Non-ideal MHD and the Formation & Fragmentation of Protostellar Disks

Recent interferometry observations reveal a large number of protoplanetary disks (PPDs) around young stellar objects with Keplerian rotation. To understand how planets form, it is crucial to study closely the formation and evolution of the host PPDs. However, the formation of such rotationally supported PPDs was previously shown to be difficult due to strong magnetic braking which removes most angular momentum of the infalling gas (Mellon & Li 2008; Hennebelle & Fromang 2008). This is the so-called magnetic braking “catastrophe” in the ideal MHD limit when matter is well frozen into the magnetic field. In reality, dense cores are only slightly ionized and magnetic fields are expected to partially decouple from neutral matter through non-ideal MHD effects, including ambipolar diffusion (AD), Ohmic dissipation, and Hall effect, all of which are determined by chemistry and microscopic physical processes (Nakano et al. 2002).

Ionization Chemical Network for Dense Cores and PPDs.

In order to accurately follow the dynamical evolution of magnetic fields in dense cores and PPDs, we developed a chemical code ARCHEM (Zhao et al. 2018b) to pre-compute fractional abundances and non-ideal MHD diffusivities, ready to be tabulated in numerical simulations. Currently, we account for 21 neutral species, 31 ion species, and singly charged (±) dust grains, with ~500 reactions (can be easily expanded) and a detailed treatment of molecular freeze-out and cosmic ray desorption for different grain size distributions. Similar to Zhao et al. 2016, the complete network also show that the removal of VSGs greatly enhances the rate of both AD ηAD and Hall effect ηHall (Figure.1) by 1—2 orders of magnitude, which is key for solving both the magnetic flux problem and magnetic braking “catastrophe” in star formation. We are currently implementing multiple grain charging and more complete ionization mechanisms into ARCHEM for global non-ideal MHD simulations of PPDs.

Figure 1: Non-ideal MHD diffusivities computed from the ionization chemical network using ARCHEM, for different grain size distributions (with a fixed a-3.5 power law and amax=0.25 μm, but different amin, except for the single sized case of a=1μm). Left: Ohmic diffusivity ηOhmic.Middle: ambipolar diffusivity ηAD, the dashed purple line shows the classical ρ-1.5 power law. Right: Hall diffusivity ηHall. The chemical network can also post-process the simulation output and obtain chemical differentiations from envelope to disk.

Disk Formation & Fragmentation Enabled by Enhanced Ambipolar Diffusion in the Envelope.

Adopting the tabulated ionization chemistry and non-ideal MHD diffusivities, we carry out 3D simulations of collapsing dense cores using ZeusTW MHD code. We find that in the absence of VSGs, the enhanced AD can efficiently decouple the magnetic flux from the bulk neutral matter in the infalling envelope. Indeed, the outward drift velocity of magnetic field due to AD almost balances the bulk infall velocity at a few 100 AU – 1000 AU scale, indicating that a reduced amount of magnetic flux is dragged into the circumstellar region by the collapsing flow. As a result, the magnetic braking is much less destructive to disk formation and more angular momentum is retained for sustaining disk rotation. With faster initial rotation and/or weaker magnetic field, the initial disks tend to be Toomre-unstable, which leads to the formation of prominent spiral structures that function as centrifugal barriers. The piling-up of infall material near the centrifugal barrier often produces dense fragments of tens of Jupiter masses. Some fragments inspiral towards the central star, producing bursts in mass accretion rate; others are longer lived and have potential to become companion stellar objects (Zhao et al. 2018a).

Figure 2: Distribution of mass density for different non-ideal MHD models. Top left: VSGs present, strong B field (mass-to-flux ratio λ=2.4), and slow rotation (βrot=0.025) model. No rotationally supported disks, only magnetically dominated structure – DEMS (decoupling-enabled magnetic structures). Top right: VSGs absent, strong B (λ=2.4), and slow rotation (βrot=0.025) model. Rotationally supported disk. Bottom left: VSGs absent, strong B (λ=2.4), and fast rotation (βrot=0.1) model. Large spiral structure. Bottom right: VSGs absent, weak B (λ=4.8), and fast rotation (βrot=0.1). Triple stellar system.

Turbulence Spectrum and Grain Growth in PPDs.

As a first step towards the understanding of grain size evolution in PPDs, we investigate the properties of realistic turbulence generated by MRI in the disks and its impact on the grain growth models using Athena shearing box simulations. Conventionally, grain growth models adopt the standard Kolmogorov turbulence for the calculation of relative velocities between colliding particles (Ormel & Cuzzi 2007). However, the turbulence generated by MRI is very different from the Kolmogorov turbulence. The existence of magnetic fields results in a power spectrum proportional to k-4/3, flatter than the standard k-5/3 in Kolmogorov turbulence. Moreover, the shearing motion induced by the Keplerian rotation and the flat magnetic energy spectrum result in much shorter turbulence turnover times than the standard estimations. Therefore, the grain collisional velocities from realistic MRI turbulence are very different from that in standard Kolmogorov turbulence models: large grains collide at lower velocities, and small grains at much higher velocities (Gong et al. 2019). This can significantly alter the grain size evolution in current models. We aim next to investigate the interplay between the grain growth and non-ideal MHD effects in PPDs, and develop self-consistent numerical models, as a pivotal step towards planet formation.

Selected References

[1] Gong, M., Ivlev, A., Caselli, P. & Zhao, B. 2019, in preparation
[2] Hennebelle, P., & Fromang, S. 2008, A&A, 477, 9
[3] Mellon, R. R., & Li, Z.-Y. 2008, ApJ, 681, 1356
[4] Nakano, T., Nishi, R., & Umebayashi, T. 2002, ApJ, 573, 199
[5] Ormel, C. W., & Cuzzi, J. N. 2007, A&A, 466, 413
[6] Zhao, B., Caselli, P., Li, Z.-Y., Krasnopolsky, R., Shang, H., & Nakamura,
F. 2016, MNRAS, 111, 22
[7] Zhao, B., Caselli, P., Li, Z.-Y., & Krasnopolsky, R. 2018a, MNRAS, 473, 4868
[8] Zhao, B., Caselli, P., & Li, Z.-Y. 2018b, MNRAS, 478, 2723

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