Fast ray-tracing algorithm for circumstellar structures (FRACS) I.
Algorithm description and parameter-space study for mid-IR interferometry of
B[e] stars
The physical interpretation of spectro-interferometric data is strongly
model-dependent. On one hand, models involving elaborate radiative transfer
solvers are too time consuming in general to perform an automatic fitting
procedure and derive astrophysical quantities and their related errors. On the
other hand, using simple geometrical models does not give sufficient insights
into the physics of the object. We propose to stand in between these two
extreme approaches by using a physical but still simple parameterised model for
the object under consideration. Based on this philosophy, we developed a
numerical tool optimised for mid-infrared (mid-IR) interferometry, the fast
ray-tracing algorithm for circumstellar structures (FRACS) which can be used as
a stand-alone model, or as an aid for a more advanced physical description or
even for elaborating observation strategies. FRACS is based on the ray-tracing
technique without scattering, but supplemented with the use of quadtree meshes
and the full symmetries of the axisymmetrical problem to significantly decrease
the necessary computing time to obtain e.g. monochromatic images and
visibilities. We applied FRACS in a theoretical study of the dusty
circumstellar environments (CSEs) of B[e] supergiants (sgB[e]) in order to
determine which information (physical parameters) can be retrieved from present
mid-IR interferometry (flux and visibility). From a set of selected dusty CSE
models typical of sgB[e] stars we show that together with the geometrical
parameters (position angle, inclination, inner radius), the temperature
structure (inner dust temperature and gradient) can be well constrained by the
mid-IR data alone. Our results also indicate that the determination of the
parameters characterising the CSE density structure is more challenging but, in
some cases, upper limits as well as correlations on the parameters
characterising the mass loss can be obtained. Good constraints for the sgB[e]
central continuum emission (central star and inner gas emissions) can be
obtained whenever its contribution to the total mid-IR flux is only as high as
a few percents. Ray-tracing parameterised models such as FRACS are thus well
adapted to prepare and/or interpret long wavelengths (from mid-IR to radio)
observations at present (e.g. VLTI/MIDI) and near-future (e.g. VLTI/MATISSE,
ALMA) interferometers