dirichlet_coefficients¶
- skypy.galaxies.spectrum.dirichlet_coefficients(redshift, alpha0, alpha1, z1=1.0, weight=None)[source] [edit on github]¶
Dirichlet-distributed SED coefficients.
- Spectral coefficients to calculate the rest-frame spectral energy
distribution of a galaxy following the Herbel et al. model in [1].
- Parameters:
- redshift(nz,) array_like
The redshift values of the galaxies for which the coefficients want to be sampled.
- alpha0, alpha1(nc,) array_like
Factors parameterising the Dirichlet distribution according to Equation (3.9) in [1].
- z1float or scalar, optional
Reference redshift at which alpha = alpha1. The default value is 1.0.
- weight(nc,) array_like, optional
Different weights for each component.
- Returns:
- coefficients(nz, nc) ndarray
The spectral coefficients of the galaxies. The shape is (n, nc) with nz the number of redshifts and nc the number of coefficients.
Notes
One example is the rest-frame spectral energy distribution of galaxies which can be written as a linear combination of the five kcorrect [2] template spectra \(f_i\) (see [1])
\[f(\lambda) = \sum_{i=1}^5 c_i f_i(\lambda) \;,\]where the coefficients \(c_i\) were shown to follow a Dirichlet distribution of order 5. The five parameters describing the Dirichlet distribution are given by
\[\alpha_i(z) = (\alpha_{i,0})^{1-z/z_1} \cdot (\alpha_{i,1})^{z/z_1} \;.\]Here, \(\alpha_{i,0}\) describes the galaxy population at redshift \(z=0\) and \(\alpha_{i,1}\) the population at \(z=z_1 > 0\). These parameters depend on the galaxy type and we chose \(z_1=1\).
Beside this example, this code works for a general number of templates.
References