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

Class for isolated rotating stars. More...

#include <star_rot.h>

Inheritance diagram for Lorene::Star_rot:
Lorene::Star Lorene::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 Scalarget_bbb () const
 Returns the metric factor B.
const Scalarget_a_car () const
 Returns the square of the metric factor A.
const Scalarget_b_car () const
 Returns the square of the metric factor B.
const Scalarget_nphi () const
 Returns the metric coefficient $N^\varphi$.
const Scalarget_tnphi () const
 Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector.
const Scalarget_uuu () const
 Returns the norm of u_euler.
const Scalarget_nuf () const
 Returns the part of the Metric potential $\nu = \ln N$ = logn generated by the matter terms.
const Scalarget_nuq () const
 Returns the Part of the Metric potential $\nu = \ln N$ = logn generated by the quadratic terms.
const Scalarget_dzeta () const
 Returns the Metric potential $\zeta = \ln(AN)$.
const Scalarget_tggg () const
 Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$.
const Vectorget_w_shift () const
 Returns the vector $W^i$ used in the decomposition of shift , following Shibata's prescription [Prog.
const Scalarget_khi_shift () const
 Returns the scalar $\chi$ used in the decomposition of shift following Shibata's prescription [Prog.
const Sym_tensorget_tkij () const
 Returns the tensor ${\tilde K_{ij}}$ related to the extrinsic curvature tensor by ${\tilde K_{ij}} = B^{-2} K_{ij}$.
const Scalarget_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 Itbll_surf () const
 Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$.
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 area () const
 Integrated surface area in ${\rm km}^2$.
virtual double mean_radius () const
 Mean star radius from the area $ r_{\rm mean} = \sqrt{\mathcal{A}} / 4\pi$.
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 const Tblsurf_grav () const
 Surface gravity (table along the theta direction).
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.
Mapset_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 Mapget_mp () const
 Returns the mapping.
int get_nzet () const
 Returns the number of domains occupied by the star.
const Eosget_eos () const
 Returns the equation of state.
const Scalarget_ent () const
 Returns the enthalpy field.
const Scalarget_nbar () const
 Returns the proper baryon density.
const Scalarget_ener () const
 Returns the proper total energy density.
const Scalarget_press () const
 Returns the fluid pressure.
const Scalarget_ener_euler () const
 Returns the total energy density with respect to the Eulerian observer.
const Scalarget_s_euler () const
 Returns the trace of the stress tensor in the Eulerian frame.
const Scalarget_gam_euler () const
 Returns the Lorentz factor between the fluid and Eulerian observers.
const Vectorget_u_euler () const
 Returns the fluid 3-velocity with respect to the Eulerian observer.
const Tensorget_stress_euler () const
 Returns the spatial part of the stress-energy tensor with respect to the Eulerian observer.
const Scalarget_logn () const
 Returns the logarithm of the lapse N.
const Scalarget_nn () const
 Returns the lapse function N.
const Vectorget_beta () const
 Returns the shift vector $\beta^i$.
const Scalarget_lnq () const
const Metricget_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 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 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_area
 Integrated surface area.
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.
Tblp_surf_grav
 Surface gravity (along the theta direction).
Mapmp
 Mapping associated with the star.
int nzet
 Number of domains of *mp occupied by the star.
const Eoseos
 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 $\theta=0$.
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

class Star
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 1.8 2017/10/20 13:55:41 j_novak Exp

Definition at line 92 of file star_rot.h.


Constructor & Destructor Documentation

Lorene::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 92 of file star_rot.C.

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

Lorene::Star_rot::Star_rot ( const Star_rot et  ) 

Copy constructor.

Definition at line 162 of file star_rot.C.

References set_der_0x0().

Lorene::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 195 of file star_rot.C.

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

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

Destructor.

Definition at line 293 of file star_rot.C.

References del_deriv().


Member Function Documentation

double Lorene::Star_rot::angu_mom (  )  const [virtual]
double Lorene::Star_rot::aplat (  )  const [virtual]

Flatening r_pole/r_eq.

Definition at line 435 of file star_rot_global.C.

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

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

Deletes all the derived quantities.

Reimplemented from Lorene::Star.

Definition at line 303 of file star_rot.C.

References p_angu_mom, p_aplat, p_area, 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_surf_grav, p_tsw, p_z_eqb, p_z_eqf, p_z_pole, and set_der_0x0().

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

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

Reimplemented from Lorene::Star.

Definition at line 353 of file star_rot.C.

References del_deriv().

void Lorene::Star_rot::display_poly ( ostream &  ost  )  const [virtual]
void Lorene::Star::equation_of_state (  )  [inherited]
void Lorene::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 74 of file star_rot_equil.C.

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

void Lorene::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 101 of file star_equil_spher.C.

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

double Lorene::Star_rot::espec_isco (  )  const [virtual]

Energy of a particle on the ISCO.

Definition at line 292 of file star_rot_isco.C.

References p_espec_isco, and r_isco().

void Lorene::Star_rot::extrinsic_curvature (  ) 
double Lorene::Star_rot::f_eq (  )  const [virtual]

Orbital frequency at the equator.

Definition at line 310 of file star_rot_isco.C.

References p_f_eq, and r_isco().

double Lorene::Star_rot::f_isco (  )  const [virtual]

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

Definition at line 258 of file star_rot_isco.C.

References p_f_isco, and r_isco().

void Lorene::Star_rot::fait_nphi (  ) 

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

Definition at line 756 of file star_rot.C.

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

void Lorene::Star_rot::fait_shift (  ) 
const Scalar& Lorene::Star_rot::get_a_car (  )  const [inline]

Returns the square of the metric factor A.

Definition at line 326 of file star_rot.h.

References a_car.

const Scalar& Lorene::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 410 of file star_rot.h.

References ak_car.

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

Returns the square of the metric factor B.

Definition at line 329 of file star_rot.h.

References b_car.

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

Returns the metric factor B.

Definition at line 323 of file star_rot.h.

References bbb.

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

Returns the shift vector $\beta^i$.

Definition at line 402 of file star.h.

References Lorene::Star::beta.

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

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

Definition at line 353 of file star_rot.h.

References dzeta.

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

Returns the proper total energy density.

Definition at line 370 of file star.h.

References Lorene::Star::ener.

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

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

Definition at line 376 of file star.h.

References Lorene::Star::ener_euler.

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

Returns the enthalpy field.

Definition at line 364 of file star.h.

References Lorene::Star::ent.

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

Returns the equation of state.

Definition at line 361 of file star.h.

References Lorene::Star::eos.

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

Returns the Lorentz factor between the fluid and Eulerian observers.

Definition at line 382 of file star.h.

References Lorene::Star::gam_euler.

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

Returns the 3-metric $\gamma$.

Definition at line 409 of file star.h.

References Lorene::Star::gamma.

const Scalar& Lorene::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 384 of file star_rot.h.

References khi_shift.

const Scalar& Lorene::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 396 of file star.h.

References Lorene::Star::logn.

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

Returns the mapping.

Definition at line 355 of file star.h.

References Lorene::Star::mp.

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

Returns the proper baryon density.

Definition at line 367 of file star.h.

References Lorene::Star::nbar.

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

Returns the lapse function N.

Definition at line 399 of file star.h.

References Lorene::Star::nn.

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

Returns the metric coefficient $N^\varphi$.

Definition at line 332 of file star_rot.h.

References nphi.

const Scalar& Lorene::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 345 of file star_rot.h.

References nuf.

const Scalar& Lorene::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 350 of file star_rot.h.

References nuq.

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

Returns the number of domains occupied by the star.

Definition at line 358 of file star.h.

References Lorene::Star::nzet.

double Lorene::Star_rot::get_omega_c (  )  const [virtual]

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

Definition at line 648 of file star_rot.C.

References omega.

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

Returns the fluid pressure.

Definition at line 373 of file star.h.

References Lorene::Star::press.

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

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

Definition at line 379 of file star.h.

References Lorene::Star::s_euler.

const Tensor& Lorene::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 390 of file star.h.

References Lorene::Star::stress_euler.

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

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

Definition at line 356 of file star_rot.h.

References tggg.

const Sym_tensor& Lorene::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 391 of file star_rot.h.

References tkij.

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

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

Definition at line 337 of file star_rot.h.

References tnphi.

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

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

Definition at line 385 of file star.h.

References Lorene::Star::u_euler.

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

Returns the norm of u_euler.

Definition at line 340 of file star_rot.h.

References uuu.

const Vector& Lorene::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 370 of file star_rot.h.

References w_shift.

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

Error on the virial identity GRV2.

This indicator is only valid for relativistic computations.

Definition at line 213 of file star_rot_global.C.

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

double Lorene::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 244 of file star_rot_global.C.

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

void Lorene::Star_rot::hydro_euler (  )  [virtual]
bool Lorene::Star_rot::is_relativistic (  )  const [inline]

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

Definition at line 315 of file star_rot.h.

References relativistic.

const Itbl & Lorene::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 Lorene::Star.

Definition at line 77 of file star_rot_global.C.

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

double Lorene::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 69 of file star_rot_lambda_grv2.C.

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

double Lorene::Star_rot::lspec_isco (  )  const [virtual]

Angular momentum of a particle on the ISCO.

Definition at line 275 of file star_rot_isco.C.

References p_lspec_isco, and r_isco().

double Lorene::Star_rot::mass_b (  )  const [virtual]
double Lorene::Star_rot::mass_g (  )  const [virtual]
double Lorene::Star_rot::mean_radius (  )  const [virtual]

Mean star radius from the area $ r_{\rm mean} = \sqrt{\mathcal{A}} / 4\pi$.

Definition at line 425 of file star_rot_global.C.

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

double Lorene::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 530 of file star_rot_global.C.

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

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

Assignment to another Star_rot.

Reimplemented from Lorene::Star.

Reimplemented in Lorene::Gravastar.

Definition at line 367 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 & Lorene::Star_rot::operator>> ( ostream &  ost  )  const [protected, virtual]
void Lorene::Star_rot::partial_display ( ostream &  ost  )  const [protected, virtual]
double Lorene::Star_rot::r_circ (  )  const [virtual]
double Lorene::Star_rot::r_isco ( ostream *  ost = 0x0  )  const [virtual]
double Lorene::Star::ray_eq (  )  const [inherited]
double Lorene::Star::ray_eq_3pis2 (  )  const [inherited]
double Lorene::Star::ray_eq_pi (  )  const [inherited]
double Lorene::Star::ray_eq_pis2 (  )  const [inherited]
double Lorene::Star::ray_pole (  )  const [inherited]
void Lorene::Star_rot::sauve ( FILE *  fich  )  const [virtual]
void Lorene::Star_rot::set_der_0x0 (  )  const [protected, virtual]

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Star.

Definition at line 329 of file star_rot.C.

References p_angu_mom, p_aplat, p_area, 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_surf_grav, p_tsw, p_z_eqb, p_z_eqf, and p_z_pole.

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

Assignment of the enthalpy field.

Definition at line 382 of file star.C.

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

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

Read/write of the mapping.

Definition at line 322 of file star.h.

References Lorene::Star::mp.

const Tbl & Lorene::Star_rot::surf_grav (  )  const [virtual]
double Lorene::Star_rot::tsw (  )  const [virtual]
void Lorene::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 54 of file star_rot_upmetr.C.

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

const Tbl & Lorene::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 92 of file star_global.C.

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

double Lorene::Star_rot::z_eqb (  )  const [virtual]
double Lorene::Star_rot::z_eqf (  )  const [virtual]
double Lorene::Star_rot::z_pole (  )  const [virtual]

Redshift factor at North pole.

Definition at line 511 of file star_rot_global.C.

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


Friends And Related Function Documentation

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

Display.


Member Data Documentation

Square of the metric factor A.

Definition at line 110 of file star_rot.h.

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 192 of file star_rot.h.

Square of the metric factor B.

Definition at line 116 of file star_rot.h.

Metric factor B.

Definition at line 113 of file star_rot.h.

Vector Lorene::Star::beta [protected, inherited]

Shift vector.

Definition at line 228 of file star.h.

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

Definition at line 140 of file star_rot.h.

Scalar Lorene::Star::ener [protected, inherited]

Total energy density in the fluid frame.

Definition at line 193 of file star.h.

Scalar Lorene::Star::ener_euler [protected, inherited]

Total energy density in the Eulerian frame.

Definition at line 198 of file star.h.

Scalar Lorene::Star::ent [protected, inherited]

Log-enthalpy.

Definition at line 190 of file star.h.

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

Equation of state of the stellar matter.

Definition at line 185 of file star.h.

Scalar Lorene::Star::gam_euler [protected, inherited]

Lorentz factor between the fluid and Eulerian observers.

Definition at line 204 of file star.h.

Metric Lorene::Star::gamma [protected, inherited]

3-metric

Definition at line 235 of file star.h.

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 166 of file star_rot.h.

Scalar Lorene::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 222 of file star.h.

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

Mapping associated with the star.

Definition at line 180 of file star.h.

Scalar Lorene::Star::nbar [protected, inherited]

Baryon density in the fluid frame.

Definition at line 192 of file star.h.

Scalar Lorene::Star::nn [protected, inherited]

Lapse function N .

Definition at line 225 of file star.h.

Metric coefficient $N^\varphi$.

Definition at line 119 of file star_rot.h.

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

Definition at line 132 of file star_rot.h.

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

Definition at line 137 of file star_rot.h.

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

Number of domains of *mp occupied by the star.

Definition at line 183 of file star.h.

double Lorene::Star_rot::omega [protected]

Rotation angular velocity ([f_unit] ).

Definition at line 107 of file star_rot.h.

double* Lorene::Star_rot::p_angu_mom [mutable, protected]

Angular momentum.

Definition at line 238 of file star_rot.h.

double* Lorene::Star_rot::p_aplat [mutable, protected]

Flatening r_pole/r_eq.

Definition at line 243 of file star_rot.h.

double* Lorene::Star_rot::p_area [mutable, protected]

Integrated surface area.

Definition at line 244 of file star_rot.h.

double* Lorene::Star_rot::p_espec_isco [mutable, protected]

Specific energy of a particle on the ISCO.

Definition at line 252 of file star_rot.h.

double* Lorene::Star_rot::p_f_eq [mutable, protected]

Orbital frequency at the equator.

Definition at line 255 of file star_rot.h.

double* Lorene::Star_rot::p_f_isco [mutable, protected]

Orbital frequency of the ISCO.

Definition at line 250 of file star_rot.h.

double* Lorene::Star_rot::p_grv2 [mutable, protected]

Error on the virial identity GRV2.

Definition at line 240 of file star_rot.h.

double* Lorene::Star_rot::p_grv3 [mutable, protected]

Error on the virial identity GRV3.

Definition at line 241 of file star_rot.h.

Itbl* Lorene::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 260 of file star.h.

double* Lorene::Star_rot::p_lspec_isco [mutable, protected]

Specific angular momentum of a particle on the ISCO.

Definition at line 254 of file star_rot.h.

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

Baryon mass.

Definition at line 268 of file star.h.

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

Gravitational mass.

Definition at line 269 of file star.h.

double* Lorene::Star_rot::p_mom_quad [mutable, protected]

Quadrupole moment.

Definition at line 248 of file star_rot.h.

double* Lorene::Star_rot::p_r_circ [mutable, protected]

Circumferential radius.

Definition at line 242 of file star_rot.h.

double* Lorene::Star_rot::p_r_isco [mutable, protected]

Circumferential radius of the ISCO.

Definition at line 249 of file star_rot.h.

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

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

Definition at line 242 of file star.h.

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

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

Definition at line 251 of file star.h.

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

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

Definition at line 248 of file star.h.

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

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

Definition at line 245 of file star.h.

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

Coordinate radius at $\theta=0$.

Definition at line 254 of file star.h.

Tbl* Lorene::Star_rot::p_surf_grav [mutable, protected]

Surface gravity (along the theta direction).

Definition at line 256 of file star_rot.h.

double* Lorene::Star_rot::p_tsw [mutable, protected]

Ratio T/W.

Definition at line 239 of file star_rot.h.

Tbl* Lorene::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 266 of file star.h.

double* Lorene::Star_rot::p_z_eqb [mutable, protected]

Backward redshift factor at equator.

Definition at line 246 of file star_rot.h.

double* Lorene::Star_rot::p_z_eqf [mutable, protected]

Forward redshift factor at equator.

Definition at line 245 of file star_rot.h.

double* Lorene::Star_rot::p_z_pole [mutable, protected]

Redshift factor at North pole.

Definition at line 247 of file star_rot.h.

Scalar Lorene::Star::press [protected, inherited]

Fluid pressure.

Definition at line 194 of file star.h.

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

Definition at line 100 of file star_rot.h.

Scalar Lorene::Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 201 of file star.h.

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

Definition at line 209 of file star_rot.h.

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 222 of file star_rot.h.

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

Definition at line 198 of file star_rot.h.

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

Definition at line 204 of file star_rot.h.

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

Definition at line 214 of file star_rot.h.

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 231 of file star_rot.h.

Sym_tensor Lorene::Star::stress_euler [protected, inherited]

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

Definition at line 212 of file star.h.

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

Definition at line 143 of file star_rot.h.

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 173 of file star_rot.h.

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

Definition at line 124 of file star_rot.h.

Vector Lorene::Star::u_euler [protected, inherited]

Fluid 3-velocity with respect to the Eulerian observer.

Definition at line 207 of file star.h.

double Lorene::Star_rot::unsurc2 [protected]

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

Definition at line 105 of file star_rot.h.

Norm of u_euler.

Definition at line 127 of file star_rot.h.

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 156 of file star_rot.h.


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

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