Transcript Highligh in Physics 2005

Congresso del Dipartimento di Fisica
Highlights in Physics 2005
11–14 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 submm 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. 3 The typical double-peaked shape of the 12CO
emission line profile at 110 GHz based on the selfgravitating disk model used in Fig. 1 (solid line) and
based on a Keplerian model (dotted line).
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 quasisteady state is reached. In the case shown here the
disk mass is Mdisc=0.1M* (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 selfconsistent 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
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)
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 limited sampling capability
of the u-v plane of existing nearIR interferometers, at present it is
not possible to recover full images
from
the
available
data.
Therefore, for a comparison of
theoretical predictions with the
observations, one has to resort to
the analysis of the coherence
functions of the source. Starting
from synthetic images of the inner
rim, it is thus necessary to
compute the complex visibility for
different baseline lengths and
hour angles.
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).
Fig. 4 Best fit inner rim model (Isella et al., in
prep) for the star MWC758 (T=8000K, L=22L,
M=2M) 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), NorthWest (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).
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