We exploit ALMA 870- \mu m ( 345 GHz ) observations of sub-millimetre sources in the Extended Chandra Deep Field South to investigate the far-infrared properties of high-redshift sub-millimetre galaxies ( SMGs ) .
Using the precisely located 870 \mu m ALMA positions of 99 SMGs , together with 24 \mu m and radio imaging of this field , we deblend the Herschel / SPIRE imaging of this region to extract their far-infrared fluxes and colours .
The median redshifts for ALMA LESS ( ALESS ) SMGs which are detected in at least two SPIRE bands increases as expected with wavelength of the peak in their SEDs , with z = 2.3 \pm 0.2 , 2.5 \pm 0.3 and 3.5 \pm 0.5 for the 250 , 350 and 500- \mu m peakers respectively .
We find that 34 ALESS SMGs do not have a > 3 \sigma counterpart at 250 , 350 or 500 \mu m. These galaxies have a median photometric redshift derived from the rest-frame UV–mid-infrared SEDs of z = 3.3 \pm 0.5 , which is higher than the full ALESS SMG sample ; z = 2.5 \pm 0.2 .
Using the photometric redshifts together with the 250–870 \mu m photometry , we estimate the far-infrared luminosities and characteristic dust temperature of each SMG .
The median infrared luminosity and characteristic dust temperature of the S _ { 870 \mu m } > 2 mJy SMGs is L _ { IR } = ( 3.0 \pm 0.3 ) \times 10 ^ { 12 } L _ { \odot } ( star formation rate of SFR = 300 \pm 30 M _ { \odot } yr ^ { -1 } ) and T _ { d } = 32 \pm 1 K ( \lambda _ { peak } = 93 \pm 4 \mu m ) .
At a fixed luminosity , the characteristic dust temperature of these high-redshift SMGs is \Delta T _ { d } = 3–5 K lower than comparably luminous galaxies at z = 0 , reflecting the more extended star formation occurring in these systems .
By extrapolating the 870 \mu m number counts to S _ { 870 } = 1 mJy , we show that the contribution of S _ { 870 \mu m } \geq 1 mJy SMGs to the cosmic star formation budget is 20 % of the total over the redshift range z \sim 1–4 .
We derive a median dust mass for these galaxies of M _ { d } = ( 3.6 \pm 0.3 ) \times 10 ^ { 8 } M _ { \odot } and by adopting an appropriate gas-to-dust ratio , we estimate that the typical molecular mass of the ALESS SMGs in our sample is M _ { H _ { 2 } } = ( 4.2 \pm 0.4 ) \times 10 ^ { 10 } M _ { \odot } .
Together with the average stellar masses of SMGs , M _ { \star } = ( 8 \pm 1 ) \times 10 ^ { 10 } M _ { \odot } , this suggests an average molecular gas fraction of \sim 40 % .
Finally , we use our estimates of the H _ { 2 } masses to show that SMGs with S _ { 870 \mu m } > 1 mJy ( L _ { IR } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 % pt \hbox { { $ \scriptstyle \sim$ } } } 10 ^ { 12 } L _ { \odot } ) contain \sim 10 % of the z \sim 2 volume-averaged H _ { 2 } mass density at this epoch .