Context : Submillimetre galaxies ( SMGs ) in the early universe are the potential antecedents of the most massive galaxies we see in the present-day universe .
An important step towards quantifying this galactic evolutionary connection is to investigate the fundamental physical properties of SMGs , like their stellar mass content ( M _ { \star } ) and star formation rate ( SFR ) .

Aims : We attempt to characterise the physical nature of a 1.1 mm-selected , flux-limited , and interferometrically followed up sample of SMGs in the COSMOS field .

Methods : We used the latest release of the MAGPHYS code to fit the multiwavelength ( UV to radio ) spectral energy distributions ( SEDs ) of 16 of the target SMGs , which lie at redshifts z \simeq 1.6 - 5.3 .
We also constructed the pure radio SEDs of our SMGs using three different radio bands ( 325 MHz , 1.4 GHz , and 3 GHz ) .
Moreover , since two SMGs in our sample , AzTEC1 and AzTEC3 , benefit from previous ^ { 12 } C ^ { 16 } O line observations , we studied their properties in more detail .

Results : The median and 16th–84th percentile ranges of M _ { \star } , infrared ( 8 - 1 000 ~ { } \mu m ) luminosity ( L _ { IR } ) , SFR , dust temperature ( T _ { dust } ) , and dust mass ( M _ { dust } ) were derived to be \log ( M _ { \star } / { M } _ { \sun } ) = 10.96 ^ { +0.34 } _ { -0.19 } , \log ( L _ { IR } / { L } _ { \sun } ) = 12.93 ^ { +0.09 } _ { -0.19 } , { SFR } = 856 ^ { +191 } _ { -310 } { M } _ { \sun } ~ { } { yr } ^ { -1 } , T _ { dust } = 40.6 ^ { +7.5 } _ { -8.1 } K , and \log ( M _ { dust } / { M } _ { \sun } ) = 9.17 ^ { +0.03 } _ { -0.33 } , respectively .
We found that 63 \% of our target SMGs lie above the galaxy main-sequence by more than a factor of 3 , and hence are starbursts .
The 3 GHz radio sizes we have previously measured for the target SMGs were compared with the present M _ { \star } estimates , and we found that the z > 3 SMGs are fairly consistent with the mass–size relationship of z \sim 2 compact , quiescent galaxies ( cQGs ) .
The median radio spectral index is found to be \alpha = -0.77 ^ { +0.28 } _ { -0.42 } .
The median IR-radio correlation parameter is found to be q = 2.27 ^ { +0.27 } _ { -0.13 } , which is lower than measured locally ( median q = 2.64 ) .
The gas-to-dust mass ratio for AzTEC1 is derived to be \delta _ { gdr } = 90 ^ { +23 } _ { -19 } , while that for AzTEC3 is 33 ^ { +28 } _ { -18 } .
AzTEC1 is found to have a sub-Eddington SFR surface density ( by a factor of 2.6 ^ { +0.2 } _ { -0.1 } ) , while AzTEC3 appears to be an Eddington-limited starburster .
The gas reservoir in these two high- z SMGs would be exhausted in only \sim 86 and 19 Myr at the current SFR , respectively .

Conclusions : A comparison of the MAGPHYS -based properties of our SMGs with those of equally bright 870 \mu m-selected , ALMA followed-up SMGs in the ECDFS field ( the ALESS SMGs ) , suggests that the two populations share fairly similar physical characteristics , including the q parameter .
The somewhat higher L _ { dust } for our sources ( factor of 1.9 ^ { +9.3 } _ { -1.6 } on average ) can originate in the longer selection wavelength of 1.1 mm .
Although the derived median \alpha is consistent with a canonical synchrotron spectral index , some of our SMGs exhibit spectral flattening or steepening , which can be attributed to different cosmic-ray energy gain and loss mechanisms .
A hint of negative correlation is found between the 3 GHz size and the level of starburstiness , and hence cosmic-ray electrons in more compact starbursts might be more susceptible to free-free absorption .
Some of the derived low and high q values ( compared to the local median ) could be the result of a specific merger/post-starburst phase of galaxy evolution .
Overall , our results , like the M _ { \star } –3 GHz radio size analysis and comparison with the stellar masses of z \sim 2 cQGs , in concert with the star formation properties of AzTEC1 and 3 , support the scenario where z > 3 SMGs evolve into today ’ s giant , gas-poor ellipticals .