hmf.core.mass_variance.n_eff_kernel

hmf.core.mass_variance.n_eff_kernel(dlnsigma_dlnm: ArrayLike) → ndarray[tuple[Any, ...], dtype[float64]]

The effective spectral index at a mass, from the slope of sigma(m).

\[n_{\rm eff} = -3\left(2\frac{d\ln\sigma}{d\ln m} + 1\right),\]

the index n of the power law \(P \propto k^n\) that has the same slope of sigma at this mass: for a power law, \(\sigma \propto m^{-(n+3)/6}\), so \(n_{\rm eff} = n\) exactly. It is the n_eff input of the fits in hmf.core.fits. A pure, elementwise kernel on plain arrays (see hmf.core._kernels).

Parameters:

dlnsigma_dlnm – \(d\ln\sigma/d\ln m\), dimensionless (e.g. the second result of MassVariance.ln_sigma_and_slope_kernel()).

Returns:

\(n_{\rm eff}\), dimensionless, with the shape of dlnsigma_dlnm.

Return type:

numpy.ndarray

Raises:

DomainError – If a value is not finite.