Angular momentum profiles of Class 0 protostellar envelopes

Context. Understanding the initial properties of star forming material and how they affect the star formation process is a key question. The infalling gas must redistribute most of its initial angular momentum inherited from prestellar cores before reaching the central stellar embryo. Disk formation has been naturally considered as a possible solution to this "angular momentum problem". However, how the initial angular momentum of protostellar cores is distributed and evolves during the main accretion phase and the beginning of disk formation has largely remained unconstrained up to now. Aims. In the framework of the IRAM CALYPSO survey, we obtained observations of the dense gas kinematics that we used to quantify the amount and distribution of specific angular momentum at all scales in collapsing-rotating Class 0 protostellar envelopes. Methods. We used the high dynamic range (CO)-O-18 (2-1) and N2H+ (1-0) datasets to produce centroid velocity maps and probe the rotational motions in the sample of 12 envelopes from scales similar to 50 to similar to 5000 au. Results. We identify differential rotation motions at scales less than or similar to 1600 au in 11 out of the 12 protostellar envelopes of our sample by measuring the velocity gradient along the equatorial axis, which we fit with a power-law model v proportional to r(alpha). This suggests that coherent motions dominate the kinematics in the inner protostellar envelopes. The radial distributions of specific angular momentum in the CALYPSO sample suggest the following two distinct regimes within protostellar envelopes: the specific angular momentum decreases as j proportional to r(1.6 +/- 0.2) down to similar to 1600 au and then tends to become relatively constant around similar to 6 x 10(-4) km s(-1) pc down to similar to 50 au. Conclusions. The values of specific angular momentum measured in the inner Class 0 envelopes suggest that material directly involved in the star formation process (<1600 au) has a specific angular momentum on the same order of magnitude as what is inferred in small T-Tauri disks. Thus, disk formation appears to be a direct consequence of angular momentum conservation during the collapse. Our analysis reveals a dispersion of the directions of velocity gradients at envelope scales >1600 au, suggesting that these gradients may not be directly related to rotational motions of the envelopes. We conclude that the specific angular momentum observed at these scales could find its origin in other mechanisms, such as core-forming motions (infall, turbulence), or trace an imprint of the initial conditions for the formation of protostellar cores.