et_rot_global.C
/*
* Methods for computing global quantities within the class Etoile_rot
*
* (see file etoile.h for documentation)
*/
/*
* Copyright (c) 2000-2001 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
*
*/
char et_rot_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_global.C,v 1.9 2015/06/12 12:38:25 j_novak Exp $" ;
/*
* $Id: et_rot_global.C,v 1.9 2015/06/12 12:38:25 j_novak Exp $
* $Log: et_rot_global.C,v $
* Revision 1.9 2015/06/12 12:38:25 j_novak
* Implementation of the corrected formula for the quadrupole momentum.
*
* Revision 1.8 2015/06/10 14:37:44 a_sourie
* Corrected the formula for the quadrupole.
*
* Revision 1.7 2014/10/13 08:52:57 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.6 2014/10/06 15:13:09 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.5 2012/08/12 17:48:35 p_cerda
* Magnetstar: New classes for magnetstar. Allowing for non-equatorial symmetry in Etoile et al. Adding B_phi in Et_rot_mag.
*
* Revision 1.4 2004/03/25 10:29:06 j_novak
* All LORENE's units are now defined in the namespace Unites (in file unites.h).
*
* Revision 1.3 2003/11/03 16:47:13 e_gourgoulhon
* Corrected error in grv2() in the Newtonian case.
*
* Revision 1.2 2002/04/05 09:09:37 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 1.1.1.1 2001/11/20 15:19:28 e_gourgoulhon
* LORENE
*
* Revision 1.5 2000/11/19 18:52:09 eric
* grv2() operationnelle.
*
* Revision 1.4 2000/10/12 15:34:55 eric
* Calcul de la masse grav, de GRV3 et du moment quadrupolaire.
*
* Revision 1.3 2000/08/31 11:25:58 eric
* *** empty log message ***
*
* Revision 1.2 2000/08/25 12:28:16 eric
* *** empty log message ***
*
* Revision 1.1 2000/07/20 15:32:56 eric
* Initial revision
*
*
* $Header: /cvsroot/Lorene/C++/Source/Etoile/et_rot_global.C,v 1.9 2015/06/12 12:38:25 j_novak Exp $
*
*/
// Headers C
#include <cstdlib>
#include <cmath>
// Headers Lorene
#include "etoile.h"
#include "unites.h"
//--------------------------//
// Stellar surface //
//--------------------------//
namespace Lorene {
const Itbl& Etoile_rot::l_surf() const {
if (p_l_surf == 0x0) { // a new computation is required
assert(p_xi_surf == 0x0) ; // consistency check
int np = mp.get_mg()->get_np(0) ;
int nt = mp.get_mg()->get_nt(0) ;
p_l_surf = new Itbl(np, nt) ;
p_xi_surf = new Tbl(np, nt) ;
double ent0 = 0 ; // definition of the surface
double precis = 1.e-15 ;
int nitermax = 100 ;
int niter ;
(ent().va).equipot(ent0, nzet, precis, nitermax, niter, *p_l_surf,
*p_xi_surf) ;
}
return *p_l_surf ;
}
//--------------------------//
// Baryon mass //
//--------------------------//
double Etoile_rot::mass_b() const {
if (p_mass_b == 0x0) { // a new computation is required
if (relativistic) {
Cmp dens = a_car() * bbb() * gam_euler() * nbar() ;
dens.std_base_scal() ;
p_mass_b = new double( dens.integrale() ) ;
}
else{ // Newtonian case
assert(nbar.get_etat() == ETATQCQ) ;
p_mass_b = new double( nbar().integrale() ) ;
}
}
return *p_mass_b ;
}
//----------------------------//
// Gravitational mass //
//----------------------------//
double Etoile_rot::mass_g() const {
if (p_mass_g == 0x0) { // a new computation is required
if (relativistic) {
Tenseur source = nnn * (ener_euler + s_euler)
+ 2 * bbb * (ener_euler + press)
* tnphi * uuu ;
source = a_car * bbb * source ;
source.set_std_base() ;
p_mass_g = new double( source().integrale() ) ;
}
else{ // Newtonian case
p_mass_g = new double( mass_b() ) ; // in the Newtonian case
// M_g = M_b
}
}
return *p_mass_g ;
}
//----------------------------//
// Angular momentum //
//----------------------------//
double Etoile_rot::angu_mom() const {
if (p_angu_mom == 0x0) { // a new computation is required
Cmp dens = uuu() ;
dens.mult_r() ; // Multiplication by
dens.va = (dens.va).mult_st() ; // r sin(theta)
if (relativistic) {
dens = a_car() * b_car() * (ener_euler() + press())
* dens ;
}
else { // Newtonian case
dens = nbar() * dens ;
}
dens.std_base_scal() ;
p_angu_mom = new double( dens.integrale() ) ;
}
return *p_angu_mom ;
}
//----------------------------//
// T/W //
//----------------------------//
double Etoile_rot::tsw() const {
if (p_tsw == 0x0) { // a new computation is required
double tcin = 0.5 * omega * angu_mom() ;
if (relativistic) {
Cmp dens = a_car() * bbb() * gam_euler() * ener() ;
dens.std_base_scal() ;
double mass_p = dens.integrale() ;
p_tsw = new double( tcin / ( mass_p + tcin - mass_g() ) ) ;
}
else { // Newtonian case
Cmp dens = 0.5 * nbar() * logn() ;
dens.std_base_scal() ;
double wgrav = dens.integrale() ;
p_tsw = new double( tcin / fabs(wgrav) ) ;
}
}
return *p_tsw ;
}
//----------------------------//
// GRV2 //
//----------------------------//
double Etoile_rot::grv2() const {
using namespace Unites ;
if (p_grv2 == 0x0) { // a new computation is required
Tenseur sou_m(mp) ;
if (relativistic) {
sou_m = 2 * qpig * a_car * (press + (ener_euler+press)
* uuu*uuu ) ;
}
else {
sou_m = 2 * qpig * (press + nbar * uuu*uuu ) ;
}
Tenseur sou_q = 1.5 * ak_car
- flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() ) ;
p_grv2 = new double( double(1) - lambda_grv2(sou_m(), sou_q()) ) ;
}
return *p_grv2 ;
}
//----------------------------//
// GRV3 //
//----------------------------//
double Etoile_rot::grv3(ostream* ost) const {
using namespace Unites ;
if (p_grv3 == 0x0) { // a new computation is required
Tenseur source(mp) ;
// Gravitational term [cf. Eq. (43) of Gourgoulhon & Bonazzola
// ------------------ Class. Quantum Grav. 11, 443 (1994)]
if (relativistic) {
Tenseur alpha = dzeta - logn ;
Tenseur beta = log( bbb ) ;
beta.set_std_base() ;
source = 0.75 * ak_car
- flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() )
+ 0.5 * flat_scalar_prod(alpha.gradient_spher(),
beta.gradient_spher() ) ;
Cmp aa = alpha() - 0.5 * beta() ;
Cmp daadt = aa.srdsdt() ; // 1/r d/dth
// What follows is valid only for a mapping of class Map_radial :
const Map_radial* mpr = dynamic_cast<const Map_radial*>(&mp) ;
if (mpr == 0x0) {
cout << "Etoile_rot::grv3: the mapping does not belong"
<< " to the class Map_radial !" << endl ;
abort() ;
}
// Computation of 1/tan(theta) * 1/r daa/dtheta
if (daadt.get_etat() == ETATQCQ) {
Valeur& vdaadt = daadt.va ;
vdaadt = vdaadt.ssint() ; // division by sin(theta)
vdaadt = vdaadt.mult_ct() ; // multiplication by cos(theta)
}
Cmp temp = aa.dsdr() + daadt ;
temp = ( bbb() - a_car()/bbb() ) * temp ;
temp.std_base_scal() ;
// Division by r
Valeur& vtemp = temp.va ;
vtemp = vtemp.sx() ; // division by xi in the nucleus
// Id in the shells
// division by xi-1 in the ZEC
vtemp = (mpr->xsr) * vtemp ; // multiplication by xi/r in the nucleus
// by 1/r in the shells
// by r(xi-1) in the ZEC
// In the ZEC, a multiplication by r has been performed instead
// of the division:
temp.set_dzpuis( temp.get_dzpuis() + 2 ) ;
source = bbb() * source() + 0.5 * temp ;
}
else{
source = - 0.5 * flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() ) ;
}
source.set_std_base() ;
double int_grav = source().integrale() ;
// Matter term
// -----------
if (relativistic) {
source = qpig * a_car * bbb * s_euler ;
}
else{
source = qpig * ( 3 * press + nbar * uuu * uuu ) ;
}
source.set_std_base() ;
double int_mat = source().integrale() ;
// Virial error
// ------------
if (ost != 0x0) {
*ost << "Etoile_rot::grv3 : gravitational term : " << int_grav
<< endl ;
*ost << "Etoile_rot::grv3 : matter term : " << int_mat
<< endl ;
}
p_grv3 = new double( (int_grav + int_mat) / int_mat ) ;
}
return *p_grv3 ;
}
//----------------------------//
// R_circ //
//----------------------------//
double Etoile_rot::r_circ() const {
if (p_r_circ == 0x0) { // a new computation is required
// Index of the point at phi=0, theta=pi/2 at the surface of the star:
const Mg3d* mg = mp.get_mg() ;
int l_b = nzet - 1 ;
int i_b = mg->get_nr(l_b) - 1 ;
int j_b;
if (mg->get_type_t() == SYM) {
j_b = mg->get_nt(l_b) - 1 ;
}else{
j_b = (mg->get_nt(l_b) - 1)/2 ;
}
int k_b = 0 ;
p_r_circ = new double( bbb()(l_b, k_b, j_b, i_b) * ray_eq() ) ;
}
return *p_r_circ ;
}
//----------------------------//
// Surface area //
//----------------------------//
double Etoile_rot::area() const {
if (p_area == 0x0) { // a new computation is required
const Mg3d& mg = *(mp.get_mg()) ;
int np = mg.get_np(0) ;
int nt = mg.get_nt(0) ;
assert(np == 1) ; //Only valid for axisymmetric configurations
const Map_radial* mp_rad = dynamic_cast<const Map_radial*>(&mp) ;
assert(mp_rad != 0x0) ;
Valeur va_r(mg.get_angu()) ;
va_r.annule_hard() ;
Itbl lsurf = l_surf() ;
Tbl xisurf = xi_surf() ;
for (int k=0; k<np; k++) {
for (int j=0; j<nt; j++) {
int l_star = lsurf(k, j) ;
double xi_star = xisurf(k, j) ;
va_r.set(0, k, j, 0) = mp_rad->val_r_jk(l_star, xi_star, j, k) ;
}
}
va_r.std_base_scal() ;
Valeur integ(mg.get_angu()) ;
Valeur dr = va_r.dsdt() ;
integ = sqrt(va_r*va_r + dr*dr) ;
Cmp aaaa = get_a_car()() ;
Valeur a2 = aaaa.va ; a2.std_base_scal() ;
Cmp bbbb = get_bbb()() ;
Valeur b = bbbb.va ; b.std_base_scal() ;
for (int k=0; k<np; k++) {
for (int j=0; j<nt; j++) {
integ.set(0, k, j, 0) *= sqrt(a2.val_point_jk(lsurf(k, j), xisurf(k, j), j, k))
* b.val_point_jk(lsurf(k, j), xisurf(k, j), j, k) * va_r(0, k, j, 0) ;
}
}
integ.std_base_scal() ;
Valeur integ2 = integ.mult_st() ;
double surftot = 0. ;
for (int j=0; j<nt; j++) {
surftot += (*integ2.c_cf)(0, 0, j, 0) / double(2*j+1) ;
}
p_area = new double( 4*M_PI*surftot) ;
}
return *p_area ;
}
double Etoile_rot::mean_radius() const {
return sqrt(area()/(4*M_PI)) ;
}
//----------------------------//
// Flattening //
//----------------------------//
double Etoile_rot::aplat() const {
if (p_aplat == 0x0) { // a new computation is required
p_aplat = new double( ray_pole() / ray_eq() ) ;
}
return *p_aplat ;
}
//----------------------------//
// Z_eq_f //
//----------------------------//
double Etoile_rot::z_eqf() const {
if (p_z_eqf == 0x0) { // a new computation is required
// Index of the point at phi=0, theta=pi/2 at the surface of the star:
const Mg3d* mg = mp.get_mg() ;
int l_b = nzet - 1 ;
int i_b = mg->get_nr(l_b) - 1 ;
int j_b;
if (mg->get_type_t() == SYM) {
j_b = mg->get_nt(l_b) - 1 ;
}else{
j_b = (mg->get_nt(l_b) - 1)/2 ;
}
int k_b = 0 ;
double u_eq = uuu()(l_b, k_b, j_b, i_b) ;
double n_eq = nnn()(l_b, k_b, j_b, i_b) ;
double nphi_eq = nphi()(l_b, k_b, j_b, i_b) ;
p_z_eqf = new double( sqrt((1.-u_eq)/(1.+u_eq))
/ (n_eq + nphi_eq * r_circ() )
- 1. ) ;
}
return *p_z_eqf ;
}
//----------------------------//
// Z_eq_b //
//----------------------------//
double Etoile_rot::z_eqb() const {
if (p_z_eqb == 0x0) { // a new computation is required
// Index of the point at phi=0, theta=pi/2 at the surface of the star:
const Mg3d* mg = mp.get_mg() ;
int l_b = nzet - 1 ;
int i_b = mg->get_nr(l_b) - 1 ;
int j_b;
if (mg->get_type_t() == SYM) {
j_b = mg->get_nt(l_b) - 1 ;
}else{
j_b = (mg->get_nt(l_b) - 1) / 2 ;
}
int k_b = 0 ;
double u_eq = uuu()(l_b, k_b, j_b, i_b) ;
double n_eq = nnn()(l_b, k_b, j_b, i_b) ;
double nphi_eq = nphi()(l_b, k_b, j_b, i_b) ;
p_z_eqb = new double( sqrt((1.+u_eq)/(1.-u_eq))
/ (n_eq - nphi_eq * r_circ() )
- 1. ) ;
}
return *p_z_eqb ;
}
//----------------------------//
// Z_pole //
//----------------------------//
double Etoile_rot::z_pole() const {
if (p_z_pole == 0x0) { // a new computation is required
double n_pole = nnn().val_point(ray_pole(), 0., 0.) ;
p_z_pole = new double( 1. / n_pole - 1. ) ;
}
return *p_z_pole ;
}
//----------------------------//
// Quadrupole moment //
//----------------------------//
double Etoile_rot::mom_quad() const {
using namespace Unites ;
if (p_mom_quad == 0x0) { // a new computation is required
p_mom_quad = new double( mom_quad_old() ) ;
if (relativistic) {
double b = mom_quad_Bo() / ( mass_g() * mass_g() ) ;
*p_mom_quad -= 4./3. * ( 1./4. + b ) * pow(mass_g(), 3) * ggrav * ggrav ;
}
}
return *p_mom_quad ;
}
double Etoile_rot::mom_quad_Bo() const {
using namespace Unites ;
if (p_mom_quad_Bo == 0x0) { // a new computation is required
Cmp dens(mp) ;
dens = press() ;
dens = a_car() * bbb() * nnn() * dens ;
dens.mult_rsint() ;
dens.std_base_scal() ;
p_mom_quad_Bo = new double( - 32. * dens.integrale() / qpig ) ;
}
return *p_mom_quad_Bo ;
}
double Etoile_rot::mom_quad_old() const {
using namespace Unites ;
if (p_mom_quad_old == 0x0) { // a new computation is required
// Source for of the Poisson equation for nu
// -----------------------------------------
Tenseur source(mp) ;
if (relativistic) {
Tenseur beta = log(bbb) ;
beta.set_std_base() ;
source = qpig * a_car *( ener_euler + s_euler )
+ ak_car - flat_scalar_prod(logn.gradient_spher(),
logn.gradient_spher() + beta.gradient_spher()) ;
}
else {
source = qpig * nbar ;
}
source.set_std_base() ;
// Multiplication by -r^2 P_2(cos(theta))
// [cf Eq.(7) of Salgado et al. Astron. Astrophys. 291, 155 (1994) ]
// ------------------------------------------------------------------
// Multiplication by r^2 :
// ----------------------
Cmp& csource = source.set() ;
csource.mult_r() ;
csource.mult_r() ;
if (csource.check_dzpuis(2)) {
csource.inc2_dzpuis() ;
}
// Muliplication by cos^2(theta) :
// -----------------------------
Cmp temp = csource ;
// What follows is valid only for a mapping of class Map_radial :
assert( dynamic_cast<const Map_radial*>(&mp) != 0x0 ) ;
if (temp.get_etat() == ETATQCQ) {
Valeur& vtemp = temp.va ;
vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
vtemp = vtemp.mult_ct() ; // multiplication by cos(theta)
}
// Muliplication by -P_2(cos(theta)) :
// ----------------------------------
source = 0.5 * source() - 1.5 * temp ;
// Final result
// ------------
p_mom_quad_old = new double(- source().integrale() / qpig ) ;
}
return *p_mom_quad_old ;
}
}
Lorene::Cmp
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
Lorene::Cmp::mult_rsint
void mult_rsint()
Multiplication by .
Definition cmp_r_manip.C:116
Lorene::Cmp::get_etat
int get_etat() const
Returns the logical state.
Definition cmp.h:899
Lorene::Cmp::va
Valeur va
The numerical value of the Cmp.
Definition cmp.h:464
Lorene::Cmp::std_base_scal
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition cmp.C:644
Lorene::Cmp::get_dzpuis
int get_dzpuis() const
Returns dzpuis.
Definition cmp.h:903
Lorene::Cmp::mult_r
void mult_r()
Multiplication by r everywhere.
Definition cmp_r_manip.C:91
Lorene::Cmp::inc2_dzpuis
void inc2_dzpuis()
Increases by 2 the value of dzpuis and changes accordingly the values of the Cmp in the external comp...
Definition cmp_r_manip.C:192
Lorene::Cmp::set_dzpuis
void set_dzpuis(int)
Set a value to dzpuis.
Definition cmp.C:654
Lorene::Cmp::integrale
double integrale() const
Computes the integral over all space of *this .
Definition cmp_integ.C:55
Lorene::Cmp::srdsdt
const Cmp & srdsdt() const
Returns of *this .
Definition cmp_deriv.C:105
Lorene::Cmp::check_dzpuis
bool check_dzpuis(int dzi) const
Returns false if the last domain is compactified and *this is not zero in this domain and dzpuis is n...
Definition cmp.C:715
Lorene::Cmp::dsdr
const Cmp & dsdr() const
Returns of *this .
Definition cmp_deriv.C:84
Lorene::Etoile_rot::uuu
Tenseur uuu
Norm of u_euler.
Definition etoile.h:1518
Lorene::Etoile_rot::omega
double omega
Rotation angular velocity ([f_unit] ).
Definition etoile.h:1501
Lorene::Etoile_rot::p_z_pole
double * p_z_pole
Redshift factor at North pole.
Definition etoile.h:1640
Lorene::Etoile_rot::mom_quad
virtual double mom_quad() const
Quadrupole moment.
Definition et_rot_global.C:600
Lorene::Etoile_rot::p_z_eqf
double * p_z_eqf
Forward redshift factor at equator.
Definition etoile.h:1638
Lorene::Etoile_rot::r_circ
virtual double r_circ() const
Circumferential radius.
Definition et_rot_global.C:390
Lorene::Etoile_rot::logn
Tenseur & logn
Metric potential = logn_auto.
Definition etoile.h:1521
Lorene::Etoile_rot::l_surf
virtual const Itbl & l_surf() const
Description of the stellar surface: returns a 2-D Itbl containing the values of the domain index l on...
Definition et_rot_global.C:95
Lorene::Etoile_rot::p_mom_quad_old
double * p_mom_quad_old
Part of the quadrupole moment.
Definition etoile.h:1642
Lorene::Etoile_rot::p_z_eqb
double * p_z_eqb
Backward redshift factor at equator.
Definition etoile.h:1639
Lorene::Etoile_rot::mass_g
virtual double mass_g() const
Gravitational mass.
Definition et_rot_global.C:157
Lorene::Etoile_rot::p_r_circ
double * p_r_circ
Circumferential radius.
Definition etoile.h:1635
Lorene::Etoile_rot::mom_quad_Bo
virtual double mom_quad_Bo() const
Part of the quadrupole moment.
Definition et_rot_global.C:618
Lorene::Etoile_rot::aplat
virtual double aplat() const
Flatening r_pole/r_eq.
Definition et_rot_global.C:496
Lorene::Etoile_rot::grv3
virtual double grv3(ostream *ost=0x0) const
Error on the virial identity GRV3.
Definition et_rot_global.C:285
Lorene::Etoile_rot::get_bbb
const Tenseur & get_bbb() const
Returns the metric factor B.
Definition etoile.h:1712
Lorene::Etoile_rot::tsw
virtual double tsw() const
Ratio T/W.
Definition et_rot_global.C:220
Lorene::Etoile_rot::nphi
Tenseur nphi
Metric coefficient .
Definition etoile.h:1510
Lorene::Etoile_rot::mass_b
virtual double mass_b() const
Baryon mass.
Definition et_rot_global.C:125
Lorene::Etoile_rot::lambda_grv2
static double lambda_grv2(const Cmp &sou_m, const Cmp &sou_q)
Computes the coefficient which ensures that the GRV2 virial identity is satisfied.
Definition et_rot_lambda_grv2.C:79
Lorene::Etoile_rot::bbb
Tenseur bbb
Metric factor B.
Definition etoile.h:1504
Lorene::Etoile_rot::p_area
double * p_area
Surface area.
Definition etoile.h:1636
Lorene::Etoile_rot::ak_car
Tenseur ak_car
Scalar .
Definition etoile.h:1586
Lorene::Etoile_rot::dzeta
Tenseur & dzeta
Metric potential = beta_auto.
Definition etoile.h:1534
Lorene::Etoile_rot::mean_radius
virtual double mean_radius() const
Mean radius.
Definition et_rot_global.C:472
Lorene::Etoile_rot::p_grv3
double * p_grv3
Error on the virial identity GRV3.
Definition etoile.h:1634
Lorene::Etoile_rot::p_grv2
double * p_grv2
Error on the virial identity GRV2.
Definition etoile.h:1633
Lorene::Etoile_rot::p_aplat
double * p_aplat
Flatening r_pole/r_eq.
Definition etoile.h:1637
Lorene::Etoile_rot::p_mom_quad_Bo
double * p_mom_quad_Bo
Part of the quadrupole moment.
Definition etoile.h:1643
Lorene::Etoile_rot::grv2
virtual double grv2() const
Error on the virial identity GRV2.
Definition et_rot_global.C:254
Lorene::Etoile_rot::p_mom_quad
double * p_mom_quad
Quadrupole moment.
Definition etoile.h:1641
Lorene::Etoile_rot::area
virtual double area() const
Surface area.
Definition et_rot_global.C:420
Lorene::Etoile_rot::p_angu_mom
double * p_angu_mom
Angular momentum.
Definition etoile.h:1631
Lorene::Etoile_rot::angu_mom
virtual double angu_mom() const
Angular momentum.
Definition et_rot_global.C:188
Lorene::Etoile_rot::z_eqf
virtual double z_eqf() const
Forward redshift factor at equator.
Definition et_rot_global.C:513
Lorene::Etoile_rot::mom_quad_old
virtual double mom_quad_old() const
Part of the quadrupole moment.
Definition et_rot_global.C:641
Lorene::Etoile_rot::p_tsw
double * p_tsw
Ratio T/W.
Definition etoile.h:1632
Lorene::Etoile_rot::b_car
Tenseur b_car
Square of the metric factor B.
Definition etoile.h:1507
Lorene::Etoile_rot::z_eqb
virtual double z_eqb() const
Backward redshift factor at equator.
Definition et_rot_global.C:545
Lorene::Etoile_rot::tnphi
Tenseur tnphi
Component of the shift vector.
Definition etoile.h:1515
Lorene::Etoile_rot::z_pole
virtual double z_pole() const
Redshift factor at North pole.
Definition et_rot_global.C:580
Lorene::Etoile::nzet
int nzet
Number of domains of *mp occupied by the star.
Definition etoile.h:432
Lorene::Etoile::p_mass_b
double * p_mass_b
Baryon mass.
Definition etoile.h:547
Lorene::Etoile::p_mass_g
double * p_mass_g
Gravitational mass.
Definition etoile.h:548
Lorene::Etoile::p_xi_surf
Tbl * p_xi_surf
Description of the stellar surface: 2-D Tbl containing the values of the radial coordinate on the su...
Definition etoile.h:545
Lorene::Etoile::ray_eq
double ray_eq() const
Coordinate radius at , [r_unit].
Definition etoile_global.C:120
Lorene::Etoile::nnn
Tenseur nnn
Total lapse function.
Definition etoile.h:509
Lorene::Etoile::nbar
Tenseur nbar
Baryon density in the fluid frame.
Definition etoile.h:459
Lorene::Etoile::p_l_surf
Itbl * p_l_surf
Description of the stellar surface: 2-D Itbl containing the values of the domain index l on the surfa...
Definition etoile.h:539
Lorene::Etoile::gam_euler
Tenseur gam_euler
Lorentz factor between the fluid and Eulerian observers.
Definition etoile.h:471
Lorene::Etoile::mp
Map & mp
Mapping associated with the star.
Definition etoile.h:429
Lorene::Etoile::ener
Tenseur ener
Total energy density in the fluid frame.
Definition etoile.h:460
Lorene::Etoile::get_a_car
const Tenseur & get_a_car() const
Returns the total conformal factor .
Definition etoile.h:733
Lorene::Etoile::press
Tenseur press
Fluid pressure.
Definition etoile.h:461
Lorene::Etoile::relativistic
bool relativistic
Indicator of relativity: true for a relativistic star, false for a Newtonian one.
Definition etoile.h:437
Lorene::Etoile::ener_euler
Tenseur ener_euler
Total energy density in the Eulerian frame.
Definition etoile.h:465
Lorene::Etoile::s_euler
Tenseur s_euler
Trace of the stress tensor in the Eulerian frame.
Definition etoile.h:468
Lorene::Etoile::ent
Tenseur ent
Log-enthalpy (relativistic case) or specific enthalpy (Newtonian case).
Definition etoile.h:457
Lorene::Etoile::xi_surf
const Tbl & xi_surf() const
Description of the stellar surface: returns a 2-D Tbl containing the values of the radial coordinat...
Definition etoile_global.C:101
Lorene::Etoile::a_car
Tenseur a_car
Total conformal factor .
Definition etoile.h:515
Lorene::Etoile::ray_pole
double ray_pole() const
Coordinate radius at [r_unit].
Definition etoile_global.C:415
Lorene::Itbl
Basic integer array class.
Definition itbl.h:122
Lorene::Map_radial
Base class for pure radial mappings.
Definition map.h:1536
Lorene::Map_radial::xsr
Coord xsr
in the nucleus; \ 1/R in the non-compactified shells; \ in the compactified outer domain.
Definition map.h:1549
Lorene::Map_radial::val_r_jk
virtual double val_r_jk(int l, double xi, int j, int k) const =0
Returns the value of the radial coordinate r for a given and a given collocation point in in a give...
Lorene::Mg3d
Multi-domain grid.
Definition grilles.h:273
Lorene::Mg3d::get_angu
const Mg3d * get_angu() const
Returns the pointer on the associated angular grid.
Definition mg3d.C:473
Lorene::Mg3d::get_type_t
int get_type_t() const
Returns the type of sampling in the direction: SYM : : symmetry with respect to the equatorial pl...
Definition grilles.h:485
Lorene::Mg3d::get_np
int get_np(int l) const
Returns the number of points in the azimuthal direction ( ) in domain no. l.
Definition grilles.h:462
Lorene::Mg3d::get_nt
int get_nt(int l) const
Returns the number of points in the co-latitude direction ( ) in domain no. l.
Definition grilles.h:457
Lorene::Mg3d::get_nr
int get_nr(int l) const
Returns the number of points in the radial direction ( ) in domain no. l.
Definition grilles.h:452
Lorene::Tbl
Basic array class.
Definition tbl.h:161
Lorene::Tenseur
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Lorene::Tenseur::set
Cmp & set()
Read/write for a scalar (see also operator=(const Cmp&) ).
Definition tenseur.C:824
Lorene::Tenseur::set_std_base
void set_std_base()
Set the standard spectal basis of decomposition for each component.
Definition tenseur.C:1170
Lorene::Tenseur::gradient_spher
const Tenseur & gradient_spher() const
Returns the gradient of *this (Spherical coordinates) (scalar field only).
Definition tenseur.C:1548
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Lorene::Valeur::mult_ct
const Valeur & mult_ct() const
Returns applied to *this.
Definition valeur_mult_ct.C:98
Lorene::Valeur::val_point_jk
double val_point_jk(int l, double x, int j, int k) const
Computes the value of the field represented by *this at an arbitrary point in , but collocation point...
Definition valeur.C:900
Lorene::Valeur::sx
const Valeur & sx() const
Returns (r -sampling = RARE ) \ Id (r sampling = FIN ) \ (r -sampling = UNSURR ).
Definition valeur_sx.C:110
Lorene::Valeur::dsdt
const Valeur & dsdt() const
Returns of *this.
Definition valeur_dsdt.C:112
Lorene::Valeur::set
Tbl & set(int l)
Read/write of the value in a given domain (configuration space).
Definition valeur.h:363
Lorene::Valeur::ssint
const Valeur & ssint() const
Returns of *this.
Definition valeur_ssint.C:112
Lorene::Valeur::c_cf
Mtbl_cf * c_cf
Coefficients of the spectral expansion of the function.
Definition valeur.h:302
Lorene::Valeur::mult_st
const Valeur & mult_st() const
Returns applied to *this.
Definition valeur_mult_st.C:97
Lorene::Valeur::std_base_scal
void std_base_scal()
Sets the bases for spectral expansions (member base ) to the standard ones for a scalar.
Definition valeur.C:824
Lorene::Valeur::annule_hard
void annule_hard()
Sets the Valeur to zero in a hard way.
Definition valeur.C:723
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::pow
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Lorene::log
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
Lorene::flat_scalar_prod
Tenseur flat_scalar_prod(const Tenseur &t1, const Tenseur &t2)
Scalar product of two Tenseur when the metric is : performs the contraction of the last index of t1 w...
Definition tenseur_operateur.C:653
Lorene
Lorene prototypes.
Definition app_hor.h:64
Lorene::integrale
virtual Tbl * integrale(const Cmp &) const =0
Computes the integral over all space of a Cmp .
Unites
Standard units of space, time and mass.