redback.transient_models.spectral_models.p_cygni_profile

redback.transient_models.spectral_models.p_cygni_profile(wavelength, lambda_rest, tau_sobolev, v_phot, continuum_flux, source_function='thermal', v_max=None, **kwargs)[source]

P-Cygni line profile using Sobolev approximation

Creates characteristic emission + blueshifted absorption from expanding envelope

Parameters:

  • wavelength (array) – Wavelength array in Angstroms (observer frame)

  • lambda_rest (float) – Rest wavelength of transition in Angstroms (e.g., 6355 for Si II)

  • tau_sobolev (float) – Sobolev optical depth (0.1-100)

  • v_phot (float) – Photospheric velocity in km/s (5000-20000 for SNe)

  • continuum_flux (array or float) – Continuum flux level

  • source_function (str or float) – ‘thermal’ (Planckian), ‘scattering’ (electron scat), or float value

  • v_max (float, optional) – Maximum velocity of envelope in km/s (default: 1.5 * v_phot)

Returns:

flux – Spectrum with P-Cygni profile

Return type:

array

References

  • Kasen & Branch 2001 (ApJ, 560, 439) - Analytic inversion

  • Jeffery & Branch 1990 - P-Cygni atlas

  • Branch et al. 2002 (ApJ, 566, 1005) - Direct analysis of SN spectra

Notes

Sobolev approximation valid when: v_thermal << v_phot (typically 10 km/s << 10,000 km/s)

The profile consists of: - Blueshifted absorption trough (v < 0, |v| < v_max) - Emission peak (v > 0, near rest wavelength)

Examples

>>> # Si II 6355 line at 10,000 km/s
>>> wave = np.linspace(5000, 7000, 1000)
>>> flux = p_cygni_profile(wave, lambda_rest=6355, tau_sobolev=3.0,
...                        v_phot=10000, continuum_flux=1.0)