GOODS-$Herschel$: Gas-to-dust mass ratios and CO-to-H$_2$ conversion factors in normal and starbursting galaxies at high-z

International audienceWe explore the gas-to-dust mass ratio (M$_{gas}$/M$_d$) and the CO luminosity-to-M$_{gas}$ conversion factor ($\alpha_{CO}$) of two well studied galaxies in the GOODS-N field, that are expected to have different star forming modes, the starburst GN20 at z=4.05 and the normal star-forming galaxy BzK-21000 at z=1.52. Detailed sampling is available for their Rayleigh-Jeans emission via ground based mm interferometry (1.1-6.6mm) along with $Herschel$, PACS and SPIRE data that probe the peak of their infrared emission. Using the physically motivated Draine & Li (2007) models, as well as a modified black body function, we measure the dust mass (M$_{dust}$) of the sources and find (2.0$^{+0.7}$$_{-0.6}$ x 10$^{9}$) $M \odot$ for GN20 and (8.6$^{+0.6}$$_{-0.9}$ x 10$^8$) $M \odot$ for BzK-21000. The addition of mm data reduces the uncertainties of the derived $M_{dust}$ by a factor of ~2, allowing the use of the local M$_{gas}$/M$_d$ vs metallicity relation to place constraints on the $\alpha_{CO}$ values of the two sources. For GN20 we derive a conversion factor of $\alpha_{CO}$ < 1.0 $M_\odot$ $pc^{-2}$ (K km $s^{-1}$)$^{-1}$, consistent with that of local ULIRGs, while for BzK-21000 we find a considerably higher value, $\alpha_{CO}$ ~4.0 $M \odot$$ pc^{-2}$(K km $s^{-1})^{-1}$, in agreement with an independent kinematic derivation reported previously. The implied star formation efficiency is ~25 L$\odot$/M$\odot$ for BzK-21000, a factor of ~5$-$10 lower than that of GN20. The findings for these two sources support the existence of different disk-like and starburst star-formation modes in distant galaxies, although a larger sample is required to draw statistically robust result