The relation between gas and dust in the Taurus Molecular Cloud
  (abridged) We report a study of the relation between dust and gas over a
100deg^2 area in the Taurus molecular cloud. We compare the H2 column density
derived from dust extinction with the CO column density derived from the 12CO
and 13CO J= 1-0 lines. We derive the visual extinction from reddening
determined from 2MASS data. The comparison is done at an angular size of 200",
corresponding to 0.14pc at a distance of 140pc. We find that the relation
between visual extinction Av and N(CO) is linear between Av~3 and 10 mag in the
region associated with the B213--L1495 filament. In other regions the linear
relation is flattened for Av > 4 mag. We find that the presence of temperature
gradients in the molecular gas affects the determination of N(CO) by ~30--70%
with the largest difference occurring at large column densities. Adding a
correction for this effect and accounting for the observed relation between the
column density of CO and CO2 ices and Av, we find a linear relationship between
the column of carbon monoxide and dust for observed visual extinctions up to
the maximum value in our data 23mag. We have used these data to study a sample
of dense cores in Taurus. Fitting an analytical column density profile to these
cores we derive an average volume density of about 1.4e4 cm^-3 and a CO
depletion age of about 4.2e5 years. We estimate the H2 mass of Taurus to be
about 1.5e4 M_sun, independently derived from the Av and N(CO) maps. We derive
a CO integrated intensity to H2 conversion factor of about 2.1e20 cm^-2 (K
km/s)^-1, which applies even in the region where the [CO]/[H_2] ratio is
reduced by up to two orders of magnitude. The distribution of column densities
in our Taurus maps resembles a log--normal function but shows tails at large
and low column densities.
