  We present evidence that the mid infrared (MIR) is a good tracer of the total
infrared luminosity, L(IR), and star formation rate (SFR), of galaxies up to z
1.3. We use deep MIR images from the Infrared Space Observatory (ISO) and the
Spitzer Space Telescope in the Northern field of the Great Observatories
Origins Deep Survey (GOODS-N) together with VLA radio data to compute three
independant estimates of L(IR). The L(IR,MIR) derived from the observed 15
and/or 24 um flux densities using a library of template SEDs, and L(IR,radio),
derived from the radio (1.4 and/or 8.5 GHz) using the radio-far infrared
correlation, agree with a 1-sigma dispersion of 40 %. We use the k-correction
as a tool to probe different parts of the MIR spectral energy distribution
(SED) of galaxies as a function of their redshift and find that on average
distant galaxies present MIR SEDs very similar to local ones. However, in the
redshift range z= 0.4-1.2, L(IR,24um) is in better agreement with L(IR,radio)
than L(IR,15 um) by 20 %, suggesting that the warm dust continuum is a better
tracer of the SFR than the broad emission features due to polycyclic aromatic
hydrocarbons (PAHs). We find marginal evidence for an evolution with redshift
of the MIR SEDs: two thirds of the distant galaxies exhibit rest-frame MIR
colors (L(12 um)/L(7 um) and L(10 um)/L(15 um) luminosity ratios) below the
median value measured for local galaxies. Possible explanations are examined
but these results are not sufficient to constrain the physics of the emitting
regions. We compare three commonly used SED libraries which reproduce the
color-luminosity correlations of local galaxies with our data and discuss
possible refinements to the relative intensities of PAHs, warm dust continuum
and silicate absorption.
