pttools.omgw0.noise
Functions
- pttools.omgw0.noise.N_AE(f, ft=FT_LISA, L=const.LISA_ARM_LENGTH, W_abs2=None)
A and E channels of LISA instrument noise
\[N_A = N_E = ...\]Gowling & Hindmarsh, 2021 eq. 3.4
- pttools.omgw0.noise.P_acc(f, L=const.LISA_ARM_LENGTH)
LISA single test mass acceleration noise Gowling & Hindmarsh, 2021 eq. 3.3
- pttools.omgw0.noise.P_oms(L=const.LISA_ARM_LENGTH)
LISA optical metrology noise
\[P_\text{oms}(f) = \left( \frac{1.5 \cdot 10^{-11} \text{m}}{L} \right)^2 \text{Hz}^{-1}\]Gowling & Hindmarsh, 2021 eq. 3.2 This is white noise and therefore independent of the frequency. Note that there is a typo on Gowling & Hindmarsh, 2021 p. 12: the correct \(L = 2.5 \cdot 10^9 \text{m}\).
- pttools.omgw0.noise.R_AE(f, ft=FT_LISA, W_abs2=None)
Gravitational wave response function for the A and E channels Gowling & Hindmarsh, 2021 eq. 3.6
- pttools.omgw0.noise.S(N, R)
Noise power spectral density
\[S = \frac{N}{\mathcal{R}}\]Gowling & Hindmarsh, 2021 eq. 3.1
- pttools.omgw0.noise.S_AE(f, ft=FT_LISA, L=const.LISA_ARM_LENGTH, both_channels=True)
Noise power spectral density for the LISA A and E channels
\[S_A = S_E = \frac{N_A}{\mathcal{R}_A}\]Gowling & Hindmarsh, 2021 eq. 3.7
- pttools.omgw0.noise.S_AE_approx(f, L=const.LISA_ARM_LENGTH, both_channels=True)
Approximate noise power spectral density for the LISA A and E channels
\[S_A = S_E = \frac{N_A}{\mathcal{R}_A} \approx \frac{40}{3} ({P}_\text{oms} + {4P}_\text{acc}) \left( 1 + \frac{3f}{4f_t} \right)^2\]Gowling & Hindmarsh, 2021 eq. 3.7
- pttools.omgw0.noise.S_gb(f, A=9e-35, f_ref_gb=1, fk=1.13e-3, a=0.138, b=-221, c=521, d=1680)
Noise power spectral density for galactic binaries
- pttools.omgw0.noise.W(f, ft)
Round trip modulation
\[W(f,f_t) = 1 - e^{-2i \frac{f}{f_t}}\]Gowling & Hindmarsh, 2021 p. 12
- pttools.omgw0.noise.ft(L=const.LISA_ARM_LENGTH)
Transfer frequency
\[f_t = \frac{c}{2\pi L}\]Gowling & Hindmarsh, 2021 p. 12
- pttools.omgw0.noise.omega(f, S)
Convert an effective noise power spectral density (aka. sensitivity) \(S\) to a fractional GW energy density power spectrum \(\Omega\)
\[\Omega = \frac{4 \pi^2}{3 H_0^2} f^3 S(f)\]Gowling & Hindmarsh, 2021 eq. 3.8, Gowling et al., 2023 eq. 3.8, Smith & Caldwell, 2019 p. 1
- pttools.omgw0.noise.omega_eb(f, f_ref_eb=25, omega_ref_eb=8.9e-10)
- pttools.omgw0.noise.omega_gb(f)
- pttools.omgw0.noise.omega_ins(f)
LISA instrument noise
\[\Omega_\text{ins} = \frac{4 \pi^2}{3 H_0^2} f^3 S_A(f)\]
- pttools.omgw0.noise.omega_noise(f)
- \[\Omega_\text{noise} = \Omega_\text{ins} + \Omega_\text{eb} + \Omega_\text{gb}\]
- pttools.omgw0.noise.signal_to_noise_ratio(f, signal, noise, obs_time=const.LISA_OBS_TIME)
Signal-to-noise ratio $$rho = sqrt{T_{text{obs}} int_{{f}_text{min}}^{{f}_text{max}} df frac{ h^2 Omega_{text{gw},0}^2}{ h^2 Omega_{text{n}}^2}} Gowling & Hindmarsh, 2021 eq. 3.12, Smith & Caldwell, 2019 p. 1