Star_rot Class Reference
[Stars and black holes]

Class for isolated rotating stars. More...

#include <star_rot.h>

Inheritance diagram for Star_rot:
Star Gravastar

List of all members.

Public Member Functions

 Star_rot (Map &mp_i, int nzet_i, bool relat, const Eos &eos_i)
 Standard constructor.
 Star_rot (const Star_rot &)
 Copy constructor.
 Star_rot (Map &mp_i, const Eos &eos_i, FILE *fich)
 Constructor from a file (see sauve(FILE*) ).
virtual ~Star_rot ()
 Destructor.
void operator= (const Star_rot &)
 Assignment to another Star_rot.
bool is_relativistic () const
 Returns true for a relativistic star, false for a Newtonian one.
virtual double get_omega_c () const
 Returns the central value of the rotation angular velocity ([f_unit] ).
const Scalar & get_bbb () const
 Returns the metric factor B.
const Scalar & get_a_car () const
 Returns the square of the metric factor A.
const Scalar & get_b_car () const
 Returns the square of the metric factor B.
const Scalar & get_nphi () const
 Returns the metric coefficient $N^\varphi$.
const Scalar & get_tnphi () const
 Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
const Scalar & get_uuu () const
 Returns the norm of u_euler.
const Scalar & get_nuf () const
 Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
const Scalar & get_nuq () const
 Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
const Scalar & get_dzeta () const
 Returns the Metric potential $\zeta = \ln(AN)$.
const Scalar & get_tggg () const
 Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$.
const Vector & get_w_shift () const
 Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
const Scalar & get_khi_shift () const
 Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.
const Sym_tensor & get_tkij () const
 Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
const Scalar & get_ak_car () const
 Returns the scalar $A^2 K_{ij} K^{ij}$.
virtual void sauve (FILE *) const
 Save in a file.
virtual void display_poly (ostream &) const
 Display in polytropic units.
virtual const Itbl & l_surf () const
 Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
virtual double mass_b () const
 Baryon mass.
virtual double mass_g () const
 Gravitational mass.
virtual double angu_mom () const
 Angular momentum.
virtual double tsw () const
 Ratio T/W.
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_circ () const
 Circumferential 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 mom_quad () const
 Quadrupole moment.
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_eq () const
 Orbital frequency at the equator.
virtual void hydro_euler ()
 Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
void update_metric ()
 Computes metric coefficients from known potentials.
void fait_shift ()
 Computes shift from w_shift and khi_shift according to Shibata's prescription [Prog.
void fait_nphi ()
 Computes tnphi and nphi from the Cartesian components of the shift, stored in shift .
void extrinsic_curvature ()
 Computes tkij and ak_car from shift , nnn and b_car .
virtual void equilibrium (double ent_c, double omega0, double fact_omega, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, double mbar_wanted, double aexp_mass, Tbl &diff, Param *=0x0)
 Computes an equilibrium configuration.
Map & set_mp ()
 Read/write of the mapping.
void set_enthalpy (const Scalar &)
 Assignment of the enthalpy field.
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 *pent_limit=0x0)
 Computes a spherical static configuration.
const Map & get_mp () const
 Returns the mapping.
int get_nzet () const
 Returns the number of domains occupied by the star.
const Eos & get_eos () const
 Returns the equation of state.
const Scalar & get_ent () const
 Returns the enthalpy field.
const Scalar & get_nbar () const
 Returns the proper baryon density.
const Scalar & get_ener () const
 Returns the proper total energy density.
const Scalar & get_press () const
 Returns the fluid pressure.
const Scalar & get_ener_euler () const
 Returns the total energy density with respect to the Eulerian observer.
const Scalar & get_s_euler () const
 Returns the trace of the stress tensor in the Eulerian frame.
const Scalar & get_gam_euler () const
 Returns the Lorentz factor between the fluid and Eulerian observers.
const Vector & get_u_euler () const
 Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tensor & get_stress_euler () const
 Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.
const Scalar & get_logn () const
 Returns the logarithm of the lapse N.
const Scalar & get_nn () const
 Returns the lapse function N.
const Vector & get_beta () const
 Returns the shift vector $\beta^i$.
const Scalar & get_lnq () const
const Metric & get_gamma () const
 Returns the 3-metric $\gamma$.
double ray_eq () const
 Coordinate radius at $\phi=0$, $\theta=\pi/2$ [r_unit].
double ray_eq_pis2 () const
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$ [r_unit].
double ray_eq_pi () const
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$ [r_unit].
double ray_eq_3pis2 () const
 Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$ [r_unit].
double ray_pole () const
 Coordinate radius at $\theta=0$ [r_unit].
const Tbl & xi_surf () const
 Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.

Static Public Member Functions

static double lambda_grv2 (const Scalar &sou_m, const Scalar &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.
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.

Protected Attributes

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.
double omega
 Rotation angular velocity ([f_unit] ).
Scalar a_car
 Square of the metric factor A.
Scalar bbb
 Metric factor B.
Scalar b_car
 Square of the metric factor B.
Scalar nphi
 Metric coefficient $N^\varphi$.
Scalar tnphi
 Component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
Scalar uuu
 Norm of u_euler.
Scalar nuf
 Part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
Scalar nuq
 Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
Scalar dzeta
 Metric potential $\zeta = \ln(AN)$.
Scalar tggg
 Metric potential $\tilde G = (NB-1) r\sin\theta$.
Vector w_shift
 Vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
Scalar khi_shift
 Scalar $\chi$ used in the decomposition of shift , following Shibata's prescription [Prog.
Sym_tensor tkij
 Tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
Scalar ak_car
 Scalar $A^2 K_{ij} K^{ij}$.
Scalar ssjm1_nuf
 Effective source at the previous step for the resolution of the Poisson equation for nuf by means of Map_et::poisson .
Scalar ssjm1_nuq
 Effective source at the previous step for the resolution of the Poisson equation for nuq by means of Map_et::poisson .
Scalar ssjm1_dzeta
 Effective source at the previous step for the resolution of the Poisson equation for dzeta .
Scalar ssjm1_tggg
 Effective source at the previous step for the resolution of the Poisson equation for tggg .
Scalar 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 .
Vector 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_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_r_isco
 Circumferential radius of the ISCO.
double * p_f_isco
 Orbital frequency of the ISCO.
double * p_espec_isco
 Specific energy of a particle on the ISCO.
double * p_lspec_isco
 Specific angular momentum of a particle on the ISCO.
double * p_f_eq
 Orbital frequency at the equator.
Map & mp
 Mapping associated with the star.
int nzet
 Number of domains of *mp occupied by the star.
const Eos & eos
 Equation of state of the stellar matter.
Scalar ent
 Log-enthalpy.
Scalar nbar
 Baryon density in the fluid frame.
Scalar ener
 Total energy density in the fluid frame.
Scalar press
 Fluid pressure.
Scalar ener_euler
 Total energy density in the Eulerian frame.
Scalar s_euler
 Trace of the stress scalar in the Eulerian frame.
Scalar gam_euler
 Lorentz factor between the fluid and Eulerian observers.
Vector u_euler
 Fluid 3-velocity with respect to the Eulerian observer.
Sym_tensor stress_euler
 Spatial part of the stress-energy tensor with respect to the Eulerian observer.
Scalar logn
 Logarithm of the lapse N .
Scalar nn
 Lapse function N .
Vector beta
 Shift vector.
Scalar lnq
Metric gamma
 3-metric
double * p_ray_eq
 Coordinate radius at $\phi=0$, $\theta=\pi/2$.
double * p_ray_eq_pis2
 Coordinate radius at $\phi=\pi/2$, $\theta=\pi/2$.
double * p_ray_eq_pi
 Coordinate radius at $\phi=\pi$, $\theta=\pi/2$.
double * p_ray_eq_3pis2
 Coordinate radius at $\phi=3\pi/2$, $\theta=\pi/2$.
double * p_ray_pole
 Coordinate radius at $\theta=0$.
Itbl * p_l_surf
 Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
Tbl * p_xi_surf
 Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$.
double * p_mass_b
 Baryon mass.
double * p_mass_g
 Gravitational mass.

Friends

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

Detailed Description

Class for isolated rotating stars.

()

The metric is

\[ ds^2 = - N^2 dt^2 + A^2 (dr^2 + r^2 d\theta^2) + B^2 r^2 \sin^2\theta (d\varphi - N^\varphi dt)^2 \]

A star of class Star_rot can be either relativistic or Newtonian, depending on the boolean indicator relativistic . For a Newtonian star, the metric coefficients N, A, and B are set to 1, and $N^\varphi$ is set to zero; the only relevant gravitational quantity in this case is logn which represents the Newtonian gravitational potential generated by the star.

Version:
Id
star_rot.h,v 1.4 2010/02/08 10:56:30 j_novak Exp

Definition at line 79 of file star_rot.h.

Constructor & Destructor Documentation

Star_rot::Star_rot ( Map &  mp_i,
int  nzet_i,
bool  relat,
const Eos &  eos_i 
)

Standard constructor.

Parameters:
mp_i Mapping on which the star is contructed
nzet_i Number of domains occupied by the star
relat true for a relativistic star, false for a Newtonian one
eos_i Equation of state of the stellar matter

Definition at line 79 of file star_rot.C.

References a_car, ak_car, b_car, bbb, Star::beta, dzeta, Map::get_bvect_cart(), khi_shift, Star::mp, nphi, nuf, nuq, omega, relativistic, set_der_0x0(), Tensor::set_etat_zero(), Tensor::set_triad(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, Scalar::std_spectral_base(), tggg, tkij, tnphi, unsurc2, uuu, and w_shift.

Star_rot::Star_rot ( const Star_rot &  et  ) 

Copy constructor.

Definition at line 149 of file star_rot.C.

References set_der_0x0().

Star_rot::Star_rot ( Map &  mp_i,
const Eos &  eos_i,
FILE *  fich 
)

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

Parameters:
mp_i Mapping on which the star is constructed
eos_i Equation of state of the stellar matter
fich input file (must have been created by the function Star_rot::sauve )

Definition at line 182 of file star_rot.C.

References a_car, ak_car, b_car, bbb, dzeta, fait_nphi(), fait_shift(), fread_be(), Map::get_bvect_cart(), Map::get_mg(), khi_shift, Star::mp, nuf, nuq, omega, relativistic, set_der_0x0(), Tensor::set_etat_zero(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tkij, unsurc2, uuu, and w_shift.

Star_rot::~Star_rot (  )  [virtual]

Destructor.

Definition at line 280 of file star_rot.C.

References del_deriv().

Member Function Documentation

double Star_rot::angu_mom (  )  const [virtual]

Angular momentum.

Definition at line 150 of file star_rot_global.C.

References a_car, b_car, Star::ener_euler, Scalar::get_spectral_va(), Scalar::integrale(), Scalar::mult_r(), Star::nbar, p_angu_mom, Star::press, relativistic, Scalar::set_spectral_va(), and uuu.

double Star_rot::aplat (  )  const [virtual]

Flatening r_pole/r_eq.

Definition at line 373 of file star_rot_global.C.

References p_aplat, Star::ray_eq(), and Star::ray_pole().

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

Deletes all the derived quantities.

Reimplemented from Star.

Definition at line 290 of file star_rot.C.

References p_angu_mom, p_aplat, p_espec_isco, p_f_eq, p_f_isco, p_grv2, p_grv3, p_lspec_isco, p_mom_quad, p_r_circ, p_r_isco, p_tsw, p_z_eqb, p_z_eqf, p_z_pole, and set_der_0x0().

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

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

Reimplemented from Star.

Definition at line 336 of file star_rot.C.

References del_deriv().

void Star_rot::display_poly ( ostream &  ost  )  const [virtual]

Display in polytropic units.

Definition at line 636 of file star_rot.C.

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

void Star::equation_of_state (  )  [inherited]

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

Reimplemented in Gravastar.

Definition at line 458 of file star.C.

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

void Star_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]

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.)

Definition at line 67 of file star_rot_equil.C.

References a_car, abs(), Map::adapt(), Param::add_cmp_mod(), Param::add_double(), Param::add_double_mod(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Param::add_tenseur_mod(), ak_car, Tensor::annule_domain(), bbb, Star::beta, Valeur::c_cf, Vector::change_triad(), Map::cmp_zero(), Valeur::coef(), contract(), cos(), Scalar::derive_con(), Scalar::derive_cov(), diffrel(), Scalar::dsdr(), dzeta, Star::ener_euler, Star::ent, Star::equation_of_state(), fait_nphi(), Map::flat_met_cart(), Map::flat_met_spher(), Star::gam_euler, Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Mg3d::get_type_t(), grv2(), Map_et::homothetie(), hydro_euler(), khi_shift, log(), log10(), Star::logn, mass_b(), mass_g(), Star::mp, Scalar::mult_rsint(), Star::nbar, Star::nn, nphi, nuf, nuq, Star::nzet, omega, partial_display(), Map::phi, Scalar::poisson(), Map::poisson2d(), pow(), Star::press, Star::ray_eq(), Star::ray_pole(), Map::reevaluate(), relativistic, Star::s_euler, Vector::set(), Tenseur::set(), Tbl::set(), Scalar::set_dzpuis(), Tenseur::set_etat_qcq(), Tbl::set_etat_qcq(), Map::sint, sqrt(), ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, Scalar::std_spectral_base(), Scalar::test_poisson(), tggg, tkij, Star::u_euler, Tensor::up(), update_metric(), uuu, Scalar::val_grid_point(), and w_shift.

void Star::equilibrium_spher ( double  ent_c,
double  precis = 1.e-14,
const Tbl *  pent_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 91 of file star_equil_spher.C.

References Map_et::adapt(), Param::add_double(), Param::add_int(), Param::add_int_mod(), Param::add_tbl(), Scalar::annule(), diffrel(), Scalar::dsdr(), Map_af::dsdr(), Star::ener, Star::ener_euler, Star::ent, Star::equation_of_state(), exp(), Star::gam_euler, Star::gamma, Map_et::get_alpha(), Map_af::get_alpha(), Map_et::get_beta(), Map_af::get_beta(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Map_af::homothetie(), Scalar::integrale(), Star::logn, Star::mass_b(), Star::mass_g(), Star::mp, Star::nn, norme(), Star::nzet, Map_af::poisson(), Star::press, Star::s_euler, Vector::set(), Map_af::set_alpha(), Map_af::set_beta(), Scalar::set_dzpuis(), Cmp::set_etat_qcq(), Scalar::set_etat_zero(), sqrt(), Scalar::std_spectral_base(), Star::u_euler, Scalar::val_grid_point(), and Map::val_r().

double Star_rot::espec_isco (  )  const [virtual]

Energy of a particle on the ISCO.

Definition at line 285 of file star_rot_isco.C.

References p_espec_isco, and r_isco().

void Star_rot::extrinsic_curvature (  ) 

Computes tkij and ak_car from shift , nnn and b_car .

Definition at line 106 of file star_rot_upmetr.C.

References ak_car, b_car, Star::beta, contract(), Tensor::derive_cov(), Scalar::dsdr(), Map::flat_met_cart(), Scalar::get_etat(), Map::get_mg(), Scalar::get_spectral_va(), Star::mp, Scalar::mult_rsint(), Star::nn, nphi, Tensor::set(), Tensor::set_etat_qcq(), Tensor::set_etat_zero(), Scalar::set_spectral_va(), Scalar::srdsdt(), and tkij.

double Star_rot::f_eq (  )  const [virtual]

Orbital frequency at the equator.

Definition at line 303 of file star_rot_isco.C.

References p_f_eq, and r_isco().

double Star_rot::f_isco (  )  const [virtual]

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

Definition at line 251 of file star_rot_isco.C.

References p_f_isco, and r_isco().

void Star_rot::fait_nphi (  ) 

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

Definition at line 735 of file star_rot.C.

References Star::beta, Map::comp_p_from_cartesian(), Scalar::div_rsint(), Star::mp, nphi, and tnphi.

void Star_rot::fait_shift (  ) 

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

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

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

Definition at line 690 of file star_rot.C.

References Star::beta, contract(), Map::cosp, Map::cost, Tensor::dec_dzpuis(), Tensor::derive_con(), Scalar::derive_con(), Scalar::domain(), Map::flat_met_cart(), Map::get_bvect_cart(), Map::get_mg(), Mg3d::get_nzone(), khi_shift, Star::mp, Tbl::set(), Tensor::set(), Scalar::set_domain(), Map::sinp, Map::sint, w_shift, Map::x, Map::y, and Map::z.

const Scalar& Star_rot::get_a_car (  )  const [inline]

Returns the square of the metric factor A.

Definition at line 311 of file star_rot.h.

References a_car.

const Scalar& Star_rot::get_ak_car (  )  const [inline]

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 395 of file star_rot.h.

References ak_car.

const Scalar& Star_rot::get_b_car (  )  const [inline]

Returns the square of the metric factor B.

Definition at line 314 of file star_rot.h.

References b_car.

const Scalar& Star_rot::get_bbb (  )  const [inline]

Returns the metric factor B.

Definition at line 308 of file star_rot.h.

References bbb.

const Vector& Star::get_beta (  )  const [inline, inherited]

Returns the shift vector $\beta^i$.

Definition at line 398 of file star.h.

References Star::beta.

const Scalar& Star_rot::get_dzeta (  )  const [inline]

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

Definition at line 338 of file star_rot.h.

References dzeta.

const Scalar& Star::get_ener (  )  const [inline, inherited]

Returns the proper total energy density.

Definition at line 366 of file star.h.

References Star::ener.

const Scalar& Star::get_ener_euler (  )  const [inline, inherited]

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

Definition at line 372 of file star.h.

References Star::ener_euler.

const Scalar& Star::get_ent (  )  const [inline, inherited]

Returns the enthalpy field.

Definition at line 360 of file star.h.

References Star::ent.

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

Returns the equation of state.

Definition at line 357 of file star.h.

References Star::eos.

const Scalar& Star::get_gam_euler (  )  const [inline, inherited]

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 378 of file star.h.

References Star::gam_euler.

const Metric& Star::get_gamma (  )  const [inline, inherited]

Returns the 3-metric $\gamma$.

Definition at line 405 of file star.h.

References Star::gamma.

const Scalar& Star_rot::get_khi_shift (  )  const [inline]

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 369 of file star_rot.h.

References khi_shift.

const Scalar& Star::get_logn (  )  const [inline, inherited]

Returns the logarithm of the lapse N.

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

Definition at line 392 of file star.h.

References Star::logn.

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

Returns the mapping.

Definition at line 351 of file star.h.

References Star::mp.

const Scalar& Star::get_nbar (  )  const [inline, inherited]

Returns the proper baryon density.

Definition at line 363 of file star.h.

References Star::nbar.

const Scalar& Star::get_nn (  )  const [inline, inherited]

Returns the lapse function N.

Definition at line 395 of file star.h.

References Star::nn.

const Scalar& Star_rot::get_nphi (  )  const [inline]

Returns the metric coefficient $N^\varphi$.

Definition at line 317 of file star_rot.h.

References nphi.

const Scalar& Star_rot::get_nuf (  )  const [inline]

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

Definition at line 330 of file star_rot.h.

References nuf.

const Scalar& Star_rot::get_nuq (  )  const [inline]

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

Definition at line 335 of file star_rot.h.

References nuq.

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

Returns the number of domains occupied by the star.

Definition at line 354 of file star.h.

References Star::nzet.

double Star_rot::get_omega_c (  )  const [virtual]

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

Definition at line 627 of file star_rot.C.

References omega.

const Scalar& Star::get_press (  )  const [inline, inherited]

Returns the fluid pressure.

Definition at line 369 of file star.h.

References Star::press.

const Scalar& Star::get_s_euler (  )  const [inline, inherited]

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

Definition at line 375 of file star.h.

References Star::s_euler.

const Tensor& Star::get_stress_euler (  )  const [inline, inherited]

Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 386 of file star.h.

References Star::stress_euler.

const Scalar& Star_rot::get_tggg (  )  const [inline]

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

Definition at line 341 of file star_rot.h.

References tggg.

const Sym_tensor& Star_rot::get_tkij (  )  const [inline]

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 376 of file star_rot.h.

References tkij.

const Scalar& Star_rot::get_tnphi (  )  const [inline]

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

Definition at line 322 of file star_rot.h.

References tnphi.

const Vector& Star::get_u_euler (  )  const [inline, inherited]

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

Definition at line 381 of file star.h.

References Star::u_euler.

const Scalar& Star_rot::get_uuu (  )  const [inline]

Returns the norm of u_euler.

Definition at line 325 of file star_rot.h.

References uuu.

const Vector& Star_rot::get_w_shift (  )  const [inline]

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 355 of file star_rot.h.

References w_shift.

double Star_rot::grv2 (  )  const [virtual]

Error on the virial identity GRV2.

This indicator is only valid for relativistic computations.

Definition at line 210 of file star_rot_global.C.

References a_car, ak_car, Scalar::derive_cov(), Star::ener_euler, Map::flat_met_spher(), lambda_grv2(), Star::logn, Star::mp, Star::nbar, p_grv2, Star::press, relativistic, and uuu.

double Star_rot::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.

Definition at line 241 of file star_rot_global.C.

References a_car, ak_car, bbb, Scalar::derive_cov(), Scalar::dsdr(), dzeta, Map::flat_met_spher(), Scalar::get_dzpuis(), Scalar::get_etat(), Scalar::integrale(), log(), Star::logn, Star::mp, Valeur::mult_ct(), Star::nbar, p_grv3, Star::press, relativistic, Star::s_euler, Scalar::set_dzpuis(), Scalar::set_spectral_va(), Scalar::srdsdt(), Valeur::ssint(), Scalar::std_spectral_base(), Valeur::sx(), uuu, and Map_radial::xsr.

void Star_rot::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 , ener , press , and a_car , which are supposed to be up to date. From these, the following fields are updated: gam_euler , u_euler , ener_euler , s_euler .

Reimplemented from Star.

Definition at line 53 of file star_rot_hydro.C.

References a_car, Tensor::annule_domain(), b_car, Star::beta, Vector::change_triad(), del_deriv(), Star::ener, Star::ener_euler, Star::gam_euler, Map::get_bvect_cart(), Map::get_bvect_spher(), Scalar::get_etat(), Map::get_mg(), Mg3d::get_nzone(), Star::mp, Star::nn, omega, Star::press, Star::s_euler, Vector::set(), Tensor::set_etat_qcq(), Tensor::set_etat_zero(), Scalar::set_spectral_va(), Tensor::set_triad(), sqrt(), Scalar::std_spectral_base(), Vector::std_spectral_base(), Star::u_euler, unsurc2, uuu, Map::x, and Map::y.

bool Star_rot::is_relativistic (  )  const [inline]

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

Definition at line 300 of file star_rot.h.

References relativistic.

const Itbl & Star_rot::l_surf (  )  const [virtual]

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

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

Reimplemented from Star.

Definition at line 61 of file star_rot_global.C.

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

double Star_rot::lambda_grv2 ( const Scalar &  sou_m,
const Scalar &  sou_q 
) [static]

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 58 of file star_rot_lambda_grv2.C.

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

double Star_rot::lspec_isco (  )  const [virtual]

Angular momentum of a particle on the ISCO.

Definition at line 268 of file star_rot_isco.C.

References p_lspec_isco, and r_isco().

double Star_rot::mass_b (  )  const [virtual]

Baryon mass.

Implements Star.

Definition at line 91 of file star_rot_global.C.

References a_car, bbb, Star::gam_euler, Scalar::get_etat(), Scalar::integrale(), Star::nbar, Star::p_mass_b, and relativistic.

double Star_rot::mass_g (  )  const [virtual]

Gravitational mass.

Implements Star.

Definition at line 120 of file star_rot_global.C.

References a_car, bbb, Star::ener_euler, mass_b(), Star::nn, Star::p_mass_g, Star::press, relativistic, Star::s_euler, Scalar::std_spectral_base(), tnphi, and uuu.

double Star_rot::mom_quad (  )  const [virtual]

Quadrupole moment.

The quadrupole moment Q is defined according to Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and Haensel, Astron. Astrophys. 291 , 155 (1994)]. At the Newtonian limit it is related to the component ${\bar I}_{zz}$ of the MTW (1973) reduced quadrupole moment ${\bar I}_{ij}$ by: $Q = -3/2 {\bar I}_{zz}$. Note that Q is the negative of the quadrupole moment defined by Laarakkers and Poisson, Astrophys. J. 512 , 282 (1999).

Definition at line 468 of file star_rot_global.C.

References a_car, ak_car, bbb, Scalar::check_dzpuis(), Scalar::derive_cov(), Star::ener_euler, Map::flat_met_spher(), Scalar::get_etat(), Scalar::inc_dzpuis(), Scalar::integrale(), log(), Star::logn, Star::mp, Valeur::mult_ct(), Scalar::mult_r(), Star::nbar, p_mom_quad, relativistic, Star::s_euler, Scalar::set_spectral_va(), and Scalar::std_spectral_base().

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

Assignment to another Star_rot.

Reimplemented from Star.

Reimplemented in Gravastar.

Definition at line 350 of file star_rot.C.

References a_car, ak_car, b_car, bbb, del_deriv(), dzeta, khi_shift, nphi, nuf, nuq, omega, relativistic, ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, tkij, tnphi, unsurc2, uuu, and w_shift.

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

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

Reimplemented from Star.

Reimplemented in Gravastar.

Definition at line 419 of file star_rot.C.

References a_car, angu_mom(), aplat(), b_car, diffrel(), dzeta, f_isco(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), get_omega_c(), Tbl::get_taille(), grv2(), grv3(), khi_shift, Star::logn, mass_g(), mom_quad(), Star::mp, nphi, Star::nzet, omega, pow(), r_circ(), r_isco(), Star::ray_eq(), relativistic, sqrt(), tsw(), uuu, Scalar::val_grid_point(), w_shift, z_eqb(), z_eqf(), and z_pole().

void Star_rot::partial_display ( ostream &  ost  )  const [protected, virtual]

Printing of some informations, excluding all global quantities.

Definition at line 577 of file star_rot.C.

References a_car, aplat(), b_car, dzeta, Star::ener, Star::ent, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), get_omega_c(), Star::logn, Star::mp, Star::nbar, Star::nn, nphi, Star::nzet, Star::press, Star::ray_eq(), uuu, and Scalar::val_grid_point().

double Star_rot::r_circ (  )  const [virtual]

Circumferential radius.

Definition at line 348 of file star_rot_global.C.

References bbb, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Star::mp, Star::nzet, p_r_circ, Star::ray_eq(), and Scalar::val_grid_point().

double Star_rot::r_isco ( ostream *  ost = 0x0  )  const [virtual]

Circumferential radius of the innermost stable circular orbit (ISCO).

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

Definition at line 67 of file star_rot_isco.C.

References Param::add_int(), Param::add_scalar(), Tensor::annule_domain(), bbb, Scalar::dsdr(), Map::get_mg(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Star::mp, Star::nn, nphi, Star::nzet, p_espec_isco, p_f_eq, p_f_isco, p_lspec_isco, p_r_isco, Map::r, Star::ray_eq(), sqrt(), Scalar::std_spectral_base(), Valeur::val_point(), Map::val_r(), and zerosec().

double Star::ray_eq (  )  const [inherited]

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

Definition at line 104 of file star_global.C.

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

double Star::ray_eq_3pis2 (  )  const [inherited]

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

Definition at line 229 of file star_global.C.

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

double Star::ray_eq_pi (  )  const [inherited]

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

Definition at line 182 of file star_global.C.

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

double Star::ray_eq_pis2 (  )  const [inherited]

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

Definition at line 134 of file star_global.C.

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

double Star::ray_pole (  )  const [inherited]

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

Definition at line 274 of file star_global.C.

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

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

Save in a file.

Reimplemented from Star.

Definition at line 392 of file star_rot.C.

References dzeta, fwrite_be(), khi_shift, nuf, nuq, omega, relativistic, Tensor::sauve(), Scalar::sauve(), ssjm1_dzeta, ssjm1_khi, ssjm1_nuf, ssjm1_nuq, ssjm1_tggg, ssjm1_wshift, tggg, and w_shift.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Star.

Definition at line 314 of file star_rot.C.

References p_angu_mom, p_aplat, p_espec_isco, p_f_eq, p_f_isco, p_grv2, p_grv3, p_lspec_isco, p_mom_quad, p_r_circ, p_r_isco, p_tsw, p_z_eqb, p_z_eqf, and p_z_pole.

void Star::set_enthalpy ( const Scalar &  ent_i  )  [inherited]

Assignment of the enthalpy field.

Definition at line 375 of file star.C.

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

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

Read/write of the mapping.

Definition at line 318 of file star.h.

References Star::mp.

double Star_rot::tsw (  )  const [virtual]

Ratio T/W.

Definition at line 179 of file star_rot_global.C.

References a_car, angu_mom(), bbb, Star::ener, Star::gam_euler, Scalar::integrale(), Star::logn, mass_g(), Star::nbar, omega, p_tsw, and relativistic.

void Star_rot::update_metric (  ) 

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, as well as the 3-metric gamma.

Definition at line 47 of file star_rot_upmetr.C.

References a_car, b_car, bbb, del_deriv(), Scalar::div_rsint(), dzeta, exp(), extrinsic_curvature(), Star::gamma, Map::get_bvect_spher(), Star::logn, Star::mp, Star::nn, Tensor::set(), Scalar::std_spectral_base(), tggg, and unsurc2.

const Tbl & Star::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 85 of file star_global.C.

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

double Star_rot::z_eqb (  )  const [virtual]

Backward redshift factor at equator.

Definition at line 418 of file star_rot_global.C.

References Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Star::mp, Star::nn, nphi, Star::nzet, p_z_eqb, r_circ(), sqrt(), uuu, and Scalar::val_grid_point().

double Star_rot::z_eqf (  )  const [virtual]

Forward redshift factor at equator.

Definition at line 390 of file star_rot_global.C.

References Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Star::mp, Star::nn, nphi, Star::nzet, p_z_eqf, r_circ(), sqrt(), uuu, and Scalar::val_grid_point().

double Star_rot::z_pole (  )  const [virtual]

Redshift factor at North pole.

Definition at line 449 of file star_rot_global.C.

References Star::nn, p_z_pole, Star::ray_pole(), and Scalar::val_point().

Friends And Related Function Documentation

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

Display.

Member Data Documentation

Scalar Star_rot::a_car [protected]

Square of the metric factor A.

Definition at line 97 of file star_rot.h.

Scalar Star_rot::ak_car [protected]

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 179 of file star_rot.h.

Scalar Star_rot::b_car [protected]

Square of the metric factor B.

Definition at line 103 of file star_rot.h.

Scalar Star_rot::bbb [protected]

Metric factor B.

Definition at line 100 of file star_rot.h.

Vector Star::beta [protected, inherited]

Shift vector.

Definition at line 224 of file star.h.

Scalar Star_rot::dzeta [protected]

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

Definition at line 127 of file star_rot.h.

Scalar Star::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 189 of file star.h.

Scalar Star::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 194 of file star.h.

Scalar Star::ent [protected, inherited]

Log-enthalpy.

Definition at line 186 of file star.h.

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

Equation of state of the stellar matter.

Definition at line 181 of file star.h.

Scalar Star::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 200 of file star.h.

Metric Star::gamma [protected, inherited]

3-metric

Definition at line 231 of file star.h.

Scalar Star_rot::khi_shift [protected]

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 153 of file star_rot.h.

Scalar Star::logn [protected, inherited]

Logarithm of the lapse N .

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

Definition at line 218 of file star.h.

Map& Star::mp [protected, inherited]

Mapping associated with the star.

Definition at line 176 of file star.h.

Scalar Star::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 188 of file star.h.

Scalar Star::nn [protected, inherited]

Lapse function N .

Definition at line 221 of file star.h.

Scalar Star_rot::nphi [protected]

Metric coefficient $N^\varphi$.

Definition at line 106 of file star_rot.h.

Scalar Star_rot::nuf [protected]

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

Definition at line 119 of file star_rot.h.

Scalar Star_rot::nuq [protected]

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

Definition at line 124 of file star_rot.h.

int Star::nzet [protected, inherited]

Number of domains of *mp occupied by the star.

Definition at line 179 of file star.h.

double Star_rot::omega [protected]

Rotation angular velocity ([f_unit] ).

Definition at line 94 of file star_rot.h.

double* Star_rot::p_angu_mom [mutable, protected]

Angular momentum.

Definition at line 225 of file star_rot.h.

double* Star_rot::p_aplat [mutable, protected]

Flatening r_pole/r_eq.

Definition at line 230 of file star_rot.h.

double* Star_rot::p_espec_isco [mutable, protected]

Specific energy of a particle on the ISCO.

Definition at line 238 of file star_rot.h.

double* Star_rot::p_f_eq [mutable, protected]

Orbital frequency at the equator.

Definition at line 241 of file star_rot.h.

double* Star_rot::p_f_isco [mutable, protected]

Orbital frequency of the ISCO.

Definition at line 236 of file star_rot.h.

double* Star_rot::p_grv2 [mutable, protected]

Error on the virial identity GRV2.

Definition at line 227 of file star_rot.h.

double* Star_rot::p_grv3 [mutable, protected]

Error on the virial identity GRV3.

Definition at line 228 of file star_rot.h.

Itbl* Star::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 256 of file star.h.

double* Star_rot::p_lspec_isco [mutable, protected]

Specific angular momentum of a particle on the ISCO.

Definition at line 240 of file star_rot.h.

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

Baryon mass.

Definition at line 264 of file star.h.

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

Gravitational mass.

Definition at line 265 of file star.h.

double* Star_rot::p_mom_quad [mutable, protected]

Quadrupole moment.

Definition at line 234 of file star_rot.h.

double* Star_rot::p_r_circ [mutable, protected]

Circumferential radius.

Definition at line 229 of file star_rot.h.

double* Star_rot::p_r_isco [mutable, protected]

Circumferential radius of the ISCO.

Definition at line 235 of file star_rot.h.

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

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

Definition at line 238 of file star.h.

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

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

Definition at line 247 of file star.h.

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

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

Definition at line 244 of file star.h.

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

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

Definition at line 241 of file star.h.

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

Coordinate radius at $\theta=0$.

Definition at line 250 of file star.h.

double* Star_rot::p_tsw [mutable, protected]

Ratio T/W.

Definition at line 226 of file star_rot.h.

Tbl* Star::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 262 of file star.h.

double* Star_rot::p_z_eqb [mutable, protected]

Backward redshift factor at equator.

Definition at line 232 of file star_rot.h.

double* Star_rot::p_z_eqf [mutable, protected]

Forward redshift factor at equator.

Definition at line 231 of file star_rot.h.

double* Star_rot::p_z_pole [mutable, protected]

Redshift factor at North pole.

Definition at line 233 of file star_rot.h.

Scalar Star::press [protected, inherited]

Fluid pressure.

Definition at line 190 of file star.h.

bool Star_rot::relativistic [protected]

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

Definition at line 87 of file star_rot.h.

Scalar Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 197 of file star.h.

Scalar Star_rot::ssjm1_dzeta [protected]

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

Definition at line 196 of file star_rot.h.

Scalar Star_rot::ssjm1_khi [protected]

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

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

Definition at line 209 of file star_rot.h.

Scalar Star_rot::ssjm1_nuf [protected]

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

Definition at line 185 of file star_rot.h.

Scalar Star_rot::ssjm1_nuq [protected]

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

Definition at line 191 of file star_rot.h.

Scalar Star_rot::ssjm1_tggg [protected]

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

Definition at line 201 of file star_rot.h.

Vector Star_rot::ssjm1_wshift [protected]

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 218 of file star_rot.h.

Sym_tensor Star::stress_euler [protected, inherited]

Spatial part of the stress-energy tensor with respect to the Eulerian observer.

Definition at line 208 of file star.h.

Scalar Star_rot::tggg [protected]

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

Definition at line 130 of file star_rot.h.

Sym_tensor Star_rot::tkij [protected]

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 160 of file star_rot.h.

Scalar Star_rot::tnphi [protected]

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

Definition at line 111 of file star_rot.h.

Vector Star::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 203 of file star.h.

double Star_rot::unsurc2 [protected]

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

Definition at line 92 of file star_rot.h.

Scalar Star_rot::uuu [protected]

Norm of u_euler.

Definition at line 114 of file star_rot.h.

Vector Star_rot::w_shift [protected]

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 143 of file star_rot.h.

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