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.