Multi-wavelength properties of 850-$\mu$m selected sources from the North Ecliptic Pole SCUBA-2 survey

We present the multi-wavelength counterparts of 850-$\mu$m selected submillimetre sources over a 2-deg$^2$ field centred on the North Ecliptic Pole. In order to overcome the large beam size (15 arcsec) of the 850-$\mu$m images, deep optical to near-infrared (NIR) photometric data and arcsecond-resolution 20-cm images are used to identify counterparts of submillimetre sources. Among 647 sources, we identify 514 reliable counterparts for 449 sources (69 per cent in number), based either on probabilities of chance associations calculated from positional offsets or offsets combined with the optical-to-NIR colours. In the radio imaging, the fraction of 850-$\mu$m sources having multiple counterparts is 7 per cent. The photometric redshift, infrared luminosity, stellar mass, star-formation rate (SFR), and the AGN contribution to the total infrared luminosity of the identified counterparts are investigated through spectral energy distribution fitting. The SMGs are infrared-luminous galaxies at an average $\langle z\rangle=2.5$ with $\mathrm{log}_{10} (L_\mathrm{IR}/\mathrm{L}_\odot)=11.5-13.5$, with a mean stellar mass of $\mathrm{log}_{10} (M_\mathrm{star}/\mathrm{M}_\odot)=10.90$ and SFR of $\mathrm{log}_{10} (\mathrm{SFR/M_\odot\,yr^{-1}})=2.34$. The SMGs show twice as large SFR as galaxies on the star-forming main sequence, and about 40 per cent of the SMGs are classified as objects with bursty star formation. At $z\ge4$, the contribution of AGN luminosity to total luminosity for most SMGs is larger than 30 per cent. The FIR-to-radio correlation coefficient of SMGs is consistent with that of main-sequence galaxies at $z\simeq2$.