Photodissociation region models of photoevaporating circumstellar disks and application to the proplyds in Orion

We have modeled the neutral flows emerging from circumstellar disks or smal l clumps of size r(0) illuminated by an external source of ultraviolet radi ation. The models are applied to the disks (proplyds) in the Orion Nebula, most of which are illuminated by theta(1)C Ori. Our models improve upon the simpler models of Johnstone, Hollenbach, & Ballyby including the results o f both equilibrium and nonequilibrium photodissociation region (PDR) codes, and by treating the flow speed off the disk surface in a more consistent m anner. We present a study that delineates the parameter space (G(0), r(0), and sigma(ext)) in which far-ultraviolet (FUV)-dominated, as opposed to ext reme-ultraviolet (EUV)-dominated, flows exist. G(0) is the FUV (6 eV < hv < 13.6 eV) flux (in units of the local average interstellar flux) incident o n the neutral how at the ionization front (IF), and sigma(ext) is the dust FUV extinction cross section per H nucleus in the flow region. FUV-dominate d flows are extended with sizes of the IF r(IF) greater than or similar to 2r(0), have a shock between the disk surface and IF, and the mass-loss rate s are determined by FUV photons. For sigma(ext) = 8 x 10(-22) cm(2) and a U V source similar to theta(1) C Ori, the FUV-dominated region extends from G (0) approximate to 5 x 10(4) to G(0) approximate to 2 x 10(7) (or distances from theta(1) C Ori of 0.3-0.01 pc), for disk or clump size of r(0) approx imate to 10(14)-10(15) cm. Outside this parameter space, hydrogen-ionizing EUV photons dominate the photoevaporation, and the IF is close to the disk surface (r(IF) less than or equal to 2r(0)). We show that FUV-dominated flows can explain the observed sizes of the ioni zation fronts around many of the photoevaporating disks in Orion. The size of the neutral flow region, I-IF, depends mainly on r(0), G(0), and sigma(e xt) inside the flow region. Using ten objects in Orion for which both r(0) and r(IF) are directly observed, and for which G(0) can be estimated from t he observed projected distance of the proplyd from theta(1)C Ori, we find t hat sigma(ext) approximate to 8 x 10(-22) cm(2) best fits the observations. In these models, the disk mass-loss rates are roughly 10(-7) M. yr(-1). We have determined the disk masses for circular and radial proplyd orbits. Fo r circular orbits around theta(1)C Ori, the disk masses range between 0.005 and 0.04(t(i)/10(5) yr) M., where t(i) is the illumination timescale. Comp arison with millimeter observations of the disk masses (less than or simila r to 0.02 M.) indicate t(i) approximate to 10(5) yr, suggesting that theta( 1)C Ori is a young (less than or similar to 10(5) yr old) O star in this sc enario. The timescale for the disks to significantly lose mass and shrink i s similar to 10(5) yr. If the disks cross the Trapezium cluster on radial o rbits, the proplyd masses range between 0.002 and 0.01 M.. For radial orbit s, the lifetime of the proplyds can be as large as the age of the Orion Clu ster (similar to 1 Myr), and theta(1)C Ori can be significantly older than 10(5) yr. We have calculated the thermal and chemical structure of the flow region in the observationally best studied object HST 182-413 (HST 10) and the repre sentative object HST 155-338. A region of atomic hydrogen extends from the IF toward the disk surface, but dose to the surface hydrogen becomes molecu lar. The temperatures inside the atomic layer are several thousand K. We ha ve calculated the H-2 1-0 S(1) and the H-2 2-1 S(1) vibrational line intens ities, the [C II] 158 mu m and [O I] 63 mu m fine-structure line intensitie s, and the [O I] 6300 Angstrom line intensity. We find good agreement betwe en the observed H-2 1-0 S(1) line intensity and the theoretically predicted one. The models can also reproduce the [O I] 6300 Angstrom line emission o bserved dose to the disk surface in HST 182-413, HST 155-338, and the other proplyds where the disks can be resolved in the [O I] line. The other line s are not yet observed; we present them here as predictions for future obse rvations.