Deep Herschel PACS/SPIRE imaging and ^ { 12 } CO ( 2-1 ) line luminosities from the IRAM Plateau de Bure Interferometer are combined for a sample of 17 galaxies at z > 1 from the GOODS-N field .
The sample includes galaxies both on and above the main sequence ( MS ) traced by star-forming galaxies in the SFR-M _ { \ast } plane .
The far-infrared data are used to derive dust masses , M _ { { dust } } , following the Draine & Li ( 2007 ) models .
Combined with an empirical prescription for the dependence of the gas-to-dust ratio on metallicity ( \delta _ { { \scriptsize { GDR } } } ( \mu _ { 0 } ) ) , the CO luminosities and M _ { { dust } } values are used to derive for each galaxy the CO-to-H _ { 2 } conversion factor , \alpha _ { { CO } } .
Like in the local Universe , the value of \alpha _ { { CO } } is a factor of \sim 5 smaller in starbursts compared to normal star-forming galaxies ( SFGs ) .
We additionally uncover a relation between \alpha _ { { CO } } and dust temperature ( T _ { { dust } } ; \alpha _ { { CO } } decreasing with increasing T _ { { dust } } ) as obtained from modified blackbody fits to the far-infrared data .
While the absolute normalization of the \alpha _ { { CO } } ( T _ { { dust } } ) relation is uncertain , the global trend is robust against possible systematic biases in the determination of M _ { { dust } } , \delta _ { { \scriptsize { GDR } } } ( \mu _ { 0 } ) or metallicity .
Although we can not formally distinguish between a step and a smooth evolution of \alpha _ { { CO } } with the dust temperature , we can unambiguously conclude that in galaxies of near-solar metallicity , a critical value of T _ { { dust } } = 30 K can be used to determine whether the appropriate \alpha _ { { CO } } is closer to the “ starburst ” value ( 1.0 M _ { \odot } ( K km s ^ { -1 } pc ^ { 2 } ) ^ { -1 } , when T _ { { dust } } > 30 K ) or closer to the Galactic value ( 4.35 M _ { \odot } ( K km s ^ { -1 } pc ^ { 2 } ) ^ { -1 } , when T _ { { dust } } < 30 K ) .
This indicator has the great advantage of being less subjective than visual morphological classifications of mergers/SFGs , which can be difficult at high z because of the clumpy nature of SFGs .
Using T _ { { dust } } to select the appropriate \alpha _ { { CO } } is also more indicative of ISM conditions than a fixed L _ { { IR } } criterion .
In the absence of far-infrared data , the offset of a galaxy from the star formation main sequence ( i.e. , { \Delta log ( SSFR ) _ { MS } = log [ SSFR ( galaxy ) / SSFR _ { MS } } ( M _ { \ast } ,z ) ] ) can be used to identify galaxies requiring the use of an \alpha _ { { CO } } conversion factor lower than the Galactic value ( i.e. , when { \Delta log ( SSFR ) _ { MS } } \gtrsim 0.3 dex ) .