We present simultaneous mappings of J = 1 - 0 emission of ^ { 12 } CO , ^ { 13 } CO , and C ^ { 18 } O molecules toward the whole disk ( 8 ^ { \prime } \times 5 ^ { \prime } or 20.8 kpc \times 13.0 kpc ) of the nearby barred spiral galaxy NGC 2903 with the Nobeyama Radio Observatory 45-m telescope at an effective angular resolution of 20 ^ { \prime \prime } ( or 870 pc ) .
We detected ^ { 12 } CO ( J = 1 - 0 ) emission over the disk of NGC 2903 .
In addition , significant ^ { 13 } CO ( J = 1 - 0 ) emission was found at the center and bar-ends , whereas we could not detect any significant C ^ { 18 } O ( J = 1 - 0 ) emission .
In order to improve the signal-to-noise ratio of CO emission and to obtain accurate line ratios of ^ { 12 } CO ( J = 2 - 1 ) / ^ { 12 } CO ( J = 1 - 0 ) ( R _ { 2 - 1 / 1 - 0 } ) and ^ { 13 } CO ( J = 1 - 0 ) / ^ { 12 } CO ( J = 1 - 0 ) ( R _ { 13 / 12 } ) , we performed the stacking analysis for our ^ { 12 } CO ( J = 1 - 0 ) , ^ { 13 } CO ( J = 1 - 0 ) , and archival ^ { 12 } CO ( J = 2 - 1 ) spectra with velocity-axis alignment in nine representative regions of NGC 2903 .
We successfully obtained the stacked spectra of the three CO lines , and could measure averaged R _ { 2 - 1 / 1 - 0 } and R _ { 13 / 12 } with high significance for all the regions .
We found that both R _ { 2 - 1 / 1 - 0 } and R _ { 13 / 12 } differ according to the regions , which reflects the difference in the physical properties of molecular gas ; i.e. , density ( n _ { H _ { 2 } } ) and kinetic temperature ( T _ { K } ) .
We determined n _ { H _ { 2 } } and T _ { K } using R _ { 2 - 1 / 1 - 0 } and R _ { 13 / 12 } based on the large velocity gradient approximation .
The derived n _ { H _ { 2 } } ranges from \sim 1000 cm ^ { -3 } ( in the bar , bar-ends , and spiral arms ) to 3700 cm ^ { -3 } ( at the center ) and the derived T _ { K } ranges from 10 K ( in the bar and spiral arms ) to 30 K ( at the center ) .
We examined the dependence of star formation efficiencies ( SFEs ) on n _ { H _ { 2 } } and T _ { K } , and found the positive correlation between SFE and n _ { H _ { 2 } } with the correlation coefficient for the least-square power-law fit R ^ { 2 } of 0.50 .
This suggests that molecular gas density governs the spatial variations in SFEs .