We present new Karl G. Jansky Very Large Array radio continuum images of the nuclei of Arp 220 , the nearest ultra-luminous infrared galaxy .
These new images have both the angular resolution to study the detailed morphologies of the two nuclei that power the galaxy merger and sensitivity to a wide range of spatial scales .
At 33 GHz , we achieve a resolution of 0 \farcs 081 \times 0 \farcs 063 ( \mathrm { 29.9 \times 23.3 ~ { } pc } ) and resolve the radio emission surrounding both nuclei .
We conclude from the decomposition of the radio spectral energy distribution that a majority of the 33 GHz emission is synchrotron radiation .
The spatial distributions of radio emission in both nuclei are well-described by exponential profiles .
These have deconvolved half-light radii ( { R _ { 50 d } } ) of 51 and 35 pc for the eastern and western nuclei , respectively , and they match the number density profile of radio supernovae observed with very long baseline interferometry .
This similarity might be due to the fast cooling of cosmic rays electrons caused by the presence of a strong ( \sim mG ) magnetic field in this system .
We estimate extremely high molecular gas surface densities of 2.2 ^ { +2.1 } _ { -1.0 } \times 10 ^ { 5 } ( east ) and 4.5 ^ { +4.5 } _ { -1.9 } \times 10 ^ { 5 } ( west ) M _ { \odot } pc ^ { -2 } , corresponding to total hydrogen column densities of N _ { H } = 2.7 ^ { +2.7 } _ { -1.2 } \times 10 ^ { 25 } ( east ) and 5.6 ^ { +5.5 } _ { -2.4 } \times 10 ^ { 25 } cm ^ { -2 } ( west ) .
The implied gas volume densities are similarly high , { n _ { H _ { { } _ { 2 } } } \sim 3.8 ^ { +3.8 } _ { -1.6 } 10 ^ { 4 } } ( east ) and \sim 11 ^ { +12 } _ { -4.5 } \times 10 ^ { 4 } cm ^ { -3 } ( west ) .
We also estimate very high luminosity surface densities of \mathrm { \Sigma _ { IR } \sim 4.2 ^ { +1.6 } _ { -0.7 } \times 10 ^ { 13 } } ( east ) and \mathrm { \Sigma _ { IR } \sim 9.7 ^ { +3.7 } _ { -2.4 } \times 10 ^ { 13 } ~ { } ( west ) ~ { } L _ { \odot } ~ { % } kpc ^ { -2 } } , and star formation rate surface densities of \mathrm { \Sigma _ { SFR } \sim 10 ^ { 3.7 \pm 0.1 } } ( east ) and \mathrm { \Sigma _ { SFR } \sim 10 ^ { 4.1 \pm 0.1 } ~ { } ( west ) ~ { } M _ { \odot } ~ { } yr ^ { -1 } ~ { } kpc ^ % { -2 } } .
These values , especially for the western nucleus are , to our knowledge , the highest luminosity surface densities and star formation rate surface densities measured for any star-forming system .
Despite these high values , the nuclei appear to lie below the dusty Eddington limit in which radiation pressure is balanced only by self-gravity .
The small measured sizes also imply that at wavelengths shorter than \lambda = 1 mm , dust absorption effects must play an important role in the observed light distribution while below 5 GHz free-free absorption contributes substantial opacity .
According to these calculations , the nuclei of Arp 220 are only transparent in the frequency range \sim 5 to 350 GHz .
Our results offer no clear evidence that an active galactic nucleus dominates the emission from either nucleus at 33 GHz .