Effect of multi-dust species on the inner rim of magnetized protoplanetary disks

¹ Max-Planck Institute for Astronomy (MPIA), Königstuhl 17, 69117 Heidelberg, Germany
² Charles University, Fac Math & Phys, Astronomical Institute, V Holešovičkách 747/2, 180 00 Prague 8, Czech Republic
³ Center for Astrophysics, Harvard & Smithsonian, 60 Garden Street, M208, Cambridge, MA 02138, USA
⁴ HUN-REN Research Centre for Astronomy and Earth Sciences, Konkoly Observatory, Konkoly-Thege Miklós út 15–17, 1121 Budapest, Hungary
⁵ CSFK, MTA Centre of Excellence, Konkoly-Thege Miklós út 15–17, 1121 Budapest, Hungary

^★ Corresponding author: flock@mpia.de

Received: 22 November 2024
Accepted: 31 July 2025

Abstract

Context. Terrestrial planets are born in the inner regions of protoplanetary disks, that is, in the region within ten astronomical units (au). It is crucial to develop multi-physics models of this environment to understand how planets form. By developing a new class of multi-dust radiative magnetized inner rim models and comparing them with recent near-IR observational data, we can gain valuable insights into the conditions during planet formation.

Aims. Our goal is to study the influence of highly refractory dust species on the shape of the inner rim and to determine how the magnetic field affects the structure of the inner disk. The resulting temperature and density structures were analyzed and compared to observations. The comparison focused on the median spectral energy distribution of Herbig stars and interferometric constraints from the H, K, and N bands of three Herbig-type star-disk systems: HD 100546, HD 163296, and HD 169142.

Methods. With the new models, we investigated the influence of a large-scale magnetic field on the structure of the inner disk, and we studied the effect that the four most important dust species (corundum, iron, forsterite, and enstatite) shape the rim, each with its sublimation temperatures. Further, we improved our model by using frequency-dependent irradiation and the effect of accretion heating. With the Optool package, we obtained frequency-dependent opacities for each dust-grain family and calculated the corresponding temperature-dependent Planck and Rosseland opacities.

Results. When multiple dust species are considered, the dust sublimation front, that is, the inner rim, becomes smoother and radially more extended. The emission flux of strongly magnetized disks increases substantially between the L and N bands. Our results show that weakly magnetized disk models with large-scale vertical magnetic fields ≤0.3 Gauss at 1 au best fit with near-IR interferometric observations. Our model comparison supports the existence of moderate magnetic fields (β ≥ 10⁴) that might drive a magnetic wind in the inner disk. Our results show that multi-dust models, including magnetic fields, still lack near-IR emission, especially in the H band. Half-light radii derived from H-band emission by near-IR interferometry indicate that the missing flux originates within the inner rim, where even corundum grains sublimate. One potential solution might be a heated gas disk or evaporating objects such as planetesimals close to the star.