The physical processes driving jets during the formation of massive stars

1. Physics and grid

The simulations are a continuation of the work on the formation of massive stars in Oliva & Kuiper 2020, but considering the following physical effects:

• Magnetohydrodynamics (PLUTO: Mignone et al 2007)
• Magnetic dissipation (Machida et al. 2007)
• Self-gravity (Haumea: Kuiper, et al. 2010)
• Radiation transport (Makemake: Kuiper, Yorke & Mignone 2020)
  • Frequency-dependent stellar irradiation
  • Diffuse thermal (re-)emission by dust and gas
• Stellar evolution (tracks from Hosokawa & Omukai 2009)

We used a time-independent grid in spherical coordinates, with axial symmetry. The radial coordinate scales logarithmically and the polar coordinate scales linearly.

2. Initial conditions and evolution

We start from the gravitational collapse of a $100 \mathrm{\,M_\odot}$ cloud with a density profile $\propto r^{-3/2}$. An hour-glass-shaped magnetic field is formed during the collapse. The massive protostar is formed at the center of the cloud, and represented by a sink cell of 3 au in radius. Due to angular momentum conservation, an accretion disk is formed after ~5 kyr, and a high-speed jet is launched via the magneto-centrifugal mechanism. At ~15 kyr, magnetic braking starts to dominate in the inner region, and the magnetic pressure gradient becomes the dominant mechanism for driving the outflows.

Simulation setup and overview of the time evolution (click to enlarge).

3. Launching mechanism

The magneto-centrifugal mechanism ( Blandford & Payne 1982 ) launches and drives the high-speed jet (> 100 km/s) in the early phase of the simulation. The interactivity below shows the simulation domain, and both the morphology (density, velocity, magnetic field lines), and a force analysis of a snapshot in time (click to alternate between plots). A Keplerian-like accretion disk is formed thanks to the dominance of magnetic diffusion in that region (see Kölligan & Kuiper 2018 ). The forces plot shows the launching region, where the centrifugal force in the co-moving frame dominates over the cylindrically radial component of the gravitational force, and where the flow becomes sub-Alfvénic.

morphology · forces

4. Other physical processes

Cavity wall ejections. Between infall and outflow, a cavity wall is formed. This wall contributes sometimes to the infall, and sometimes to the outflow. When it contributes to the outflow, it is lifted by the centrifugal force; the high density of the wall is enough for magnetic dissipation to reconnect the magnetic field, and a portion of the wall to be ejected. This process happens periodically.

Magnetic tower flow. As time progresses, the rotation of the disk drags the magnetic field lines on top of it until the magnetic pressure gradient is high enough to launch a low-speed, wide-angle tower flow (Lynden-Bell 2003).

Outflow collimation. The wound magnetic field lines cause a hoop stress (Lorentz force) that collimates the magnetically-driven outflows.

wall ejection: morphology · wall ejection: plasma $\beta$ · tower flow · jet collimation

High densities both in the disk and the cavity wall allow magnetic diffusion to occurr. Magnetic energy is lowered and partly transformed into thermal energy when reconnection happens.

Magnetic field lines wound by rotation generate a pressure gradient outside of the jet-launching region, and on top of the disk, which is enough to drive a low-speed outflow.

The hoop stress generated by wound magnetic field lines is revealed by computing the equilibrium between the Lorentz force against centrifugal force. The magnetically-driven outflows are collimated.

5. The role of magnetic braking

As time progresses and magnetic field lines are dragged by rotation, magnetic tension tends to brake the gas until it loses gravito-centrifugal support. The cavity wall collapses and contributes to the infall. At the same time, the disk loses its inner region, which becomes almost pure infall. The outflow cavity becomes narrow and the magneto-centrifugal mechanism stops. However, the magnetic pressure gradient is enough to launch another magnetically-driven outflow at later times (~20-30 kyr).

morphology · braking · outflow

The contour of gravito-centrifugal equilibrium reveals that the cavity wall undergoes infall, as well as the inner part of the disk. The magneto-centrifugal mechanism cannot act, since some regions of the cavity are dominated by gravity and not centrifugal force. In some regions, magnetic braking not only decelerates the gas, but also makes it counter-rotate.

A comparison between gravity and the magnetic pressure gradient reveals that the narrow outflow is actually driven by magnetic pressure that arises because of rotation.