Measurements of angular momentum in jets and outflows, and feedback on the disk

Abstract

The problem of understanding how a newly forming solar system manages to lose angular momentum from the stage of collapsing core to the final main sequence phase is a long-standing one. This is especially pertinent regarding the evolution of the accretion disks. Both theoretical studies and recent observational surveys have questioned the paradigm of viscosity-driven disk evolution, while at the same time alternative scenarios considering the action of magnetically driven winds have gained credit. In recent years, observers have struggled to provide constraints to establish which mechanism is principally responsible, and one of the most interesting findings proved to be the detection and characterisation of rotational motions in the wind components, coupled with the rotation signatures in the associated disk. Such results allowed the estimate of the angular momentum transported by the winds and confirmed the validity of the magneto-hydrodynamic models for the acceleration of outflows and simultaneous disk braking. Importantly, the rotation estimates proved to allow the derivation of the region of origin of the winds in the disk (‘footpoint’), thus enabling a direct evaluation of the feedback of the outflows on the disk in the planet formation region. Here we present an overview on the observational efforts in this direction, from the first detection of jet rotation with the Hubble Space Telescope, to the current state of play, in which ALMA is providing the most stringent constraints to both wind models and related disk evolution. Finally, we mention the future observational directions to further explore this intriguing topic.

1 Introduction

For gas in a protostellar disk to accrete onto the central star, it must lose angular momentum; otherwise centrifugal support prevents inward motion and the disk would remain largely static. In the classical framework of viscous disk evolution developed by Shakura and Sunyaev (1973), angular momentum transport is parameterised through an effective turbulent “-viscosity,” later physically associated with the magnetorotational instability (MRI) proposed by Balbus and Hawley (1991). However, both theoretical studies and recent observational surveys have challenged the universality of viscosity-driven evolution. Non-ideal magnetohydrodynamic (MHD) effects (Ohmic resistivity, ambipolar diffusion, Hall drift) can suppress or strongly modify MRI turbulence in protoplanetary disks (e.g., Bai and Stone, 2013), and high-resolution molecular line observations often reveal low turbulence levels inconsistent with strong viscous transport (e.g., Flaherty et al., 2015). At the same time, alternative scenarios invoking magnetically driven winds [originally formulated in magnetocentrifugal form by Blandford and Payne (1982)] have gained increasing support. In these models, large-scale magnetic fields extract angular momentum vertically from the disk surface and carry it away along outflows, enabling accretion even in weakly turbulent disks (e.g., Bai, 2016; Lesur et al., 2023). Growing observational evidence for rotating jets and winds further strengthens this paradigm, suggesting that wind-driven angular momentum removal may play a central (and in some systems dominant) role in regulating disk evolution and dispersal.

1.1 Magnetohydrodynamic winds

There are several flavours of MHD winds, which can be differentiated primarily by their launch point within the star–disk system and by the physical conditions that enable their acceleration. For example, stellar winds are launched directly from the stellar surface, while X-winds originate from a narrow region near the inner truncation radius of the accretion disk, close to the magnetospheric boundary. In contrast, disk winds are magnetically driven from a broader range of radii along the accretion disk surface. Each of these wind types differs in magnetic field configuration, mass-loading, collimation efficiency, and dynamical impact on the surrounding environment [See review by Ray and Ferreira (2021)].

1.2 Angular momentum transport in jets and outflows

To establish whether jets and outflows play a significant role in angular momentum transport and thereby regulate disk evolution, it is essential to directly measure rotational motion within the flow. When the inferred angular velocity is combined with an estimate of the mass outflow rate, it becomes possible to calculate the angular momentum flux carried by the wind. This provides a direct measure of how efficiently the outflow extracts angular momentum from the star–disk system.

Furthermore, under the assumption that the jet/outflow is a cold MHD self similar disk wind, it is possible to estimate the footpoint region of the outflow (i.e., the location on the disk from which the material is launched). With this, one can relate the observed jet kinematics to specific disk radii. This, in turn, enables a comparison between the angular momentum transported by the jet and/or wind and the amount that must be removed from the disk to drive accretion at the observed rate. Such a consistency check is crucial for assessing whether magnetically driven outflows can account for the angular momentum budget required for disk accretion.

2 Observing jet rotation

2.1 Measurement method

In order to investigate if rotational motions are present in the outflow, measurements are made of the radial velocity of the gas at two positions that are symmetrically located on opposite sides of the central axis. If a systematic difference in radial velocity is detected between these two equidistant points, this asymmetry can be interpreted as evidence for jet rotation. Under the assumption of axisymmetry and steady flow, this transverse velocity gradient reflects the presence of a toroidal (rotational) velocity component. Furthermore, by combining the measured radial velocity difference with knowledge of the jet’s inclination angle relative to the line of sight, it is possible to disentangle the velocity components and derive both the poloidal velocity and the toroidal velocity. This decomposition provides crucial constraints on the jet launching mechanism and the distribution of angular momentum within the outflow.

2.2 First observations of jet rotation

Although searches for rotational signatures in jets can in principle be carried out across a wide range of wavelengths, such studies are observationally demanding because they require a combination of high spatial resolution (to resolve the jet width), high spectral resolution (to detect small transverse velocity shifts of a few km/s), and sufficient sensitivity to measure faint emission at offset positions from the axis. These stringent requirements have historically limited the number of suitable instruments and targets. Early optical studies harnessed the diffraction-limited resolution of the Hubble Space Telescope (HST) (e.g., Bacciotti et al., 2002; Woitas et al., 2005; Coffey et al., 2004; 2007). Follow-up work extended these investigations into the near-ultraviolet (NUV), again with HST, probing hotter and faster jet components (e.g., Coffey et al., 2007; Coffey et al., 2012). At longer wavelengths, near-infrared observations with facilities such as the Very Large Telescope (VLT) and Gemini Observatory enabled the study of embedded sources through molecular hydrogen and [Fe II] emission (e.g., Chrysostomou et al., 2008; Coffey et al., 2011).

3 Interpreting jet rotation in the framework of the accretion/ejection magnetic engine

3.1 Jet footpoint

Interpreting transverse differences in radial velocity as evidence of jet rotation is most physically meaningful when the flow can be described within the framework of steady, axisymmetric, self-similar, cold magnetohydrodynamic (MHD) disk-wind models, such as the magneto-centrifugal scenario proposed by Blandford and Payne (1982). In these models, matter is centrifugally accelerated from the disk surface along large-scale magnetic field lines, thereby removing angular momentum from the disk and thus allowing the transfer of mass through the disk to smaller radii and finally the accretion onto the central object.

Building on this framework, Anderson et al. (2003) derived an expression relating the observed toroidal and poloidal velocity components at a given location in the jet to the footpoint radius in the disk from which the material was launched, . This is possible because in this class of models, for any given launching radius, a specific relation between toroidal and poloidal velocities is predicted. A visualization of such relationship is offered in the diagram first proposed in Ferreira et al. (2006), in which the theoretical curves corresponding to the different classes of MHD solutions, such as X-winds or extended disk winds, occupy distinct regions in the parameter space defined by the specific angular momentum and the poloidal velocity.

Early observational detections of transverse velocity gradients in T Tauri jets with the HST (e.g., Bacciotti et al., 2002; Coffey et al., 2004; Coffey et al., 2007) provided the first estimates of jet toroidal velocities and corresponding footpoint radii, , Table 1. Inferred launching regions for the high-velocity, axial atomic jet component were typically found within a few astronomical units (up to 4 au, depending on the tracer) from the central star along the disk plane. Such values are difficult to reconcile with narrow X-wind models launched exclusively near the inner truncation radius (e.g., Shu et al., 1994), but are instead broadly consistent with extended disk-wind solutions. The first theoretical reviews on the subject (e.g., Ray et al., 2007; Frank et al., 2014) discussed these results in the light of competing MHD launching models.

It is important to recall, however, that protostellar outflows are stratified and layered, consisting of multiple kinematic and excitation components (e.g., a high-velocity, well-collimated atomic jet surrounded by lower-velocity molecular or atomic disk-wind material). Consequently, any inferred footpoint radius strictly applies only to the specific layer being probed observationally. The distinction appeared evident with the advent of Atacama Large millimeter/submillimeter Array (ALMA), because of its superior spectral resolution. In fact, in a number of molecular jets the footpoint radii determined from ALMA observations were found to be compatible with an X-wind interpretation (see Section 4).

3.2 Fraction of angular momentum transported by the outflow components

In all cases where reliable transverse velocity gradients were measured in the high-velocity axial collimated jet, the angular momentum flux carried by this component was calculated by combining the inferred toroidal velocity with the mass outflow rate. From observations obtained with the HST, the angular momentum transported by the flow was found to constitute a substantial fraction of that required to sustain accretion at the observed disk accretion rates. For example, in RW Aurigae, Woitas et al. (2005) showed that the jet could remove a significant portion (about 60%) of the disk’s excess angular momentum. Similarly, for DG Tauri, Maurri et al. (2014) found that the angular momentum flux in the atomic jet is dynamically important in the overall accretion–ejection balance (about 1/3 of the excess angular momentum in the disk). These results suggest that even a single, well-collimated jet component can play a major role in regulating disk evolution.

With the advent of high-resolution (sub-)millimeter interferometry using ALMA, it is now possible to probe both the more collimated molecular jet components and the wider-angle molecular disk winds. This allows a more complete accounting of angular momentum transport across the different layers of the outflow, providing a fuller picture of how jets and winds contribute to disk evolution.

3.3 Alternative interpretations

Although transverse Doppler gradients have often been interpreted as signatures of jet rotation, several observations highlight the need for caution. In some cases, apparent counter-rotation between the jet and its associated disk has been reported, such as in RW Aurigae (Cabrit et al., 2006) and Th 28 (Louvet et al., 2016), challenging a simple magneto-centrifugal interpretation (Tu et al., 2026). Moreover, modeling work by Pesenti et al., 2004 showed that optical observations preferentially sample only the outer streamlines of a disk wind, potentially biasing inferred footpoint radii. It has also been demonstrated that shocks can self-generate apparent rotation signatures in jets (Fendt, 2011). More generally, transverse Doppler gradients may arise from asymmetric shocks induced by a warped disk (Soker, 2005) or by inhomogeneities in the ambient medium, as well as from jet wiggling caused by precession (Cerqueira et al., 2006) or orbital motion in a binary system.

With improvements in spatial resolution, microjet wiggling has been revealed to be common, and detailed kinematic modeling has successfully reproduced such structures through orbital motion of the jet source fitting in the bipolar jet from Th 28 using VLT/MUSE (Murphy et al., 2021) and in the HH 111 bipolar outflow with HST/WFC3 (Erkal et al., 2021a). Similarly, precession modeling of the DO Tauri bipolar jet using Gemini Observatory/NIFS has reproduced observed velocity gradients without invoking intrinsic rotation (Erkal et al., 2021b). Together, these studies demonstrate that Doppler gradients do not uniquely imply jet rotation and must be interpreted in the broader dynamical context of the source. The final confirmation of rotational motions in the outflows had to wait for the advent of ALMA (Section 4)

4 Jet rotation observed with micro-wave interferometry

4.1 Jet rotation confirmed

The first studies focussed on T Tauri stars which are less embedded and so have jets which are optically visible. Early studies of younger more embedded sources struggled due to the lack of suitable adaptive optics guide stars. Some efforts were made (Coffey et al., 2011) but it was not until the advent of interferometry that real progress was achievable.

High-resolution (sub-)millimeter interferometry with ALMA has opened a new window on rotation in molecular jets and outflows. Breakthrough advancements in the field have been made possible thanks to the combination of a subarcsecond spatial resolution comparable and even higher than that of HST and an outstanding 0.1–0.2 km velocity resolution. This allowed great precision in measurement of the small velocity gradients across the flows, as well as probing closer to the launching region.

One of the first of these studies (see Coffey, 2017) was by Lee et al. (2017) reporting on the Class 0 protostar HH 212. They reported compelling radial velocity differences (1–2 km/s) across the collimated SiO jet consistent with a magneto-centrifugally launched disk wind. Subsequent analysis by Tabone et al. (2020) further constrained the launching radii (i.e. 0.05 au) and angular momentum extraction (30 au km/s). More recently, Lee et al. (2025) reported on HH 211, using ALMA to resolve the molecular jet spine at its base. This revealed a fast flow (107 km/s) with low specific angular momentum (4 au km/s), implying a launch radius very close to the disk’s inner edge (i.e. 0.02 au). For review, see Ray and Ferreira (2021).

4.2 Rotation in outflows from higher mass protostars

To date, most observational studies of jet rotation have focused on low-mass protostars, which are more common and generally less embedded than their intermediate- and high-mass counterparts, making them more accessible to high-resolution observations. However, recent studies are increasingly extending these investigations to higher-mass regimes.

For example, VLBI O maser observations by Moscadelli et al. (2019); 2022) traced rotating outflows in the massive protostar IRAS 21078 + 5211. The masers exhibit spiral motions near the jet axis and velocity gradients consistent with co-rotation at launch radii of 10–50 au, in agreement with magneto-centrifugal disk-wind models. Subsequently, high-resolution ALMA observations by Matsushita et al. (2021) revealed transverse velocity gradients of 25–50 km/s across the jet from the Class 0 intermediate-mass source FIR 6b, providing strong evidence for jet rotation and efficient angular-momentum extraction in this early phase. Most recently, polarization and rotation-measure studies of HH 80–81 provide the first direct evidence of a helical magnetic field in a massive protostellar jet, revealing its 3D structure and supporting a universal role for magnetic geometry in jet collimation and angular-momentum transport (Rodríguez-Kamenetzky et al., 2025).

It is evident, even from this modest sample, that the trends observed in lower-mass, more evolved protostars are confirmed in studies of jets from higher-mass sources.

5 From jets to shells

The latest investigations have increasingly focused on the rotation of so-called molecular “shells” or wide-angle winds detected in low-mass Class 0/I protostars. These components are traced in molecular lines such as SO, and CO, observed at (sub-)millimeter wavelengths with high angular resolution, and are detected very close to the source indicating that they are not merely swept-up ambient material but represent genuine disk-launched winds. Characteristically, these flows exhibit relatively low velocities compared to the axial jet, wide opening angles, and a nested morphology in which a collimated high-velocity jet is embedded within a broader molecular wind [see review by Pascucci et al. (2023)]. An increasing number of protostellar systems now show evidence for rotation in molecular shells observed at (sub-) millimeter wavelengths, with inferred launching radii typically in the range of 10–100 au, consistent with extended disk-wind models.

5.1 Measurement method

A rotating, expanding shell produces a characteristic tilted elliptical pattern in the transverse position–velocity (PV) diagram: the ellipse arises from the projection of a hollow, radially expanding structure, while any systematic tilt of the ellipse indicates a velocity difference between the two sides of the flow consistent with rotation. By performing ellipse fitting to the PV emission (i.e., fitting the locus of peak intensity with a parametric elliptical model) one can simultaneously constrain the shell radius, expansion (poloidal) velocity, and toroidal velocity component. The magnitude and sign of the tilt provide a direct measure of the rotational velocity, while the ellipse geometry constrains the inclination and expansion speed [see, e.g., De Valon et al. (2022)].

5.2 Rotating molecular shells

To date, around ten rotating molecular outflows structured in nested shells have been found, spanning a range of stellar masses. These are presented in Table 1 but also listed in a group here for clarity: CB 26 (Launhardt et al., 2009); DG Tau B (Zapata et al., 2015; de Valon et al., 2020); TMC1A (Bjerkeli et al., 2016); Ori-S6 (Zapata et al., 2010); Orion Source I (Hirota et al., 2017); NGC 1333 IRAS 4C [(Zhang et al., 2018)]; HH 212 (Tabone et al., 2017), HH 211 (Lee et al., 2018); HH 30 (Louvet et al., 2018; López-Vázquez et al., 2023). Finally, Bacciotti et al. (2025) presented ALMA CO observations which reveal that the nested molecular shells in the HL Tau outflow exhibit rotation in the same sense as the protoplanetary disk, and that the three outermost shells have footpoint locations compatible with the position of three consecutive outer dusty rings in the disk, Figure 1.

FIGURE 1

Bacciotti et al. (2025). Image Credit: F. Bacciotti.

Together, these studies indicate that rotation in molecular outflows is widespread. Along with previous studies, these investigations present convincing observational basis for magneto-centrifugal launching models across evolutionary phases and mass regimes, implying that this angular-momentum extraction mechanism is universal. See Table 1 for an overview of the current observational status of rotation studies.

5.3 Mass and angular momentum flux

Estimates of mass-loss rates in protostellar systems increasingly suggest that the slow, wide-angle molecular wind can dominate over the collimated jet in terms of mass ejection per unit time. In HH 212, Tabone et al. (2020) found that the slow disk wind extracts between one and ten times the mass flux of the axial jet. An even more extreme case is DG Tau B, where estimated a wind mass-loss rate (De Valon et al., 2020) roughly 35 times higher than that of the jet (Podio et al., 2011). For HH 30, the jet mass flux is about 50 times lower than the molecular wind component (Bacciotti et al., 1999; Louvet et al., 2018), implying that the wind mass flux is approximately five times the accretion rate if one assumes a canonical jet-to-accretion ratio of 0.1. Combined with the estimates of disk rotational speed, these results indicate that the slow wind may be the dominant contributor to angular momentum extraction from the disk. Indeed, in the systems where the necessary parameters are sufficiently well constrained the estimated angular momentum flux carried by the rotating wind as a whole appears sufficient, within a factor of about 2–3, to drive steady accretion across the wind-launching region compatible with the accretion rate measured at the star.

6 Future observational prospects

With current facilities we are beginning to spatially disentangle the individual nested layers of protostellar outflows, such as in DG Tau B and HH 30, allowing the possibility of determining a distinct launching (footpoint) radius for each kinematic component (e.g., axial jet, wide-angle wind). However, these individual layers can be intrinsically faint, strongly collimated and often overlap along the line of sight, demanding exceptional spatial resolution, spectral resolution, and sensitivity. With ALMA, we are operating in relatively good conditions to detect and measure rotation, but only for the molecular winds revealed at mm wavelengths. In contrast, the inner components emitting in the optical/infrared regime are more difficult to sample for rotation. Early studies with HST were conducted at the technical limit of the spectrograph, and were only possible for bright outflows. The James Webb Space Telescope provides superb spatial resolution and sensitivity, but its velocity resolution ( 100 km ) is far from that required to measure the small transverse velocity shifts that trace rotation. Therefore, the new instruments installed at ground-based telescopes equipped with adaptive optics are particularly promising. These include ERIS and CRIRES + on the Very Large Telescope (VLT) offering spatial resolution 0.05” and 0.2” combined with velocity resolution 30 km and 3 km respectively, and, in perspective, the future facilities with large collecting area like the Extremely Large Telescope (ELT) offering spatial resolution (0.005–0.01”) combined with velocity resolution 3 km . By resolving and characterising each outflow layer, and measuring the angular momentum extracted at different radii, we will be able to indirectly probe the disk magnetisation which cannot be measured directly. In this way, angular momentum measurements in jets and winds may ultimately allow us to quantify the dynamical importance of magnetic fields in governing protoplanetary disk evolution.

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