Local galaxies with compact cores as the possible descendants of massive
  compact quiescent galaxies at high redshift
  In order to test a possible evolutionary scenario of high-$z$ compact
quiescent galaxies (cQGs) that they can survive as local compact cores embedded
in local massive galaxies with different morphology classes, we explore the
star formation histories of local compact cores according to their spectral
analysis. We build a sample of 182 massive galaxies with compact cores
(${M}_{*,{\rm core}} > 10^{10.6} {\rm M}_\odot$) at $0.02 \leq z \leq 0.06$
from SDSS DR7 spectroscopic catalogue. STARLIGHT package is used to analyze the
median stacked spectra and derive the stellar ages and metallicities. Our main
results show that local compact cores have the average age of about
$12.1\pm0.6$ Gyr, indicating their early formation at $z > 3$, which is
consistent with the formation redshifts of cQGs at $1<z<3$. Together with
previous studies, our result that local compact cores have similar formation
redshifts as those of high-$z$ cQGs, supports that local massive galaxies with
compact cores are possible descendants of cQGs. Morphological study of local
galaxies with compact cores suggests that there would be multiple possible
evolutionary paths for high-$z$ cQGs: most of them ($> 80\%$) will evolve into
local massive ETGs according to dry minor merger, while some of them ($\sim
15\%$) will build a substantial stellar/gas discs according to the late-time
gas accretion and sustaining star formation, and finally grow up to spiral
galaxies.
