PROBING THE MASS-LOSS HISTORY OF THE YELLOW HYPERGIANT IRC+10420

As shown in Figure 1, the 1.3 mm continuum emission from IRC+10420 was well detected in our SMA data. The emission is not resolved and has a flux density ∼45 mJy. A previous single-dish observation by Walmsley et al. (1991) also at 1.3 mm gives a flux of 101 mJy. That suggests that the dust emission is extended, with about 55% of the continuum flux resolved out by the interferometer. Assuming the central star to have a black body spectrum with a temperature of T_eff = 7000 K, it contributes only a negligible amount of the flux at 1.3 mm of S_* ∼ 0.1 mJy. Thus, most of the 1.3 mm continuum emission is produced by the warm dust in the envelope around IRC+10420.

In Figure 3, we show the channel maps of the ¹²CO J = 2–1 emission obtained with the compact configuration of the SMA. At our angular resolution of ∼3'', the envelope is well resolved. At both blueshifted and redshifted velocities the emission appears to be circularly symmetric, as is expected for a spherically expanding envelope. More interestingly, at velocities between 59 and 89 km s⁻¹, centered around the systemic velocity, the envelope is clearly elongated in approximately the northeast to southwest direction. By fitting a two-dimensional Gaussian to the intensity distribution of the ¹²CO J = 2–1 emission at systemic velocity V_LSR = 74 km s⁻¹, we obtain a position angle for the ¹²CO J = 2–1 envelope of PA = 70°. The orientation of the CO emission is consistent with the elongation found by Castro-Carrizo et al. (2007). The position–velocity (PV) diagrams of the ¹²CO J = 2–1 emission along the major (PA ∼70°) and minor (PA ∼160°) axes of the envelope as presented in Figure 7 are typical of an expanding envelope at an expansion velocity of ∼40 km s⁻¹.

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We show in Figure 4 the channel maps of the ¹²CO J = 2–1 emission, which is obtained by combining the data from both compact and extended configurations of the SMA. The ¹²CO J = 2–1 emission is further resolved into more complex structures. In the velocity channels between 59 and 89 km s⁻¹, centered around the systemic velocity, the ¹²CO J = 2–1 emission consists of a central prominent hollow shell structure of ∼1''–2'' in radius and a more clumpy arc or shell located between radii of 3'' and 6'', which is more prominent in the southwest quadrant of the envelope. Close inspection of the velocity channels around the systemic velocity V_LSR ∼ 74 km s⁻¹ indicates that the central hollow shell-like structure is clumpy and shows stronger emission toward the southwestern side. The outer arc or shell of emission can be seen more easily in the azimuthal average of the ¹²CO J = 2–1 brightness temperature as shown in Figure 13. We can clearly see a central depression within a radius of ∼1'' and enhanced emission between the radii of 3'' and 6''.

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The channel maps of ¹³CO J = 2–1 emission obtained from the compact configuration data at an angular resolution of ∼35 are shown in Figure 5. The emission in the ¹³CO J = 2–1 line appears fainter and more compact then seen in the main isotope ¹²CO J = 2–1 line. Like in ¹²CO J = 2–1 emission, near the systemic velocity, the envelope traced by ¹³CO J = 2–1 emission is elongated at position angle of PA ∼70°. The centroid of the emission appears to be slightly offset from the stellar position. Also like in ¹²CO J = 2–1 emission, at higher velocities in both blue-shifted and redshifted parts the ¹³CO J = 2–1 emission again shows a roughly circularly symmetric morphology, as would be expected for a spherically expanding envelope. The spatial kinematics of the ¹³CO J = 2–1 emission can be more clearly seen in the PV diagram (Figure 7) along the major axis (PA ∼70°) of the envelope. In the PV diagram, there is a small velocity gradient in the velocity range between 70 and 100 km s⁻¹. Closer inspection of the channel maps suggests that the small velocity gradient corresponds to the slight shift of the emission centroid toward the northeast quadrant of the envelope in the above-mentioned velocity range.

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In Figure 6, we show channel maps of the SO 6₅–5₄ emission obtained from the data of the compact configuration. The emission is well resolved in some of the velocity channels. A close inspection reveals that the distribution of SO 6₅–5₄ emission is different from that of ¹²CO J = 2–1. At extreme redshifted velocities, the centroid of the emission is shifted to the east, whereas at extreme blueshifted velocities the centroid of the emission is shifted to the west. In addition, the SO 6₅–5₄ emission in velocity channels centered around the systemic velocity is clearly elongated to the southwest. This elongation is very similar to that seen in ¹²CO J = 2–1 emission at the same angular resolution (see Figure 3). More interestingly, at the opposing redshifted velocities of 84–102 km s⁻¹ (see Figure 6) the emission is very compact and shifts to the northeast of the central star. Such positional shift is shown more clearly in the PV diagram of the SO J_K = 6₅–5₄ emission along the major axis (PA ∼ 70°) of the envelope (see Figure 7). There is a clear velocity gradient in the velocity range between 70 and 90 km s⁻¹, which is similar but more pronounced that that seen in ¹³CO J = 2–1 line.

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Thus, the SO 6₅–5₄ emission in particular but also the ¹³CO J = 2–1 emission seem to better trace the asymmetric structure inside the envelope. The small velocity gradient seen in both lines points to the presence of an ejecta in the envelope of IRC+10420. From the above-mentioned elongation of the envelope and the orientation of the positional velocity shift, we estimate that the ejecta is oriented at position angle of PA = 70°. We note that SO emission is known to be enhanced in asymptotic giant branch (AGB) and post-AGB envelopes where collimated high velocity outflows are present. Examples can be found in the rotten egg nebula OH 231.8+4.2 (Sánchez Contreras et al. 2000) and VY CMa (Muller et al. 2007). In both cases, SO emission is found to be strongly enhanced in the bipolar lobes. The SO enhancement in bipolar outflows could be related to the synthesis of SO in the shocked molecular gas in these outflows. Alternatively, the warm environment around supergiants such as VY CMa and IRC+10420 could facilitate the synthesis of SO through chemical pathways such as S + OH $\longrightarrow$ SO + H or HS + O $\longrightarrow$ SO + H (Willacy & Millar 1997).

To determine the heating process in the detected molecular shells requires knowledge of the momentum transfer coefficient (or the flux-averaged extinction coefficient 〈Q〉) between the dust particles and the gas molecules. To estimate this quantity, we follow the treatment of Oudmaijer et al. (1996) who modeled in detail the spectral energy distribution (SED) of IRC+10420. We emphasize here that by following the treatment of Oudmaijer et al. (1996) the structure of the molecular envelope as seen in our SMA data and previously in the data of Castro-Carrizo et al. (2007) is not considered explicitly.

We use the photometric data of IRC+10420 collected by Jones et al. (1993) and Oudmaijer et al. (1996), i.e., the 1992 photometric data set. We also assume that the dust consists of silicate particles with a radius of a = 0.05 μm. The dust opacity as a function of wavelength is taken from the work of Volk & Kwok (1988). Following Oudmaijer et al. (1996), we scale the opacity law to match the absolute value of the opacity at 60 μm of $\kappa _{60\; \mu {\rm m}}$ = 150 cm² g⁻¹. We also a use a specific density for dust particles of ρ = 2 g cm⁻³ and assume a dust to gas ratio Ψ = 5 × 10⁻³ as used by Oudmaijer et al. (1996).

To fit the SED of IRC+10420, especially in the mid-IR region between 5 and 20 μm, Oudmaijer et al. (1996) suggest that two dust shells are needed: a hot inner shell with a low mass-loss rate and an outer cooler shell with a higher mass-loss rate. We note that Blöcker et al. (1999) also reached the same conclusion in their attempt to fit the SED of IRC+10420. In our model, we also use two dust shells: a hot inner shell with a low mass-loss rate of $\dot{M} = 8\times 10^{-5}\; M_\odot$ yr⁻¹ located between 2.6 × 10¹⁵ cm (70 stellar radii) and 1.8 × 10¹⁶ cm (486 stellar radii) and an outer cooler shell with a higher mass-loss rate of $\dot{M} = 1.2 \times 10^{-3}\; M_\odot$ yr⁻¹ extending to a radial distance of 10¹⁸ cm where the dust particle number density drops to very low values. We also infer a stellar luminosity of 6 × 10⁵ L_☉. The size of the dust shells, the mass-loss rates, and the stellar luminosity are very similar to that derived by Oudmaijer et al. (1996) scaled to the adopted distance of 5 kpc. The results of our radiative transfer model are presented in Figures 8 and 9. The fluxes from the model are corrected for an interstellar extinction of A_V = 5 as suggested by Oudmaijer et al. (1996). As can be seen in Figure 8, the results of our model are in close agreement with that shown in Oudmaijer et al. (1996) and match reasonably the observed SED of IRC+10420. As shown in Figure 9, the dust temperature decreases monotonically from ∼1000 K at the inner radius to ∼50 K at the outer radius of the dust envelope, even though there is a jump in mass-loss rate between the inner hot dust shell and the outer cooler dust shell at a radial distance of 1.8 × 10¹⁶ cm.

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From the flux F_λ of the radiation field at each point in the envelope we can define the flux-averaged extinction coefficient 〈Q〉, which characterizes the transfer of angular momentum from radiation photons to dust particles during the absorption and reemission processes of the continuum radiation. Because in our case we do not consider the scattering of radiation, the extinction coefficient Q_λ is simply the opacity κ_λ, where λ is the wavelength of the radiation,

$$\begin{equation} \langle Q \rangle = \frac{\int _{0}^{\infty } F_\lambda Q_\lambda d\lambda }{\int _{0}^{\infty }F_\lambda d\lambda } = \frac{\int _{0}^{\infty } F_\lambda \kappa _\lambda d\lambda }{\int _{0}^{\infty }F_\lambda d\lambda }. \end{equation} \tag{ 1 }$$

The flux-averaged extinction coefficient 〈Q〉 changes significantly in the inner part of the dust envelope but reaches a constant value in the outer part. Because the molecular shells are located in the outer part of the dust envelope, at radii larger than a few times 10¹⁶ cm; for simplicity, we will adopt a constant value 〈Q〉 = 0.025 (see Figure 9).

The temperature of the molecular gas at any point in the envelope is determined by the balance between cooling due to adiabatic expansion and molecular emissions, and the heating, which is mainly due to collisions of molecules with dust grains (Goldreich & Scoville 1976). As the dust grains stream through the gas under radiation pressure, the grains transfer angular momentum to the gas by collisions. The heating term is therefore directly related to the drift velocity:

$$\begin{equation} H = \case{1}{2}\rho \pi a^2 n_d v_{\rm drift}^3, \end{equation} \tag{ 2 }$$

where n_d is the number density of dust particles. The drift velocity is determined by the relation

$$\begin{equation} v_{\rm drift} = \left(\frac{L_{*}V_{\exp }\langle Q \rangle }{\dot{M}c}\right)^{1/2}, \end{equation} \tag{ 3 }$$

where L_* is the stellar luminosity, V_exp is the expansion velocity, $\dot{M}$ is the mass-loss rate, c is the speed of light, and 〈Q〉 is the flux-averaged extinction coefficient of dust particles estimated in the previous section. The same dust to gas ratio of Ψ = 5 × 10⁻³ is used to calculate the heating rate.

Generally, in oxygen-rich envelopes the main coolants are H₂O and CO molecules. The contribution of H₂O molecules to the cooling process in IRC+10420 is quite uncertain. We note that far-IR emission lines of H₂O are not detected in the ISO data (Molster et al. 2002). In addition, OH masers are seen in a shell of radius 1''–15 (Nedoluha & Bowers 1992). Because OH radical is the photodissociation product of H₂O, it is likely that H₂O molecules can only exist at even smaller radii, i.e., inside the central cavity discussed previously. Therefore, we do not expect the H₂O molecules to be present in significant quantity in the part of the molecular envelope traced in CO emission As a result, we do not include the cooling due to the H₂O molecule in our model and calculate the cooling solely due to CO molecule and its isotopomer ¹³CO.

We use the thermal balance and radiative transfer model published by Dinh-V-Trung & Nguyen-Q-Rieu (2000) to derive the temperature profile of the molecular gas and to calculate the excitation of CO molecules and predict the strength of CO rotational transitions. We take into account all rotational levels of CO molecules up to J = 20. The collisional cross sections with H₂ are taken from Flower (2001), assuming an ortho to para ratio of 3 for molecular hydrogen. The local linewidth is determined by the turbulence velocity and the local thermal linewidth. Because the expansion velocity of the gas in the envelope of IRC+10420 is large and the observed CO line profiles have smooth slopes at both blueshifted and redshifted edges (see Figure 11), we need to assume a constant turbulence velocity of 3 km s⁻¹. We note that this is higher than normally used (about 1 km s⁻¹) for the envelope around AGB stars where the expansion velocity is lower (Justtanont et al. 1994). In our model, the spherical envelope is covered with a grid of 90 radial points. For each rotational transition, the radiative transfer equation is integrated accurately through the envelope to determine the average radiation field at each radial mesh point. We use the approximate lambda operator method together with Ng-acceleration to update the populations of CO molecules of different energy levels. Once convergence is achieved, we convolve the predicted radial distribution of the line intensity with a Gaussian of specified FWHM to produce simulated data for comparison with observations.

As discussed in the previous section, there is a clear evidence for the presence of two molecular shells from our SMA data. The size and location of each molecular shell are determined from fits to the interferometric data. In our model, we adjust both the mass-loss rates and the relative abundance of CO molecules in the two molecular shells to match both the single dish and interferometric data. We find that a relatively low mass-loss rate similar to that derived by Castro-Carrizo et al. (2007) would result in a too high gas temperature in the envelope as the heating term becomes more dominant in comparison to the cooling term. We also find that a high abundance of CO of a few times 10⁻⁴ as usually used for oxygen-rich envelopes (Kemper et al. 2003; Castro-Carrizo et al. 2007) would result in CO lines that are too strong. Instead, a relative abundance of 10⁻⁴ for CO molecules with respect to H₂ provides reasonable fit to all the available data. The radial profile of the gas temperature is shown in Figure 10. The sudden jump in gas temperature at the inner radius of the second shell (∼1.85 × 10¹⁷ cm) is due to the change in the mass-loss rate. We can see that the gas temperature in the envelope of IRC+10420, although lower than assumed in Castro-Carrizo et al. (2007), is higher than that typically found in circumstellar envelopes. Even at the outermost radius of the envelope, the gas temperature is still around 50 K. For comparison, in the envelope around OH/IR stars, the gas temperature at similar radial distances from the central star is predicted to be much lower, 10 K or even less (Justtanont et al. 1994; Groenewegen 1994). The main reason for the elevated gas temperature in the envelope of IRC+10420 is the strong heating due to the enormous luminosity of the central yellow hypergiant. The cooling due to molecular emissions is also affected by the lower abundance of CO, that we find necessary to match the data. A summary of the parameters used in our model is presented in Table 3.

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Table 3. Parameters of the Model for IRC+10420 Envelope

Parameters	Shell I	Shell II
Inner radius	3.5 × 1016 cm	1.85 × 1017 cm
Outer radius	1.5 × 1017 cm	5 × 1017 cm
Mass-loss rate, $\dot{M}$	9 × 10−4 M☉ yr−1	7 × 10−4 M☉ yr−1
Expansion velocity, Vexp	38 km s−1	38 km s−1
Dust to gas ratio, Ψ	5 × 10−3	5 × 10−3
Momentum transfer coefficient, 〈Q〉	0.025	0.025
12CO/H2	10−4	10−4
13CO/H2	1.5 × 10−5	1.5 × 10−5
Turbulent velocity	3 km s−1	3 km s−1

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As shown in Figures 11–14, the results of our model are in reasonable agreement with both the strengths of CO lines measured by single dish telescopes and the radial distribution of brightness temperature of J = 1–0 and J = 2–1 lines observed with interferometers. We note that except for the extra emission in the blue part of the line profile between 65 and 75 km s⁻¹, the shape of the J = 2–1 and J = 3–2 is in close agreement with observation. Higher transitions J = 4–3 and 6–5 show some evidence of narrower linewidth than predicted by the model. One possible explanation is that the expansion velocity in the inner region traced by these high-lying transitions has slightly lower expansion velocity than in the outer part of the envelope.

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By comparing the model predictions with the strengths of ¹³CO J = 1–0 and J = 2–1 lines observed with the IRAM 30 m telescope (Bujarrabal et al. 2001), we derive a relative abundance for ¹³CO/H₂ of 1.5 × 10⁻⁵, or an isotopic ratio ¹²C/¹³C ∼ 6. This ratio is very similar to the values ¹²C/¹³C = 6 and 12, respectively, found in the red supergiants α Ori and α Sco (Harris & Lambert 1984; Hinkle et al. 1976). Such a low isotopic ratio suggests that IRC+10420 has experienced a significant mixing of H burning products to its surface prior to the ejection of the material in the envelope.

The difference between the mass-loss rates and gas temperature profile derived from our modeling and that obtained by Castro-Carrizo et al. (2007) can be understood as the consequence of the higher gas temperature and higher CO abundance adopted in their work. For the same strength of the CO rotational lines, the higher CO abundance can be almost exactly compensated by a corresponding decrease in the mass-loss rate.

Our results indicate the presence of two separate shells (shell I and shell II, see Table 3) with slightly different mass-loss rates. With an expansion velocity of 38 km s⁻¹, the time interval between the two shells is ∼200 yr. The cavity inside shell I also implies a dramatic decrease in mass loss from IRC+10420 over the last ∼300 yr. Thus, IRC+10420 loses mass in intense bursts, separated by relatively quiet periods of a few hundreds years in duration.

In our model, we consider separately the dust and gas component in the envelope of IRC+10420. The dust continuum emission model is used as a simple way to estimate the 〈Q〉 parameter of dust particles, which is needed for the thermal balance calculation in the molecular shells. It turned out that the mass-loss rates of the molecular shells between 9 × 10⁻⁴ M_☉ yr⁻¹ for shell I and 7 × 10⁻⁴ M_☉ yr⁻¹ for shell II are lower but quite close to the mass-loss rate of 1.2 × 10⁻³ M_☉ yr⁻¹ of the cool outer dust shell inferred from the modeling the SED of the envelope. Our approach, although less ad hoc than simply assuming a value of the 〈Q〉 parameter for dust particles, is not fully self-consistent in the treatment of the dust and gas component. It would be desirable in the future to treat both the dust and gas component together when high angular resolution data on the dust continuum emission and higher J lines of CO become available.

Another caveat of our model is the assumption that the heating of molecular gas is mainly due to collision between dust particles and gas molecules. The high luminosity of the central star of IRC+10420 suggests that radiation pressure on dust particles is a possible mechanism for driving the wind as assumed in our mode. However, given the high expansion velocity and the presence of many small scale features in high angular resolution optical images of the envelope (Humphreys et al. 1997), which has been interpreted as jets or condensations, other mechanisms such as shocks produced by interaction between higher velocity ejecta and the envelope should be considered. The heating due shocks within the envelope might contribute to the thermal balance of the molecular gas in IRC+10420.