Units

These helpers convert between characteristic strain and GW energy-density conventions.

hc_to_omega

hc_to_omega(hc, f)

Convert characteristic strain into \(\Omega_{\rm GW} h^2\).

The conversion assumes the standard observer-frame relation

\[ \Omega_{\rm GW}(f)\,h^2 = \frac{2\pi^2}{3 H_{100}^2}\, f^2 h_c(f)^2, \]

where \(H_{100} = 100\,{\rm km\,s^{-1}\,Mpc^{-1}}\) is encoded in fastropop.constants.H100.

Parameters:

• hc (float or Array) –

  Characteristic strain \(h_c(f)\).

• f (float or Array) –

  Observer-frame gravitational-wave frequency in Hz.

Returns:

• float or Array –

  Energy-density spectrum \(\Omega_{\rm GW}(f) h^2\).

omega_to_hc

omega_to_hc(omega_gwh2, f)

Convert \(\Omega_{\rm GW} h^2\) into characteristic strain.

This is the inverse of hc_to_omega:

\[ h_c(f) = \sqrt{\Omega_{\rm GW}(f) h^2 \frac{3 H_{100}^2}{2\pi^2 f^2}}. \]

Parameters:

• omega_gwh2 (float or Array) –

  Energy-density spectrum \(\Omega_{\rm GW}(f) h^2\).

• f (float or Array) –

  Observer-frame gravitational-wave frequency in Hz.

Returns:

• float or Array –

  Characteristic strain \(h_c(f)\).