Rotationally-supported disks around Class I sources in Taurus: disk formation constraints

(Abridged) Disks are observed around pre-main sequence stars, but how and when they form is still heavily debated. While disks around young stellar objects have been identified through thermal dust emission, spatially and spectrally resolved molecular line observations are needed to determine their nature. We present subarcsecond observations of dust and gas toward four Class I low-mass young stellar objects in Taurus. The 13CO and C18O J=2-1 transitions at 220 GHz were observed with the Plateau de Bure Interferometer at a spatial resolution of ~0.8'' and analyzed using uv-space position velocity diagrams to determine the nature of their observed velocity radient. Rotationally supported disks (RSDs) are detected around 3 of the 4 Class I sources studied. The derived masses identify them as Stage I objects; i.e., their stellar mass is higher than their envelope and disk masses. The outer radii of the Keplerian disks toward our sample of Class I sources are <~ 100 AU. The lack of on-source C18O emission for TMR1 puts an upper limit of 50 AU on its size. Flattened structures at radii > 100 AU around these sources are dominated by infalling motion (v propto r^-1). A large-scale envelope model is required to estimate the basic parameters of the flattened structure from spatially resolved continuum data. Similarities and differences between the gas and dust disk are discussed. Combined with literature data, the sizes of the RSDs around Class I objects are best described with evolutionary models with an initial rotation of 10^-14 Hz and slow sound speeds. Based on the comparison of gas and dust disk masses, little CO is frozen out within 100 AU in these disks. RSDs with radii up to 100 AU are present around Class I embedded objects. Larger surveys of both Class 0 and I objects are needed to determine whether most disks form late or early in the embedded phase.