# LISA Detector¶

Functions relative to the LISA detector.

kerrgeodesic_gw.lisa_detector.power_spectral_density(freq)

Return the effective power spectral density (PSD) of the detector noise at a given frequency.

INPUT:

• freq – frequency $$f$$ (in $$\mathrm{Hz}$$)

OUTPUT:

• effective power spectral density $$S(f)$$ (in $$\mathrm{Hz}^{-1}$$)

EXAMPLES:

sage: from kerrgeodesic_gw import lisa_detector
sage: Sn = lisa_detector.power_spectral_density
sage: Sn(1.e-1)  # tol 1.0e-13
3.3944027493062926e-39
sage: Sn(1.e-2)  # tol 1.0e-13
2.738383947022306e-40
sage: Sn(1.e-3)  # tol 1.0e-13
3.269807574220045e-38

kerrgeodesic_gw.lisa_detector.power_spectral_density_RCLfit(freq)

Return the effective power spectral density (PSD) of the detector noise at a given frequency, according to the analytical fit by Robson, Cornish and Liu, Arxiv 1803.01944

INPUT:

• freq – frequency $$f$$ (in $$\mathrm{Hz}$$)

OUTPUT:

• effective power spectral density $$S(f)$$ (in $$\mathrm{Hz}^{-1}$$)

EXAMPLES:

sage: from kerrgeodesic_gw import lisa_detector
sage: Sn = lisa_detector.power_spectral_density_RCLfit
sage: Sn(1.e-1)  # tol 1.0e-13
2.12858262120861e-39
sage: Sn(1.e-2)  # tol 1.0e-13
1.44307343517977e-40
sage: Sn(1.e-3)  # tol 1.0e-13
1.63410027259543e-38

kerrgeodesic_gw.lisa_detector.strain_sensitivity(freq)

Return LISA strain spectral sensitivity at a given frequency.

The strain spectral sensitivity is the square root of the effective noise power spectral density (cf. power_spectral_density()).

INPUT:

• freq – frequency $$f$$ (in $$\mathrm{Hz}$$)

OUTPUT:

• strain sensitivity $$S(f)^{1/2}$$ (in $$\mathrm{Hz}^{-1/2}$$)

EXAMPLES:

sage: from kerrgeodesic_gw import lisa_detector
sage: hn = lisa_detector.strain_sensitivity
sage: hn(1.e-1)  # tol 1.0e-13
5.82615031500758e-20
sage: hn(1.e-2)  # tol 1.0e-13
1.654806317072275e-20
sage: hn(1.e-3)  # tol 1.0e-13
1.8082609253700212e-19

sage: plot_loglog(hn, (1e-5, 1), plot_points=2000, ymin=1e-20, ymax=1e-14,
....:             axes_labels=[r"$f\ [\mathrm{Hz}]$",
....:                          r"$S(f)^{1/2} \ \left[\mathrm{Hz}^{-1/2}\right]$"],
....:             gridlines='minor', frame=True, axes=False)
Graphics object consisting of 1 graphics primitive