Luminosity profile

In contrast to spirals galaxies, elliptical have smooth surface brightness (SB) profiles, ellipsoidal in shape. The SB profile of some elliptical are shown in Figure (7.1). Note how in the center the isophotes are well defined and elliptical, whereas in the outer parts they become less smooth (noisier) because the SB decreases. Also note the presence of foreground MW stars.

Figure 7.1: (Taken from astro-ph/0206097) Lines of constant surface brightness (isophotes) in the K band for four elliptical galaxies. In successive isophotes, the surface brightness increases by 0.25 magnitudes.

A plot of the average surface brightness as function of radius for these same ellipticals is shown in Figure (7.2). The drawn line which fits the data well, is an $r^{1/4}$ fit, Eq. (3.2). Often, these profiles are plotted as SB vs $r^{1/4}$ in which case the profile is a straight line, as in Figure (7.3). For most ellipticals this profile shape fits their SB-distribution well. A more general fit which sometimes used, is $I(r)\propto \exp[-(r/r_e)^{1/n}]$, where $n=4$ corresponds to the de Vaucouleurs $r^{1/4}$ fit.

Figure 7.2: (Taken from astro-ph/0206097) Surface brightness as function of distance to the center. The drawn line is the best $r^{1/4}$ fit.

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Figure 7.3: Luminosity profile for galaxy NGC 3379 (open symbols) and $r^{1/4}$ fit (drawn line). Taken from de Vaucoleurs & Capaccioli, ApJS 40, 1979.

Figure 7.4: SB profile for NGC 1399 from Schombert (filled symbols; ApJS, 1989). The outer parts of the profile do not follow the $r^{1/4}$ fit (bottom panel), but are nearly a straight line in a SB-$\log(r)$ (i.e. a $\log-\log$) plot (top panel), meaning the profile is close to a power-law.

Figure 7.5: Image of NGC 1399 with smooth, best fit $r^{1/4}$ profile subtracted (Bridges et al., AJ 101, 469 (1991). The centre of NGC 1399 is at the left, the object toward the top right is another galaxy in the galaxy cluster. The other extended objects in the image are other galaxies. Clearly seen are hundreds of high SB unresolved objects, which are GCs in the halo of NGC 1399.

Some of the giant elliptical galaxies that are invariably found in the centers of big clusters of galaxies have an extended halo that is not fit well by the de Vaucouleurs profile. Such galaxies are called cD galaxies. Fig. (7.4) show the profile of NGC 1399, which is the cD galaxy in the nearby Fornax cluster of galaxies. This very extended halo of stars is truly enormous: it can be traced to around a Mpc. Even though the distance to Fornax is large, it means that the extent on the sky of NGC 1399 is about the size of the moon! This gigantic size has prompted the suggestion that may be we should associate such a halo with the cluster of galaxies, rather than with any individual galaxy. This suggestion has some support from the observations of some clusters where we observe a faint halo, but without a galaxy in the center!

Es also have many globular clusters. Figure (7.5) is an image of NGC 1399, where an $r^{1/4}$ fit to the SB-profile of the galaxy has been subtracted. Clearly visible are 100s of high SB objects, indistinguishable on this plate from foreground stars, which are in fact GCs in the halo of the galaxy. The GC luminosity function (i.e., the number of clusters as function of their magnitude) has been used as a standard candle: by measuring the luminosity function of GCs of a galaxy, and comparing it to the luminosity function of a galaxy with known distance, one can obtain a distance estimate.

Why do ellipticals have an $r^{1/4}$ SB-profile? As I explained earlier, there seems to be a strong connection between the density of galaxies (in the sense of how many galaxies you find per Mpc$^{3}$ in a given region, say) and their types: high density regions invariably contain a much larger fraction of Es than low density regions, where Ss dominate. So, may be interactions between galaxies have something to do with it?

Recent numerical simulations of collisions between two spiral galaxies do produce objects with SB-profiles not too different from $r^{1/4}$ appropriate for an E. And although this is a good hint that we're on the right track, in fact, also in the simulations we don't really know why this is. In a famous paper, Donald Lynden-Bell suggested that during a galaxy merger, the gravitational potential $\Phi$ which the stars feel, changes very rapidly and this might produce a characteristic density profile^7.1. He termed this process violent relaxation. And so the suggestion is that, as (predominantly spiral) galaxies fall into galaxy clusters, they will violently interact with other galaxies, transforming them somehow into Es. And although this is certainly an important piece of the puzzle, it can't be the whole story, because the stellar populations of Es and Ss differ.