2026/05/18 by Taichi K. Watanabe, Akimasa Kataoka
Physics and Astronomy · #Astrophysics and Star Formation Studies #Astro and Planetary Science #Planetary Science and Exploration
paper · pdf · doi:10.1051/0004-6361/202558713
Context . Dust properties, such as mass, porosity, electric charge, and chemical composition, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, the available ways to calculate the multicomponent coagulation-fragmentation equation are highly time-consuming. Aims . We present a fast and accurate tree algorithm for calculating the multicomponent coagulation equation. We assumed that similar pairs of colliding aggregates reproduce similar outcomes and that the ratio of dust properties in logarithmic space provides the similarity as a “distance”. These assumptions enabled us to apply the tree algorithm, which groups distant bins and calculates averaged interactions, to coagulation. The algorithm reduces the computational complexity from 𝒪( N 2 d ) to 𝒪( dN d log N ), considering N bins per d components. Methods . We tested the tree algorithm by comparing it with the conventional direct method for cases where analytic solutions are known. We measured the dependencies of the wall-clock time, the L 2 error in the distribution, and the relative error of the total mass on d, N , the critical opening angle ( θ c ), and the maximum dust distribution width after coagulation ( k c ). Results . The algorithm was found to calculate coagulation consistently. For d = 1, the tree method is faster than the direct method for only a specific range of parameters. For d = 2, however, the tree method is faster for all parameter regions surveyed, speeding the calculation up by tens to one hundred times. Increasing N and decreasing θ c or k c made it slower and more accurate. Additionally, using a small k c produces worse outcomes than when using a large k c , suggesting that limiting k c is unnecessary. Conclusions . The fast tree algorithm for the coagulation equation will allow us to evolve the multicomponent dust distribution, such as in mass-porosity space, in protoplanetary disks, ultimately revising planet formation models.