The surface density profiles from three different lines of sight along each of the principal axes are measured by fitting elliptical contours to the observed density map. Figure 6 shows the log surface density plotted versus . Another axis is included showing the equivalent surface brightness assuming for the stars.
Figure 6: The surface brightness profile of the galaxy along elliptical isophotes plotted versus for the principal axis projections of the galaxy. The simulated galaxy follows a deVaucouleurs law closely and would be classified as a giant elliptical. A cD galaxy envelope did not form in this simulation.
The nearly linear dependence on from 3-100 kpc reveal that the galaxy follows a deVaucouleurs light profile. The profile is similar to measured profiles of giant ellipticals (gE) rather than cD galaxies which show an excess of light at large radii. deVaucouleurs profiles are fit for the effective radius, , and the total mass. The effective radii (calculated as ) is between 18-22 kpc depending on the projection. The fitted total mass is M corresponding to a total luminosity of 6 (assuming and L). The regularity of the isophotes and the measured scales and luminosities of the merger remant are consistent with observations of giant elliptical galaxies.
The 3-dimensional density profile of the merger remnant reveals the
relative distribution of stars and dark matter in an elliptical galaxy (Fig.
7). The Hernquist density profile (1990),
provides convenient model fits to both the stellar and dark matter profiles. The fitted masses and scale radii are M and kpc for the stars and M and kpc for the dark matter as shown in Figure 7.
Figure 7: The spherically averaged density profile for the stars, dark matter and the all of the matter. The Hernquist profile is fitted separately to the stars and dark matter profile and the lines are shown. The solid line is the sum of the two fits. The stellar density is about 3 times the dark matter density within 10 kpc or 0.5 and so central kinematics are dominated by the observed stars.
Stellar mass dominates within r<10 kpc (), although the stellar density is only about 3 times the dark matter density at the center. The stellar and dark matter density are equal in the range of 10-20 kpc () while beyond 40 kpc () the dark matter density is at least ten times the stellar density. The merging process tends to enhance the ratio of dark mass to luminous mass within in the central regions. In the initial population of disk+bulge galaxies the dark to luminous mass ratio at the half light radius is 0.4, while the giant elliptical has a ratio of about 1.0 at a nominal effective radius of 20 kpc, a factor of 2.5 enhancement. The most likely reason for this enhancement is the tendency for disk stars to be heated more effectively than the dark matter particles. The same resonant interactions which create tidal tails during mergers add energy more effectively to disk stars than to dark matter particles with the same initial binding energy. The dark matter density may then be enhanced slightly with respect to the stars in the merger remnant in comparison to the initial disks.
The overall trend for increasing dark to luminous mass ratio is shown in Figure 8. Stars dominate the central density and the dark to luminous mass ratio is only about 0.3. At , the ratio starts to grow linearly reaching 1.0 at continuing to rise to 3.3 at . These mass ratios and general behaviour are in accord with recent models of the dark matter in ellipticals derived from combining surface brightness and kinematical information (e.g. Saglia et al. 1992, 1993; Rix et al. 1997).
Figure 8: The ratio of dark to luminous mass in the BCG over 5. Dark mass still represents about 30% of the mass at the center in this model. The ratio grows almost linearly with radius.