/usr/include/lorene/C++/Include/etoile.h is in liblorene-dev 0.0.0~cvs20161116+dfsg-1.
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2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060 2061 2062 2063 2064 2065 2066 2067 2068 2069 2070 2071 2072 2073 2074 2075 2076 2077 2078 2079 2080 2081 2082 2083 2084 2085 2086 2087 2088 2089 2090 2091 2092 2093 2094 2095 2096 2097 | /*
* Definition of Lorene classes Etoile
* Etoile_bin
* Etoile_rot
*
*/
/*
* Copyright (c) 2000-2001 Eric Gourgoulhon
* Copyright (c) 2000-2001 Keisuke Taniguchi
*
* 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 __ETOILE_H_
#define __ETOILE_H_
/*
* $Id: etoile.h,v 1.35 2015/06/12 12:38:24 j_novak Exp $
* $Log: etoile.h,v $
* Revision 1.35 2015/06/12 12:38:24 j_novak
* Implementation of the corrected formula for the quadrupole momentum.
*
* Revision 1.34 2015/06/11 13:50:19 j_novak
* Minor corrections
*
* Revision 1.33 2015/06/10 14:36:39 a_sourie
* Corrected the formula for the computation of the quadrupole momentum.
*
* Revision 1.32 2014/10/13 08:52:34 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.31 2011/10/06 14:55:36 j_novak
* equation_of_state() is now virtual to be able to call to the magnetized
* Eos_mag.
*
* Revision 1.30 2010/02/02 21:05:49 e_gourgoulhon
* Etoile_bin:equilibrium : suppressed the argument method_khi added by
* mistake during previous commit.
*
* Revision 1.29 2010/02/02 13:34:12 e_gourgoulhon
* Marked DEPRECATED (in the documentation).
*
* Revision 1.28 2008/11/14 13:51:08 e_gourgoulhon
* Added the parameter ent_limit to Etoile::equilibrium_spher and
* Etoile_bin::equilibrium.
*
* Revision 1.27 2005/10/05 15:14:47 j_novak
* Added a Param* as parameter of Etoile_rot::equilibrium
*
* Revision 1.26 2005/08/29 15:10:12 p_grandclement
* Addition of things needed :
* 1) For BBH with different masses
* 2) Provisory files for the mixted binaries (Bh and NS) : THIS IS NOT
* WORKING YET !!!
*
* Revision 1.25 2005/01/18 22:35:51 k_taniguchi
* Delete a pointer for Etoile::ray_eq(int kk).
*
* Revision 1.24 2005/01/18 20:34:14 k_taniguchi
* Addition of Etoile::ray_eq(int kk).
*
* Revision 1.23 2005/01/17 20:39:32 k_taniguchi
* Addition of Etoile::ray_eq_3pis2().
*
* Revision 1.22 2004/11/30 20:40:06 k_taniguchi
* Addition of the method for calculating a spherical star with falloff
* condition at the outer boundary.
*
* Revision 1.21 2004/05/10 10:18:33 f_limousin
* Change to avoid warning in the compilation of Lorene
*
* Revision 1.20 2004/05/07 12:37:12 f_limousin
* Add new member ssjm1_psi
*
* Revision 1.19 2004/04/08 16:42:31 f_limousin
* Add a function velocity_potential with argument ssjm1_psi for the
* case of strange stars.
*
* Revision 1.18 2004/03/22 13:12:41 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.17 2003/10/24 12:24:41 k_taniguchi
* Suppress the methods of update metric for NS-BH
*
* Revision 1.16 2003/10/21 11:44:43 k_taniguchi
* Delete various things for the Bin_ns_bh project.
* They are moved to et_bin_nsbh.h.
*
* Revision 1.15 2003/10/20 14:50:04 k_taniguchi
* Addition of various things for the Bin_ns_bh project
* which are related with the part of the neutron star.
*
* Revision 1.14 2003/10/20 13:11:03 k_taniguchi
* Back to version 1.12
*
* Revision 1.13 2003/10/20 12:15:55 k_taniguchi
* Addition of various things for the Bin_ns_bh project
* which are related with the part of the neutron star.
*
* Revision 1.12 2003/06/20 14:13:16 f_limousin
* Change to virtual the functions equilibrium_spher() and kinematics().
*
* Revision 1.11 2003/02/13 16:40:24 p_grandclement
* Addition of various things for the Bin_ns_bh project, non of them being
* completely tested
*
* Revision 1.10 2003/02/04 16:20:35 f_limousin
* Change to virtual the routine extrinsic_curvature
*
* Revision 1.9 2003/01/31 16:57:12 p_grandclement
* addition of the member Cmp decouple used to compute the K_ij auto, once
* the K_ij total is known
*
* Revision 1.8 2002/12/19 14:48:00 e_gourgoulhon
*
* Class Etoile_bin: added the new functions:
* void update_metric(const Bhole& comp)
* void update_metric_der_comp(const Bhole& comp)
* to treat the case where the companion is a black hole
*
* Revision 1.7 2002/12/17 21:17:08 e_gourgoulhon
* Class Etoile_bin: suppression of the member p_companion
* as well as the associated functions set_companion
* and get_companion.
*
* Revision 1.6 2002/09/13 09:17:33 j_novak
* Modif. commentaires
*
* Revision 1.5 2002/06/17 14:05:16 j_novak
* friend functions are now also declared outside the class definition
*
* Revision 1.4 2002/04/05 09:09:36 j_novak
* The inversion of the EOS for 2-fluids polytrope has been modified.
* Some errors in the determination of the surface were corrected.
*
* Revision 1.3 2002/01/11 14:09:34 j_novak
* Added newtonian version for 2-fluid stars
*
* Revision 1.2 2001/12/06 15:11:43 jl_zdunik
* Introduction of the new function f_eq() in the class Etoile_rot
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 2.61 2001/10/25 08:32:57 eric
* Etoile_rot::display_poly passe de protected a public.
*
* Revision 2.60 2001/10/24 15:35:55 eric
* Classe Etoile_rot: ajout de la fonction display_poly.
*
* Revision 2.59 2001/10/16 14:48:00 eric
* La fonction Etoile_rot::get_omega() devient
* virtual Etoile_rot::get_omega_c()
* (retourne la valeur centrale de Omega).
*
* Revision 2.58 2001/10/11 09:24:00 eric
* La fonction Etoile_rot::equilibrium est desormais virtuelle.
*
* Revision 2.57 2001/08/06 15:39:04 keisuke
* Addition of a new argument to Etoile_bin::equilibrium and equil_regular.
*
* Revision 2.56 2001/06/25 12:52:33 eric
* Classe Etoile_bin : ajout du membre p_companion et des fonctions
* associees set_companion() et get_companion().
*
* Revision 2.55 2001/06/13 14:11:55 eric
* Modif commentaires (mise en conformite Doc++ 3.4.7)
*
* Revision 2.54 2001/03/26 09:29:59 jlz
* Classe Etoile_rot: new members p_espec_isco and p_lspec_isco.
*
* Revision 2.53 2001/02/08 15:37:09 eric
* *** empty log message ***
*
* Revision 2.52 2001/02/08 15:12:42 eric
* Ajout de la fonction Etoile_rot::f_eccentric.
*
* Revision 2.51 2000/11/23 15:43:24 eric
* Ajout de l'argument ent_limit a Etoile_rot::equilibrium.
*
* Revision 2.50 2000/11/19 18:51:13 eric
* Etoile_rot: ajout de la fonction (static) lambda_grv2
*
* Revision 2.49 2000/11/18 23:17:32 eric
* Ajout de l'argument ost a Etoile_rot::r_isco.
*
* Revision 2.48 2000/11/18 21:08:33 eric
* Classe Etoile_rot: ajout des fonctions r_isco() et f_isco()
* ainsi que des membres associes p_r_isco et p_f_isco.
*
* Revision 2.47 2000/11/10 15:15:38 eric
* Modif arguments Etoile_rot::equilibrium.
*
* Revision 2.46 2000/10/20 13:10:23 eric
* Etoile_rot::equilibrium: ajout de l'argument nzadapt.
*
* Revision 2.45 2000/10/17 15:59:14 eric
* Modif commentaires Etoile_rot::equilibrium
*
* Revision 2.44 2000/10/12 15:22:29 eric
* Modif commentaires Etoile_rot.
*
* Revision 2.43 2000/10/12 10:20:12 eric
* Ajout de la fonction Etoile_rot::fait_nphi().
*
* Revision 2.42 2000/09/22 15:50:13 keisuke
* d_logn_auto_div devient desormais un membre de la classe Etoile
* et non plus de la classe derivee Etoile_bin.
*
* Revision 2.41 2000/09/18 16:14:37 eric
* Classe Etoile_rot: ajout du membre tkij et de la fonction
* extrinsic curvature().
*
* Revision 2.40 2000/09/07 14:31:09 keisuke
* Ajout des membres logn_auto_regu et get_logn_auto_regu() a la classe Etoile.
* Ajout des membres d_logn_auto_regu et get_d_logn_auto_regu()
* a la classe Etoile_bin.
*
* Revision 2.39 2000/09/07 10:25:50 keisuke
* Ajout du membre get_logn_auto_div() a la classe Etoile.
* Ajout du membre get_d_logn_auto_div() a la classe Etoile_bin.
*
* Revision 2.38 2000/08/31 11:25:24 eric
* Classe Etoile_rot: ajout des membres tnphi et ak_car.
*
* Revision 2.37 2000/08/29 11:37:06 eric
* Ajout des membres k_div et logn_auto_div a la classe Etoile.
* Ajout du membre d_logn_auto_div a la classe Etoile_bin.
*
* Revision 2.36 2000/08/25 10:25:57 keisuke
* Ajout de Etoile_bin::equil_regular.
*
* Revision 2.35 2000/08/18 14:01:07 eric
* Modif commentaires.
*
* Revision 2.34 2000/08/17 12:38:30 eric
* Modifs classe Etoile_rot : ajout des membres nuf, nuq, ssjm1_nuf et ssjm1_nuq
* Modif arguments Etoile_rot::equilibrium.
* .\
*
* Revision 2.33 2000/08/07 12:11:13 keisuke
* Ajout de Etoile::equil_spher_regular.
*
* Revision 2.32 2000/07/21 12:02:55 eric
* Suppression de Etoile_rot::relaxation.
*
* Revision 2.31 2000/07/20 15:32:28 eric
* *** empty log message ***
*
* Revision 2.30 2000/07/06 09:39:12 eric
* Ajout du membre p_xa_barycenter a Etoile_bin, ainsi que de la
* fonction associee xa_barycenter().
*
* Revision 2.29 2000/05/25 13:47:38 eric
* Modif Etoile_bin::equilibrium: ajout de l'argument thres_adapt
*
* Revision 2.28 2000/03/22 16:41:45 eric
* Ajout de la sortie de nouvelles erreurs dans Etoile_bin::equilibrium.
*
* Revision 2.27 2000/03/22 12:54:44 eric
* Nouveau prototype d'Etoile_bin::velocity_potential : l'erreur est
* retournee en double.
* Nouveau prototype d'Etoile_bin::equilibrium : diff_ent est remplace
* par le Tbl diff.
*
* Revision 2.26 2000/03/15 11:04:15 eric
* Ajout des fonctions Etoile_bin::set_w_shift() et Etoile_bin::set_khi_shift()
* Amelioration des commentaires.
*
* Revision 2.25 2000/03/08 12:12:49 eric
* Ajout de la fonction Etoile_bin::is_irrotational().
*
* Revision 2.24 2000/03/07 14:48:01 eric
* Ajout de la fonction Etoile_bin::extrinsic_curvature().
*
* Revision 2.23 2000/02/21 13:57:57 eric
* classe Etoile_bin: suppression du membre psi: remplacement par psi0.
*
* Revision 2.22 2000/02/17 16:51:22 eric
* Ajout de l'argument diff_ent dans Etoile_bin::equilibrium.
*
* Revision 2.21 2000/02/17 15:29:38 eric
* Ajout de la fonction Etoile_bin::relaxation.
*
* Revision 2.20 2000/02/17 13:54:21 eric
* Ajout de la fonction Etoile_bin::velocity_potential.
*
* Revision 2.19 2000/02/16 15:05:14 eric
* Ajout des membres w_shift et khi_shift.
* (sauves dans les fichiers a la place de shift_auto).
* Ajout de la fonction Etoile_bin::fait_shift_auto.
*
* Revision 2.18 2000/02/16 13:47:02 eric
* Classe Etoile_bin: ajout des membres ssjm1_khi et ssjm1_wshift.
*
* Revision 2.17 2000/02/16 11:54:13 eric
* Classe Etoile_bin : ajout des membres ssjm1_logn et ssjm1_beta.
*
* Revision 2.16 2000/02/15 15:40:07 eric
* Ajout de Etoile_bin::equilibrium.
*
* Revision 2.15 2000/02/12 18:40:15 eric
* Modif commentaires.
*
* Revision 2.14 2000/02/12 14:44:26 eric
* Ajout des fonctions Etoile_bin::set_logn_comp et set_pot_centri.
*
* Revision 2.13 2000/02/10 20:22:25 eric
* Modif commentaires.
*
* Revision 2.12 2000/02/10 16:11:24 eric
* Classe Etoile_bin : ajout des accesseurs get_psi, etc...
* ajout de la fonction fait_d_psi
*
* Revision 2.11 2000/02/08 19:28:29 eric
* La fonction Etoile_bin::scal_prod est rebaptisee Etoile_bin::sprod
*
* Revision 2.10 2000/02/04 17:15:15 eric
* Classe Etoile_bin: ajout du membre ref_triad.
*
* Revision 2.9 2000/02/04 16:36:48 eric
* Ajout des fonctions update_metric* et kinematics.
*
* Revision 2.8 2000/02/02 10:12:37 eric
* Ajout des fonctions de lecture/ecriture mp, nzet, eos, etc...
*
* Revision 2.7 2000/02/01 15:59:43 eric
* Ajout de la fonction Etoile_bin::scal_prod.
*
* Revision 2.6 2000/01/31 15:56:45 eric
* Introduction de la classe derivee Etoile_bin.
*
* Revision 2.5 2000/01/28 17:17:45 eric
* Ajout des fonctions de calcul des quantites globales.
*
* Revision 2.4 2000/01/27 16:46:59 eric
* Ajout des fonctions get_ent(), etc....
*
* Revision 2.3 2000/01/24 17:19:48 eric
* Modif commentaires.
*
* Revision 2.2 2000/01/24 17:13:04 eric
* Le mapping mp n'est plus constant.
* Ajout de la fonction equilibrium_spher.
*
* Revision 2.1 2000/01/24 13:37:19 eric
* *** empty log message ***
*
* Revision 2.0 2000/01/20 17:04:33 eric
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Include/etoile.h,v 1.35 2015/06/12 12:38:24 j_novak Exp $
*
*/
// Headers Lorene
#include "tenseur.h"
namespace Lorene {
class Eos ;
class Bhole ;
//---------------------------//
// base class Etoile //
//---------------------------//
/**
* Base class for stars *** DEPRECATED : use class \c Star instead ***.
\ingroup (star)
*
* An \c Etoile is constructed upon (i) a mapping
* (derived class of \c Map ), the center of which defines the center of the
* star, and (ii) an equation of state (derived class of \c Eos ).
* It contains tensor fields (class \c Tenseur ) which describle the
* hydrodynamical quantities as well as the gravitational field (spacetime
* metric).
*
* According to the 3+1 formalism, the spacetime metric is written
* \f[ \label{eetoilemetrique}
* ds^2 = - (N^2 - N_i N^i) dt^2 - 2 N_i \, dt\, dx^i
* + A^2 \, {\tilde h}_{ij} \, dx^i dx^j
* \f]
* where \f${\tilde h}_{ij}\f$ is a 3-metric, the exact form of which is specified
* in the derived classes of \c Etoile . The base class \c Etoile by
* itself provides only storage for the lapse function \e N (member \c nnn ),
* the shift vector \f$N^i\f$ (member \c shift ) and the conformal factor
* \f$A^2\f$ (member \c a_car ).
*
* The 3+1 formalism introduces two kinds of priviledged observers: the
* fluid comoving observer and the Eulerian observer, whose 4-velocity
* is the unit future directed normal to the \e t = const hypersurfaces.
* The hydrodynamical quantities measured by the fluid observer correspond
* to the members \c ent , \c nbar , \c ener , and \c press .
* The hydrodynamical quantities measured by the Eulerian observer correspond
* to the members \c ener_euler , \c s_euler , \c gam_euler , and
* \c u_euler .
*
* A star of class \c Etoile can be either relativistic or Newtonian,
* depending on the boolean indicator \c relativistic . For a Newtonian
* star, the metric coefficients \e N and \e A are set to 1, and \f$N^i\f$ is
* set to zero; the only relevant gravitational quantity in this case is
* \c logn_auto which represents the (regular part of) the
* Newtonian gravitational potential
* generated by the star.
*/
class Etoile {
// Data :
// -----
protected:
Map& mp ; ///< Mapping associated with the star
/// Number of domains of \c *mp occupied by the star
int nzet ;
/** 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 ;
/** Index of regularity of the gravitational potential \c logn_auto .
* If \c k_div=0 , \c logn_auto contains the total potential
* generated principaly by the star, otherwise it should be
* supplemented by \c logn_auto_div .
*/
int k_div ;
const Eos& eos ; ///< Equation of state of the stellar matter
// Fluid quantities with respect to the fluid frame
// ------------------------------------------------
/// Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case)
Tenseur ent ;
Tenseur nbar ; ///< Baryon density in the fluid frame
Tenseur ener ; ///< Total energy density in the fluid frame
Tenseur press ; ///< Fluid pressure
// Fluid quantities with respect to the Eulerian frame
// ---------------------------------------------------
Tenseur ener_euler ; ///< Total energy density in the Eulerian frame
/// Trace of the stress tensor in the Eulerian frame
Tenseur s_euler ;
/// Lorentz factor between the fluid and Eulerian observers
Tenseur gam_euler ;
/// Fluid 3-velocity with respect to the Eulerian observer
Tenseur u_euler ;
// Metric potentials
// -----------------
/** Total of the logarithm of the part of the lapse \e N
* generated principaly by the star. In the Newtonian case,
* this is the Newtonian gravitational potential
* (in units of \f$c^2\f$).
*/
Tenseur logn_auto ;
/** Regular part of the logarithm of the part of the lapse \e N
* generated principaly by the star. In the Newtonian case,
* this is the Newtonian gravitational potential
* (in units of \f$c^2\f$).
*/
Tenseur logn_auto_regu ;
/** Divergent part (if \c k_div!=0 )
* of the logarithm of the part of the lapse \e N
* generated principaly by the star.
*/
Tenseur logn_auto_div ;
/** Gradient of \c logn_auto_div (if \c k_div!=0 )
*/
Tenseur d_logn_auto_div ;
/** Logarithm of the part of the product \e AN generated principaly by
* by the star
*/
Tenseur beta_auto ;
/// Total lapse function
Tenseur nnn ;
/// Total shift vector
Tenseur shift ;
/// Total conformal factor \f$A^2\f$
Tenseur a_car ;
// Derived data :
// ------------
protected:
/// Coordinate radius at \f$\phi=0\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq ;
/// Coordinate radius at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_pis2 ;
/// Coordinate radius at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_pi ;
/// Coordinate radius at \f$\phi=3\pi/2\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq_3pis2 ;
/// Coordinate radius at \f$\theta=0\f$.
mutable double* p_ray_pole ;
/** Description of the stellar surface: 2-D \c Itbl containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$
*/
mutable Itbl* p_l_surf ;
/** Description of the stellar surface: 2-D \c Tbl containing the
* values of the radial coordinate \f$\xi\f$ on the surface at the
* collocation points in \f$(\theta', \phi')\f$
*/
mutable Tbl* p_xi_surf ;
mutable double* p_mass_b ; ///< Baryon mass
mutable double* p_mass_g ; ///< Gravitational mass
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star will be defined
* @param nzet_i Number of domains occupied by the star
* @param relat should be \c true for a relativistic
* star, \c false for a Newtonian one
* @param eos_i Equation of state of the stellar matter
*
*/
Etoile(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i) ;
Etoile(const Etoile& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve )
*/
Etoile(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Etoile() ; ///< 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 Etoile
void operator=(const Etoile&) ;
/// Read/write of the mapping
Map& set_mp() {return mp; } ;
/// Assignment of the enthalpy field.
void set_enthalpy(const Cmp& ) ;
/** Computes the proper baryon and energy density, as well as
* pressure from the enthalpy.
*/
virtual void equation_of_state() ;
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame (\c nbar , \c ener
* and \c press ).
*/
virtual void hydro_euler() ;
/** Computes a spherical static configuration.
*
* @param ent_c [input] central value of the enthalpy
* @param 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)
* @param 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.
*/
virtual void equilibrium_spher(double ent_c, double precis = 1.e-14,
const Tbl* ent_limit = 0x0 ) ;
/** Computes a spherical static configuration.
* The sources for Poisson equations are regularized
* by extracting analytical diverging parts.
*
* @param ent_c [input] central value of the enthalpy
* @param 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)
*/
void equil_spher_regular(double ent_c, double precis = 1.e-14) ;
/** Computes a spherical static configuration with the outer
* boundary condition at a finite radius
*
* @param ent_c [input] central value of the enthalpy
* @param 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)
*/
virtual void equil_spher_falloff(double ent_c,
double precis = 1.e-14) ;
// Accessors
// ---------
public:
/// Returns the mapping
const Map& get_mp() const {return mp; } ;
/// Returns the number of domains occupied by the star
int get_nzet() const {return nzet; } ;
/** Returns \c true for a relativistic star, \c false for
* a Newtonian one
*/
bool is_relativistic() const {return relativistic; } ;
/// Returns the equation of state
const Eos& get_eos() const {return eos; } ;
/// Returns the enthalpy field
const Tenseur& get_ent() const {return ent;} ;
/// Returns the proper baryon density
const Tenseur& get_nbar() const {return nbar;} ;
/// Returns the proper total energy density
const Tenseur& get_ener() const {return ener;} ;
/// Returns the fluid pressure
const Tenseur& get_press() const {return press;} ;
/// Returns the total energy density with respect to the Eulerian observer
const Tenseur& get_ener_euler() const {return ener_euler;} ;
/// Returns the trace of the stress tensor in the Eulerian frame
const Tenseur& get_s_euler() const {return s_euler;} ;
/// Returns the Lorentz factor between the fluid and Eulerian observers
const Tenseur& get_gam_euler() const {return gam_euler;} ;
/// Returns the fluid 3-velocity with respect to the Eulerian observer
const Tenseur& get_u_euler() const {return u_euler;} ;
/** Returns the logarithm of the part of the lapse \e N generated
* principaly by the star.
* In the Newtonian case, this is the Newtonian
* gravitational potential (in units of \f$c^2\f$).
*/
const Tenseur& get_logn_auto() const {return logn_auto;} ;
/** Returns the regular part of the logarithm of the part of
* the lapse \e N generated principaly by the star.
* In the Newtonian case, this is the Newtonian
* gravitational potential (in units of \f$c^2\f$).
*/
const Tenseur& get_logn_auto_regu() const {return logn_auto_regu;} ;
/** Returns the divergent part of the logarithm of the part of
* the lapse \e N generated principaly by the star.
* In the Newtonian case, this is the diverging part of
* the Newtonian gravitational potential (in units of \f$c^2\f$).
*/
const Tenseur& get_logn_auto_div() const {return logn_auto_div;} ;
/** Returns the gradient of \c logn_auto_div
*/
const Tenseur& get_d_logn_auto_div() const {return d_logn_auto_div;} ;
/** Returns the logarithm of the part of the product \e AN generated
* principaly by the star.
*/
const Tenseur& get_beta_auto() const {return beta_auto;} ;
/// Returns the total lapse function \e N
const Tenseur& get_nnn() const {return nnn;} ;
/// Returns the total shift vector \f$N^i\f$
const Tenseur& get_shift() const {return shift;} ;
/// Returns the total conformal factor \f$A^2\f$
const Tenseur& get_a_car() const {return a_car;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
/// Display
friend ostream& operator<<(ostream& , const Etoile& ) ;
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Coordinate radius at \f$\phi=0\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq() const ;
/// Coordinate radius at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_pis2() const ;
/// Coordinate radius at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_pi() const ;
/// Coordinate radius at \f$\phi=3\pi/2\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq_3pis2() const ;
/// Coordinate radius at \f$\theta=0\f$ [r_unit].
double ray_pole() const ;
/// Coordinate radius at \f$\phi=2k\pi/np\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq(int kk) const ;
/** 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 ;
/** Description of the stellar surface: returns a 2-D \c Tbl
* containing the values of the radial coordinate \f$\xi\f$
* 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.
*/
const Tbl& xi_surf() const ;
/// Baryon mass
virtual double mass_b() const ;
/// Gravitational mass
virtual double mass_g() const ;
};
ostream& operator<<(ostream& , const Etoile& ) ;
//---------------------------//
// class Etoile_bin //
//---------------------------//
/**
* Class for stars in binary system. \ingroup (star)
*
* This class implements the formalism for corotating or irrotational
* systems presented in Bonazzola, Gourgoulhon \& Marck \a Phys. \a Rev. \a Lett.
* \b 82 , 892 (1999). In particular, the conformal 3-metric
* \f$\tilde h_{ij}\f$ introduced in Eq.~(\ref{eetoilemetrique}) is flat.
*
* An \c Etoile_bin can be construted in two states, represented by
* the \c bool member \c irrotational : (i) irrotational
* (i.e. the fluid motion is irrotational) or (ii) rigidly corotating
* with respect to the orbital motion (synchronized binary).
*
*/
class Etoile_bin : public Etoile {
// Data :
// -----
protected:
/** \c true for an irrotational star, \c false for a
* corotating one
*/
bool irrotational ;
/** Reference triad ("absolute frame"), with
* respect to which the components of all the member \c Tenseur 's
* are defined, except for \c w_shift and \c ssjm1_wshift .
*/
const Base_vect& ref_triad ;
/** Scalar potential \f$\Psi_0\f$ of the non-translational part of
* fluid 4-velocity (in the irrotational case)
*/
Tenseur psi0 ;
/** Gradient of \f$\Psi\f$ (in the irrotational case)
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_psi ;
/** Spatial projection of the fluid 3-velocity with respect to
* the co-orbiting observer.
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur wit_w ;
/** Logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
Tenseur loggam ;
/** Part of the lapse logarithm (gravitational potential at the
* Newtonian limit) generated principaly by the companion star.
*/
Tenseur logn_comp ;
/** Gradient of \c logn_auto
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_logn_auto ;
/** Gradient of \c logn_auto_regu
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_logn_auto_regu ;
/** Gradient of \c logn_comp
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_logn_comp ;
/** Part of the logarithm of \e AN generated principaly by the
* companion star.
*/
Tenseur beta_comp ;
/** Gradient of \c beta_auto
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_beta_auto ;
/** Gradient of \c beta_comp
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur d_beta_comp ;
/** Part of the shift vector \f$N^i\f$ generated principaly by the star.
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur shift_auto ;
/** Part of the shift vector \f$N^i\f$ generated principaly by the
* companion star.
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur shift_comp ;
/** Vector \f$W^i\f$ used in the decomposition of \c shift_auto ,
* 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 .
*/
Tenseur w_shift ;
/** Scalar \f$\chi\f$ used in the decomposition of \c shift_auto ,
* 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]
*/
Tenseur khi_shift ;
/** Part of the extrinsic curvature tensor
* \f$\tilde K^{ij} = A^2 K^{ij}\f$
* generated by \c shift_auto .
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur_sym tkij_auto ;
/** Part of the extrinsic curvature tensor
* \f$\tilde K^{ij} = A^2 K^{ij}\f$
* generated by \c shift_comp .
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur_sym tkij_comp ;
/** Part of the scalar \f$A^2 K_{ij} K^{ij}\f$
* generated by \c shift_auto , i.e.
* \f$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm auto}\f$
*/
Tenseur akcar_auto ;
/** Part of the scalar \f$A^2 K_{ij} K^{ij}\f$
* generated by \c shift_auto and \c shift_comp , i.e.
* \f$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm comp}\f$
*/
Tenseur akcar_comp ;
/** 3-vector shift, divided by \e N , of the rotating coordinates,
* \f$B^i/N\f$.
* (Cartesian components with respect to \c ref_triad )
*/
Tenseur bsn ;
/// Centrifugal potential
Tenseur pot_centri ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c logn_auto by means of
* \c Map_et::poisson .
*/
Cmp ssjm1_logn ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c beta_auto by means of
* \c Map_et::poisson .
*/
Cmp ssjm1_beta ;
/** 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$N^i\f$
*/
Cmp ssjm1_khi ;
/** Effective source at the previous step for the resolution of
* the vector Poisson equation for \f$W^i\f$ by means of
* \c Map_et::poisson .
* \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 )
*/
Tenseur ssjm1_wshift ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for the scalar \f$\psi\f$ by means of
* \c Map_et::poisson_interne .
*/
Cmp ssjm1_psi ;
/**
* Function used to construct the part of \f$K^{ij}\f$ generated by
* the star from the total \f$K^{ij}\f$. Only used for a binary system
* where the other member is a black hole.
*
* Mainly this \c Cmp is 1 around the hole and 0 around the companion
* and the sum of \c decouple for the hole and his companion is 1
* everywhere.
*/
Cmp decouple ;
// Derived data :
// ------------
protected:
/// Absolute coordinate X of the barycenter of the baryon density
mutable double* p_xa_barycenter ;
// Constructors - Destructor
// -------------------------
public:
/** Standard constructor.
*
* @param mp_i Mapping on which the star will be defined
* @param nzet_i Number of domains occupied by the star
* @param relat should be \c true for a relativistic
* star, \c false for a Newtonian one
* @param eos_i Equation of state of the stellar matter
* @param irrot should be \c true for an irrotational star,
* \c false for a corotating one
* @param ref_triad_i Reference triad ("absolute frame"), with
* respect to which the components of all the member
* \c Tenseur 's are defined, except for \c w_shift
* and \c ssjm1_wshift whose components are defined
* with respect to the mapping \c mp Cartesian triad.
*/
Etoile_bin(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i,
bool irrot, const Base_vect& ref_triad_i) ;
Etoile_bin(const Etoile_bin& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param ref_triad_i Reference triad ("absolute frame"), with
* respect to which the components of all the member
* \c Tenseur 's are defined, except for \c w_shift
* and \c ssjm1_wshift whose components are defined
* with respect to the mapping \c mp Cartesian triad.
* @param fich input file (must have been created by the function
* \c sauve )
*/
Etoile_bin(Map& mp_i, const Eos& eos_i, const Base_vect& ref_triad_i,
FILE* fich) ;
virtual ~Etoile_bin() ; ///< 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 Etoile_bin
void operator=(const Etoile_bin& ) ;
/** Read/write the part of the lapse logarithm (gravitational potential
* at the Newtonian limit) generated principaly by the companion star.
*/
Tenseur& set_logn_comp() ;
/// Read/write the centrifugal potential
Tenseur& set_pot_centri() ;
/// Read/write of \c w_shift
Tenseur& set_w_shift() ;
/// Read/write of \c khi_shift
Tenseur& set_khi_shift() ;
// Accessors
// ---------
public:
/** Returns \c true for an irrotational motion, \c false for
* a corotating one.
*/
bool is_irrotational() const {return irrotational; } ;
/// Returns the non-translational part of the velocity potential
const Tenseur& get_psi0() const {return psi0;} ;
/** Returns the gradient of the velocity potential
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_psi() const {return d_psi;} ;
/** Returns the spatial projection of the fluid 3-velocity with
* respect to the co-orbiting observer.
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_wit_w() const {return wit_w;} ;
/** Returns the logarithm of the Lorentz factor between the fluid and
* the co-orbiting observer.
*/
const Tenseur& get_loggam() const {return loggam;} ;
/** Returns the part of the lapse logarithm (gravitational potential
* at the Newtonian limit) generated principaly by the companion star.
*/
const Tenseur& get_logn_comp() const {return logn_comp;} ;
/** Returns the gradient of \c logn_auto
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_logn_auto() const {return d_logn_auto;} ;
/** Returns the gradient of \c logn_auto_regu
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_logn_auto_regu() const {return d_logn_auto_regu;} ;
/** Returns the gradient of \c logn_comp
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_logn_comp() const {return d_logn_comp;} ;
/** Returns the part of the logarithm of \e AN generated principaly
* by the companion star.
*/
const Tenseur& get_beta_comp() const {return beta_comp;} ;
/** Returns the gradient of \c beta_auto
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_beta_auto() const {return d_beta_auto;} ;
/** Returns the gradient of \c beta_comp
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_d_beta_comp() const {return d_beta_comp;} ;
/** Returns the part of the shift vector \f$N^i\f$ generated principaly
* by the star.
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_shift_auto() const {return shift_auto;} ;
/** Returns the part of the shift vector \f$N^i\f$ generated principaly
* by the companion star.
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_shift_comp() const {return shift_comp;} ;
/** Returns the vector \f$W^i\f$ used in the decomposition of
* \c shift_auto ,
* 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 Tenseur& get_w_shift() const {return w_shift;} ;
/** Returns the scalar \f$\chi\f$ used in the decomposition of
* \c shift_auto
* 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 Tenseur& get_khi_shift() const {return khi_shift;} ;
/** Returns the part of the extrinsic curvature tensor
* \f$\tilde K^{ij} = A^2 K^{ij}\f$ generated by \c shift_auto .
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur_sym& get_tkij_auto() const {return tkij_auto;} ;
/** Returns the part of the extrinsic curvature tensor
* \f$\tilde K^{ij} = A^2 K^{ij}\f$ generated by \c shift_comp .
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur_sym& get_tkij_comp() const {return tkij_comp;} ;
/** Returns the part of the scalar \f$A^2 K_{ij} K^{ij}\f$
* generated by \c shift_auto , i.e.
* \f$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm auto}\f$
*/
const Tenseur& get_akcar_auto() const {return akcar_auto;} ;
/** Returns the part of the scalar \f$A^2 K_{ij} K^{ij}\f$
* generated by \c shift_auto and \c shift_comp , i.e.
* \f$A^2 K_{ij}^{\rm auto} K^{ij}_{\rm comp} \f$
*/
const Tenseur& get_akcar_comp() const {return akcar_comp;} ;
/** Returns the shift vector, divided by \e N , of the rotating
* coordinates, \f$B^i/N\f$.
* (Cartesian components with respect to \c ref_triad )
*/
const Tenseur& get_bsn() const {return bsn;} ;
/// Returns the centrifugal potential
const Tenseur& get_pot_centri() const {return pot_centri;} ;
/**
* Returns the function used to construct \c tkij_auto
from \c tkij_tot .
*/
const Cmp get_decouple() const {return decouple ;}
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
protected:
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Baryon mass
virtual double mass_b() const ;
/// Gravitational mass
virtual double mass_g() const ;
/** Absolute coordinate X of the barycenter of the baryon density,
* defined according to the formula
* \f[
* X_G := \int A^3 \Gamma_{\rm n} \, n \, X \, d^3x \ ,
* \f]
* where \f$\Gamma_{\rm n}\f$ is the Lorentz factor between the fluid
* and Eulerian observers.
*/
virtual double xa_barycenter() const ;
// Computational routines
// ----------------------
public:
/** Performs the scalar product of two tensors by contracting
* the last index of \c t1 with the first index of \c t2 .
* Both indices are supposed to be contravariant, so that a
* multiplication by \f$A^2\f$ is performed to lower one index.
* For instance, for two vectors \f$V^i\f$ and \f$W^i\f$, this function
* returns the scalar \f$h_{ij} V^i W^j = A^2 f_{ij} V^i W^j\f$.
*/
virtual Tenseur sprod(const Tenseur& t1, const Tenseur& t2) const ;
/** Computes the hydrodynamical quantities relative to the Eulerian
* observer from those in the fluid frame, as well as
* \c wit_w and \c loggam .
*
* The calculation is performed starting from the quantities
* \c ent , \c ener , \c press , \c a_car and \c bsn ,
* 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 ,
* \c wit_w and \c loggam .
*
*/
virtual void hydro_euler() ;
/** Computes metric coefficients from known potentials,
* when the companion is another star.
*
* The calculation is performed starting from the quantities
* \c logn_auto , \c beta_auto , \c shift_auto ,
* \c comp.logn_auto , \c comp.beta_auto ,
* \c comp.shift_auto
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c logn_comp , \c beta_comp , \c shift_comp ,
* \c nnn , \c a_car , \c shift ,
* \c d_logn_auto , \c d_beta_auto , \c tkij_auto ,
* \c akcar_auto .
*
* @param comp companion star.
*
*/
void update_metric(const Etoile_bin& comp) ;
/** Same as \c update_metric(const Etoile_bin\& \c ) but with
* relaxation.
*
* @param comp companion star.
* @param star_prev previous value of the star.
* @param relax relaxation parameter.
*/
void update_metric(const Etoile_bin& comp, const Etoile_bin& star_prev,
double relax) ;
/** Computes the derivative of metric functions related to the
* companion star.
*
* The calculation is performed starting from the quantities
* \c comp.d_logn_auto , \c comp.d_beta_auto ,
* \c comp.tkij_auto
* which are supposed to be up to date.
* From these, the following fields are updated:
* \c d_logn_comp , \c d_beta_comp , \c tkij_comp ,
* \c akcar_comp .
*
* @param comp companion star.
*
*/
void update_metric_der_comp(const Etoile_bin& comp) ;
/** Computes the quantities \c bsn and \c pot_centri .
*
* The calculation is performed starting from the quantities
* \c nnn , \c shift , \c a_car ,
* which are supposed to be up to date.
*
* @param omega angular velocity with respect to an asymptotically
* inertial observer
* @param x_axe absolute X coordinate of the rotation axis
*/
virtual void kinematics(double omega, double x_axe) ;
/** Computes the gradient of the total velocity potential \f$\psi\f$.
*
*/
void fait_d_psi() ;
/** Computes \c shift_auto 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_auto() ;
/** Computes \c tkij_auto and \c akcar_auto from
* \c shift_auto , \c nnn and \c a_car .
*/
virtual void extrinsic_curvature() ;
/** Computes an equilibrium configuration.
*
* The values of \c logn_comp , \c beta_comp , \c pot_centri
* are held fixed during the iteration.
*
* @param ent_c [input] Central enthalpy
* @param mermax [input] Maximum number of steps
* @param mermax_poisson [input] Maximum number of steps in
* Map_et::poisson
* @param relax_poisson [input] Relaxation factor in Map_et::poisson
* @param mermax_potvit [input] Maximum number of steps in
* Map_radial::poisson_compact
* @param relax_potvit [input] Relaxation factor in
* Map_radial::poisson_compact
* @param thres_adapt [input] Threshold on dH/dr for the adaptation
* of the mapping
* @param fact [input] 1-D \c Tbl for the input
* of some factors :
* \li \c fact(0) : A resizing factor for the first shell
* @param diff [output] 1-D \c Tbl 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 returned by the routine
* \c Etoile_bin::velocity_potential
* \li \c diff(2) : Relative error in the resolution of the
* Poisson equation for \c logn_auto
* \li \c diff(3) : Relative error in the resolution of the
* Poisson equation for \c beta_auto
* \li \c diff(4) : Relative error in the resolution of the
* equation for \c shift_auto (x comp.)
* \li \c diff(5) : Relative error in the resolution of the
* equation for \c shift_auto (y comp.)
* \li \c diff(6) : Relative error in the resolution of the
* equation for \c shift_auto (z comp.)
* @param 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.
*/
void equilibrium(double ent_c,
int mermax, int mermax_poisson,
double relax_poisson, int mermax_potvit,
double relax_potvit, double thres_adapt,
const Tbl& fact, Tbl& diff, const Tbl* ent_limit = 0x0) ;
/** Computes an equilibrium configuration by regularizing
* the diverging source.
*
* The values of \c logn_comp , \c beta_comp , \c pot_centri
* are held fixed during the iteration.
*
* @param ent_c [input] Central enthalpy
* @param ent_limit is the table of enthalpy values on the domain borders
*
* @param mermax [input] Maximum number of steps
* @param mermax_poisson [input] Maximum number of steps in
* Map_et::poisson
* @param relax_poisson [input] Relaxation factor in Map_et::poisson
* @param mermax_potvit [input] Maximum number of steps in
* Map_radial::poisson_compact
* @param relax_potvit [input] Relaxation factor in
* Map_radial::poisson_compact
* @param thres_adapt [input] Threshold on dH/dr for the adaptation
* of the mapping
* @param fact [input] 1-D \c Tbl for the input
* of some factors :
* \li \c fact(0) : A resizing factor for the first shell
* @param diff [output] 1-D \c Tbl 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 returned by the routine
* \c Etoile_bin::velocity_potential
* \li \c diff(2) : Relative error in the resolution of the
* Poisson equation for \c logn_auto
* \li \c diff(3) : Relative error in the resolution of the
* Poisson equation for \c beta_auto
* \li \c diff(4) : Relative error in the resolution of the
* equation for \c shift_auto (x comp.)
* \li \c diff(5) : Relative error in the resolution of the
* equation for \c shift_auto (y comp.)
* \li \c diff(6) : Relative error in the resolution of the
* equation for \c shift_auto (z comp.)
*/
void equil_regular(double ent_c, int mermax, int mermax_poisson,
double relax_poisson, int mermax_potvit,
double relax_potvit, double thres_adapt,
const Tbl& fact, Tbl& diff) ;
/** Computes the non-translational part of the velocity scalar potential
* \f$\psi0\f$ by solving the continuity equation.
*
* @param mermax [input] Maximum number of steps in the iteration
* @param precis [input] Required precision: the iteration will
* be stopped when the relative difference
* on \f$\psi0\f$ between two successive steps
* is lower than \c precis .
* @param relax [input] Relaxation factor.
*
* @return Relative error of the resolution obtained by comparing
* the operator acting on the solution with the source.
*/
double velocity_potential(int mermax, double precis, double relax) ;
/** Performs a relaxation on \c ent , \c logn_auto , \c beta_auto
* and \c shift_auto .
* @param star_prev [input] star at the previous step.
* @param relax_ent [input] Relaxation factor for \c ent
* @param relax_met [input] Relaxation factor for \c logn_auto ,
* \c beta_auto , \c shift_auto ,
* only if \c (mer \% fmer_met == 0) .
* @param mer [input] Step number
* @param fmer_met [input] Step interval between metric updates
*/
void relaxation(const Etoile_bin& star_prev, double relax_ent,
double relax_met, int mer, int fmer_met) ;
friend class Bin_ns_bh ; ///< Friend class Bin_ns_bh
};
//---------------------------//
// class Etoile_rot //
//---------------------------//
/**
* Class for isolated rotating stars *** DEPRECATED : use class \c Star_rot instead ***. \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]
*
*
*/
class Etoile_rot : public Etoile {
// Data :
// -----
protected:
double omega ; ///< Rotation angular velocity (\c [f_unit] )
/// Metric factor \e B
Tenseur bbb ;
/// Square of the metric factor \e B
Tenseur b_car ;
/// Metric coefficient \f$N^\varphi\f$
Tenseur nphi ;
/** Component \f$\tilde N^\varphi = N^\varphi r\sin\theta\f$ of the
* shift vector
*/
Tenseur tnphi ;
/// Norm of \c u_euler
Tenseur uuu ;
/// Metric potential \f$\nu = \ln N\f$ = \c logn_auto
Tenseur& logn ;
/** Part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the matter terms
*/
Tenseur nuf ;
/** Part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the quadratic terms
*/
Tenseur nuq ;
/// Metric potential \f$\zeta = \ln(AN)\f$ = \c beta_auto
Tenseur& dzeta ;
/// Metric potential \f$\tilde G = (NB-1) r\sin\theta\f$
Tenseur 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 .
*/
Tenseur 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]
*/
Tenseur 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${\tilde K_{ij}}\f$.
*/
Tenseur_sym 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]
*/
Tenseur 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 .
*/
Cmp 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 .
*/
Cmp ssjm1_nuq ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c dzeta .
*/
Cmp ssjm1_dzeta ;
/** Effective source at the previous step for the resolution of
* the Poisson equation for \c tggg .
*/
Cmp 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$N^i\f$
*/
Cmp 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 )
*/
Tenseur 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_area ; ///< Surface area
mutable double* p_aplat ; ///< Flatening r_pole/r_eq
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_mom_quad_old ; ///< Part of the quadrupole moment
mutable double* p_mom_quad_Bo ; ///< Part of the 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 will be defined
* @param nzet_i Number of domains occupied by the star
* @param relat should be \c true for a relativistic
* star, \c false for a Newtonian one
* @param eos_i Equation of state of the stellar matter
*/
Etoile_rot(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i) ;
Etoile_rot(const Etoile_rot& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve )
*/
Etoile_rot(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Etoile_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 Etoile_rot
void operator=(const Etoile_rot& ) ;
// Accessors
// ---------
public:
/** 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 Tenseur& get_bbb() const {return bbb;} ;
/// Returns the square of the metric factor \e B
const Tenseur& get_b_car() const {return b_car;} ;
/// Returns the metric coefficient \f$N^\varphi\f$
const Tenseur& get_nphi() const {return nphi;} ;
/** Returns the component \f$\tilde N^\varphi = N^\varphi r\sin\theta\f$
* of the shift vector
*/
const Tenseur& get_tnphi() const {return tnphi;} ;
/// Returns the norm of \c u_euler
const Tenseur& get_uuu() const {return uuu;} ;
/// Returns the metric potential \f$\nu = \ln N\f$ = \c logn_auto
const Tenseur& get_logn() const {return logn;} ;
/** Returns the part of the Metric potential \f$\nu = \ln N\f$ = \c logn
* generated by the matter terms
*/
const Tenseur& 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 Tenseur& get_nuq() const {return nuq;} ;
/// Returns the Metric potential \f$\zeta = \ln(AN)\f$ = \c beta_auto
const Tenseur& get_dzeta() const {return dzeta;} ;
/// Returns the Metric potential \f$\tilde G = (NB-1) r\sin\theta\f$
const Tenseur& 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 Tenseur& 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 Tenseur& 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 Tenseur_sym& 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 Tenseur& 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 area() const ; ///< Surface area
virtual double mean_radius() const ; ///< Mean radius
virtual double aplat() const ; ///< Flatening r_pole/r_eq
virtual double z_eqf() const ; ///< Forward redshift factor at equator
virtual double z_eqb() const ; ///< Backward redshift factor at equator
virtual double z_pole() const ; ///< Redshift factor at North pole
/** Quadrupole moment.
* The quadrupole moment \e Q is defined according to Eq. (11) of
* [Pappas and Apostolatos, \a Physical \a Review \a Letters
* \b 108, 231104 (2012)]. This is a corrected version of the quadrupole
* moment defined by [Salgado, Bonazzola, Gourgoulhon and Haensel,
* \a Astron. \a Astrophys. \b 291 , 155 (1994)]. Following this
* definition, \f$Q = {\bar Q } - 4/3 (1/4 + b) M^3 \f$, where
* \f${\bar Q }\f$ is defined as the negative of the (wrong) quadrupole
* moment defined in Eq. (7) of [Salgado, Bonazzola, Gourgoulhon and
* Haensel, \a Astron. \a Astrophys. \b 291 , 155 (1994)], \e b is
* defined by Eq. (3.37) of [Friedman and Stergioulas, \a Rotating
* \a Relativistic \a Stars, Cambridge Monograph on mathematical
* physics] and \e M is the gravitational mass of the star.
*/
virtual double mom_quad() const ;
/** Part of the quadrupole moment.
* This term \f${\bar Q }\f$ is defined by Laarakkers and Poisson,
* \a Astrophys. \a J. \b 512 , 282 (1999). Note that \f${\bar Q }\f$
* is the negative of the (wrong) quadrupole moment defined in Eq. (7) of
* [Salgado, Bonazzola, Gourgoulhon and Haensel, \a Astron. \a Astrophys.
* \b 291 , 155 (1994)].
*/
virtual double mom_quad_old() const ;
/** Part of the quadrupole moment.
* \f$B_o\f$ is defined as \f$bM^2\f$, where \e b is given by
* Eq. (3.37) of [Friedman and Stergioulas, \a Rotating \a
* Relativistic \a Stars, Cambridge Monograph on mathematical
* physics] and \e M is the the gravitational mass of the star.
*/
virtual double mom_quad_Bo() 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 ;
/** Computation of frequency of eccentric orbits.
*
* @param ecc eccentricity of the orbit
* @param periasrt periastron of the orbit
* @param ost output stream to give details of the computation;
* if set to 0x0 [default value], no details will be
* given.
*
* @return orbital frequency
*/
virtual double f_eccentric(double ecc, double periast,
ostream* ost = 0x0) 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 .
*
*/
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 Cmp& sou_m, const Cmp& 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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