Magnetic Wind Models in Astrophysics

• Magnetic wind models are astrophysical frameworks where magnetic fields actively shape plasma escape, control geometry, and mediate mass loading and angular momentum transfer.
• They range from geometric, analytic approximations to fully self-consistent 3D MHD simulations, capturing both magnetic field topology and dynamic plasma processes.
• These models are applied in solar, stellar, and disc environments to explain wind acceleration, energy deposition, and the feedback between magnetic fields and plasma dynamics.

A magnetic wind model is an astrophysical formulation in which magnetic field structure is not treated as a passive diagnostic of outflow, but as the organizing agent that sets where plasma can escape, how angular momentum is transported, how energy is deposited, and how open and closed flux are partitioned. In the literature represented here, the term spans several related but non-identical uses: a solar coronal field model that connects a dipolar low corona to a current-sheet-dominated heliosphere (Veselovsky et al., 2012); a wave-modified Parker wind along open magnetic flux tubes in which the magnetic field profile is the only required input (Woolsey, 2015); observation-driven 3D stellar-wind simulations using reconstructed surface magnetic maps (Vidotto, 2014); reduced global wind pipelines that solve a Parker-like flow along magnetically reconstructed open field lines (Lowder et al., 2024); and accretion-driven outflows in discs and X-ray binaries where magnetic stresses launch or structure the wind [(Teitler, 2011); (Ratheesh et al., 2020)]. This suggests that “magnetic wind model” is best understood as a family of models unified by magnetic control of geometry, mass loading, and stress transmission, rather than a single formalism.

1. Conceptual scope and defining features

Across the cited literature, magnetic wind models share several recurrent elements. The outflow is tied to an open magnetic geometry, and the magnetic field enters either through flux-tube area variation, explicit Lorentz stresses, current-sheet structure, or field-line connectivity [(Woolsey, 2015); (Veselovsky et al., 2012)]. In solar and stellar applications, the field determines where flux is open and how rapidly tubes expand; in disc winds, it removes angular momentum vertically; in accretion-disc winds, it organizes a stratified outflow with density, velocity, and ionisation varying systematically with radius [(Kadam et al., 31 Jan 2025); (Teitler, 2011); (Ratheesh et al., 2020)].

A common distinction runs through the literature between models that solve plasma dynamics self-consistently and models that use magnetic structure kinematically or parametrically. The simple coronal model of Veselovsky and Panasenco is explicitly geometric rather than a self-consistent MHD solution (Veselovsky et al., 2012). TEMPEST solves only the momentum equation and infers temperature and Alfvénic heating rate from magnetic-field correlations calibrated to ZEPHYR (Woolsey, 2015). FLUXPipe first relaxes a current-carrying coronal field and then computes a one-dimensional isothermal Parker-like wind along each open fluxon, with wind back-reaction neglected (Lowder et al., 2024). Observation-driven cool-star wind models instead solve the ideal MHD equations in 3D with the observed radial magnetic field imposed at the stellar surface (Vidotto, 2014). This suggests a useful classification into geometry-first models, reduced magnetically closed Parker-like models, and full or fuller MHD wind models.

Another shared feature is the central role of open magnetic flux. Solar-wind source models repeatedly distinguish open flux tubes from closed loops, and several papers emphasize that open field alone is not sufficient unless plasma is actually loaded onto those heliospherically connected lines [(Chen et al., 15 Sep 2025); (Cranmer et al., 2010)]. In protostellar and protoplanetary discs, the equivalent distinction is between matter tied to the disc and matter accelerated along large-scale poloidal field lines into a magnetocentrifugal or MHD wind [(Teitler, 2011); (Kadam et al., 31 Jan 2025)].

2. Coronal and heliospheric magnetic structure

One analytically explicit magnetic wind model for the Sun is the extended-corona configuration constructed as a superposition of a point magnetic dipole at the Sun’s center, a thin equatorial ring current sheet carrying azimuthal current $j_\varphi$, and a central magnetic quadrupole (Veselovsky et al., 2012). In the simplest axisymmetric form, with solar rotation neglected in the inner heliosphere because $\Omega r/V \ll 1$, the field is written

$$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$

$B_\theta = \mu r^{-3}\sin\theta.$

The current sheet has surface azimuthal current density

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$

so $j_\varphi \propto r^{-3}$, and the magnetic-field jump across the sheet is $\Delta B = 2B_0$ (Veselovsky et al., 2012).

This construction is designed to be asymptotically correct both near the Sun, where the large-scale field is approximately dipolar, and at large distance, where the heliospheric current sheet dominates and the field becomes nearly radial with $|B_r(\theta)| \approx \mathrm{const}$, matching the Ulysses result cited in the paper (Veselovsky et al., 2012). The exact axisymmetric field-line equation integrates to

$$\rho = \sin^2\theta \,\bigl(C - 2|\cos\theta|\bigr)^{-1},$$

and the topology depends on the sign of $a=2\mu/\Phi$, yielding either a separator between closed equatorial loops and open polar-hole flux or a configuration with two magnetic null points on the symmetry axis (Veselovsky et al., 2012). The quadrupole extension introduces North–South asymmetry without changing the leading far-field current-sheet asymptotics.

A different middle-ground coronal model is the “outflow field” of Rice and Yeates, which modifies magneto-frictional equilibrium by imposing a radial solar-wind profile (Rice et al., 2021). Starting from

$\Omega r/V \ll 1$0

with $\Omega r/V \ll 1$1, the equilibrium is defined by

$\Omega r/V \ll 1$2

With the ansatz $\Omega r/V \ll 1$3, the problem reduces to

$\Omega r/V \ll 1$4

so the classical potential-field Laplace problem is replaced by an advection-modified elliptic equation (Rice et al., 2021). Relative to PFSS, the outflow field increases open magnetic flux, reduces the open-flux discrepancy with in situ measurements, and removes the need to impose an artificial source surface as the main radializing mechanism (Rice et al., 2021).

A more explicitly field-line-based coronal-wind pipeline is FLUXPipe, which uses HMI synoptic $\Omega r/V \ll 1$5 maps, discretizes them into equal-flux footpoints, traces initial topology with pfsspy, relaxes the coronal field into a current-carrying near-force-free state using fluxons, and then solves an isothermal Parker-like wind along each open fluxon (Lowder et al., 2024). The wind equation is

$\Omega r/V \ll 1$6

with

$\Omega r/V \ll 1$7

Here the magnetic field affects the wind through the flux-tube area $\Omega r/V \ll 1$8 and the super-radial expansion factor $\Omega r/V \ll 1$9, extracted from the relaxed fluxon hull geometry (Lowder et al., 2024). This suggests a recurrent magnetic-wind pattern: reconstruct coronal magnetic topology first, then solve the outflow along the resulting open structures.

3. Open-flux-tube Parker models, wave pressure, and turbulence dissipation

TEMPEST is an explicit example of a magnetically informed, wave-modified Parker wind model in which the only required input is the magnetic field profile $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$0 along a single open flux tube (Woolsey, 2015). Starting from the time-steady momentum equation combined with mass conservation, Woolsey writes

$$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$1

with wave-modified critical speed

$$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$2

The term $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$3 represents the direct effect of magnetic flux-tube divergence, while the $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$4 and $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$5 terms encode Alfvénic heating and wave pressure (Woolsey, 2015). TEMPEST does not solve the energy equation self-consistently; instead, it uses extensive calibration from a large grid of ZEPHYR models to infer $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$6 and $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$7 from the supplied $$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$8 (Woolsey, 2015).

Within this framework, magnetic geometry controls terminal wind speed through the expansion factor. The paper discusses the WSA-type relation in which low expansion corresponds to fast wind and larger or strongest expansion corresponds to slower wind (Woolsey, 2015). The magnetic field therefore affects both the nozzle geometry of the flow and the transport and dissipation of Alfvén-wave energy. This is one of the clearest published formulations in which a “magnetic wind model” means more than MHD stress: it means that the wind solution is functionally determined by the magnetic profile.

A related but more self-consistent axisymmetric model is the coupled dynamo–wind calculation of Réville and Brun, which solves compressible ideal MHD in the wind region and a mean-field dynamo induction equation inside the star (Perri et al., 2019). The wind equations are

$$B_r = 2\mu r^{-3}\cos\theta + B_0\left(\frac{r_0}{r}\right)^2 \operatorname{sign}\!\left(\theta-\frac{\pi}{2}\right),$$9

$B_\theta = \mu r^{-3}\sin\theta.$0

$B_\theta = \mu r^{-3}\sin\theta.$1

$B_\theta = \mu r^{-3}\sin\theta.$2

The wind is a nearly isothermal polytropic flow with $B_\theta = \mu r^{-3}\sin\theta.$3, and the model shows cycle-dependent variations in wind speed, mass loss, angular-momentum loss, and average Alfvén radius (Perri et al., 2019). Most importantly, wind opening of magnetic field lines feeds back on the dynamo through the surface magnetic boundary condition, altering parity and amplifying quadrupolar content (Perri et al., 2019). This suggests that in some stellar settings the magnetic wind is not just an output of magnetic activity but part of a nonlinear dynamo–wind feedback loop.

Warnecke and collaborators push this coupling in a related direction by solving an axisymmetric mean-field model for induction, momentum, and continuity using an isothermal equation of state, so that a Parker wind develops simultaneously with a self-generated dynamo field (Jakab et al., 2020). In that model, the wind remains broadly Parker-like, but the large-scale field opens into a split-monopole-like topology in much of the domain, the magnetic energy flux peaks between the stellar surface and the Parker critical point, and the angular momentum flux becomes highly variable and can reach negative values, especially at midlatitudes (Jakab et al., 2020). A plausible implication is that even simple magnetic self-consistency can qualitatively change the torque structure relative to fixed-field Parker wind models.

4. Reconnection, current sheets, and magnetic mass loading

Several papers frame magnetic wind models not primarily as wave-heating problems, but as problems of topology change and plasma loading. Chen et al. present a self-consistent 3D radiative MHD model of a coronal-hole source region in which interchange reconnection between closed and open magnetic fields transfers plasma from closed loops onto open flux that reaches the top boundary (Chen et al., 15 Sep 2025). They define an open-field filling factor $B_\theta = \mu r^{-3}\sin\theta.$4 and derive an open-component mass transport equation

$B_\theta = \mu r^{-3}\sin\theta.$5

which, after volume integration, yields a reconnection mass-transfer term $B_\theta = \mu r^{-3}\sin\theta.$6 interpreted as mass transfer from closed to open field by interchange reconnection (Chen et al., 15 Sep 2025). For the modeled coronal-hole source region, the average mass loaded into open regions by interchange reconnection above $B_\theta = \mu r^{-3}\sin\theta.$7 Mm is

$B_\theta = \mu r^{-3}\sin\theta.$8

which the paper states is about $B_\theta = \mu r^{-3}\sin\theta.$9 times higher than the classic value required to sustain the solar wind (Chen et al., 15 Sep 2025).

The same paper decomposes magnetic-energy transport into boundary Poynting fluxes, reconnection transfer $$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$0, dissipation $$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$1, and storage, using

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$2

At $$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$3 Mm they find an average net upward Poynting flux of $$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$4, and argue that reconnection supplies mass to open field and launches upward disturbances, while wave/turbulence and Poynting flux then help heat and accelerate that plasma farther out (Chen et al., 15 Sep 2025). This is a narrower but more concrete claim than “reconnection drives the wind”: reconnection is modeled as the magnetic mass-loading mechanism.

A more skeptical assessment of reconnection as the primary wind driver appears in Cranmer and van Ballegooijen’s magnetic-carpet loop-opening study (Cranmer et al., 2010). They define the open-flux recycling time

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$5

and compare it with the solar-wind acceleration time

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$6

They also estimate the energy flux released in closed-to-open events through

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$7

Their conclusion is that for quiet regions and mixed-polarity coronal holes these reconnection energy fluxes are much lower than required to accelerate the solar wind, and that even in the most imbalanced coronal holes the recycling times are far longer than the time it takes the solar wind to accelerate into the low corona (Cranmer et al., 2010). This establishes an explicit controversy within magnetic-wind modeling: magnetic topology change is almost certainly relevant, but its role as the dominant energy source for the bulk solar wind is disputed.

The work on GRS 1915+105 shows a different reconnection-adjacent use of the term in accretion systems. There the relevant question is not interchange loading of solar open flux but whether a self-similar MHD disc wind can explain a stratified absorption spectrum (Ratheesh et al., 2020). The density law

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$8

and the ionisation parameter

$$j_\varphi = - \frac{c}{2\pi}\frac{r_0^2}{r^3}\, \delta\!\left(\theta-\frac{\pi}{2}\right) B_0,$$9

generate a single continuous wind in which different ions trace different radii. The scaling relations

$j_\varphi \propto r^{-3}$0

are used to interpret the observed multi-ion absorption as radial stratification of one magnetic outflow rather than disconnected absorbing clouds (Ratheesh et al., 2020).

5. Stellar-wind generalizations beyond the solar case

For cool, low-mass stars, Vidotto describes a 3D ideal-MHD stellar-wind framework computed with BATS-R-US in which the observed radial magnetic field $j_\varphi \propto r^{-3}$1, reconstructed primarily by Zeeman-Doppler Imaging, is imposed at the stellar surface (Vidotto, 2014). The model solves the ideal MHD equations for mass, momentum, induction, and energy, with a polytropic closure $j_\varphi \propto r^{-3}$2, and initializes the coronal field by a PFSS extrapolation before evolving the coupled wind–field system to steady state in the co-rotating frame (Vidotto, 2014). The key result highlighted in the paper is that the wind mass flux is essentially modulated by the local value of $j_\varphi \propto r^{-3}$3, so stars with more non-axisymmetric observed fields produce more asymmetric wind mass fluxes (Vidotto, 2014).

This observationally anchored framework broadens the meaning of magnetic wind model from a solar-physics problem to a method for predicting stellar spin-down, planetary wind pressure, and astrospheric structure. Because the model predicts 3D distributions of velocity, density, pressure, and magnetic field, it can map total wind pressure around the star and estimate orbit-dependent variability in the external forcing of exoplanets (Vidotto, 2014). A plausible implication is that realistic magnetic topology matters as much as mean field strength for wind–planet interaction studies.

The Betelgeuse model of Thirumalai and Heyl uses the term in still another sense: a steady-state equatorial hybrid Weber–Davis plus dust-driven outflow (Thirumalai et al., 2011). The gas radial velocity satisfies

$j_\varphi \propto r^{-3}$4

with $j_\varphi \propto r^{-3}$5, $j_\varphi \propto r^{-3}$6, and a dust contribution introduced through a Heaviside-switched reduction of effective gravity by $j_\varphi \propto r^{-3}$7 once dust condenses beyond $j_\varphi \propto r^{-3}$8 (Thirumalai et al., 2011). The favored Betelgeuse solution is a pure Weber–Davis magneto-rotational wind from the photosphere to about $j_\varphi \propto r^{-3}$9, where the temperature falls to $\Delta B = 2B_0$0 K and silicate dust forms; beyond that radius, radiation pressure on dust adds a second acceleration channel and the terminal gas speed reaches about $\Delta B = 2B_0$1–$\Delta B = 2B_0$2 km s$\Delta B = 2B_0$3 (Thirumalai et al., 2011). Here the magnetic wind model provides the missing inner transport mechanism to lift material from the photosphere to the distant dust shell.

The AGB-star analogue is developed in an explicitly “1.5-dimensional” steady-state equatorial model combining a Weber–Davis magneto-rotational wind with a dust/radiation-driven component (Thirumalai et al., 2010). The same normalized wind equation appears,

$\Delta B = 2B_0$4

and the paper shows that a successful hybrid wind for AGB parameters requires $\Delta B = 2B_0$5 when dust condenses in the physically relevant inner envelope (Thirumalai et al., 2010). This suggests that in evolved stars a magnetic wind model often means not a purely magnetic accelerator, but a magnetic inner wind that enables a dust-driven outer wind.

6. Disk winds, accretion outflows, and model limitations

Protostellar and protoplanetary disc winds extend magnetic wind modeling into rotationally supported systems. In the global self-similar protostellar disk/wind formulation of Wardle, the disk is treated in non-ideal MHD using the conductivity tensor formalism, while the wind above the disk is an ideal, cold Blandford–Payne-type outflow (Teitler, 2011). The disk is governed by mass conservation, momentum conservation, induction, and generalized Ohm’s law

$\Delta B = 2B_0$6

and the field-line flux function scales as $\Delta B = 2B_0$7 (Teitler, 2011). The global model determines three eigenparameters—$\Delta B = 2B_0$8, the normalized midplane accretion speed $\Delta B = 2B_0$9, and the normalized magnetic-flux migration speed $|B_r(\theta)| \approx \mathrm{const}$0—by requiring regular passage through the sonic point in the disk, regular passage through the Alfvén point in the wind, and consistency with the disk-surface field inclination constraint (Teitler, 2011). This is a particularly explicit example of a magnetic wind model in which accretion, launching geometry, and magnetic-flux transport are solved together.

For secular protoplanetary disk evolution, Molyarova and collaborators propose a global thin-disk model in FEOSAD in which magnetic wind-driven accretion is added as a source of both vertical torque and mass loss (Kadam et al., 31 Jan 2025). The gas continuity equation becomes

$|B_r(\theta)| \approx \mathrm{const}$1

and the wind enters the momentum budget through the vertical Maxwell stress $|B_r(\theta)| \approx \mathrm{const}$2 (Kadam et al., 31 Jan 2025). Their effective prescriptions for mass loss and stress are

$|B_r(\theta)| \approx \mathrm{const}$3

$|B_r(\theta)| \approx \mathrm{const}$4

with $|B_r(\theta)| \approx \mathrm{const}$5 and $|B_r(\theta)| \approx \mathrm{const}$6 introduced as pragmatic correction factors (Kadam et al., 31 Jan 2025). The model concludes that magnetic disk winds generally yield disks that are smaller and less massive than purely gravitoviscous models and often more consistent with ALMA demographic constraints (Kadam et al., 31 Jan 2025). Here the magnetic wind model is not a local launching calculation but a global evolution prescription guided by local MHD simulations.

A more specialized reduction appears in the 2D hydrodynamic disc–planet model of Weber and collaborators, who prescribe an MHD-based azimuthal force

$|B_r(\theta)| \approx \mathrm{const}$7

to mimic the radial profile of angular-momentum flux measured in 3D MHD simulations of planets in wind-driven discs (Hammer et al., 13 May 2025). The model uses a background torque coefficient $|B_r(\theta)| \approx \mathrm{const}$8, a gap enhancement factor $|B_r(\theta)| \approx \mathrm{const}$9, and a modest viscosity $$\rho = \sin^2\theta \,\bigl(C - 2|\cos\theta|\bigr)^{-1},$$0, finding that these three components can reproduce gap profiles for planets above the thermal mass, but not as successfully for lower-mass planets (Hammer et al., 13 May 2025). The same prescription drives rapid inward migration because of the excess torque in the gap (Hammer et al., 13 May 2025). This is a useful reminder that “magnetic wind model” may also denote an effective surrogate for explicit MHD in contexts where full 3D simulations are too expensive.

A recurring limitation across these varied implementations is the tension between magnetic fidelity and dynamical self-consistency. The solar coronal current-sheet model is deliberately kinematic (Veselovsky et al., 2012). TEMPEST inherits its heating closure from ZEPHYR rather than solving the energy equation (Woolsey, 2015). FLUXPipe neglects wind back-reaction on the magnetic field (Lowder et al., 2024). The turbulence-driven solar model applied along prescribed 2D field lines finds that sharp slow/fast transitions likely violate transverse force balance in a genuine multidimensional MHD equilibrium (Lionello et al., 2014). Protostellar and protoplanetary disc prescriptions often require fitted or effective parameters because magnetic flux transport and launching are not evolved from first principles [(Teitler, 2011); (Kadam et al., 31 Jan 2025)]. These limitations do not negate the models, but they indicate that the term “magnetic wind model” covers a spectrum from analytic magnetic skeletons to fully coupled MHD systems, with the main unresolved issue being how to preserve magnetic realism while solving the plasma dynamics self-consistently.