beta_ellipticity

skypy.galaxy.ellipticity.beta_ellipticity(e_ratio, e_sum, size=None)

Galaxy ellipticities sampled from a reparameterized beta distribution.

The ellipticities follow a beta distribution parameterized by \(e_{\rm ratio}\) and \(e_{\rm sum}\) as presented in [1] Section III.A.

Parameters

e_ratioarray_like

Mean ellipticity of the distribution, must be between 0 and 1.

e_sumarray_like

Parameter controlling the width of the distribution, must be positive.

Notes

The probability distribution function \(p(e)\) for ellipticity \(e\) is given by a beta distribution:

\[p(e) \sim \frac{\Gamma(a+b)}{\Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1}\]

for \(0 <= e <= 1\), \(a = e_{\rm sum} e_{\rm ratio}\), \(b = e_{\rm sum} (1 - e_{\rm ratio})\), \(0 < e_{\rm ratio} < 1\) and \(e_{\rm sum} > 0\), where \(\Gamma\) is the gamma function.

References

1

Kacprzak T., Herbel J., Nicola A. et al., arXiv:1906.01018

Examples

Sample 10000 random variates from the Kacprzak model with \(e_{\rm ratio} = 0.5\) and \(e_{\rm sum} = 1.0\):

>>> from skypy.galaxy.ellipticity import beta_ellipticity
>>> ellipticity = beta_ellipticity(0.5, 1.0, size=10000)