How dead are dead galaxies? Mid-Infrared fluxes of quiescent galaxies at
  redshift 0.3 < z < 2.5: implications for star formation rates and dust
  heating
  We investigate the star formation rates of quiescent galaxies at high
redshift (0.3 < z < 2.5) using 3D-HST WFC3 grism spectroscopy and Spitzer
mid-infrared data. We select quiescent galaxies on the basis of the widely used
UVJ color-color criteria. Spectral energy distribution fitting (rest frame
optical and near-IR) indicates very low star formation rates for quiescent
galaxies (sSFR ~ 10^-12 yr^-1). However, SED fitting can miss star formation if
it is hidden behind high dust obscuration and ionizing radiation is re-emitted
in the mid-infrared. It is therefore fundamental to measure the dust-obscured
SFRs with a mid-IR indicator. We stack the MIPS-24um images of quiescent
objects in five redshift bins centered on z = 0.5, 0.9, 1.2, 1.7, 2.2 and
perform aperture photometry. Including direct 24um detections, we find sSFR ~
10^-11.9 * (1+z)^4 yr^-1. These values are higher than those indicated by SED
fitting, but at each redshift they are 20-40 times lower than those of typical
star forming galaxies. The true SFRs of quiescent galaxies might be even lower,
as we show that the mid-IR fluxes can be due to processes unrelated to ongoing
star formation, such as cirrus dust heated by old stellar populations and
circumstellar dust. Our measurements show that star formation quenching is very
efficient at every redshift. The measured SFR values are at z > 1.5 marginally
consistent with the ones expected from gas recycling (assuming that mass loss
from evolved stars refuels star formation) and well above that at lower
redshifts.
