GW Sources Characterization

Sky Localization

In GWDALI we deal with astronomical coordinates (RA, Dec) aligned with geocentric coordinates (longitude ‘lon’ and latitude ‘lat’ ) such that \(Ra//lon\) and \(Dec//lat\):

Source Coordinates

Free Parameters

  • m1: Redshifted Mass of the first object \(\longrightarrow (1+z)m_1\) [\(M_{\odot}\)]

  • m2: Redshifted Mass of the second object \(\longrightarrow (1+z)m_2\) [\(M_{\odot}\)]

  • eta: Symetric mass ratio \(\longrightarrow \eta \equiv m_1m_2/(m_1+m_2)^2\)

  • Mc: Redshifted Chirp Mass \(\longrightarrow (1+z)M_c \equiv (1+z)\eta^{3/5}(m_1+m_2)\) [\(M_{\odot}\)]

  • q: Mass Ratio \(\longrightarrow q=m_1/m_2\) with \(m_2>m_1\)

  • DL: Luminosity Distance \(\longrightarrow d_L\) [Gpc]

  • inv_dL: Inverse of Luminosity Distance \(\longrightarrow d_L^{-1}\) [\(Gpc^{-1}\)]

  • ln_dL: Logarithm of Luminosity Distance \(\longrightarrow ln(d_L/Gpc)\)

  • RA: Right Ascencion \(\longrightarrow Ra\) [deg]

  • Dec: Declination \(\longrightarrow Dec\) [deg]

  • iota: Binary Inclination \(\longrightarrow \iota\) [rad]

  • cos_iota: Cosine of Inclination \(\longrightarrow cos(\iota)\)

  • psi: Polarization Angle \(\longrightarrow \psi\) [rad]

  • phi_coal: Coalescence Phase \(\longrightarrow \phi_{coal}\) [rad]

  • t_coal: Coalescence Time \(\longrightarrow t_{coal}\) [seconds]

  • sx1: X-Component of First Object Spin \(\longrightarrow S_{x_1}\)

  • sy1: Y-Component of First Object Spin \(\longrightarrow S_{y_1}\)

  • sz1: Z-Component of First Object Spin \(\longrightarrow S_{z_1}\)

  • sx2: X-Component of Second Object Spin \(\longrightarrow S_{x_2}\)

  • sy2: Y-Component of Second Object Spin \(\longrightarrow S_{y_2}\)

  • sz2: Z-Component of Second Object Spin \(\longrightarrow S_{z_2}\)

  • S1: Magnitude of the First Object Spin \(\longrightarrow |\vec{S}_1|\)

  • theta_1: Polar Angle of the First Object Spin \(\longrightarrow \theta_1\) [rad]

  • phi_1: Azimuthal Angle of the First Object Spin \(\longrightarrow \phi_1\) [rad]

  • S2 Magnitude of the Second Object Spin \(\longrightarrow |\vec{S}_2|\)

  • theta_2: Polar Angle of the Second Object Spin \(\longrightarrow \theta_2\) [rad]

  • phi_2: Azimuthal Angle of the Second Object Spin \(\longrightarrow \phi_2\) [rad]