Molecular clouds in Cygnus .2. Statistical studies of star-forming regions

We report results of large-scale (CO)-C-13(J = 1-0) observations of molecular clouds in the Cygnus region, made with the two 4 m millimeter-wave telescopes (HPBW = 2'.7) at Nagoya University. An area of 432 deg(2) (80 degrees < l < 104 degrees and -7 degrees.5 < b < 10 degrees.5) was covered at an 8' grid spacing, and 159 molecular clouds (similar to 2.4 x 10(5) M. in total) were detected within a velocity range of -25 < V-LSR < 25 km s(-1). Among these clouds, 61 are apparently associated with 215 protostellar candidates selected from the IRAS Point Source Catalog, and 24 clouds are associated with seven H II regions. In this paper, we investigate the statistical properties of the clouds and the relationship between the (CO)-C-13 clouds and the young stellar objects (YSOs): The mass spectrum of the molecular clouds is found to be well approximated by a power law dN/dM(CL) proportional to M(CL)(-1.6) for clouds with mass larger than 100 M.. The stability of the molecular clouds is investigated. The most massive clouds appear to be in virial equilibrium or collapsing, while the smallest are not, if not contained by the external pressure from the surrounding intercloud medium. We study the possible influence of the H II regions on star formation. We find that small clouds with masses less than 10(2) M. in H II regions have a tendency to form stars with higher masses than other clouds away from the H II regions. When clouds associated with the H II regions are excluded, the empirical IRAS luminosity function for YSOs is determined to be dn(IR)/dL = 8.4 x 10(-3)(M(CL)/M.)(0.9)(L/L.)(-1.6) for sources with luminosities higher than 10 L.. This luminosity function implies that the total number of protostars formed in molecular clouds is almost proportional to the cloud mass. On the other hand, the luminosity distribution of protostars follows a power law with the index of -1.6 over a large cloud mass range (similar to 10(2)-10(5) M,). Therefore, we propose that the initial stellar mass function and the star formation efficiency in Cygnus are largely independent of the parent cloud mass, except for clouds in H II regions in which stars with higher masses (by a factor of 2-4) are formed. As the luminosity function derived in Cygnus seems to represent well other data sets, we argue that these conclusions may also hold for other star-forming regions. Finally, the maximum luminosity of the IRAS sources is examined as a function of the parent cloud mass. For clouds inside and outside the H II regions, the maximum IRAS luminosity is fitted by L(max) proportional to M(CL)(1.5) for clouds with M(CL) < 10(3) M..