LALSimInspiraldEnergyFlux.c

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/*
*  Copyright (C) 2007 David Churches, Jolien Creighton, David McKechan, B.S. Sathyaprakash, Thomas Cokelaer, Duncan Brown, Riccardo Sturani, Laszlo Vereb, Drew Keppel
*
*  This program 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.
*
*  This program 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 with program; see the file COPYING. If not, write to the
*  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
*  MA  02110-1301  USA
*/
 
/**
 * \author Sathyaprakash, B. S.
 * \file
 * \ingroup LALSimInspiral_h
 *
 * \brief Module containing the energy and flux functions for waveform generation.
 *
 * ### Prototypes ###
 *
 * <tt>REAL8 SAMPLEFUNCTION()</tt>
 * <ul>
 * <li> \c v: PN parameter.<\li>
 * <li> \c ak: Input containing the PN expnasion coefficients.</li>
 * </ul>
 *
 * ### Description ###
 *
 * This module gives the post-Newtonian expansions and/or P-approximants
 * to the energy, its derivative and gravitational-wave flux functions. More
 * specifically, the <tt>REAL8</tt> functions below give Taylor expansions
 * of \f$dE/dv,\f$ and \f${\cal F}(v),\f$ P-approximants of \f$e(v),\f$ \f$dE/dv\f$
 * (derived from \f$e(v)\f$) and \f${\cal F}(v).\f$
 *
 * ### Notes ###
 *
 * <ul>
 * <li> See Damour, Iyer and Sathyaprakash, PRD 57, 885, 1998 for further details.
 * Damour, Iyer and Sathyaprakash, PRD 63, 044023, 2001 is a resource paper that
 * summarizes how to generate waveforms in different approximations to the dynamics
 * of a compact binary under radiation reaction.</li>
 * <li> The Pade Approximant for the 1PN expansion is undefined as also
 * EOB at orders less than 2PN. BCV is independent of the PN order.
 * Spinning waveforms are only defined at the highest PN order.</li>
 * </ul>
 *
 */
 
#ifndef LALSIMINSPIRALDENERGYFLUC_C
#define LALSIMINSPIRALDENERGYFLUC_C
 
#ifdef __GNUC__
#define UNUSED __attribute__ ((unused))
#else
#define UNUSED
#endif
 
#include <math.h>
#include <lal/LALStdlib.h>
 
typedef struct
{
   /* coefficients in the Pade expression of new energy function */
   REAL8 ePaN, ePa1, ePa2, ePa3;
   /* coefficients in the Taylor expansion of usual energy function */
   REAL8 ETaN, ETa1, ETa2, ETa3, ETa5, ETa6;
   /* coefficients in the Taylor expansion of the derivative of the
    usual energy function */
   REAL8 dETaN, dETa1, dETa2, dETa3, dETa5, dETa6;
 
   /* Taylor expansion coefficients of energy flux*/
   REAL8 FTaN, FTa1, FTa2, FTa3, FTa4, FTa5, FTa6, FTa7, FTa8, FTl6, FTl8, FTa10, FTa12;
   /* Coefficients of the corresponding P-approximant */
   REAL8 fPaN, fPa1, fPa2, fPa3, fPa4, fPa5, fPa6, fPa7, fPa8;
 
   /* symmetric mass ratio, total mass, component masses */
   REAL8 eta, totalmass;
 
   /* initial and final values of frequency, time, velocity; lso
    values of velocity and frequency; final phase. */
   REAL8 vlso;
 
   /* last stable orbit and pole defined by various Taylor and P-approximants */
   REAL8 vlsoT0, vlsoT2, vlsoT4, vlsoT6;
   REAL8 vlsoP0, vlsoP2, vlsoP4, vlsoP6;
   REAL8 vlsoPP;
   REAL8 vpoleP4, vpoleP6;
   REAL8 vpolePP;
}  expnCoeffsdEnergyFlux;
 
 
typedef REAL8 (*EnergyFunction)(
   REAL8 v,
   expnCoeffsdEnergyFlux *ak);
 
 
typedef REAL8 (*FluxFunction)(
   REAL8 v,
   expnCoeffsdEnergyFlux *ak);
 
 
typedef struct
{
   EnergyFunction dEnergy;
   FluxFunction flux;
   expnCoeffsdEnergyFlux *coeffs;
} TofVIntegrandIn;
 
 
typedef struct
{
   REAL8 t;
   REAL8 v0;
   REAL8 t0;
   REAL8 vlso;
   REAL8 totalmass;
   EnergyFunction dEnergy;
   FluxFunction flux;
   expnCoeffsdEnergyFlux *coeffs;
} TofVIn;
 
 
static REAL8 UNUSED XLALSimInspiralEt0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 dEnergy;
   REAL8 x = v*v;
   dEnergy = ak->ETaN * x;
   return (dEnergy);
}
 
static REAL8 UNUSED XLALSimInspiralEt2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 Energy;
   REAL8 x = v*v;
   REAL8 x5 = x*x*x*x*x;
   REAL8 x6 = x*x5;
   Energy = ak->ETaN * x * (1. + ak->ETa1*x + ak->ETa5*x5 + ak->ETa6*x6);
   return Energy;
}
 
static REAL8 UNUSED XLALSimInspiralEt4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 Energy;
   REAL8 x = v*v;
   REAL8 x2 = x*x;
   REAL8 x5 = x*x2*x2;
   REAL8 x6 = x*x5;
   Energy = ak->ETaN * x * (1. + ak->ETa1*x + ak->ETa2*x2 + ak->ETa5*x5
          + ak->ETa6*x6);
   return Energy;
}
 
static REAL8 UNUSED XLALSimInspiralEt6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 Energy;
   REAL8 x = v*v;
   REAL8 x2 = x*x;
   REAL8 x3 = x*x2;
   REAL8 x5 = x3*x2;
   REAL8 x6 = x*x5;
   Energy = ak->ETaN * x * (1. + ak->ETa1*x + ak->ETa2*x2 + ak->ETa3*x3
          + ak->ETa5*x5 + ak->ETa6*x6);
   return Energy;
}
 
static REAL8 UNUSED XLALSimInspiraldEt0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 dEnergy;
   dEnergy = ak->dETaN * v;
   return (dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiraldEt2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 dEnergy;
   REAL8 x = v*v;
   REAL8 x5 = x*x*x*x*x;
   REAL8 x6 = x*x5;
   dEnergy = ak->dETaN * v * (1. + ak->dETa1*x + ak->dETa5*x5 + ak->dETa6*x6);
   return (dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiraldEt4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 dEnergy;
   REAL8 x = v*v;
   REAL8 x2 = x*x;
   REAL8 x5 = x*x2*x2;
   REAL8 x6 = x*x5;
   dEnergy = ak->dETaN * v * (1. + ak->dETa1*x + ak->dETa2*x2 + ak->dETa5*x5
           + ak->dETa6*x6);
   return (dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiraldEt6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 dEnergy;
   REAL8 x = v*v;
   REAL8 x2 = x*x;
   REAL8 x3 = x*x2;
   REAL8 x5 = x3*x2;
   REAL8 x6 = x*x5;
   dEnergy = ak->dETaN * v * (1. + ak->dETa1*x + ak->dETa2*x2 + ak->dETa3*x3
           + ak->dETa5*x5 + ak->dETa6*x6);
   return (dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->FTaN * v10;
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1. + ak->FTa2*v2 + ak->FTa10*v10 + ak->FTa12*v12);
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt3(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1. + ak->FTa2*v2 + ak->FTa3*v2*v + ak->FTa10*v10
        + ak->FTa12*v12);
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1. + ak->FTa2*v2 + ak->FTa3*v2*v + ak->FTa4*v4
        + ak->FTa10*v10 + ak->FTa12*v12);
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt5(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1.+ ak->FTa2*v2 + ak->FTa3*v2*v + ak->FTa4*v4
        + ak->FTa5*v4*v + ak->FTa10*v10 + ak->FTa12*v12);
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1.+ ak->FTa2*v2 + ak->FTa3*v2*v + ak->FTa4*v4
        + ak->FTa5*v4*v + (ak->FTa6 + ak->FTl6*log(v))*v6 + ak->FTa10*v10
        + ak->FTa12*v12);
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFt7(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10,v12;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   v12 = v10*v2;
   flux = ak->FTaN * v10 * (1.+ ak->FTa2*v2 + ak->FTa3*v2*v + ak->FTa4*v4
        + ak->FTa5*v4*v + (ak->FTa6 + ak->FTl6*log(v))*v6 + ak->FTa7*v6*v
        + ak->FTa10*v10 + ak->FTa12*v12);
   return (flux);
}
 
 
/*
static REAL8 UNUSED XLALSimInspiralep0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 x, energy;
   ak = NULL;
   x = v*v;
   energy = -x;
   return (energy);
}
*/
 
 
static REAL8 UNUSED XLALSimInspiralep2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 x, energy;
   x = v*v;
   energy = -x / (1. + ak->ePa1 * x);
   return (energy);
}
 
 
static REAL8 UNUSED XLALSimInspiralep4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 x, energy;
   x = v*v;
   energy = -x / (1. + ak->ePa1*x /(1. + ak->ePa2*x));
   return (energy);
}
 
 
static REAL8 UNUSED XLALSimInspiralep6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 x, energy;
   x = v*v;
   energy = -x / (1. + ak->ePa1*x /(1. + ak->ePa2*x /(1. + ak->ePa3*x)));
   return (energy);
}
 
 
/*
static REAL8 UNUSED XLALSimInspiraldEp0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 energy, denergy, Energy, dEnergy, y;
   energy = ep0(v, ak);
   y = sqrt(1.+energy);
   Energy = sqrt(1. + 2.* ak->eta * (y - 1.)) - 1.;
   denergy = -1;
   dEnergy = v * ak->eta * denergy /((1.+Energy) * y);
   return(dEnergy);
}
*/
 
 
static REAL8 UNUSED XLALSimInspiraldEp2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 energy, denergy, Energy, dEnergy, x, y;
   x = v*v;
   energy = XLALSimInspiralep2(v, ak);
   y = sqrt(1.+energy);
   Energy = sqrt(1. + 2.* ak->eta * (y - 1.)) - 1.;
   denergy = -1. / ((1. + ak->ePa1*x)*(1. + ak->ePa1*x));
   dEnergy = v * ak->eta * denergy /((1.+Energy) * y);
   return(dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiraldEp4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 energy, denergy, Energy, dEnergy, denom, x, y;
   x = v*v;
   energy = XLALSimInspiralep4(v, ak);
   y = sqrt(1.+energy);
   Energy = sqrt(1. + 2.* ak->eta * (y - 1.)) - 1.;
 
   denom = 1. + (ak->ePa1 + ak->ePa2) * x;
   denom = denom * denom;
   denergy = (1. + 2.*ak->ePa2*x + ((ak->ePa1 + ak->ePa2) * ak->ePa2 * x*x))/denom;
   dEnergy = - v * ak->eta * denergy /((1.+Energy) * y);
   return(dEnergy);
}
 
 
static REAL8 UNUSED XLALSimInspiraldEp6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 energy, denergy, Energy, dEnergy, denom, x, y;
   x = v*v;
   energy = XLALSimInspiralep6(v, ak);
   y = sqrt(1.+energy);
   Energy = sqrt(1. + 2.* ak->eta * (y - 1.)) - 1.;
 
   denom = 1. + (ak->ePa1 + ak->ePa2 + ak->ePa3) * x + ak->ePa1*ak->ePa3*x*x;
   denom = denom * denom;
 
   denergy = (1. + 2.*(ak->ePa2+ak->ePa3)*x + (ak->ePa1*ak->ePa2
           + ak->ePa2*ak->ePa2 + 2.* ak->ePa2*ak->ePa3
           + ak->ePa3*ak->ePa3) * x*x)
           /denom;
   dEnergy = - v * ak->eta * denergy /((1.+Energy) * y);
   return(dEnergy);
}
 
 
/*
static REAL8 UNUSED XLALSimInspiralFp0(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10;
   return (flux);
}
*/
 
 
/*
static REAL8 UNUSED XLALSimInspiralFp1(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v) * (1.-v/ak->vpoleP4));
   return (flux);
}
*/
 
 
/*
static REAL8 UNUSED XLALSimInspiralFp2(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v / (1.+ak->fPa2*v)) * (1.-v/ak->vpoleP4));
   return (flux);
}
*/
 
 
static REAL8 UNUSED XLALSimInspiralFp3(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v)))
        * (1.-v/ak->vpoleP4));
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFp4(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v)))) * (1.-v/ak->vpoleP4));
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFp5(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v / (1.+ak->fPa5*v))))) * (1.-v/ak->vpoleP4));
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFp6(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v / (1.+ak->fPa5*v / (1.+ak->fPa6*v))))))
        * (1.-v/ak->vpoleP6));
   /* */
   flux *= (1.+  log(v/ak->vlsoP4) * ak->FTl6*v6) ;
   return (flux);
}
 
 
static REAL8 UNUSED XLALSimInspiralFp7(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v / (1.+ak->fPa5*v / (1.+ak->fPa6*v / (1.+ak->fPa7*v)))))))
        * (1.-v/ak->vpoleP6));
   flux *= (1.+  log(v/ak->vlsoP4) * ak->FTl6*v6) ;
   return (flux);
}
 
 
/* Flux for the EOBNRv2 model */
static REAL8 UNUSED XLALSimInspiralFp8PP(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10, l6, l8;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   l6 = ak->FTl6;
   l8 = ak->FTl8 - ak->FTa2*ak->FTl6;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v / (1.+ak->fPa5*v / (1.+ak->fPa6*v / (1.+ak->fPa7*v
        / (1.+ak->fPa8*v))))))))
        * (1.-v/ak->vpolePP));
   flux *= (1.+  log(v/ak->vlsoPP) * (l6*v6 + l8*v8) ) ;
   return (flux);
}
 
 
/*
static REAL8 UNUSED XLALSimInspiralFp8(REAL8 v, expnCoeffsdEnergyFlux *ak)
{
   REAL8 flux,v2,v4,v6,v8,v10, l6, l8;
   v2 = v*v;
   v4 = v2*v2;
   v6 = v4*v2;
   v8 = v4*v4;
   v10 = v8*v2;
   l6 = ak->FTl6;
   l8 = ak->FTl8 - ak->FTa2*ak->FTl6;
   flux = ak->fPaN * v10/ ((1.+ak->fPa1*v/(1.+ak->fPa2*v/ (1.+ak->fPa3*v
        / (1.+ak->fPa4*v / (1.+ak->fPa5*v / (1.+ak->fPa6*v / (1.+ak->fPa7*v
        / (1.+ak->fPa8*v))))))))
        * (1.-v/ak->vpoleP6));
   flux *= (1.+  log(v/ak->vlsoP4) * (l6*v6 + l8*v8) ) ;
   return (flux);
}
*/
 
#endif /* LALSIMINSPIRALDENERGYFLUC_C */