ALMACAL II: Extreme star-formation-rate densities in a pair of dusty   starbursts at $z = 3.442$ revealed by ALMA 20-milliarcsec resolution imaging
  We present ALMA ultra-high-spatial resolution ($\sim 20 \, {\rm mas}$) observations of dust continuum at $920 \, {\rm \mu m}$ and $1.2 \, {\rm mm}$ in a pair of submm galaxies (SMGs) at $z = 3.442$, ALMACAL-1 (A-1: $S_{\rm 870 \mu m} = 6.5 \pm 0.2 \, {\rm mJy}$) and ALMACAL-2 (A-2: $S_{\rm 870 \mu m} = 4.4 \pm 0.2 \, {\rm mJy}$). The spectroscopic redshifts of A-1 and A-2 have been confirmed via serendipitous detection of up to nine emission lines. Our ultra-high-spatial resolution data reveal that about half of the star formation in each of these starbursts is dominated by a single compact clump (FWHM size of $\sim 350 \, {\rm pc}$). This structure is confirmed by independent datasets at $920 \, {\rm \mu m}$ and $1.2 \, {\rm mm}$. The star-formation rate (SFR) surface densities of all these clumps are extremely high, $\Sigma_{\rm SFR} \sim 1200$ to $\sim 3000 \, {M_\odot \, {\rm yr}^{-1} \, {\rm kpc}^{-2}}$, the highest found in high-redshift galaxies. There is a small probability that A-1 and A-2 are the lensed components of a background source gravitationally amplified by the blazar host. If this was the case, the effective radius of the source would be $R_{\rm eff} \sim 40 \, {\rm pc}$, and the de-magnified SFR surface density would be $\Sigma_{\rm SFR} \sim 10000 \, {M_\odot \, {\rm yr}^{-1} \, {\rm kpc}^{-2}}$, comparable with the eastern nucleus of Arp 220. Despite being unable to rule out an AGN contribution, our results suggest that a significant percentage of the enormous far-IR luminosity in some dusty starbursts is concentrated in very small star-forming regions. The high $\Sigma_{\rm SFR}$ in our pair of SMGs could only be measured thanks to the ultra-high-resolution ALMA observations used in this work, demonstrating that long-baseline observations are essential to study and interpret the properties of dusty starbursts in the early Universe. 
I. Oteo, M. A. Zwaan, R. J. Ivison, I. Smail and A. D. Biggs
astro-ph.GA