LALSimIMRSpinEOBHamiltonianPrec.c File Reference

Prototypes
static UNUSED REAL8	XLALSimIMRSpinPrecEOBHamiltonianDeltaR (SpinEOBHCoeffs *coeffs, const REAL8 r, const REAL8 eta, const REAL8 a)
	This function calculates the DeltaR potential function in the spin EOB Hamiltonian. More...
static REAL8	XLALSimIMRSpinPrecEOBHamiltonian (const REAL8 eta, REAL8Vector *restrict x, REAL8Vector *restrict p, REAL8Vector *restrict s1Vec, REAL8Vector *restrict s2Vec, REAL8Vector *restrict sigmaKerr, REAL8Vector *restrict sigmaStar, int tortoise, SpinEOBHCoeffs *coeffs)
static REAL8	XLALSimIMRSpinPrecEOBHamiltonianDeltaT (SpinEOBHCoeffs *coeffs, const REAL8 r, const REAL8 eta, const REAL8 a)
	This function calculates the function \(\Delta_t(r)\) which appears in the spinning EOB potential function. More...
static REAL8	inner_product (const REAL8 values1[], const REAL8 values2[])
	Functions to compute the inner product and cross products between vectors. More...
static REAL8 *	cross_product (const REAL8 values1[], const REAL8 values2[], REAL8 result[])
static REAL8 *	rotate_vector (const REAL8 v[], const REAL8 k[], const REAL8 theta, REAL8 result[])
	Rotate the vector v around the axis k by an angle theta, counterclockwise Note that this assumes that the rotation axis k is normalized. More...
static UNUSED REAL8	XLALSimIMRSpinPrecEOBNonKeplerCoeff (const REAL8 values[], SpinEOBParams *funcParams)
	Function to calculate the non-Keplerian coefficient for the PRECESSING EOB model. More...
static REAL8	XLALSimIMRSpinPrecEOBCalcOmega (const REAL8 values[], SpinEOBParams *funcParams)
	Function to calculate the value of omega for the PRECESSING EOB waveform. More...
static int	XLALSpinPrecHcapRvecDerivative (double UNUSED t, const REAL8 values[], REAL8 dvalues[], void *funcParams)
	Function to calculate numerical derivatives of the spin EOB Hamiltonian, to get \(dr/dt\), as decribed in Eqs. More...
static double	GSLSpinPrecHamiltonianWrapperForRvecDerivs (double x, void *params)
	Wrapper for GSL to call the Hamiltonian function. More...
static double	GSLSpinPrecHamiltonianWrapperFordHdpphi (double x, void *params)
	Wrapper for GSL to call the Hamiltonian function. More...
static REAL8	XLALSimIMRSpinPrecEOBHamiltonian (const REAL8 eta, REAL8Vector *restrict x, REAL8Vector *restrict p, REAL8Vector *restrict s1Vec, REAL8Vector *restrict s2Vec, REAL8Vector *restrict sigmaKerr, REAL8Vector *restrict sigmaStar, INT4 tortoise, SpinEOBHCoeffs *coeffs)
	Function to calculate the value of the spinning Hamiltonian for given values of the dynamical variables (in a Cartesian co-ordinate system). More...

Go to the source code of this file.

Macros
#define	_LALSIMIMRSPINEOBHAMILTONIANPREC_C

Macro Definition Documentation

_LALSIMIMRSPINEOBHAMILTONIANPREC_C

#define _LALSIMIMRSPINEOBHAMILTONIANPREC_C

Author

Craig Robinson, Yi Pan, Stas Babak, Prayush Kumar, Andrea Taracchini

Functions for calculating the effective one-body Hamiltonian for spinning binaries, as described in Taracchini et al. ( PRD 86, 024011 (2012), arXiv 1202.0790 ). All equation numbers in this file refer to equations of this paper, unless otherwise specified. This code borrows hugely from a C implementation originally written by Enrico Barausse, following Barausse and Buonanno PRD 81, 084024 (2010) and PRD 84, 104027 (2011), henceforth BB1 and BB2

Definition at line 15 of file LALSimIMRSpinEOBHamiltonianPrec.c.

Function Documentation

XLALSimIMRSpinPrecEOBHamiltonianDeltaR()

static REAL8 XLALSimIMRSpinPrecEOBHamiltonianDeltaR ( SpinEOBHCoeffs *  coeffs, const REAL8  r, const REAL8  eta, const REAL8  a  )

static

This function calculates the DeltaR potential function in the spin EOB Hamiltonian.

This function calculates the function \(\Delta_r(r)\) which appears in the spinning EOB potential function.

Eqs. 5.83 of PRD 81, 084024 (2010)

Parameters

coeffs	< Pre-computed coefficients which appear in the function
r	< Current orbital radius (in units of total mass)
eta	< Symmetric mass ratio
a	< Normalized deformed Kerr spin

Definition at line 649 of file LALSimIMRSpinEOBHamiltonianPrec.c.

XLALSimIMRSpinPrecEOBHamiltonian() [1/2]

static REAL8 XLALSimIMRSpinPrecEOBHamiltonian ( const REAL8  eta, REAL8Vector *restrict  x, REAL8Vector *restrict  p, REAL8Vector *restrict  s1Vec, REAL8Vector *restrict  s2Vec, REAL8Vector *restrict  sigmaKerr, REAL8Vector *restrict  sigmaStar, int  tortoise, SpinEOBHCoeffs *  coeffs  )

static

XLALSimIMRSpinPrecEOBHamiltonianDeltaT()

static REAL8 XLALSimIMRSpinPrecEOBHamiltonianDeltaT ( SpinEOBHCoeffs *  coeffs, const REAL8  r, const REAL8  eta, const REAL8  a  )

static

This function calculates the function \(\Delta_t(r)\) which appears in the spinning EOB potential function.

Eqs. 5.73 of PRD 81, 084024 (2010) augmented by 4PN, linear-in-eta corrections: see also section "New 4PN term in the radial potential" of https://dcc.ligo.org/T1400476

Parameters

coeffs	< Pre-computed coefficients which appear in the function
r	< Current orbital radius (in units of total mass)
eta	< Symmetric mass ratio
a	< Normalized deformed Kerr spin

Definition at line 605 of file LALSimIMRSpinEOBHamiltonianPrec.c.

inner_product()

static REAL8 inner_product ( const REAL8  values1[], const REAL8  values2[]  )

static

Functions to compute the inner product and cross products between vectors.

Definition at line 684 of file LALSimIMRSpinEOBHamiltonianPrec.c.

cross_product()

static REAL8 * cross_product ( const REAL8  values1[], const REAL8  values2[], REAL8  result[]  )

static

Definition at line 694 of file LALSimIMRSpinEOBHamiltonianPrec.c.

rotate_vector()

static UNUSED REAL8 * rotate_vector ( const REAL8  v[], const REAL8  k[], const REAL8  theta, REAL8  result[]  )

static

Rotate the vector v around the axis k by an angle theta, counterclockwise Note that this assumes that the rotation axis k is normalized.

Definition at line 709 of file LALSimIMRSpinEOBHamiltonianPrec.c.

XLALSimIMRSpinPrecEOBNonKeplerCoeff()

static REAL8 XLALSimIMRSpinPrecEOBNonKeplerCoeff ( const REAL8  values[], SpinEOBParams *  funcParams  )

static

Function to calculate the non-Keplerian coefficient for the PRECESSING EOB model.

radius \(r\) times the cuberoot of the returned number is \(r_\Omega\) defined in Eq. A2, i.e. the function returns \((r_{\Omega} / r)^3\) = \(1/(r^3 (\partial Hreal/\partial p_\phi |p_r=0)^2)\).

Parameters

values	< Dynamical variables
funcParams	< EOB parameters

Definition at line 988 of file LALSimIMRSpinEOBHamiltonianPrec.c.

XLALSimIMRSpinPrecEOBCalcOmega()

static REAL8 XLALSimIMRSpinPrecEOBCalcOmega ( const REAL8  values[], SpinEOBParams *  funcParams  )

static

Function to calculate the value of omega for the PRECESSING EOB waveform.

Needs the dynamics in Cartesian coordinates.

First, the frame is rotated so that L is along the y-axis. this rotation includes the spins.

Second, \(\vec{r}\) and \(\vec{p}\) are converted to polar coordinates (and not the spins). As L is along the y-axis, \(\theta\) defined as the angle between L and the y-axis is 0, which is a cyclic coordinate now and that fixes \(p_\theta = 0\).

Third, \(p_r\) is set to 0.

Fourth, the polar \((r,\phi,p_r=0,p_\phi)\) and the Cartesian spin vectors are used to compute the derivative \(\partial Hreal/\partial p_\phi |p_r=0\).

the polarvalues, respectively, are \({r, \theta, \phi, p_r, p_\theta, p_\phi}\)

Parameters

values	< Dynamical variables
funcParams	< EOB parameters

Definition at line 738 of file LALSimIMRSpinEOBHamiltonianPrec.c.

XLALSpinPrecHcapRvecDerivative()

static int XLALSpinPrecHcapRvecDerivative ( double UNUSED  t, const REAL8  values[], REAL8  dvalues[], void *  funcParams  )

static

Function to calculate numerical derivatives of the spin EOB Hamiltonian, to get \(dr/dt\), as decribed in Eqs.

A4 of PRD 81, 084041 (2010) This function is not used by the spin-aligned SEOBNRv1 model.

• set the tortoise flag to 2 *‍/

Parameters

t	< UNUSED
values	< Dynamical variables
dvalues	< Time derivatives of variables (returned)
funcParams	< EOB parameters

Definition at line 1026 of file LALSimIMRSpinEOBHamiltonianPrec.c.

GSLSpinPrecHamiltonianWrapperForRvecDerivs()

static double GSLSpinPrecHamiltonianWrapperForRvecDerivs ( double  x, void *  params  )

static

Wrapper for GSL to call the Hamiltonian function.

This is simply the function GSLSpinPrecHamiltonianWrapper copied over. The alternative was to make it non-static which increases runtime as static functions can be better optimized.

Definition at line 1634 of file LALSimIMRSpinEOBHamiltonianPrec.c.

GSLSpinPrecHamiltonianWrapperFordHdpphi()

static double GSLSpinPrecHamiltonianWrapperFordHdpphi ( double  x, void *  params  )

static

Wrapper for GSL to call the Hamiltonian function.

This is simply the function GSLSpinPrecHamiltonianWrapper copied over. The alternative was to make it non-static which increases runtime as static functions can be better optimized.

Definition at line 1742 of file LALSimIMRSpinEOBHamiltonianPrec.c.

XLALSimIMRSpinPrecEOBHamiltonian() [2/2]

static REAL8 XLALSimIMRSpinPrecEOBHamiltonian ( const REAL8  eta, REAL8Vector *restrict  x, REAL8Vector *restrict  p, REAL8Vector *restrict  s1Vec, REAL8Vector *restrict  s2Vec, REAL8Vector *restrict  sigmaKerr, REAL8Vector *restrict  sigmaStar, INT4  tortoise, SpinEOBHCoeffs *  coeffs  )

static

Function to calculate the value of the spinning Hamiltonian for given values of the dynamical variables (in a Cartesian co-ordinate system).

The inputs are as follows:

x - the separation vector r expressed in Cartesian co-ordinates p - the momentum vector (with the radial component tortoise pr*) sigmaKerr - spin of the effective Kerr background (a combination of the individual spin vectors) sigmaStar - spin of the effective particle (a different combination of the individual spins). coeffs - coefficients which crop up in the Hamiltonian. These can be calculated using the XLALCalculateSpinEOBParams() function.

The function returns a REAL8, which will be the value of the Hamiltonian if all goes well; otherwise, it will return the XLAL REAL8 failure NaN. The Hamiltonian function is described in PRD 81, 084024 (2010) and PRD 84, 104027 (2011)

Parameters

eta	< Symmetric mass ratio
x	< Position vector
p	< Momentum vector (tortoise radial component pr*)
s1Vec	< Spin vector 1
s2Vec	< Spin vector 2
sigmaKerr	< Spin vector sigma_kerr
sigmaStar	< Spin vector sigma_star
tortoise	< flag to state whether the momentum is the tortoise co-ord
coeffs	< Structure containing various coefficients

Definition at line 126 of file LALSimIMRSpinEOBHamiltonianPrec.c.