The Far-Infrared--Radio Correlation at High Redshifts: Physical Considerations and Prospects for the Square Kilometer Array

(Abridged) I present a predictive analysis for the behavior of the FIR--radio correlation as a function of redshift in light of the deep radio continuum surveys which may become possible using the SKA. To keep a fixed ratio between the FIR and predominantly non-thermal radio continuum emission of a normal star-forming galaxy requires a nearly constant ratio between galaxy magnetic field and radiation field energy densities. While the additional term of IC losses off of the cosmic microwave background (CMB) is negligible in the local Universe, the rapid increase in the strength of the CMB energy density (i.e. $\sim(1+z)^{4})$ suggests that evolution in the FIR-radio correlation should occur with infrared (IR; $8-1000 \micron$)/radio ratios increasing with redshift. At present, observations do not show such a trend with redshift; $z\sim6$ radio-quiet QSOs appear to lie on the local FIR-radio correlation while a sample of $z\sim4.4$ and $z\sim2.2$ SMGs exhibit ratios that are a factor of $\sim$2.5 {\it below} the canonical value. I also derive a 5$\sigma$ point-source sensitivity goal of $\approx$20 nJy (i.e. $\sigma_{\rm RMS} \sim 4$ nJy) requiring that the SKA specified be $A_{\rm eff}/T_{\rm sys}\approx 15000$ m$^{2}$ K$^{-1}$; achieving this sensitivity should enable the detection of galaxies forming stars at a rate of $\ga25 M_{\sun} {\rm yr}^{-1}$, at all redshifts if present. By taking advantage of the fact that the non-thermal component of a galaxy's radio continuum emission will be quickly suppressed by IC losses off of the CMB, leaving only the thermal (free-free) component, I argue that deep radio continuum surveys at frequencies $\ga$10 GHz may prove to be the best probe for characterizing the high-$z$ star formation history of the Universe unbiased by dust.