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We report the first detection of a mid-J isotopic CO line from an
external galaxy. We detected the 13CO (6-5) line from the
starburst nucleus of NGC 253. The line is suprisingly bright with
an integrated intensity 7% of the 12CO (6-5) line,
indicating optical depth in the 12CO line. Our LVG modeling
shows that a single warm (T ~ 120 K), dense (n ~ 104
cm-3) component emits most of the 12CO and 13CO line
emission from J = 2-1 through J = 7-6. The CO(1-0) line comes from
an additional lower excitation envelope. About 60% of the total
molecular gas mass within 70 pc of the nucleus is in the warm, dense
component. We show that stellar far-UV photons or X-ray photons
from a nuclear source are unlikely to be the primary sources of the
gas heating. The most likely sources of heat are cosmic rays from
the nuclear starburst or microturbulence within molecular clouds.
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