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.