Impact of discontinuous grain size distributions on the spectral energy distribution of debris disks

¹ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
e-mail: minjae.k.kim@warwick.ac.uk
² Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK
³ Institute of Theoretical Physics and Astrophysics, University of Kiel, Leibnizstraße 15, 24118 Kiel, Germany

Received: 13 June 2023
Accepted: 8 January 2024

Abstract

Context. The collisional evolution of debris disks is expected to cause the characteristic wavy pattern, that is, an under- or overabundance of particles of specific sizes, of grain size distributions. This perturbed grain size distribution potentially leaves characteristic patterns in the spectral energy distribution (SED) of the disk system.

Aims. We aim to quantify and understand the specific influence of discontinuous particle size distributions on the appearance of debris disks. For this purpose, we considered dust emission models based on two different grain size distributions, namely, one with a single power law and one with a broken power law. In particular, our study is focused on the impact of an overabundance of small grains and an underabundance of medium-sized grains on the far-IR and (sub-)millimeter regime on the dust reemission radiation and the potential to constrain discontinuities in the grain size distribution from (sub-)millimeter photometric measurements of debris disks.

Methods. We compared the spectral index α (F_ν ∝ ν^α) in the case of a continuous grain size distribution with that of a discontinuous grain size distribution. We performed this comparison for central stars with different spectral types and two different disk structures (e.g., slim and broad debris dust rings).

Results. Within the considered parameter space, we found a characteristic difference between the spectral slopes of the SED in the different scenarios. In particular, the overabundance of small grains resulting from collisional events and thus parameters defining the outcome of disk events in debris disks is potentially observable by comparison with the SED corresponding to a grain size distribution resulting from an ideal collisional cascade. More specifically, the overabundance of small grains leads to a steeper slope in the far-IR and sub-millimeter regime, while the spectral index in the millimeter regime is hardly affected. On the other hand, the underabundance of medium-sized grains results in a slight steepening of the far-IR slope of the SED, but its primary effect is on the millimeter slope of the SED, causing it to become shallower. We also found that the impact of an overabundance of small dust particles is more pronounced than that of an underabundance of medium-sized dust particles. We also found that the difference between the spectral indices for the two different grain size distributions is largest for debris disks around brighter central stars and broader disks. However, the impact of the considered spatial distributions described by the fractional width of the disk system is weak. Our results also show that the dust composition is not the sole physical mechanism responsible for the spectral inversion observed in the far-IR to millimeter part of the SED of debris disk systems. Furthermore, the location of the spectral break is placed at different wavelength regimes if the grain size distribution is considered as a function of blowout size and stellar type.