13CO and C18O emission from a dense gas disk at z=2.3: abundance
  variations, cosmic rays and the initial conditions for star formation
  We analyse the SLEDs of 13CO and C18O for the J=1-0 up to J=7-6 transitions
in the gravitationally lensed ultraluminous infrared galaxy SMMJ2135-0102 at
z=2.3. This is the first detection of 13CO and C18O in a high-redshift
star-forming galaxy. These data comprise observations of six transitions taken
with PdBI and we combine these with 33GHz JVLA data and our previous 12CO and
continuum emission information to better constrain the properties of the ISM
within this system. We study both the velocity-integrated and kinematically
decomposed properties of the galaxy and coupled with an LVG model we find that
the star-forming regions in the system vary in their cold gas properties. We
find strong C18O emission both in the velocity-integrated emission and in the
two kinematic components at the periphery of the system, where the C18O line
flux is equivalent to or higher than the 13CO. We derive an average
velocity-integrated flux ratio of 13CO/C18O~1 suggesting a [13CO]/[C18O]
abundance ratio at least 7x lower than that in the Milky Way. This may suggest
enhanced C18O abundance, perhaps indicating star formation preferentially
biased to high-mass stars. We estimate the relative contribution to the ISM
heating from cosmic rays and UV of (30-3300)x10^(-25)erg/s and 45x10^(-25)erg/s
per H2 molecule respectively and both are comparable to the total cooling rate
of (0.8-20)x10^(-25)erg/s from the CO. However, our LVG models indicate high
(>100K) temperatures and densities (>10^(3))cm^(-3) in the ISM which may
suggest that cosmic rays play a more important role than UV heating in this
system. If cosmic rays dominate the heating of the ISM, the increased
temperature in the star forming regions may favour the formation of massive
stars and so explain the enhanced C18O abundance. This is a potentially
important result for a system which may evolve into a local elliptical galaxy.
