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LALInspiral 5.0.3.1-8a6b96f
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LALInspiral 5.0.3.1-8a6b96f
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NONE.
In a parameter space defined by \(m_1\) and \(m_2\), or equivalently, \(M=m_1+m_2\) and \(\eta=\frac{m_1 m_2}{M^2}\), the conversion to chirp-time parameter such as \(\tau_0\) and \(\tau_3\) si quite common. In particular, it is interesting to get the value of \(\tau_3\) when only \(\tau_0\) is known, and a constraint on the masses exists (e.g., \(m_1=m_2\) or one of the mass equals mMin or mMax. This modules contains a few functions to perform these conversion.
We know that
\begin{equation} \label{eq_tau0a} \tau_0 = \frac{A_0}{\eta} M^{-5/2}, \end{equation}
and
\begin{equation} \tau_3 = \frac{A_3}{\eta} M^{-2/3}, \end{equation}
where
\begin{equation} A_0 = \frac{5}{256 (\pi *f_L)^{8/3}}, \end{equation}
and
\begin{equation} A_3 = \frac{\pi}{8 (\pi *f_L)^{5/3}}, \end{equation}
Therefore, it is straightforward to express \(\tau_3\) as a function of \(\tau_0\) amd \(\eta\):
\begin{equation} \label{eq_tau3b} \tau_3 = \frac{A3}{\eta} \left( \frac{\tau_0 \eta}{ A_0} \right)^{2/5} \end{equation}
if \(\eta=0.25\) on the equal-mass line, then
\begin{equation} \label{eq_tau3a} \tau_3 = 4 A3 \left( \frac{\tau_0}{ 4 A_0} \right)^{2/5} \end{equation}
Eq. \eqref{eq_tau3b} returns \(\tau_3\) given in \(M, \eta\) and \(f_L\) and is defined inXLALInspiralTau3FromNonEqualMass().
Eq. \eqref{eq_tau3a} returns tau3 in the particular case \(m_1=m_2\), given \(\tau_0\) only, and is defined in XLALInspiralTau3FromTau0AndEqualMassLine().
Eq. \eqref{eq_tau0a} returns \(tau_0\) given \(M, \eta\) and \(f_L\), and is defined XLALInspiralTau0FromMEta().
Finally, XLALInspiralMFromTau0AndNonEqualMass() returns \(M\) when \(\tau_0\) is known and a constraint exists on one of the individual mass (e.g., \(m_1=\textrm{mMax}\) or \(m_1=\textrm{mMin}\)). This functions requires a little more algebra and is used in the HybridHexagonal placement. The Module LALInspiralHybridHexagonalBank.c describes this algebra.
Prototypes | |
| REAL4 | XLALInspiralTau3FromTau0AndEqualMassLine (REAL4 tau0, REAL4 fL) |
| REAL4 | XLALInspiralTau3FromNonEqualMass (REAL4 M, REAL4 eta, REAL4 fL) |
| REAL4 | XLALInspiralTau0FromMEta (REAL4 M, REAL4 eta, REAL4 fL) |
| REAL8 | XLALInspiralMFromTau0AndNonEqualMass (REAL8 tau0, REAL8 extremMass, REAL8 fL) |
Definition at line 94 of file LALInspiralBankUtils.c.
Definition at line 113 of file LALInspiralBankUtils.c.
Definition at line 130 of file LALInspiralBankUtils.c.
Definition at line 150 of file LALInspiralBankUtils.c.
1.9.4