hmf.density_field.filters.Filter.dlnss_dlnr

Filter.dlnss_dlnr(r)

The derivative of the mass variance with radius.

Parameters

r (array_like) – Radii

Returns

dlnss_dlnr – The derivative of the the mass variance with radius.

Return type

array_like

Notes

Given a prescription for how radius grows with mass (typically with a log-slope of 1/3, and set in dlnr_dlnm()), this specifies the quantity \(\frac{d \ln \sigma^2}{d\ln m}\).

The general formula is

\[\frac{d\ln \sigma^2}{d\ln R} = \frac{1}{\pi^2\sigma^2} \int_0^\infty W(kR) \frac{dW(kR)}{d\ln(kR)} P(k)k^2 dk\]