Relative error in the resolution of the equation for shift_auto (z comp.)
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 180 of file et_bin_equilibrium.C.

References Etoile::a_car, abs(), Map::adapt(), Param::add_cmp_mod(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Param::add_tenseur_mod(), akcar_auto, akcar_comp, Etoile::beta_auto, Tenseur::change_triad(), contract(), d_beta_auto, d_beta_comp, d_logn_auto, d_logn_comp, Tenseur::dec2_dzpuis(), diffrel(), Etoile::ener_euler, Etoile::ent, Etoile::equation_of_state(), Cmp::filtre(), flat_scalar_prod_desal(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tenseur::gradient(), Map_et::homothetie(), hydro_euler(), Tenseur::inc2_dzpuis(), irrotational, khi_shift, loggam, Etoile::logn_auto, Etoile::logn_auto_regu, logn_comp, max(), Etoile::mp, Etoile::nbar, Etoile::nnn, Etoile::nzet, Tenseur::poisson_vect(), pot_centri, Etoile::press, Etoile::ray_eq(), Etoile::ray_pole(), Map::reevaluate_symy(), ref_triad, Etoile::relativistic, Map::resize(), Etoile::s_euler, Tenseur::set(), Tbl::set(), Tbl::set_etat_qcq(), Tenseur::set_std_base(), shift_auto, sqrt(), ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_wshift, tkij_auto, Etoile::u_euler, Map::val_r(), velocity_potential(), and w_shift.

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

Computes a spherical static configuration.

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

Definition at line 83 of file etoile_equil_spher.C.

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

void Etoile_bin::extrinsic_curvature (  )  [virtual]

Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .

Definition at line 60 of file et_bin_extr_curv.C.

References Etoile::a_car, akcar_auto, Tenseur::change_triad(), contract(), Map::get_bvect_cart(), Tenseur::gradient(), Etoile::mp, Etoile::nnn, ref_triad, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), shift_auto, and tkij_auto.

void Etoile_bin::fait_d_psi (  ) 

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

Definition at line 760 of file etoile_bin.C.

References Etoile::a_car, Tenseur::annule(), Cmp::annule(), bsn, Tenseur::change_triad(), d_psi, Etoile::ent, exp(), Etoile::gam_euler, Tenseur::get_etat(), Map::get_mg(), Mg3d::get_nzone(), Tenseur::get_triad(), Tenseur::gradient(), irrotational, Etoile::mp, Etoile::nzet, psi0, ref_triad, Tenseur::set(), Valeur::set_base(), Tenseur::set_etat_nondef(), Tenseur::set_etat_qcq(), Tenseur::set_triad(), Etoile::unsurc2, and Cmp::va.

void Etoile_bin::fait_shift_auto (  ) 

Computes shift_auto 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 822 of file etoile_bin.C.

References Tenseur::change_triad(), Tenseur::dec2_dzpuis(), Tenseur::dec_dzpuis(), Tenseur::get_etat(), Tenseur::get_triad(), Tenseur::gradient(), khi_shift, ref_triad, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_triad(), shift_auto, skxk(), and w_shift.

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

Returns the total conformal factor $A^2$.

Definition at line 718 of file etoile.h.

References Etoile::a_car.

const Tenseur& Etoile_bin::get_akcar_auto (  )  const [inline]

Returns the part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto , i.e.

$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm auto}$

Definition at line 1189 of file etoile.h.

References akcar_auto.

const Tenseur& Etoile_bin::get_akcar_comp (  )  const [inline]

Returns the part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto and shift_comp , i.e.

$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm comp} $

Definition at line 1195 of file etoile.h.

References akcar_comp.

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

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

Definition at line 709 of file etoile.h.

References Etoile::beta_auto.

const Tenseur& Etoile_bin::get_beta_comp (  )  const [inline]

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

Definition at line 1121 of file etoile.h.

References beta_comp.

const Tenseur& Etoile_bin::get_bsn (  )  const [inline]

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

(Cartesian components with respect to ref_triad )

Definition at line 1201 of file etoile.h.

References bsn.

const Tenseur& Etoile_bin::get_d_beta_auto (  )  const [inline]

Returns the gradient of beta_auto (Cartesian components with respect to ref_triad ).

Definition at line 1126 of file etoile.h.

References d_beta_auto.

const Tenseur& Etoile_bin::get_d_beta_comp (  )  const [inline]

Returns the gradient of beta_comp (Cartesian components with respect to ref_triad ).

Definition at line 1131 of file etoile.h.

References d_beta_comp.

const Tenseur& Etoile_bin::get_d_logn_auto (  )  const [inline]

Returns the gradient of logn_auto (Cartesian components with respect to ref_triad ).

Definition at line 1106 of file etoile.h.

References d_logn_auto.

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

Returns the gradient of logn_auto_div.

Definition at line 704 of file etoile.h.

References Etoile::d_logn_auto_div.

const Tenseur& Etoile_bin::get_d_logn_auto_regu (  )  const [inline]

Returns the gradient of logn_auto_regu (Cartesian components with respect to ref_triad ).

Definition at line 1111 of file etoile.h.

References d_logn_auto_regu.

const Tenseur& Etoile_bin::get_d_logn_comp (  )  const [inline]

Returns the gradient of logn_comp (Cartesian components with respect to ref_triad ).

Definition at line 1116 of file etoile.h.

References d_logn_comp.

const Tenseur& Etoile_bin::get_d_psi (  )  const [inline]

Returns the gradient of the velocity potential (Cartesian components with respect to ref_triad ).

Definition at line 1085 of file etoile.h.

References d_psi.

const Cmp Etoile_bin::get_decouple (  )  const [inline]

Returns the function used to construct tkij_auto from tkij_tot .

Definition at line 1209 of file etoile.h.

References decouple.

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

Returns the proper total energy density.

Definition at line 664 of file etoile.h.

References Etoile::ener.

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

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

Definition at line 670 of file etoile.h.

References Etoile::ener_euler.

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

Returns the enthalpy field.

Definition at line 658 of file etoile.h.

References Etoile::ent.

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

Returns the equation of state.

Reimplemented in Et_rot_bifluid.

Definition at line 655 of file etoile.h.

References Etoile::eos.

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

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 676 of file etoile.h.

References Etoile::gam_euler.

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

Returns the scalar $\chi$ used in the decomposition of shift_auto 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 1171 of file etoile.h.

References khi_shift.

const Tenseur& Etoile_bin::get_loggam (  )  const [inline]

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

Definition at line 1096 of file etoile.h.

References loggam.

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

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

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

Definition at line 686 of file etoile.h.

References Etoile::logn_auto.

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

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

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

Definition at line 700 of file etoile.h.

References Etoile::logn_auto_div.

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

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

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

Definition at line 693 of file etoile.h.

References Etoile::logn_auto_regu.

const Tenseur& Etoile_bin::get_logn_comp (  )  const [inline]

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

Definition at line 1101 of file etoile.h.

References logn_comp.

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

Returns the mapping.

Definition at line 644 of file etoile.h.

References Etoile::mp.

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

Returns the proper baryon density.

Definition at line 661 of file etoile.h.

References Etoile::nbar.

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

Returns the total lapse function N.

Definition at line 712 of file etoile.h.

References Etoile::nnn.

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

Returns the number of domains occupied by the star.

Definition at line 647 of file etoile.h.

References Etoile::nzet.

const Tenseur& Etoile_bin::get_pot_centri (  )  const [inline]

Returns the centrifugal potential.

Definition at line 1204 of file etoile.h.

References pot_centri.

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

Returns the fluid pressure.

Definition at line 667 of file etoile.h.

References Etoile::press.

const Tenseur& Etoile_bin::get_psi0 (  )  const [inline]

Returns the non-translational part of the velocity potential.

Definition at line 1080 of file etoile.h.

References psi0.

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

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

Definition at line 673 of file etoile.h.

References Etoile::s_euler.

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

Returns the total shift vector $N^i$.

Definition at line 715 of file etoile.h.

References Etoile::shift.

const Tenseur& Etoile_bin::get_shift_auto (  )  const [inline]

Returns the part of the shift vector $N^i$ generated principaly by the star.

(Cartesian components with respect to ref_triad )

Definition at line 1137 of file etoile.h.

References shift_auto.

const Tenseur& Etoile_bin::get_shift_comp (  )  const [inline]

Returns the part of the shift vector $N^i$ generated principaly by the companion star.

(Cartesian components with respect to ref_triad )

Definition at line 1143 of file etoile.h.

References shift_comp.

const Tenseur_sym& Etoile_bin::get_tkij_auto (  )  const [inline]

Returns the part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_auto .

(Cartesian components with respect to ref_triad )

Reimplemented in Et_bin_nsbh.

Definition at line 1177 of file etoile.h.

References tkij_auto.

const Tenseur_sym& Etoile_bin::get_tkij_comp (  )  const [inline]

Returns the part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_comp .

(Cartesian components with respect to ref_triad )

Definition at line 1183 of file etoile.h.

References tkij_comp.

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

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

Definition at line 679 of file etoile.h.

References Etoile::u_euler.

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

Returns the vector $W^i$ used in the decomposition of shift_auto , 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 1157 of file etoile.h.

References w_shift.

const Tenseur& Etoile_bin::get_wit_w (  )  const [inline]

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

(Cartesian components with respect to ref_triad )

Definition at line 1091 of file etoile.h.

References wit_w.

void Etoile_bin::hydro_euler (  )  [virtual]

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

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

Reimplemented from Etoile.

Definition at line 102 of file et_bin_hydro.C.

References Etoile::a_car, Tenseur::annule(), bsn, d_psi, del_deriv(), Etoile::ener, Etoile::ener_euler, Etoile::ent, exp(), flat_scalar_prod_desal(), Etoile::gam_euler, Tenseur::get_etat(), Map::get_mg(), Mg3d::get_nzone(), Tenseur::get_triad(), irrotational, log(), loggam, Etoile::mp, Etoile::press, Etoile::relativistic, Etoile::s_euler, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_std_base(), Tenseur::set_triad(), sprod(), sqrt(), Etoile::u_euler, Etoile::unsurc2, and wit_w.

bool Etoile_bin::is_irrotational (  )  const [inline]

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

Definition at line 1077 of file etoile.h.

References irrotational.

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

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

Definition at line 652 of file etoile.h.

References Etoile::relativistic.

void Etoile_bin::kinematics ( double  omega,
double  x_axe 
) [virtual]

Computes the quantities bsn and pot_centri .

The calculation is performed starting from the quantities nnn , shift , a_car , which are supposed to be up to date.

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

Reimplemented in Et_bin_nsbh.

Definition at line 77 of file et_bin_kinema.C.

References Tenseur::annule(), bsn, del_deriv(), Map::get_mg(), Mg3d::get_nzone(), log(), Etoile::mp, Etoile::nnn, pot_centri, Etoile::relativistic, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_std_base(), Etoile::shift, sprod(), sqrt(), Map::xa, and Map::ya.

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

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

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

Reimplemented in Et_rot_bifluid, and Etoile_rot.

Definition at line 71 of file etoile_global.C.

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

double Etoile_bin::mass_b (  )  const [virtual]

Baryon mass.

Reimplemented from Etoile.

Definition at line 96 of file et_bin_global.C.

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

double Etoile_bin::mass_g (  )  const [virtual]

Gravitational mass.

Reimplemented from Etoile.

Definition at line 133 of file et_bin_global.C.

References Etoile::a_car, Etoile::ener_euler, Cmp::integrale(), mass_b(), Etoile::nnn, Etoile::p_mass_g, Etoile::relativistic, Etoile::s_euler, sqrt(), and Cmp::std_base_scal().

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

Assignment to another Etoile_bin.

Reimplemented from Etoile.

Reimplemented in Et_bin_bhns_extr, and Et_bin_nsbh.

Definition at line 478 of file etoile_bin.C.

References akcar_auto, akcar_comp, beta_comp, bsn, d_beta_auto, d_beta_comp, d_logn_auto, d_logn_auto_regu, d_logn_comp, d_psi, decouple, del_deriv(), irrotational, khi_shift, loggam, logn_comp, pot_centri, psi0, ref_triad, shift_auto, shift_comp, ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_psi, ssjm1_wshift, tkij_auto, tkij_comp, w_shift, and wit_w.

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

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

Reimplemented from Etoile.

Reimplemented in Et_bin_nsbh.

Definition at line 578 of file etoile_bin.C.

References akcar_auto, akcar_comp, Etoile::beta_auto, beta_comp, bsn, d_beta_auto, d_beta_comp, d_logn_auto, d_logn_comp, d_psi, Etoile::gam_euler, Map::get_ori_x(), Map::get_rot_phi(), irrotational, khi_shift, loggam, Etoile::logn_auto, logn_comp, max(), min(), Etoile::mp, Etoile::ray_eq(), Etoile::ray_eq_pi(), Etoile::shift, shift_auto, shift_comp, tkij_auto, tkij_comp, Etoile::u_euler, Map::val_r(), w_shift, wit_w, and xa_barycenter().

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

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

Definition at line 436 of file etoile_global.C.

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

double Etoile::ray_eq (  )  const [inherited]

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

Definition at line 116 of file etoile_global.C.

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

double Etoile::ray_eq_3pis2 (  )  const [inherited]

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

Definition at line 331 of file etoile_global.C.

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

double Etoile::ray_eq_pi (  )  const [inherited]

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

Definition at line 252 of file etoile_global.C.

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

double Etoile::ray_eq_pis2 (  )  const [inherited]

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

Definition at line 165 of file etoile_global.C.

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

double Etoile::ray_pole (  )  const [inherited]

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

Definition at line 411 of file etoile_global.C.

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

void Etoile_bin::relaxation ( const Etoile_bin &  star_prev,
double  relax_ent,
double  relax_met,
int  mer,
int  fmer_met 
)

Performs a relaxation on ent , logn_auto , beta_auto and shift_auto .

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

Definition at line 859 of file etoile_bin.C.

References Etoile::beta_auto, Etoile::d_logn_auto_div, del_deriv(), Etoile::ent, Etoile::equation_of_state(), Etoile::logn_auto, Etoile::logn_auto_div, Etoile::logn_auto_regu, and shift_auto.

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

Save in a file.

Reimplemented from Etoile.

Reimplemented in Et_bin_bhns_extr, and Et_bin_nsbh.

Definition at line 555 of file etoile_bin.C.

References Etoile::gam_euler, irrotational, khi_shift, psi0, Cmp::sauve(), Tenseur::sauve(), ssjm1_beta, ssjm1_khi, ssjm1_logn, ssjm1_wshift, and w_shift.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Etoile.

Definition at line 455 of file etoile_bin.C.

References p_xa_barycenter.

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

Assignment of the enthalpy field.

Definition at line 461 of file etoile.C.

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

Tenseur & Etoile_bin::set_khi_shift (  ) 

Read/write of khi_shift.

Definition at line 541 of file etoile_bin.C.

References del_deriv(), and khi_shift.

Tenseur & Etoile_bin::set_logn_comp (  ) 

Read/write the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.

Definition at line 520 of file etoile_bin.C.

References del_deriv(), and logn_comp.

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

Read/write of the mapping.

Definition at line 591 of file etoile.h.

References Etoile::mp.

Tenseur & Etoile_bin::set_pot_centri (  ) 

Read/write the centrifugal potential.

Definition at line 527 of file etoile_bin.C.

References del_deriv(), and pot_centri.

Tenseur & Etoile_bin::set_w_shift (  ) 

Read/write of w_shift.

Definition at line 534 of file etoile_bin.C.

References del_deriv(), and w_shift.

Tenseur Etoile_bin::sprod ( const Tenseur &  t1,
const Tenseur &  t2 
) const [virtual]

Performs the scalar product of two tensors by contracting the last index of t1 with the first index of t2 .

Both indices are supposed to be contravariant, so that a multiplication by $A^2$ is performed to lower one index. For instance, for two vectors $V^i$ and $W^i$, this function returns the scalar $h_{ij} V^i W^j = A^2 f_{ij} V^i W^j$.

Definition at line 744 of file etoile_bin.C.

References Etoile::a_car, flat_scalar_prod(), Tenseur::get_type_indice(), and Tenseur::get_valence().

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

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

Parameters:
comp companion star.
star_prev previous value of the star.
relax relaxation parameter.

Definition at line 200 of file et_bin_upmetr.C.

References Etoile::a_car, Etoile::beta_auto, beta_comp, Tenseur::change_triad(), d_beta_auto, d_logn_auto, Etoile::d_logn_auto_div, d_logn_auto_regu, del_deriv(), exp(), extrinsic_curvature(), get_beta_comp(), Map::get_bvect_cart(), get_logn_comp(), get_shift_comp(), Tenseur::get_triad(), Tenseur::gradient(), Etoile::logn_auto, Etoile::logn_auto_regu, logn_comp, Etoile::mp, Etoile::nnn, ref_triad, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_std_base(), Tenseur::set_triad(), Etoile::shift, shift_auto, shift_comp, and Etoile::unsurc2.

void Etoile_bin::update_metric ( const Etoile_bin &  comp  ) 

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

The calculation is performed starting from the quantities logn_auto , beta_auto , shift_auto , comp.logn_auto , comp.beta_auto , comp.shift_auto which are supposed to be up to date. From these, the following fields are updated: logn_comp , beta_comp , shift_comp , nnn , a_car , shift , d_logn_auto , d_beta_auto , tkij_auto , akcar_auto .

Parameters:
comp companion star.

Definition at line 96 of file et_bin_upmetr.C.

References Etoile::a_car, Etoile::beta_auto, beta_comp, Tenseur::change_triad(), d_beta_auto, d_logn_auto, Etoile::d_logn_auto_div, d_logn_auto_regu, del_deriv(), exp(), extrinsic_curvature(), Map::get_bvect_cart(), Tenseur::get_triad(), Tenseur::gradient(), Etoile::logn_auto, Etoile::logn_auto_regu, logn_comp, Etoile::mp, Etoile::nnn, ref_triad, Etoile::relativistic, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_std_base(), Tenseur::set_triad(), Etoile::shift, shift_auto, shift_comp, and Etoile::unsurc2.

void Etoile_bin::update_metric_der_comp ( const Etoile_bin &  comp  ) 

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

The calculation is performed starting from the quantities comp.d_logn_auto , comp.d_beta_auto , comp.tkij_auto which are supposed to be up to date. From these, the following fields are updated: d_logn_comp , d_beta_comp , tkij_comp , akcar_comp .

Parameters:
comp companion star.

Definition at line 80 of file et_bin_upmetr_der.C.

References Etoile::a_car, akcar_comp, beta_comp, Tenseur::change_triad(), contract(), d_beta_auto, d_beta_comp, d_logn_auto, d_logn_comp, del_deriv(), Map::get_bvect_cart(), Tenseur::gradient(), logn_comp, Etoile::mp, Etoile::nnn, ref_triad, Etoile::relativistic, Tenseur::set(), Tenseur::set_etat_qcq(), Tenseur::set_etat_zero(), Tenseur::set_std_base(), Tenseur::set_triad(), shift_comp, tkij_auto, and tkij_comp.

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

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

Parameters:
mermax [input] Maximum number of steps in the iteration
precis [input] Required precision: the iteration will be stopped when the relative difference on $\psi0$ between two successive steps is lower than precis .
relax [input] Relaxation factor.
Returns:
Relative error of the resolution obtained by comparing the operator acting on the solution with the source.

Definition at line 138 of file et_bin_vel_pot.C.

References Etoile::a_car, Param::add_cmp_mod(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Cmp::annule(), Tenseur::annule(), Tbl::annule_hard(), Etoile::beta_auto, beta_comp, bsn, Tenseur::change_triad(), contract(), d_psi, Eos::der_nbar_ent(), Tenseur::derive_cov(), diffrel(), Cmp::dsdr(), Etoile::ent, Etoile::eos, exp(), flat_scalar_prod(), Etoile::gam_euler, Mg3d::get_angu(), Map::get_bvect_cart(), Map::get_bvect_spher(), Tenseur::get_etat(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Tenseur::get_triad(), Tenseur::gradient(), Tenseur::gradient_spher(), Eos::identify(), log(), Etoile::mp, Etoile::nnn, norme(), Etoile::nzet, Map::poisson_compact(), psi0, Map::r, ref_triad, Tenseur::set(), Cmp::set(), Scalar::set_domain(), Tenseur::set_etat_qcq(), Scalar::set_outer_boundary(), Tenseur::set_std_base(), Tenseur::set_triad(), sqrt(), ssjm1_psi, Etoile::unsurc2, Cmp::va, Valeur::ylm(), and Valeur::ylm_i().

double Etoile_bin::xa_barycenter (  )  const [virtual]

Absolute coordinate X of the barycenter of the baryon density, defined according to the formula

\[ X_G := \int A^3 \Gamma_{\rm n} \, n \, X \, d^3x \ , \]

where $\Gamma_{\rm n}$ is the Lorentz factor between the fluid and Eulerian observers.

Definition at line 166 of file et_bin_global.C.

References Etoile::a_car, Etoile::gam_euler, Cmp::integrale(), mass_b(), Etoile::mp, Etoile::nbar, p_xa_barycenter, sqrt(), Cmp::std_base_scal(), and Map::xa.

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

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

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

Definition at line 97 of file etoile_global.C.

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

Friends And Related Function Documentation

friend class Bin_ns_bh [friend]

Friend class Bin_ns_bh.

Reimplemented in Et_bin_nsbh.

Definition at line 1462 of file etoile.h.

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

Display.

Member Data Documentation

Tenseur Etoile::a_car [protected, inherited]

Total conformal factor $A^2$.

Definition at line 503 of file etoile.h.

Tenseur Etoile_bin::akcar_auto [protected]

Part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto , i.e.

$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm auto}$

Definition at line 923 of file etoile.h.

Tenseur Etoile_bin::akcar_comp [protected]

Part of the scalar $A^2 K_{ij} K^{ij}$ generated by shift_auto and shift_comp , i.e.

$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm comp}$

Definition at line 929 of file etoile.h.

Tenseur Etoile::beta_auto [protected, inherited]

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

Definition at line 494 of file etoile.h.

Tenseur Etoile_bin::beta_comp [protected]

Part of the logarithm of AN generated principaly by the companion star.

Definition at line 859 of file etoile.h.

Tenseur Etoile_bin::bsn [protected]

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

(Cartesian components with respect to ref_triad )

Definition at line 935 of file etoile.h.

Tenseur Etoile_bin::d_beta_auto [protected]

Gradient of beta_auto (Cartesian components with respect to ref_triad ).

Definition at line 864 of file etoile.h.

Tenseur Etoile_bin::d_beta_comp [protected]

Gradient of beta_comp (Cartesian components with respect to ref_triad ).

Definition at line 869 of file etoile.h.

Tenseur Etoile_bin::d_logn_auto [protected]

Gradient of logn_auto (Cartesian components with respect to ref_triad ).

Definition at line 844 of file etoile.h.

Tenseur Etoile::d_logn_auto_div [protected, inherited]

Gradient of logn_auto_div (if k_div!=0 ).

Definition at line 489 of file etoile.h.

Tenseur Etoile_bin::d_logn_auto_regu [protected]

Gradient of logn_auto_regu (Cartesian components with respect to ref_triad ).

Definition at line 849 of file etoile.h.

Tenseur Etoile_bin::d_logn_comp [protected]

Gradient of logn_comp (Cartesian components with respect to ref_triad ).

Definition at line 854 of file etoile.h.

Tenseur Etoile_bin::d_psi [protected]

Gradient of $\Psi$ (in the irrotational case) (Cartesian components with respect to ref_triad ).

Definition at line 823 of file etoile.h.

Cmp Etoile_bin::decouple [protected]

Function used to construct the part of $K^{ij}$ generated by the star from the total $K^{ij}$.

Only used for a binary system where the other member is a black hole.

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

Definition at line 985 of file etoile.h.

Tenseur Etoile::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 448 of file etoile.h.

Tenseur Etoile::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 453 of file etoile.h.

Tenseur Etoile::ent [protected, inherited]

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

Definition at line 445 of file etoile.h.

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

Equation of state of the stellar matter.

Reimplemented in Et_rot_bifluid.

Definition at line 440 of file etoile.h.

Tenseur Etoile::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 459 of file etoile.h.

bool Etoile_bin::irrotational [protected]

true for an irrotational star, false for a corotating one

Definition at line 807 of file etoile.h.

int Etoile::k_div [protected, inherited]

Index of regularity of the gravitational potential logn_auto .

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

Definition at line 438 of file etoile.h.

Tenseur Etoile_bin::khi_shift [protected]

Scalar $\chi$ used in the decomposition of shift_auto , 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 903 of file etoile.h.

Tenseur Etoile_bin::loggam [protected]

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

Definition at line 834 of file etoile.h.

Tenseur Etoile::logn_auto [protected, inherited]

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

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

Definition at line 472 of file etoile.h.

Tenseur Etoile::logn_auto_div [protected, inherited]

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

Definition at line 485 of file etoile.h.

Tenseur Etoile::logn_auto_regu [protected, inherited]

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

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

Definition at line 479 of file etoile.h.

Tenseur Etoile_bin::logn_comp [protected]

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

Definition at line 839 of file etoile.h.

Map& Etoile::mp [protected, inherited]

Mapping associated with the star.

Definition at line 416 of file etoile.h.

Tenseur Etoile::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 447 of file etoile.h.

Tenseur Etoile::nnn [protected, inherited]

Total lapse function.

Definition at line 497 of file etoile.h.

int Etoile::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 421 of file etoile.h.

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

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

Definition at line 527 of file etoile.h.

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

Baryon mass.

Definition at line 535 of file etoile.h.

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

Gravitational mass.

Definition at line 536 of file etoile.h.

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

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

Definition at line 509 of file etoile.h.

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

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

Definition at line 518 of file etoile.h.

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

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

Definition at line 515 of file etoile.h.

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

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

Definition at line 512 of file etoile.h.

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

Coordinate radius at $\theta=0$.

Definition at line 521 of file etoile.h.

double* Etoile_bin::p_xa_barycenter [mutable, protected]

Absolute coordinate X of the barycenter of the baryon density.

Definition at line 991 of file etoile.h.

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

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

Definition at line 533 of file etoile.h.

Tenseur Etoile_bin::pot_centri [protected]

Centrifugal potential.

Definition at line 938 of file etoile.h.

Tenseur Etoile::press [protected, inherited]

Fluid pressure.

Definition at line 449 of file etoile.h.

Tenseur Etoile_bin::psi0 [protected]

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

Definition at line 818 of file etoile.h.

const Base_vect& Etoile_bin::ref_triad [protected]

Reference triad ("absolute frame"), with respect to which the components of all the member Tenseur 's are defined, except for w_shift and ssjm1_wshift .

Definition at line 813 of file etoile.h.

bool Etoile::relativistic [protected, inherited]

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

Definition at line 426 of file etoile.h.

Tenseur Etoile::s_euler [protected, inherited]

Trace of the stress tensor in the Eulerian frame.

Definition at line 456 of file etoile.h.

Tenseur Etoile::shift [protected, inherited]

Total shift vector.

Definition at line 500 of file etoile.h.

Tenseur Etoile_bin::shift_auto [protected]

Part of the shift vector $N^i$ generated principaly by the star.

(Cartesian components with respect to ref_triad )

Definition at line 874 of file etoile.h.

Tenseur Etoile_bin::shift_comp [protected]

Part of the shift vector $N^i$ generated principaly by the companion star.

(Cartesian components with respect to ref_triad )

Definition at line 880 of file etoile.h.

Cmp Etoile_bin::ssjm1_beta [protected]

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

Definition at line 950 of file etoile.h.

Cmp Etoile_bin::ssjm1_khi [protected]

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

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

Definition at line 958 of file etoile.h.

Cmp Etoile_bin::ssjm1_logn [protected]

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

Definition at line 944 of file etoile.h.

Cmp Etoile_bin::ssjm1_psi [protected]

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

Definition at line 974 of file etoile.h.

Tenseur Etoile_bin::ssjm1_wshift [protected]

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

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

Definition at line 968 of file etoile.h.

Tenseur_sym Etoile_bin::tkij_auto [protected]

Part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_auto .

(Cartesian components with respect to ref_triad )

Reimplemented in Et_bin_nsbh.

Definition at line 910 of file etoile.h.

Tenseur_sym Etoile_bin::tkij_comp [protected]

Part of the extrinsic curvature tensor $\tilde K^{ij} = A^2 K^{ij}$ generated by shift_comp .

(Cartesian components with respect to ref_triad )

Definition at line 917 of file etoile.h.

Tenseur Etoile::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 462 of file etoile.h.

double Etoile::unsurc2 [protected, inherited]

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

Definition at line 431 of file etoile.h.

Tenseur Etoile_bin::w_shift [protected]

Vector $W^i$ used in the decomposition of shift_auto , 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 893 of file etoile.h.

Tenseur Etoile_bin::wit_w [protected]

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

(Cartesian components with respect to ref_triad )

Definition at line 829 of file etoile.h.

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