(Abridged) Transition disks are recognized by the absence of emission of small dust grains inside a radius of up to several 10s of AUs. Due to the lack of angular resolution and sensitivity, the gas content of such dust holes has not yet been determined, but is of importance to constrain the mechanism leading to the dust holes. Transition disks are thought to currently undergo the process of dispersal, setting an end to the giant planet formation process. We present new high-resolution observations with the Atacama Large Millimeter/ submillimeter Array (ALMA) of gas lines towards the transition disk Oph IRS 48 previously shown to host a large dust trap. ALMA has detected the $J=6-5$ line of $^{12}$CO and C$^{17}$O around 690 GHz (434 $mu$m) at a resolution of $sim$0.25$$ corresponding to $sim$30 AU (FWHM). The observed gas lines are used to set constraints on the gas surface density profile. New models of the physical-chemical structure of gas and dust in Oph IRS 48 are developed to reproduce the CO line emission together with the spectral energy distribution (SED) and the VLT-VISIR 18.7 $mu$m dust continuum images. Integrated intensity cuts and the total spectrum from models having different trial gas surface density profiles are compared to observations. Using the derived surface density profiles, predictions for other CO isotopologues are made, which can be tested by future ALMA observations of the object. The derived gas surface density profile points to the clearing of the cavity by one or more massive planet/companion rather than just photoevaporation or grain-growth.
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