  It is known that merging galaxies with luminous starbursts and high
far-infrared luminosities tend to have higher $R_{1-0}
=^{12}CO(J=1-0)/^{13}CO(J=1-0)$ integrated line intensity ratios ($R_{1-0}
\simeq 20-50$) than normal spiral galaxies ($R_{1-0} \simeq 5-15$). Comparing
far-infrared luminosities [L(FIR)] with those of ^{12}CO(J=1-0) and
^{13}CO(J=1-0) for a sample of normal and starburst galaxies, Taniguchi &
Ohyama found that the observed high $R_{1-0}$ values for the luminous starburst
mergers are attributed to their lower ^{13}CO line intensities by a factor of 3
on the average. They suggested the following two possibilities; in the luminous
starburst mergers, 1) ^{13}CO is underabundant with respect to ^{12}CO, or 2)
exitation and/or optical depth effects are responsible for the change in
$R_{1-0}$. In this paper, we investigate the second possibility using higher
transition data of both ^{12}CO and ^{13}CO emission lines. Applying the same
method proposed by Taniguchi & Ohyama to both ^{12}CO(J=2-1) and
^{13}CO(J=2-1), we find that ^{13}CO(J=2-1) is also depressed with respect to
^{12}CO(J=2-1). This suggests that the ^{13}CO gas may be underabundant in the
high-$R_{1-0}$ starburst mergers although we cannot rule out the possibility
that excitation and optical depth effects are still affecting $R_{2-1}$, for
example due to the large velocity widths in the CO emission lines. Additional
observations of both ^{12}CO and ^{13}CO lines at $J \geq 3$ are required to
better constrain the conditions of the molecular gas in luminous starburst
galaxies.
