Systematic determination of dust properties for a sample of 133 spatially resolved debris discs

Abstract

Determination of the composition and size distribution of dust grains in debris discs is strongly dependent on constraining the underlying spatial distribution of that dust through multi-wavelength, spatially resolved imaging spanning near-infrared to millimetre wavelengths. To date, spatially resolved imaging exists for well over a hundred debris disc systems. Simple analytical radiative transfer models of debris dust emission can reveal trends in disc properties as a function of their host stars' luminosities. Here we present such an analysis for 133 debris discs, calculating the dust grain minimum sizes ($s_{\rm min}$), dust masses ($M_{\rm dust}$), and exponents of the size distribution ($q$) in conjunction with their architectures determined at far-infrared or millimetre wavelengths. The distribution of $q$ at far-infrared to millimetre wavelengths is characterised for the first time, finding a value of $3.49^{+0.38}_{-0.33}$. We further newly identify a trend between $q$ and $R_{\rm disc}$, which may be indicative of velocity dependent fragmentation, or grain growth at large radii. We find the disc masses inferred from this analysis are consistent with those of protoplanetary discs. Finally, we identify samples of debris discs suitable for further characterisation at millimetre and centimetre wavelengths, expanding the number of spatially resolved systems upon which future studies of these statistics can be based.

Figures (9)

• Figure 1: Plot of $s_{\rm min}$ vs. $s_{\rm blow}$. The dashed line denotes equivalence between $s_{\rm min}$ and $s_{\rm blow}$, whilst the hatched region denotes the range of calculated blowout grain sizes that are not meaningful as the associated stellar luminosity is too small to produce high $\beta$ grains. It is clear that for most systems, particularly around high luminosity stars, a substantial contribution to their excess emission comes from sub-blow out grains.
• Figure 2: Top: Plot of $s_{\rm min}/s_{\rm blow}$ vs. $L_{\star}$. Blue data points are for Herschel-resolved architectures, whereas orange data points are for ALMA- or SMA-resolved architectures. Uncertainties are 1-$\sigma$. The shaded region denotes stellar luminosities for which no blowout grain size exists and the hatched region denotes stellar luminosities for which a range of grain sizes are blown out. The two straight lines denote the relationship between $s_{\rm min}/s_{\rm blow}$ determined by 2014Pawellek (grey line) and the fit to the ensemble presented here (black line). Bottom: Same as above, except the white data points denote discs with $q = 3.5$.
• Figure 3: Histogram of $q$ values derived from modelling. The distribution is assembled from the posterior probability distributions of individual systems. Hatched regions on the plot denote the regions associated with $q$ expected for different collisional models (see text for details).
• Figure 4: Plot of $q$ vs. $R_{\rm disc}$. Circular data points are for systems for which $q$ could be determined from modelling. Square data points denote systems that have also been detected at 7 or 9 mm (dubbed 'mm-bright'). The solid line denotes a power law fit to the observations illustrating a trend between $R_{\rm disc}$ and $q$.
• Figure 5: Plot of $q$ vs. $v_{\rm rel}$. Data points are for debris discs with measured $q$ values from this work and the relative velocities are calculated from the disc scale heights in 2023Terrill. We see no strong trend between $q$ and $v_{\rm rel}$, contrary to what might expected from theoretical modelling 2012Gaspar, suggesting other factors are contributing to the value of $q$ determined from the observations.