One dimensional, convective, vertical structure models and one dimensional, time dependent, radial di usion models are combined to create a self{consistent picture in which FU Orionis outbursts occur in young stellar objects (YSOs) as the result of a large scale, self{regulated, thermal ionization instability in the surrounding protostellar accretion disk. Although active accretion disks have long been postulated to be ubiquitous among low mass young stellar objects, few constraints have until now been imposed on physical conditions in these disks. By tting the results of time dependent disk models to observed time scales of FU Orionis events, we estimate the magnitude of the e ective viscous stress in the inner disk (r < 1 AU) to be, in accordance with an ad hoc \alpha" prescription, the product of the local sound speed, pressure scale height, and an e ciency factor of 10 4 where hydrogen is neutral and 10 3 where hydrogen is ionized.We hypothesize that all YSOs receive infall onto their outer disks which is steady (or slowly declining with time) and that FU Orionis outbursts are self-regulated, disk outbursts which occur only in systems which transport matter inward at a rate su ciently high to cause hydrogen to be ionized in the inner disk. We estimate a critical mass ux of _ M crit = 5 10 7 M = yr independent of the magnitude of for systems with one solar mass, three solar radius central objects. Infall accretion rates in the range of _ M in = (1 10) 10 6 M = yr produce observed FU Orionis time scales consistent with estimates of spherical molecular cloud core collapse rates. Modeled ionization fronts are typically initiated near the inner edge of the disk and propagate out to a distance of 1 Lick Observatory Bulletin No. 2 Send proofs to M. Bivens, UCO/Lick Observatory, University of California, Santa Cruz 95064 { 2 { several tens of stellar radii. Beyond this region, the disk transports mass steadily inward at the supplied constant infall rate. Mass owing through the innermost disk annulus is equal to _ M in only in a time averaged sense and is regulated by the ionization of hydrogen in the inner disk such that long intervals ( 1000 yrs) of low mass ux: (1 30) 10 8 M = yr, are punctuated by short intervals ( 100 yrs) of high mass ux: (1 30) 10 5 M = yr. Time scales and mass uxes derived for quiescent and outburst stages are consistent with estimates from observations of T Tauri and FU Orionis systems respectively.

Vertical structure models are used to investigate the structure of protostellar, a-law, accretion disks. Conditions investigated cover a range of mass Ñuxes (10~9 to 10~5 yr~1), viscous efficiencies M _ (a \ 10~2 and 10~4), and stellar masses (0.5È3 Analytic formulae for midplane temperatures, M _ ). optical depths, and volume and surface densities are derived and are shown to agree well with numerical results. The temperature dependence of the opacity is shown to be the crucial factor in determining radial trends. We also consider the e †ect on disk structure of illumination from a uniform Ðeld of radiation such as might be expected of a system immersed in a molecular cloud core or other star-forming environment :20, and 100 K. Model results are compared to Hubble Space T elescope obser-T amb \ 10, vations of HH30 and the Orion proplyds.Disk shape is derived in both the Rosseland mean approximation and as viewed at particular wavelengths (jj \ 0.66, 2.2, 60, 100, 350, and 1000 km). In regions where the opacity is an increasing function of temperature (as in the molecular regions where i P T 2), the disk does not Ñare, but decreases in relative thickness with radius under both Rosseland mean and single wavelength approximations. The radius at which the disk becomes shadowed from central object illumination depends on radial mass Ñow and varies from a few tenths to about 5 au over the range of mass Ñuxes tested. This suggests that most planet formation occurred in environments unheated by stellar radiation. Viewing the system at any single wavelength increases the apparent Ñaring of the disk but leaves the shadow radius essentially unchanged. External heating further enhances Ñaring at large radii, but, except under extreme illumination (100 K), the inner disk will shield the planet-forming regions of all but the lowest mass Ñux disks from radiation originating near the origin such as from the star or from an FU Orionis outburst.

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Observed spectral energy distributions (SEDs) of FU Orionis, V1057 Cygni, and V1515 Cygni are Ðtted by theoretical spectra, which are calculated from models consisting of outbursting accretion disks together with Ñattened envelopes. Temperature in the envelopes is determined by approximate radiative equilibrium with a central source. The disk models are two-dimensional and include reprocessing of disk radiation by the disk. The theoretical spectra are calculated using a radiative transfer code and frequency-dependent opacities, at a spectral resolution of j/*j \ 14. Excellent matches to the data are obtained for all three objects with reasonable model parameters. Radiative transfer is also used to calculate a time series of images showing the progress of an outburst as imaged through a B-band Ðlter.