# Lorene::Et_bin_bhns_extr Class Reference [Stars and black holes]

Class for a neutron star in black hole - neutron star binary systems. More...

#include <et_bin_bhns_extr.h>

Inheritance diagram for Lorene::Et_bin_bhns_extr:

List of all members.

## Public Member Functions

Et_bin_bhns_extr (Map &mp_i, int nzet_i, bool relat, const Eos &eos_i, bool irrot, const Base_vect &ref_triad_i, bool kerrs, bool multi)
Standard constructor.
Et_bin_bhns_extr (const Et_bin_bhns_extr &)
Copy constructor.
Et_bin_bhns_extr (Map &mp_i, const Eos &eos_i, const Base_vect &ref_triad_i, FILE *fich)
Constructor from a file (see sauve(FILE*) ).
virtual ~Et_bin_bhns_extr ()
Destructor.
void operator= (const Et_bin_bhns_extr &)
Assignment to another Et_bin_bhns_extr.
bool in_kerrschild () const
Returns true for the Kerr-Schild background metric, false for the conformally flat one.
bool with_multipole () const
Returns true for the multipole falloff boundary condition, false for the one.
virtual void sauve (FILE *) const
Save in a file.
void hydro_euler_extr (const double &mass, const double &sepa)
Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame, as well as wit_w and loggam in the Kerr-Schild background metric or in the conformally flat one.
void update_metric_extr (const double &mass, const double &sepa)
Computes metric coefficients from known potentials, when the companion is a black hole with the Kerr-Schild metric or with the conformally flat one.
void update_metric_der_comp_extr (const double &mass, const double &sepa)
Computes the derivative of metric functions related to the companion black hole with the Kerr-Schild metric or with the conformally flat one.
void kinematics_extr (double omega, const double &mass, const double &sepa)
Computes the quantities bsn and pot_centri in the Kerr-Schild background metric or in the conformally flat one.
void extrinsic_curv_extr (const double &mass, const double &sepa)
Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .
void equil_bhns_extr_ks (double ent_c, const double &mass, const double &sepa, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl &diff)
Computes an equilibrium configuration of a BH-NS binary system in the Kerr-Schild background metric using the falloff boundary condition.
void equil_bhns_extr_cf (double ent_c, const double &mass, const double &sepa, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl &diff)
Computes an equilibrium configuration of a BH-NS binary system in the conformally flat background metric using the falloff boundary condition.
void equil_bhns_extr_ylm_ks (double ent_c, const double &mass, const double &sepa, double *nu_int, double *beta_int, double *shift_int, int mermax, int mermax_poisson, double relax_poisson, double relax_ylm, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl &diff)
Computes an equilibrium configuration of a BH-NS binary system in the Kerr-Schild background metric using the multipole falloff boundary condition.
void equil_bhns_extr_ylm_cf (double ent_c, const double &mass, const double &sepa, double *nu_int, double *beta_int, double *shift_int, int mermax, int mermax_poisson, double relax_poisson, double relax_ylm, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl &diff)
Computes an equilibrium configuration of a BH-NS binary system in the conformally flat background metric using the multipole falloff boundary condition.
void test_bhns_extr (const double &mass, const double &sepa, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, Tbl &diff)
Tests the resolution of the Poisson equations when the NS has no matter source.
double velocity_pot_extr (const double &mass, const double &sepa, int mermax, double precis, double relax)
Computes the non-translational part of the velocity scalar potential by solving the continuity equation in the Kerr-Schild background metric or in the conformally flat one.
void ent_max_search (double &xx, double &yy) const
Searches the position of the maximum enthalpy.
double phi_longest_rad (double x_max, double y_max) const
Searches the position (phi) of the longest radius of NS from the position of the maximum enthalpy.
void get_ylm (int nylm, Cmp **ylmvec) const
Constructs spherical harmonics.
void get_integrals (int nylm, double *intvec, Cmp **ylmvec, Cmp source) const
Computes multipole moments.
Tenseurset_logn_comp ()
Read/write the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.
Tenseurset_pot_centri ()
Tenseurset_w_shift ()
Read/write of w_shift.
Tenseurset_khi_shift ()
Read/write of khi_shift.
bool is_irrotational () const
Returns true for an irrotational motion, false for a corotating one.
const Tenseurget_psi0 () const
Returns the non-translational part of the velocity potential.
const Tenseurget_d_psi () const
Returns the gradient of the velocity potential (Cartesian components with respect to ref_triad ).
const Tenseurget_wit_w () const
Returns the spatial projection of the fluid 3-velocity with respect to the co-orbiting observer.
const Tenseurget_loggam () const
Returns the logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
const Tenseurget_logn_comp () const
Returns the part of the lapse logarithm (gravitational potential at the Newtonian limit) generated principaly by the companion star.
const Tenseurget_d_logn_auto () const
Returns the gradient of logn_auto (Cartesian components with respect to ref_triad ).
const Tenseurget_d_logn_auto_regu () const
Returns the gradient of logn_auto_regu (Cartesian components with respect to ref_triad ).
const Tenseurget_d_logn_comp () const
Returns the gradient of logn_comp (Cartesian components with respect to ref_triad ).
const Tenseurget_beta_comp () const
Returns the part of the logarithm of AN generated principaly by the companion star.
const Tenseurget_d_beta_auto () const
Returns the gradient of beta_auto (Cartesian components with respect to ref_triad ).
const Tenseurget_d_beta_comp () const
Returns the gradient of beta_comp (Cartesian components with respect to ref_triad ).
const Tenseurget_shift_auto () const
Returns the part of the shift vector generated principaly by the star.
const Tenseurget_shift_comp () const
Returns the part of the shift vector generated principaly by the companion star.
const Tenseurget_w_shift () const
Returns the vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.
const Tenseurget_khi_shift () const
Returns the scalar used in the decomposition of shift_auto following Shibata's prescription [Prog.
const Tenseur_symget_tkij_auto () const
Returns the part of the extrinsic curvature tensor generated by shift_auto .
const Tenseur_symget_tkij_comp () const
Returns the part of the extrinsic curvature tensor generated by shift_comp .
const Tenseurget_akcar_auto () const
Returns the part of the scalar generated by shift_auto , i.e.
const Tenseurget_akcar_comp () const
Returns the part of the scalar generated by shift_auto and shift_comp , i.e.
const Tenseurget_bsn () const
Returns the shift vector, divided by N , of the rotating coordinates, .
const Tenseurget_pot_centri () const
Returns the centrifugal potential.
const Cmp get_decouple () const
Returns the function used to construct tkij_auto from tkij_tot .
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

where 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 .
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 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 .
Mapset_mp ()
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 Mapget_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 Eosget_eos () const
Returns the equation of state.
const Tenseurget_ent () const
Returns the enthalpy field.
const Tenseurget_nbar () const
Returns the proper baryon density.
const Tenseurget_ener () const
Returns the proper total energy density.
const Tenseurget_press () const
Returns the fluid pressure.
const Tenseurget_ener_euler () const
Returns the total energy density with respect to the Eulerian observer.
const Tenseurget_s_euler () const
Returns the trace of the stress tensor in the Eulerian frame.
const Tenseurget_gam_euler () const
Returns the Lorentz factor between the fluid and Eulerian observers.
const Tenseurget_u_euler () const
Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tenseurget_logn_auto () const
Returns the logarithm of the part of the lapse N generated principaly by the star.
const Tenseurget_logn_auto_regu () const
Returns the regular part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseurget_logn_auto_div () const
Returns the divergent part of the logarithm of the part of the lapse N generated principaly by the star.
const Tenseurget_d_logn_auto_div () const
Returns the gradient of logn_auto_div.
const Tenseurget_beta_auto () const
Returns the logarithm of the part of the product AN generated principaly by the star.
const Tenseurget_nnn () const
Returns the total lapse function N.
const Tenseurget_shift () const
Returns the total shift vector .
const Tenseurget_a_car () const
Returns the total conformal factor .
double ray_eq () const
double ray_eq (int kk) const
double ray_eq_pis2 () const
double ray_eq_pi () const
double ray_eq_3pis2 () const
double ray_pole () const
virtual const Itbll_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 .
const Tblxi_surf () const
Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate on the surface at the collocation points in .

## 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 kerrschild
Indicator of the background metric: true for the Kerr-Shild metric, false for the conformally flat one.
bool multipole
Indicator of the boundary condition: true for the multipole falloff condition, false for the one.
bool irrotational
true for an irrotational star, false for a corotating one
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 of the non-translational part of fluid 4-velocity (in the irrotational case).
Tenseur d_psi
Gradient of (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 generated principaly by the star.
Tenseur shift_comp
Part of the shift vector generated principaly by the companion star.
Tenseur w_shift
Vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Tenseur khi_shift
Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.
Tenseur_sym tkij_auto
Part of the extrinsic curvature tensor generated by shift_auto .
Tenseur_sym tkij_comp
Part of the extrinsic curvature tensor generated by shift_comp .
Tenseur akcar_auto
Part of the scalar generated by shift_auto , i.e.
Tenseur akcar_comp
Part of the scalar generated by shift_auto and shift_comp , i.e.
Tenseur bsn
3-vector shift, divided by N , of the rotating coordinates, .
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 by means of Map_et::poisson .
Tenseur ssjm1_wshift
Effective source at the previous step for the resolution of the vector Poisson equation for 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 by means of Map_et::poisson_interne .
Cmp decouple
Function used to construct the part of generated by the star from the total .
double * p_xa_barycenter
Absolute coordinate X of the barycenter of the baryon density.
Mapmp
Mapping associated with the star.
int nzet
Number of domains of *mp occupied by the star.
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
double unsurc2
: unsurc2=1 for a relativistic star, 0 for a Newtonian one.
int k_div
Index of regularity of the gravitational potential logn_auto .
const Eoseos
Equation of state of the stellar matter.
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).
Tenseur nbar
Baryon density in the fluid frame.
Tenseur ener
Total energy density in the fluid frame.
Tenseur press
Fluid pressure.
Tenseur ener_euler
Total energy density in the Eulerian frame.
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Tenseur u_euler
Fluid 3-velocity with respect to the Eulerian observer.
Tenseur logn_auto
Total of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur logn_auto_regu
Regular part of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur logn_auto_div
Divergent part (if k_div!=0 ) of the logarithm of the part of the lapse N generated principaly by the star.
Tenseur d_logn_auto_div
Gradient of logn_auto_div (if k_div!=0 ).
Tenseur beta_auto
Logarithm of the part of the product AN generated principaly by by the star.
Tenseur nnn
Total lapse function.
Tenseur shift
Total shift vector.
Tenseur a_car
Total conformal factor .
double * p_ray_eq
double * p_ray_eq_pis2
double * p_ray_eq_pi
double * p_ray_eq_3pis2
double * p_ray_pole
Itblp_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 .
Tblp_xi_surf
Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate on the surface at the collocation points in .
double * p_mass_b
Baryon mass.
double * p_mass_g
Gravitational mass.

## Friends

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

## Detailed Description

Class for a neutron star in black hole - neutron star binary systems.

()

In this class, we assume that the mass ratio of NS to BH is extreme, and the effect from a black hole is treated as the external, background field of the Kerr-Schild metric or the conformally flat metric. They are splitted by the boolian indicator.

Definition at line 68 of file et_bin_bhns_extr.h.

## Constructor & Destructor Documentation

 Lorene::Et_bin_bhns_extr::Et_bin_bhns_extr ( Map & mp_i, int nzet_i, bool relat, const Eos & eos_i, bool irrot, const Base_vect & ref_triad_i, bool kerrs, bool multi )

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. kerrs should be true for the Kerr-Schild background metric, false for the conformally flat one multi should be true for the multipol falloff boundary condition, false for the one

Definition at line 68 of file et_bin_bhns_extr.C.

 Lorene::Et_bin_bhns_extr::Et_bin_bhns_extr ( const Et_bin_bhns_extr & ns )

Copy constructor.

Definition at line 79 of file et_bin_bhns_extr.C.

 Lorene::Et_bin_bhns_extr::Et_bin_bhns_extr ( 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 87 of file et_bin_bhns_extr.C.

References kerrschild, and multipole.

 Lorene::Et_bin_bhns_extr::~Et_bin_bhns_extr ( )  [virtual]

Destructor.

Definition at line 104 of file et_bin_bhns_extr.C.

## Member Function Documentation

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

Deletes all the derived quantities.

Reimplemented from Lorene::Etoile.

Definition at line 450 of file etoile_bin.C.

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

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

Reimplemented from Lorene::Etoile.

Definition at line 470 of file etoile_bin.C.

References Lorene::Etoile_bin::del_deriv().

 void Lorene::Et_bin_bhns_extr::ent_max_search ( double & xx, double & yy ) const

Searches the position of the maximum enthalpy.

Parameters:
 xx [output] x-coordinate of the maximum enthalpy yy [output] y-coordinate of the maximum enthalpy

Definition at line 59 of file et_bin_bhns_extr_max.C.

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

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

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

Definition at line 569 of file etoile.C.

 void Lorene::Et_bin_bhns_extr::equil_bhns_extr_cf ( double ent_c, const double & mass, const double & sepa, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl & diff )

Computes an equilibrium configuration of a BH-NS binary system in the conformally flat background metric using the falloff boundary condition.

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

Parameters:
 ent_c [input] Central enthalpy mass [input] Mass of BH sepa [input] Orbital separation 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 np_filter [input] Number of coefficients in phi which are deleted by filter thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping diff [output] 1-D Tbl for the storage of some error indicators : 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 842 of file et_bin_bhns_extr_equil.C.

 void Lorene::Et_bin_bhns_extr::equil_bhns_extr_ks ( double ent_c, const double & mass, const double & sepa, int mermax, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl & diff )

Computes an equilibrium configuration of a BH-NS binary system in the Kerr-Schild background metric using the falloff boundary condition.

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

Parameters:
 ent_c [input] Central enthalpy mass [input] Mass of BH sepa [input] Orbital separation 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 np_filter [input] Number of coefficients in phi which are deleted by filter thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping diff [output] 1-D Tbl for the storage of some error indicators : 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 91 of file et_bin_bhns_extr_equil.C.

 void Lorene::Et_bin_bhns_extr::equil_bhns_extr_ylm_cf ( double ent_c, const double & mass, const double & sepa, double * nu_int, double * beta_int, double * shift_int, int mermax, int mermax_poisson, double relax_poisson, double relax_ylm, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl & diff )

Computes an equilibrium configuration of a BH-NS binary system in the conformally flat background metric using the multipole falloff boundary condition.

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

Parameters:
 ent_c [input] Central enthalpy mass [input] Mass of BH sepa [input] Orbital separation nu_int [input] Multipole moment for logn in the previous step beta_int [input] Multipole moment for beta in the previous step shift_int [input] Multipole moment for shift in the previous step 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 relax_ylm [input] Relaxation factor on the outer boundary condition mermax_potvit [input] Maximum number of steps in Map_radial::poisson_compact relax_potvit [input] Relaxation factor in Map_radial::poisson_compact np_filter [input] Number of coefficients in phi which are deleted by filter thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping diff [output] 1-D Tbl for the storage of some error indicators : 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 972 of file et_bin_bhns_extr_eq_ylm.C.

 void Lorene::Et_bin_bhns_extr::equil_bhns_extr_ylm_ks ( double ent_c, const double & mass, const double & sepa, double * nu_int, double * beta_int, double * shift_int, int mermax, int mermax_poisson, double relax_poisson, double relax_ylm, int mermax_potvit, double relax_potvit, int np_filter, double thres_adapt, Tbl & diff )

Computes an equilibrium configuration of a BH-NS binary system in the Kerr-Schild background metric using the multipole falloff boundary condition.

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

Parameters:
 ent_c [input] Central enthalpy mass [input] Mass of BH sepa [input] Orbital separation nu_int [input] Multipole moment for logn in the previous step beta_int [input] Multipole moment for beta in the previous step shift_int [input] Multipole moment for shift in the previous step 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 relax_ylm [input] Relaxation factor on the outer boundary condition mermax_potvit [input] Maximum number of steps in Map_radial::poisson_compact relax_potvit [input] Relaxation factor in Map_radial::poisson_compact np_filter [input] Number of coefficients in phi which are deleted by filter thres_adapt [input] Threshold on dH/dr for the adaptation of the mapping diff [output] 1-D Tbl for the storage of some error indicators : 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 82 of file et_bin_bhns_extr_eq_ylm.C.

 void Lorene::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 )  [inherited]

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 147 of file et_bin_equil_regu.C.

 void Lorene::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 60 of file etoile_eqsph_falloff.C.

 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.

 void Lorene::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 )  [inherited]

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 187 of file et_bin_equilibrium.C.

 void Lorene::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 90 of file etoile_equil_spher.C.

 void Lorene::Et_bin_bhns_extr::extrinsic_curv_extr ( const double & mass, const double & sepa )

Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .

in the Kerr-Schild background metric or in the conformally flat one

Parameters:
 mass mass of the BH sepa separation between NS and BH

In the codes related BH-NS binary systems with extreme mass ratio, "tkij_auto" means A_{tot}^2 A_{NS}^{ij} =-0.5/nnn*(DN_{NS}+DN_{NS}-2/3gammaDN_{NS}) and "akcar_auto" A_{tot}^2 A^{NS}_{ij} A_{NS}^{ij} =A_{tot}^2 gamma gamma tkij_auto tkij_auto

In the codes related BH-NS binary systems with an extreme mass ratio, "tkij_auto" means A_{tot}^2 A_{NS}^{ij} =-0.5/nnn*(DN_{NS}+DN_{NS}-2/3gammaDN_{NS}) and "akcar_auto" A_{tot}^2 A^{NS}_{ij} A_{NS}^{ij} =A_{tot}^2 eta eta tkij_auto tkij_auto

Definition at line 65 of file et_bin_bhns_extr_excurv.C.

 void Lorene::Etoile_bin::extrinsic_curvature ( )  [virtual, inherited]

Computes tkij_auto and akcar_auto from shift_auto , nnn and a_car .

Definition at line 67 of file et_bin_extr_curv.C.

 void Lorene::Etoile_bin::fait_d_psi ( )  [inherited]
 void Lorene::Etoile_bin::fait_shift_auto ( )  [inherited]

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

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

Definition at line 829 of file etoile_bin.C.

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

Returns the total conformal factor .

Definition at line 733 of file etoile.h.

References Lorene::Etoile::a_car.

 const Tenseur& Lorene::Etoile_bin::get_akcar_auto ( ) const [inline, inherited]

Returns the part of the scalar generated by shift_auto , i.e.

Definition at line 1204 of file etoile.h.

References Lorene::Etoile_bin::akcar_auto.

 const Tenseur& Lorene::Etoile_bin::get_akcar_comp ( ) const [inline, inherited]

Returns the part of the scalar generated by shift_auto and shift_comp , i.e.

Definition at line 1210 of file etoile.h.

References Lorene::Etoile_bin::akcar_comp.

 const Tenseur& Lorene::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 724 of file etoile.h.

References Lorene::Etoile::beta_auto.

 const Tenseur& Lorene::Etoile_bin::get_beta_comp ( ) const [inline, inherited]

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

Definition at line 1136 of file etoile.h.

References Lorene::Etoile_bin::beta_comp.

 const Tenseur& Lorene::Etoile_bin::get_bsn ( ) const [inline, inherited]

Returns the shift vector, divided by N , of the rotating coordinates, .

(Cartesian components with respect to ref_triad )

Definition at line 1216 of file etoile.h.

References Lorene::Etoile_bin::bsn.

 const Tenseur& Lorene::Etoile_bin::get_d_beta_auto ( ) const [inline, inherited]

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

Definition at line 1141 of file etoile.h.

References Lorene::Etoile_bin::d_beta_auto.

 const Tenseur& Lorene::Etoile_bin::get_d_beta_comp ( ) const [inline, inherited]

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

Definition at line 1146 of file etoile.h.

References Lorene::Etoile_bin::d_beta_comp.

 const Tenseur& Lorene::Etoile_bin::get_d_logn_auto ( ) const [inline, inherited]

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

Definition at line 1121 of file etoile.h.

References Lorene::Etoile_bin::d_logn_auto.

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

Returns the gradient of logn_auto_div.

Definition at line 719 of file etoile.h.

References Lorene::Etoile::d_logn_auto_div.

 const Tenseur& Lorene::Etoile_bin::get_d_logn_auto_regu ( ) const [inline, inherited]

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

Definition at line 1126 of file etoile.h.

References Lorene::Etoile_bin::d_logn_auto_regu.

 const Tenseur& Lorene::Etoile_bin::get_d_logn_comp ( ) const [inline, inherited]

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

Definition at line 1131 of file etoile.h.

References Lorene::Etoile_bin::d_logn_comp.

 const Tenseur& Lorene::Etoile_bin::get_d_psi ( ) const [inline, inherited]

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

Definition at line 1100 of file etoile.h.

References Lorene::Etoile_bin::d_psi.

 const Cmp Lorene::Etoile_bin::get_decouple ( ) const [inline, inherited]

Returns the function used to construct tkij_auto from tkij_tot .

Definition at line 1224 of file etoile.h.

References Lorene::Etoile_bin::decouple.

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

Returns the proper total energy density.

Definition at line 679 of file etoile.h.

References Lorene::Etoile::ener.

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

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

Definition at line 685 of file etoile.h.

References Lorene::Etoile::ener_euler.

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

Returns the enthalpy field.

Definition at line 673 of file etoile.h.

References Lorene::Etoile::ent.

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

Returns the equation of state.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 670 of file etoile.h.

References Lorene::Etoile::eos.

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

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 691 of file etoile.h.

References Lorene::Etoile::gam_euler.

 void Lorene::Et_bin_bhns_extr::get_integrals ( int nylm, double * intvec, Cmp ** ylmvec, Cmp source ) const

Computes multipole moments.

Definition at line 258 of file et_bin_bhns_extr_ylm.C.

 const Tenseur& Lorene::Etoile_bin::get_khi_shift ( ) const [inline, inherited]

Returns the scalar used in the decomposition of shift_auto following Shibata's prescription [Prog.

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

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

Definition at line 1186 of file etoile.h.

References Lorene::Etoile_bin::khi_shift.

 const Tenseur& Lorene::Etoile_bin::get_loggam ( ) const [inline, inherited]

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

Definition at line 1111 of file etoile.h.

References Lorene::Etoile_bin::loggam.

 const Tenseur& Lorene::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 ).

Definition at line 701 of file etoile.h.

References Lorene::Etoile::logn_auto.

 const Tenseur& Lorene::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 ).

Definition at line 715 of file etoile.h.

References Lorene::Etoile::logn_auto_div.

 const Tenseur& Lorene::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 ).

Definition at line 708 of file etoile.h.

References Lorene::Etoile::logn_auto_regu.

 const Tenseur& Lorene::Etoile_bin::get_logn_comp ( ) const [inline, inherited]

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

Definition at line 1116 of file etoile.h.

References Lorene::Etoile_bin::logn_comp.

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

Returns the mapping.

Definition at line 659 of file etoile.h.

References Lorene::Etoile::mp.

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

Returns the proper baryon density.

Definition at line 676 of file etoile.h.

References Lorene::Etoile::nbar.

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

Returns the total lapse function N.

Definition at line 727 of file etoile.h.

References Lorene::Etoile::nnn.

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

Returns the number of domains occupied by the star.

Definition at line 662 of file etoile.h.

References Lorene::Etoile::nzet.

 const Tenseur& Lorene::Etoile_bin::get_pot_centri ( ) const [inline, inherited]

Returns the centrifugal potential.

Definition at line 1219 of file etoile.h.

References Lorene::Etoile_bin::pot_centri.

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

Returns the fluid pressure.

Definition at line 682 of file etoile.h.

References Lorene::Etoile::press.

 const Tenseur& Lorene::Etoile_bin::get_psi0 ( ) const [inline, inherited]

Returns the non-translational part of the velocity potential.

Definition at line 1095 of file etoile.h.

References Lorene::Etoile_bin::psi0.

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

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

Definition at line 688 of file etoile.h.

References Lorene::Etoile::s_euler.

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

Returns the total shift vector .

Definition at line 730 of file etoile.h.

References Lorene::Etoile::shift.

 const Tenseur& Lorene::Etoile_bin::get_shift_auto ( ) const [inline, inherited]

Returns the part of the shift vector generated principaly by the star.

(Cartesian components with respect to ref_triad )

Definition at line 1152 of file etoile.h.

References Lorene::Etoile_bin::shift_auto.

 const Tenseur& Lorene::Etoile_bin::get_shift_comp ( ) const [inline, inherited]

Returns the part of the shift vector generated principaly by the companion star.

(Cartesian components with respect to ref_triad )

Definition at line 1158 of file etoile.h.

References Lorene::Etoile_bin::shift_comp.

 const Tenseur_sym& Lorene::Etoile_bin::get_tkij_auto ( ) const [inline, inherited]

Returns the part of the extrinsic curvature tensor generated by shift_auto .

(Cartesian components with respect to ref_triad )

Reimplemented in Lorene::Et_bin_nsbh.

Definition at line 1192 of file etoile.h.

References Lorene::Etoile_bin::tkij_auto.

 const Tenseur_sym& Lorene::Etoile_bin::get_tkij_comp ( ) const [inline, inherited]

Returns the part of the extrinsic curvature tensor generated by shift_comp .

(Cartesian components with respect to ref_triad )

Definition at line 1198 of file etoile.h.

References Lorene::Etoile_bin::tkij_comp.

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

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

Definition at line 694 of file etoile.h.

References Lorene::Etoile::u_euler.

 const Tenseur& Lorene::Etoile_bin::get_w_shift ( ) const [inline, inherited]

Returns the vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.

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

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

Definition at line 1172 of file etoile.h.

References Lorene::Etoile_bin::w_shift.

 const Tenseur& Lorene::Etoile_bin::get_wit_w ( ) const [inline, inherited]

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 1106 of file etoile.h.

References Lorene::Etoile_bin::wit_w.

 void Lorene::Et_bin_bhns_extr::get_ylm ( int nylm, Cmp ** ylmvec ) const

Constructs spherical harmonics.

Definition at line 66 of file et_bin_bhns_extr_ylm.C.

 void Lorene::Etoile_bin::hydro_euler ( )  [virtual, inherited]

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 Lorene::Etoile.

Definition at line 109 of file et_bin_hydro.C.

 void Lorene::Et_bin_bhns_extr::hydro_euler_extr ( const double & mass, const double & sepa )

Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame, as well as wit_w and loggam in the Kerr-Schild background metric or in the conformally flat one.

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 .

Parameters:
 mass mass of the BH sepa separation between NS and BH

Definition at line 59 of file et_bin_bhns_extr_hydro.C.

 bool Lorene::Et_bin_bhns_extr::in_kerrschild ( ) const [inline]

Returns true for the Kerr-Schild background metric, false for the conformally flat one.

Definition at line 145 of file et_bin_bhns_extr.h.

References kerrschild.

 bool Lorene::Etoile_bin::is_irrotational ( ) const [inline, inherited]

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

Definition at line 1092 of file etoile.h.

References Lorene::Etoile_bin::irrotational.

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

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

Definition at line 667 of file etoile.h.

References Lorene::Etoile::relativistic.

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

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 Lorene::Et_bin_nsbh.

Definition at line 84 of file et_bin_kinema.C.

 void Lorene::Et_bin_bhns_extr::kinematics_extr ( double omega, const double & mass, const double & sepa )

Computes the quantities bsn and pot_centri in the Kerr-Schild background metric or in the conformally flat one.

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 mass mass of the BH sepa separation between NS and BH

Definition at line 58 of file et_bin_bhns_extr_kinema.C.

 const Itbl & Lorene::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 .

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

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

Definition at line 78 of file etoile_global.C.

 double Lorene::Etoile_bin::mass_b ( ) const [virtual, inherited]

Baryon mass.

Reimplemented from Lorene::Etoile.

Definition at line 103 of file et_bin_global.C.

 double Lorene::Etoile_bin::mass_g ( ) const [virtual, inherited]

Gravitational mass.

Reimplemented from Lorene::Etoile.

Definition at line 140 of file et_bin_global.C.

 void Lorene::Et_bin_bhns_extr::operator= ( const Et_bin_bhns_extr & ns )

Assignment to another Et_bin_bhns_extr.

Reimplemented from Lorene::Etoile_bin.

Definition at line 113 of file et_bin_bhns_extr.C.

References kerrschild, and multipole.

 ostream & Lorene::Etoile_bin::operator>> ( ostream & ost ) const [protected, virtual, inherited]
 double Lorene::Et_bin_bhns_extr::phi_longest_rad ( double x_max, double y_max ) const

Searches the position (phi) of the longest radius of NS from the position of the maximum enthalpy.

Parameters:
 x_max [input] x-coordinate of the maximum enthalpy y_max [input] y-coordinate of the maximum enthalpy

Definition at line 61 of file et_bin_bhns_extr_phi.C.

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

Definition at line 443 of file etoile_global.C.

 double Lorene::Etoile::ray_eq ( ) const [inherited]

Definition at line 123 of file etoile_global.C.

 double Lorene::Etoile::ray_eq_3pis2 ( ) const [inherited]

Definition at line 338 of file etoile_global.C.

 double Lorene::Etoile::ray_eq_pi ( ) const [inherited]

Definition at line 259 of file etoile_global.C.

 double Lorene::Etoile::ray_eq_pis2 ( ) const [inherited]

Definition at line 172 of file etoile_global.C.

 double Lorene::Etoile::ray_pole ( ) const [inherited]

Definition at line 418 of file etoile_global.C.

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

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 866 of file etoile_bin.C.

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

Save in a file.

Reimplemented from Lorene::Etoile_bin.

Definition at line 130 of file et_bin_bhns_extr.C.

References kerrschild, and multipole.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Etoile.

Definition at line 462 of file etoile_bin.C.

References Lorene::Etoile_bin::p_xa_barycenter.

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

Assignment of the enthalpy field.

Definition at line 468 of file etoile.C.

 Tenseur & Lorene::Etoile_bin::set_khi_shift ( )  [inherited]

Read/write of khi_shift.

Definition at line 548 of file etoile_bin.C.

References Lorene::Etoile_bin::del_deriv(), and Lorene::Etoile_bin::khi_shift.

 Tenseur & Lorene::Etoile_bin::set_logn_comp ( )  [inherited]

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

Definition at line 527 of file etoile_bin.C.

References Lorene::Etoile_bin::del_deriv(), and Lorene::Etoile_bin::logn_comp.

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

Definition at line 601 of file etoile.h.

References Lorene::Etoile::mp.

 Tenseur & Lorene::Etoile_bin::set_pot_centri ( )  [inherited]

Definition at line 534 of file etoile_bin.C.

References Lorene::Etoile_bin::del_deriv(), and Lorene::Etoile_bin::pot_centri.

 Tenseur & Lorene::Etoile_bin::set_w_shift ( )  [inherited]

Read/write of w_shift.

Definition at line 541 of file etoile_bin.C.

References Lorene::Etoile_bin::del_deriv(), and Lorene::Etoile_bin::w_shift.

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

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 is performed to lower one index. For instance, for two vectors and , this function returns the scalar .

Definition at line 751 of file etoile_bin.C.

 void Lorene::Et_bin_bhns_extr::test_bhns_extr ( const double & mass, const double & sepa, int mermax_poisson, double relax_poisson, int mermax_potvit, double relax_potvit, Tbl & diff )

Tests the resolution of the Poisson equations when the NS has no matter source.

The solution should be the same as the Kerr-Schild metric

Parameters:
 mass [input] Mass of BH sepa [input] Orbital separation 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 diff [output] 1-D Tbl for the storage of some error indicators : diff(0) : Relative error returned by the routine Etoile_bin::velocity_potential diff(1) : Relative error in the resolution of the Poisson equation for logn_auto diff(2) : Relative error in the resolution of the Poisson equation for beta_auto diff(3) : Relative error in the resolution of the equation for shift_auto (x comp.) diff(4) : Relative error in the resolution of the equation for shift_auto (y comp.) diff(5) : Relative error in the resolution of the equation for shift_auto (z comp.)
 void Lorene::Etoile_bin::update_metric ( const Etoile_bin & comp, const Etoile_bin & star_prev, double relax )  [inherited]

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 207 of file et_bin_upmetr.C.

 void Lorene::Etoile_bin::update_metric ( const Etoile_bin & comp )  [inherited]

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 103 of file et_bin_upmetr.C.

 void Lorene::Etoile_bin::update_metric_der_comp ( const Etoile_bin & comp )  [inherited]

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 87 of file et_bin_upmetr_der.C.

 void Lorene::Et_bin_bhns_extr::update_metric_der_comp_extr ( const double & mass, const double & sepa )

Computes the derivative of metric functions related to the companion black hole with the Kerr-Schild metric or with the conformally flat one.

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:
 mass mass of the BH sepa separation between NS and BH

The definition of tkij_comp: A_{tot}^2 A_{BH}^{ij} =-0.5/nnn*(DN_{BH}+DN_{BH}-2/3gammaDN_{BH})

Definition at line 64 of file et_bin_bhns_extr_um_der.C.

 void Lorene::Et_bin_bhns_extr::update_metric_extr ( const double & mass, const double & sepa )

Computes metric coefficients from known potentials, when the companion is a black hole with the Kerr-Schild metric or with the conformally flat one.

The calculation is performed starting from the quantities logn_auto , beta_auto , shift_auto which are supposed to be up to date. Using the analytical form of the lapse of BH, the conformal factor of BH, and the shift vector of BH, the following fields are updated: nnn , a_car , shift , d_logn_auto , d_beta_auto , tkij_auto , akcar_auto .

Parameters:
 mass mass of the BH sepa separation between NS and BH

Definition at line 68 of file et_bin_bhns_extr_upmetr.C.

 double Lorene::Et_bin_bhns_extr::velocity_pot_extr ( const double & mass, const double & sepa, int mermax, double precis, double relax )

Computes the non-translational part of the velocity scalar potential by solving the continuity equation in the Kerr-Schild background metric or in the conformally flat one.

Parameters:
 mass [input] Mass of BH sepa [input] Orbital separation mermax [input] Maximum number of steps in the iteration precis [input] Required precision: the iteration will be stopped when the relative difference on 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 70 of file et_bin_bhns_extr_velpot.C.

 double Lorene::Etoile_bin::velocity_potential ( int mermax, double precis, double relax )  [inherited]

Computes the non-translational part of the velocity scalar potential 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 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 145 of file et_bin_vel_pot.C.

 bool Lorene::Et_bin_bhns_extr::with_multipole ( ) const [inline]

Returns true for the multipole falloff boundary condition, false for the one.

Definition at line 150 of file et_bin_bhns_extr.h.

References multipole.

 double Lorene::Etoile_bin::xa_barycenter ( ) const [virtual, inherited]

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

where is the Lorentz factor between the fluid and Eulerian observers.

Definition at line 173 of file et_bin_global.C.

 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 on the surface at the collocation points in .

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

Definition at line 104 of file etoile_global.C.

## Friends And Related Function Documentation

 friend class Bin_ns_bh [friend, inherited]

Friend class Bin_ns_bh.

Reimplemented in Lorene::Et_bin_nsbh.

Definition at line 1476 of file etoile.h.

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

Display.

## Member Data Documentation

 Tenseur Lorene::Etoile::a_car [protected, inherited]

Total conformal factor .

Definition at line 515 of file etoile.h.

 Tenseur Lorene::Etoile_bin::akcar_auto [protected, inherited]

Part of the scalar generated by shift_auto , i.e.

Definition at line 938 of file etoile.h.

 Tenseur Lorene::Etoile_bin::akcar_comp [protected, inherited]

Part of the scalar generated by shift_auto and shift_comp , i.e.

Definition at line 944 of file etoile.h.

 Tenseur Lorene::Etoile::beta_auto [protected, inherited]

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

Definition at line 506 of file etoile.h.

 Tenseur Lorene::Etoile_bin::beta_comp [protected, inherited]

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

Definition at line 874 of file etoile.h.

 Tenseur Lorene::Etoile_bin::bsn [protected, inherited]

3-vector shift, divided by N , of the rotating coordinates, .

(Cartesian components with respect to ref_triad )

Definition at line 950 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_beta_auto [protected, inherited]

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

Definition at line 879 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_beta_comp [protected, inherited]

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

Definition at line 884 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_logn_auto [protected, inherited]

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

Definition at line 859 of file etoile.h.

 Tenseur Lorene::Etoile::d_logn_auto_div [protected, inherited]

Gradient of logn_auto_div (if k_div!=0 ).

Definition at line 501 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_logn_auto_regu [protected, inherited]

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

Definition at line 864 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_logn_comp [protected, inherited]

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

Definition at line 869 of file etoile.h.

 Tenseur Lorene::Etoile_bin::d_psi [protected, inherited]

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

Definition at line 838 of file etoile.h.

 Cmp Lorene::Etoile_bin::decouple [protected, inherited]

Function used to construct the part of generated by the star from the total .

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 1000 of file etoile.h.

 Tenseur Lorene::Etoile::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 460 of file etoile.h.

 Tenseur Lorene::Etoile::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 465 of file etoile.h.

 Tenseur Lorene::Etoile::ent [protected, inherited]

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

Definition at line 457 of file etoile.h.

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

Equation of state of the stellar matter.

Reimplemented in Lorene::Et_rot_bifluid.

Definition at line 451 of file etoile.h.

 Tenseur Lorene::Etoile::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 471 of file etoile.h.

 bool Lorene::Etoile_bin::irrotational [protected, inherited]

true for an irrotational star, false for a corotating one

Definition at line 822 of file etoile.h.

 int Lorene::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 449 of file etoile.h.

 bool Lorene::Et_bin_bhns_extr::kerrschild [protected]

Indicator of the background metric: true for the Kerr-Shild metric, false for the conformally flat one.

Definition at line 78 of file et_bin_bhns_extr.h.

 Tenseur Lorene::Etoile_bin::khi_shift [protected, inherited]

Scalar used in the decomposition of shift_auto , following Shibata's prescription [Prog.

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

Definition at line 918 of file etoile.h.

 Tenseur Lorene::Etoile_bin::loggam [protected, inherited]

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

Definition at line 849 of file etoile.h.

 Tenseur Lorene::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 ).

Definition at line 484 of file etoile.h.

 Tenseur Lorene::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 497 of file etoile.h.

 Tenseur Lorene::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 ).

Definition at line 491 of file etoile.h.

 Tenseur Lorene::Etoile_bin::logn_comp [protected, inherited]

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

Definition at line 854 of file etoile.h.

 Map& Lorene::Etoile::mp [protected, inherited]

Mapping associated with the star.

Definition at line 429 of file etoile.h.

 bool Lorene::Et_bin_bhns_extr::multipole [protected]

Indicator of the boundary condition: true for the multipole falloff condition, false for the one.

Definition at line 84 of file et_bin_bhns_extr.h.

 Tenseur Lorene::Etoile::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 459 of file etoile.h.

 Tenseur Lorene::Etoile::nnn [protected, inherited]

Total lapse function.

Definition at line 509 of file etoile.h.

 int Lorene::Etoile::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 432 of file etoile.h.

 Itbl* Lorene::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 .

Definition at line 539 of file etoile.h.

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

Baryon mass.

Definition at line 547 of file etoile.h.

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

Gravitational mass.

Definition at line 548 of file etoile.h.

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

Definition at line 521 of file etoile.h.

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

Definition at line 530 of file etoile.h.

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

Definition at line 527 of file etoile.h.

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

Definition at line 524 of file etoile.h.

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

Definition at line 533 of file etoile.h.

 double* Lorene::Etoile_bin::p_xa_barycenter [mutable, protected, inherited]

Absolute coordinate X of the barycenter of the baryon density.

Definition at line 1006 of file etoile.h.

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

Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate on the surface at the collocation points in .

Definition at line 545 of file etoile.h.

 Tenseur Lorene::Etoile_bin::pot_centri [protected, inherited]

Centrifugal potential.

Definition at line 953 of file etoile.h.

 Tenseur Lorene::Etoile::press [protected, inherited]

Fluid pressure.

Definition at line 461 of file etoile.h.

 Tenseur Lorene::Etoile_bin::psi0 [protected, inherited]

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

Definition at line 833 of file etoile.h.

 const Base_vect& Lorene::Etoile_bin::ref_triad [protected, inherited]

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 828 of file etoile.h.

 bool Lorene::Etoile::relativistic [protected, inherited]

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

Definition at line 437 of file etoile.h.

 Tenseur Lorene::Etoile::s_euler [protected, inherited]

Trace of the stress tensor in the Eulerian frame.

Definition at line 468 of file etoile.h.

 Tenseur Lorene::Etoile::shift [protected, inherited]

Total shift vector.

Definition at line 512 of file etoile.h.

 Tenseur Lorene::Etoile_bin::shift_auto [protected, inherited]

Part of the shift vector generated principaly by the star.

(Cartesian components with respect to ref_triad )

Definition at line 889 of file etoile.h.

 Tenseur Lorene::Etoile_bin::shift_comp [protected, inherited]

Part of the shift vector generated principaly by the companion star.

(Cartesian components with respect to ref_triad )

Definition at line 895 of file etoile.h.

 Cmp Lorene::Etoile_bin::ssjm1_beta [protected, inherited]

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 965 of file etoile.h.

 Cmp Lorene::Etoile_bin::ssjm1_khi [protected, inherited]

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

is an intermediate quantity for the resolution of the elliptic equation for the shift vector

Definition at line 973 of file etoile.h.

 Cmp Lorene::Etoile_bin::ssjm1_logn [protected, inherited]

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 959 of file etoile.h.

 Cmp Lorene::Etoile_bin::ssjm1_psi [protected, inherited]

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

Definition at line 989 of file etoile.h.

 Tenseur Lorene::Etoile_bin::ssjm1_wshift [protected, inherited]

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

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

Definition at line 983 of file etoile.h.

 Tenseur_sym Lorene::Etoile_bin::tkij_auto [protected, inherited]

Part of the extrinsic curvature tensor generated by shift_auto .

(Cartesian components with respect to ref_triad )

Reimplemented in Lorene::Et_bin_nsbh.

Definition at line 925 of file etoile.h.

 Tenseur_sym Lorene::Etoile_bin::tkij_comp [protected, inherited]

Part of the extrinsic curvature tensor generated by shift_comp .

(Cartesian components with respect to ref_triad )

Definition at line 932 of file etoile.h.

 Tenseur Lorene::Etoile::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 474 of file etoile.h.

 double Lorene::Etoile::unsurc2 [protected, inherited]

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

Definition at line 442 of file etoile.h.

 Tenseur Lorene::Etoile_bin::w_shift [protected, inherited]

Vector used in the decomposition of shift_auto , following Shibata's prescription [Prog.

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

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

Definition at line 908 of file etoile.h.

 Tenseur Lorene::Etoile_bin::wit_w [protected, inherited]

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

(Cartesian components with respect to ref_triad )

Definition at line 844 of file etoile.h.

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

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