THE NON-UNIFORM, DYNAMIC ATMOSPHERE OF BETELGEUSE OBSERVED AT MID-INFRARED WAVELENGTHS

The ISI consists of three 1.65 m aperture telescopes with a heterodyne detection system at each telescope. The double-sideband detection systems are sensitive to 9–12 μm radiation within single-sideband widths of ∼2.7 GHz. The ¹³CO₂ laser local oscillators can operate at numerous wavelengths corresponding to vibrational molecular transitions between wavelengths of 9 μm and 12 μm. For the observations reported here, the local oscillators at each telescope were tuned to a wavelength of 11.15 μm, chosen so as to exclude strong stellar and telluric spectral lines from the detection band (Weiner et al. 2003b).

The van Cittert–Zernicke theorem equates the complex cross-correlation of the electric fields detected at two spatially separated telescopes with the two-dimensional Fourier transform of the source brightness distribution within the telescope fields of view. Instead of measuring complex cross-correlations, the ISI, like all optical/IR interferometers, measures the normalized cross-correlation amplitude, known as the Michelson fringe visibility. The Michelson fringe visibility, V, is given by

$$\begin{equation} V=\frac{P_{\rm fringe}}{\sqrt{I_{A}I_{B}}}, \end{equation} \tag{ 1 }$$

where the fringe power, P_fringe is the cross-correlation amplitude between signals measured at two telescopes, A and B, and I_A and I_B are the source powers measured at telescopes A and B, respectively. Visibility amplitudes are recorded for each ISI telescope baseline pair. The visibility phase in the mid-IR for a given baseline is, however, strongly affected by randomly varying atmospheric path lengths above each telescope, and cannot be recovered from the data. The ISI instead measures the closure phase, or the sum of the measured visibility phases for each baseline. The closure phase is independent of optical path-length differences between pairs of telescopes (Jennison 1958) and it provides information about the point-inversion symmetry of the source. The spatial frequency sampled by the projection of a baseline of length b, perpendicular to the direction of a source, at a wavelength λ, is proportional to b/λ. By obtaining measurements at different source hour angles, multiple spatial frequencies at different position angles are sampled.

Visibility and closure phase data were recorded for Betelgeuse over time spans of five weeks or less each year between 2006 and 2010 (see Table 1). During this time period, the three ISI telescopes were configured in an approximately equilateral triangle with baseline lengths between 34 m and 40 m. For Betelgeuse, this configuration allows spatial frequencies between 20 SFU and 37 SFU (Spatial Frequency Unit; 1 SFU = 1 × 10⁵ cycles rad⁻¹) to be sampled. For all observations, tip-tilt corrections were applied to center the source on K-band guider cameras operating at frame rates of 27 Hz. A standard observing sequence consisted of 4.5 minute data set intervals of staring at the source and position switching between the source and blank fields on either side of the source. The position-switching measurements moved the telescopes between the source and the sky every 15 s. The source powers were measured using additional 140 Hz chopping between the source, or the sky, and cold loads with temperatures near that of the sky. A single visibility measurement consisted of either (1) a fringe power measured during a chopping/position-switching data set, normalized using the source powers during that data set, or (2) a fringe power measured during a staring data set, normalized by weighted averages of source powers measured during the nearest chopping/position-switching data sets. Closure phases were calculated for each triplet of visibility measurements.

Visibility magnitudes and closure phase zero-point offsets were calibrated using observations of Aldebaran (α Taurus) conducted on the same night. Aldebaran was assumed to have a diameter of 20 mas and zero closure phase. The visibility calibrations for the two kinds of visibility measurements were different because of the different times spent on-source during chopping and staring data sets. Data that were affected by systematic errors or poor atmospheric conditions were discarded. The total flux densities of Betelgeuse during each observing epoch were also estimated using Aldebaran, assumed to have a flux density at 11.15 μm of 615 Jy (Monnier et al. 1998), as a calibrator. These total flux density values are given in Table 1, and represent the total power of Betelgeuse within the 5''×5''fields of view of the ISI detectors.

Image models were fitted to the calibrated visibility and closure phase data sets for each epoch. The data, analytic fits, and coverage of the UV spatial frequency plane are shown in Figure 1. Effective model-independent image reconstruction was not possible because of the sparsity of the UV coverage in all epochs. Our model images include a centered uniform disk (UD), and up to two point sources offset from the image centers. The UDs represent the apparent stellar surface, and the point sources represent localized intensity fluctuations in this surface. Emission from the dust surrounding the star at large angular scales, while contributing to the total detected intensity, was assumed not to contribute to the visibility at the sampled spatial frequencies. The intensity of each image component was fitted to a fraction of the total intensity. Other free parameters included the UD radius and the positions of the point sources. The model complex visibility at a point (u, v) in the UV plane was given by

$$\begin{eqnarray} V(u,v)&=&\frac{2AJ_{1}(2\pi r\sqrt{u^{2}+v^{2}})}{2\pi r\sqrt{u^{2}+v^{2}}}\nonumber\\ &&+ P_{1}e^{-2\pi i(ux_{1}+vy_{1})}+P_{2}e^{-2\pi i(ux_{2}+vy_{2})}, \end{eqnarray} \tag{ 2 }$$

where A is the fraction of the total intensity contributed by the UD, r is the UD angular radius, J₁ denotes a Bessel function of the first kind and of order unity, P_n represents the fractions of the total intensity of the point sources, and x_n and y_n represent angular offsets to the west and north for the point sources, with n = {1, 2}.

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We used a weighted least-squares-fitting technique for each epoch, with each baseline and the closure phase data given equal weights. The differing quality of data from different epochs necessitated using models with different numbers of free parameters to fit different epochs. Data from 2006 were fitted with a single point source in addition to a UD, data from 2007 and 2008 were only fitted with UDs, and data from 2009 and 2010 were each fitted with a UD and two point sources. An additional point source was added to the fit for a given epoch only if the reduced χ² values calculated for the full data set, and for the closure phase data alone, were both decreased upon the addition of the point source. We also attempted to fit other image models. These included uniform ellipses, uniform ellipses with point sources, and UDs with offset UDs or offset two-dimensional Gaussian profiles in place of the point sources. None of these trials, however, converged to a satisfactory image, and the angular sizes of the fitted point sources are not determined. The fractions of the total intensity contributed by the point sources were not constrained to be positive, as our data are sensitive to both bright and dark features on the stellar disk.

Simulations were conducted to assess possible degeneracies in fitted image model parameters given the sparsity of the UV coverage of our data sets, in order to ensure that our data were not being overfitted. No significant degeneracies were found for any epoch. For example, the 2006, 2009, and 2010 data sets constrain both the locations and brightnesses of the point sources. Closure phase measurements at multiple array position angles constrain the position angles of the point sources, and both the closure phase measurements and the visibility measurements constrain the angular offsets of the point sources from the image centers.

The results of the fits, as well as the reduced χ² for each epoch, are given in Table 2. All the fits have reduced χ² values that are greater than unity. This implies that the data contain minor features besides Gaussian noise that are not being fitted by the free parameters of the image models.

ISI data for Betelgeuse obtained during 2006 were also analyzed by Tatebe et al. (2007). Despite our choice of different observing dates, a different method of calibration and slightly different image fitting procedures, our results match those of Tatebe et al. (2007) within the margins of error. We however do not adopt Tatebe et al.'s results for the 2006 epoch in order to maintain the same analysis procedure across all epochs.

Using ISI observations over the period 1993–2009, Townes et al. (2009) reported a systematic decrease of 15% in the mid-IR continuum UD diameter of Betelgeuse. Here, we augment this finding with new measurements of the UD diameter of Betelgeuse. Figure 2 shows the data plotted in Figure 1 of Townes et al. (2009), with the new results also included. Though the present work re-analyzes some previous observations examined by Tatebe et al. (2007), the diameter measurements are obtained from different data sets and analyses from those reported by Townes et al. (2009). The measurement of the UD diameter of Betelgeuse at 11.15 μm by Perrin et al. (2007), obtained using the Very Large Telescope Interferometer in 2003, is also plotted. Recently, Ohnaka et al. (2011) showed that K-band diameter measurements, made over a similar time period, vary less than the mid-IR diameters plotted in Figure 2.

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While our results from 2006–2008 are consistent to within the margins of error with the trend toward a smaller size (Townes et al. 2009), the UD diameters of Betelgeuse in 2009 and 2010 are significantly larger than those during 2006–2008. Our analysis method for the 2007 and 2008 data sets essentially matched that of Townes et al. (2009), in that only UDs were fitted to the data. Our technique however differed somewhat in the methods of calibration and fitting. We consider the variability in the apparent size of Betelgeuse in the mid-IR further in Section 5.2.

Effective temperatures of stellar surfaces are among the fundamental parameters of stars (van Belle et al. 2010). The ISI measurements of the flux density of Betelgeuse, and of the UD sizes and fractions of the total intensity, allow the effective temperature of the 11.15 μm apparent stellar surface to be determined at each observing epoch. We use a Planck function for the power emitted by a blackbody to express the effective temperature, T_eff, as

$$\begin{equation} T_{{\rm eff}}=\frac{h\nu }{k_{B}{\rm ln}\big(1+\frac{2h\nu ^{3}\Omega }{c^{2}P}\big)}, \end{equation} \tag{ 3 }$$

where h is Planck's constant, ν is the observing frequency, k_B is Boltzmann's constant, Ω is the solid angle subtended by the stellar disk, c is the vacuum speed of light, and P is the measured power from the stellar disk in units of W m⁻² Hz⁻¹. We do not use the widely applied technique of calculating effective temperatures using estimates for the bolometric flux from the star (e.g., Perrin et al. 2004; Boyajian et al. 2009) for two reasons: radiation at mid-IR wavelengths is strongly affected by thermal emission from circumstellar dust shells and bolometric correction factors at these wavelengths are unique to individual stars; and also because the correspondence between the 11.15 μm scattering surface and the photosphere of Betelgeuse is not certain.

The calculated effective temperatures for the observed stellar disk of Betelgeuse during each observing epoch are plotted in Figure 3. We do not account for attenuation by the interstellar medium, estimated as modifying the observed flux density by a factor of 0.975 (Bester et al. 1996). We also do not account for absorption of the stellar radiation by the dust that surrounds Betelgeuse at angular scales of 1''or larger, or for the emission from this dust in the line of sight to the stellar face. This is because the dust shells are extremely optically thin at mid-IR wavelengths when viewed radially, with a total line-of-sight optical depth of approximately 0.0065 (Danchi et al. 1994).

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Our measured effective temperatures of the mid-IR surface of Betelgeuse are consistently lower than the value of 3641 K derived by Perrin et al. (2004) for the photospheric component of a photosphere-and-layer model. Furthermore, significant variability is evident between the effective temperatures measured at different epochs. We therefore consider sources of mid-IR continuum opacity in the atmosphere of Betelgeuse in an attempt to elucidate the scattering surface probed by our observations and the cause of the observed variability.

Stellar atmospheres have opacities that vary with wavelength. Stars appear smaller at wavelengths where the atmospheric opacity is smaller. The surface of a star, when observed at a given wavelength, can be approximated as the location where the optical depth at that wavelength, measured from the observer, is approximately unity. The photosphere of a star, however, is the apparent stellar surface observed at a wavelength where the opacity matches the Rosseland mean opacity (Rosseland 1924). The Rosseland mean opacity, κ_R, is given by

$$\begin{equation} \frac{1}{\kappa _{R}}=\left(\int _{0}^{\infty }\frac{\partial B(\nu)}{\partial T}\frac{d\nu }{\kappa (\nu)}\right) \left(\int _{0}^{\infty }\frac{\partial B(\nu)}{\partial T}d\nu \right)^{-1}, \end{equation} \tag{ 4 }$$

where B(ν) is the intensity of radiation from a point in a stellar atmosphere, T is the temperature at that point, and κ(ν) is the opacity at a frequency ν. Regions of a stellar spectrum with large radiation intensity but low opacity contribute most to determining the Rosseland mean opacity. Weiner et al. (2003a) concluded that the mid-IR continuum opacity of a gas with solar atomic abundances under surface conditions present on red giant stars closely matches the Rosseland mean opacity of such a gas.

Molecular layers surrounding red giant stars have, however, been shown to significantly change the mid-IR opacity from that of a solar abundance atomic gas, while remaining relatively transparent in shorter wavelength IR bands (Weiner 2004; Perrin et al. 2004; Verhoelst et al. 2006; Woodruff et al. 2009). The Perrin et al. (2004) model for Betelgeuse, combining K-band visibility data and a 11.15 μm ISI visibility curve (Weiner et al. 2000), includes a shell with a K-band optical depth of 0.06 and a 11.15 μm optical depth of 2.33. Perrin et al. (2007) showed that this shell was composed of water, amorphous alumina dust, and SiO gas, and that the 11.15 μm opacity was dominated by alumina. The presence of alumina in a layer surrounding Betelgeuse, within 1.5 R_*, was suggested by Verhoelst et al. (2006) as the only dust species that could condense at the temperatures present in this region. Alumina dust grains forming close to stars possibly play a role as nucleation sites for dust species that condense at lower temperatures (e.g., Salpeter 1977).

Bremsstrahlung interactions between electrons and neutral hydrogen atoms also contribute to the mid-IR continuum opacity in red giant stars (Tatebe & Townes 2006). This emission mechanism was adduced by Reid & Menten (1997) to explain the variation with wavelength of the apparent sizes of the radio photospheres of long-period variables, and ascribed to Betelgeuse by Lim et al. (1998). We discuss this opacity model further in Section 3.4.

Prior work, the dramatic variations in apparent mid-IR diameters of Betelgeuse, and the low effective temperatures all provide clear motivation to model the new ISI observational results in terms of a photosphere and a molecular layer. Our method is similar to that of Perrin et al. (2007) in that we modeled a spherically symmetric layer surrounding an opaque stellar photosphere with an assumed diameter of 004371 and an assumed surface temperature of 3641 K (Perrin et al. 2004). Visibility and closure phase models for any observed point sources were subtracted from the data during each observation epoch in order to allow the model to be spherically symmetric. We did not attempt to fit an asymmetric layer because of the large number of free parameters involved. The free parameters of our model were: the temperature, T, of the layer; the optical depth, τ, of the layer along the line of sight to the center of the star; and, the outer radius, R, of the layer.

The layer was assumed to have uniform temperature and opacity, and was also assumed to have an inner radius that corresponds to the photospheric radius. Radiation within the ISI band was assumed to arise only from blackbody emission by the layer.

The modeling procedure involved fitting visibilities derived from a model image, created using a trial set of free parameters, to the measured visibilities. The measured visibilities for each epoch, and their errors, were scaled by the measurements of the measured power emitted by the UD surface of Betelgeuse. The flux density of a pixel in the model image grid was calculated as,

for z ⩽ R_*,

$$\begin{equation} I=S(\nu,T_{*})\Omega e^{-\alpha _{S} L(z)}+S(\nu,T)\Omega (1-e^{-\alpha _{S} L(z)}), \end{equation} \tag{ 5 }$$

and, for z > R_*,

$$\begin{equation} I=S(\nu,T)\Omega (1-e^{-2\alpha _{S} L(z)}). \end{equation} \tag{ 6 }$$

Here, L(z) describes the optical path length through the layer, α_S is the absorption coefficient, z is the radial distance of a pixel from the image center, Ω is the solid angle subtended by a single pixel, S(ν, T) is the specific intensity radiated by a blackbody of temperature T at frequency ν, and T_* = 3641 K is the assumed temperature of the photosphere. L(z) and α_S are given by

$$\begin{eqnarray} L(z)&=&\sqrt{R^{2}-z^{2}}-\sqrt{R_{*}^{2}-z^{2}},\quad z\le R_{*}\\ L(z)&=&\sqrt{R^{2}-z^{2}},\quad z> R_{*}\\ \alpha _{S}&=&\tau /(R-R_{*}). \end{eqnarray} \tag{ 7 }$$

The pixel size of the model images was 1.2 × 1.2 mas. For each iteration of the fit, a model image was generated and integrated along one dimension, and a one-dimensional Fourier transform was performed in order to generate a set of visibilities. Each model visibility was compared to measured visibilities that were closest to it (i.e., within ±0.5 SFU) in spatial frequency. A Levenberg–Marquardt fitting algorithm was employed to calculate the free parameter set that minimized the global χ².

The results of the fit for each observing epoch are given in Table 3. Errors for each parameter were calculated using the resulting covariance matrix. In order to confirm the validity of our analyses, we added the visibility and closure phase models of the point sources, which were earlier subtracted from the visibility data from each epoch, to the best-fit model visibilities. χ² values relating this sum to the original visibility data were calculated for each epoch, and were found to be comparable to the χ² values of the fits to UDs and point sources shown in Table 2.

The changes with time of the fitted layer temperatures and outer radii are similar to the changes with time in the effective stellar temperatures and the apparent UD radii, respectively. All our fitted layer radii and temperatures are roughly consistent with the 1.3−1.5 R_* (0057–0065 diameter) and 1500–2000 K layers modeled by most authors (Tsuji 2000a; Ohnaka 2004; Tsuji 2006; Verhoelst et al. 2006; Perrin et al. 2007). The values we calculate for the 11.15 μm optical depth of ∼1 are half of those resulting from the models of Perrin et al. (2004) and Perrin et al. (2007).

The lack of wideband mid-IR spectral information during our observing epochs limits modeling of molecular gas and dust species that contribute to the layer opacity. We are able, however, to investigate some basic physical characteristics of the layer using the opacity mechanism described by Tatebe & Townes (2006). This work showed that, for solar abundance gas at temperatures similar to those in red giant atmospheres, collision processes between neutral hydrogen atoms and free electrons dominate the mid-IR opacity. For temperatures of 2500 K to 3000 K, the primary sources of free electrons were found to be thermally ionized Na and Al. The abundances of H⁻, H₂, and H⁺ relative to H were found to be too low to contribute to the opacity through collisions with electrons, and photoionization and photodissociation processes were also found to be insignificant. The absorption coefficient due to electron–hydrogen-atom collisions, first derived by Dalgarno & Lane (1966), is given in simplified form as

$$\begin{equation} \alpha _{e}=\frac{k_{B}Tn_{e}n_{{\rm H}}A}{\nu ^{2}}, \end{equation} \tag{ 10 }$$

where n_e is the electron number density, n_H is the hydrogen-atom number density, and A is expressed as a third-order polynomial in T (Tatebe & Townes 2006). This opacity mechanism is used to explain the sizes of the radio photospheres of red giant stars (Reid & Menten 1997; Lim et al. 1998), at different wavelengths. For example, Lim et al. (1998) found that the radio photosphere of Betelgeuse appeared larger, yet cooler, for longer wavelengths.

We consider the implications of this mechanism dominating the mid-IR continuum opacity. Equation (10) can be used to calculate hydrogen-atom number densities from the fitted layer optical depths. The electron number densities were obtained from Table 2 of Tatebe & Townes (2006), which gives the fractional ionizations, relative to n_H, of various metals at different temperatures. We further used the hydrogen number densities to calculate the total layer mass, M_layer, for each epoch, using a distance of 197 ± 45 pc to Betelgeuse (Harper et al. 2008). Our results are given in Table 4.

We find masses for the layer of between 3 × 10⁻⁴ M_☉ and 6 × 10⁻⁴ M_☉. Our values for the hydrogen number density of between 3.5 × 10¹¹ cm⁻³ and 9 × 10¹¹ cm⁻³, using a hydrogen atomic mass of 1.67 × 10⁻²⁴ g, are equivalent to mass densities of ∼10⁻¹³ g cm⁻³. Such values are consistent with the hydrogen density derived for the Betelgeuse layer modeled by Perrin et al. (2007), where they derived their hydrogen density by assuming a ratio between the H₂O number density and the hydrogen number density of $n_{\rm H_{2}O}/n_{{\rm H}}\sim 10^{-7}$ (Jennings & Sada 1998) and using their calculated values of $n_{\rm H_{2}O}$ for the layer. Our values for the hydrogen density are therefore also consistent with the values for the water density derived by Perrin et al. (2007), though they result from very different methods of calculation.

Molecular layers directly surrounding the photospheres of red supergiant stars, and in particular Betelgeuse, have been modeled by a variety of authors under differing assumptions for the layer geometry and the dominant opacity source. A layer of water with a column density of 10²⁰ cm⁻² at a temperature of ∼1500 K was first suggested by Tsuji (2000a) for Betelgeuse, based on modeling of near-IR spectra. A combination of spectral and interferometric modeling by Ohnaka (2004), assuming a layer geometry identical to ours, suggested a layer temperature of 2050 K and an outer radius of 1.45 R_*, while modeling the mid-IR opacity as being dominated by a continuum of water emission and absorption lines. Under the assumption of a layer with a well-defined inner radius, Tsuji (2006) modeled a shell beyond 1.3 R_* with a temperature of 2250 K, again dominated by water opacity. More advanced spectral modeling by Verhoelst et al. (2006) revealed that water could not play a dominant role in determining the mid-IR continuum opacity, and instead suggested the presence of amorphous alumina in the molecular layer. This model was consolidated by Perrin et al. (2007) to suggest a shell between 1.32 R_* and 1.42 R_* at a temperature of 1520 K.

The properties we derive for a layer surrounding Betelgeuse, summarized in Table 3 for each observing epoch, are largely consistent with these results. We find temperatures that vary between 1900 K and 2800 K and outer radii that vary between 1.14 R_* and 1.36 R_*. Our modeling technique most closely matched that of Perrin et al. (2004) in assuming thermal continuum emission from the layer within our observing band. This assumption is justified by the featureless spectrum of Betelgeuse within, and around, our observing band and by the lack of any significant water lines within and surrounding our band (Weiner et al. 2003b). The results are consistent with previous models of the Betelgeuse layer.

A consistent picture of the composition of the layer has, however, not been achieved. While spectral modeling has uncovered the presence of numerous molecular species, including H₂O, CO, SiO, and possibly CN, as well as alumina dust (Tsuji 2006; Perrin et al. 2007; Kervella et al. 2009), the opacity of the layer as a function of wavelength is not yet fully determined. Our results for the optical depth of the layer of ∼1 at 11.15 μm wavelength are not in agreement with those of Perrin et al. (2004) and Perrin et al. (2007), who obtain optical depths of ∼2.

The number density of atomic hydrogen, based on the 11.15 μm opacity arising from electron–hydrogen-atom collisions, is ∼10¹¹ cm⁻³. This density, given the derived layer size, corresponds to H₂O column densities of 10¹⁹ cm⁻²; this result is consistent with H₂O column densities measured by Jennings & Sada (1998) and those derived from spectral modeling (e.g., Tsuji 2006). We therefore suggest that electron–hydrogen-atom collisions play a significant role in determining the mid-IR continuum opacity of the Betelgeuse layer, and that this mechanism must also be accounted for in models for the layer composition.

We have shown that the layer of material surrounding the photosphere of Betelgeuse has a non-uniform intensity distribution. A similar result was recently reported by Ohnaka et al. (2011) based on interferometric measurements of the one-dimensional intensity and velocity profile of CO gas in the inner atmosphere of Betelgeuse. Ohnaka et al. (2011) also reported a change in the one-dimensional CO intensity and velocity profile between two epochs spaced by a year. We find that the intensity distribution of the layer varies between each the five observing epochs we present, which are also spaced by approximately one year.

The non-uniformities that we observe in the layer reflect, on much smaller spatial scales, the non-uniformities observed in various components of the circumstellar environment of Betelgeuse. A gaseous component at similar temperatures to the Betelgeuse layer was shown to have an asymmetric intensity distribution by Lim et al. (1998). Our observations and those of Lim et al. (1998) could be linked by the opacities in both wavelength bands being partly caused by electron–hydrogen-atom collisions. The opacity due to this mechanism is proportional to ν⁻², implying that the observed stellar size decreases with shorter observing wavelengths. Material at chromospheric temperatures is also observed to be asymmetrically distributed (Hebden et al. 1987; Gilliland & Dupree 1996), and observations of a circumstellar envelope by Kervella et al. (2009) at near-IR wavelengths also reveal significant asymmetry. Asymmetry in the large-scale (∼1'') dust distribution surrounding Betelgeuse was also observed by Bloemhof et al. (1985).

Molecular layer models have been applied to the few red supergiant stars that have been observed with sufficient spatial resolution, such as μ Cephei (Perrin et al. 2005; Tsuji 2006) and α Herculis (Ohnaka 2004). Similar layers are identified around AGB stars (Weiner et al. 2003a; Ohnaka et al. 2005). The properties of individual red supergiant layers vary significantly from star to star, and a greater sample of measurements is required to understand what determines individual layer properties.

The processes by which red supergiant stars form and accelerate dust, while crucial to mass-loss scenarios, are little understood. Existing models of stellar atmospheres (e.g., Gustafsson et al. 2008; Plez 2010) cannot predict locations for dust condensation, and attempts to model dust acceleration through radiation pressure have also so far been unsuccessful (e.g., Woitke 2007). Our multi-epoch study of a layer directly surrounding Betelgeuse provides new insight into the processes involved in red supergiant mass loss.

We have shown that the basic properties of the layer, given in Table 3, exhibit striking variability from year to year. The layer is found to decrease in size and increase in optical depth over the years 2006–2008, and increase in size and decrease in optical depth between 2009 and 2010. The layer temperature does not show such systematic variability, although the largest layer size (in 2010) does correspond to the highest temperature. The variability in the apparent mid-IR size of Betelgeuse reported by Townes et al. (2009) can also be interpreted to indicate variations in the layers. Intriguingly, a similar phenomenon was reported by Pease (1922), who noted a decrease in the size of Betelgeuse at visible wavelengths followed by an increase.

Figure 5 shows measurements of the visual magnitude of Betelgeuse between 2006 and 2010, as well as the ISI measurements of the total 11.15 μm flux density (also listed in Table 1). The time spans of the ISI observing epochs are also plotted. The visual magnitude measurements were obtained from the online database² of the American Association of Variable Star Observers (AAVSO). The data, collected by a multitude of volunteer observers, were averaged over 30 day time spans; each time span with less than 10 measurements was discarded. The visual variability of Betelgeuse over our observing epochs was approximately 0.9 magnitudes. The visual intensity of Betelgeuse is not likely to represent that of the photosphere because the apparent stellar diameter at visible wavelengths is greater than that at near-IR wavelengths (Young et al. 2000). Also, using contemporaneous interferometric observations of Betelgeuse at different wavelengths, Young et al. (2000) found that hot spots evident in the visible were not present in the near-IR. Observations of Betelgeuse at visible wavelengths could represent regions within the layer observed at mid-IR wavelengths. It is interesting that the mid-IR flux density of Betelgeuse, as well as the effective temperatures plotted in Figure 3, and the visual magnitude appear somewhat correlated, particularly in their increase during the 2009 and 2010 epochs. Previous authors (Kiss et al. 2006) have concluded that the visual variability of Betelgeuse is probably indicative of quasi-periodic pulsations, and is too great to be explained by variations in the hot-spot distribution.

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The layer of material surrounding Betelgeuse is a candidate location for the onset of dust formation. A number of authors have identified the presence of alumina dust directly above the photosphere (Verhoelst et al. 2006; Perrin et al. 2007; Verhoelst et al. 2009). The derived physical parameters of the layer, such as the temperatures and hydrogen mass densities, are suitable for the formation of amorphous alumina (Woitke 2006; Dirks et al. 2008). While some aspects of the modeled variability of the layer might be due to variations in the photosphere, measurements of changes in the apparent mid-IR appearance of Betelgeuse must be largely caused by variations in the layer. If alumina contributes significantly to the mid-IR continuum opacity, these variations would represent variations in the dust content of the layer. Our estimates of changes in the mass of the layer, on the order of 10⁻⁴ M_☉ (see Table 4), might indicate evolution in the layer.

The point sources we observe in the layer of material surrounding Betelgeuse and their changes suggest that the layer dynamics are anisotropic. Asymmetries observed in the circumstellar environment of Betelgeuse are generally linked to the presence of giant convection cells on the stellar surface. Such convection cells are thought to shape the circumstellar environment of Betelgeuse by elevating cool photospheric material (Lim et al. 1998) and driving large-scale chromospheric motions (Gilliland & Dupree 1996). Our results indicate that giant convection cells have a significant role in shaping the Betelgeuse layer. This is because the mechanism that elevates the layer material above the photosphere is clearly anisotropic. The large intensities of the observed point-source components imply the action of large-scale photospheric features, and their variability between observing epochs demonstrates the transient nature of the cause of the point sources. Changes in the distribution of convection cells on the photosphere of Betelgeuse could also influence the overall layer properties. While the nature of the non-uniform brightness distribution of the layer is yet to be determined, our observations represent evidence for the role of giant convection cells in shaping the inner atmosphere of Betelgeuse.

Observations of a sample of red supergiant stars with high spatial resolution and wide bandwidth, over multiple epochs, are necessary to form a general picture for the role of molecular layers in mass-loss processes. More detailed interferometric imaging of Betelgeuse at mid-IR wavelengths is also required to understand the true role of giant convection cells in shaping the layer. Simultaneous visible, near-IR, and mid-IR interferometry could also provide interesting information on correspondences between different regions of the layer. Interferometric studies with both high spatial resolution and high spectral resolution are planned for the ISI (Wishnow et al. 2010), and have been performed at near-IR wavelengths by Ohnaka et al. (2009) and Ohnaka et al. (2011). Such investigations are aimed at revealing the molecular compositions, kinematic structures, and true extents of red supergiant layers. More detailed modeling of layer opacities is also required, taking into account contributions from molecular absorption and emission, dust, and electron–hydrogen-atom collisions. Upcoming optical and infrared interferometer systems, such as the Magdalena Ridge Observatory Interferometer and the MATISSE instrument at the Very Large Telescope Interferometer, as well as high spatial resolution observations with the next generation of extremely large telescopes, could finally clarify our understanding of red supergiant mass loss.