The Synthetic ALMA Multiband Analysis of the Dust Properties of the TW
  Hya Protoplanetary Disk
  Analyzing multiband observations of dust continuum emission is one of the
useful tools to constrain dust properties which help us to understand the
physical properties of the disks. We perform the synthetic ALMA multiband
analysis to find the best ALMA band set for constraining the dust properties of
the TW Hya protoplanetary disk. We find that the Band [10,6,3] set is the best
set among the possible combinations of ALMA Band [3,4,5,6,7,8,9,10]. We also
find two conditions for the good ALMA band sets providing narrow constraint
ranges on dust properties; (1) Band 9 or 10 is included in the band set and (2)
Enough frequency intervals between the bands. These are related with the
conditions which give good constraints on dust properties: the combination of
optically thick and thin bands are required, and large beta (beta is the
power-law index of dust opacity), and low dust temperature are preferable. To
examine our synthetic analysis results, we apply the multiband analysis to ALMA
archival data of the TW Hya disk at Band 4, 6, 7, and 9. Band [9,6,4] set
provides the dust properties close to the model profile, while Band [7,6,4] set
gives the dust properties deviating from the model at all radii with too broad
constraint range to specify the accurate values of dust temperature, optical
depth, and \b{eta}. Since these features are expected by the synthetic
multiband analysis, we confirm that the synthetic multiband analysis is well
consistent with the results derived from real data.
