Max Planck Institute for Astronomy - Annual Report 2005

III.2 Radiative Transfer – Link between Simulation and Observation
Almost all information about the objects in the Universe
is obtained through the analysis of the radiation we
receive from them. One therefore might expect that the
calculation of the transfer of radiation within an object
and in the interstellar medium is an astrophysical problem
that has been solved long ago. Surprisingly the
reverse is true: Among the numerous processes important
in astrophysics, radiative transfer is one of the most
difficult problems.
The MPIA is among the few institutes worldwide
where programs are used that are able to trace the radiation
even in complex three-dimensional structures. This
is particularly important for objects surrounded by gas
and dust envelopes – such as forming and young stars or
debris disks around main-sequence stars where planets
are possibly forming, as well as the central black holes in
active galactic nuclei.
The Seven Dimensions of Radiative Transfer
According to current notion, star formation starts with
the gravitational collapse of the cores of cold molecular
clouds. Due to the conservation of angular momentum,
the gas and dust distribution around the forming protostar
flattens, creating a circumstellar disk in later stages.
In order to follow the evolution from a molecular cloud
core to a completed star sophisticated simulations are
required where the motion of the gas and dust is being
traced using magnetohydrodynamical calculations. Here,
radiative transfer is playing an important double role: On
the one hand, the radiation carries energy through the
structure, contributing to its heating or cooling; on the
other hand, the appearance of the structure at a certain
wavelength can only be determined from the calculation
of radiative transfer.
Yet radiative transfer was still neglected or calculated
in a much simplified way in simulations so far. The reason
for this is the high dimensionality of the problem:
The radiation field is not only a function of space and
time but also of direction and wavelength. Compared to
other physical quantities like density or magnetic field
it thus has three additional dimensions. Accordingly, a
simulation calculating the magnetohydrodynamics and
the radiative transfer equally correctly would use almost
all the computing time for the radiative transfer.
In approximative radiative transfer calculations, at
least the transfer of the mean energy through the system
is calculated correctly. Within the »flux limited diffu-
sion«, e.g., the radiation field is calculated correctly in
the optically very thin or very thick case, which suffices
for many applications. However, as soon as spectral
energy distributions or spatially resolved images of the
objects have to be calculated, a correct radiative transfer
is required. This is due to the fact that the appearance of
the object at a certain wavelength is dominated by the
radiation originating from the spatial region where the
optical depths equal unity. But exactly in this region, the
approximations break down – which is why it is also the
numerically most demanding region.
Radiative Hydrodynamics: Diffusion plus Ray-tracing
Thus, the numerical calculation of the hydrodynamic
evolution of accretion disks under simultaneous consideration
of radiative transfer is still a great challenge.
Realistic thermodynamics of the disk, however, cannot
be done without radiative transfer. Flux limited diffusion
so far has been the method of choice in this field
since correct radiative transfer without approximations
would consume too much computing time to be able
to follow the dynamical evolution of the optically thick
disk. Concerning the incoming radiation of the central
star the diffusion approximation can be used only under
certain circumstances. But if the simple local diffusion
approximation with an assumed local black-body radiation
is replaced by a wavelength dependent diffusion
approach, as has been done by colleagues in Pasadena,
even with modern computers the numerical effort is so
high again that the time evolution of a disk can no longer
be simulated in all three spatial dimensions. Therefore,
in collaboration with Willy Kley (Tübingen), we have
extended the simple diffusion approach by a ray-tracer.
This ray-tracer allows to calculate precisely the absorption
of the stellar radiation in the accretion disk. The
radiation energy absorbed is then added to the diffusion
approach as a source term.
The test results are encouraging, showing that the
»diffusion plus ray-tracing« approach and an exact continuum
radiative transfer are providing quantitatively comparable
results (Fig. III.2.1). Although the errors are too
large for a reliable determination of the spectral energy
distribution or an intensity map of the disk they allow to
determine locally a sufficiently accurate sound velocity,
which is just the quantity needed for hydrodynamics.
This new algorithm is being applied first to protoplanetary
accretion disks around luminous young stars and
young planets embedded in their parent disk.
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