NcWindowTophat

NcWindowTophat — A top-hat window function.

Object Hierarchy

    GObject
    ╰── NcWindow
        ╰── NcWindowTophat

Description

This object implements the NcWindow class for a top-hat window function.

This object returns the top hat window function in the real space. \begin{align} W_{TH}(r, R) = \frac{3}{4\pi R^3} \left{ \begin{array} {ll} 1 & \leq R\ 0 & > R. \end{array} \right. \end{align} The mass enclosed within the volume selected by this window function is $M_{TH}(R)= \frac{4\pi}{3}\overline{\rho} R^3$,where $\overline{\rho}(z)$ is the mean density of the universe at redshift $z$.

The top-hat window function in the Fourier space is given by

\begin{align} W_{th}(k, R) &= \frac{3}{(kR)^3}(\sin kR - (kR)\cos kR) \ &= \frac{3}{(kR)} j_1(kR), \end{align} where $j_\nu(kR)$ is the spherical Bessel function.

The first derivative with respect to $R$ \begin{equation} \frac{dW_{TH}(k, R)}{dR} = \frac{-9}{k^3 R^4} (\sin kR - (kR)\cos kR) + \frac{3}{k R^2} \sin kR. \end{equation}

Functions

nc_window_tophat_new ()

NcWindow *
nc_window_tophat_new (void);

This function returns a NcWindow with a NcWindowTophat implementation.

Returns

A new NcWindow.


NC_WINDOW_VOLUME_TOPHAT

#define NC_WINDOW_VOLUME_TOPHAT (4.0 * M_PI / 3.0)

Types and Values