References Bell, R. & Lin, D. N. C., 1994, ApJ, 427, 987 Bertin, G., Coppi, B., Rousseau, F., 2005, APS, 47 th Annual Meeting of the Division of Plasma Physics, LP [2] Bertin, G. & Lodato, G., 1999, A&A, 350, 694 Coppi, B., 2005, Phys. Plasmas, 12, Hartmann, L. & Kenyon, K. 1996, ARA&A, 34, 207 Kenyon, K. & Hartmann, L., 1991, ApJ, 383, 664 Lodato, G. & Bertin, G., 2001, A&A, 375, 455 [1] Lodato, G. & Bertin, G., 2003,, A&A, 408, 1015 Lodato, G. & Rice, K., 2004, MNRAS, 352, 630 Lodato, G. & Rice, K. 2005, MNRAS, 358, 1489 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). Congresso del Dipartimento di Fisica Highlights in Physics –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 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 near- IR 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. 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), 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). Dullemond, K. Dominik, C. & Natta, A. 2001, ApJ, 560, 957 Eisner, J. et al., 2004, ApJ, 613, 1049 Isella, A. & Natta, A. 2005, A&A, 438, 899 [3] Isella, A., Testi, L. & Natta, A., in prep. Monnier et al. 2005, ApJ, 624, 840 Natta, A. & al., 2001, A&A, 371, 186 Tuthill, Monnier & Danchi, 2001, Nature, 409, 1012 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 M  /yr), during the outburst the accretion rate can reach a few times 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. 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). 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. 3 The typical double-peaked shape of the 12CO emission line profile at 110 GHz based on the self- gravitating 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 quasi- steady state is reached. In the case shown here the disk mass is M disc =0.1M * (Lodato & Rice 2004).