Star_rot_Dirac Class Reference
[Stars and black holes]

Class for relativistic rotating stars in Dirac gauge and maximal slicing. More...

#include <star_rot_dirac.h>

Inheritance diagram for Star_rot_Dirac:

Public Member Functions
	Star_rot_Dirac (Map &mp_i, int nzet_i, const Eos &eos_i, int filter=0)
	Standard constructor.
	Star_rot_Dirac (const Star_rot_Dirac &)
	Copy constructor.
	Star_rot_Dirac (Map &mp_i, const Eos &eos_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ).
virtual	~Star_rot_Dirac ()
	Destructor.
void	operator= (const Star_rot_Dirac &)
	Assignment to another `Star_rot_Dirac`.
int	spectral_filter_order () const
	Returns the filtering order.
double	get_omega () const
	Returns the rotation angular velocity $\Omega$ .
const Scalar &	get_psi4 () const
	Returns the conformal factor $\Psi^4$ .
const Scalar &	get_psi2 () const
	Returns $\Psi^2$ .
const Scalar &	get_qqq () const
	Returns $Q=\Psi^2 N$ .
const Scalar &	get_ln_psi () const
	Returns $ln(\Psi)$ .
const Vector &	get_j_euler () const
	Returns the momentum density 3-vector with respect to the Eulerian observer.
const Scalar &	get_v2 () const
	Reutrns $\gamma_{ij}v^i v^j$ .
const Metric	get_tgamma () const
	Returns the conformal metric $\tilde{\gamma}_{ij}$ .
const Sym_tensor	get_aa () const
	Returns $A^{ij}$ .
const Sym_tensor	get_taa () const
	Returns $\tilde{A}_{ij}$ .
const Scalar	get_aa_quad () const
	Returns $\tilde{A}_{ij} A^{ij}$ .
const Sym_tensor_trans	get_hh () const
	Returns $h^{ij}$ .
virtual void	sauve (FILE *) const
	Save in a file.
virtual double	mass_b () const
	Baryonic mass.
virtual double	mass_g () const
	Gravitational mass.
virtual double	angu_mom () const
	Angular momentum.
virtual double	grv2 () const
	Error on the virial identity GRV2.
virtual double	grv3 () const
	Error on the virial identity GRV3.
virtual double	tsw () const
	Ratio T/W.
virtual double	aplat () const
	Flattening r_pole/r_eq.
virtual double	r_circ () const
	Circumferential equatorial radius.
virtual double	rp_circ () const
	Circumferential polar radius.
virtual double	ellipt () const
	Ellipticity e.
virtual void	hydro_euler ()
	Computes the hydrodynamical quantities relative to the Eulerian observer from those in the fluid frame.
void	update_metric ()
	Computes metric quantities from known potentials.
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)
	Computes an equilibrium configuration.
void	solve_logn_f (Scalar &ln_f_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.
void	solve_logn_q (Scalar &ln_q_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.
void	solve_qqq (Scalar &q_new) const
	Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.
void	solve_shift (Vector &shift_new) const
	Solution of the shift equation for rotating stars in Dirac gauge.
void	solve_hij (Sym_tensor_trans &hij_new) const
	Solution of the tensor Poisson equation for rotating stars in Dirac gauge.
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].
virtual const Itbl &	l_surf () const
	Description of the stellar surface: returns a 2-D `Itbl` containing the values of the domain index l on the surface at the collocation points in $(\theta', \phi')$ .
const Tbl &	xi_surf () const
	Description of the stellar surface: returns a 2-D `Tbl` containing the values of the radial coordinate $\xi$ on the surface at the collocation points in $(\theta', \phi')$ .
Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities.
void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities.
virtual void	del_hydro_euler ()
	Sets to `ETATNONDEF` (undefined state) the hydrodynamical quantities relative to the Eulerian observer.
virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<).
Protected Attributes
int	spectral_filter
	Spectral exponential filtering order.
double	omega
	Rotation angular velocity ([f_unit] ).
Scalar	psi4
	Conformal factor $\Psi^4$ .
Scalar	psi2
	$\Psi^2$
Scalar	qqq
	$Q = \Psi^2 N$
Scalar	ln_psi
	$ln(\Psi)$
Vector	j_euler
	Momentum density 3-vector with respect to the Eulerian observer.
Scalar	v2
	$\gamma_{ij}v^i v^j$
const Metric_flat &	flat
	flat metric $f_{ij}$ (spherical components)
Metric	tgamma
	$\tilde{\gamma}_{ij}$
Sym_tensor	aa
	$A^{ij}$
Sym_tensor	taa
	$\tilde{A}_{ij}$
Scalar	aa_quad
	$\tilde{A}_{ij} A^{ij}$
Sym_tensor_trans	hh
	$h^{ij}$ is defined by $\tilde{\gamma}^{ij}=f^{ij}+h^{ij}$ .
double *	p_angu_mom
	Angular momentum.
double *	p_grv2
	Error on the virial identity GRV2.
double *	p_grv3
	Error on the virial identity GRV3.
double *	p_tsw
	Ratio T/W.
double *	p_r_circ
	Circumferential equatorial radius.
double *	p_rp_circ
	Circumferential polar radius.
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 relativistic rotating stars in Dirac gauge and maximal slicing.

(*** Under development ***) ()

Definition at line 45 of file star_rot_dirac.h.

Constructor & Destructor Documentation

Star_rot_Dirac::Star_rot_Dirac	(	Map &	mp_i,
		int	nzet_i,
		const Eos &	eos_i,
		int	filter = `0`
	)

Standard constructor.

Parameters:

	mp_i	Mapping on which the star will be defined
	nzet_i	Number of domains occupied by the star
	eos_i	Equation of state of the stellar matter
	filter	order for spectral exponential filtering

Definition at line 89 of file star_rot_dirac.C.

References aa, aa_quad, hh, j_euler, ln_psi, omega, psi2, psi4, qqq, set_der_0x0(), Tensor::set_etat_zero(), spectral_filter, taa, and v2.

Star_rot_Dirac::Star_rot_Dirac ( const Star_rot_Dirac & star )

Copy constructor.

Definition at line 133 of file star_rot_dirac.C.

References omega, and set_der_0x0().

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

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

Parameters:

	mp_i	Mapping on which the star will be defined
	eos_i	Equation of state of the stellar matter
	fich	input file (must have been created by the function `sauve` )

Definition at line 160 of file star_rot_dirac.C.

References Star::beta, Star::equation_of_state(), fread_be(), Map::get_bvect_spher(), hydro_euler(), omega, set_der_0x0(), spectral_filter, and update_metric().

Star_rot_Dirac::~Star_rot_Dirac ( ) [virtual]

Destructor.

Definition at line 203 of file star_rot_dirac.C.

References del_deriv().

Member Function Documentation

double Star_rot_Dirac::angu_mom ( ) const [virtual]

Angular momentum.

Definition at line 139 of file strot_dirac_global.C.

References contract(), Metric::cov(), Metric::determinant(), Star::gamma, Map::get_bvect_spher(), Scalar::integrale(), j_euler, Star::mp, p_angu_mom, sqrt(), and Scalar::std_spectral_base().

double Star_rot_Dirac::aplat ( ) const [virtual]

Flattening r_pole/r_eq.

Definition at line 414 of file strot_dirac_global.C.

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

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

Deletes all the derived quantities.

Reimplemented from Star.

Definition at line 214 of file star_rot_dirac.C.

References p_angu_mom, p_grv2, p_grv3, p_r_circ, p_rp_circ, p_tsw, and set_der_0x0().

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

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

Reimplemented from Star.

Definition at line 242 of file star_rot_dirac.C.

References del_deriv(), j_euler, Scalar::set_etat_nondef(), Tensor::set_etat_nondef(), and v2.

double Star_rot_Dirac::ellipt ( ) const [virtual]

Ellipticity e.

Defined as $e = \sqrt{1 - \left( \frac{R^c_e}{R^c_p} \right)^2}$ , where $R^c_e$ and $R^c_p$ are, respectively, the equatorial and polar circumferential radius, given by r_circ() and rp_circ().

Definition at line 424 of file strot_dirac_global.C.

References r_circ(), rp_circ(), and sqrt().

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_Dirac::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
	)

Computes an equilibrium configuration.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 91 of file strot_dirac_equilibrium.C.

References abs(), Scalar::annule(), Tbl::annule_hard(), Star::beta, contract(), Metric::cov(), diffrel(), Star::ent, Star::equation_of_state(), flat, Star::gam_euler, Star::gamma, Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Mg3d::get_type_t(), grv2(), hh, Map::homothetie(), hydro_euler(), log(), log10(), Star::logn, mass_b(), mass_g(), Star::mp, Scalar::mult_rsint(), Star::nn, Star::nzet, omega, pow(), qqq, Vector::set(), Tbl::set(), Scalar::set_etat_zero(), solve_hij(), solve_logn_f(), solve_logn_q(), solve_qqq(), solve_shift(), sqrt(), Scalar::std_spectral_base(), Star::u_euler, update_metric(), v2, and Scalar::val_grid_point().

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().

const Sym_tensor Star_rot_Dirac::get_aa ( ) const [inline]

Returns $A^{ij}$ .

Definition at line 228 of file star_rot_dirac.h.

References aa.

const Scalar Star_rot_Dirac::get_aa_quad ( ) const [inline]

Returns $\tilde{A}_{ij} A^{ij}$ .

Definition at line 238 of file star_rot_dirac.h.

References aa_quad.

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::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 Sym_tensor_trans Star_rot_Dirac::get_hh ( ) const [inline]

Returns $h^{ij}$ .

Definition at line 243 of file star_rot_dirac.h.

References hh.

const Vector& Star_rot_Dirac::get_j_euler ( ) const [inline]

Returns the momentum density 3-vector with respect to the Eulerian observer.

Definition at line 208 of file star_rot_dirac.h.

References j_euler.

const Scalar& Star_rot_Dirac::get_ln_psi ( ) const [inline]

Returns $ln(\Psi)$ .

Definition at line 198 of file star_rot_dirac.h.

References ln_psi.

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.

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_Dirac::get_omega ( ) const [inline]

Returns the rotation angular velocity $\Omega$ .

Definition at line 177 of file star_rot_dirac.h.

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_rot_Dirac::get_psi2 ( ) const [inline]

Returns $\Psi^2$ .

Definition at line 188 of file star_rot_dirac.h.

References psi2.

const Scalar& Star_rot_Dirac::get_psi4 ( ) const [inline]

Returns the conformal factor $\Psi^4$ .

Definition at line 183 of file star_rot_dirac.h.

References psi4.

const Scalar& Star_rot_Dirac::get_qqq ( ) const [inline]

Returns $Q=\Psi^2 N$ .

Definition at line 193 of file star_rot_dirac.h.

References qqq.

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 Sym_tensor Star_rot_Dirac::get_taa ( ) const [inline]

Returns $\tilde{A}_{ij}$ .

Definition at line 233 of file star_rot_dirac.h.

References taa.

const Metric Star_rot_Dirac::get_tgamma ( ) const [inline]

Returns the conformal metric $\tilde{\gamma}_{ij}$ .

Definition at line 221 of file star_rot_dirac.h.

References tgamma.

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_Dirac::get_v2 ( ) const [inline]

Reutrns $\gamma_{ij}v^i v^j$ .

Definition at line 213 of file star_rot_dirac.h.

References v2.

double Star_rot_Dirac::grv2 ( ) const [virtual]

Error on the virial identity GRV2.

Definition at line 200 of file strot_dirac_global.C.

References aa, Metric::con(), Metric::cov(), Scalar::div_r_dzpuis(), Scalar::dsdr(), Scalar::dsdt(), Star::ener_euler, Star::gamma, Star::logn, p_grv2, Star::press, sqrt(), Scalar::std_spectral_base(), taa, and v2.

double Star_rot_Dirac::grv3 ( ) const [virtual]

Error on the virial identity GRV3.

Definition at line 269 of file strot_dirac_global.C.

References aa_quad, Metric::con(), Metric::connect(), contract(), Scalar::derive_con(), Scalar::derive_cov(), Metric::determinant(), Star::gamma, Connection::get_delta(), Scalar::integrale(), Star::logn, p_grv3, Star::s_euler, sqrt(), and Scalar::std_spectral_base().

void Star_rot_Dirac::hydro_euler ( ) [virtual]

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

More later......

Reimplemented from Star.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 67 of file strot_dirac_hydro.C.

References Star::beta, Metric::con(), contract(), Metric::cov(), del_deriv(), Star::ener, Star::ener_euler, Sym_tensor::exponential_filter_r(), Vector::exponential_filter_r(), Scalar::exponential_filter_r(), Star::gam_euler, Star::gamma, j_euler, Scalar::mult_rsint(), Star::nn, Star::nzet, omega, Star::press, Star::s_euler, Vector::set(), Scalar::set_etat_zero(), spectral_filter, sqrt(), Tensor::std_spectral_base(), Vector::std_spectral_base(), Scalar::std_spectral_base(), Star::stress_euler, Star::u_euler, and v2.

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

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

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

Reimplemented in Star_rot.

Definition at line 59 of file star_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_Dirac::mass_b ( ) const [virtual]

Baryonic mass.

Implements Star.

Definition at line 90 of file strot_dirac_global.C.

References Metric::determinant(), Star::gam_euler, Star::gamma, Scalar::integrale(), Star::nbar, Star::p_mass_b, sqrt(), and Scalar::std_spectral_base().

double Star_rot_Dirac::mass_g ( ) const [virtual]

Gravitational mass.

Implements Star.

Definition at line 113 of file strot_dirac_global.C.

References Star::beta, contract(), Metric::cov(), Metric::determinant(), Star::ener_euler, Star::gamma, Scalar::integrale(), j_euler, Star::nn, Star::p_mass_g, Star::s_euler, sqrt(), and Scalar::std_spectral_base().

void Star_rot_Dirac::operator= ( const Star_rot_Dirac & star )

Assignment to another Star_rot_Dirac.

Reimplemented from Star.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 262 of file star_rot_dirac.C.

References aa, aa_quad, del_deriv(), flat, hh, j_euler, ln_psi, omega, psi2, psi4, qqq, spectral_filter, tgamma, and v2.

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

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

Reimplemented from Star.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 311 of file star_rot_dirac.C.

References angu_mom(), aplat(), ellipt(), Map::get_mg(), Mg3d::get_np(), grv2(), grv3(), mass_g(), Star::mp, omega, pow(), r_circ(), Star::ray_eq(), rp_circ(), spectral_filter, and tsw().

double Star_rot_Dirac::r_circ ( ) const [virtual]

Circumferential equatorial radius.

Definition at line 327 of file strot_dirac_global.C.

References Metric::cov(), Star::gamma, Map::get_mg(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_type_t(), Star::mp, Star::nzet, p_r_circ, Star::ray_eq(), and sqrt().

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().

double Star_rot_Dirac::rp_circ ( ) const [virtual]

Circumferential polar radius.

Definition at line 353 of file strot_dirac_global.C.

References Scalar::annule(), Scalar::annule_hard(), Valeur::c_cf, Valeur::coef(), Metric::cov(), Scalar::dsdt(), Star::gamma, Map::get_mg(), Mg3d::get_np(), Mg3d::get_nr(), Mg3d::get_nt(), Mg3d::get_nzone(), Scalar::get_spectral_va(), Star::l_surf(), Star::mp, Star::nzet, p_rp_circ, Scalar::set_grid_point(), Scalar::set_spectral_va(), sqrt(), Scalar::std_spectral_base(), Map::tet, Valeur::val_point_jk(), Map::val_r(), and Star::xi_surf().

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

Save in a file.

Reimplemented from Star.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 295 of file star_rot_dirac.C.

References Star::beta, fwrite_be(), hh, omega, qqq, Tensor::sauve(), Tensor_sym::sauve(), Scalar::sauve(), and spectral_filter.

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

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Star.

Definition at line 230 of file star_rot_dirac.C.

References p_angu_mom, p_grv2, p_grv3, p_r_circ, p_rp_circ, and p_tsw.

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.

void Star_rot_Dirac::solve_hij ( Sym_tensor_trans & hij_new ) const

Solution of the tensor Poisson equation for rotating stars in Dirac gauge.

Definition at line 74 of file strot_dirac_solvehij.C.

References aa, Star::beta, Metric::con(), contract(), Metric::cov(), Tensor_sym::derive_con(), Scalar::derive_con(), Tensor::derive_cov(), Tensor_sym::derive_cov(), Scalar::derive_cov(), Scalar::derive_lie(), Sym_tensor::derive_lie(), Vector::divergence(), Map::flat_met_spher(), Map::get_bvect_spher(), Map::get_mg(), Mg3d::get_np(), hh, Scalar::inc_dzpuis(), Tensor::inc_dzpuis(), ln_psi, Star::mp, Star::nn, Vector::ope_killing_conf(), Sym_tensor_trans::poisson(), psi2, psi4, qqq, Star::s_euler, Tensor::set(), Scalar::set_dzpuis(), Scalar::set_etat_zero(), Star::stress_euler, tgamma, and Tensor::trace().

void Star_rot_Dirac::solve_logn_f ( Scalar & ln_f_new ) const

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 58 of file strot_dirac_solvenq.C.

References Star::ener_euler, Scalar::poisson(), psi4, and Star::s_euler.

void Star_rot_Dirac::solve_logn_q ( Scalar & ln_q_new ) const

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 72 of file strot_dirac_solvenq.C.

References aa_quad, contract(), Scalar::derive_con(), Tensor::derive_cov(), Scalar::derive_cov(), Map::flat_met_spher(), Map::get_bvect_spher(), hh, Tensor::inc_dzpuis(), ln_psi, Star::logn, Star::mp, Scalar::poisson(), psi4, tgamma, and Tensor::up_down().

void Star_rot_Dirac::solve_qqq ( Scalar & q_new ) const

Solution of the two scalar Poisson equations for rotating stars in Dirac gauge.

Definition at line 101 of file strot_dirac_solvenq.C.

References aa_quad, contract(), Metric::cov(), Scalar::derive_con(), Tensor::derive_cov(), Tensor_sym::derive_cov(), Scalar::derive_cov(), Map::flat_met_spher(), Scalar::get_etat(), hh, Tenseur::inc_dzpuis(), ln_psi, Star::mp, Star::nn, Scalar::poisson(), psi2, psi4, qqq, Star::s_euler, Scalar::std_spectral_base(), and tgamma.

void Star_rot_Dirac::solve_shift ( Vector & shift_new ) const

Solution of the shift equation for rotating stars in Dirac gauge.

Definition at line 50 of file strot_dirac_solveshift.C.

References aa, Star::beta, Metric::connect(), contract(), Tensor::derive_cov(), Scalar::derive_cov(), Vector::div_free(), Vector::divergence(), Map::flat_met_spher(), Connection::get_delta(), hh, Tensor::inc_dzpuis(), j_euler, ln_psi, Star::mp, Star::nn, Vector_divfree::poisson(), psi4, Vector::set(), Scalar::set_dzpuis(), and tgamma.

int Star_rot_Dirac::spectral_filter_order ( ) const [inline]

Returns the filtering order.

Definition at line 172 of file star_rot_dirac.h.

References spectral_filter.

double Star_rot_Dirac::tsw ( ) const [virtual]

Ratio T/W.

Reimplemented in Star_rot_Dirac_diff.

Definition at line 173 of file strot_dirac_global.C.

References angu_mom(), Metric::determinant(), Star::ener, Star::gam_euler, Star::gamma, Scalar::integrale(), mass_g(), omega, p_tsw, sqrt(), and Scalar::std_spectral_base().

void Star_rot_Dirac::update_metric ( )

Computes metric quantities from known potentials.

The calculation is performed starting from qqq, logn, shift, hh, which are supposed to be up to date. From these, the following fields are updated: nnn, psi4, psi2, ln_psi, tgamma, aa, taa, and aa_quad.

Definition at line 55 of file strot_dirac_upmetr.C.

References aa, aa_quad, Star::beta, Metric::con(), Metric_flat::con(), contract(), del_deriv(), Sym_tensor::derive_lie(), exp(), flat, Star::gamma, hh, ln_psi, log(), Star::logn, Star::nn, Vector::ope_killing_conf(), psi2, psi4, qqq, sqrt(), Scalar::std_spectral_base(), taa, tgamma, and Tensor::up_down().

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.

Friends And Related Function Documentation

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

Display.

Member Data Documentation

Sym_tensor Star_rot_Dirac::aa [protected]

$A^{ij}$

Definition at line 86 of file star_rot_dirac.h.

Scalar Star_rot_Dirac::aa_quad [protected]

$\tilde{A}_{ij} A^{ij}$

Definition at line 88 of file star_rot_dirac.h.

Vector Star::beta [protected, inherited]

Shift vector.

Definition at line 224 of file star.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.

const Metric_flat& Star_rot_Dirac::flat [protected]

flat metric $f_{ij}$ (spherical components)

Definition at line 83 of file star_rot_dirac.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.

Sym_tensor_trans Star_rot_Dirac::hh [protected]

$h^{ij}$ is defined by $\tilde{\gamma}^{ij}=f^{ij}+h^{ij}$ .

We impose the Dirac gauge $D_j h^{ij}$ explicitly by defining $h^{ij}$ to be a symmetric transverse tensor.

Definition at line 95 of file star_rot_dirac.h.

Vector Star_rot_Dirac::j_euler [protected]

Momentum density 3-vector with respect to the Eulerian observer.

Definition at line 76 of file star_rot_dirac.h.

Scalar Star_rot_Dirac::ln_psi [protected]

$ln(\Psi)$

Definition at line 66 of file star_rot_dirac.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.

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_Dirac::omega [protected]

Rotation angular velocity ([f_unit] ).

Definition at line 58 of file star_rot_dirac.h.

double* Star_rot_Dirac::p_angu_mom [mutable, protected]

Angular momentum.

Definition at line 105 of file star_rot_dirac.h.

double* Star_rot_Dirac::p_grv2 [mutable, protected]

Error on the virial identity GRV2.

Definition at line 106 of file star_rot_dirac.h.

double* Star_rot_Dirac::p_grv3 [mutable, protected]

Error on the virial identity GRV3.

Definition at line 107 of file star_rot_dirac.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::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_Dirac::p_r_circ [mutable, protected]

Circumferential equatorial radius.

Definition at line 109 of file star_rot_dirac.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_Dirac::p_rp_circ [mutable, protected]

Circumferential polar radius.

Definition at line 110 of file star_rot_dirac.h.

double* Star_rot_Dirac::p_tsw [mutable, protected]

Ratio T/W.

Definition at line 108 of file star_rot_dirac.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.

Scalar Star::press [protected, inherited]

Fluid pressure.

Definition at line 190 of file star.h.

Scalar Star_rot_Dirac::psi2 [protected]

$\Psi^2$

Definition at line 64 of file star_rot_dirac.h.

Scalar Star_rot_Dirac::psi4 [protected]

Conformal factor $\Psi^4$ .

Definition at line 63 of file star_rot_dirac.h.

Scalar Star_rot_Dirac::qqq [protected]

$Q = \Psi^2 N$

Definition at line 65 of file star_rot_dirac.h.

Scalar Star::s_euler [protected, inherited]

Trace of the stress scalar in the Eulerian frame.

Definition at line 197 of file star.h.

int Star_rot_Dirac::spectral_filter [protected]

Spectral exponential filtering order.

If 0, no filtering is done (see also Scalar::exponential_filter_r). Filtering is performed only in shells containing matter, i.e. for domain numbers l such that $0 < l <$ nzet .