We present sígame ( SImulator of GAlaxy Millimetre/submillimetre Emission ) , a new numerical code designed to simulate the ^ { 12 } CO rotational line spectrum of galaxies .
Using sub-grid physics recipes to post-process the outputs of smoothed particle hydrodynamics ( SPH ) simulations , a molecular gas phase is condensed out of the hot and partly ionised SPH gas .
The gas is subjected to far-UV radiation fields and CR ionisation rates which are set to scale with the local star formation rate volume density .
Level populations and radiative transport of the CO lines are solved with the 3-D radiative transfer code lime .
We have applied sígame to cosmological SPH simulations of three disk galaxies at z = 2 with stellar masses in the range \sim 0.5 - 2 \times 10 ^ { 11 } M _ { \odot } and star formation rates \sim 40 - 140 M _ { \odot } yr ^ { -1 } .
Global CO luminosities and line ratios are in agreement with observations of disk galaxies at z \sim 2 up to and including J = 3 - 2 but falling short of the few existing J = 5 - 4 observations .
The central 5 { kpc } regions of our galaxies have CO 3 - 2 / 1 - 0 and 7 - 6 / 1 - 0 brightness temperature ratios of \sim 0.55 - 0.65 and \sim 0.02 - 0.08 , respectively , while further out in the disk the ratios drop to more quiescent values of \sim 0.5 and < 0.01 .
Global CO-to-H _ { 2 } conversion ( \alpha _ { CO } ) factors are \simeq 1.5 { \mbox { $M _ { \odot } $ } pc ^ { -2 } ( K km s ^ { -1 } ) ^ { -1 } } , i.e. , \sim 2 - 3 \times below the typically adopted values for disk galaxies , and \alpha _ { CO } increases with radius , in agreement with observations of nearby galaxies .
Adopting a top-heavy Giant Molecular Cloud ( GMC ) mass spectrum does not significantly change the results .
Steepening the GMC density profiles leads to higher global line ratios for J _ { up } \geq 3 and CO-to-H _ { 2 } conversion factors ( \simeq 3.6 { \mbox { $M _ { \odot } $ } pc ^ { -2 } ( K km s ^ { -1 } ) ^ { -1 } } ) .