schechter_smf

skypy.galaxy.stellar_mass.schechter_smf(alpha, m_star, x_min, x_max, resolution=100, size=None)

Stellar masses following the Schechter mass function [1].

Parameters

alphafloat

The alpha parameter in the Schechter stellar mass function.

m_star(nm,) array-like

Characteristic stellar mass M_*.

size: int, optional

Output shape of stellar mass samples. If size is None and m_star is a scalar, a single sample is returned. If size is None and m_star is an array, an array of samples is returned with the same shape as m_star.

x_min, x_maxfloat

Lower and upper bounds for the random variable x in units of M_*.

resolutionint, optional

Resolution of the inverse transform sampling spline. Default is 100.

Returns

stellar mass(nm,) array_like

Drawn stellar masses from the Schechter stellar mass function in units of the solar mass.

Notes

The stellar mass probability distribution (pdf) follows a Schechter profile of the form

\[\Phi(M) = \frac{1}{M_*} \left(\frac{M}{M_*}\right)^\alpha \exp\left(-\frac{M}{M_*}\right) \;.\]

From this pdf one can sample the stellar masses.

References

1

Mo, H., Van den Bosch, F., & White, S. (2010). Galaxy Formation and Evolution. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511807244

Examples

>>> from skypy.galaxy import stellar_mass

Sample 100 stellar masses values at redshift z = 1.0 with alpha = -1.4, m_star = 10**10.67, x_min = 0.0002138 and x_max = 213.8

>>> masses = stellar_mass.schechter_smf(-1.4, 10**10.67, 0.0002138,
...                               213.8, size=100)