Lorene::Et_rot_bifluid Class Reference
[Stars and black holes]

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

#include <et_rot_bifluid.h>

Inheritance diagram for Lorene::Et_rot_bifluid:
Lorene::Etoile_rot Lorene::Etoile

List of all members.

Public Member Functions

 Et_rot_bifluid (Map &mp_i, int nzet_i, bool relat, const Eos_bifluid &eos_i)
 Standard constructor.
 Et_rot_bifluid (const Et_rot_bifluid &)
 Copy constructor.
 Et_rot_bifluid (Map &mp_i, const Eos_bifluid &eos_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) ) Works only for relativistic stars.
virtual ~Et_rot_bifluid ()
 Destructor.
void operator= (const Et_rot_bifluid &)
 Assignment to another Et_rot_bifluid.
void set_enthalpies (const Cmp &, const Cmp &)
 Sets both enthalpy profiles.
void equilibrium_spher_bi (double ent_c, double ent_c2, double precis=1.e-14)
 Computes a spherical static configuration.
void equil_spher_regular (double ent_c, double ent_c2, double precis=1.e-14)
 Computes a spherical static configuration.
const Eos_bifluidget_eos () const
 Returns the equation of state.
const Tenseurget_ent2 () const
 Returns the enthalpy field for fluid 2.
const Tenseurget_nbar2 () const
 Returns the proper baryon density for fluid 2.
const Tenseurget_K_nn () const
 Returns the coefficient $K_{nn}$.
const Tenseurget_K_np () const
 Returns the coefficient $K_{np}$.
const Tenseurget_K_pp () const
 Returns the coefficient $K_{pp}$.
const Tenseurget_alpha_eos () const
 Returns the coefficient $\alpha$ (entrainment parameter).
const Tenseurget_delta_car () const
 Returns the "relative velocity" (squared) $\Delta^2$ of the two fluids.
const Tenseurget_gam_euler2 () const
 Returns the Lorentz factor between the fluid 2 and Eulerian observers.
double get_omega2 () const
 Returns the rotation angular velocity of fluid 2([f_unit] ).
const Tenseurget_uuu2 () const
 Returns the norm of the fluid 2 3-velocity with respect to the eulerian frame.
virtual void sauve (FILE *) const
 Save in a file.
virtual ostream & operator>> (ostream &) const
 Operator >> (virtual function called by the operator <<).
virtual void partial_display (ostream &) const
 Printing of some informations, excluding all global quantities.
virtual const Itbll_surf () const
 Description of the surface of fluid 1: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
const Itbll_surf2 () const
 Description of the surface of fluid 2: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
const Tblxi_surf2 () const
 Description of the surface of fluid 2: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double ray_eq2 () const
 Coordinate radius for fluid 2 at $\phi=0$, $\theta=\pi/2$ [r_unit].
double ray_eq2_pis2 () const
 Coordinate radius for fluid 2 at $\phi=\pi/2$, $\theta=\pi/2$ [r_unit].
double ray_eq2_pi () const
 Coordinate radius for fluid 2 at $\phi=\pi$, $\theta=\pi/2$ [r_unit].
double ray_pole2 () const
 Coordinate radius for fluid 2 at $\theta=0$ [r_unit].
double mass_b1 () const
 Baryon mass of fluid 1.
double mass_b2 () const
 Baryon mass of fluid 2.
virtual double mass_b () const
 Total Baryon mass.
virtual double mass_g () const
 Gravitational mass.
virtual double angu_mom () const
 Angular momentum.
virtual double grv2 () const
 Error on the virial identity GRV2.
virtual double grv3 (ostream *ost=0x0) const
 Error on the virial identity GRV3.
virtual double r_circ2 () const
 Circumferential radius for fluid 2.
virtual double area2 () const
 Surface area for fluid 2.
virtual double mean_radius2 () const
 Mean radius for fluid 2.
virtual double aplat2 () const
 Flatening r_pole/r_eq for fluid 2.
virtual double mom_quad () const
 Quadrupole moment.
virtual double mom_quad_old () const
 Part of the quadrupole moment.
virtual double mom_quad_Bo () const
 Part of the quadrupole moment.
virtual double angu_mom_1 () const
 Angular momentum of fluid 1.
virtual double angu_mom_2 () const
 Angular momentum of fluid 2.
virtual double coupling_mominert_1 () const
 Quantities used to study the different fluid couplings: $\tilde{I}_X$, $\tilde{\varepsilon}_X\tilde{I}_X$ and $\tilde{\omega}_X\tilde{I}_X$ .
virtual double coupling_mominert_2 () const
virtual double coupling_entr () const
virtual double coupling_LT_1 () const
virtual double coupling_LT_2 () const
virtual void hydro_euler ()
 Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
virtual void equation_of_state ()
 Computes the proper baryon and energy densities, as well as pressure and the coefficients Knn, Knp and Kpp, from the enthalpies and both velocities.
void equilibrium_bi (double ent_c, double ent_c2, double omega0, double omega20, const Tbl &ent_limit, const Tbl &ent2_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, int mer_mass, double mbar1_wanted, double mbar2_wanted, double aexp_mass)
 Computes an equilibrium configuration.
virtual double get_omega_c () const
 Returns the central value of the rotation angular velocity ([f_unit] ).
const Tenseurget_bbb () const
 Returns the metric factor B.
const Tenseurget_b_car () const
 Returns the square of the metric factor B.
const Tenseurget_nphi () const
 Returns the metric coefficient $N^\varphi$.
const Tenseurget_tnphi () const
 Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
const Tenseurget_uuu () const
 Returns the norm of u_euler.
const Tenseurget_logn () const
 Returns the metric potential $\nu = \ln N$ = logn_auto.
const Tenseurget_nuf () const
 Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
const Tenseurget_nuq () const
 Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
const Tenseurget_dzeta () const
 Returns the Metric potential $\zeta = \ln(AN)$ = beta_auto.
const Tenseurget_tggg () const
 Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$.
const Tenseurget_w_shift () const
 Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
const Tenseurget_khi_shift () const
 Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.
const Tenseur_symget_tkij () const
 Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
const Tenseurget_ak_car () const
 Returns the scalar $A^2 K_{ij} K^{ij}$.
virtual void display_poly (ostream &) const
 Display in polytropic units.
virtual double tsw () const
 Ratio T/W.
virtual double r_circ () const
 Circumferential radius.
virtual double area () const
 Surface area.
virtual double mean_radius () const
 Mean radius.
virtual double aplat () const
 Flatening r_pole/r_eq.
virtual double z_eqf () const
 Forward redshift factor at equator.
virtual double z_eqb () const
 Backward redshift factor at equator.
virtual double z_pole () const
 Redshift factor at North pole.
virtual double r_isco (ostream *ost=0x0) const
 Circumferential radius of the innermost stable circular orbit (ISCO).
virtual double f_isco () const
 Orbital frequency at the innermost stable circular orbit (ISCO).
virtual double espec_isco () const
 Energy of a particle on the ISCO.
virtual double lspec_isco () const
 Angular momentum of a particle on the ISCO.
virtual double f_eccentric (double ecc, double periast, ostream *ost=0x0) const
 Computation of frequency of eccentric orbits.
virtual double f_eq () const
 Orbital frequency at the equator.
void update_metric ()
 Computes metric coefficients from known potentials.
void fait_shift ()
 Computes shift from w_shift and khi_shift according to Shibata's prescription [Prog.
void fait_nphi ()
 Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
void extrinsic_curvature ()
 Computes tkij and ak_car from shift , nnn and b_car .
virtual void equilibrium (double ent_c, double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, double mbar_wanted, double aexp_mass, Tbl &diff, Param *=0x0)
 Computes an equilibrium configuration.
Mapset_mp ()
 Read/write of the mapping.
void set_enthalpy (const Cmp &)
 Assignment of the enthalpy field.
virtual void equilibrium_spher (double ent_c, double precis=1.e-14, const Tbl *ent_limit=0x0)
 Computes a spherical static configuration.
void equil_spher_regular (double ent_c, double precis=1.e-14)
 Computes a spherical static configuration.
virtual void equil_spher_falloff (double ent_c, double precis=1.e-14)
 Computes a spherical static configuration with the outer boundary condition at a finite radius.
const 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 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 $N^i$.
const Tenseurget_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].
const Tblxi_surf () const
 Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Static Public Member Functions

static double lambda_grv2 (const Cmp &sou_m, const Cmp &sou_q)
 Computes the coefficient $\lambda$ which ensures that the GRV2 virial identity is satisfied.

Protected Member Functions

virtual void del_deriv () const
 Deletes all the derived quantities.
virtual void set_der_0x0 () const
 Sets to 0x0 all the pointers on derived quantities.
virtual void del_hydro_euler ()
 Sets to ETATNONDEF (undefined state) the hydrodynamical quantities relative to the Eulerian observer.

Protected Attributes

const Eos_bifluideos
 Equation of state for two-fluids model.
double omega2
 Rotation angular velocity for fluid 2 ([f_unit] ).
Tenseur ent2
 Log-enthalpy for the second fluid.
Tenseur nbar2
 Baryon density in the fluid frame, for fluid 2.
Tenseur K_nn
 Coefficient $K_{nn}$.
Tenseur K_np
 Coefficient $K_{np}$.
Tenseur K_pp
 Coefficient $K_{pp}$.
Tenseur alpha_eos
 Coefficient $\alpha$ relative to entrainment effects.
Tenseur sphph_euler
 The component $S^\varphi_\varphi$ of the stress tensor ${S^i}_j$.
Tenseur j_euler
 Total angular momentum (flat-space!) 3-vector $J_\mathrm{euler}$, which is related to $J^i$ of the "3+1" decomposition, but expressed in a flat-space triad.
Tenseur j_euler1
 To compute $J_n$.
Tenseur j_euler2
 To compute $J_p$.
Tenseur enerps_euler
 the combination $E+S_i^i$: useful because in the Newtonian limit $\rightarrow \rho$.
Tenseur uuu2
 Norm of the (fluid no.2) 3-velocity with respect to the eulerian observer.
Tenseur gam_euler2
 Lorentz factor between the fluid 2 and Eulerian observers.
Tenseur delta_car
 The "relative velocity" (squared) $\Delta^2$ of the two fluids.
double * p_ray_eq2
 Coordinate radius at $\phi=0$, $\theta=\pi/2$.
double * p_ray_eq2_pis2
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$.
double * p_ray_eq2_pi
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$.
double * p_ray_pole2
 Coordinate radius at $\theta=0$.
Itblp_l_surf2
 Description of the surface of fluid 2: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
Tblp_xi_surf2
 Description of the surface of fluid 2: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double * p_r_circ2
 Circumferential radius of fluid no.2.
double * p_area2
 Surface area of fluid no.2.
double * p_aplat2
 Flatening r_pole/r_eq of fluid no.2.
double * p_mass_b1
 Baryon mass of fluid 1.
double * p_mass_b2
 Baryon mass of fluid 2.
double * p_angu_mom_1
 Angular momentum of fluid 1.
double * p_angu_mom_2
 Angular momentum of fluid 2.
double * p_coupling_mominert_1
 Quantities used to describe the different couplings between the fluids.
double * p_coupling_mominert_2
 $\tilde{I}_p$
double * p_coupling_entr
 $\tilde{\varepsilon}_n\tilde{I}_n = \tilde{\varepsilon}_p\tilde{I}_p$
double * p_coupling_LT_1
 $\tilde{\omega}_n\tilde{I}_n$
double * p_coupling_LT_2
 $\tilde{\omega}_p\tilde{I}_p$
double omega
 Rotation angular velocity ([f_unit] ).
Tenseur bbb
 Metric factor B.
Tenseur b_car
 Square of the metric factor B.
Tenseur nphi
 Metric coefficient $N^\varphi$.
Tenseur tnphi
 Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
Tenseur uuu
 Norm of u_euler.
Tenseurlogn
 Metric potential $\nu = \ln N$ = logn_auto.
Tenseur nuf
 Part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
Tenseur nuq
 Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
Tenseurdzeta
 Metric potential $\zeta = \ln(AN)$ = beta_auto.
Tenseur tggg
 Metric potential $\tilde G = (NB-1) r\sin\theta$.
Tenseur w_shift
 Vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
Tenseur khi_shift
 Scalar $\chi$ used in the decomposition of shift , following Shibata's prescription [Prog.
Tenseur_sym tkij
 Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
Tenseur ak_car
 Scalar $A^2 K_{ij} K^{ij}$.
Cmp ssjm1_nuf
 Effective source at the previous step for the resolution of the Poisson equation for nuf by means of Map_et::poisson .
Cmp ssjm1_nuq
 Effective source at the previous step for the resolution of the Poisson equation for nuq by means of Map_et::poisson .
Cmp ssjm1_dzeta
 Effective source at the previous step for the resolution of the Poisson equation for dzeta .
Cmp ssjm1_tggg
 Effective source at the previous step for the resolution of the Poisson equation for tggg .
Cmp ssjm1_khi
 Effective source at the previous step for the resolution of the Poisson equation for the scalar $\chi$ by means of Map_et::poisson .
Tenseur ssjm1_wshift
 Effective source at the previous step for the resolution of the vector Poisson equation for $W^i$.
double * p_angu_mom
 Angular momentum.
double * p_tsw
 Ratio T/W.
double * p_grv2
 Error on the virial identity GRV2.
double * p_grv3
 Error on the virial identity GRV3.
double * p_r_circ
 Circumferential radius.
double * p_area
 Surface area.
double * p_aplat
 Flatening r_pole/r_eq.
double * p_z_eqf
 Forward redshift factor at equator.
double * p_z_eqb
 Backward redshift factor at equator.
double * p_z_pole
 Redshift factor at North pole.
double * p_mom_quad
 Quadrupole moment.
double * p_mom_quad_old
 Part of the quadrupole moment.
double * p_mom_quad_Bo
 Part of the quadrupole moment.
double * p_r_isco
 Circumferential radius of the ISCO.
double * p_f_isco
 Orbital frequency of the ISCO.
double * p_espec_isco
 Specific energy of a particle on the ISCO.
double * p_lspec_isco
 Specific angular momentum of a particle on the ISCO.
double * p_f_eq
 Orbital frequency at the equator.
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
 $1/c^2$ : unsurc2=1 for a relativistic star, 0 for a Newtonian one.
int k_div
 Index of regularity of the gravitational potential logn_auto .
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 $\theta=0$.
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 $(\theta', \phi')$.
Tblp_xi_surf
 Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double * p_mass_b
 Baryon mass.
double * p_mass_g
 Gravitational mass.

Friends

ostream & operator<< (ostream &, const Etoile &)
 Display.

Detailed Description

Class for two-fluid rotating relativistic stars.

()

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

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

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

Definition at line 150 of file et_rot_bifluid.h.


Constructor & Destructor Documentation

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

Copy constructor.

Definition at line 174 of file et_rot_bifluid.C.

References omega2, and set_der_0x0().

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

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

This has to be improved....

Definition at line 201 of file et_rot_bifluid.C.

References delta_car, ent2, Lorene::fread_be(), Lorene::Etoile::mp, omega2, set_der_0x0(), and uuu2.

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

Destructor.

Definition at line 247 of file et_rot_bifluid.C.

References del_deriv().


Member Function Documentation

double Lorene::Et_rot_bifluid::angu_mom (  )  const [virtual]
double Lorene::Et_rot_bifluid::angu_mom_1 (  )  const [virtual]
double Lorene::Et_rot_bifluid::angu_mom_2 (  )  const [virtual]
double Lorene::Etoile_rot::aplat (  )  const [virtual, inherited]

Flatening r_pole/r_eq.

Definition at line 504 of file et_rot_global.C.

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

double Lorene::Et_rot_bifluid::aplat2 (  )  const [virtual]

Flatening r_pole/r_eq for fluid 2.

Definition at line 559 of file et_bfrot_global.C.

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

double Lorene::Etoile_rot::area (  )  const [virtual, inherited]
double Lorene::Et_rot_bifluid::area2 (  )  const [virtual]
double Lorene::Et_rot_bifluid::coupling_mominert_1 (  )  const [virtual]

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

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

Definition at line 282 of file et_bfrot_global.C.

References Lorene::Etoile::a_car, Lorene::Etoile_rot::b_car, Lorene::Etoile_rot::bbb, Lorene::Etoile::ent, eos, Lorene::exp(), Lorene::Eos_bifluid::get_m1(), Lorene::Cmp::integrale(), Lorene::Etoile::mp, Lorene::Cmp::mult_rsint(), Lorene::Etoile::nbar, Lorene::Etoile::nnn, p_coupling_mominert_1, Lorene::Tenseur::set_std_base(), Lorene::Cmp::std_base_scal(), and Lorene::Etoile::unsurc2.

void Lorene::Et_rot_bifluid::del_deriv (  )  const [protected, virtual]
void Lorene::Et_rot_bifluid::del_hydro_euler (  )  [protected, virtual]

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 311 of file et_rot_bifluid.C.

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

void Lorene::Etoile_rot::display_poly ( ostream &  ost  )  const [virtual, inherited]
void Lorene::Et_rot_bifluid::equation_of_state (  )  [virtual]
void Lorene::Etoile::equil_spher_falloff ( double  ent_c,
double  precis = 1.e-14 
) [virtual, inherited]
void Lorene::Etoile::equil_spher_regular ( double  ent_c,
double  precis = 1.e-14 
) [inherited]

Computes a spherical static configuration.

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

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

Definition at line 118 of file et_equil_spher_regu.C.

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

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

Computes a spherical static configuration.

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

Parameters:
ent_c [input] central value of the enthalpy 1
ent_c2 [input] central value of the enthalpy 2
precis [input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)
void Lorene::Etoile_rot::equilibrium ( double  ent_c,
double  omega0,
double  fact_omega,
int  nzadapt,
const Tbl ent_limit,
const Itbl icontrol,
const Tbl control,
double  mbar_wanted,
double  aexp_mass,
Tbl diff,
Param = 0x0 
) [virtual, inherited]

Computes an equilibrium configuration.

Parameters:
ent_c [input] Central enthalpy
omega0 [input] Requested angular velocity (if fact_omega=1. )
fact_omega [input] 1.01 = search for the Keplerian frequency, 1. = otherwise.
nzadapt [input] Number of (inner) domains where the mapping adaptation to an iso-enthalpy surface should be performed
ent_limit [input] 1-D Tbl of dimension nzet which defines the enthalpy at the outer boundary of each domain
icontrol [input] Set of integer parameters (stored as a 1-D Itbl of size 8) to control the iteration:

  • icontrol(0) = mer_max : maximum number of steps
  • icontrol(1) = mer_rot : step at which the rotation is switched on
  • icontrol(2) = mer_change_omega : step at which the rotation velocity is changed to reach the final one
  • icontrol(3) = mer_fix_omega : step at which the final rotation velocity must have been reached
  • icontrol(4) = mer_mass : the absolute value of mer_mass is the step from which the baryon mass is forced to converge, by varying the central enthalpy (mer_mass>0 ) or the angular velocity (mer_mass<0 )
  • icontrol(5) = mermax_poisson : maximum number of steps in Map_et::poisson
  • icontrol(6) = mer_triax : step at which the 3-D perturbation is switched on
  • icontrol(7) = delta_mer_kep : number of steps after mer_fix_omega when omega starts to be increased by fact_omega to search for the Keplerian velocity
control [input] Set of parameters (stored as a 1-D Tbl of size 7) to control the iteration:

  • control(0) = precis : threshold on the enthalpy relative change for ending the computation
  • control(1) = omega_ini : initial angular velocity, switched on only if mer_rot<0 , otherwise 0 is used
  • control(2) = relax : relaxation factor in the main iteration
  • control(3) = relax_poisson : relaxation factor in Map_et::poisson
  • control(4) = thres_adapt : threshold on dH/dr for freezing the adaptation of the mapping
  • control(5) = ampli_triax : relative amplitude of the 3-D perturbation
  • control(6) = precis_adapt : precision for Map_et::adapt
mbar_wanted [input] Requested baryon mass (effective only if mer_mass > mer_max )
aexp_mass [input] Exponent for the increase factor of the central enthalpy to converge to the requested baryon mass
diff [output] 1-D Tbl of size 7 for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field between two successive steps
  • diff(1) : Relative error in the resolution of the Poisson equation for nuf
  • diff(2) : Relative error in the resolution of the Poisson equation for nuq
  • diff(3) : Relative error in the resolution of the Poisson equation for dzeta
  • diff(4) : Relative error in the resolution of the Poisson equation for tggg
  • diff(5) : Relative error in the resolution of the equation for shift (x comp.)
  • diff(6) : Relative error in the resolution of the equation for shift (y comp.)

Reimplemented in Lorene::Et_rot_diff.

Definition at line 150 of file et_rot_equilibrium.C.

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

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

Computes an equilibrium configuration.

Parameters:
ent_c [input] Central enthalpy for fluid 1
ent_c2 [input] Central enthalpy for fluid 2
omega0 [input] Requested angular velocity for fluid 1
omega20 [input] Requested angular velocity for fluid 2
ent_limit [input] 1-D Tbl of dimension nzet which defines the enthalpy for fluid 1 at the outer boundary of each domain
ent2_limit [input] 1-D Tbl of dimension nzet which defines the enthalpy for fluid 2 at the outer boundary of each domain
icontrol [input] Set of integer parameters (stored as a 1-D Itbl of size 5) to control the iteration:

  • icontrol(0) = mer_max : maximum number of steps
  • icontrol(1) = mer_rot : step at which the rotation is switched on
  • icontrol(2) = mer_change_omega : step at which the rotation velocity is changed to reach the final one
  • icontrol(3) = mer_fix_omega : step at which the final rotation velocity must have been reached
  • icontrol(4) = mermax_poisson : maximum number of steps in Map_et::poisson
control [input] Set of parameters (stored as a 1-D Tbl of size 5) to control the iteration:

  • control(0) = precis : threshold on the enthalpy relative change for ending the computation
  • control(1) = omega_ini : initial angular velocity, switched on only if mer_rot < 0 , otherwise 0 is used
  • control(2) = omega2_ini : initial angular velocity, switched on only if mer_rot < 0 , otherwise 0 is used
  • control(3) = relax : relaxation factor in the main iteration
  • control(4) = relax_poisson : relaxation factor in Map_et::poisson
diff [output] 1-D Tbl of size 8 for the storage of some error indicators :

  • diff(0) : Relative change in the enthalpy field 1 between two successive steps
  • diff(1) : Relative change in the enthalpy field 2 between two successive steps
  • diff(2) : Relative error in the resolution of the Poisson equation for nuf
  • diff(3) : Relative error in the resolution of the Poisson equation for nuq
  • diff(4) : Relative error in the resolution of the Poisson equation for dzeta
  • diff(5) : Relative error in the resolution of the Poisson equation for tggg
  • diff(6) : Relative error in the resolution of the equation for shift (x comp.)
  • diff(7) : Relative error in the resolution of the equation for shift (y comp.)

Definition at line 141 of file et_bfrot_equilibre.C.

References Lorene::Map_et::adapt(), Lorene::Param::add_cmp_mod(), Lorene::Param::add_double(), Lorene::Param::add_double_mod(), Lorene::Param::add_int(), Lorene::Param::add_int_mod(), Lorene::Param::add_tbl(), Lorene::Param::add_tenseur_mod(), Lorene::Valeur::c_cf, Lorene::Tenseur::change_triad(), Lorene::Valeur::coef(), Lorene::cos(), Lorene::diffrel(), Lorene::flat_scalar_prod(), Lorene::Eos_bf_poly::get_beta(), Lorene::Tenseur::get_etat(), Lorene::Eos_bf_poly::get_kap1(), Lorene::Eos_bf_poly::get_kap2(), Lorene::Eos_bf_poly::get_kap3(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_t(), Lorene::Tenseur::gradient_spher(), Lorene::Map_et::homothetie(), Lorene::log(), Lorene::log10(), Lorene::pow(), Lorene::Cmp::set(), Lorene::Tenseur::set(), Lorene::Tbl::set(), Lorene::Tbl::set_etat_qcq(), Lorene::Tenseur::set_std_base(), and Lorene::sqrt().

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.

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

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

Computes a spherical static configuration.

Parameters:
ent_c [input] central value of the enthalpy 1
ent_c2 [input] central value of the enthalpy 2
precis [input] threshold in the relative difference between the enthalpy fields of two consecutive steps to stop the iterative procedure (default value: 1.e-14)
double Lorene::Etoile_rot::espec_isco (  )  const [virtual, inherited]

Energy of a particle on the ISCO.

Definition at line 304 of file et_rot_isco.C.

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

void Lorene::Etoile_rot::extrinsic_curvature (  )  [inherited]
double Lorene::Etoile_rot::f_eccentric ( double  ecc,
double  periast,
ostream *  ost = 0x0 
) const [virtual, inherited]

Computation of frequency of eccentric orbits.

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

Definition at line 81 of file et_rot_f_eccentric.C.

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

double Lorene::Etoile_rot::f_eq (  )  const [virtual, inherited]

Orbital frequency at the equator.

Definition at line 322 of file et_rot_isco.C.

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

double Lorene::Etoile_rot::f_isco (  )  const [virtual, inherited]

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

Definition at line 270 of file et_rot_isco.C.

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

void Lorene::Etoile_rot::fait_nphi (  )  [inherited]

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

Definition at line 784 of file etoile_rot.C.

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

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

Returns the total conformal factor $A^2$.

Definition at line 733 of file etoile.h.

References Lorene::Etoile::a_car.

const Tenseur& Lorene::Etoile_rot::get_ak_car (  )  const [inline, inherited]

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

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

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

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

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

Definition at line 1799 of file etoile.h.

References Lorene::Etoile_rot::ak_car.

const Tenseur& Lorene::Et_rot_bifluid::get_alpha_eos (  )  const [inline]

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

Definition at line 340 of file et_rot_bifluid.h.

References alpha_eos.

const Tenseur& Lorene::Etoile_rot::get_b_car (  )  const [inline, inherited]

Returns the square of the metric factor B.

Definition at line 1715 of file etoile.h.

References Lorene::Etoile_rot::b_car.

const Tenseur& Lorene::Etoile_rot::get_bbb (  )  const [inline, inherited]

Returns the metric factor B.

Definition at line 1712 of file etoile.h.

References Lorene::Etoile_rot::bbb.

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::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::Et_rot_bifluid::get_delta_car (  )  const [inline]

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

Definition at line 343 of file et_rot_bifluid.h.

References delta_car.

const Tenseur& Lorene::Etoile_rot::get_dzeta (  )  const [inline, inherited]

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

Definition at line 1742 of file etoile.h.

References Lorene::Etoile_rot::dzeta.

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 Tenseur& Lorene::Et_rot_bifluid::get_ent2 (  )  const [inline]

Returns the enthalpy field for fluid 2.

Definition at line 325 of file et_rot_bifluid.h.

References ent2.

const Eos_bifluid& Lorene::Et_rot_bifluid::get_eos (  )  const [inline]

Returns the equation of state.

Reimplemented from Lorene::Etoile.

Definition at line 322 of file et_rot_bifluid.h.

References 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.

const Tenseur& Lorene::Et_rot_bifluid::get_gam_euler2 (  )  const [inline]

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

Definition at line 346 of file et_rot_bifluid.h.

References gam_euler2.

const Tenseur& Lorene::Et_rot_bifluid::get_K_nn (  )  const [inline]

Returns the coefficient $K_{nn}$.

Definition at line 331 of file et_rot_bifluid.h.

References K_nn.

const Tenseur& Lorene::Et_rot_bifluid::get_K_np (  )  const [inline]

Returns the coefficient $K_{np}$.

Definition at line 334 of file et_rot_bifluid.h.

References K_np.

const Tenseur& Lorene::Et_rot_bifluid::get_K_pp (  )  const [inline]

Returns the coefficient $K_{pp}$.

Definition at line 337 of file et_rot_bifluid.h.

References K_pp.

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

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

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

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

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

Definition at line 1773 of file etoile.h.

References Lorene::Etoile_rot::khi_shift.

const Tenseur& Lorene::Etoile_rot::get_logn (  )  const [inline, inherited]

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

Definition at line 1729 of file etoile.h.

References Lorene::Etoile_rot::logn.

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 $c^2$).

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 $c^2$).

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 $c^2$).

Definition at line 708 of file etoile.h.

References Lorene::Etoile::logn_auto_regu.

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::Et_rot_bifluid::get_nbar2 (  )  const [inline]

Returns the proper baryon density for fluid 2.

Definition at line 328 of file et_rot_bifluid.h.

References nbar2.

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.

const Tenseur& Lorene::Etoile_rot::get_nphi (  )  const [inline, inherited]

Returns the metric coefficient $N^\varphi$.

Definition at line 1718 of file etoile.h.

References Lorene::Etoile_rot::nphi.

const Tenseur& Lorene::Etoile_rot::get_nuf (  )  const [inline, inherited]

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

Definition at line 1734 of file etoile.h.

References Lorene::Etoile_rot::nuf.

const Tenseur& Lorene::Etoile_rot::get_nuq (  )  const [inline, inherited]

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

Definition at line 1739 of file etoile.h.

References Lorene::Etoile_rot::nuq.

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.

double Lorene::Et_rot_bifluid::get_omega2 (  )  const [inline]

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

Definition at line 349 of file et_rot_bifluid.h.

References omega2.

double Lorene::Etoile_rot::get_omega_c (  )  const [virtual, inherited]

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

Reimplemented in Lorene::Et_rot_diff.

Definition at line 683 of file etoile_rot.C.

References Lorene::Etoile_rot::omega.

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::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 $N^i$.

Definition at line 730 of file etoile.h.

References Lorene::Etoile::shift.

const Tenseur& Lorene::Etoile_rot::get_tggg (  )  const [inline, inherited]

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

Definition at line 1745 of file etoile.h.

References Lorene::Etoile_rot::tggg.

const Tenseur_sym& Lorene::Etoile_rot::get_tkij (  )  const [inline, inherited]

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

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

Definition at line 1780 of file etoile.h.

References Lorene::Etoile_rot::tkij.

const Tenseur& Lorene::Etoile_rot::get_tnphi (  )  const [inline, inherited]

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

Definition at line 1723 of file etoile.h.

References Lorene::Etoile_rot::tnphi.

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_rot::get_uuu (  )  const [inline, inherited]

Returns the norm of u_euler.

Definition at line 1726 of file etoile.h.

References Lorene::Etoile_rot::uuu.

const Tenseur& Lorene::Et_rot_bifluid::get_uuu2 (  )  const [inline]

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

Definition at line 352 of file et_rot_bifluid.h.

References uuu2.

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

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

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

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

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

Definition at line 1759 of file etoile.h.

References Lorene::Etoile_rot::w_shift.

double Lorene::Et_rot_bifluid::grv2 (  )  const [virtual]

Error on the virial identity GRV2.

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 412 of file et_bfrot_global.C.

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

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

Error on the virial identity GRV3.

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

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 437 of file et_bfrot_global.C.

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

void Lorene::Et_rot_bifluid::hydro_euler (  )  [virtual]

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

The calculation is performed starting from the quantities ent , ent2 , ener , press , K_nn , K_np , K_pp and a_car, which are supposed to be up to date. From these, the following fields are updated: delta_car , gam_euler , gam_euler2 , ener_euler , s_euler , sphph_euler and j_euler .

Reimplemented from Lorene::Etoile_rot.

Definition at line 735 of file et_rot_bifluid.C.

References Lorene::Tenseur::annule(), Lorene::Etoile_rot::bbb, Lorene::Tenseur::change_triad(), del_deriv(), delta_car, Lorene::Etoile::ener_euler, enerps_euler, Lorene::Etoile::ent, eos, Lorene::Etoile::gam_euler, gam_euler2, Lorene::Map::get_bvect_cart(), Lorene::Map::get_bvect_spher(), Lorene::Tenseur::get_etat(), Lorene::Eos_bifluid::get_m1(), Lorene::Eos_bifluid::get_m2(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nr(), Lorene::Mg3d::get_nt(), Lorene::Mg3d::get_nzone(), j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, Lorene::Etoile::mp, Lorene::Etoile::nbar, nbar2, Lorene::Etoile::nnn, Lorene::Etoile_rot::nphi, Lorene::Etoile::nzet, Lorene::Etoile_rot::omega, omega2, Lorene::Etoile::press, Lorene::Etoile::relativistic, Lorene::Etoile::s_euler, Lorene::Tenseur::set(), Lorene::Tenseur::set_etat_nondef(), Lorene::Tenseur::set_etat_qcq(), Lorene::Tenseur::set_std_base(), Lorene::Tenseur::set_triad(), sphph_euler, Lorene::sqrt(), Lorene::Etoile::u_euler, Lorene::Etoile::unsurc2, Lorene::Etoile_rot::uuu, and uuu2.

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.

const Itbl & Lorene::Et_rot_bifluid::l_surf (  )  const [virtual]

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

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 752 of file et_bfrot_global.C.

References Lorene::Cmp::annule(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Etoile::mp, Lorene::Etoile::nbar, Lorene::Etoile::nzet, Lorene::Etoile::p_l_surf, Lorene::Etoile::p_xi_surf, and Lorene::Cmp::va.

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

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

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

Definition at line 785 of file et_bfrot_global.C.

References Lorene::Cmp::annule(), Lorene::Map::get_mg(), Lorene::Mg3d::get_np(), Lorene::Mg3d::get_nt(), Lorene::Etoile::mp, nbar2, Lorene::Etoile::nzet, p_l_surf2, p_xi_surf2, and Lorene::Cmp::va.

double Lorene::Etoile_rot::lambda_grv2 ( const Cmp sou_m,
const Cmp sou_q 
) [static, inherited]

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

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

\[ \Delta_2 u = \sigma_m + \sigma_q \]

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

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

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

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

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

Parameters:
sou_m [input] matter source term $\sigma_m$
sou_q [input] quadratic source term $\sigma_q$
Returns:
value of $\lambda$

Definition at line 82 of file et_rot_lambda_grv2.C.

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

double Lorene::Etoile_rot::lspec_isco (  )  const [virtual, inherited]

Angular momentum of a particle on the ISCO.

Definition at line 287 of file et_rot_isco.C.

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

double Lorene::Et_rot_bifluid::mass_b (  )  const [virtual]

Total Baryon mass.

Reimplemented from Lorene::Etoile_rot.

Definition at line 154 of file et_bfrot_global.C.

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

double Lorene::Et_rot_bifluid::mass_b1 (  )  const
double Lorene::Et_rot_bifluid::mass_b2 (  )  const
double Lorene::Et_rot_bifluid::mass_g (  )  const [virtual]
double Lorene::Etoile_rot::mean_radius (  )  const [virtual, inherited]

Mean radius.

Definition at line 480 of file et_rot_global.C.

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

double Lorene::Et_rot_bifluid::mean_radius2 (  )  const [virtual]

Mean radius for fluid 2.

Definition at line 631 of file et_bfrot_global.C.

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

double Lorene::Et_rot_bifluid::mom_quad (  )  const [virtual]

Quadrupole moment.

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 644 of file et_bfrot_global.C.

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

double Lorene::Et_rot_bifluid::mom_quad_Bo (  )  const [virtual]

Part of the quadrupole moment.

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 660 of file et_bfrot_global.C.

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

double Lorene::Et_rot_bifluid::mom_quad_old (  )  const [virtual]

Part of the quadrupole moment.

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

Reimplemented from Lorene::Etoile_rot.

Definition at line 683 of file et_bfrot_global.C.

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

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

Assignment to another Et_rot_bifluid.

Reimplemented from Lorene::Etoile_rot.

Definition at line 352 of file et_rot_bifluid.C.

References alpha_eos, del_deriv(), delta_car, enerps_euler, ent2, eos, gam_euler2, j_euler, j_euler1, j_euler2, K_nn, K_np, K_pp, nbar2, omega2, sphph_euler, and uuu2.

ostream & Lorene::Et_rot_bifluid::operator>> ( ostream &  ost  )  const [virtual]
void Lorene::Et_rot_bifluid::partial_display ( ostream &  ost  )  const [virtual]
double Lorene::Etoile_rot::r_circ (  )  const [virtual, inherited]
double Lorene::Et_rot_bifluid::r_circ2 (  )  const [virtual]
double Lorene::Etoile_rot::r_isco ( ostream *  ost = 0x0  )  const [virtual, inherited]
double Lorene::Etoile::ray_eq ( int  kk  )  const [inherited]
double Lorene::Etoile::ray_eq (  )  const [inherited]
double Lorene::Et_rot_bifluid::ray_eq2 (  )  const
double Lorene::Et_rot_bifluid::ray_eq2_pi (  )  const
double Lorene::Et_rot_bifluid::ray_eq2_pis2 (  )  const
double Lorene::Etoile::ray_eq_3pis2 (  )  const [inherited]
double Lorene::Etoile::ray_eq_pi (  )  const [inherited]
double Lorene::Etoile::ray_eq_pis2 (  )  const [inherited]
double Lorene::Etoile::ray_pole (  )  const [inherited]
double Lorene::Et_rot_bifluid::ray_pole2 (  )  const

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

Definition at line 977 of file et_bfrot_global.C.

References Lorene::Map::get_mg(), l_surf2(), Lorene::Etoile::mp, p_ray_pole2, Lorene::Map::val_r(), and xi_surf2().

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

Save in a file.

Reimplemented from Lorene::Etoile_rot.

Definition at line 386 of file et_rot_bifluid.C.

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

void Lorene::Et_rot_bifluid::set_der_0x0 (  )  const [protected, virtual]
void Lorene::Et_rot_bifluid::set_enthalpies ( const Cmp ent_i,
const Cmp ent2_i 
)

Sets both enthalpy profiles.

Definition at line 332 of file et_rot_bifluid.C.

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

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

Assignment of the enthalpy field.

Definition at line 468 of file etoile.C.

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

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

Read/write of the mapping.

Definition at line 601 of file etoile.h.

References Lorene::Etoile::mp.

double Lorene::Etoile_rot::tsw (  )  const [virtual, inherited]
void Lorene::Etoile_rot::update_metric (  )  [inherited]

Computes metric coefficients from known potentials.

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

Definition at line 72 of file et_rot_upmetr.C.

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

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

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

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

Definition at line 104 of file etoile_global.C.

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

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

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

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

Definition at line 819 of file et_bfrot_global.C.

References l_surf2(), p_l_surf2, and p_xi_surf2.

double Lorene::Etoile_rot::z_eqb (  )  const [virtual, inherited]
double Lorene::Etoile_rot::z_eqf (  )  const [virtual, inherited]
double Lorene::Etoile_rot::z_pole (  )  const [virtual, inherited]

Redshift factor at North pole.

Definition at line 588 of file et_rot_global.C.

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


Friends And Related Function Documentation

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

Display.


Member Data Documentation

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

Total conformal factor $A^2$.

Definition at line 515 of file etoile.h.

Tenseur Lorene::Etoile_rot::ak_car [protected, inherited]

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

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

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

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

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

Definition at line 1586 of file etoile.h.

Coefficient $\alpha$ relative to entrainment effects.

Definition at line 170 of file et_rot_bifluid.h.

Tenseur Lorene::Etoile_rot::b_car [protected, inherited]

Square of the metric factor B.

Definition at line 1507 of file etoile.h.

Tenseur Lorene::Etoile_rot::bbb [protected, inherited]

Metric factor B.

Definition at line 1504 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::d_logn_auto_div [protected, inherited]

Gradient of logn_auto_div (if k_div!=0 ).

Definition at line 501 of file etoile.h.

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

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

Definition at line 204 of file et_rot_bifluid.h.

Tenseur& Lorene::Etoile_rot::dzeta [protected, inherited]

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

Definition at line 1534 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.

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

Definition at line 192 of file et_rot_bifluid.h.

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

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

Definition at line 457 of file etoile.h.

Log-enthalpy for the second fluid.

Definition at line 163 of file et_rot_bifluid.h.

Equation of state for two-fluids model.

Reimplemented from Lorene::Etoile.

Definition at line 155 of file et_rot_bifluid.h.

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

Lorentz factor between the fluid and Eulerian observers.

Definition at line 471 of file etoile.h.

Lorentz factor between the fluid 2 and Eulerian observers.

Definition at line 198 of file et_rot_bifluid.h.

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

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

Definition at line 186 of file et_rot_bifluid.h.

To compute $J_n$.

Definition at line 188 of file et_rot_bifluid.h.

To compute $J_p$.

Definition at line 189 of file et_rot_bifluid.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.

Coefficient $K_{nn}$.

Definition at line 167 of file et_rot_bifluid.h.

Coefficient $K_{np}$.

Definition at line 168 of file et_rot_bifluid.h.

Coefficient $K_{pp}$.

Definition at line 169 of file et_rot_bifluid.h.

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

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

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

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

Definition at line 1560 of file etoile.h.

Tenseur& Lorene::Etoile_rot::logn [protected, inherited]

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

Definition at line 1521 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 $c^2$).

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 $c^2$).

Definition at line 491 of file etoile.h.

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

Mapping associated with the star.

Definition at line 429 of file etoile.h.

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

Baryon density in the fluid frame.

Definition at line 459 of file etoile.h.

Baryon density in the fluid frame, for fluid 2.

Definition at line 165 of file et_rot_bifluid.h.

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

Total lapse function.

Definition at line 509 of file etoile.h.

Tenseur Lorene::Etoile_rot::nphi [protected, inherited]

Metric coefficient $N^\varphi$.

Definition at line 1510 of file etoile.h.

Tenseur Lorene::Etoile_rot::nuf [protected, inherited]

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

Definition at line 1526 of file etoile.h.

Tenseur Lorene::Etoile_rot::nuq [protected, inherited]

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

Definition at line 1531 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.

double Lorene::Etoile_rot::omega [protected, inherited]

Rotation angular velocity ([f_unit] ).

Definition at line 1501 of file etoile.h.

double Lorene::Et_rot_bifluid::omega2 [protected]

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

Definition at line 157 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_angu_mom [mutable, protected, inherited]

Angular momentum.

Definition at line 1631 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_angu_mom_1 [mutable, protected]

Angular momentum of fluid 1.

Definition at line 240 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_angu_mom_2 [mutable, protected]

Angular momentum of fluid 2.

Definition at line 241 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_aplat [mutable, protected, inherited]

Flatening r_pole/r_eq.

Definition at line 1637 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_aplat2 [mutable, protected]

Flatening r_pole/r_eq of fluid no.2.

Definition at line 235 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_area [mutable, protected, inherited]

Surface area.

Definition at line 1636 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_area2 [mutable, protected]

Surface area of fluid no.2.

Definition at line 234 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_coupling_entr [mutable, protected]

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

Definition at line 246 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_coupling_LT_1 [mutable, protected]

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

Definition at line 247 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_coupling_LT_2 [mutable, protected]

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

Definition at line 248 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_coupling_mominert_1 [mutable, protected]

Quantities used to describe the different couplings between the fluids.

$\tilde{I}_n$

Definition at line 244 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_coupling_mominert_2 [mutable, protected]

$\tilde{I}_p$

Definition at line 245 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_espec_isco [mutable, protected, inherited]

Specific energy of a particle on the ISCO.

Definition at line 1647 of file etoile.h.

double* Lorene::Etoile_rot::p_f_eq [mutable, protected, inherited]

Orbital frequency at the equator.

Definition at line 1650 of file etoile.h.

double* Lorene::Etoile_rot::p_f_isco [mutable, protected, inherited]

Orbital frequency of the ISCO.

Definition at line 1645 of file etoile.h.

double* Lorene::Etoile_rot::p_grv2 [mutable, protected, inherited]

Error on the virial identity GRV2.

Definition at line 1633 of file etoile.h.

double* Lorene::Etoile_rot::p_grv3 [mutable, protected, inherited]

Error on the virial identity GRV3.

Definition at line 1634 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 $(\theta', \phi')$.

Definition at line 539 of file etoile.h.

Itbl* Lorene::Et_rot_bifluid::p_l_surf2 [mutable, protected]

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

Definition at line 225 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_lspec_isco [mutable, protected, inherited]

Specific angular momentum of a particle on the ISCO.

Definition at line 1649 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::Et_rot_bifluid::p_mass_b1 [mutable, protected]

Baryon mass of fluid 1.

Definition at line 237 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_mass_b2 [mutable, protected]

Baryon mass of fluid 2.

Definition at line 238 of file et_rot_bifluid.h.

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

Gravitational mass.

Definition at line 548 of file etoile.h.

double* Lorene::Etoile_rot::p_mom_quad [mutable, protected, inherited]

Quadrupole moment.

Definition at line 1641 of file etoile.h.

double* Lorene::Etoile_rot::p_mom_quad_Bo [mutable, protected, inherited]

Part of the quadrupole moment.

Definition at line 1643 of file etoile.h.

double* Lorene::Etoile_rot::p_mom_quad_old [mutable, protected, inherited]

Part of the quadrupole moment.

Definition at line 1642 of file etoile.h.

double* Lorene::Etoile_rot::p_r_circ [mutable, protected, inherited]

Circumferential radius.

Definition at line 1635 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_r_circ2 [mutable, protected]

Circumferential radius of fluid no.2.

Definition at line 233 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_r_isco [mutable, protected, inherited]

Circumferential radius of the ISCO.

Definition at line 1644 of file etoile.h.

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

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

Definition at line 521 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_ray_eq2 [mutable, protected]

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

Definition at line 210 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_ray_eq2_pi [mutable, protected]

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

Definition at line 216 of file et_rot_bifluid.h.

double* Lorene::Et_rot_bifluid::p_ray_eq2_pis2 [mutable, protected]

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

Definition at line 213 of file et_rot_bifluid.h.

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

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

Definition at line 530 of file etoile.h.

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

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

Definition at line 527 of file etoile.h.

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

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

Definition at line 524 of file etoile.h.

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

Coordinate radius at $\theta=0$.

Definition at line 533 of file etoile.h.

double* Lorene::Et_rot_bifluid::p_ray_pole2 [mutable, protected]

Coordinate radius at $\theta=0$.

Definition at line 219 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_tsw [mutable, protected, inherited]

Ratio T/W.

Definition at line 1632 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 $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Definition at line 545 of file etoile.h.

Tbl* Lorene::Et_rot_bifluid::p_xi_surf2 [mutable, protected]

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

Definition at line 231 of file et_rot_bifluid.h.

double* Lorene::Etoile_rot::p_z_eqb [mutable, protected, inherited]

Backward redshift factor at equator.

Definition at line 1639 of file etoile.h.

double* Lorene::Etoile_rot::p_z_eqf [mutable, protected, inherited]

Forward redshift factor at equator.

Definition at line 1638 of file etoile.h.

double* Lorene::Etoile_rot::p_z_pole [mutable, protected, inherited]

Redshift factor at North pole.

Definition at line 1640 of file etoile.h.

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

Fluid pressure.

Definition at line 461 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.

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

Definition at line 179 of file et_rot_bifluid.h.

Cmp Lorene::Etoile_rot::ssjm1_dzeta [protected, inherited]

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

Definition at line 1603 of file etoile.h.

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

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 1616 of file etoile.h.

Cmp Lorene::Etoile_rot::ssjm1_nuf [protected, inherited]

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

Definition at line 1592 of file etoile.h.

Cmp Lorene::Etoile_rot::ssjm1_nuq [protected, inherited]

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

Definition at line 1598 of file etoile.h.

Cmp Lorene::Etoile_rot::ssjm1_tggg [protected, inherited]

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

Definition at line 1608 of file etoile.h.

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

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

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

Definition at line 1625 of file etoile.h.

Tenseur Lorene::Etoile_rot::tggg [protected, inherited]

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

Definition at line 1537 of file etoile.h.

Tenseur_sym Lorene::Etoile_rot::tkij [protected, inherited]

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

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

Definition at line 1567 of file etoile.h.

Tenseur Lorene::Etoile_rot::tnphi [protected, inherited]

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

Definition at line 1515 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]

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

Definition at line 442 of file etoile.h.

Tenseur Lorene::Etoile_rot::uuu [protected, inherited]

Norm of u_euler.

Definition at line 1518 of file etoile.h.

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

Definition at line 195 of file et_rot_bifluid.h.

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

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

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

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

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

Definition at line 1550 of file etoile.h.


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

Generated on 7 Dec 2019 for LORENE by  doxygen 1.6.1