An interferometric CO survey of luminous submillimetre galaxies

In this paper, we present results from an Institut de Radio Astronomie Millimetrique (IRAM) Plateau de Bure millimetre-wave Interferometer (PdBI) survey for carbon monoxide (CO) emission towards radio-detected submillimetre galaxies (SMGs) with known optical and near-infrared spectroscopic redshifts. Five sources in the redshift range z similar to 1-3.5 were detected, nearly doubling the number of SMGs detected in CO. We summarize the properties of all 12 CO-detected SMGs, as well as six sources not detected in CO by our survey, and use this sample to explore the bulk physical properties of the submillimetre galaxy (SMG) population as a whole. The median CO line luminosity of the SMGs is < L'(CO)>= (3.8 +/- 2.0) x 10(10) K km s(-1) pc(2). Using a CO-to-H-2 conversion factor appropriate for starburst galaxies, this corresponds to a molecular gas mass < M(H-2)>= (3.0 +/- 1.6) x 10(10) M-circle dot within an similar to 2 kpc radius, approximately 4 times greater than the most luminous local ultraluminous infrared galaxies (ULIRGs) but comparable to that of the most extreme high-redshift radio galaxies (HzRGs) and quasi-sellar objects (QSOs). The median CO FWHM linewidth is broad, < FWHM >= 780 +/- 320 km s(-1), and the SMGs often have double-peaked line profiles, indicative of either a merger or a disc. From their median gas reservoirs (similar to 3 x 10(10) M-circle dot) and star formation rates (greater than or similar to 700 M-circle dot yr(-1)), we estimate a lower limit on the typical gas-depletion time-scale of greater than or similar to 40 Myr in SMGs. This is marginally below the typical age expected for the starbursts in SMGs and suggests that negative feedback processes may play an important role in prolonging the gas consumption time-scale. We find a statistically significant correlation between the far-infrared and CO luminosities of the SMGs, which extends the observed correlation for local ULIRGs to higher luminosities and higher redshifts. The non-linear nature of the correlation implies that SMGs have higher far-infrared to CO luminosity ratios and possibly higher star formation efficiencies (SFEs), than local ULIRGs. Assuming a typical CO source diameter of theta similar to 0.5 arcsec (D similar to 4 kpc), we estimate a median dynamical mass of < M-dyn >similar or equal to (1.2 +/- 1.5) x 10(11) M-circle dot for the SMG sample. Both the total gas and stellar masses imply that SMGs are very massive systems, dominated by baryons in their central regions. The baryonic and dynamical properties of these systems mirror those of local giant ellipticals and are consistent with numerical simulations of the formation of the most massive galaxies. We have been able to impose a lower limit of greater than or similar to 5 x 10(-6) Mpc(-3) to the comoving number density of massive galaxies in the redshift range z similar to 2-3.5, which is in agreement with results from recent spectroscopic surveys and the most recent model predictions.