compobj_QI_global.C
/*
* Method of class Compobj_QI to compute the location of the ISCO
*
* (see file compobj.h for documentation).
*
*/
/*
* Copyright (c) 2012 Odele Straub, Claire Some, 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 compobj_QI_global_C[] = "$Header: /cvsroot/Lorene/C++/Source/Compobj/compobj_QI_global.C,v 1.11 2014/10/13 08:52:49 j_novak Exp $" ;
/*
* $Id: compobj_QI_global.C,v 1.11 2014/10/13 08:52:49 j_novak Exp $
* $Log: compobj_QI_global.C,v $
* Revision 1.11 2014/10/13 08:52:49 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.10 2014/10/06 15:13:04 j_novak
* Modified #include directives to use c++ syntax.
*
* Revision 1.9 2014/02/12 16:46:54 o_straub
* Rmb : cleaner prompt
*
* Revision 1.8 2014/01/14 20:52:53 e_gourgoulhon
* ISCO searched downwards
*
* Revision 1.7 2014/01/14 16:35:46 e_gourgoulhon
* Changed output printing in ISCO search
*
* Revision 1.6 2013/11/13 11:20:01 j_novak
* Minor correction to compile with older versions of g++
*
* Revision 1.5 2013/07/25 19:44:11 o_straub
* calculation of the marginally bound radius
*
* Revision 1.4 2013/04/04 15:32:32 e_gourgoulhon
* Better computation of the ISCO
*
* Revision 1.3 2012/11/22 16:04:51 c_some
* Minor modifications
*
* Revision 1.2 2012/11/21 14:53:45 c_some
* corrected mom_euler
*
* Revision 1.1 2012/11/16 16:14:11 c_some
* New class Compobj_QI
*
*
* $Header: /cvsroot/Lorene/C++/Source/Compobj/compobj_QI_global.C,v 1.11 2014/10/13 08:52:49 j_novak Exp $
*
*/
// Headers C
#include <cmath>
// Headers Lorene
#include "compobj.h"
#include "param.h"
#include "utilitaires.h"
namespace Lorene {
double funct_compobj_QI_isco(double, const Param&) ;
double funct_compobj_QI_rmb(double, const Param&) ;
//----------------------------//
// Angular momentum //
//----------------------------//
double Compobj_QI::angu_mom() const {
if (p_angu_mom == 0x0) { // a new computation is required
cerr << "Compobj_QI::angu_mom() : not implemented yet !" << endl ; //## provisory
abort() ;
}
return *p_angu_mom ;
}
//=============================================================================
// r_isco()
//=============================================================================
double Compobj_QI::r_isco(int lmin, ostream* ost) const {
if (p_r_isco == 0x0) { // a new computation is required
// First and second derivatives of metric functions
// ------------------------------------------------
int nzm1 = mp.get_mg()->get_nzone() - 1 ;
Scalar dnphi = nphi.dsdr() ;
dnphi.annule_domain(nzm1) ;
Scalar ddnphi = dnphi.dsdr() ; // d^2/dr^2 N^phi
Scalar tmp = nn.dsdr() ;
tmp.annule_domain(nzm1) ;
Scalar ddnnn = tmp.dsdr() ; // d^2/dr^2 N
tmp = bbb.dsdr() ;
tmp.annule_domain(nzm1) ;
Scalar ddbbb = tmp.dsdr() ; // d^2/dr^2 B
// Constructing the velocity of a particle corotating with the star
// ----------------------------------------------------------------
Scalar bdlog = bbb.dsdr() / bbb ;
Scalar ndlog = nn.dsdr() / nn ;
Scalar bsn = bbb / nn ;
Scalar r(mp) ;
r = mp.r ;
Scalar r2= r*r ;
bdlog.annule_domain(nzm1) ;
ndlog.annule_domain(nzm1) ;
bsn.annule_domain(nzm1) ;
r2.annule_domain(nzm1) ;
// ucor_plus - the velocity of corotating particle on the circular orbit
Scalar ucor_plus = (r2 * bsn * dnphi +
sqrt ( r2 * r2 * bsn *bsn * dnphi * dnphi +
4 * r2 * bdlog * ndlog + 4 * r * ndlog) ) /
2 / (1 + r * bdlog ) ;
Scalar factor_u2 = r2 * (2 * ddbbb / bbb - 2 * bdlog * bdlog +
4 * bdlog * ndlog ) +
2 * r2 * r2 * bsn * bsn * dnphi * dnphi +
4 * r * ( ndlog - bdlog ) - 6 ;
Scalar factor_u1 = 2 * r * r2 * bsn * ( 2 * ( ndlog - bdlog ) *
dnphi - ddnphi ) ;
Scalar factor_u0 = - r2 * ( 2 * ddnnn / nn - 2 * ndlog * ndlog +
4 * bdlog * ndlog ) ;
// Scalar field the zero of which will give the marginally stable orbit
Scalar orbit = factor_u2 * ucor_plus * ucor_plus +
factor_u1 * ucor_plus + factor_u0 ;
orbit.std_spectral_base() ;
// Search for the zero
// -------------------
double r_ms, theta_ms, phi_ms, xi_ms,
xi_min = -1, xi_max = 1;
int l_ms = lmin, l ;
bool find_status = false ;
const Valeur& vorbit = orbit.get_spectral_va() ;
// Preliminary location of the zero
// of the orbit function with an error = 0.01
theta_ms = M_PI / 2. ; // pi/2
phi_ms = 0. ;
for(l = nzm1-1; l >= lmin; l--) {
xi_min = -1. ;
xi_max = 1. ;
double resloc_old ;
double xi_f = xi_min;
double resloc = vorbit.val_point(l, xi_min, theta_ms, phi_ms) ;
for (int iloc=0; iloc<200; iloc++) {
xi_f = xi_f + 0.01 ;
resloc_old = resloc ;
resloc = vorbit.val_point(l, xi_f, theta_ms, phi_ms) ;
if ( resloc * resloc_old < double(0) ) {
xi_min = xi_f - 0.01 ;
xi_max = xi_f ;
l_ms = l ;
find_status = true ;
break ;
}
}
if (find_status) break ;
}
Param par_ms ;
par_ms.add_int(l_ms) ;
par_ms.add_scalar(orbit) ;
if(find_status) {
double precis_ms = 1.e-12 ; // precision in the determination of xi_ms
int nitermax_ms = 100 ; // max number of iterations
int niter ;
xi_ms = zerosec(funct_compobj_QI_isco, par_ms, xi_min, xi_max,
precis_ms, nitermax_ms, niter) ;
if (ost != 0x0) {
*ost << "ISCO search: " << endl ;
*ost << " Domain number: " << l_ms << endl ;
*ost << " xi_min, xi_max : " << xi_min << " , " << xi_max << endl ;
*ost << " number of iterations used in zerosec: " << niter << endl ;
*ost << " zero found at xi = " << xi_ms << endl ;
}
r_ms = mp.val_r(l_ms, xi_ms, theta_ms, phi_ms) ;
} else {
// ISCO not found
r_ms = -1 ;
xi_ms = -1 ;
l_ms = lmin ;
}
p_r_isco = new double (r_ms) ;
// p_r_isco = new double (
// (bbb.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms, phi_ms) * r_ms
// ) ;
// Determination of the frequency at the marginally stable orbit
// -------------------------------------------------------------
ucor_plus.std_spectral_base() ;
double ucor_msplus = (ucor_plus.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms,
phi_ms) ;
double nobrs = (bsn.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms, phi_ms) ;
double nphirs = (nphi.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms, phi_ms) ;
p_f_isco = new double ( ( ucor_msplus / nobrs / r_ms + nphirs ) /
(double(2) * M_PI) ) ;
// Specific angular momentum on ms orbit
// -------------------------------------
p_lspec_isco=new double (ucor_msplus/sqrt(1.-ucor_msplus*ucor_msplus)*
((bbb.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms, phi_ms)) * r_ms );
// Specific energy on ms orbit
// ---------------------------
p_espec_isco=new double (( 1./nobrs / r_ms / ucor_msplus + nphirs) *
(ucor_msplus/sqrt(1.-ucor_msplus*ucor_msplus)*
((bbb.get_spectral_va()).val_point(l_ms, xi_ms, theta_ms, phi_ms)) * r_ms ));
} // End of computation
return *p_r_isco ;
}
//=============================================================================
// f_isco()
//=============================================================================
double Compobj_QI::f_isco(int lmin) const {
if (p_f_isco == 0x0) { // a new computation is required
r_isco(lmin) ; // f_isco is computed in the method r_isco()
assert(p_f_isco != 0x0) ;
}
return *p_f_isco ;
}
//=============================================================================
// lspec_isco()
//=============================================================================
double Compobj_QI::lspec_isco(int lmin) const {
if (p_lspec_isco == 0x0) { // a new computation is required
r_isco(lmin) ; // lspec_isco is computed in the method r_isco()
assert(p_lspec_isco != 0x0) ;
}
return *p_lspec_isco ;
}
//=============================================================================
// espec_isco()
//=============================================================================
double Compobj_QI::espec_isco(int lmin) const {
if (p_espec_isco == 0x0) { // a new computation is required
r_isco(lmin) ; // espec_isco is computed in the method r_isco()
assert(p_espec_isco != 0x0) ;
}
return *p_espec_isco ;
}
//=============================================================================
// r_mb()
//=============================================================================
double Compobj_QI::r_mb(int lmin, ostream* ost) const {
if (p_r_mb == 0x0) { // a new computation is required
// Coefficients of the effective potential (A) and its derivative (B)
// ------------------------------------------------
int nzm1 = mp.get_mg()->get_nzone() - 1 ;
Scalar r(mp) ;
r = mp.r ;
Scalar r2 = r*r ;
r2.annule_domain(nzm1) ;
Scalar ndn = nn*nn.dsdr() ;
ndn.annule_domain(nzm1) ;
// Scalar V_eff = A1 + A2 * E^2 + A3 * E * L + A4 * L^2 ;
// Scalar dV_eff = B1 + B2 * E^2 + B3 * E * L + B4 * L^2 ;
Scalar A1 =-bbb*bbb * nn*nn * r2 ;
Scalar A2 = bbb*bbb * r2 ;
Scalar A3 =-2. * bbb*bbb * r2 * nphi ;
Scalar A4 =-nn*nn + bbb*bbb * r2 * nphi*nphi ;
Scalar B1 =-2.*r * bbb*bbb * nn*nn - 2.*r2 * bbb*bbb.dsdr() * nn*nn - 2.*r2 * bbb*bbb * nn*nn.dsdr() ;
Scalar B2 = 2.*r * bbb*bbb + 2.*r2 * bbb*bbb.dsdr() ;
Scalar B3 =-2.*nphi*B2 - 2.*r2 * bbb*bbb * nphi.dsdr() ;
Scalar B4 = 2.*r * bbb*bbb * nphi*nphi + 2.*r2 * bbb*bbb.dsdr() * nphi*nphi - 2.*ndn + 2.*r2 * bbb*bbb * nphi*nphi.dsdr() ;
Scalar C1 = (A1 * B3 - A3 * B1) ;
Scalar C2 = (A2 * B3 - A3 * B2) ;
Scalar C3 = (A4 * B3 - A3 * B4) ;
Scalar D1 = B4 * C1 - B1 * C3 ;
Scalar D2 = B4 * C2 - B2 * C3 ;
Scalar D3 = B3 * B3 * C1 * C3 ;
Scalar D4 = B3 * B3 * C2 * C3 ;
// Constructing the orbital energy of a particle corotating with the star
// ----------------------------------------------------------------
/* B3 * V_eff - A3 * dV_eff = 0. ; // solve eq. for L
Scalar L = sqrt((C1 + C2 * E2) / C3) ; // substitute into the eq. dVeff=0, then solve for E
Scalar EE = (-(2.*D1*D2 + D3) + sqrt((2.*D1*D2 + D3) * (2.*D1*D2 + D3) - 4.*D1*D1 * (D2*D2 +
D4))) / (2.*(D2*D2 + D4)) ; // solve eq. EE = 1 for r
*/
Scalar bound_orbit = -(2.*D1*D2 + D3) - sqrt((2.*D1*D2 + D3) * (2.*D1*D2 + D3) - 4.*D1*D1 *
(D2*D2 + D4)) - 2.*(D2*D2 + D4) ;
// cout << "bound_orbit :" << bound_orbit << endl ;
bound_orbit.std_spectral_base() ;
// Search for the zero
// -------------------
const int noz(10) ; // number of zeros
double zeros[2][noz] ; // define array for zeros
int i = 0 ; // counter
int l ; // number of domain
double rmb, theta_mb, phi_mb, xi_mb;
double xi_min = -1, xi_max = 1 ;
const Valeur& vorbit = bound_orbit.get_spectral_va() ;
// Preliminary location of the zero
// of the bound_orbit function with an error = dx
double dx = 0.001 ;
theta_mb = M_PI / 2. ;
phi_mb = 0. ;
for(l = lmin; l <= nzm1; l++) {
xi_min = -1. ;
double resloc_old ;
double xi_f = xi_min;
double resloc = vorbit.val_point(l, xi_f, theta_mb, phi_mb) ;
while(xi_f <= xi_max) {
xi_f = xi_f + dx ;
resloc_old = resloc ;
resloc = vorbit.val_point(l, xi_f, theta_mb, phi_mb) ;
if ( resloc * resloc_old < double(0) ) {
zeros[0][i] = xi_f ; // xi_max
zeros[1][i] = l ; // domain number l
i++ ;
}
}
}
int number_of_zeros = i ;
cout << "number of zeros: " << number_of_zeros << endl ;
double precis_mb = 1.e-9 ; // precision in the determination of xi_mb: 1.e-12
int nitermax_mb = 100 ; // max number of iterations
for(int i = 0; i < number_of_zeros; i++) {
//cout << i << " " << zeros[0][i] << " " << zeros[1][i] << endl ;
int l_mb = int(zeros[1][i]) ;
xi_max = zeros[0][i] ;
xi_min = xi_max - dx ;
Param par_mb ;
par_mb.add_scalar(bound_orbit) ;
par_mb.add_int(l_mb) ;
int niter ;
xi_mb = zerosec(funct_compobj_QI_rmb, par_mb, xi_min, xi_max, precis_mb, nitermax_mb, niter) ;
if (ost != 0x0) {
*ost << "RMB search: " << endl ;
*ost << " Domain number: " << l_mb << endl ;
*ost << " xi_min, xi_max : " << xi_min << " , " << xi_max << endl ;
*ost << " number of iterations used in zerosec: " << niter << endl ;
*ost << " zero found at xi = " << xi_mb << endl ;
}
if (niter < nitermax_mb) {
double zero_mb = mp.val_r(l_mb, xi_mb, theta_mb, phi_mb) ;
//double r_hor = radius_hor(0); // set to 1 in the condition below
double r_ms = r_isco(0) ;
if (zero_mb < (1 + r_ms)/2){
rmb = zero_mb ;
}
}
}
p_r_mb = new double (rmb) ;
//delete [] zeros ; not used, causes "core dump" in Code kerr_qi
} // End of computation
return *p_r_mb ;
}
//=============================================================================
// Function used to locate the MS orbit
//=============================================================================
double funct_compobj_QI_isco(double xi, const Param& par){
// Retrieval of the information:
int l_ms = par.get_int() ;
const Scalar& orbit = par.get_scalar() ;
const Valeur& vorbit = orbit.get_spectral_va() ;
// Value et the desired point
double theta = M_PI / 2. ;
double phi = 0 ;
return vorbit.val_point(l_ms, xi, theta, phi) ;
}
//=============================================================================
// Function used to locate the MB orbit
//=============================================================================
double funct_compobj_QI_rmb(double zeros, const Param& par){
// Retrieval of the information:
int l_mb = par.get_int() ;
const Scalar& orbit = par.get_scalar() ;
const Valeur& vorbit = orbit.get_spectral_va() ;
// Value et the desired point
double theta = M_PI / 2. ;
double phi = 0 ;
return vorbit.val_point(l_mb, zeros, theta, phi) ;
}
}
Lorene::Compobj_QI::p_lspec_isco
double * p_lspec_isco
Specific angular momentum of a particle at the ISCO.
Definition compobj.h:327
Lorene::Compobj_QI::f_isco
virtual double f_isco(int lmin) const
Orbital frequency at the innermost stable circular orbit (ISCO).
Definition compobj_QI_global.C:286
Lorene::Compobj_QI::p_r_mb
double * p_r_mb
Coordinate r of the marginally bound orbit.
Definition compobj.h:328
Lorene::Compobj_QI::p_r_isco
double * p_r_isco
Coordinate r of the ISCO.
Definition compobj.h:322
Lorene::Compobj_QI::lspec_isco
virtual double lspec_isco(int lmin) const
Angular momentum of a particle at the ISCO.
Definition compobj_QI_global.C:303
Lorene::Compobj_QI::angu_mom
virtual double angu_mom() const
Angular momentum.
Definition compobj_QI_global.C:90
Lorene::Compobj_QI::r_isco
virtual double r_isco(int lmin, ostream *ost=0x0) const
Coordinate r of the innermost stable circular orbit (ISCO).
Definition compobj_QI_global.C:108
Lorene::Compobj_QI::nphi
Scalar nphi
Metric coefficient .
Definition compobj.h:296
Lorene::Compobj_QI::espec_isco
virtual double espec_isco(int lmin) const
Energy of a particle at the ISCO.
Definition compobj_QI_global.C:320
Lorene::Compobj_QI::bbb
Scalar bbb
Metric factor B.
Definition compobj.h:290
Lorene::Compobj_QI::p_espec_isco
double * p_espec_isco
Specific energy of a particle at the ISCO.
Definition compobj.h:325
Lorene::Compobj_QI::p_angu_mom
double * p_angu_mom
Angular momentum.
Definition compobj.h:321
Lorene::Compobj_QI::p_f_isco
double * p_f_isco
Orbital frequency of the ISCO.
Definition compobj.h:323
Lorene::Compobj_QI::r_mb
virtual double r_mb(int lmin, ostream *ost=0x0) const
Coordinate r of the marginally bound circular orbit (R_mb).
Definition compobj_QI_global.C:341
Lorene::Compobj::nn
Scalar nn
Lapse function N .
Definition compobj.h:135
Lorene::Compobj::mp
Map & mp
Mapping describing the coordinate system (r,theta,phi).
Definition compobj.h:132
Lorene::Param
Parameter storage.
Definition param.h:125
Lorene::Param::get_int
const int & get_int(int position=0) const
Returns the reference of a int stored in the list.
Definition param.C:292
Lorene::Param::get_scalar
const Scalar & get_scalar(int position=0) const
Returns the reference of a Scalar stored in the list.
Definition param.C:1393
Lorene::Param::add_scalar
void add_scalar(const Scalar &ti, int position=0)
Adds the address of a new Scalar to the list.
Definition param.C:1348
Lorene::Param::add_int
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition param.C:246
Lorene::Scalar
Tensor field of valence 0 (or component of a tensorial field).
Definition scalar.h:387
Lorene::Scalar::std_spectral_base
virtual void std_spectral_base()
Sets the spectral bases of the Valeur va to the standard ones for a scalar field.
Definition scalar.C:784
Lorene::Scalar::dsdr
const Scalar & dsdr() const
Returns of *this .
Definition scalar_deriv.C:113
Lorene::Scalar::get_spectral_va
const Valeur & get_spectral_va() const
Returns va (read only version).
Definition scalar.h:601
Lorene::Valeur
Values and coefficients of a (real-value) function.
Definition valeur.h:287
Lorene::Valeur::val_point
double val_point(int l, double x, double theta, double phi) const
Computes the value of the field represented by *this at an arbitrary point, by means of the spectral ...
Definition valeur.C:882
Lorene::sqrt
Cmp sqrt(const Cmp &)
Square root.
Definition cmp_math.C:220
Lorene::zerosec
double zerosec(double(*f)(double, const Param &), const Param &par, double a, double b, double precis, int nitermax, int &niter, bool abort=true)
Finding the zero a function.
Definition zerosec.C:89
Lorene::Tensor::annule_domain
void annule_domain(int l)
Sets the Tensor to zero in a given domain.
Definition tensor.C:666
Lorene
Lorene prototypes.
Definition app_hor.h:64
Lorene::phi
Coord phi
coordinate centered on the grid
Definition map.h:720
Lorene::r
Coord r
r coordinate centered on the grid
Definition map.h:718