Constraining MHD disk winds with ALMA

Context. Large millimeter interferometers (ALMA, NOEMA, SMA), with their high spectral resolution and sensitivity, are revealing a growing number of rotating outflows, which are suggested to trace magneto-centrifugal disk winds (MHD DWs). However, the angular momentum flux that they extract and its impact on disk accretion are not yet well quantified. Aims. We aim to identify systematic bias in the process of retrieving the true launch zone, magnetic lever arm, and associated angular momentum flux of an MHD DW from apparent rotation signatures, as measured by observers from position-velocity (PV) diagrams at ALMA-like resolution. Methods. We constructed synthetic PV cuts from self-similar MHD DW solutions over a broad range of parameters. We examine three methods for estimating the specific angular momentum jobs from PV cuts: the “double-peak separation” method (relevant for edge-on systems), and the “rotation curve” and “flow width” methods (applicable at any view angle). The launch radius and magnetic lever arm are then derived from jobs through the widely used theory of MHD flow invariants, and are compared to their true values on the outermost streamline. Predictions for the “double-peak separation” method are tested on published ALMA observations of the HH212 rotating SO wind at resolutions from ~250 au to ~18 au. Results. The double-peak separation method and the flow width method provide only a lower limit to the true outer launch radius rout. This bias is mostly independent of angular resolution, but increases with the wind radial extension and radial emissivity gradient and can reach a factor of ten. In contrast, the rotation curve method leads to a good estimate of rout when the flow is well resolved, and an upper limit at low angular resolution. The magnetic lever arm is always underestimated due to invisible angular momentum stored as magnetic field torsion. ALMA data of HH212 confirm our predictions of the bias associated with the double-peak separation method, and the large rout ≃ 40 au and small magnetic lever arm first suggested by Tabone et al. (2017, A&A, 607, L6) from PV cut modeling. We also derive an analytical expression for the fraction of disk angular momentum extraction performed by a self-similar MHD disk wind of given radial extent, magnetic lever arm, and mass ejection-to-accretion ratio. The MHD DW candidate in HH212 extracts enough angular momentum to sustain steady accretion through the whole disk at the current observed rate. Conclusions. The launch radius estimated from observed rotation signatures in an MHD DW can markedly differ from the true outermost launch radius rout. Similar results would apply in a wider range of flow geometries. While in principle it is possible to bracket rout by combining two observational methods with opposite bias, only comparison with synthetic predictions can properly take into account all observational effects, and also constrain the true magnetic lever arm. The present comparison with ALMA observations of HH212 represents the most stringent observational test of MHD DW models to date, and shows that MHD DWs are serious candidates for the angular momentum extraction process in protoplanetary disks.