Highligh in Physics 2005

1

• Congresso del Dipartimento di Fisica
• Highlights in Physics 2005
• 1114 October 2005, Dipartimento di Fisica,
  Università di Milano
• Accretion and proto-stellar disks
• G. Bertin, B. Coppi, A. Isella,, G. Lodato,
  A. Natta, and L. Testi
• Dipartimento di Fisica, Università di Milano
• Massachusetts Institute of Technology,
  Cambridge, MA, USA
• INAF Osservatorio di Arcetri, Firenze, Italy
• Institute of Astronomy, Cambridge, UK

The paradigm of accretion has had a major impact
on a variety of phenomena in astrophysics in
particular, it has often been applied to the
context of proto-stellar disks. We have studied
the role of the disk self-gravity on the
properties of accretion disks and found that this
role may help explain a number of observational
properties of young proto-stellar objects,
especially of FU Orionis stars 1. The theory
of such self-gravitating disks recognizes that
disks in their outer parts cannot be too cold,
otherwise they would be Jeans unstable Jeans
related instabilities, combined with dissipation,
are thus bound to enforce a sort of
self-regulation, with properties that can be
calculated analytically or studied by numerical
simulations. These concepts might be extended to
the case in which electric currents and magnetic
fields are also dynamically important work is in
progress to find a consistent model for the
transition region from a warm, plasma-dominated,
magnetized inner disk 2 to a cool, neutral,
self-gravitating outer disk. To explain the
observations of young stellar objects, many
models do not rely on the accretion paradigm but
rather on the role of irradiation of the disk by
the central star under a suitable geometry. The
predictions of a new hydrostatic, axisymmetric,
radiative equilibrium model for the innermost
region of passive irradiated dusty disks have
been compared 3 with the present
interferometric observations of some
intermediate-mass young stellar objects. The
model incorporates the variation of the dust
grain evaporation temperature with the gas
density the resulting inner rim has a curved
surface and is puffed up in comparison with a
standard flared disk model. The effect of the rim
surface bending may solve the problem of the
vanishing flux of a vertical rim at face-on
inclination. The calculated inner radius of the
rim, at the vaporization radius of the grains in
the mid-plane, is consistent with the
interferometric observations of Herbig Ae stars.
Effects of the disk self-gravity in FU Orionis
objects
FU Orionis objects are a small class of young
stellar objects undergoing periods of enhanced
disk accretion activity (outbursts). While T
Tauri stars usually have rather low accretion
rates (of the order of 10-8 M?/yr), during the
outburst the accretion rate can reach a few times
10-4 M?/yr. Even if the spread in outburst
properties is rather large, they are supposed to
last for a few thousand years. Most of the mass
of the star might therefore be accreted during
such events.The importance of self-gravity in the
dynamics of the disk in these objects was early
recognized by Bell and Lin (1994), who showed
that these disks, if sufficiently massive, are
likely to be gravitationally unstable in their
outer parts. Numerical simulations (see Fig. 1,
Lodato Rice 2004, 2005) of self-gravitating
disks have shown that self-gravity is very
effective in (i) redistributing angular momentum
in the disk (therefore promoting accretion) and
(ii) heating the disk up, so that a
self-regulated equilibrium is rapidly reached,
where the stability parameter Q is maintained
close to its marginal value Q ? 1. We have
constructed simple models of self-regulated disks
(Bertin Lodato1999) and have shown that these
disks are likely to be hotter in their outer
parts than the corresponding non-self-gravitating
disks and that they could possibly show
deviations from Keplerian rotation. Such a hotter
outer disk is significantly more luminous than a
standard disk in the far infrared and could be a
viable alternative to the proposed scenario of
infalling envelopes (Kenyon and Hartmann 1991),
as an explanation for the flat FIR SED of FU
Orionis (Lodato Bertin 2001) see Fig. 1. We
have also computed the shape of global sub-mm
line profiles under various assumptions, in order
to check whether deviations from Keplerian
rotation might be observable (Lodato Bertin
2003) and we have come to the conclusion that
optically thick lines in this wavelength range
(such as, for example, the 110 GHz emission of
CO) might be able to test this behaviour see
Fig. 2.
Fig. 1 Smoothed Particle Hydrodynamics simulation
of self-gravitating disks. The disk develops a
spiral structure that redistributes angular
momentum through the disk and heats it up,
allowing it to reach a quasi-steady state, where
cooling is balanced by internal dissipation due
to the spiral instability. The image shows the
surface density of the disk when such
self-regulated quasi-steady state is reached. In
the case shown here the disk mass is Mdisc0.1M
(Lodato Rice 2004).
These concepts might be extended to the case in
which electric currents and magnetic fields are
also dynamically important work is in progress
to find a consistent model for the transition
region from a warm, plasma-dominated, magnetized
inner disk 2 to a cool, neutral,
self-gravitating outer disk. In the plasma
dominated region, one interesting self-consistent
equilibrium solution that has been identified and
investigated recently is characterized by a
crystal structure consisting of a sequence of
toroidal current filaments that can involve null
points of the magnetic field (Coppi 2005).
Fig. 2 Observed SED of FU Ori (the prototypical
FU Orionis object, triangles), along with the SED
of a self-gravitating disk model (Lodato Bertin
2001, solid line) and with a non-self-gravitating
disk model (dotted line).
The inner region of proto-planetary disks from
near-infrared interferometric observations
Dust evaporation and the puffed-up inner rim
Fig. 3 Sketch of the structure of the inner disk
as proposed by Isella and Natta (2005) for a star
with temperature of 10000K, luminosity of 50 and
mass of 2.5 in solar units. (a) The circumstellar
disk is truncated internally at about 0.5AU from
the star by dust evaporation, which produces a
dust depleted inner hole and a puffed-up inner
rim. (b) The inner rim appears as a bright ring
in the sky when the disk is seen face-on. The
figure shows the image of the rim calculated for
an inclination of 30 and the color scale
describes the brightness distribution. (c) If
the dust evaporation temperature is taken to
depend on the gas density, the surface of the rim
is curved (the ratio between the height and the
width is 0.7 in the particular case shown here).

Near-infrared interferometric observations
(Monnier et al. 2005, Eisner et al. 2004, Tuthill
et al. 2001) show that the inner disk structure
around young stellar objects of intermediate mass
(Herbig Ae/Be stars) deviates substantially from
that of a flared disk, being often well explained
in terms of a ring-like structure of uniform
brightness. This result strongly supports the
idea that proto-planetary disks are internally
truncated by dust evaporation, which introduces a
strong discontinuity in the opacity and leads to
a puffed-up rim at the dust destruction radius
(Natta et al. 2001, Dullemond et al. 2001). The
concept of such an inner rim has been widely used
to interpret near-IR interferometric data for
Herbig Ae stars and T Tauri stars (low mass young
stellar objects). To better understand the
structure of the inner rim and the effect of the
inclination of the disk on the rim emission,
Isella and Natta (2005) have recently revised the
puffed-up rim model by introducing a relation
between the dust evaporation temperature and the
gas density. The resulting puffed-up rim thus
appears as a bright ring when seen face-on, while
its surface brightness becomes more and more
asymmetric for increasing inclinations (see Fig.
3)
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Fig. 4 Best fit inner rim model (Isella et al.,
in prep) for the star MWC758 (T8000K, L22L?,
M2M?) obtained by analysing the Palomar Testbed
Interferometer (PTI) observations at 2.2micron
(Eisner et al. 2004). The top-left panel shows
the predicted image of the inner rim,
characterized by an inner radius of 0.32AU seen
from an inclination of 38. The bottom-left panel
shows the relative visibility, obtained through
the Fourier transform of the image, as a function
of the baseline length (green dashed line) and
the observed visibility with the relative error
bars. The three bottom-right panels show a
comparison between the observed and the
predicted visibility for each of the three
available PTI baselines, in the North-South (NS),
North-West (NW), and South-West (SW) directions,
as a function of the hour angle of the star in
the sky. Finally, the top-right panel shows a
comparison between the observed flux of the star
and the predicted SED (green dashed line).
From images to Visibility
Only interferometers with angular resolution of
few milli arcsec can resolve the emission arising
from the inner rim. Unfortunately, due to the
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