On the multiplicity of red- <i>Herschel</i> sources and its implications for extreme star formation

ABSTRACT We study the multiplicity of galaxies in the largest sample of red-Herschel sources ($S_{250 \, \mu \mathrm{m}} &amp;lt; S_{350 \, \mu \mathrm{m}} &amp;lt; S_{500 \, \mu \mathrm{m}}$) using archival Atacama Large Millimeter/submillimeter Array (ALMA) observations. Out of 2416 fields with ALMA detections (from a total of 3089 analysed maps), we identify 474 multiple systems within a radius of 16 arcsec (equivalent to the 500 $\mu$m Herschel beam size): 420 doubles, 51 triples, and 3 quadruples. In each case, the brightest source contributes, on average, 64, 48, and 42 per cent of the total flux in double, triple, and quadruple systems. The average combined ALMA flux density of the sources in double systems is comparable to that of the two brightest components within triple and quadruple systems. Non-parametric tests suggest that only a small fraction of the double systems (${\lesssim} 13$ per cent) are composed of sources with compatible redshifts, while 47–67 per cent of triple and quadruple fields contain at least one potentially associated pair. Simulations using a mock catalogue of dusty star-forming galaxies suggest that 32 per cent of the double systems are likely physically associated ($\Delta z &amp;lt; 0.01$, i.e. $\lesssim$10 cMpc at $z = 3$) and, while only 8 per cent of the triple and none of the quadruple systems meet this criterion, ${\sim}$70 per cent of them include at least one likely associated pair. Our results suggest that enhanced star formation rates in submillimetre galaxies are primarily driven by internal processes rather than large-scale interactions. This study also provides a catalogue of potential overdensities for follow-up observations, offering insights into protocluster formation and evolution.