Tracing Recent Star Formation of Red Early-type Galaxies out to $z$
  $\sim$ 1
  We study the mid-infrared (IR) excess emission of early-type galaxies (ETGs)
on the red-sequence at $z <$ 1 using a spectroscopic sample of galaxies in the
fields of Great Observatories Origins Deep Survey (GOODS). In the mass-limited
sample of 1025 galaxies with $M_{star}$ $>$ 10$^{10.5}$ $M_{\odot}$ and
$0.4<z<1.05$, we identify 696 $Spitzer$ 24 $\mu$m detected (above the
5$\sigma$) galaxies and find them to have a wide range of NUV-$r$ and $r$-[12
$\mu$m] colors despite their red optical $u-r$ colors. Even in the sample of
very massive ETGs on the red sequence with $M_{star}$ $>$ 10$^{11.2}$
$M_{\odot}$, more than 18% show excess emission over the photospheric emission
in the mid-IR. The combination with the results of red ETGs in the local
universe suggests that the recent star formation is not rare among quiescent,
red ETGs at least out to $z \sim 1$ if the mid-IR excess emission results from
intermediate-age stars or/and from low-level ongoing star formation. Our
color$-$color diagram including near-UV and mid-IR emissions are efficient not
only for identifying ETGs with recent star formation, but also for
distinguishing quiescent galaxies from dusty star-forming galaxies.
