### Gini/M20

(Gini-M20)
(an automatable method of detecting whether a galaxy has recently merged)

Gini/M20 (or Gini-M20) is a method of classifying galaxies both regarding morphology and whether they are recent mergers, using pixel data. It can be done algorithmically, thus is suitable for application to survey data, and classifying whole populations of galaxies.

It is based upon a graph of two statistics: Gini (or G) and M20 (or M20) applied to the flux measure at each pixel:

Gini (G) is a statistic regarding the distribution of flux among the pixels, varying from G = 0 meaning each pixel received the same flux, to G = 1 meaning all the flux was to a single pixel. (The statistic is borrowed from economics where it is used to describe wealth distribution of populations, e.g., few rich with lots of wealth, or a wider spread.)

M20 is a statistic regarding how the brightness is positioned across the galaxy: in particular how far the bright pixels are from the center. The statistic is the log of a ratio: a "moment" regarding a bright group of pixels versus the same moment for all the galaxy's pixels. The "bright group" is the pixels receiving the most flux, the set cut off when their sum constitutes 20% of all the flux. The "moment" is the sum of products for each pixel, the product being pixel's flux received multiplied by the square of its distance from the center of the galaxy, presumably a center-of-mass type center based on flux received, pixel by pixel.

(galaxies,statistics,mergers,flux,technique)
http://en.wikipedia.org/wiki/Gini_coefficient
https://arxiv.org/abs/astro-ph/0311352
http://astrostatistics.psu.edu/su11scma5/lectures/freeman_scmav_poster.pdf
https://lavinia.as.arizona.edu/~gbesla/ASTR_520_files/Lecture16_GalaxyStructure.pdf

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