Class for stationary axisymmetric boson stars (under development). More...

#include <boson_star.h>

Inheritance diagram for Lorene::Boson_star:

Public Member Functions
	Boson_star (Map &mp_i, double m, int k)
	Standard constructor. More...

	Boson_star (const Boson_star &)
	Copy constructor. More...

	Boson_star (Map &mp_i, FILE *fich)
	Constructor from a file (see `sauve(FILE*)` ). More...

virtual	~Boson_star ()
	Destructor. More...

void	operator= (const Boson_star &)
	Assignment to another `Boson_star`. More...

const Scalar &	get_rphi () const
	Returns the real part of the scalar field. More...

const Scalar &	get_iphi () const
	Returns the imaginary part of the scalar field. More...

Scalar &	set_rphi ()
	Sets a value to the real part of the scalar field. More...

Scalar &	set_iphi ()
	Sets a value to the imaginary part of the scalar field. More...

virtual void	sauve (FILE *) const
	Save in a file. More...

void	update_ener_mom ()
	Computes the 3+1 components of the energy-momentum tensor (E, P_i and S_{ij}) from the values of the scalar field and the metric. More...

virtual void	equilibrium (double rphi_c, double iphi_c, int nzadapt, const Tbl &ent_limit, const Itbl &icontrol, const Tbl &control, Tbl &diff, Param *=0x0)
	Solves the equation satisfied by the scalar field. More...

const Scalar &	get_logn () const
	Returns the logarithm of the lapse N. More...

const Scalar &	get_tnphi () const
	Returns the component $\tilde N^\varphi = N^\varphi r\sin\theta$ of the shift vector. More...

const Scalar &	get_nuf () const
	Returns the part of the Metric potential $\nu = \ln N$ = `logn` generated by the matter terms. More...

const Scalar &	get_nuq () const
	Returns the Part of the Metric potential $\nu = \ln N$ = `logn` generated by the quadratic terms. More...

const Scalar &	get_dzeta () const
	Returns the Metric potential $\zeta = \ln(AN)$ . More...

const Scalar &	get_tggg () const
	Returns the Metric potential $\tilde G = (NB-1) r\sin\theta$ . More...

const Vector &	get_w_shift () const
	Returns the vector used in the decomposition of `shift` , following Shibata's prescription [Prog. More...

const Scalar &	get_khi_shift () const
	Returns the scalar $\chi$ used in the decomposition of `shift` following Shibata's prescription [Prog. More...

virtual double	mass_g () const
	Gravitational mass. More...

virtual double	angu_mom () const
	Angular momentum. More...

virtual double	grv2 () const
	Error on the virial identity GRV2. More...

virtual double	grv3 (ostream *ost=0x0) const
	Error on the virial identity GRV3. More...

virtual double	mom_quad () const
	Quadrupole moment. More...

void	update_metric ()
	Computes metric coefficients from known potentials. More...

void	fait_shift ()
	Computes `shift` from `w_shift` and `khi_shift` according to Shibata's prescription [Prog. More...

void	fait_nphi ()
	Computes `tnphi` and `nphi` from the Cartesian components of the shift, stored in `shift` . More...

const Scalar &	get_bbb () const
	Returns the metric factor B. More...

const Scalar &	get_a_car () const
	Returns the square of the metric factor A. More...

const Scalar &	get_b_car () const
	Returns the square of the metric factor B. More...

const Scalar &	get_nphi () const
	Returns the metric coefficient $N^\varphi$ . More...

const Scalar &	get_ak_car () const
	Returns the scalar $A^2 K_{ij} K^{ij}$ . More...

void	gyoto_data (const char *file_name) const
	Save in a file for GYOTO. More...

virtual double	r_isco (int lmin, ostream *ost=0x0) const
	Coordinate r of the innermost stable circular orbit (ISCO). More...

virtual double	f_isco (int lmin) const
	Orbital frequency at the innermost stable circular orbit (ISCO). More...

virtual double	espec_isco (int lmin) const
	Energy of a particle at the ISCO. More...

virtual double	lspec_isco (int lmin) const
	Angular momentum of a particle at the ISCO. More...

virtual double	r_mb (int lmin, ostream *ost=0x0) const
	Coordinate r of the marginally bound circular orbit (R_mb). More...

virtual void	extrinsic_curvature ()
	Computes the extrinsic curvature and `ak_car` from `nphi` , `nn` and `b_car` . More...

Map &	set_mp ()
	Read/write of the mapping. More...

const Map &	get_mp () const
	Returns the mapping. More...

const Scalar &	get_nn () const
	Returns the lapse function N . More...

const Vector &	get_beta () const
	Returns the shift vector $\beta^i$ . More...

const Metric &	get_gamma () const
	Returns the 3-metric $\gamma_{ij}$ . More...

const Scalar &	get_ener_euler () const
	Returns the total energy density E in the Eulerian frame. More...

const Vector &	get_mom_euler () const
	Returns the total 3-momentum density in the Eulerian frame. More...

const Sym_tensor &	get_stress_euler () const
	Returns the stress tensor $S_{ij}$ with respect to the Eulerian observer. More...

const Sym_tensor &	get_kk () const
	Returns the extrinsic curvature tensor $K_{ij}$ . More...

virtual double	adm_mass () const
	ADM mass (computed as a surface integral at spatial infinity) More...

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. More...

Protected Member Functions
virtual void	del_deriv () const
	Deletes all the derived quantities. More...

virtual void	set_der_0x0 () const
	Sets to `0x0` all the pointers on derived quantities. More...

virtual ostream &	operator>> (ostream &) const
	Operator >> (virtual function called by the operator <<). More...

Protected Attributes
Scalar	rphi
	Real part of the scalar field Phi. More...

Scalar	iphi
	Imaginary part of the scalar field Phi. More...

double	omega
	Coefficient omega in the time dependence of Phi. More...

int	kkk
	Coefficient kkk in the azimuthal dependence of Phi. More...

double	mmm
	Boson mass. More...

double	m2
	Boson mass squared. More...

Scalar	logn
	Logarithm of the lapse N . More...

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

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

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

Scalar	dzeta
	Metric potential $\zeta = \ln(AN)$ . More...

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

Vector	w_shift
	Vector used in the decomposition of `shift` , following Shibata's prescription [Prog. More...

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

Scalar	ssjm1_nuf
	Effective source at the previous step for the resolution of the Poisson equation for `nuf` by means of `Map_et::poisson` . More...

Scalar	ssjm1_nuq
	Effective source at the previous step for the resolution of the Poisson equation for `nuq` by means of `Map_et::poisson` . More...

Scalar	ssjm1_dzeta
	Effective source at the previous step for the resolution of the Poisson equation for `dzeta` . More...

Scalar	ssjm1_tggg
	Effective source at the previous step for the resolution of the Poisson equation for `tggg` . More...

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` . More...

Vector	ssjm1_wshift
	Effective source at the previous step for the resolution of the vector Poisson equation for . More...

double *	p_grv2
	Error on the virial identity GRV2. More...

double *	p_grv3
	Error on the virial identity GRV3. More...

double *	p_mom_quad
	Quadrupole moment. More...

double *	p_mass_g
	Gravitational mass (ADM mass as a volume integral) More...

Scalar	a_car
	Square of the metric factor A. More...

Scalar	bbb
	Metric factor B. More...

Scalar	b_car
	Square of the metric factor B. More...

Scalar	nphi
	Metric coefficient $N^\varphi$ . More...

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

double *	p_angu_mom
	Angular momentum. More...

double *	p_r_isco
	Coordinate r of the ISCO. More...

double *	p_f_isco
	Orbital frequency of the ISCO. More...

double *	p_espec_isco
	Specific energy of a particle at the ISCO. More...

double *	p_lspec_isco
	Specific angular momentum of a particle at the ISCO. More...

double *	p_r_mb
	Coordinate r of the marginally bound orbit. More...

Map &	mp
	Mapping describing the coordinate system (r,theta,phi) More...

Scalar	nn
	Lapse function N . More...

Vector	beta
	Shift vector $\beta^i$ . More...

Metric	gamma
	3-metric $\gamma_{ij}$ More...

Scalar	ener_euler
	Total energy density E in the Eulerian frame. More...

Vector	mom_euler
	Total 3-momentum density in the Eulerian frame. More...

Sym_tensor	stress_euler
	Stress tensor $S_{ij}$ with respect to the Eulerian observer. More...

Sym_tensor	kk
	Extrinsic curvature tensor $K_{ij}$ . More...

double *	p_adm_mass
	ADM mass. More...

Detailed Description

Class for stationary axisymmetric boson stars (under development).

()

Definition at line 64 of file boson_star.h.

Constructor & Destructor Documentation

◆ Boson_star() [1/3]

Lorene::Boson_star::Boson_star	(	Map &	mp_i,
		double	m,
		int	k
	)

Standard constructor.

Parameters

mp_i	Mapping on which the star is contructed
m	Boson mass //## which unit ?
k	Coefficient k in the azimuthal dependence of Phi

Definition at line 67 of file boson_star.C.

References iphi, rphi, and set_der_0x0().

◆ Boson_star() [2/3]

Lorene::Boson_star::Boson_star ( const Boson_star & st )

Copy constructor.

Definition at line 87 of file boson_star.C.

References set_der_0x0().

◆ Boson_star() [3/3]

Lorene::Boson_star::Boson_star	(	Map &	mp_i,
		FILE *	fich
	)

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

Parameters

mp_i	Mapping on which the star is constructed
fich	input file (must have been created by the function `Boson_star::sauve` )

Definition at line 103 of file boson_star.C.

References Lorene::fread_be(), kkk, m2, mmm, omega, and set_der_0x0().

◆ ~Boson_star()

Lorene::Boson_star::~Boson_star ( )

virtual

Destructor.

Definition at line 122 of file boson_star.C.

References del_deriv().

Member Function Documentation

◆ adm_mass()

double Lorene::Compobj::adm_mass ( ) const

virtualinherited

ADM mass (computed as a surface integral at spatial infinity)

Definition at line 313 of file compobj.C.

References Lorene::Metric::cov(), Lorene::Tensor::derive_con(), Lorene::Tensor_sym::derive_con(), Lorene::Vector::flux(), Lorene::Compobj::gamma, Lorene::Tensor::get_triad(), Lorene::Compobj::mp, Lorene::Compobj::p_adm_mass, Lorene::Tensor::trace(), and Lorene::Tensor::up().

◆ angu_mom()

double Lorene::Star_QI::angu_mom ( ) const

virtualinherited

Angular momentum.

Reimplemented from Lorene::Compobj_QI.

Definition at line 99 of file star_QI_global.C.

References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, Lorene::Map::get_bvect_spher(), Lorene::Tensor::get_triad(), Lorene::Compobj::mom_euler, Lorene::Compobj::mp, and Lorene::Compobj_QI::p_angu_mom.

◆ del_deriv()

void Lorene::Boson_star::del_deriv ( ) const

protectedvirtual

Deletes all the derived quantities.

Reimplemented from Lorene::Star_QI.

Definition at line 133 of file boson_star.C.

References Lorene::Star_QI::del_deriv(), and set_der_0x0().

◆ equilibrium()

void Lorene::Boson_star::equilibrium	(	double	rphi_c,
		double	iphi_c,
		int	nzadapt,
		const Tbl &	ent_limit,
		const Itbl &	icontrol,
		const Tbl &	control,
		Tbl &	diff,
		Param *	= `0x0`
	)

virtual

Solves the equation satisfied by the scalar field.

Computes an equilibrium configuration.

Parameters

rphi_c	[input] Central value of the real part of the scalar field
iphi_c	[input] Central value of the imaginary part of the scalar field
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`
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 73 of file boson_star_equil.C.

References Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_t(), and Lorene::Compobj::mp.

◆ espec_isco()

double Lorene::Compobj_QI::espec_isco ( int lmin ) const

virtualinherited

Energy of a particle at the ISCO.

Definition at line 323 of file compobj_QI_global.C.

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

◆ extrinsic_curvature()

void Lorene::Compobj_QI::extrinsic_curvature ( )

virtualinherited

Computes the extrinsic curvature and ak_car from nphi , nn and b_car .

Reimplemented from Lorene::Compobj.

Reimplemented in Lorene::AltBH_QI.

Definition at line 342 of file compobj_QI.C.

References Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::del_deriv(), Lorene::Scalar::dsdr(), Lorene::Scalar::dsdt(), Lorene::Compobj::extrinsic_curvature(), Lorene::Map::get_mg(), Lorene::Scalar::inc_dzpuis(), Lorene::Compobj::kk, Lorene::Compobj::mp, Lorene::Scalar::mult_rsint(), Lorene::Scalar::mult_sint(), Lorene::Compobj::nn, Lorene::Compobj_QI::nphi, and Lorene::Tensor::set().

◆ f_isco()

double Lorene::Compobj_QI::f_isco ( int lmin ) const

virtualinherited

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

Definition at line 289 of file compobj_QI_global.C.

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

◆ fait_nphi()

void Lorene::Star_QI::fait_nphi ( )

inherited

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

Definition at line 389 of file star_QI.C.

References Lorene::Compobj::beta.

◆ fait_shift()

void Lorene::Star_QI::fait_shift ( )

inherited

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 343 of file star_QI.C.

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

◆ get_a_car()

const Scalar& Lorene::Compobj_QI::get_a_car ( ) const

inlineinherited

Returns the square of the metric factor A.

Definition at line 381 of file compobj.h.

References Lorene::Compobj_QI::a_car.

◆ get_ak_car()

const Scalar& Lorene::Compobj_QI::get_ak_car ( ) const

inlineinherited

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 407 of file compobj.h.

References Lorene::Compobj_QI::ak_car.

◆ get_b_car()

const Scalar& Lorene::Compobj_QI::get_b_car ( ) const

inlineinherited

Returns the square of the metric factor B.

Definition at line 384 of file compobj.h.

References Lorene::Compobj_QI::b_car.

◆ get_bbb()

const Scalar& Lorene::Compobj_QI::get_bbb ( ) const

inlineinherited

Returns the metric factor B.

Definition at line 378 of file compobj.h.

References Lorene::Compobj_QI::bbb.

◆ get_beta()

const Vector& Lorene::Compobj::get_beta ( ) const

inlineinherited

Returns the shift vector $\beta^i$ .

Definition at line 216 of file compobj.h.

References Lorene::Compobj::beta.

◆ get_dzeta()

const Scalar& Lorene::Star_QI::get_dzeta ( ) const

inlineinherited

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

Definition at line 658 of file compobj.h.

References Lorene::Star_QI::dzeta.

◆ get_ener_euler()

const Scalar& Lorene::Compobj::get_ener_euler ( ) const

inlineinherited

Returns the total energy density E in the Eulerian frame.

Definition at line 222 of file compobj.h.

References Lorene::Compobj::ener_euler.

◆ get_gamma()

const Metric& Lorene::Compobj::get_gamma ( ) const

inlineinherited

Returns the 3-metric $\gamma_{ij}$ .

Definition at line 219 of file compobj.h.

References Lorene::Compobj::gamma.

◆ get_iphi()

const Scalar& Lorene::Boson_star::get_iphi ( ) const

inline

Returns the imaginary part of the scalar field.

Definition at line 150 of file boson_star.h.

References iphi.

◆ get_khi_shift()

const Scalar& Lorene::Star_QI::get_khi_shift ( ) const

inlineinherited

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 689 of file compobj.h.

References Lorene::Star_QI::khi_shift.

◆ get_kk()

const Sym_tensor& Lorene::Compobj::get_kk ( ) const

inlineinherited

Returns the extrinsic curvature tensor $K_{ij}$ .

Definition at line 231 of file compobj.h.

References Lorene::Compobj::kk.

◆ get_logn()

const Scalar& Lorene::Star_QI::get_logn ( ) const

inlineinherited

Returns the logarithm of the lapse N.

Definition at line 639 of file compobj.h.

References Lorene::Star_QI::logn.

◆ get_mom_euler()

const Vector& Lorene::Compobj::get_mom_euler ( ) const

inlineinherited

Returns the total 3-momentum density $P^i$ in the Eulerian frame.

Definition at line 225 of file compobj.h.

References Lorene::Compobj::mom_euler.

◆ get_mp()

const Map& Lorene::Compobj::get_mp ( ) const

inlineinherited

Returns the mapping.

Definition at line 210 of file compobj.h.

References Lorene::Compobj::mp.

◆ get_nn()

const Scalar& Lorene::Compobj::get_nn ( ) const

inlineinherited

Returns the lapse function N .

Definition at line 213 of file compobj.h.

References Lorene::Compobj::nn.

◆ get_nphi()

const Scalar& Lorene::Compobj_QI::get_nphi ( ) const

inlineinherited

Returns the metric coefficient $N^\varphi$ .

Definition at line 387 of file compobj.h.

References Lorene::Compobj_QI::nphi.

◆ get_nuf()

const Scalar& Lorene::Star_QI::get_nuf ( ) const

inlineinherited

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

Definition at line 650 of file compobj.h.

References Lorene::Star_QI::nuf.

◆ get_nuq()

const Scalar& Lorene::Star_QI::get_nuq ( ) const

inlineinherited

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

Definition at line 655 of file compobj.h.

References Lorene::Star_QI::nuq.

◆ get_rphi()

const Scalar& Lorene::Boson_star::get_rphi ( ) const

inline

Returns the real part of the scalar field.

Definition at line 146 of file boson_star.h.

References rphi.

◆ get_stress_euler()

const Sym_tensor& Lorene::Compobj::get_stress_euler ( ) const

inlineinherited

Returns the stress tensor $S_{ij}$ with respect to the Eulerian observer.

Definition at line 228 of file compobj.h.

References Lorene::Compobj::stress_euler.

◆ get_tggg()

const Scalar& Lorene::Star_QI::get_tggg ( ) const

inlineinherited

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

Definition at line 661 of file compobj.h.

References Lorene::Star_QI::tggg.

◆ get_tnphi()

const Scalar& Lorene::Star_QI::get_tnphi ( ) const

inlineinherited

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

Definition at line 645 of file compobj.h.

References Lorene::Star_QI::tnphi.

◆ get_w_shift()

const Vector& Lorene::Star_QI::get_w_shift ( ) const

inlineinherited

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 675 of file compobj.h.

References Lorene::Star_QI::w_shift.

◆ grv2()

double Lorene::Star_QI::grv2 ( ) const

virtualinherited

Error on the virial identity GRV2.

This indicator is only valid for relativistic computations.

Definition at line 126 of file star_QI_global.C.

References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::b_car, Lorene::Scalar::derive_cov(), Lorene::Map::flat_met_spher(), Lorene::Map::get_bvect_spher(), Lorene::Tensor::get_triad(), Lorene::Star_QI::lambda_grv2(), Lorene::Star_QI::logn, Lorene::Compobj::mp, Lorene::Star_QI::p_grv2, and Lorene::Compobj::stress_euler.

◆ grv3()

double Lorene::Star_QI::grv3 ( ostream * ost = 0x0 ) const

virtualinherited

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 151 of file star_QI_global.C.

References Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::bbb, Lorene::Scalar::derive_cov(), Lorene::Star_QI::dzeta, Lorene::Map::flat_met_spher(), Lorene::Scalar::get_etat(), Lorene::log(), Lorene::Star_QI::logn, Lorene::Compobj::mp, Lorene::Star_QI::p_grv3, Lorene::Scalar::srdsdt(), and Lorene::Scalar::std_spectral_base().

◆ gyoto_data()

void Lorene::Compobj_QI::gyoto_data ( const char * file_name ) const

inherited

Save in a file for GYOTO.

Definition at line 235 of file compobj_QI.C.

References Lorene::Compobj::beta, Lorene::Metric::con(), Lorene::Metric::cov(), Lorene::fwrite_be(), Lorene::Compobj::gamma, Lorene::Map::get_mg(), Lorene::Compobj::kk, Lorene::Compobj::mp, Lorene::Compobj::nn, Lorene::Compobj_QI::r_isco(), Lorene::Compobj_QI::r_mb(), Lorene::Mg3d::sauve(), Lorene::Map::sauve(), Lorene::Tensor::sauve(), Lorene::Scalar::sauve(), and Lorene::Tensor_sym::sauve().

◆ lambda_grv2()

double Lorene::Star_QI::lambda_grv2	(	const Scalar &	sou_m,
		const Scalar &	sou_q
	)

staticinherited

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 324 of file star_QI_global.C.

References Lorene::Scalar::check_dzpuis(), Lorene::Map::get_mg(), Lorene::Tensor::get_mp(), Lorene::Mg3d::get_nzone(), Lorene::Mg3d::get_type_r(), and Lorene::Map::val_r().

◆ lspec_isco()

double Lorene::Compobj_QI::lspec_isco ( int lmin ) const

virtualinherited

Angular momentum of a particle at the ISCO.

Definition at line 306 of file compobj_QI_global.C.

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

◆ mass_g()

double Lorene::Star_QI::mass_g ( ) const

virtualinherited

Gravitational mass.

Definition at line 67 of file star_QI_global.C.

References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, Lorene::Compobj::ener_euler, Lorene::Compobj::gamma, Lorene::Compobj::mom_euler, Lorene::Compobj::nn, Lorene::Star_QI::p_mass_g, Lorene::Scalar::std_spectral_base(), Lorene::Compobj::stress_euler, Lorene::Star_QI::tnphi, and Lorene::Tensor::trace().

◆ mom_quad()

double Lorene::Star_QI::mom_quad ( ) const

virtualinherited

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 253 of file star_QI_global.C.

References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::ak_car, Lorene::Compobj_QI::bbb, Lorene::Scalar::check_dzpuis(), Lorene::Scalar::derive_cov(), Lorene::Compobj::ener_euler, Lorene::Map::flat_met_spher(), Lorene::Compobj::gamma, Lorene::Scalar::get_etat(), Lorene::Scalar::inc_dzpuis(), Lorene::log(), Lorene::Star_QI::logn, Lorene::Compobj::mp, Lorene::Scalar::mult_r(), Lorene::Star_QI::p_mom_quad, Lorene::Scalar::std_spectral_base(), Lorene::Compobj::stress_euler, and Lorene::Tensor::trace().

◆ operator=()

void Lorene::Boson_star::operator= ( const Boson_star & st )

Assignment to another Boson_star.

Definition at line 151 of file boson_star.C.

References del_deriv(), iphi, kkk, m2, mmm, omega, Lorene::Star_QI::operator=(), and rphi.

◆ operator>>()

ostream & Lorene::Boson_star::operator>> ( ostream & ost ) const

protectedvirtual

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

Reimplemented from Lorene::Star_QI.

Definition at line 186 of file boson_star.C.

References iphi, kkk, Lorene::Star_QI::mass_g(), mmm, omega, Lorene::Star_QI::operator>>(), rphi, and Lorene::Scalar::val_grid_point().

◆ r_isco()

double Lorene::Compobj_QI::r_isco	(	int	lmin,
		ostream *	ost = `0x0`
	)		const

virtualinherited

Coordinate r of the innermost stable circular orbit (ISCO).

Parameters

lmin	index of the innermost domain in which the ISCO is searched: the ISCO is searched inwards from the last but one domain to the domain of index lmin.
ost	output stream to give details of the computation; if set to 0x0 [default value], no details will be given.

Definition at line 111 of file compobj_QI_global.C.

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

◆ r_mb()

double Lorene::Compobj_QI::r_mb	(	int	lmin,
		ostream *	ost = `0x0`
	)		const

virtualinherited

Coordinate r of the marginally bound circular orbit (R_mb).

Definition at line 344 of file compobj_QI_global.C.

References Lorene::Param::add_int(), Lorene::Param::add_scalar(), Lorene::Tensor::annule_domain(), Lorene::Compobj_QI::bbb, Lorene::Scalar::dsdr(), Lorene::Map::get_mg(), Lorene::Mg3d::get_nzone(), Lorene::Scalar::get_spectral_va(), Lorene::Compobj::mp, Lorene::Compobj::nn, Lorene::Compobj_QI::nphi, Lorene::Compobj_QI::p_r_mb, Lorene::Map::r, Lorene::Compobj_QI::r_isco(), Lorene::sqrt(), Lorene::Scalar::std_spectral_base(), Lorene::Valeur::val_point(), Lorene::Map::val_r(), and Lorene::zerosec().

◆ sauve()

void Lorene::Boson_star::sauve ( FILE * fich ) const

virtual

Save in a file.

Reimplemented from Lorene::Star_QI.

Definition at line 172 of file boson_star.C.

References Lorene::fwrite_be(), iphi, kkk, mmm, omega, rphi, Lorene::Star_QI::sauve(), and Lorene::Scalar::sauve().

◆ set_der_0x0()

void Lorene::Boson_star::set_der_0x0 ( ) const

protectedvirtual

Sets to 0x0 all the pointers on derived quantities.

Reimplemented from Lorene::Star_QI.

Definition at line 141 of file boson_star.C.

◆ set_iphi()

Scalar& Lorene::Boson_star::set_iphi ( )

inline

Sets a value to the imaginary part of the scalar field.

Definition at line 158 of file boson_star.h.

References del_deriv(), and iphi.

◆ set_mp()

Map& Lorene::Compobj::set_mp ( )

inlineinherited

Read/write of the mapping.

Definition at line 203 of file compobj.h.

References Lorene::Compobj::mp.

◆ set_rphi()

Scalar& Lorene::Boson_star::set_rphi ( )

inline

Sets a value to the real part of the scalar field.

Definition at line 154 of file boson_star.h.

References del_deriv(), and rphi.

◆ update_ener_mom()

void Lorene::Boson_star::update_ener_mom ( )

Computes the 3+1 components of the energy-momentum tensor (E, P_i and S_{ij}) from the values of the scalar field and the metric.

Definition at line 214 of file boson_star.C.

References Lorene::Metric::cov(), Lorene::Scalar::derive_cov(), Lorene::Compobj::ener_euler, Lorene::Map::flat_met_spher(), Lorene::Compobj::gamma, Lorene::Scalar::inc_dzpuis(), iphi, kkk, m2, Lorene::Compobj::mom_euler, Lorene::Compobj::mp, Lorene::Compobj::nn, Lorene::Compobj_QI::nphi, omega, rphi, Lorene::Vector::set(), Lorene::Compobj::stress_euler, and Lorene::Tensor::trace().

◆ update_metric()

void Lorene::Star_QI::update_metric ( )

virtualinherited

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.

Reimplemented from Lorene::Compobj_QI.

Definition at line 413 of file star_QI.C.

References Lorene::Compobj_QI::a_car, Lorene::Compobj_QI::b_car, Lorene::Compobj_QI::bbb, Lorene::Star_QI::del_deriv(), Lorene::Scalar::div_rsint(), Lorene::Star_QI::dzeta, Lorene::exp(), Lorene::Star_QI::logn, Lorene::Compobj::nn, Lorene::Scalar::std_spectral_base(), Lorene::Star_QI::tggg, and Lorene::Compobj_QI::update_metric().

Member Data Documentation

◆ a_car

Scalar Lorene::Compobj_QI::a_car

protectedinherited

Square of the metric factor A.

Definition at line 290 of file compobj.h.

◆ ak_car

Scalar Lorene::Compobj_QI::ak_car

protectedinherited

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 318 of file compobj.h.

◆ b_car

Scalar Lorene::Compobj_QI::b_car

protectedinherited

Square of the metric factor B.

Definition at line 296 of file compobj.h.

◆ bbb

Scalar Lorene::Compobj_QI::bbb

protectedinherited

Metric factor B.

Definition at line 293 of file compobj.h.

◆ beta

Vector Lorene::Compobj::beta

protectedinherited

Shift vector $\beta^i$ .

Definition at line 141 of file compobj.h.

◆ dzeta

Scalar Lorene::Star_QI::dzeta

protectedinherited

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

Definition at line 516 of file compobj.h.

◆ ener_euler

Scalar Lorene::Compobj::ener_euler

protectedinherited

Total energy density E in the Eulerian frame.

Definition at line 147 of file compobj.h.

◆ gamma

Metric Lorene::Compobj::gamma

protectedinherited

3-metric $\gamma_{ij}$

Definition at line 144 of file compobj.h.

◆ iphi

Scalar Lorene::Boson_star::iphi

protected

Imaginary part of the scalar field Phi.

Definition at line 76 of file boson_star.h.

◆ khi_shift

Scalar Lorene::Star_QI::khi_shift

protectedinherited

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 542 of file compobj.h.

◆ kk

Sym_tensor Lorene::Compobj::kk

protectedinherited

Extrinsic curvature tensor $K_{ij}$ .

Definition at line 156 of file compobj.h.

◆ kkk

int Lorene::Boson_star::kkk

protected

Coefficient kkk in the azimuthal dependence of Phi.

Definition at line 84 of file boson_star.h.

◆ logn

Scalar Lorene::Star_QI::logn

protectedinherited

Logarithm of the lapse N .

Definition at line 498 of file compobj.h.

◆ m2

double Lorene::Boson_star::m2

protected

Boson mass squared.

Definition at line 92 of file boson_star.h.

◆ mmm

double Lorene::Boson_star::mmm

protected

Boson mass.

Definition at line 88 of file boson_star.h.

◆ mom_euler

Vector Lorene::Compobj::mom_euler

protectedinherited

Total 3-momentum density $P^i$ in the Eulerian frame.

Definition at line 150 of file compobj.h.

◆ mp

Map& Lorene::Compobj::mp

protectedinherited

Mapping describing the coordinate system (r,theta,phi)

Definition at line 135 of file compobj.h.

◆ nn

Scalar Lorene::Compobj::nn

protectedinherited

Lapse function N .

Definition at line 138 of file compobj.h.

◆ nphi

Scalar Lorene::Compobj_QI::nphi

protectedinherited

Metric coefficient $N^\varphi$ .

Definition at line 299 of file compobj.h.

◆ nuf

Scalar Lorene::Star_QI::nuf

protectedinherited

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

Definition at line 508 of file compobj.h.

◆ nuq

Scalar Lorene::Star_QI::nuq

protectedinherited

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

Definition at line 513 of file compobj.h.

◆ omega

double Lorene::Boson_star::omega

protected

Coefficient omega in the time dependence of Phi.

Definition at line 80 of file boson_star.h.

◆ p_adm_mass

double* Lorene::Compobj::p_adm_mass

mutableprotectedinherited

ADM mass.

Definition at line 161 of file compobj.h.

◆ p_angu_mom

double* Lorene::Compobj_QI::p_angu_mom

mutableprotectedinherited

Angular momentum.

Definition at line 324 of file compobj.h.

◆ p_espec_isco

double* Lorene::Compobj_QI::p_espec_isco

mutableprotectedinherited

Specific energy of a particle at the ISCO.

Definition at line 328 of file compobj.h.

◆ p_f_isco

double* Lorene::Compobj_QI::p_f_isco

mutableprotectedinherited

Orbital frequency of the ISCO.

Definition at line 326 of file compobj.h.

◆ p_grv2

double* Lorene::Star_QI::p_grv2

mutableprotectedinherited

Error on the virial identity GRV2.

Definition at line 588 of file compobj.h.

◆ p_grv3

double* Lorene::Star_QI::p_grv3

mutableprotectedinherited

Error on the virial identity GRV3.

Definition at line 589 of file compobj.h.

◆ p_lspec_isco

double* Lorene::Compobj_QI::p_lspec_isco

mutableprotectedinherited

Specific angular momentum of a particle at the ISCO.

Definition at line 330 of file compobj.h.

◆ p_mass_g

double* Lorene::Star_QI::p_mass_g

mutableprotectedinherited

Gravitational mass (ADM mass as a volume integral)

Definition at line 591 of file compobj.h.

◆ p_mom_quad

double* Lorene::Star_QI::p_mom_quad

mutableprotectedinherited

Quadrupole moment.

Definition at line 590 of file compobj.h.

◆ p_r_isco

double* Lorene::Compobj_QI::p_r_isco

mutableprotectedinherited

Coordinate r of the ISCO.

Definition at line 325 of file compobj.h.

◆ p_r_mb

double* Lorene::Compobj_QI::p_r_mb

mutableprotectedinherited

Coordinate r of the marginally bound orbit.

Definition at line 331 of file compobj.h.

◆ rphi

Scalar Lorene::Boson_star::rphi

protected

Real part of the scalar field Phi.

Definition at line 72 of file boson_star.h.

◆ ssjm1_dzeta

Scalar Lorene::Star_QI::ssjm1_dzeta

protectedinherited

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

Definition at line 559 of file compobj.h.

◆ ssjm1_khi

Scalar Lorene::Star_QI::ssjm1_khi

protectedinherited

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 572 of file compobj.h.

◆ ssjm1_nuf

Scalar Lorene::Star_QI::ssjm1_nuf

protectedinherited

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

Definition at line 548 of file compobj.h.

◆ ssjm1_nuq

Scalar Lorene::Star_QI::ssjm1_nuq

protectedinherited

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

Definition at line 554 of file compobj.h.

◆ ssjm1_tggg

Scalar Lorene::Star_QI::ssjm1_tggg

protectedinherited

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

Definition at line 564 of file compobj.h.

◆ ssjm1_wshift

Vector Lorene::Star_QI::ssjm1_wshift

protectedinherited

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 581 of file compobj.h.

◆ stress_euler

Sym_tensor Lorene::Compobj::stress_euler

protectedinherited

Stress tensor $S_{ij}$ with respect to the Eulerian observer.

Definition at line 153 of file compobj.h.

◆ tggg

Scalar Lorene::Star_QI::tggg

protectedinherited

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

Definition at line 519 of file compobj.h.

◆ tnphi

Scalar Lorene::Star_QI::tnphi

protectedinherited

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

Definition at line 503 of file compobj.h.

◆ w_shift

Vector Lorene::Star_QI::w_shift

protectedinherited

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 532 of file compobj.h.

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Boson_star() [1/3]

◆ Boson_star() [2/3]

◆ Boson_star() [3/3]

◆ ~Boson_star()

Member Function Documentation

◆ adm_mass()

◆ angu_mom()

◆ del_deriv()

◆ equilibrium()

◆ espec_isco()

◆ extrinsic_curvature()

◆ f_isco()

◆ fait_nphi()

◆ fait_shift()

◆ get_a_car()

◆ get_ak_car()

◆ get_b_car()

◆ get_bbb()

◆ get_beta()

◆ get_dzeta()

◆ get_ener_euler()

◆ get_gamma()

◆ get_iphi()

◆ get_khi_shift()

◆ get_kk()

◆ get_logn()

◆ get_mom_euler()

◆ get_mp()

◆ get_nn()

◆ get_nphi()

◆ get_nuf()

◆ get_nuq()

◆ get_rphi()

◆ get_stress_euler()

◆ get_tggg()

◆ get_tnphi()

◆ get_w_shift()

◆ grv2()

◆ grv3()

◆ gyoto_data()

◆ lambda_grv2()

◆ lspec_isco()

◆ mass_g()

◆ mom_quad()

◆ operator=()

◆ operator>>()

◆ r_isco()

◆ r_mb()

◆ sauve()

◆ set_der_0x0()

◆ set_iphi()

◆ set_mp()

◆ set_rphi()

◆ update_ener_mom()

◆ update_metric()

Member Data Documentation

◆ a_car

◆ ak_car

◆ b_car

◆ bbb

◆ beta

◆ dzeta

◆ ener_euler

◆ gamma

◆ iphi

◆ khi_shift

◆ kk

◆ kkk

◆ logn

◆ m2

◆ mmm

◆ mom_euler

◆ mp

◆ nn