We present ^ { 13 } CO ( J = 1 - 0 ) line emission observations with the Nobeyama 45-m telescope toward the giant H \emissiontype II region NGC 604 in the spiral galaxy M 33 .
We detected ^ { 13 } CO ( J = 1 - 0 ) line emission in 3 major giant molecular clouds ( GMCs ) labeled as GMC-A , B , and C beginning at the north .
We derived two line intensity ratios , ^ { 13 } CO ( J = 1 - 0 ) / ^ { 12 } CO ( J = 1 - 0 ) , R _ { 13 / 12 } , and ^ { 12 } CO ( J = 3 - 2 ) / ^ { 12 } CO ( J = 1 - 0 ) , R _ { 31 } , for each GMC at an angular resolution of 25 ^ { \prime \prime } ( 100 pc ) .
Averaged values of R _ { 13 / 12 } and R _ { 31 } are 0.06 and 0.31 within the whole GMC-A , 0.11 and 0.67 within the whole GMC-B , and 0.05 and 0.36 within the whole GMC-C , respectively .
In addition , we obtained R _ { 13 / 12 } = 0.09 \pm 0.02 and R _ { 31 } = 0.76 \pm 0.06 at the ^ { 12 } CO ( J = 1 - 0 ) peak position of the GMC-B .
Under the Large Velocity Gradient approximation , we determined gas density of 2.8 \times 10 ^ { 3 } cm ^ { -3 } and kinetic temperature of 33 ^ { +9 } _ { -5 } K at the ^ { 12 } CO ( J = 1 - 0 ) peak position of the GMC-B .
Moreover , we determined 2.5 \times 10 ^ { 3 } cm ^ { -3 } and 25 \pm 2 K as averaged values within the whole GMC-B .
We concluded that dense molecular gas is formed everywhere in the GMC-B because derived gas density not only at the peak position of the GMC but also averaged over the whole GMC exceeds 10 ^ { 3 } cm ^ { -3 } .
On the other hand , kinetic temperature averaged over the whole GMC-B , 25 K , is significantly lower than that at the peak position , 33 K. This is because H \emissiontype II regions are lopsided to the northern part of the GMC-B , thus OB stars can heat only the northern part , including the ^ { 12 } CO ( J = 1 - 0 ) peak position , of this GMC .