The Spitzer C2D Legacy Results: Star-Formation Rates and Efficiencies; Evolution and Lifetimes

The c2d Spitzer Legacy project obtained images and photometry with both IRAC and MIPS instruments for five large, nearby molecular clouds. Three of the clouds were also mapped in dust continuum emission at 1.1 mm, and optical spectroscopy has been obtained for some clouds. This paper combines inFormation drawn from studies of individual clouds into a combined and updated statistical analysis of star-Formation rates and efficiencies, numbers and lifetimes for spectral energy distribution (SED) classes, and clustering properties. Current star-Formation efficiencies range from 3% to 6%; if star Formation continues at current rates for 10 Myr, efficiencies could reach 15-30%. Star-Formation rates and rates per unit area vary from cloud to cloud; taken together, the five clouds are producing about 260 M(circle dot) of stars per Myr. The star-Formation surface density is more than an order of magnitude larger than would be predicted from the Kennicutt relation used in extragalactic studies, reflecting the fact that those relations apply to larger scales, where more diffuse matter is included in the gas surface density. Measured against the dense gas probed by the maps of dust continuum emission, the efficiencies are much higher, with stellar masses similar to masses of dense gas, and the current stock of dense cores would be exhausted in 1.8 Myr on average. Nonetheless, star Formation is still slow compared to that expected in a free-fall time, even in the dense cores. The derived lifetime for the Class I phase is 0.54 Myr, considerably longer than some estimates. Similarly, the lifetime for the Class 0 SED class, 0.16 Myr, with the notable exception of the Ophiuchus cloud, is longer than early estimates. If photometry is corrected for estimated extinction before calculating class indicators, the lifetimes drop to 0.44 Myr for Class I and to 0.10 for Class 0. These lifetimes assume a continuous flow through the Class II phase and should be considered median lifetimes or half-lives. Star Formation is highly concentrated to regions of high extinction, and the youngest objects are very strongly associated with dense cores. The great majority (90%) of young stars lie within loose clusters with at least 35 members and a stellar density of 1 M(circle dot) pc(-3). Accretion at the sound speed from an isothermal sphere over the lifetime derived for the Class I phase could build a star of about 0.25 M(circle dot), given an efficiency of 0.3. Building larger mass stars by using higher mass accretion rates could be problematic, as our data confirm and aggravate the "luminosity problem" for protostars. At a given T(bol), the values for L(bol) are mostly less than predicted by standard infall models and scatter over several orders of magnitude. These results strongly suggest that accretion is time variable, with prolonged periods of very low accretion. Based on a very simple model and this sample of sources, half the mass of a star would be accreted during only 7% of the Class I lifetime, as represented by the eight most luminous objects.