1998ApJ...499..758J

We present a model for the photoevaporation of circumstellar disks or dense clumps of gas by an external source of ultraviolet radiation. Our model includes the thermal and dynamic effects of 6-13.6 eV far-ultraviolet (FUV) photons and Lyman continuum EUV photons incident upon disks or clumps idealized as spheres of radius r_d and enclosed mass M_*. For sufficiently large values of r_d/M_*, the radiation field evaporates the surface gas and dust. Analytical and numerical approximations to the resulting flows are presented; the model depends on r_d, M_*, the flux of FUV and EUV photons, and the column density of neutral gas heated by FUV photons to high temperatures. Application of this model shows that the circumstellar disks (r_d ∼ 10¹⁴-10¹⁵ cm) in the Orion Nebula (``proplyds'') are rapidly destroyed by the external UV radiation field.

Close (d ≲ 10¹⁷ cm) to θ¹ Ori C, the ionizing EUV photon flux controls the mass-loss rate, and the ionization front (IF) is approximately coincident with the disk surface. Gas evaporated from the cold disk moves subsonically through a relatively thin photodissociation region (PDR) dominated by FUV photons and heated to ∼1000 K. As the distance from θ¹ Ori C increases, the Lyman continuum flux declines, the PDR thickens, and the IF moves away from the disk surface. At d ∼ 3x10¹⁷ cm, the thickness of the PDR becomes comparable to the disk radius. Between 3x10¹⁷ cm ≲ d ≲ 10¹⁸ cm, spherical divergence and the resultant pressure gradient in the 10³ K PDR forms a mildly supersonic (∼3-6 km.s^–1) but neutral Parker wind. This wind flows outward until it passes through a shock, beyond which gas moves subsonically through a stationary D-type IF. The IF is moved away from the disk surface to a standoff distance r_IF ≳ 2.5r_d. In this regime, the mass-loss rate is determined by the incident FUV photon flux and not the ionizing flux. However, at very large distances, d ≳ 10¹⁸ cm, the FUV photon flux drops to values that cannot maintain the disk surface temperature at ∼10³ K. As the PDR temperature drops, the pressure of the FUV-powered flow declines with increasing distance from θ¹ Ori C, and again the EUV ionizing photons can penetrate close to the disk surface and dominate the evaporation rate.

Radio, Hα, and [O III] observations of externally illuminated young stellar objects in the Trapezium region are used to determine r_IF and the projected distances, d_{bottom}, from θ¹ Ori C. The observed values of r_IF and d_{bottom} are combined with the theory to estimate the disk sizes, mass-loss rates, surface densities, and disk masses for the ensemble of extended sources in the Trapezium cluster. Observations of r_IF, d_{bottom}, and r_d in HST 182-413 and a few other sources are used to calibrate parameters of the theory, especially the column of heated PDR gas. The disks have a range in sizes between 14 < log [r_d/(cm)] < 15.2, mass-loss rates of -7.7 < log [M{dot}/(M_☉/yr)]←6.2, surface densities at disk edge 0.7 < log [Σ(r_d)/(g.cm^–2)] < 2.5 which imply disk surface densities at 1 AU from the central, embedded star of 2.8 < log [Σ₀/(g.cm^–2)] < 3.8 and disk masses of 0.002 < M_d/M_☉ < 0.07. Σ and M_d scale with the adopted ionization time, t_i, which we take to be 10⁵ yr. The inferred Σ(r_d) for the ensemble of disks suggest that the initial surface density power law of an individual disk, Σ ∝ r^–α, is bounded by 1 ≲ α ≲ 1.5.