Galaxies are unique in their own way. However, they can also be characterized in a statistical way. Galaxy morphology was first defined from their appearance, but later turned out to be tightly related to various physical quantities. Dependence of luminosity, dynamical mass, gas mass, and the mass-to-light ratio on the galaxy morphology is first introduced. The galaxy morphology is also connected to the star formation activity in galaxies, reflected in their optical colors and emission line intensity. Then we introduce the morphology–density relation, a remarkable correlation between the spatial density and morphology of galaxies. This relation is originally discovered in a dense environment of clusters of galaxies, but then found to continue to lower density, even to the large-scale structures. Another important statistical property is the luminosity of galaxies. We define the luminosity function (LF) as the probability density function of galaxy luminosity, and derive some useful formulae from the LF. Two representative nonparametric statistical methods to estimate the galaxy LF are discussed in detail. Further, we introduce a recently developed method to extend the LF to multidimensional, in order to deal with present-day multiwavelength surveys. We show the formulation of galaxy number count and how the LF works to describe the evolution of galaxies. Finally, we discuss the scaling relations of galaxies.

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Statistical Properties of Galaxies

  • Tsutomu T. Takeuchi

摘要

Galaxies are unique in their own way. However, they can also be characterized in a statistical way. Galaxy morphology was first defined from their appearance, but later turned out to be tightly related to various physical quantities. Dependence of luminosity, dynamical mass, gas mass, and the mass-to-light ratio on the galaxy morphology is first introduced. The galaxy morphology is also connected to the star formation activity in galaxies, reflected in their optical colors and emission line intensity. Then we introduce the morphology–density relation, a remarkable correlation between the spatial density and morphology of galaxies. This relation is originally discovered in a dense environment of clusters of galaxies, but then found to continue to lower density, even to the large-scale structures. Another important statistical property is the luminosity of galaxies. We define the luminosity function (LF) as the probability density function of galaxy luminosity, and derive some useful formulae from the LF. Two representative nonparametric statistical methods to estimate the galaxy LF are discussed in detail. Further, we introduce a recently developed method to extend the LF to multidimensional, in order to deal with present-day multiwavelength surveys. We show the formulation of galaxy number count and how the LF works to describe the evolution of galaxies. Finally, we discuss the scaling relations of galaxies.