Constraining MHD disk winds with ALMA. Apparent rotation signatures and application to HH212

Large millimeter interferometers are revealing a growing number of rotating outflows, which are suggested to trace magneto-centrifugal disk winds (MHD DWs). However, their impact on disk accretion is not yet well quantified. Here we identify systematic biases in retrieving the true launch zone, magnetic lever arm, and angular momentum flux of an MHD DW from apparent rotation signatures. Synthetic position-velocity cuts are constructed from self-similar MHD DWs over a broad range of parameters, and three different methods are applied for estimating the specific angular momentum. We find that the launch radius inferred using the well-known relation from Anderson et al. (2006) can markedly differ from the true outermost launch radius $r_{out}$ of the DW. The "double-peak separation" and "flow width" methods provide only a strict lower limit to $r_{out}$. This bias is independent of angular resolution and can reach a factor ten. In contrast, the "rotation curve" method gives a good estimate of $r_{out}$ when the flow is well resolved, and an upper limit otherwise. The magnetic lever arm is always underestimated. Only comparison with synthetic predictions can take into account properly all observational effects. As an application, we present a comparison with ALMA observations of HH212 at resolutions from 250 au to 16 au, which represents the most stringent observational test of MHD DW to date. This comparison confirms our predicted biases for the double-peak separation method, and the large $r_{out}\sim40~$au and small magnetic lever arm first suggested by Tabone et al. (2017). We also derive the first accurate analytical expression for the fraction of disk angular momentum extracted by an MHD disk wind of given radial extent, magnetic lever arm, and mass flux. Application to HH212 confirms that MHD DWs are serious candidates for the steady angular momentum extraction process in young disks.