ON RADIATION PRESSURE IN STATIC, DUSTY H ii REGIONS

Equation (1) assumes the dust to be tightly coupled to the gas, so that the radiation pressure force on the dust can be considered to act directly on the gas. In reality, radiation pressure will drive the dust grains through the plasma. If the grains approach their terminal velocities (i.e., acceleration can be neglected), then, as before, it can be assumed that the radiation pressure force is effectively applied to the gas. However, the motion of the dust grains will lead to changes in the dust/gas ratio, due to the movement of the grains from one zone to another, as well as because of grain destruction. Here, we estimate the drift velocities of grains.

Let Q_prπa² be the radiation pressure cross section for a grain of radius a. Figure 7 shows Q_pr(a, λ) averaged over blackbody radiation fields with T = 25,000 K, 32,000 K, and 40,000 K, for carbonaceous grains and amorphous silicate grains. For spectra characteristic of O stars, 〈Q_pr〉 ≈ 1.5 for 0.02 μm ≲ a ≲ 0.25 μm.

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If the magnetic field B = 0, the terminal velocity v_d for a grain at distance r is determined by balancing the forces due to radiation pressure and gas drag:

$$\begin{eqnarray} \frac{L(r)}{4\pi r^2 c}\pi a^2 \langle Q_{\rm pr}\rangle &=& 2\pi a^2 nkT\,G(s), \quad s \equiv \frac{v_d}{\sqrt{2kT/m_{\rm H}}},\quad \ \ \ \ \end{eqnarray} \tag{ 24 }$$

where the drag function G(s), including both collisional drag and Coulomb drag, can be approximated by (Draine & Salpeter 1979)

$$\begin{eqnarray} G(s) &\approx & \frac{8s}{3\sqrt{\pi }}\left(1+\frac{9\pi }{64}s^2\right)^{1/2} + \left(\frac{eU}{kT}\right)^2 \ln \Lambda \frac{s}{(3\sqrt{\pi }/4+s^3)},\nonumber\\ \end{eqnarray} \tag{ 25 }$$

$$\begin{eqnarray} \Lambda &=&\frac{3}{2ae}\frac{kT}{|eU|}\left(\frac{kT}{\pi n_e}\right)^{1/2} = 6.6\times 10^6 a_{-5}^{-1} \frac{kT}{|eU|} T_4^{1/2} n_3^{-1/2},\nonumber\\ \end{eqnarray} \tag{ 26 }$$

where U is the grain potential, a₋₅ ≡ a/10⁻⁵ cm, and n₃ ≡ n_e/10³ cm⁻³. The drag force from the electrons is smaller than that from the ions by at least $\sqrt{m_e/m_p}$, and can be neglected. The charge on the grains will be determined by collisional charging and photoelectric emission. Collisional charging would result in eU/kT ≈ −2.51 (Spitzer 1968), or U ≈ −2.16T₄ V. Photoelectric charging will dominate close to the star, but is expected to result in potentials U ≲ 10 V. Taking |eU/kT| ≈ 2.5 and ln Λ ≈ 14.8 as representative,

$$\begin{equation} G(s)\approx \left[1.50\left(1+\frac{9\pi }{64}s^2\right)^{1/2} +\frac{69.5}{1+4s^3/3\sqrt{\pi }}\right]s. \end{equation} \tag{ 27 }$$

Note that G(s) is not monotonic: as s increases from 0, G(s) reaches a peak value ∼42 for s ≈ 0.89, but then begins to decline with increasing s as the Coulomb drag contribution falls. At sufficiently large s, the direct collisional term becomes large enough that G(s) rises above ∼42 and continues to rise thereafter.

The drag time for a grain of density ρ = 3 g cm⁻³ in H ii gas is

$$\begin{equation} \tau _{\rm drag} = \frac{Mv}{F_{\rm drag}} = 295 \left(\frac{a_{-5}}{n_3 T_4^{1/2}}\right) \frac{s}{G(s)}\,{\rm yr}. \end{equation} \tag{ 28 }$$

For n₃ ≳ 0.01, this is sufficiently short that each grain can be assumed to be moving at its terminal velocity v_d, with the isothermal Mach number $s\equiv v_d/\sqrt{2kT/m_{\rm H}}$ determined by the dimensionless equation

$$\begin{equation} G(s) = [\phi (y)+\beta e^{-\tau (y)}]\frac{u(y)}{y^2}\langle Q_{\rm pr}\rangle, \;\;y\equiv \frac{r}{\lambda _0}. \end{equation} \tag{ 29 }$$

Equation (29) is solved to find s(r). For 20 < G < 42, there are three values of s for which the drag force balances the radiation pressure force. The intermediate solution is unstable; we choose the smaller solution,³ which means that s undergoes a discontinuous jump from ∼0.9 to 6.2 at G ≈ 42. The resulting terminal velocity v(r) is shown in Figure 8 for seven values of Q_0,49n_rms. The velocities in the interior can be very large, but the velocities where most of the dust is located (τ(r)/τ(R)>0.5) are much smaller.

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In the outer part of the bubble, where most of the gas and dust are located, the drift velocities are much more modest. This is visible in Figure 8(a), where the drift speeds become small as r → R, but is more clearly seen in Figure 8(b), showing drift speeds as a function of normalized optical depth. The range 0.5 < τ(r)/τ(R) < 1 contains more than 50% of the dust, and throughout this zone the drift speeds are ≲0.3 km s⁻¹ even for Q_0,49n_rms as large as 10⁷ cm⁻³. With drift speeds v_d ≲ 0.3 km s⁻¹, grains will not be destroyed, except perhaps by shattering in occasional collisions between grains with different drift speeds. However, for large values of n_rms, these grains are located close to the boundary, the drift times may be short, and the grains may be driven out of the H ii and into the surrounding shell of dense neutral gas. This will be discussed further below.

Let _B ≡ B²/16πnkT be the ratio of magnetic pressure to gas pressure. The importance of magnetic fields for the grain dynamics is determined by the dimensionless ratio ωτ_drag, where ω ≡ QB/Mc is the gyrofrequency for a grain with charge Q and mass M in a magnetic field B:

$$\begin{eqnarray} (\omega \tau _{\rm drag})^2 &=& 17.3 \frac{T_4^2}{n_3 a_{-5}^2} \left(\frac{\epsilon _B}{0.1}\right) \left(\frac{eU/kT}{2.5}\right)^2 \left(\frac{71}{G(s)/s}\right)^2,\nonumber\\ && \epsilon _B\equiv \left(\frac{B^2/8\pi }{2nkT}\right). \end{eqnarray} \tag{ 30 }$$

If |eU/kT| ≈ 2.5 and ln Λ ≈ 15, then (G(s)/s) ≈ 71 for s ≲ 0.5.

Let the local magnetic field be ${\bf B}=B(\hat{{\bf r}}\cos \theta +\hat{{\bf y}}\sin \theta)$. The steady-state drift velocity is

$$\begin{eqnarray} v_d &=& \left(\frac{F_{\rm rad}\tau _{\rm drag}}{M}\right) \sqrt{\frac{1+(\omega \tau _{\rm drag})^2\cos ^2\theta }{1+(\omega \tau _{\rm drag})^2}}, \end{eqnarray} \tag{ 31 }$$

$$\begin{eqnarray} v_{d,r} &=& \left(\frac{F_{\rm rad}\tau _{\rm drag}}{M}\right) \frac{1+(\omega \tau _{\rm drag})^2\cos ^2\theta }{1+(\omega \tau _{\rm drag})^2}, \end{eqnarray} \tag{ 32 }$$

$$\begin{eqnarray} v_{d,y} &=& \left(\frac{F_{\rm rad}\tau _{\rm drag}}{M}\right) \frac{(\omega \tau _{\rm drag})^2\sin \theta \cos \theta }{1+(\omega \tau _{\rm drag})^2}, \end{eqnarray} \tag{ 33 }$$

$$\begin{eqnarray} v_{d,z} &=& -\left(\frac{F_{\rm rad}\tau _{\rm drag}}{M}\right) \frac{\omega \tau _{\rm drag}\sin \theta }{1+(\omega \tau _{\rm drag})^2}, \end{eqnarray} \tag{ 34 }$$

where v_d,r, v_d,y, and v_d,z are the radial and transverse components. If sin θ → 0, the magnetic field does not affect the radiation-pressure-driven drift velocity, but in the limit sin θ → 1 magnetic effects can strongly suppress the radial drift if ωτ_drag ≫ 1 and cos θ ≪ 1.

The magnetic field strength is uncertain, but it is unlikely that the magnetic energy density will be comparable to the gas pressure; hence, _B ≲ 0.1. From Equation (30), it is then apparent that if the magnetic field is strong (_B ≈ 0.1), magnetic effects on the grain dynamics can be important in low-density H ii regions, but will not be important for very high densities: (ωτ_drag)² ≲ 1 for n₃ ≳ 170a⁻²_−5B.

When radiation pressure effects are important, the gas and dust are concentrated in a shell that becomes increasingly thin as Q₀n_rms is increased. The drift velocities where most of the dust is located are not large (see Figure 8(b)), but the grains are also not far from the ionization front. The timescale on which dust drift would be important can be estimated by calculating the drift velocity at the radius r_0.5 defined by τ(r_0.5) = 0.5τ(R). More than 50% of the dust has r_0.5 < r < R. Figure 9 shows the characteristic drift time

$$\begin{equation} t_{\rm drift} \equiv \frac{R-r_{0.5}}{v_{d,r}(r_{0.5})}. \end{equation} \tag{ 35 }$$

If no magnetic field is present, the drift velocity depends only on T and the dimensionless quantities {ϕ, τ, u, y, 〈Q_pr〉} (see Equation (29)). It is easy to see that for fixed T and Q₀n_rms, the radius R ∝ Q₀; thus t_drift ∝ Q₀. Figure 9 shows t_drift/Q_0,49. For Q_0,49 = 1, H ii regions with n_rms>10³ cm⁻³ have t_drift < 10⁶ yr if magnetic effects are negligible. If a magnetic field is present with B ⊥ r and _B = 0.1, then the grain drift is slowed, but drift times of <1 Myr are found for n_rms>10⁴ cm⁻³. Therefore, compact and ultracompact H ii regions around single O stars are able to lower the dust/gas ratio by means of radial drift of the dust on timescales of ≲ Myr. However, if the O star is moving relative to the gas cloud with a velocity of more than a few  km s⁻¹, then individual fluid elements pass through the ionized zone on timescales that may be shorter than the drift timescale, precluding substantial changes in the dust-to-gas ratio.

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Grain removal by drift can also occur for giant H ii regions. As an example, consider a giant H ii region ionized by a compact cluster of ∼10³ O stars emitting ionizing photons at a rate Q₀ = 10⁵² s⁻¹. For n_rms = 10³ cm⁻³, we have Q_0,49n_rms = 10⁶ cm⁻³, and we see that if B = 0, the drift timescale is only t_drift ≈ 2 × 10⁵ yr. If a magnetic field is present with B ⊥ r and _B = 0.1, then from Figure 9 the drift timescale t_drift is increased, but only to ∼10⁶ yr. It therefore appears possible for radiation-pressure-driven drift to remove dust from giant H ii regions provided they are sufficiently dense.

Aside from magnetic effects, the drift speeds at a given location depend only on 〈Q_pr〉 and T₄ (see Equation (29)). Figure 7 shows that 〈Q_pr〉 is constant to within a factor ∼1.5 for a ≳ 0.010 μm. Hence, radiation-pressure-driven drift would act to drive grains with a ≳ 0.01 μm outward. Smaller grains will drift as well, but more slowly. Because of this, the gas-to-dust ratio in the centers of H ii regions should in general be lower than the gas-to-dust ratio in the gas prior to ionization. The dust-to-gas ratio will first be reduced in the center, where the drift speeds (see Figure 8) are large. Dust drift will also alter the dust-to-gas ratio in the outer ionized material, initially raising it by moving dust outward from the center. In an initially uniform neutral cloud, the ionization front expands rapidly at early times (see, e.g., Figure 37.3 in Draine 2011) but in gas with n₃ ≳ 1, at late times the ionization front will slow to velocities small enough for dust grains to actually drift outward across the ionization front, lowering the overall dust-to-gas ratio within the H ii region.

Arthur et al. (2004) computed models of uniform-density H ii regions including the effects of dust destruction by sublimation or evaporation, finding that the dust/gas ratio can be substantially reduced near the star. If the maximum temperature at which a grain can survive is T_sub, and the Planck-averaged absorption efficiencies are Q_uv and Q_ir for T = T_⋆ and T = T_max, then grains will be destroyed within a distance r_sub with

$$\begin{eqnarray} \frac{r_{\rm sub}}{R_{s0}} &=& 2.82\times 10^{-3}L_{39}^{1/6}n_{\rm rms,3}^{2/3} \left(\frac{10^3\,{\rm K}}{T_{\rm sub}}\right)^2\nonumber\\ &&\times \left(\frac{L_{39}}{Q_{0,49}}\right)^{1/3} \left(\frac{Q_{\rm uv}/Q_{\rm ir}}{10^2}\right)^{1/2}. \end{eqnarray} \tag{ 36 }$$

For parameters of interest (e.g., L₃₉/Q_0,49 ≈ 1, L₃₉ ≲ 10²) we find r_sub/R_s0 ≪ 1 for n_rms ≲ 10⁵ cm⁻³, and sublimation would therefore destroy only a small fraction of the dust.

As we have seen, we expect radiation pressure to drive grains through the gas, with velocity given by Equation (31). Drift velocities v_d ≳ 75 km s⁻¹ will lead to sputtering by impacting He ions, with sputtering yield Y(He) ≈ 0.2 for 80 ≲ v ≲ 500 km s⁻¹ (Draine 1995). For hypersonic motion, the grain of initial radius a will be destroyed after traversing a column density

$$\begin{equation} n_{\rm H}\Delta r = \frac{n_{\rm H}}{n_{\rm He}}\frac{4\rho a}{Y({\rm He})\mu } \approx 2\times 10^{20}a_{-5}\left(\frac{Y({\rm He})}{0.2}\right)\,{\rm cm}^{-2}, \end{equation} \tag{ 37 }$$

for a grain density ρ/μ = 1 × 10²³ cm⁻³, appropriate for either silicates (e.g., FeMgSiO₄, ρ/μ ≈ 3.8 g cm⁻³/25m_H = 9 × 10²² cm⁻³) or carbonaceous material (2 g cm⁻³/12m_H = 1.0 × 10²³ cm⁻³). Therefore, the dust grain must traverse material with (initial) dust optical depth

$$\begin{equation} \Delta \tau _d = \sigma _d n_{\rm H}\Delta r = 0.2 \sigma _{d,-21} a_{-5} \left(\frac{Y({\rm He})}{0.2}\right) \end{equation} \tag{ 38 }$$

if it is to be substantially eroded by sputtering. However, Figure 8(b) shows that even in the absence of magnetic effects, v_d ≳ 75 km s⁻¹ occurs only in a central region with τ_d < 0.05. Therefore, sputtering arising from radiation-pressure-driven drift will not appreciably affect the dust content.

For a sample of 13 Galactic H ii regions, Inoue (2002) used infrared and radio continuum observations to obtain the values of f_ion shown in Figure 10. The estimated values of f_ion are much larger than would be expected for uniform H ii regions with dust-to-gas ratios comparable to the values found in neutral clouds. Inoue (2002) concluded that the central regions of these H ii regions must be dust-free, noting that this was likely to be due to the combined effects of stellar winds and radiation pressure on dust. As seen in Figure 10, the values of f_ion found by Inoue are entirely consistent with what is expected for static H ii regions with radiation pressure for 5 ≲ γ ≲ 20 (corresponding to 0.5 ≲ σ_d,−21 ≲ 2), with no need to appeal to stellar winds or grain destruction.

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H ii regions come in many sizes, ranging from H ii regions powered by a single O star to giant H ii regions ionized by a cluster of massive stars. The physical size of the H ii region is obviously determined both by the total ionizing output Q₀ provided by the ionizing stars, and the rms density n_rms of the ionized gas, which is regulated by the pressure p_edge of the confining medium. With the balance between photoionization and recombination determining the size of an H ii region, an anticorrelation between size D and density n_rms is expected, and was observed as soon as large samples of H ii regions became available (e.g., Habing & Israel 1979; Kennicutt 1984). For dustless H ii regions, one expects n_rms ∝ D^−1.5 for fixed Q₀, but for various samples relations close to n_rms ∝ D⁻¹ were reported (e.g., Garay et al. 1993; Garay & Lizano 1999; Kim & Koo 2001; Martín-Hernández et al. 2005). For ultracompact H ii regions, Kim & Koo (2001) attribute the n_e ∝ D⁻¹ trend to a "champagne flow" and the hierarchical structure of the dense gas in the star-forming region, but Arthur et al. (2004) and Dopita et al. (2006) argue that the n_e ∝ D⁻¹ trend is a result of both absorption by dust and radiation pressure acting on dust in static H ii regions.

Hunt & Hirashita (2009) recently re-examined the size–density relationship. They interpreted the size–density relation for different observational samples in terms of models with different star formation rates (and hence different time evolution of the ionizing output Q₀(t)), and differences in the density of the neutral cloud into which the H ii region expands. Their models did not include the effects of radiation pressure on dust; at any time the ionized gas in an H ii region was taken to have uniform density, resulting in overestimation of the dust absorption.

Figure 11(a) shows a grid of n_rms versus D for the present models, for four combinations of (β, γ). While differences between the models with different (β, γ) can be seen, especially for high Q₀ and high p_edge, the overall trends are only weakly dependent on β and γ, at least for 1 ≲ γ ≲ 20.

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Figure 11(b) shows the model grid for β = 3 and γ = 5 together with observed values of D and n_rms from a number of different studies. It appears that observed H ii regions—ranging from H ii regions ionized by one or at most a few O stars (Q₀ < 10⁵⁰ s⁻¹) to "super star clusters" powered by up to 10³–10⁵ O stars (Q₀ = 10⁵²–10⁵⁴ s⁻¹)—can be accommodated by the present static equilibrium models with external pressures in the range 10⁴ ≲ p/k ≲ 10^10.3 cm⁻³ K. Note that for diameters D ≳ 10² pc, the assumption of static equilibrium is unlikely to be justified, because the sound-crossing time (D/2)/15 km s⁻¹ ≳ 3 Myr becomes longer than the lifetimes of high-mass stars.

The fact that some H ii region samples (e.g., Garay et al. 1993; Kim & Koo 2001) seem to obey an n_rms ∝ D⁻¹ relationship appears to be an artifact of the sample selection. We see in Figure 11(b) that the overall sample of H ii regions does not have a single n_rms versus D relationship. But the observations appear to be generally consistent with the current models of dusty H ii regions.

Even without dust present, radiation pressure from photoelectric absorption by H and He can alter the density profile in a static H ii region, lowering the central density and enhancing the density near the edge of the ionized region (see Figure 2(a)). As seen in Figure 4(a), for large values of Q₀n_rms, the surface brightness profile can be noticeably flattened. If dust is assumed to be present, with properties typical of the dust in diffuse clouds, the equilibrium density profile changes dramatically, with a central cavity surrounded by a high-pressure shell of ionized gas pushed out by radiation pressure. In real H ii regions, fast stellar winds will also act to inflate a low-density cavity, or "bubble," near the star; the observed density profile will be the combined result of the stellar wind bubble and the effects of radiation pressure.

The GLIMPSE survey (Churchwell et al. 2009) has discovered and cataloged numerous interstellar "bubbles." An example is N49 (Watson et al. 2008), with a ring of free–free continuum emission at 20 cm, surrounded by a ring of 8 μm PAH emission. An O6.5V star is located near the center of the N49 ring. The image is nearly circularly symmetric, with only a modest asymmetry that could be due to the motion of the star relative to the gas. The 20 cm image has a ring-peak-to-center intensity ratio I(peak)/I(center) ≈ 2.

Is the density profile in N49 consistent with what is expected for radiation pressure acting on dust? From the 2.89 Jy flux from N49 at λ = 20 cm (Helfand et al. 2006) and distance 5.7 ± 0.6 kpc (Churchwell et al. 2006), the stellar source has Q_0,49 ≈ (0.78 ± 0.16)/f_ion. If f_ion ≈ 0.6, then Q_0,49 ≈ (1.3 ± 0.3). The H ii region, with radius (0.018 ± 0.02) deg, has n_rms ≈ 197 ± 63 cm⁻³. Hence, Q_0,49n_rms ≈ 260 cm⁻³. If σ_d,−21 = 1, then τ_d0 ≈ 1.3. From Figure 6(a), we confirm that f_ion ≈ 0.6 for τ_d0 ≈ 1.3.

Figure 5(d) shows that an H ii region with τ_d0 = 1.3 is expected to have a central minimum in the EM, but with I(peak)/I(center) ≈ 1.3 for β = 3 and γ = 10, whereas the observed I(peak)/I(center) ≈ 2. The central cavity in N49 is therefore significantly larger than would be expected based on radiation pressure alone. While the effects of radiation pressure are not negligible in N49, the observed cavity must be the result of the combined effects of radiation pressure and a dynamically important stellar wind (which is of course not unexpected for an O6.5V star).

The original ionizing photon deposits a radial momentum $h\nu {\rm_i}/c$ at the point where it is absorbed by either a neutral atom or a dust grain. A fraction (1 − f_ion) of the ionizing photons are absorbed by dust; this energy is re-radiated isotropically, with no additional force exerted on the emitting material. Because the infrared optical depth within the H ii region is small, the infrared emission escapes freely, with no dynamical effect within the H ii region.

A fraction f_ion of the ionizing energy is absorbed by the gas. Subsequent radiative recombination and radiative cooling converts this energy to photons, but the isotropic emission process itself involves no net momentum transfer to the gas. We have seen above that the H ii can have a center-to-edge dust optical depth τ(R) ≈ 1.6 for τ_d0 ≳ 5, or Q_0,49n_rms ≳ 10² cm⁻³ (cf. Figure 5(c) with β = 3 and γ = 10). This optical depth applies to the hν>13.6 eV ionizing radiation; the center-to-edge optical depth for the hν < 3.4 eV Balmer lines and collisionally excited cooling lines emitted by the ionized gas will be significantly smaller, and much of this radiation will escape dust absorption or scattering within the H ii region. That which is absorbed or scattered will exert a force on the dust at that point only to the extent that the diffuse radiation field is anisotropic. We conclude that momentum deposition from the Balmer lines and collisionally excited cooling lines within the ionized zone will be small compared to the momentum deposited by stellar photons.

Lyα is a special case. At low densities (n ≪ 10³ cm⁻³), ∼70% of Case B recombinations result in emission of a Lyα photon, increasing to >95% for n>10⁵ cm⁻³ as a result of collisionally induced 2s → 2p transitions (Brown & Mathews 1970). After being emitted isotropically, the photon may scatter many times before either escaping from the H ii or being absorbed by dust. Most of the scatterings take place near the point of emission, while the photon frequency is still close to line center. On average, the net radial momentum transfer per emitted photon will likely be dominated by the last scattering event before the photon escapes from the H ii region, or by the dust absorption event if it does not. At a given point in the nebula, the incident photons involved in these final events will be only moderately anisotropic. Since there is less than one Lyα photon created per Case B recombination, the total radial momentum deposited by these final events will be a small fraction of the radial momentum of the original ionizing photons. Henney & Arthur (1998) estimate that dust limits the Lyα radiation pressure to ∼6% of the gas pressure. We conclude that Lyα has only a minor effect on the density profile within the ionized zone.

H ii regions arise when massive stars begin to emit ionizing radiation. The development of the H ii region over time depends on the growth of the ionizing output from the central star, and the expansion of the initially high-pressure ionizing gas. Many authors (e.g., Kahn 1954; Spitzer 1978) have discussed the development of an H ii region in gas that is initially neutral and uniform. If the ionizing output from the star turns on suddenly, the ionization front is initially "strong R-type," propagating supersonically without affecting the density of the gas, slowing until it becomes "R-critical," at which point it makes a transition to "D-type," with the ionization front now preceded by a shock wave producing a dense (expanding) shell of neutral gas bounding the ionized region.

While the front is R-type, the gas density and pressure are essentially uniform within the ionized zone. When the front becomes D-type, a rarefaction wave propagates inward from the ionization front, but the gas pressure (if radiation pressure effects are not important) remains relatively uniform within the ionized region, because the motions in the ionized gas are subsonic.

When radiation pressure effects are included, the instantaneous density profile interior to the ionization front is expected to be similar to the profile calculated for the static equilibria studied here. Let V_i be the velocity of the ionization front relative to the star. When the ionization front is weak D-type, the velocity of the ionization front relative to the ionized gas just inside the ionization front is ${\sim} 0.5 V{\rm_i}$ (Spitzer 1978). Given the small dust drift velocities v_d,r near the ionization front (i.e., τ(r) → τ(R) in Figure 8), dust is unable to drift outward across the ionization front as long as the ionization front is propagating outward with a speed (relative to the ionized gas) $V{\rm_i}\gtrsim 0.1 \,{\rm km\, s}^{-1}$.