RESOLVED RADIO EMISSION FROM MODELS OF PHOTOEVAPORATED DISKS AROUND MASSIVE YOUNG STARS

It is a matter of present study to find observational evidence of the formation of massive stars as a scaled-up version of the formation of their low mass counterparts. Thus, there is an observational search for accretion disks and outflows around massive young stars (e.g., Patel et al. 2005; Franco-Hernández et al. 2009; Kraus et al. 2010; Fallscheer et al. 2011). Up to now, there are no observations that show beyond doubt the coexistence of disks and jets in massive protostars, with masses M_*  ∼  20 M_☉ (e.g., Cesaroni et al. 2007). Since accretion disks around these massive stars will be subject to ionization and heating by Lyman continuum photons (hν > 13.6 eV), they will be photoevaporated in ∼10⁵–10⁶ yr (Hollenbach et al. 1994, hereafter H94). Thus, one needs to look for accretion disks in the very early stages of the life of massive stars, i.e., in ultracompact H ii (UCHII) and hypercompact H ii (HCHII) regions. In particular, evidence of accretion disks in HCHII regions can be obtained from the emission of photoevaporated ionized flows.

The structure of isothermal photoevaporated disk winds around massive young stars was modeled by Lugo et al. (2004, hereafter LLG04). Their parametric model gives the density and velocity of the ionized flow. LLG04 found the radio continuum emission from these models and compared with the spectral energy distribution (SED) of the radio sources MWC 349A and NGC 7538 IRS 1. These sources have massive central stars M_* ∼ 20 M_☉ and a bipolar morphology in the radio continuum emission, and are thus suspected of harboring a photoevaporated disk. Assuming a 10⁴ K temperature for the ionized wind, LLG04 fit the SED of these sources with models with inner disk radii R₁ ∼ 80–300 AU, outer disk radii R_d ∼ 300–500 AU, and mass-loss rates $\dot{M}_w \sim 10^{-6}\,{\rm to }\,10^{-5} \,{M_\odot }\,{\rm yr}^{-1}$.

Ultracompact and hypercompact H ii regions have wide thermal radio recombination lines (RRLs; e.g., Sewiło et al. 2004). Line broadening is due to a combination of thermal broadening, dynamic flow broadening, electron impact broadening, and non-thermal motions. These lines give information on the kinematics and physical conditions of the ionized gas. In particular, Sewiło et al. (2008) resolved the H53α RRL in the source G28.20-0.04N and found a velocity gradient, indicative of expansion and rotation in the ionized gas. Also, Keto et al. (2008) observed with the Submillimeter Array the H30α lines in several HCHII regions and compared their widths with lower frequency RRLs obtained with the Very Large Array (VLA), showing that RRLs get broader as frequency decreases. To date there are no self-consistent models of how these broad RRLs are produced; thus exploring the emission of RRLs in the photoevaporated disk wind models of LLG04 is a relevant task in this direction.

In this work, we obtain the radio continuum and RRLs emission from photoevaporated disk models and compare with observation of the source MWC 349A. In Section 2, we summarize the photoevaporated disk wind model of LLG04. In Section 3, we briefly discuss the radiative transfer of free–free continuum and line emission. In Section 4, we review the observations of MWC 349A. In Section 5, we explain how we obtain the best-fit model for this source, and we present the results. In Section 6, we discuss the results and the need for a modified model that includes the effects of a disk poloidal magnetic field. Finally, in Section 7 we summarize the conclusions.

LLG04 considered an isothermal photoevaporated wind from an axisymmetric thin disk around a star with mass M_*. This flow obeys the continuity and momentum equations and has a sound speed a ∼ 10 km s⁻¹. The disk self-gravity is ignored, and the ionized gas flows away from the disk conserving angular momentum. A characteristic parameter of these models is the gravitational radius, r_g = GM_*/a²  ∼  10¹⁵ M₁₀ cm, where G is the gravitational constant and M₁₀ = M_*/10 M_☉. In principle, this radius indicates where the heated ionized gas has enough speed to escape the gravitational potential of the star. Nevertheless, LLG04 found that a wind can flow inside r ∼ r_g/3 due to pressure gradients, as also found in numerical simulations (e.g., Font et al. 2004). In cylindrical coordinates, streamlines are defined by ϖ = χ(ϖ₀, ζ)ϖ₀, ϕ = ϕ, z = ζϖ₀, where ϖ₀ is the injection radius on the disk and χ(ϖ₀, ζ) is the streamline shape. The wind velocity components are given by

$$\begin{equation} \frac{v_\varpi }{a} = F(\varpi _0,\zeta)\chi ^\prime (\varpi _0,\zeta), \end{equation} \tag{ 1 }$$

$$\begin{equation} \frac{v_\phi }{a} = \frac{\epsilon _0^{1/2}}{\chi }, \end{equation} \tag{ 2 }$$

$$\begin{equation} \frac{v_z}{a} = F(\varpi _0,\zeta), \end{equation} \tag{ 3 }$$

where F(ϖ₀, ζ) is the dimensionless vertical velocity, χ' = dχ/dζ, and the parameter ₀ = r_g/ϖ₀ labels each streamline.

The streamline shape χ(ϖ₀, ζ) and the vertical velocity F(ϖ₀, ζ) are obtained from the solution of the coupled ordinary differential equations (17) and (18) of LLG04, subject to the boundary conditions at ζ = 0: F(ϖ₀, 0) = v_z0/a, where v_z0 is the injection speed at ϖ₀, χ(ϖ₀, 0) = 1, and χ'(ϖ₀, 0) = 0. Finally, the density of the flow with mean molecular mass μm_H, where μ = 0.6 is the mean molecular weight and m_H is the hydrogen mass, is given by

$$\begin{equation} \rho = \mu m_{{\rm H}} n(\varpi _0) N(\varpi _0, \zeta), \end{equation} \tag{ 4 }$$

where the injection density on the disk is assumed to be a power law, n(ϖ₀) = Aϖ^−α₀, and the density function is obtained from mass conservation, N(ϖ₀, ζ)bχ = F(ϖ₀, 0)/F(ϖ₀, ζ), where b = χ(1 + ∂ln χ/∂ln ϖ₀) − ζχ'.

The wind is ejected from the disk inner radius R₁ to the disk outer radius R_d. These radii, together with the injection parameters A, α, and f₀, define the wind model. The wind mass-loss rate is given by

$$\begin{equation} \dot{M}_w = 2 \int _{R_1}^{R_d} \rho (\varpi) v_{z0}2 \pi \varpi d\varpi, \end{equation} \tag{ 5 }$$

where the factor of 2 in front accounts for both sides of the disk. We will assume that the central star has enough Lyman photons to ionize the disk wind. This assumption is checked a posteriori by calculating the wind mass-loss rate and comparing with the radiative transfer calculations of H94.

H94 discussed two cases: the weak stellar wind and the strong stellar wind models. If the star has a weak stellar wind, a static ionized atmosphere is formed around the star. This gas cannot escape from the gravitational potential well; only gas beyond the gravitational radius will escape as a wind. On the other hand, if the star has a strong stellar wind, this wind will push the atmosphere and the disk wind until an equilibrium radius where the ram pressure of the wind is balanced by the thermal pressure of the photoevaporated disk wind, which will flow beyond this radius. The radiative transfer of the ionizing photons induces a mass injection at the base of the wind, with a density given by n(ϖ)∝ϖ^−α. The slope α varies between 2 and 2.5 for the weak wind and the strong wind case, respectively. In the weak wind case, the static ionized atmosphere at ϖ < R₁ has a density that varies as ∝ϖ^−3/2 and decays exponentially with height. The density normalization depends only on the rate of Lyman photons of the central star (see Equations (2.4) and (3.10) of H94).

We calculate the free–free continuum and RRL emission from the density structure of a photoevaporated disk wind model. For simplicity, we consider only winds from disks perpendicular to the plane of the sky. This approximation is good enough to compare with the source MWC 349A (see Section 5).

To compare with resolved continuum or line observations we use the intensity averaged over the beam, Ω_B, at a frequency ν,

$$\begin{equation} {\cal I}(\nu, {\bf x}) = {4 \ln 2 \over { \pi } \theta _{{\rm FWHM}}^2} \int I(\nu,{\bf x^\prime }) \Omega _B({\bf x} - {\bf x^\prime }) d {\bf x^\prime }, \end{equation} \tag{ 6 }$$

where we assume a Gaussian beam, Ω_B = exp [ − 4ln 2(x − x')²/θ²_FWHM], where θ_FWMH is the beam full width at half-maximum. To compare with the SED or the spatially integrated line emission, one integrates the intensity over the source solid angle, Ω_source, $S(\nu,{\bf x}) = \int _{\Omega _{{\rm source}}} I(\nu,{\bf x}) \ d \Omega.$

For the RRL emission we will assume LTE conditions; thus we will only compare with thermal RRLs. The total opacity is given by the continuum plus line opacities, τ_{l + c} = τ_c + τ_l, given by the usual expressions (e.g., Spitzer 1978).

The line profile is a Voigt profile, which results from the convolution of a Gaussian and a Lorentzian profile,

$$\begin{equation} \phi (\nu) = \phi _G (\nu) * \phi _L(\nu). \end{equation} \tag{ 7 }$$

The Gaussian profile is

$$\begin{equation} \phi _G(\nu) = \sqrt{\frac{4 \ln 2 }{ \pi \Delta \nu _{h}^2} }e^{-4 \ln 2 \, ({\Delta \nu }/\Delta \nu _{h})^2}, \end{equation} \tag{ 8 }$$

where Δν = ν − ν₀, ν₀ is the line central frequency, and the line full width at half-maximum is Δν_h = 2(2ln 2)^1/2σ(ν₀/c), where σ is the total velocity dispersion. We will assume that the velocity dispersion has a thermal and a non-thermal component, σ² = σ²_t + σ_nt², where the thermal velocity dispersion is $\sigma _{\rm t} = \sqrt{k T/(\mu m_{{\rm H}})}$ and σ_nt is constant, independent of frequency. The Lorentzian profile is

$$\begin{equation} \phi _L(\nu) = \frac{\delta }{\pi } \frac{ 1}{ \left(\nu - \nu _0 \right)^2 + \delta ^2}, \end{equation} \tag{ 9 }$$

where the width is δ = 4.7(n/100)^4.4(T/10⁴ K)^−0.1n_e, n is the quantum number, and n_e is the electron density. We obtained the Voigt profile using the numerical routine developed by Shippony & Read (1993). Finally, the line intensity is given by I_l(ν, x) = I_{l + c}(ν, x) − I_c(ν, x), which is then averaged over the beam (Equation (6)).

Classified by Merrill et al. (1932) as a Be star, MWC 349A is the brightest source in the sky at centimeter wavelengths. At a distance of 1.2 kpc, it has an estimated luminosity L ∼ 3 × 10⁴ L_☉ and is part of a binary system with the source MWC 349B, classified as a B0 III star (Cohen et al. 1985). This source was first modeled as an isothermal spherically symmetric constant velocity ionized wind by Olnon (1975). From RRLs Hartmann et al. (1980) estimated wind terminal velocities v ∼ 50 km s⁻¹ and proposed that MWC 349A was an evolved star with an unusually slow stellar wind. Nevertheless, Hamann & Simon (1986) observed emission from both hot photoionized wind gas, and cool dense neutral gas possibly located in an accretion disk. Nowadays, the observational evidence agrees in favor of MWC 349A being a young massive star with an edge- on disk and an ionized outflow. IR observations by Danchi et al. (2001), although lacking precise astrometry, give evidence of such a disk, probably located at the waist of the hourglass-shaped radio continuum emission.

MWC 349A has been extensively studied in continuum and line observations at centimeter and millimeter wavelengths. The integrated continuum flux of MWC 349A as a function of frequency is approximately S_ν∝ν^0.6, as first shown by Olnon (1975) for the frequency range 1.41–10.68 GHz and later confirmed by Tafoya et al. (2004) for the frequency range 0.33–43.34 GHz. Tafoya and coworkers also obtained a direct measurement of the source angular size as a function of frequency, θ∝ν^−0.7, as expected for an ionized wind with constant velocity. The bipolar outflow morphology of MWC 349A was first reported both by White & Becker (1985) and by Cohen et al. (1985) at 14.7 and 4.8 GHz, respectively. These spatially resolved observations show that the continuum emission arises from two lobes separated in the north–south direction. A change in the morphology of MWC 349A has been reported by Rodríguez et al. (2007), from the known hourglass shape to a square shape, without a change in the integrated flux within the error bars of the observations.

Several hydrogen RRLs have been observed toward this source; these lines give information on the kinematics of the ionized material. Millimeter and infrared RRLs of MWC 349A show evidence of maser emission (e.g., Martín-Pintado et al. 1989a; Thum et al. 1994; Smith et al. 1997). These lines have double-peaked profiles that indicate rotation, with the H30α line peaks separated by a velocity of 47 km s⁻¹ (Planesas et al. 1992). The distance between the H30α main maser velocity components has been estimated as 60 AU (Weintroub et al. 2008) along a position angle ∼100°. The maser positions and velocities show an east–west velocity gradient expected from an edge-on rotating disk around a central star with M_* ∼ 10–30 M_☉, with the west side blueshifted and the east side redshifted. The maser emission has been shown to be variable, although a variation period has not been established (Martín-Pintado et al. 1989b; Gordon et al. 2001). The central radial velocities of the observed RRLs increase with frequency toward the central star recession velocity ∼12 km s⁻¹, consistent with a partially optically thick outflow (Gordon 2003).

At radio frequencies, Rodríguez & Bastian (1994) reported resolved VLA H92α observations of MWC 349A with a blueshifted and a redshifted component, in an opposite direction to the rotation detected with RRLs at millimeter wavelength; they interpreted this behavior as emission from ionized gas that is both expanding and rotating. The spatially integrated H92α line has a width Δv  ∼  50 km s⁻¹ (L. F. Rodríguez 2011, private communication). Also, the spatially integrated H76α line has Δv ∼ 50–76 km s⁻¹ (Altenhoff et al. 1981; Escalante et al. 1989). Recently, Loinard & Rodríguez (2010, hereafter LR10) reported the spatially integrated H66α line observed with the Expanded Very Large Array (EVLA). The observed line-to-continuum ratio indicates a gas temperature, T ∼ 5700–6900 K. This line is very wide, with Δv ∼ 88.7 ± 1.6 km s⁻¹. This large line width is consistent with the width of the line H41α, Δv = 98 ± 5 km s⁻¹ reported by Martín-Pintado et al. (1989a). Thus, it seems that in MWC 349A these high-frequency lines have larger widths than the low-frequency H92α and H76α lines. This behavior is contrary to that expected from pressure broadening, which increases the width of low-frequency lines. We will discuss the implications of this behavior below.

In the next section, we obtain the radio continuum and RRL line emission of disk wind models to compare with the observations of the source MWC 349A, suspected of harboring a photoevaporated disk wind.

In this section, we find our photoevaporated disk wind model that best reproduces the existing continuum and RRL observations of MWC 349A. Following LLG04 we assume a mass of the central star M_* = 17 M_☉ and a weak wind case, with a density exponent α = 2. Then, the free parameters of the model are the disk inner and outer radii: R₁, R_d; the density normalization at the base of the disk A, such that n(ϖ) = Aϖ^−α; and the injection velocity at the disk surface v_z0 (see Section 2). In these models the wind temperature can also be varied and, as discussed in Section 3, one can include a non-thermal velocity dispersion in the Gaussian line profile.

We used the following three-step procedures to find the best-fit model for MWC 349A. (1) We fitted the SED of MWC 349A and chose a range of model parameters with values of χ² = Σ^N₁[S(ν)^mod − S(ν)]²/N < χ₀, where S(ν) is the observed integrated flux at each frequency, and N is the number of observed frequencies in the range 1 < ν < 300 GHz. We used the data compiled by LLG04 and found that a value χ₀ ∼ 1.5 produces reasonable fits of the SED. (2) We compared these models with the EVLA observations of the RRL H66α by LR10. This is the only observed RRL at centimeter wavelengths toward MWC 349A that is fully resolved in velocity and that has a well-defined continuum level. We vary the gas temperature to fit the observed line-to-continuum ratio and included a non-thermal velocity dispersion σ_nt to fit the large observed line width. The non-thermal velocity dispersion is necessary because in the disk wind models, the wind velocity field, the thermal width, and the electron impact broadening produce too narrow line widths, Δv < 60 km s⁻¹. We chose the models that fit the H66α line peak intensity at the central frequency, ν₀ = 22.3 GHz, within 10% error of the observed value, |I_66α(ν₀)/I_66α(ν₀)^mod − 1| < 0.1, and that have the correct FWHM. This procedure reduced the model set to less than 10 models. (3) Finally, the best model is the one with the highest value of the injection velocity, v_z0, because it has radio continuum images with the largest vertical size, in agreement with the observed radio continuum morphology.

Following the procedure described above, our best model for MWC 349A has an inner disk radius R₁  =  50 AU; an outer disk radius R_d = 220 AU; a density at the base of the disk n(ϖ) = 3 × 10⁷(ϖ/50 AU)⁻²; a normalized injection velocity v_z(0) = 0.26a, where the sound speed is a = 9.82 km s⁻¹, calculated at a gas temperature, T = 7000 K; and a local non-thermal velocity dispersion, σ_nt = 71.6 km s⁻¹. The gravitational radius for this model is r_g = 156.8 AU ∼ 3R₁; note that this radius depends on the sound speed a because the wind has to make a sonic transition at the disk surface.

Figure 1 shows the continuum maps of this model at 43.3, 22.3, 14.7, 8.3, and 4.8 GHz. The model produces continuum maps with similar widths as the observations but, for the high-frequency maps, the height is smaller by a factor ∼2.

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Figure 2 shows the spatially integrated RRLs H53α (43.3 GHz), H66α (22.3 GHz), H76α (14.7 GHz), and H92α (4.8 GHz). The solid lines are the best model lines with a Voigt profile. The model RRLs are very wide. The H66α line fits exactly the observations of LR10. The H53α line has not been reported; however, this RRL could be properly measured, with a well-defined continuum level, either with current single-dish radio telescopes or with the EVLA. On the other hand, the model H76α line has a full width at half-maximum Δv ∼ 93 km s⁻¹, in contrast with the reported width Δv_obs ∼ 49–76 km s⁻¹(Altenhoff et al. 1981; Escalante et al. 1989). Also, the model H92α line has Δv ∼ 94 km s⁻¹, in contrast with the narrow line observed by RB94, Δv_obs ∼ 50 km s⁻¹. Thus, the observed low-frequency RRLs (n = 76 and 92) seem to become narrower than the observed high-frequency RRLs (n = 41 and 66). As this behavior is opposite to that found in other UC/HCHII regions (Sewiło et al. 2004; Keto et al. 2008), either this is an unexpected physical effect not considered in the LLG04 models or the low-frequency RRL observations suffered from insufficient bandwidth to determine the continuum level properly (see discussion below). The dashed lines in Figure 2 are obtained using a Gaussian profile for the RRLs instead of a Voigt profile. One can see that pressure broadening produces wings mainly for the lower frequency lines (H66α and H76α).

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Figure 3 shows the line full width at half-maximum, Δv, for different quantum numbers n. The solid line shows the line width for the Voigt profile; the dotted line shows the line width for a Gaussian profile. Both profiles include a non-thermal velocity dispersion. One can see that pressure broadening is negligible for the high-frequency lines; instead, for H92α pressure broadening increases the line width by ∼12 km s⁻¹.

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Figures 4 and 5 are synthetic velocity channel maps of the H66α and H53α lines. The effect of flow rotation produces an asymmetry in the channel maps displaced by the same velocity with respect to the line center. In the maps, the velocity channels have widths of 500 kHz, which correspond to 6.7 km s⁻¹ and 3.5 km s⁻¹ for H66α and H53α, respectively.

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We model the continuum and RRL emission of the source MWC 349A using the photoevaporated disk wind models of LLG04. Although several observations are reproduced by this model, we propose below that the model needs to be modified to include the effect of a disk poloidal magnetic field.

With respect to the continuum emission, the LLG04 model fits the SED of MWC 349A, reproducing the observed dependency of the integrated flux with frequency, S_ν∝ν^−0.6. Also, the resolved continuum maps obtained in this work show the observed hourglass morphology and the change in the waist width at different frequencies (see, e.g., maps at different frequencies of MWC 349A in the early 1980s in Rodríguez et al. 2007). Nevertheless, at high frequencies the images are flatter than the observations (by a factor of ∼2). This means that the density decreases too fast in the models. One possibility to avoid this problem is to include a poloidal magnetic field in the disk that could prevent the strong wind divergence (e.g., Shu et al. 2007). In particular, Thum & Morris (1999) detected a strong magnetic field toward this source by Zeeman splitting of the H30α line. They measured a line-of-sight component, B_l.o.s.  ∼  22 mG, which implies that the field is dynamically important, close to equipartition with the thermal energy density.

With respect to the RRLs, the flow dynamics, thermal broadening, and electron pressure broadening in the LLG04 model naturally produce lines with FWHM Δv ∼ 40–60 km s⁻¹. Nevertheless, these widths are not enough to fit the very wide H66α line observed by LR10. The addition of a poloidal magnetic field anchored in the disk would accelerate the gas along the field lines as studied by Blandford & Payne (1982). In particular, in cold magnetized disk winds, the terminal velocity of the gas along each streamline is v_∞ ∼ 2^1/2v_ϕ(ϖ₀, 0)(r_A/ϖ₀), where r_A is the Alfvén radius, which is a few times ϖ₀ (e.g., Pelletier & Pudritz 1992). Thus, the terminal velocity is the rotational speed at the disk surface multiplied by the ratio of the magnetic lever arm to the streamline footpoint, ϖ₀. Beyond the sonic point, the gas suffers a smooth magnetocentrifugal acceleration along the streamlines up to approximately the Alfvén radius. This extra acceleration would help increase the RRL line widths. Also, shocks in the wind can dissipate the gas kinetic energy and can increase the local velocity dispersion.

Thus, it would be relevant to explore magnetized photoevaporated winds in a future work. Since the density and velocity field of a magnetized photoevaporated wind is not yet known, for illustrative purposes, we introduce a non-thermal velocity dispersion in the LLG04 model above the disk (beyond z = 50 AU) to mimic the acceleration of the gas to terminal velocities at the Alfvén radius by a magnetocentrifugal mechanism. With this additional velocity component the modified model reproduces the observed H66α line profile. As shown in Figure 3, the modified model predicts an increase in the line FWHM with decreasing frequency. The reason is that we have assumed a constant non-thermal velocity dispersion (independent of frequency) and that pressure broadening increases with decreasing frequency. Therefore, the relatively small widths of the observed H92α and H76α lines are not in agreement with this model, or, for that matter, with the observed behavior of HCHII regions, where the width of RRLs also increases at lower frequencies (e.g., Keto et al. 2008). This discrepancy could be due to insufficient bandwidth on the observations. If the observed frequency range is not wide enough then the line profile would fill all frequency channels and the continuum level could not be properly measured. This could lead to a line width measurement smaller than the real line width. For this reason, one needs single dish (or EVLA) observations of both H92α and H76α RRLs made with large bandwidths to establish the line widths properly and constrain the models. If the narrow line widths of low-frequency lines are confirmed, one could explore disk wind models with temperature or velocity dispersion gradients.

In the model, pressure broadening increases the line width of the H92α RRL by ∼12 km s⁻¹. This result is somewhat smaller that reported for most of the sources in Keto et al. (2008), who obtained larger line width broadening (∼20 km s⁻¹) associated with pressure broadening in RRLs from HCHII regions. This difference may be due to higher densities in the H ii regions observed by these authors.

The synthetic RRL velocity channel maps show asymmetric emission at velocities away from the line center due to the flow rotation. Because it is a stronger line, the H53α map shows a more pronounced asymmetry than the H66α map. For the disk wind model, this asymmetry is less noticeable for the lower frequency lines, due to both their larger line widths and weaker emission. Hopefully, such maps will be available in the near future taking advantage of the new EVLA extended bandwidth capabilities. Such observations would test the predictions of LLG04 models.

Finally, the best-fit model for MWC 349A has a disk mass-loss rate, $\dot{M}_w = 1.2 \times 10^{-6} \,{M_\odot }\,{\rm yr}^{-1}$. This mass-loss rate is consistent with that obtained by the radiative transfer calculations of H94 for the weak wind case (see their Equation (3.14)). For a disk mass, M_d ∼ 5 M_☉, this mass-loss rate sets an upper limit on the disk lifetime, τ ≲ 4 × 10⁶(M_d/5 M_☉) yr.

We note that the α RRLs in this work (with n > 52) were calculated assuming LTE, since it has been shown by Strelnitski et al. (1996) that for MWC 349A, stimulated emission is important for n < 40. In contrast, to compare with millimeter and submillimeter α RRL observations a non-LTE treatment is needed, as in the work done by Martín-Pintado et al. (2011). For simplicity, we considered an edge-on disk, which is a reasonable model for MWC 349A. However, for a general treatment, arbitrary position angles of the disk should be explored to determine the change in the radio continuum morphology of the source. Both a non-LTE treatment and an arbitrary inclination for the disk will be addressed in future work. Furthermore, the LLG04 models of photoevaporated disk winds are steady state models; thus, there is no time dependence of mass-loss rates or flow velocities that can produce the time variation of the radio continuum morphology, as observed by Rodríguez et al. (2007). These authors suggested that this time variation could be due to a precession of the accretion disk. However, they dismiss this possibility because the timescale for disk precession is too long to produce the morphology changes in the observed period. Since the total flux does not change with time, one possibility is that the reported morphology variation with time is a transient event related to the evaporation of density inhomogeneities in the wind (e.g., Lizano et al. 1996; Redman et al. 1998).

We obtained radio continuum and RRL emission from the photoevaporated disk wind models of LLG04 and compared with observations of the source MWC 349A. We found that the constraints of resolved continuum and line observations make it necessary to modify the model, possibly by including the effects of a disk poloidal magnetic field, as summarized below. We chose a best-fit model for MWC 349A that has an inner disk radius R₁ = 50 AU; an outer disk radius R_d = 220 AU; a density at the base of the disk n(ϖ) = 3 × 10⁷(ϖ/50 AU)⁻²; a normalized injection velocity v_z0 = 0.26a, where the sound speed a = 9.82 km s⁻¹, is calculated at a gas temperature, T = 7000 K; and a local non-thermal velocity dispersion, σ_nt = 71.6 km s⁻¹. Due to pressure gradients, this wind is able to escape from the disk at ∼1/3 of the gravitational radius, r_g = 156.8 AU.

The model reproduces well the radio continuum morphology at low frequencies, but at high frequencies (ν > 22.3 GHz), the images are flatter than the observations by a factor of two because the model's wind density drops too fast. Disk winds with poloidal magnetic fields anchored on the disk could help prevent the wind divergence and alleviate this problem.

Photoevaporated disk winds can naturally produce wide lines with FWHM Δv ∼ 40–60 km s⁻¹, as observed in several UC H ii regions (e.g., Sewiło et al. 2004). Nevertheless, these widths are not enough in the case of sources like MWC 349A, where the observed high-frequency RRLs have line widths of ∼89 km s⁻¹. We propose that the inclusion of a disk poloidal magnetic field would produce an extra magnetocentrifugal acceleration of the gas and help increase the line widths. For the lack of such models, we treated this effect simply as a non-thermal velocity dispersion σ_nt that would mimic the increase in the local velocity dispersion due to shocks and the acceleration of the flow due to magnetic fields in the wind. The modified model then reproduces the observed high-frequency H66α RRL and predicts that the line width should increase for lower frequency lines, because σ_nt is independent of frequency. Nevertheless, the observed H76α and H92α RRLs are narrower than the observed high-frequency lines. Since it is possible that these narrow widths could be due to instrumental limitations, these low-frequency lines should be observed with wide bandwidths to reliably establish their widths.

RRL velocity channel synthetic maps of the H53α and H66α lines show an asymmetry in the channel maps that is evidence of the flow rotation. High-resolution observations of these lines with the EVLA could detect this asymmetry.

It will be important to study models of photoevaporated disk winds that include the effects of dynamically important magnetic fields. These type of models could increase the gas acceleration and focus the gas in a bipolar morphology for longer distances, as suggested by the continuum and line observations of MWC 349A.

M.A. and S.L. acknowledge support from CONACyT, IN101310 PAPIIT-UNAM, and Convenio ALMA CONACyT I0110|20|11. We thank L. Loinard and L. Rodríguez for useful discussions. We also thank an anonymous referee for useful observations that help clarify the manuscript.