Multiplicity due to disk fragmentation in massive star formation

André Oliva
PhD Student - Institute of Astronomy and Astrophysics - University of Tübingen
Supervisor: Dr. Rolf Kuiper

We present the highest-resolution 3D radiation-gravito-hydrodynamical simulations to date of a fragmenting accretion disk in the context of massive star formation: from the gravitational collapse of a 200 $\mathrm{M_\odot}$ cloud, to the early stages of companion formation.

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Physics and grid

The simulations consider the following physical effects:

We used a time-independent grid in spherical coordinates. The radial coordinate scales logarithmically, the azimuthal coordinate scales linearly and the polar angle varies with the cosine function so that the maximum resolution is achieved in the midplane. Due to the very high resolution used, we could treat fragmentation self-consistently, that is, without the need for sink particles.

Initial conditions and overview

We start from the gravitational collapse of a $200 \mathrm{\,M_\odot}$ cloud with a density and rotation profiles (see figure above). Due to angular momentum conservation, an accretion disk is formed. After 4 kyr, the accretion disk forms spiral arms; they in turn form fragments. Fragmentation continues up to ~15 kyr of evolution.

Dynamics of fragmentation

The fragments have typical masses of 1 $\mathrm{M_\odot}$, and typical radii of a few up to $40 \mathrm{\,au}$. Their orbits are highly eccentric, and the average period is $\sim 1\mathrm{\,kyr}$. We observe several interactions between the fragments: mergers, changes in orbits due to gravitational interactions between fragments, inward migration due to spiral arm action. When a fragment gets accreted by the central massive protostar, an accretion burst is observed. Some of these interactions are illustrated below.

Companion formation

The fragments are hydrostatically supported and form first Larson cores (see video below), consistent with the results of core collapse simulations performed by Bandhare et al. (2018). The fragments also form secondary disks surrounding them. By tracking the central temperature of the fragments, we can estimate the point in which they reach the hydrogen dissociation limit (2000 K) and would form second Larson cores.


By estimating how many fragments evolve further into second cores, we estimate a number of companions formed in our simulation. At the end of the simulated time, the highest-resolution simulation yields ~6 companions: 3 close (possible spectroscopic) companions, and 3 in the middle and outer disk (at distances of the order of 1000 au from the primary).

Convergence study

For the first time in the context of disk fragmentation in high-mass star formation, we performed a thorough convergence study, from a largely unresolved case, down to a converged case. We ran five simulations at different resolutions (named in the figure below as x1, x2, x4, x8 and x16, in order of increasing resolution), with identical setups.

We find that, while all our simulations resolve the vertical pressure scale height and the Jeans length of the background disk (i.e., the disk without the fragments and spiral arms), only x8 and x16 resolve the Jeans length, including the fragmenting regions.

Comparing our grid to the setup of previous studies that use adaptive mesh refinement (AMR) grids, we find that only AMR grids with a minimum cell size of 5 au (AMR 5 in the figure) resolve the Jeans length, while AMR grids of bigger minimum cell sizes do not, and are therefore prone to numerical fragmentation.