  Dense gas is important for galaxy evolution and star formation.
Optically-thin dense-gas tracers, such as isotopologues of HCN, HCO+, etc., are
very helpful to diagnose excitation conditions of dense molecular gas. However,
previous studies of optically-thin dense-gas tracers were mostly focusing on
average properties of galaxies as a whole, due to limited sensitivity and
angular resolution. M82, a nearby prototype starburst galaxy, offers a unique
case for spatially-resolved studies with single-dish telescopes. With the IRAM
30-m telescope, we observed the J = 1 - 0 transition of H13CN, HC15N, H13CO+,
HN13C, H15NC, and SiO J = 2 - 1, HC3N J= 10 - 9, H2CO J = 2 - 1 toward five
positions along the major axis of M82. The intensity ratios of I(HCN)/I(H13CN)
and I(HCO+)/I(H13CO+) show a significant spatial variation along the major
axis, with lower values in the central region than those on the disk,
indicating higher optical depths in the central region. The optical depths of
HCO+ lines are found to be systematically higher than those of HCN lines at all
positions. Futhermore, we find that the 14N/15N ratios have an increasing
gradient from the center to the outer disk.
