The radio emission from the ultraluminous far-infrared galaxy NGC 6240

We present new radio observations of the ``prototypical'' ultra-luminous far- infrared galaxy NGC~6240, obtained using the VLA at 20~cm in `B' configuration and at 3.6~cm in `A' configuration. These data, along with those from four previous VLA observations, are used to perform a comprehensive study of the radio emission from NGC~6240. Approximately 70\% (~3 x 10$^{23}$ W~Hz$^{-1}$) of the total radio power at 20 cm originates from the nuclear region ( <~ 1.5 kpc), of which half is emitted by two unresolved ($R <~ 36 pc) cores and half by a diffuse component. The radio spectrum of the nuclear emission is relatively flat ($\alpha$ =~ 0.6; $S_{\nu} \propto \nu^{-\alpha}$). The supernova rate required to power the diffuse component is consistent with that predicted by the stellar evolution models of Rieke \etal (1985). If the radio emission from the two compact cores is powered by supernova remnants, then either the remnants overlap and form hot bubbles in the cores, or they are very young ( <~ 100 yr). Nearly all of the other 30\% of the total radio power comes from an ``arm-like'' region extending westward from the nuclear region. The western arm emission has a steep spectrum ($\alpha$ =~ 1.0), suggestive of aging effects from synchrotron or inverse-Compton losses, and is not correlated with starlight; we suggest that it is synchrotron emission from a shell of material driven by a galactic superwind. Inverse-Compton scattering of far-infrared photons in the radio sources is expected to produce an X-ray flux of ~2-6 x 10$^{-14}$ erg/s/cm2 in the 2-10 keV band. No significant radio emission is detected from or near the possible ultra-massive ``dark core'' hypothesized by Bland-Hawthorn, Wilson \& Tully (1991).