LORENE
bin_ns_bh_orbit.C
1/*
2 * Method of class Bin_ns_bh to compute the orbital angular velocity
3 * {\tt omega}
4 *
5 * (see file bin_ns_bh.h for documentation).
6 *
7 */
8
9/*
10 * Copyright (c) 2003 Keisuke Taniguchi
11 *
12 * This file is part of LORENE.
13 *
14 * LORENE is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU General Public License version 2
16 * as published by the Free Software Foundation.
17 *
18 * LORENE is distributed in the hope that it will be useful,
19 * but WITHOUT ANY WARRANTY; without even the implied warranty of
20 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
21 * GNU General Public License for more details.
22 *
23 * You should have received a copy of the GNU General Public License
24 * along with LORENE; if not, write to the Free Software
25 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
26 *
27 */
28
29char bin_ns_bh_orbit_C[] = "$Header: /cvsroot/Lorene/C++/Source/Bin_ns_bh/bin_ns_bh_orbit.C,v 1.7 2014/10/24 14:10:24 j_novak Exp $" ;
30
31/*
32 * $Id: bin_ns_bh_orbit.C,v 1.7 2014/10/24 14:10:24 j_novak Exp $
33 * $Log: bin_ns_bh_orbit.C,v $
34 * Revision 1.7 2014/10/24 14:10:24 j_novak
35 * Minor change to prevent weird error from g++-4.8...
36 *
37 * Revision 1.6 2014/10/13 08:52:43 j_novak
38 * Lorene classes and functions now belong to the namespace Lorene.
39 *
40 * Revision 1.5 2014/10/06 15:13:02 j_novak
41 * Modified #include directives to use c++ syntax.
42 *
43 * Revision 1.4 2004/06/09 07:26:16 k_taniguchi
44 * Minor changes.
45 *
46 * Revision 1.3 2004/06/09 06:20:11 k_taniguchi
47 * Set the standard basis for some Cmp.
48 *
49 * Revision 1.2 2004/03/25 10:28:58 j_novak
50 * All LORENE's units are now defined in the namespace Unites (in file unites.h).
51 *
52 * Revision 1.1 2003/10/24 16:57:43 k_taniguchi
53 * Method for the calculation of the orbital angular velocity
54 *
55 *
56 * $Header: /cvsroot/Lorene/C++/Source/Bin_ns_bh/bin_ns_bh_orbit.C,v 1.7 2014/10/24 14:10:24 j_novak Exp $
57 *
58 */
59
60// C headers
61#include <cmath>
62
63// Lorene headers
64#include "bin_ns_bh.h"
65#include "eos.h"
66#include "param.h"
67#include "utilitaires.h"
68#include "unites.h"
69
70namespace Lorene {
71double fonc_bin_ns_bh_orbit(double , const Param& ) ;
72
73//*************************************************************************
74
75void Bin_ns_bh::orbit_omega(double fact_omeg_min, double fact_omeg_max) {
76
77 using namespace Unites ;
78
79 //------------------------------------------------------------------
80 // Evaluation of various quantities at the center of a neutron star
81 //------------------------------------------------------------------
82
83 double dnulg, asn2, dasn2, ny, dny, npn, dnpn ;
84
85 const Map& mp = star.get_mp() ;
86
87 const Cmp& loggam = star.get_loggam()() ;
88 const Cmp& nnn = star.get_nnn()() ;
89 const Cmp& confpsi = star.get_confpsi()() ;
90 const Tenseur& shift = star.get_shift() ;
91
92 Cmp confpsi_q = pow(confpsi, 4.) ;
93 confpsi_q.std_base_scal() ;
94
95 //-----------------------------------------------------------------
96 // Calculation of d/dX( nu + ln(Gamma) ) at the center of the star
97 // ---> dnulg
98 //-----------------------------------------------------------------
99
100 // Factor for the coordinate transformation x --> X :
101 double factx ;
102 if (fabs(mp.get_rot_phi()) < 1.e-14) {
103 factx = 1. ;
104 }
105 else {
106 if (fabs(mp.get_rot_phi() - M_PI) < 1.e-14) {
107 factx = - 1. ;
108 }
109 else {
110 cout << "Bin_ns_bh::orbit_omega : unknown value of rot_phi !"
111 << endl ;
112 abort() ;
113 }
114 }
115
116 Cmp tmp = log( nnn ) + loggam ;
117 tmp.std_base_scal() ;
118
119 // ... gradient
120 dnulg = factx * tmp.dsdx()(0, 0, 0, 0) ;
121
122 //------------------------------------------------------------
123 // Calculation of A^2/N^2 at the center of the star ---> asn2
124 //------------------------------------------------------------
125 double nc = nnn(0, 0, 0, 0) ;
126 double a2c = confpsi_q(0, 0, 0, 0) ;
127 asn2 = a2c / (nc * nc) ;
128
129 if ( star.is_relativistic() ) {
130
131 //------------------------------------------------------------------
132 // Calculation of d/dX(A^2/N^2) at the center of the star ---> dasn
133 //------------------------------------------------------------------
134 double da2c = factx * confpsi_q.dsdx()(0, 0, 0, 0) ;
135 double dnc = factx * nnn.dsdx()(0, 0, 0, 0) ;
136
137 dasn2 = ( da2c - 2 * a2c / nc * dnc ) / (nc*nc) ;
138
139 //------------------------------------------------------
140 // Calculation of N^Y at the center of the star ---> ny
141 //------------------------------------------------------
142 ny = shift(1)(0, 0, 0, 0) ;
143
144 //-----------------------------------------------------------
145 // Calculation of dN^Y/dX at the center of the star ---> dny
146 //-----------------------------------------------------------
147 dny = factx * shift(1).dsdx()(0, 0, 0, 0) ;
148
149 //--------------------------------------------
150 // Calculation of (N^X)^2 + (N^Y)^2 + (N^Z)^2
151 // at the center of the star ---> npn
152 //--------------------------------------------
153 tmp = flat_scalar_prod(shift, shift)() ;
154 npn = tmp(0, 0, 0, 0) ;
155
156 //----------------------------------------------------
157 // Calculation of d/dX( (N^X)^2 + (N^Y)^2 + (N^Z)^2 )
158 // at the center of the star ---> dnpn
159 //----------------------------------------------------
160 dnpn = factx * tmp.dsdx()(0, 0, 0, 0) ;
161
162 } // Finish of the relativistic case
163 else {
164 cout << "Bin_ns_bh::orbit_omega : "
165 << "It should be the relativistic calculation !" << endl ;
166 abort() ;
167 }
168
169 cout << "Bin_ns_bh::orbit_omega: central d(nu+log(Gam))/dX : "
170 << dnulg << endl ;
171 cout << "Bin_ns_bh::orbit_omega: central A^2/N^2 : " << asn2 << endl ;
172 cout << "Bin_ns_bh::orbit_omega: central d(A^2/N^2)/dX : "
173 << dasn2 << endl ;
174 cout << "Bin_ns_bh::orbit_omega: central N^Y : " << ny << endl ;
175 cout << "Bin_ns_bh::orbit_omega: central dN^Y/dX : " << dny << endl ;
176 cout << "Bin_ns_bh::orbit_omega: central N.N : " << npn << endl ;
177 cout << "Bin_ns_bh::orbit_omega: central d(N.N)/dX : "
178 << dnpn << endl ;
179
180 //------------------------------------------------------
181 // Start of calculation of the orbital angular velocity
182 //------------------------------------------------------
183 int relat = ( star.is_relativistic() ) ? 1 : 0 ;
184
185 double ori_x = (star.get_mp()).get_ori_x() ;
186 Param parf ;
187 parf.add_int(relat) ;
188 parf.add_double( ori_x, 0) ;
189 parf.add_double( dnulg, 1) ;
190 parf.add_double( asn2, 2) ;
191 parf.add_double( dasn2, 3) ;
192 parf.add_double( ny, 4) ;
193 parf.add_double( dny, 5) ;
194 parf.add_double( npn, 6) ;
195 parf.add_double( dnpn, 7) ;
196 parf.add_double( x_axe, 8) ;
197
198 double omega1 = fact_omeg_min * omega ;
199 double omega2 = fact_omeg_max * omega ;
200
201 cout << "Bin_ns_bh::orbit_omega: omega1, omega2 [rad/s] : "
202 << omega1 * f_unit << " " << omega2 * f_unit << endl ;
203
204 // Search for the various zeros in the interval [omega1,omega2]
205 // ------------------------------------------------------------
206 int nsub = 50 ; // total number of subdivisions of the interval
207 Tbl* azer = 0x0 ;
208 Tbl* bzer = 0x0 ;
209 zero_list(fonc_bin_ns_bh_orbit, parf, omega1, omega2, nsub,
210 azer, bzer) ;
211
212 // Search for the zero closest to the previous value of omega
213 // ----------------------------------------------------------
214 double omeg_min, omeg_max ;
215 int nzer = azer->get_taille() ; // number of zeros found by zero_list
216 cout << "Bin_ns_bh:orbit_omega : " << nzer <<
217 "zero(s) found in the interval [omega1, omega2]." << endl ;
218 cout << "omega, omega1, omega2 : " << omega << " " << omega1
219 << " " << omega2 << endl ;
220 cout << "azer : " << *azer << endl ;
221 cout << "bzer : " << *bzer << endl ;
222
223 if (nzer == 0) {
224 cout << "Bin_ns_bh::orbit_omega: WARNING : "
225 << "no zero detected in the interval" << endl
226 << " [" << omega1 * f_unit << ", "
227 << omega2 * f_unit << "] rad/s !" << endl ;
228 omeg_min = omega1 ;
229 omeg_max = omega2 ;
230 }
231 else {
232 double dist_min = fabs(omega2 - omega1) ;
233 int i_dist_min = -1 ;
234 for (int i=0; i<nzer; i++) {
235 // Distance of previous value of omega from the center of the
236 // interval [azer(i), bzer(i)]
237 double dist = fabs( omega - 0.5 * ( (*azer)(i) + (*bzer)(i) ) ) ;
238
239 if (dist < dist_min) {
240 dist_min = dist ;
241 i_dist_min = i ;
242 }
243 }
244 omeg_min = (*azer)(i_dist_min) ;
245 omeg_max = (*bzer)(i_dist_min) ;
246 }
247
248 delete azer ; // Tbl allocated by zero_list
249 delete bzer ; //
250
251 cout << "Bin_ns_bh:orbit_omega : "
252 << "interval selected for the search of the zero : "
253 << endl << " [" << omeg_min << ", " << omeg_max << "] = ["
254 << omeg_min * f_unit << ", " << omeg_max * f_unit << "] rad/s "
255 << endl ;
256
257 // Computation of the zero in the selected interval by the secant method
258 // ---------------------------------------------------------------------
259
260 int nitermax = 200 ;
261 int niter ;
262 double precis = 1.e-13 ;
263 omega = zerosec_b(fonc_bin_ns_bh_orbit, parf, omeg_min, omeg_max,
264 precis, nitermax, niter) ;
265
266 cout << "Bin_ns_bh::orbit_omega : "
267 << "Number of iterations in zerosec for omega : "
268 << niter << endl ;
269
270 cout << "Bin_ns_bh::orbit_omega : omega [rad/s] : "
271 << omega * f_unit << endl ;
272
273}
274
275//***********************************************************
276// Function used for search of the orbital angular velocity
277//***********************************************************
278
279double fonc_bin_ns_bh_orbit(double om, const Param& parf) {
280
281 int relat = parf.get_int() ;
282
283 double xc = parf.get_double(0) ;
284 double dnulg = parf.get_double(1) ;
285 double asn2 = parf.get_double(2) ;
286 double dasn2 = parf.get_double(3) ;
287 double ny = parf.get_double(4) ;
288 double dny = parf.get_double(5) ;
289 double npn = parf.get_double(6) ;
290 double dnpn = parf.get_double(7) ;
291 double x_axe = parf.get_double(8) ;
292
293 double xx = xc - x_axe ;
294 double om2 = om*om ;
295
296 double dphi_cent ;
297
298 if (relat == 1) {
299 double bpb = om2 * xx*xx - 2*om * ny * xx + npn ;
300
301 dphi_cent = ( asn2* ( om* (ny + xx*dny) - om2*xx - 0.5*dnpn )
302 - 0.5*bpb* dasn2 )
303 / ( 1 - asn2 * bpb ) ;
304 }
305 else {
306 cout << "Bin_ns_bh::orbit_omega : "
307 << "It should be the relativistic calculation !" << endl ;
308 abort() ;
309 }
310
311 return dnulg + dphi_cent ;
312
313}
314}
double x_axe
Absolute X coordinate of the rotation axis.
Definition bin_ns_bh.h:140
Et_bin_nsbh star
The neutron star.
Definition bin_ns_bh.h:128
double omega
Angular velocity with respect to an asymptotically inertial observer.
Definition bin_ns_bh.h:136
void orbit_omega(double fact_omeg_min, double fact_omeg_max)
Computes the orbital angular velocity {\tt omega}.
Component of a tensorial field *** DEPRECATED : use class Scalar instead ***.
Definition cmp.h:446
void std_base_scal()
Sets the spectral bases of the Valeur va to the standard ones for a scalar.
Definition cmp.C:644
const Cmp & dsdx() const
Returns of *this , where .
Definition cmp_deriv.C:148
const Tenseur & get_confpsi() const
Returns the part of the conformal factor $\Psi$.
const Tenseur & get_loggam() const
Returns the logarithm of the Lorentz factor between the fluid and the co-orbiting observer.
Definition etoile.h:1111
const Tenseur & get_nnn() const
Returns the total lapse function N.
Definition etoile.h:727
const Tenseur & get_shift() const
Returns the total shift vector .
Definition etoile.h:730
const Map & get_mp() const
Returns the mapping.
Definition etoile.h:659
bool is_relativistic() const
Returns true for a relativistic star, false for a Newtonian one.
Definition etoile.h:667
Base class for coordinate mappings.
Definition map.h:670
double get_rot_phi() const
Returns the angle between the x –axis and X –axis.
Definition map.h:775
Parameter storage.
Definition param.h:125
void add_double(const double &x, int position=0)
Adds the the address of a new double to the list.
Definition param.C:315
const int & get_int(int position=0) const
Returns the reference of a int stored in the list.
Definition param.C:292
const double & get_double(int position=0) const
Returns the reference of a double stored in the list.
Definition param.C:361
void add_int(const int &n, int position=0)
Adds the address of a new int to the list.
Definition param.C:246
Basic array class.
Definition tbl.h:161
int get_taille() const
Gives the total size (ie dim.taille)
Definition tbl.h:397
Tensor handling *** DEPRECATED : use class Tensor instead ***.
Definition tenseur.h:301
Cmp pow(const Cmp &, int)
Power .
Definition cmp_math.C:348
Cmp log(const Cmp &)
Neperian logarithm.
Definition cmp_math.C:296
void zero_list(double(*f)(double, const Param &), const Param &par, double xmin, double xmax, int nsub, Tbl *&az, Tbl *&bz)
Locates approximatively all the zeros of a function in a given interval.
Definition zero_list.C:57
double zerosec_b(double(*f)(double, const Param &), const Param &par, double a, double b, double precis, int nitermax, int &niter)
Finding the zero a function on a bounded domain.
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...
Lorene prototypes.
Definition app_hor.h:64
Standard units of space, time and mass.