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* Definition of Lorene class Et_rot_bifluid
*
*/
/*
* Copyright (c) 2001 Jerome Novak
* (c) 2015 Aurelien Sourie
*
* 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 __ET_ROT_BIFLUID_H_
#define __ET_ROT_BIFLUID_H_
/*
* $Id: et_rot_bifluid.h,v 1.20 2015/06/26 14:10:08 j_novak Exp $
* $Log: et_rot_bifluid.h,v $
* Revision 1.20 2015/06/26 14:10:08 j_novak
* Modified comments.
*
* Revision 1.19 2015/06/11 13:50:18 j_novak
* Minor corrections
*
* Revision 1.18 2015/06/10 14:39:17 a_sourie
* New class Eos_bf_tabul for tabulated 2-fluid EoSs and associated functions for the computation of rotating stars with such EoSs.
*
* Revision 1.17 2014/10/13 08:52:34 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.16 2013/11/25 13:50:55 j_novak
* The inheritance from Etoile_rot is no longer virtual.
*
* Revision 1.15 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 1.14 2004/09/01 10:56:05 r_prix
* added option of converging baryon-mass to equilibrium_bi()
*
* Revision 1.13 2004/03/22 13:12:41 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.12 2003/12/04 14:13:32 r_prix
* added method get_typeos {return typeos}; and fixed some comments.
*
* Revision 1.11 2003/11/20 14:01:45 r_prix
* changed member names to better conform to Lorene coding standards:
* J_euler -> j_euler, EpS_euler -> enerps_euler, Delta_car -> delta_car
*
* Revision 1.10 2003/11/18 18:32:36 r_prix
* added new class-member: EpS_euler := ener_euler + s_euler
* has the advantage of a nice Newtonian limit -> rho
* (ener_euler is no longer used in this class!)
*
* Revision 1.9 2003/11/13 12:02:03 r_prix
* - adapted/extended some of the documentation
* - changed xxx2 -> Delta_car
* - added members J_euler, sphph_euler, representing 3+1 components of Tmunu
* (NOTE: these are not 2-fluid specific, and should ideally be moved into Class Etoile!)
*
* Revision 1.8 2003/09/17 08:27:50 j_novak
* New methods: mass_b1() and mass_b2().
*
* Revision 1.7 2002/10/09 07:54:29 j_novak
* Et_rot_bifluid and Et_rot_mag inheritate virtually from Etoile_rot
*
* Revision 1.6 2002/09/13 09:17:33 j_novak
* Modif. commentaires
*
* Revision 1.5 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 1.4 2002/01/16 15:03:28 j_novak
* *** empty log message ***
*
* Revision 1.3 2002/01/08 14:43:53 j_novak
* better determination of surfaces for 2-fluid stars
*
* Revision 1.2 2002/01/03 15:30:27 j_novak
* Some comments modified.
*
* Revision 1.1.1.1 2001/11/20 15:19:27 e_gourgoulhon
* LORENE
*
* Revision 1.3 2001/10/03 09:49:06 novak
* *** empty log message ***
*
* Revision 1.2 2001/08/28 14:14:10 novak
* overrided l_surf function
*
* Revision 1.1 2001/06/22 15:38:52 novak
* Initial revision
*
*
* $Header: /cvsroot/Lorene/C++/Include/et_rot_bifluid.h,v 1.20 2015/06/26 14:10:08 j_novak Exp $
*
*/
// Headers Lorene
#include "eos_bifluid.h"
#include "etoile.h"
namespace Lorene {
// Local prototype (for determining the surface)
Cmp prolonge_c1(const Cmp& uu, const int nzet) ;
/**
* Class for two-fluid rotating relativistic stars. \ingroup (star)
*
* This is a child class of \c Etoile_rot , with the same metric
* and overloaded member functions.
*
* There are two number-density fields \c nbar and \c nbar2
* (and 2 log-enthalpies, see class \c Eos_bifluid ), as well as two
* velocity fields, with phi-components (with respect to the Eulerian observer)
* \c uuu and \c uuu2 .
*
* Fluid 1 can be considered to correspond to the (superfluid) neutrons, whereas
* fluid 2 would consist of the protons (and electrons)
*.
* The quantity \c u_euler of the \c class Etoile is
* \b not \b used in this class!
* Only the "3+1" components of \f${T^\mu}_\nu\f$ should be used outside
* of \c hydro_euler() , namely \c s_euler, \c sphph_euler, \c j_euler and
* \c ener_euler.
*
*/
class Et_rot_bifluid : public Etoile_rot {
// Data :
// -----
protected:
const Eos_bifluid& eos ; ///< Equation of state for two-fluids model
double omega2 ; ///< Rotation angular velocity for fluid 2 (\c [f_unit] )
// Fluid quantities with respect to the fluid frame
// ------------------------------------------------
/// Log-enthalpy for the second fluid
Tenseur ent2 ;
Tenseur nbar2 ; ///< Baryon density in the fluid frame, for fluid 2
Tenseur K_nn ; ///< Coefficient Knn
Tenseur K_np ; ///< Coefficient Knp
Tenseur K_pp ; ///< Coefficient Kpp
// Fluid quantities with respect to the Eulerian frame
// ---------------------------------------------------
// FIXME: the following three variables are not specific to 2-fluid stars
// and should ideally be moved to class Etoile!
/// The component \f$S^\varphi_\varphi\f$ of the stress tensor \f${S^i}_j\f$.
Tenseur sphph_euler;
/** Total angular momentum (flat-space!) 3-vector \f$J_\mathrm{euler}\f$,
* which is related to \f$J^i\f$ of the "3+1" decomposition, but expressed
* in a flat-space triad. In axisymmetric circular cases, only
* \f$J_\mathrm{euler}(\varphi)=r \sin\theta\, J^\varphi\f$ is nonzero.
*/
Tenseur j_euler;
Tenseur j_euler1; ///< To compute Jn
Tenseur j_euler2; ///< To compute Jp
Tenseur j_euler11_1; ///< To compute In (1st version)
Tenseur j_euler12_1; ///< To compute Ip (1st version)
Tenseur j_euler21_1;// To compute epsN (1st version)
Tenseur j_euler22_1;// To compute epsP (1st version)
Tenseur j_euler11_2;//To compute In (2nd version)
Tenseur j_euler12_2;//To compute Ip (2nd version)
Tenseur j_euler21_2;// To compute epsN (2nd version)
Tenseur j_euler22_2;// To compute epsP (2nd version)
/// the combination \f$E+S_i^i\f$: useful because in the Newtonian limit \f$\rightarrow \rho\f$.
Tenseur enerps_euler;
/// Norm of the (fluid no.2) 3-velocity with respect to the eulerian observer
Tenseur uuu2 ;
/// Lorentz factor between the fluid 2 and Eulerian observers
Tenseur gam_euler2 ;
/**
* The "relative velocity" (squared) \f$\Delta^2\f$ of the two fluids.
* See Prix et al.(2003) and see also \c Eos_bifluid .
*/
Tenseur delta_car ;
// Derived data :
// ------------
protected:
/// Coordinate radius at \f$\phi=0\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq2 ;
/// Coordinate radius at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq2_pis2 ;
/// Coordinate radius at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$.
mutable double* p_ray_eq2_pi ;
/// Coordinate radius at \f$\theta=0\f$.
mutable double* p_ray_pole2 ;
/** Description of the surface of fluid 2: 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_surf2 ;
/** Description of the surface of fluid 2: 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_surf2 ;
mutable double* p_r_circ2 ; ///< Circumferential radius of fluid no.2
mutable double* p_area2 ; ///< Surface area of fluid no.2
mutable double* p_aplat2 ; ///< Flatening r_pole/r_eq of fluid no.2
mutable double* p_mass_b1 ; ///< Baryon mass of fluid 1
mutable double* p_mass_b2 ; ///< Baryon mass of fluid 2
mutable double* p_angu_mom_1; ///< Angular momentum of fluid 1
mutable double* p_angu_mom_2; ///< Angular momentum of fluid 2
mutable double* p_angu_mom_1_part1_1; ///< To compute In (1st version)
mutable double* p_angu_mom_2_part1_1; ///< To compute Ip (1st version)
mutable double* p_angu_mom_1_part2_1; ///< To compute Xn (1st version)
mutable double* p_angu_mom_2_part2_1; ///< To compute Xp (1st version)
mutable double* p_angu_mom_1_part1_2; ///< To compute In (2nd version)
mutable double* p_angu_mom_2_part1_2; ///< To compute Ip (2nd version)
mutable double* p_angu_mom_1_part2_2; ///< To compute Xn (2nd version)
mutable double* p_angu_mom_2_part2_2; ///< To compute Xp (2nd version)
// Constructors - Destructor
// -------------------------
public:
Et_rot_bifluid(Map& mp_i, int nzet_i, bool relat,
const Eos_bifluid& eos_i) ; ///< Standard constructor
Et_rot_bifluid(const Et_rot_bifluid& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ) Works only for
* relativistic stars.
* This has to be improved....
*/
Et_rot_bifluid(Map& mp_i, const Eos_bifluid& eos_i, FILE* fich) ;
virtual ~Et_rot_bifluid() ; ///< 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 Et_rot_bifluid
void operator=(const Et_rot_bifluid&) ;
/// Sets both enthalpy profiles
void set_enthalpies(const Cmp&, const Cmp&) ;
/** Computes a spherical static configuration.
*
* @param ent_c [input] central value of the enthalpy 1
* @param ent_c2 [input] central value of the enthalpy 2
* @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 equilibrium_spher_bi(double ent_c, double ent_c2,
double precis = 1.e-14) ;
/** 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 1
* @param ent_c2 [input] central value of the enthalpy 2
* @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 ent_c2,
double precis = 1.e-14) ;
// Accessors
// ---------
public:
/// Returns the equation of state
const Eos_bifluid& get_eos() const {return eos; } ;
/// Returns the enthalpy field for fluid 2
const Tenseur& get_ent2() const {return ent2 ; } ;
/// Returns the proper baryon density for fluid 2
const Tenseur& get_nbar2() const {return nbar2 ; } ;
/// Returns the coefficient Knn
const Tenseur& get_K_nn() const {return K_nn ; } ;
/// Returns the coefficient Knp
const Tenseur& get_K_np() const {return K_np ; } ;
/// Returns the coefficient Kpp
const Tenseur& get_K_pp() const {return K_pp ; } ;
/// Returns the "relative velocity" (squared) \f$\Delta^2\f$ of the two fluids
const Tenseur& get_delta_car() const {return delta_car ; } ;
/// Returns the Lorentz factor between the fluid 2 and Eulerian observers
const Tenseur& get_gam_euler2() const {return gam_euler2 ; } ;
/// Returns the rotation angular velocity of fluid 2(\c [f_unit] )
double get_omega2() const {return omega2 ; } ;
/// Returns the norm of the fluid 2 3-velocity with respect to the eulerian frame
const Tenseur& get_uuu2() const {return uuu2 ; } ;
// Outputs
// -------
public:
virtual void sauve(FILE *) const ; ///< Save in a file
/// 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 surface of fluid 1: returns a 2-D \c Itbl
* containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$.
* This surface is defined as the location where
* the density 1 (member \c nbar ) vanishes.
*/
virtual const Itbl& l_surf() const ;
/** Description of the surface of fluid 2: returns a 2-D \c Itbl
* containing the
* values of the domain index \e l on the surface at the
* collocation points in \f$(\theta', \phi')\f$.
* This surface is defined as the location where
* the density 2 (member \c nbar2 ) vanishes.
*/
const Itbl& l_surf2() const ;
/** Description of the surface of fluid 2: 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$(\theta', \phi')\f$.
* This surface is defined as the location where
* the density 2 (member \c nbar2 ) vanishes.
*/
const Tbl& xi_surf2() const ;
/// Coordinate radius for fluid 2 at \f$\phi=0\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq2() const ;
/// Coordinate radius for fluid 2 at \f$\phi=\pi/2\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq2_pis2() const ;
/// Coordinate radius for fluid 2 at \f$\phi=\pi\f$, \f$\theta=\pi/2\f$ [r_unit].
double ray_eq2_pi() const ;
/// Coordinate radius for fluid 2 at \f$\theta=0\f$ [r_unit].
double ray_pole2() const ;
/// Baryon mass of fluid 1
double mass_b1() const ;
/// Baryon mass of fluid 2
double mass_b2() const ;
virtual double mass_b() const ; ///< Total Baryon mass
virtual double mass_g() const ; ///< Gravitational mass
virtual double angu_mom() const ; ///< Angular momentum
/** Error on the virial identity GRV2.
* Given by the integral Eq. (4.6) in
* [Bonazzola, Gougoulhon, Salgado, Marck, A\&A \b 278 , 421 (1993)].
*/
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_circ2() const ; ///< Circumferential radius for fluid 2
virtual double area2() const ; ///< Surface area for fluid 2
virtual double mean_radius2() const ; ///< Mean radius for fluid 2
virtual double aplat2() const ; ///< Flatening r_pole/r_eq for fluid 2
/** 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.
* \e B_o 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 ;
virtual double angu_mom_1() const ; ///< Angular momentum of fluid 1
virtual double angu_mom_2() const ; ///< Angular momentum of fluid 2
virtual double angu_mom_1_part1_1() const ; ///< To compute In (1st version)
virtual double angu_mom_2_part1_1() const ; ///< To compute Ip (1st version)
virtual double angu_mom_1_part2_1() const ; ///< To compute Xn (1st version)
virtual double angu_mom_2_part2_1() const ; ///< To compute Xp (1st version)
virtual double angu_mom_1_part1_2() const ; ///< To compute In (2nd version)
virtual double angu_mom_2_part1_2() const ; ///< To compute Ip (2nd version)
virtual double angu_mom_1_part2_2() const ; ///< To compute Xn (2nd version)
virtual double angu_mom_2_part2_2() const ; ///< To compute Xp (2nd version)
// 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 ent2 , \c ener , \c press , \c K_nn , \c K_np , \c K_pp
* and \c a_car, which are supposed to be up to date. From these,
* the following fields are updated:
* \c delta_car , \c gam_euler , \c gam_euler2 , \c ener_euler ,
* \c s_euler , \c sphph_euler and \c j_euler .
*/
virtual void hydro_euler() ;
/** Computes the proper baryon and energy densities, as well as
* pressure and the coefficients Knn, Knp and Kpp, from the enthalpies
* and both velocities.
*/
virtual void equation_of_state() ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy for fluid 1
* @param ent_c2 [input] Central enthalpy for fluid 2
* @param omega0 [input] Requested angular velocity for fluid 1
* @param omega20 [input] Requested angular velocity for fluid 2
* @param ent_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy for fluid 1 at the
* outer boundary of each domain
* @param ent2_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy for fluid 2 at the
* outer boundary of each domain
* @param icontrol [input] Set of integer parameters (stored as a
* 1-D \c Itbl of size 5) 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) = mermax_poisson : maximum number of steps in
* \c Map_et::poisson
* @param control [input] Set of parameters (stored as a
* 1-D \c Tbl of size 5) 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) = omega2_ini : initial angular velocity,
* switched on only if \c mer_rot < 0 ,
* otherwise 0 is used
* \li \c control(3) = relax : relaxation factor in the main
* iteration
* \li \c control(4) = relax_poisson : relaxation factor in
* \c Map_et::poisson
* @param diff [output] 1-D \c Tbl of size 8 for the storage of
* some error indicators :
* \li \c diff(0) : Relative change in the enthalpy field 1
* between two successive steps
* \li \c diff(1) : Relative change in the enthalpy field 2
* between two successive steps
* \li \c diff(2) : Relative error in the resolution of the
* Poisson equation for \c nuf
* \li \c diff(3) : Relative error in the resolution of the
* Poisson equation for \c nuq
* \li \c diff(4) : Relative error in the resolution of the
* Poisson equation for \c dzeta
* \li \c diff(5) : Relative error in the resolution of the
* Poisson equation for \c tggg
* \li \c diff(6) : Relative error in the resolution of the
* equation for \c shift (x comp.)
* \li \c diff(7) : Relative error in the resolution of the
* equation for \c shift (y comp.)
*/
void equilibrium_bi(double ent_c, double ent_c2, double omega0,
double omega20, const Tbl& ent_limit,
const Tbl& ent2_limit, const Itbl& icontrol,
const Tbl& control, Tbl& diff,
int mer_mass, double mbar1_wanted, double mbar2_wanted,
double aexp_mass);
};
}
#endif
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