Abstract
We present ALMA ultra-high-spatial resolution ($20 \, mas$)
observations of dust continuum at $920 \, m$ and $1.2 \, mm$ in
a pair of submm galaxies (SMGs) at $z = 3.442$, ALMACAL-1 (A-1: $S_870 \mu
m = 6.5 0.2 \, mJy$) and ALMACAL-2 (A-2: $S_870 m = 4.4
0.2 \, mJy$). 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 $350 \, pc$). This structure is confirmed by independent datasets
at $920 \, m$ and $1.2 \, mm$. The star-formation rate (SFR)
surface densities of all these clumps are extremely high, $\Sigma_SFR
1200$ to $3000 \, M_\, yr^-1 \, kpc^-2$, 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 $R_eff 40 \, pc$, and the de-magnified SFR
surface density would be $\Sigma_SFR 10000 \, M_\, \rm
yr^-1 \, kpc^-2$, 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
$\Sigma_SFR$ 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.
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