linear_lognormal

skypy.galaxy.size.linear_lognormal(magnitude, a_mu, b_mu, sigma, size=None)

Lognormal distribution with linear mean. This function provides a lognormal distribution for the physical size of galaxies with a linear mean, described by equation 3.14 in [1]. See also equation 14 in [2].

Parameters

magnitudefloat or array_like.

Galaxy absolute magnitude at which evaluate the lognormal distribution.

a_mu, b_mufloat

Linear model parameters describing the mean size of galaxies, equation 3.14 in [1].

sigma: float

Standard deviation of the lognormal distribution for the physical radius of galaxies.

sizeint or tuple of ints, optional.

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if mean and sigma are both scalars. Otherwise, np.broadcast(mean, sigma).size samples are drawn.

Returns

physical_sizenumpy.ndarray or astropy.Quantity

Physical distance for a given galaxy with a given magnitude, in [kpc]. If size is None and magnitude is a scalar, a single sample is returned. If size is ns, different from None, and magnitude is scalar, shape is (ns,). If magnitude has shape (nm,) and size=None, shape is (nm,).

References

..[1] J. Herbel, T. Kacprzak, A. Amara, A. Refregier, C.Bruderer and

1. Nicola, JCAP 1708, 035 (2017).

..[2] S. Shen, H.J. Mo, S.D.M. White, M.R. Blanton, G. Kauffmann, W.Voges,

10. Brinkmann, I.Csabai, Mon. Not. Roy. Astron. Soc. 343, 978 (2003).

Examples

>>> import numpy as np
>>> from skypy.galaxy import size
>>> magnitude = -20.0
>>> a_mu, b_mu, sigma =-0.24, -4.63, 0.4
>>> s = size.linear_lognormal(magnitude, a_mu, b_mu, sigma)