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* Definition of Lorene class Star_rot
*
*/
/*
* Copyright (c) 2010 Eric Gourgoulhon
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __STAR_ROT_H_
#define __STAR_ROT_H_
/*
* $Id: star_rot.h,v 1.6 2015/05/19 09:30:55 j_novak Exp $
* $Log: star_rot.h,v $
* Revision 1.6 2015/05/19 09:30:55 j_novak
* New methods for computing the area of the star and its mean radius.
*
* Revision 1.5 2014/10/13 08:52:36 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.4 2010/02/08 10:56:30 j_novak
* Added a few things missing for the reading from resulting file.
*
* Revision 1.3 2010/02/02 13:35:00 e_gourgoulhon
* Remove the "under construction" mark.
*
* Revision 1.2 2010/01/25 18:14:05 e_gourgoulhon
* Added member unsurc2
* Added method is_relativistic()
* Suppressed method f_eccentric
*
* Revision 1.1 2010/01/24 16:07:45 e_gourgoulhon
* New class Star_rot.
*
*
* $Header: /cvsroot/Lorene/C++/Include/star_rot.h,v 1.6 2015/05/19 09:30:55 j_novak Exp $
*
*/
// Headers Lorene
#include "star.h"
namespace Lorene {
class Eos ;
//--------------------------//
// class Star_rot //
//--------------------------//
/**
* Class for isolated rotating stars. \ingroup (star)
*
* The metric is
* \f[
* 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
* \f]
*
* A star of class \c Star_rot can be either relativistic or Newtonian,
* depending on the boolean indicator \c relativistic . For a Newtonian
* star, the metric coefficients \e N, \e A, and \e B are set to 1, and \f$N^\varphi\f$ is
* set to zero; the only relevant gravitational quantity in this case is
* \c logn which represents the Newtonian gravitational potential generated by the star.
*
* \version $Id: star_rot.h,v 1.6 2015/05/19 09:30:55 j_novak Exp $
*/
class Star_rot : public Star {
// Data :
// -----
protected:
/** Indicator of relativity: \c true for a relativistic star,
* \c false for a Newtonian one.
*/
bool relativistic ;
/** \f$1/c^2\f$ : \c unsurc2=1 for a relativistic star,
* 0 for a Newtonian one.
*/
double unsurc2 ;
double omega ; ///< Rotation angular velocity (\c [f_unit] )
/// Square of the metric factor \e A
Scalar a_car ;
/// Metric factor \e B
Scalar bbb ;
/// Square of the metric factor \e B
Scalar b_car ;
/// Metric coefficient \f$N^\varphi\f$
Scalar nphi ;
/** Component \f$\tilde N^\varphi = N^\varphi r\sin\theta\f$ of the
* shift vector
*/
Scalar tnphi ;
/// Norm of \c u_euler
Scalar uuu ;
/** Part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the matter terms
*/
Scalar nuf ;
/** Part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the quadratic terms
*/
Scalar nuq ;
/// Metric potential \f$\zeta = \ln(AN)\f$
Scalar dzeta ;
/// Metric potential \f$\tilde G = (NB-1) r\sin\theta\f$
Scalar tggg ;
/** Vector \f$W^i\f$ used in the decomposition of \c shift ,
* following Shibata's prescription
* [\a Prog. \a Theor. \a Phys. \b 101 , 1199 (1999)] :
* \f[
* N^i = {7\over 8} W^i - {1\over 8}
* \left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* NB: \c w_shift contains the components of \f$W^i\f$
* with respect to the Cartesian triad associated with the
* mapping \c mp .
*/
Vector w_shift ;
/** Scalar \f$\chi\f$ used in the decomposition of \c shift ,
* following Shibata's prescription
* [\a Prog. \a Theor. \a Phys. \b 101 , 1199 (1999)] :
* \f[
* N^i = {7\over 8} W^i - {1\over 8}
* \left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
*/
Scalar khi_shift ;
/** Tensor \f${\tilde K_{ij}}\f$ related to the extrinsic curvature
* tensor by \f${\tilde K_{ij}} = B^{-2} K_{ij}\f$.
* \c tkij contains the Cartesian components of
* \f${\tilde K_{ij}}\f$.
*/
Sym_tensor tkij ;
/** Scalar \f$A^2 K_{ij} K^{ij}\f$.
* For axisymmetric stars, this quantity is related to the
* derivatives of \f$N^\varphi\f$ by
* \f[
* 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] \ .
* \f]
* In particular it is related to the quantities \f$k_1\f$ and \f$k_2\f$
* introduced by Eqs.~(3.7) and (3.8) of
* Bonazzola et al. \a Astron. \a Astrophys. \b 278 , 421 (1993)
* by
* \f[
* A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ .
* \f]
*/
Scalar ak_car ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c nuf by means of
* \c Map_et::poisson .
*/
Scalar ssjm1_nuf ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c nuq by means of
* \c Map_et::poisson .
*/
Scalar ssjm1_nuq ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c dzeta .
*/
Scalar ssjm1_dzeta ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c tggg .
*/
Scalar ssjm1_tggg ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for the scalar \f$\chi\f$ by means of
* \c Map_et::poisson .
* \f$\chi\f$ is an intermediate quantity for the resolution of the
* elliptic equation for the shift vector \f$N^i\f$
*/
Scalar ssjm1_khi ;
/** Effective source at the previous step for the resolution of
* the vector Poisson equation for \f$W^i\f$.
* \f$W^i\f$ is an intermediate quantity for the resolution of the
* elliptic equation for the shift vector \f$N^i\f$
* (Components with respect to the Cartesian triad associated with
* the mapping \c mp )
*/
Vector ssjm1_wshift ;
// Derived data :
// ------------
protected:
mutable double* p_angu_mom ; ///< Angular momentum
mutable double* p_tsw ; ///< Ratio T/W
mutable double* p_grv2 ; ///< Error on the virial identity GRV2
mutable double* p_grv3 ; ///< Error on the virial identity GRV3
mutable double* p_r_circ ; ///< Circumferential radius
mutable double* p_aplat ; ///< Flatening r_pole/r_eq
mutable double* p_area ; ///< Integrated surface area
mutable double* p_z_eqf ; ///< Forward redshift factor at equator
mutable double* p_z_eqb ; ///< Backward redshift factor at equator
mutable double* p_z_pole ; ///< Redshift factor at North pole
mutable double* p_mom_quad ; ///< Quadrupole moment
mutable double* p_r_isco ; ///< Circumferential radius of the ISCO
mutable double* p_f_isco ; ///< Orbital frequency of the ISCO
/// Specific energy of a particle on the ISCO
mutable double* p_espec_isco ;
/// Specific angular momentum of a particle on the ISCO
mutable double* p_lspec_isco ;
mutable double* p_f_eq ; ///< Orbital frequency at the equator
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star is contructed
* @param nzet_i Number of domains occupied by the star
* @param relat \c true for a relativistic
* star, \c false for a Newtonian one
* @param eos_i Equation of state of the stellar matter
*/
Star_rot(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i) ;
Star_rot(const Star_rot& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star is constructed
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c Star_rot::sauve )
*/
Star_rot(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Star_rot() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
/** Sets to \c ETATNONDEF (undefined state) the hydrodynamical
* quantities relative to the Eulerian observer.
*/
virtual void del_hydro_euler() ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another \c Star_rot
void operator=(const Star_rot& ) ;
// Accessors
// ---------
public:
/** Returns \c true for a relativistic star, \c false for
* a Newtonian one
*/
bool is_relativistic() const {return relativistic; } ;
/** Returns the central value of the rotation angular velocity
* (\c [f_unit] )
*/
virtual double get_omega_c() const ;
/// Returns the metric factor \e B
const Scalar& get_bbb() const {return bbb;} ;
/// Returns the square of the metric factor \e A
const Scalar& get_a_car() const {return a_car;} ;
/// Returns the square of the metric factor \e B
const Scalar& get_b_car() const {return b_car;} ;
/// Returns the metric coefficient \f$N^\varphi\f$
const Scalar& get_nphi() const {return nphi;} ;
/** Returns the component \f$\tilde N^\varphi = N^\varphi r\sin\theta\f$
* of the shift vector
*/
const Scalar& get_tnphi() const {return tnphi;} ;
/// Returns the norm of \c u_euler
const Scalar& get_uuu() const {return uuu;} ;
/** Returns the part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the matter terms
*/
const Scalar& get_nuf() const {return nuf;} ;
/** Returns the Part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the quadratic terms
*/
const Scalar& get_nuq() const {return nuq;} ;
/// Returns the Metric potential \f$\zeta = \ln(AN)\f$
const Scalar& get_dzeta() const {return dzeta;} ;
/// Returns the Metric potential \f$\tilde G = (NB-1) r\sin\theta\f$
const Scalar& get_tggg() const {return tggg;} ;
/** Returns the vector \f$W^i\f$ used in the decomposition of
* \c shift ,
* following Shibata's prescription
* [\a Prog. \a Theor. \a Phys. \b 101 , 1199 (1999)] :
* \f[
* N^i = {7\over 8} W^i - {1\over 8}
* \left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* NB: \c w_shift contains the components of \f$W^i\f$
* with respect to the Cartesian triad associated with the
* mapping \c mp .
*/
const Vector& get_w_shift() const {return w_shift;} ;
/** Returns the scalar \f$\chi\f$ used in the decomposition of
* \c shift
* following Shibata's prescription
* [\a Prog. \a Theor. \a Phys. \b 101 , 1199 (1999)] :
* \f[
* N^i = {7\over 8} W^i - {1\over 8}
* \left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
* NB: \c w_shift contains the components of \f$W^i\f$
* with respect to the Cartesian triad associated with the
* mapping \c mp .
*/
const Scalar& get_khi_shift() const {return khi_shift;} ;
/** Returns the tensor \f${\tilde K_{ij}}\f$ related to the extrinsic
* curvature tensor by \f${\tilde K_{ij}} = B^{-2} K_{ij}\f$.
* \c tkij contains the Cartesian components of
* \f${\tilde K_{ij}}\f$.
*/
const Sym_tensor& get_tkij() const {return tkij;} ;
/** Returns the scalar \f$A^2 K_{ij} K^{ij}\f$.
* For axisymmetric stars, this quantity is related to the
* derivatives of \f$N^\varphi\f$ by
* \f[
* 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] \ .
* \f]
* In particular it is related to the quantities \f$k_1\f$ and \f$k_2\f$
* introduced by Eqs. (3.7) and (3.8) of
* Bonazzola et al. \a Astron. \a Astrophys. \b 278 , 421 (1993)
* by
* \f[
* A^2 K_{ij} K^{ij} = 2 A^2 (k_1^2 + k_2^2) \ .
* \f]
*/
const Scalar& get_ak_car() const {return ak_car;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
/// Display in polytropic units
virtual void display_poly(ostream& ) const ;
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
/// Printing of some informations, excluding all global quantities
virtual void partial_display(ostream& ) const ;
// Global quantities
// -----------------
public:
/** Description of the stellar surface: returns a 2-D \c Itbl
* containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$.
* The stellar surface is defined as the location where
* the enthalpy (member \c ent ) vanishes.
*/
virtual const Itbl& l_surf() const ;
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
/** Error on the virial identity GRV2.
* This indicator is only valid for relativistic computations.
*/
virtual double grv2() const ;
/** Error on the virial identity GRV3.
* The error is computed as the integral defined
* by Eq. (43) of [Gourgoulhon and Bonazzola,
* \a Class. \a Quantum \a Grav. \b 11, 443 (1994)] divided by
* the integral of the matter terms.
*
* @param ost output stream to give details of the computation;
* if set to 0x0 [default value], no details will be
* given.
*
*/
virtual double grv3(ostream* ost = 0x0) const ;
virtual double r_circ() const ; ///< Circumferential radius
virtual double aplat() const ; ///< Flatening r_pole/r_eq
virtual double area() const ; ///< Integrated surface area in \f${\rm km}^2\f$
/// Mean star radius from the area \f$ r_{\rm mean} = \sqrt{\mathcal{A}} / 4\pi\f$
virtual double mean_radius() const ;
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
/** Quadrupole moment.
* The quadrupole moment \e Q is defined according to Eq. (7) of
* [Salgado, Bonazzola, Gourgoulhon and Haensel, \a Astron. \a Astrophys.
* \b 291 , 155 (1994)]. At the Newtonian limit it is related to
* the component \f${\bar I}_{zz}\f$ of the MTW (1973) reduced quadrupole
* moment \f${\bar I}_{ij}\f$ by: \f$Q = -3/2 {\bar I}_{zz}\f$.
* Note that \e Q is the negative of the quadrupole moment defined
* by Laarakkers and Poisson, \a Astrophys. \a J. \b 512 , 282 (1999).
*/
virtual double mom_quad() const ;
/** Circumferential radius of the innermost stable circular orbit (ISCO).
*
* @param ost output stream to give details of the computation;
* if set to 0x0 [default value], no details will be
* given.
*/
virtual double r_isco(ostream* ost = 0x0) const ;
/// Orbital frequency at the innermost stable circular orbit (ISCO).
virtual double f_isco() const ;
/// Energy of a particle on the ISCO
virtual double espec_isco() const ;
/// Angular momentum of a particle on the ISCO
virtual double lspec_isco() const ;
/// Orbital frequency at the equator.
virtual double f_eq() const ;
// Computational routines
// ----------------------
public:
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame.
*
* The calculation is performed starting from the quantities
* \c ent , \c ener , \c press , and \c a_car ,
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c gam_euler , \c u_euler , \c ener_euler , \c s_euler .
*
*/
virtual void hydro_euler() ;
/** Computes metric coefficients from known potentials.
*
* The calculation is performed starting from the quantities
* \c logn , \c dzeta , \c tggg and \c shift ,
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c nnn , \c a_car , \c bbb and \c b_car, as well as
* the 3-metric \c gamma.
*
*/
void update_metric() ;
/** Computes \c shift from \c w_shift and \c khi_shift
* according to Shibata's prescription
* [\a Prog. \a Theor. \a Phys. \b 101 , 1199 (1999)] :
* \f[
* N^i = {7\over 8} W^i - {1\over 8}
* \left(\nabla^i\chi+\nabla^iW^kx_k\right)
* \f]
*/
void fait_shift() ;
/** Computes \c tnphi and \c nphi from the Cartesian
* components of the shift, stored in \c shift .
*/
void fait_nphi() ;
/** Computes \c tkij and \c ak_car from
* \c shift , \c nnn and \c b_car .
*/
void extrinsic_curvature() ;
/** Computes the coefficient \f$\lambda\f$ which ensures that the
* GRV2 virial identity is satisfied.
* \f$\lambda\f$ is the coefficient by which one must multiply
* the quadratic source term \f$\sigma_q\f$ of the 2-D Poisson equation
* \f[
* \Delta_2 u = \sigma_m + \sigma_q
* \f]
* in order that the total source does not contain any monopolar term,
* i.e. in order that
* \f[
* \int_0^{2\pi} \int_0^{+\infty} \sigma(r, \theta)
* \, r \, dr \, d\theta = 0 \ ,
* \f]
* where \f$\sigma = \sigma_m + \sigma_q\f$.
* \f$\lambda\f$ is computed according to the formula
* \f[
* \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 } \ .
* \f]
* Then, by construction, the new source
* \f$\sigma' = \sigma_m + \lambda \sigma_q\f$ has a vanishing monopolar
* term.
*
* @param sou_m [input] matter source term \f$\sigma_m\f$
* @param sou_q [input] quadratic source term \f$\sigma_q\f$
* @return value of \f$\lambda\f$
*/
static double lambda_grv2(const Scalar& sou_m, const Scalar& sou_q) ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param omega0 [input] Requested angular velocity
* (if \c fact_omega=1. )
* @param fact_omega [input] 1.01 = search for the Keplerian frequency,
* 1. = otherwise.
* @param nzadapt [input] Number of (inner) domains where the mapping
* adaptation to an iso-enthalpy surface
* should be performed
* @param ent_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy at the outer boundary
* of each domain
* @param icontrol [input] Set of integer parameters (stored as a
* 1-D \c Itbl of size 8) to control the
* iteration:
* \li \c icontrol(0) = mer_max : maximum number of steps
* \li \c icontrol(1) = mer_rot : step at which the rotation is
* switched on
* \li \c icontrol(2) = mer_change_omega : step at which the rotation
* velocity is changed to reach the final one
* \li \c icontrol(3) = mer_fix_omega : step at which the final
* rotation velocity must have been reached
* \li \c icontrol(4) = mer_mass : the absolute value of
* \c mer_mass is the step from which the
* baryon mass is forced to converge,
* by varying the central enthalpy
* (\c mer_mass>0 ) or the angular
* velocity (\c mer_mass<0 )
* \li \c icontrol(5) = mermax_poisson : maximum number of steps in
* \c Map_et::poisson
* \li \c icontrol(6) = mer_triax : step at which the 3-D
* perturbation is switched on
* \li \c icontrol(7) = delta_mer_kep : number of steps
* after \c mer_fix_omega when \c omega
* starts to be increased by \c fact_omega
* to search for the Keplerian velocity
*
* @param control [input] Set of parameters (stored as a
* 1-D \c Tbl of size 7) to control the
* iteration:
* \li \c control(0) = precis : threshold on the enthalpy relative
* change for ending the computation
* \li \c control(1) = omega_ini : initial angular velocity,
* switched on only if \c mer_rot<0 ,
* otherwise 0 is used
* \li \c control(2) = relax : relaxation factor in the main
* iteration
* \li \c control(3) = relax_poisson : relaxation factor in
* \c Map_et::poisson
* \li \c control(4) = thres_adapt : threshold on dH/dr for
* freezing the adaptation of the mapping
* \li \c control(5) = ampli_triax : relative amplitude of
* the 3-D perturbation
* \li \c control(6) = precis_adapt : precision for
* \c Map_et::adapt
*
* @param mbar_wanted [input] Requested baryon mass (effective only
* if \c mer_mass > \c mer_max )
* @param aexp_mass [input] Exponent for the increase factor of the
* central enthalpy to converge to the
* requested baryon mass
* @param diff [output] 1-D \c Tbl of size 7 for the storage of
* some error indicators :
* \li \c diff(0) : Relative change in the enthalpy field
* between two successive steps
* \li \c diff(1) : Relative error in the resolution of the
* Poisson equation for \c nuf
* \li \c diff(2) : Relative error in the resolution of the
* Poisson equation for \c nuq
* \li \c diff(3) : Relative error in the resolution of the
* Poisson equation for \c dzeta
* \li \c diff(4) : Relative error in the resolution of the
* Poisson equation for \c tggg
* \li \c diff(5) : Relative error in the resolution of the
* equation for \c shift (x comp.)
* \li \c diff(6) : Relative error in the resolution of the
* equation for \c shift (y comp.)
*/
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) ;
};
}
#endif
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