The Carnegie-Irvine Galaxy Survey. IV. A Method to Determine the Average
  Mass Ratio of Mergers That Built Massive Elliptical Galaxies
  Many recent observations and numerical simulations suggest that nearby
massive, early-type galaxies were formed through a "two-phase" process. In the
proposed second phase, the extended stellar envelope was accumulated through
many dry mergers. However, details of the past merger history of present-day
ellipticals, such as the typical merger mass ratio, are difficult to constrain
observationally. Within the context and assumptions of the two-phase formation
scenario, we propose a straightforward method, using photometric data alone, to
estimate the average mass ratio of mergers that contributed to the build-up of
massive elliptical galaxies. We study a sample of nearby massive elliptical
galaxies selected from the Carnegie-Irvine Galaxy Survey, using two-dimensional
analysis to decompose their light distribution into an inner, denser component
plus an extended, outer envelope, each having a different optical color. The
combination of these two substructures accurately recovers the negative color
gradient exhibited by the galaxy as whole. The color difference between the two
components (<\Delta(B-V)> ~ 0.10 mag; <\Delta(B-R)> ~ 0.14 mag), based on the
slope of the M_stellar-color relation for nearby early-type galaxies, can be
translated into an estimate of the average mass ratio of the mergers. The rough
estimate, 1:5 to 1:10, is consistent with the expectation of the two-phase
formation scenario, suggesting that minor mergers were largely responsible for
building up to the outer stellar envelope of present-day massive ellipticals.
With the help of accurate photometry, large sample size, and more choices of
colors promised by ongoing and future surveys, the approach proposed here can
reveal more insights into the growth of massive galaxies during the last few
Gyr.
