# Coevolution of Dust Growth and Gravitational Instability in Massive Protostellar Disks

**Authors:** Ryota Yamamuro, Ryoki Matsukoba, Kei E. I. Tanaka, Eduard I. Vorobyov  
**arXiv:** [2610.28331](https://arxiv.org/abs/2610.28331)  
**Date:** 2026-10-20  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2610.28331v1/

## Key points

- The study models how dust growth and gravitational instability interact in massive protostellar disks, using self-consistent, two-dimensional gas-and-dust simulations of a collapsing 30-solar-mass cloud core.
- Two otherwise identical models compare evolving dust grains with grains fixed at a maximum radius of 1 micrometer.
- Dust grows to millimeter–centimeter sizes within a few thousand years of disk formation, with substantial growth across most of the inner 300 astronomical units by 150,000 years.
- Grain growth lowers infrared opacity by one to two orders of magnitude, enhancing cooling in the mostly optically thick disk and promoting fragmentation.
- Final stellar masses remain similar—approximately 19 solar masses with dust growth and 18 without—but dust growth greatly increases accretion variability.
- Peak accretion rates reach 0.2 solar masses per year with dust growth versus 0.006 without; high-rate episodes contribute approximately 20 percent versus 6 percent of the final stellar mass.
- The dust-growth model produces 248 luminosity bursts versus 44 without growth, with peak luminosities of approximately 10,000–10 million solar luminosities and durations from one year to several tens of years.
- Frequent collisions generally limit grain growth through fragmentation in dense regions, supporting azimuthally averaged steady models; grains in low-density regions can exceed the local fragmentation limit because destructive collisions are infrequent.
- Dust growth intensifies fragmentation and episodic accretion and may encourage multiple-star formation, but it is not necessary for accretion bursts.
- Quantitative predictions remain limited by two-dimensional geometry, unresolved processes within 5 astronomical units, simplified dust physics, uncertain fragmentation thresholds, and omitted magnetic and radiative processes.

## Summary

This paper investigates the interplay between dust growth and gravitational instability in massive protostellar disks. These disks must transport material rapidly enough to sustain the high accretion rates required for massive-star formation. Their self-gravity can produce spiral arms, fragmentation, and episodic accretion, while dust growth alters opacity and cooling efficiency. Earlier steady, axisymmetric models suggested that dust growth could promote instability but could not capture how evolving spiral arms and clumps regulate grain growth. This study therefore examines these feedback processes self-consistently in a dynamically evolving disk. The authors use FEOSAD, a two-dimensional hydrodynamics code employing the thin-disk approximation, to simulate the collapse of a rotating, 30-solar-mass cloud core and the subsequent formation of a protostar and disk. Gas and dust are modeled as interacting fluids, with separate small- and grown-grain components. Grain sizes evolve through coagulation, fragmentation, and transport, with fragmentation occurring over finite collision times rather than instantaneously. Grain-size-dependent opacities govern radiative heating and cooling. The simulations employ a 512-by-512 polar grid spanning 5–30,000 astronomical units, a turbulence parameter of 0.01, and a dust fragmentation threshold of 10 meters per second. Two otherwise identical models are compared: one allows dust growth, while the other fixes the maximum grain radius at 1 micrometer. The disk forms approximately 37,000 years after collapse begins, and dust reaches millimeter–centimeter sizes within the next few thousand years. By 150,000 years, substantial grain growth extends across most of the inner 300 astronomical units. At temperatures above approximately 100 kelvin, which characterize most of the disk, grain growth reduces infrared opacity. Opacities in the dust-growth model are one to two orders of magnitude lower than in the fixed-grain model. Because most of the disk remains optically thick, this reduction enhances cooling, lowers temperatures, and promotes fragmentation. Despite these differences, overall stellar growth remains similar: the final stellar masses are approximately 19 solar masses with dust growth and 18 solar masses without it. The strongest differences appear in accretion variability. During the main accretion phase, between 37,000 and 150,000 years, both models typically accrete at approximately 0.0001 solar masses per year. Peak rates, however, reach 0.2 solar masses per year with dust growth, compared with 0.006 solar masses per year without it. Accretion at rates above 0.001 solar masses per year contributes approximately 20 percent of the final stellar mass in the dust-growth model, versus 6 percent in the fixed-grain model. The dust-growth simulation produces 248 luminosity bursts, compared with 44 in the model without growth. Peak burst luminosities range from approximately 10,000 to 10 million solar luminosities, with durations spanning one year to several tens of years. Some bursts resemble observed outbursts from massive protostars. In dense regions, grain growth is generally fragmentation-limited because collisions occur frequently enough to constrain grain sizes before transport removes the grains. Despite nonaxisymmetric gas structures, grain sizes can therefore approach an azimuthally averaged fragmentation limit, supporting the usefulness of steady models. Newly formed outer regions have insufficient time for substantial growth. Conversely, grains transported into low-density regions can exceed the local fragmentation limit because destructive collisions are infrequent. The authors conclude that dust growth can intensify disk fragmentation and episodic accretion and may encourage multiple-star formation, although it is not required for accretion bursts to occur. Important limitations include the two-dimensional geometry, unresolved processes within 5 astronomical units, simplified grain compositions and size distributions, and uncertain fragmentation thresholds. The simulations also omit bouncing, sublimation, radiation pressure, photoevaporation, and magnetic effects. These limitations constrain quantitative predictions and motivate more comprehensive three-dimensional studies.