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Galaxies

Elliptical Galaxies

Elliptical galaxies contain very little dust and gas, and, as a consequence, they contain only old stars. These galaxies are elliptical in projection on the sky, although they may have three axes of symmetry; their three-dimensional structure cannot be determined observationally. They have little or no rotation regardless of their ellipticity. This means that there is no systematic direction of rotation for the stars within the galaxy. The stars have a wide variety of orbits the galaxy, ranging from the circular to the highly elliptical. Without a strong angular momentum, there is no possibility for the formation of a stellar disk within the galaxy. Whatever collapse occurs of the small amount of gas trapped in this type of galaxy is towards the center of the galaxy.

Surface Brightness

In projection on the sky an elliptical galaxy is brightest at its center and less bright as one moves radially outward. If one determines for a galaxy the isophotes, which are contours of constant brightness, one finds a progression of concentric ellipses from the center outward.

The variation of the surface surface brightness of an elliptical galaxy with distance R from its center is modeled by

I(R) = Ie e-7.67 [ ( R/Re)0.25 -1 ].

where Re is the effective radius, which is the radius of the isophote containing 50% of the luminosity, and Ie is the surface brightness at Re. The typical value of Re for the brightest galaxies is 3 h-1 kpc, where h is the Hubble constant in units of 100 km s-1 Mpc-1. For fainter galaxies Re is smaller than this value.

Velocity Dispersion

The average velocity of the stars within an elliptical galaxy is dependent upon the galaxy's mass, and therefore the galaxy's luminosity. From observation, the dependence of the velocity dispersion within an elliptical galaxy with galactic luminosity is given by

??p = 220 ( L/L0)1/4 km s-1,

where L0 is a characteristic luminosity for elliptical galaxies that has the value

L0 = 1010 h-2 LsV.

In this last equation, LsV is the solar luminosity in the visible wave band, and h is the Hubble constant in units of 100 km s-1 Mpc-1. These velocities are slightly smaller than one finds for spiral galaxies.

Luminosity Distribution

The distributions of luminosity L for elliptical galaxies within a given volume is given by

Φ(L) dL = n0 ( L/L0 )?? e-L/L0 d ln L.

The luminosity L0 is the characteristic luminosity defined in the last section of this page. The values of the galaxy density n0 and the power law index ?? are

n0 = 0.012 h3 Mpc-3,
?? = -1.25.

The luminosity distribution diverges as the luminosity goes to zero. Of course, there is a cutoff somewhere below the current detection range that keeps the number of galaxies per unit volume finite. The important point of this equation is that there are far more low-luminosity than high-luminosity elliptical galaxies in the universe. The luminosity function also shows that there are not too many elliptical galaxies with luminosities more than ten billion times the Sun's luminosity.

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