The presented model calculations provide two-dimensional images for the scattered intensity I(x, y), azimuthal polarization Qφ(x, y), and other radiation parameters. It is useful for the comparison with observations to deduce disk-integrated radiation parameters from these model images that are scaled to the stellar intensity, as in ${{\bar I\left( i \right)} \mathord{\left/ {\vphantom {{\bar I\left( i \right)} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}{{,{{\bar Q}_\varphi }\left( i \right)} \mathord{\left/ {\vphantom {{,{{\bar Q}_\varphi }\left( i \right)} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$I¯(i)/I⋆,Q¯φ(i)/I⋆, the disk-averaged fractional polarization 〈pφ〉, or quadrant polarization values Qxxx(i)/I⋆ or Uxxx(i)/I⋆ which can also be deduced from observations without introducing significant ambiguities by the diversity of disk morphologies. We note that the measured values must be corrected for instrumental effects, in particular for the signal convolution with the instrumental PSF, which can introduce significant cancellation of the disk signal (Schmid et al. 2006; Avenhaus et al. 2014, Avenhaus et al. 2017; Heikamp & Keller 2019; Tschudi & Schmid 2021). Unfortunately, available observational data with high accuracy and quantified uncertainties are still very limited and often only some of the radiation parameters can be determined for a given disk. Therefore, the derivation of disk parameters from the comparison with model results can be rather ambiguous. The model results presented in this work allow us to carry out a detailed investigation of the important parameter ambiguities involved in the interpretation of observations of transition disks and provide diagnostic relations that can be used to constrain key model parameters for different types of observational data. For example, Fig. B.1 shows that, for a given inclination $i,{{\bar I} \mathord{\left/ {\vphantom {{\bar I} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}{{,{{\bar Q}_\varphi }} \mathord{\left/ {\vphantom {{,{{\bar Q}_\varphi }} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$i,I¯/I⋆,Q¯φ/I⋆, and ${{\bar Q} \mathord{\left/ {\vphantom {{\bar Q} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯/I⋆ all strongly correlate with the angular wall height α and single scattering albedo ω , and anti-correlate with wall slope χ and scattering asymmetry parameter ɡ. In addition, the polarization parameters ${{{{\bar Q}_\varphi }} \mathord{\left/ {\vphantom {{{{\bar Q}_\varphi }} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯φ/I⋆ and ${{\bar Q} \mathord{\left/ {\vphantom {{\bar Q} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$Q¯/I⋆ also correlated with pmax. If only the scattered intensity ${{\bar I} \mathord{\left/ {\vphantom {{\bar I} {{I_ \star }}}} \right. \kern-\nulldelimiterspace} {{I_ \star }}}$I¯/I⋆ or only the polarized intensity is measured then it is almost impossible to constrain individual disk parameters without additional information. Therefore, it is important to select and obtain more observational information and better diagnostic parameters with more diagnostic power.
Citation: Tschudi & Schmid 2021
Citation function: Uses