We present ALMA ultra–high–spatial resolution ( \sim 20 { mas } or 150 { pc } ) observations of dust continuum at 920 { \mu 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 \pm 0.2 { mJy } ) and ALMACAL–2 ( A–2 : S _ { 870 \mu m } = 4.4 \pm 0.2 { mJy } ) .
These are the brightest and most luminous SMGs discovered so far in ALMACAL , a wide and deep ( sub ) mm survey , which is being carried out in ALMA calibrator fields and currently contains observations at sub-arcsec resolution down to an { r . m . s . } of \sim 15 { \mu Jy beam ^ { -1 } } in more than 250 calibrators fields .
The spectroscopic redshifts of A–1 and A–2 have been confirmed via serendipitous detection of up to nine emission lines , in three different ALMA bands .
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 { pc } ) .
This structure is confirmed by independent datasets at 920 { \mu m } and 1.2 { mm } .
In A–1 , two additional , fainter clumps are found .
The star-formation rate ( SFR ) surface densities of all these clumps are extremely high , \Sigma _ { SFR } \sim 1200 to \sim 3000 { M _ { \odot } { 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 dusty galaxy in the source plane would be R _ { eff } \sim 40 { pc } , and the de-magnified SFR surface density would be \Sigma _ { SFR } \sim 10000 { M _ { \odot } { 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 .