Enhanced Co J=2-1/J=1-0 ratio as a marker of supernova remnant-molecular cloud interactions:: The cases of W44 and IC 443

We present results of CO J = 2-1 line mapping of molecular clouds in the vicinity of the supernova remnants (SNRs) W44 and IC 443. Large areas spanning similar to 1.degrees 5 x 2 degrees were observed with the 9' beam of the University of Tokyo-Nobeyama Radio Observatory 60 cm Survey Telescope. We identified six giant molecular clouds (GMCs) with masses (0.3-3) x 10(5) M. around W44. Three show evidence of interaction with the SNR. In particular, one exhibits a line wing emission and an abrupt velocity shift at the position at which the cloud overlaps with the SNR. The CO J = 2-1/J = 1-0 line intensity ratio significantly exceeds unity (1.3) in the wing. In IC 443, a high-velocity line wing emission was detected in CO J = 2-1 with our 9' beam. The CO J = 2-1/J = 1-0 ratio is extremely high (>3) in the wing, which suggests that the emission comes from spatially extended optically thin (tau - 0.1), dense [n(H-2) similar to 10(5) cm(-3)], and warm (similar to 80 K) gas. W44 is established as a good example of an SNR interacting with GMCs, while IC 443 is in interaction with a low-mass dark cloud. The mass and kinetic energy of the shocked gas are, respectively, 1 x 10(3) M. and 4 x 10(48) ergs in W44, and 70 M. and 6 x 10(47) ergs in IC 443. A very high CO J = 2-1/J = 1-0 ratio in the line wings of a GMC may be a useful marker of interaction with an SNR. Such a marker would be extremely valuable for determining GMC-SNR associations in the inner Galaxy where numerous GMCs often lie along the line of sight. Such associations often provide the best means of determining SNR distances.