We show that the observed upper bound on the line-of-sight velocity dispersion of the stars in an early-type galaxy , \sigma _ { e } \lesssim 400 km s ^ { -1 } , may have a simple dynamical origin within the \Lambda CDM cosmological model , under two main hypotheses .
The first is that most of the stars now in the luminous parts of a giant elliptical formed at redshift z \gtrsim 6 .
Subsequently , the stars behaved dynamically just as an additional component of the dark matter .
The second hypothesis is that the mass distribution characteristic of a newly formed dark matter halo forgets such details of the initial conditions as the stellar “ collisionless matter ” that was added to the dense parts of earlier generations of halos .
We also assume that the stellar velocity dispersion does not evolve much at z \lesssim 6 , because a massive host halo grows mainly by the addition of material at large radii well away from the stellar core of the galaxy .
These assumptions lead to a predicted number density of ellipticals as a function of stellar velocity dispersion that is in promising agreement with the Sloan Digital Sky Survey data .