Infrared Properties of Asymptotic Giant Branch Stars in Our Galaxy and the Magellanic Clouds

Data from IRAS and AKARI have been very useful for studying AGB stars in our Galaxy (e.g., Suh & Kwon 2011; Suh 2018). Though they were also useful for studying AGB stars in the Magellanic Clouds (e.g., Jones et al. 2014), the number of cross-identified objects was very limited because of the relatively large beam sizes and weak sensitivities.

Fluxes at the J (1.25 μm), H (1.65 μm), and K (2.16 μm) bands were provided by 2MASS (Cutri et al. 2003). The field-of-view (FOV) pixel size of the 2MASS image is 2''. The WISE (Wright et al. 2010) mapped the sky at 3.4, 4.6, 12, and 22 μm. For the four WISE bands (W1, W2, W3, and W4), the FOV pixel sizes are 275, 275, 275, and 55, and the 5σ photometric sensitivities are 0.068, 0.098, 0.86, and 5.4 mJy.¹ The WISE data have been useful for studying AGB stars in our Galaxy (e.g., Suh 2018), and they would also be useful for studying AGB stars in the Magellanic Clouds.

The Spitzer Space Telescope (Gehrz et al. 2007) had Infrared Array Camera (IRAC; 3.6, 4.5, 5.8, and 8.0 μm) and Multiband Imaging Photometer (MIPS; 24, 70, and 160 μm) bands. For the four IRAC bands, the 5σ photometric sensitivities are 1.3, 2.7, 18, and 22 μJy with an FOV pixel size of 12. For the MIPS band at 24 μm, the 5σ photometric sensitivity is 110 μJy, and the FOV pixel size is 25.

Table 2 lists the IR bands used in this work. For each band, the reference wavelength (λ_ref) and zero-magnitude flux (ZMF) value, which are useful to obtain theoretical model colors (see Section 4.2), are also shown.

In this work, we use only good-quality observational data at all wavelength bands for the 2MASS and WISE photometric data (quality A for 2MASS; quality A or B for WISE). For the Spitzer photometric data, we use all of the available data because we use the SAGE catalogs with high reliability, which were extracted from the full list by placing strict restrictions on the source quality (see Sections 2.2 and 2.3).

A catalog of AGB stars for 3003 O-AGB and 1168 C-AGB objects in our Galaxy was presented by Suh & Kwon (2011). Suh & Hong (2017) presented a revised list of 3828 O-AGB and 1168 C-AGB stars based on the IRAS point-source catalog (PSC). The classification was based on IR and optical spectroscopy, IR photometry, and maser observations (see Suh & Kwon 2011; Suh & Hong 2017). The sample of 4996 Galactic AGB stars is composed of Mira variables (O-AGB: 1444; C-AGB: 292), semiregular variables (SRVs; O-AGB: 167; C-AGB: 178), and other types according to the American Association of Variable Star Observers (AAVSO) international variable star index (VSX; Watson et al. 2019). Among the 3828 O-AGB stars, 1520 objects are known to be OH/IR stars (see Section 2.5), of which 271 objects are known to be Miras according to the AAVSO. Note that most of the Galactic AGB stars with thick dust envelopes are not listed in the AAVSO catalog, which is mainly based on optical observations.

Because IRAS has a large beam size, it is tricky to find appropriate 2MASS, WISE, or Spitzer counterparts using the IRAS PSC position (see Suh 2018). We find the AKARI PSC, 2MASS, and WISE counterparts as described in Suh (2018), which considered the beam sizes and compared the fluxes. To find the Spitzer IRAC and MIPS counterparts, we use the same method that was used for finding the WISE counterpart (Suh 2018). We make cross-identifications of the Spitzer point sources by using the "A 24 and 70 Micron Survey of the Inner Galactic Disk with MIPS" (MIPSGAL) catalog, which provides the Spitzer photometric data for 933,818 sources in our Galaxy. Table 1 lists the sample AGB stars in our Galaxy and number of cross-matched 2MASS, WISE, and Spitzer counterparts.

The upper panel of Figure 1 shows the comparison of the IRAS [25] (25 μm) flux with the Spitzer S5[24] (24 μm) flux for AGB stars in our Galaxy. For the Spitzer counterparts, the Spitzer fluxes drop abnormally compared with other measurements at nearby wavelengths. This would be mainly because of the saturation effect of the Spitzer data for the bright Galactic AGB stars. There is a similar effect for the WISE data for AGB stars in our Galaxy, but it is known to be minor for a considerable portion of them (see Suh 2018). When we remove the objects with very large decreases in Spitzer S5[24] flux from the IRAS [25] flux (more than 2.5 mag; see Figure 1), more reliable data points with small deviations (see Table 1) can be distinguishable. The lower panel of Figure 1 shows the comparison of the WISE W2[4.6] flux with the Spitzer S3[5.8] flux for AGB stars in our Galaxy, which shows the saturation effect only for bright objects at W2[4.6]. We also show the objects with small deviations in the Spitzer S5[24] flux.

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The OGLE projects detected many LPVs in the Magellanic Clouds. The fourth part of the OGLE-III Catalog of Variable Stars (OIII-CVS) presents 91,995 LPVs in the LMC (Soszyński et al. 2009). The sample is composed of 1663 Mira variables, 11,132 SRVs, and 79,200 small-amplitude red giants (OSARGs). We use the 46,467 AGB candidate objects (1663 Miras, 11,132 SRVs, and 33,672 bright OSARGs) as the sample AGB stars in the LMC-OGLE3 catalog. There are 37,203 O-AGB and 9264 C-AGB objects, which are classified based on their color selection method using the photometric data at the optical and NIR bands, in the LMC-OGLE3 sample.

The 13th part of the OIII-CVS contains 19,384 LPVs detected in the SMC (Soszyński et al. 2011). They are composed of 352 Miras, 2222 SRVs, and 16,810 OSARGs. We use the 5272 AGB candidate objects (352 Miras, 2222 SRVs, and 2698 bright OSARGs) as the sample AGB stars in the SMC-OGLE3 catalog. There are 2511 O-AGB and 2761 C-AGB objects, which are classified based on their color selection method using the photometric data at the optical and NIR bands, in the SMC-OGLE3 sample.

The LMC and SMC were imaged as a part of the SAGE program (Meixner et al. 2006). The SAGE program has provided a complete infrared survey of the evolved star population in the LMC and SMC. The Spitzer IRS (λ = 5.2–38 μm) has taken high-resolution spectra for many AGB stars in the LMC and SMC.

Analyzing the Spitzer data of the SAGE program, Riebel et al. (2012) presented a list of 33,503 candidate objects for AGB stars in the LMC. They classified them into 26,210 O-AGB and 7293 C-AGB objects based on the comparison of the photometric data at the NIR and MIR bands with their Grid of AGB and RSG ModelS (GRAMS). By analyzing the IRS spectral data in the SAGE program, Jones et al. (2017) identified and classified many AGB stars, from which 34 objects were new AGB stars compared with the list of Riebel et al. (2012). Therefore, the total number of sample AGB stars in the LMC is 33,537 (O-AGB: 26,231; C-AGB: 7306).

Analyzing the data of the SAGE program for the SMC, Srinivasan et al. (2016) presented a list of 9621 candidate objects for evolved stars. Based on the selection criteria presented by Boyer et al. (2011), they classified them into 2485 O-AGB, 1714 C-AGB, 1198 anomalous-AGB, 341 extreme-AGB, and other objects. When we compare the list with the new classification by Kraemer et al. (2017), which presented a list of evolved stars in the SMC by analyzing the Spitzer IRS spectral data, we find that four objects in the list of Srinivasan et al. (2016) are newly classified as AGB stars. When we select the AGB stars in the list, we have 5742 AGB stars in the SMC that are classified as 3624 O-AGB and 2118 C-AGB based on the GRAMS chemical classification.

Sloan et al. (2016) presented a list of 184 C-AGB stars (LMC: 144; SMC: 40) by analyzing the SAGE IRS data. When we combine the lists from Sloan et al. (2016), Jones et al. (2017), and Kraemer et al. (2017), there are 77 O-AGB and 151 C-AGB stars in the LMC and five O-AGB and 40 C-AGB stars in the SMC that are identified from the SAGE IRS data. These SAGE IRS (SAGE-S) sample stars that are identified by the IRS spectra would be a more reliable sample of AGB stars in the LMC and SMC.

Table 1 lists the sample AGB stars in the LMC and SMC. Note that all of the objects in the LMC-SAGE-S and SMC-SAGE-S samples are already included in the LMC-SAGE and SMC-SAGE samples.

For SAGE sample objects in the LMC and SMC, we make cross-identifications of the sources in the OGLE3 catalogs by finding the nearest sources within 5''. From the 33,537 LMC-SAGE AGB sample objects, 22,327 objects (67%) are duplicated with the LMC-OGLE3 sample (1522 Miras, 9534 SRVs, and 11,271 OSARGs). Though the chemical classification methods for the two samples (OGLE3 and SAGE) are different (see Section 2.3), 19,082 objects (85%) from the duplicated 22,327 objects are classified as the same class (O-AGB or C-AGB). From the 5742 SMC-SAGE AGB sample objects, 4837 objects (84%) are duplicated with the SMC-OGLE3 sample (341 Miras, 2036 SRVs, and 2460 OSARGs).

For all OGLE3 and SAGE sample objects in the LMC and SMC, we make cross-identifications of the sources in the 2MASS and WISE PSC catalogs by finding the nearest sources within 5''. For WISE data, multiple sample objects may have the same cross-matched WISE point source. So we have checked all of the duplicated cross-matches and selected only one nearest sample object for the one WISE point source. Figure 2 shows the number distributions of the cross-match angular distances for OGLE3 and SAGE sample objects in the LMC to the 2MASS and WISE point sources.

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For the LMC-OGLE3 objects, we make cross-identifications of the Spitzer point sources by using the SAGE Winter 2008 IRAC Epoch 1 and Epoch 2 Catalog and SAGE Winter 2008 MIPS 24 μm Epoch 1 and Epoch 2 Catalog by finding the nearest source within 5''. For the SMC-OGLE3 objects, we make cross-identifications of Spitzer photometric data by using the SAGE-SMC IRAC Epoch 0, Epoch 1, and Epoch 2 Catalog and SAGE-SMC MIPS 24 μm Epoch 0, Epoch 1, and Epoch 2 Catalog by finding the nearest source within 5''. These SAGE catalogs were extracted from the full list by placing strict restrictions on the source quality.

For the SAGE sample objects in the LMC and SMC, we use the Spitzer photometric data given in the references (Riebel et al. 2012; Srinivasan et al. 2016), which are from the SAGE Mosaic Photometry Archive. The original SAGE survey was conducted in two epochs spaced about 3 months apart (Meixner et al. 2006), and the observations from these epochs were combined into the single mosaic photometry archive, which is deeper and has smaller photometric errors.

Therefore, the Spitzer colors for the same object in the OGLE3 and SAGE samples can be slightly different because different catalogs were used (see the IR 2CDs in Figures 7–9). Table 1 lists the sample AGB stars in the LMC and SMC and the number of cross-matched counterparts.

Figure 3 shows the comparison of the fluxes (in mag) at the Spitzer and WISE bands for the cross-identified AGB stars in the LMC (OGLE3 and SAGE samples). The overall comparison is fairly consistent for most objects. Compared with OGLE3, there are less observed data at the NIR bands, but there are more observed data at the MIR bands in the SAGE sample. This could be due to the different identification method for the SAGE sample (see Section 2.3), which would identify more optically invisible AGB stars with thick dust shells. The larger scatters at the S5[24] band for dimmer C-AGB stars would be due to the Mg_0.9Fe_0.1S dust feature at 28 μm (see Section 4.1).

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The OH/IR stars are generally considered to be more massive O-AGB stars with thicker dust envelopes and higher mass-loss rates. Chen et al. (2001) presented a list 1065 OH/IR stars in our Galaxy. The list has been corrected and updated (Suh & Kwon 2011; Kwon & Suh 2012; Suh & Hong 2017), and a new list of 1520 OH/IR stars is included in the list of 3828 O-AGB stars in our Galaxy (Suh & Hong 2017). On the IR 2CDs in Figures 4 and 5, the data for those Galactic OH/IR stars are also plotted.

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Only a small number of OH/IR stars have been identified in the LMC and SMC. Goldman et al. (2017) presented a list of 10 positively identified OH/IR stars in the LMC. All 10 OH/IR objects are included in the LMC-SAGE sample (see Table 1), and six objects from them are in the LMC-OGLE3 sample (Soszyński et al. 2009) classified as Miras.

There is no clear identification of OH/IR stars in the SMC yet (Goldman et al. 2018). Goldman et al. (2018) suspected that, compared with the OH/IR stars in the Galaxy and the LMC, the lower metallicity and star formation rate in the SMC may curtail the last dusty stellar wind phase of the most massive O-AGB stars (see Section 1).

We use the radiative transfer code DUSTY (Ivezić & Elitzur 1997) for a spherically symmetric dust shell. For all models, we use a continuous power-law (ρ ∝ r⁻²) dust density distribution. We assume that the dust formation temperature (T_c) is 1000 K. But for LMOA stars, we also use 500 and 300 K, because it is known that LMOA stars have lower T_c (e.g., Suh 2004). The inner radius of the dust shell is set by the T_c, and the outer radius of the dust shell is taken to be 10⁴ times the inner radius. The radii of spherical dust grains are assumed to be 0.1 μm uniformly. We use 10 μm as the fiducial wavelength of the dust optical depth (τ₁₀). Because the shape of the model SED is independent of the luminosity of the central star when all other parameters are fixed, the DUSTY code calculates the model SED only in relative scale.

For O-AGB stars, we use the optical constants of warm and cold silicate dust from Suh (1999). We compute 11 models (τ₁₀ = 0.001, 0.01, 0.05, 0.1, 0.5, 1, 3, 7, 15, 30, and 40) with T_c = 1000 K. We use warm silicate for LMOA stars (seven models with τ₁₀ ≤ 3) and cold silicate for HMOA stars (four models with τ₁₀ > 3). We assume that the stellar blackbody temperature is 3000 K for τ₁₀ ≤ 0.1 (four models), 2500 K for 0.1 < τ₁₀ ≤ 3 (three models), and 2000 K for τ₁₀ > 3 (four models). Figure 10 shows model SEDs for O-AGB stars (silicate; T_c = 1000 K) for six major dust optical depths.

We also use lower T_c (500 and 300 K) only for LMOA stars with thin dust shells (the four models with τ₁₀ ≤ 0.1). Also, alumina and Fe-Mg oxide grains, as well as silicates, are necessary to reproduce the observed SEDs (see Section 1). We use three different dust opacity models: a simple mixture of warm silicate and Fe_0.9Mg_0.1O (20% by number), a simple mixture of warm silicate and alumina (20% by number), and pure warm silicate. For Fe_0.9Mg_0.1O dust, we use the optical constants from Henning et al. (1995). For alumina dust, we use the optical constants from Suh (2016), which were derived from the optical constants in the narrower wavelength range obtained by Begemann et al. (1997).

For C-AGB stars, we use the optical constants of AMC and SiC dust grains from Suh (2000) and Pégourié (1988), respectively. For MgS dust, we use the optical constants of Mg_0.9Fe_0.1S dust, which is close to pure MgS, from Begemann et al. (1994). We compute eight models (τ₁₀ = 0.001, 0.01, 0.1, 0.5, 1, 2, 3, and 5) with T_c = 1000 K. We assume that the stellar blackbody temperature is 2500 K for τ₁₀ < 1 (four models) and 2000 K for τ₁₀ ≥ 1 (four models). We use three different dust opacity models: a simple mixture of AMC and Mg_0.9Fe_0.1S (20% by number), a simple mixture of AMC and SiC (10% by number), and pure AMC.

Figure 11 shows model SEDs for AGB stars (T_c = 1000 K) for major dust optical depths. For the O-AGB models, silicate dust features at 10 and 18 μm are shown for various dust optical depths (τ₁₀). For the LMOA stars, Al₂O₃ and Fe_0.9Mg_0.1O dust grains produce broad emission features at 11.8 and 19.6 μm, respectively (see Suh 2018). For the C-AGB models, SiC dust features at 11.3 μm and Mg_0.9Fe_0.1S dust features at 28 μm are shown for different dust optical depths.

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The gas-to-dust ratio (Ψ) is generally estimated to be 50–200 in our Galaxy (the average Ψ is about 100), and Ψ tends to decrease for a higher metallicity (Draine et al. 2007). Nanni et al. (2019) found that Ψ is larger in the Magellanic Clouds (Ψ ∼ 700), probably due to the lower metallicity. The optical depths of the dust shells around AGB stars would be dependent on the initial masses and metallicity (e.g., Ventura et al. 2016). In a galaxy with a higher metallicity (and a lower Ψ), the star formation in the higher mass range would be more active, and the galaxy would have a higher ratio of AGB stars with thick dust shells.

If we assume that the stellar blackbody luminosity is 10⁴ L_⊙, Ψ = 100, and the dust shell expansion velocity is 15 km s⁻¹, the mass-loss rates are 3.8 × 10⁻⁷, 7.1 × 10⁻⁶, and 6.5 × 10⁻⁵ M_⊙ yr⁻¹ for LMOA stars (T_c = 1000 K; τ₁₀ = 0.1), C-AGB stars with τ₁₀ = 1, and HMOA stars with τ₁₀ = 15, respectively.

To compare theoretical models with observations on 2CDs, we need to obtain model colors from the model SEDs. We obtain the model colors using the reference (or effective or isophotal) wavelength and ZMF given in the reference for the 2MASS, WISE, and Spitzer photometric data (see Table 2).

The color index is defined by

$$\begin{eqnarray}&&{M}_{\lambda 1}-{M}_{\lambda 2}=-2.5{\mathrm{log}}_{10}\displaystyle \frac{{F}_{\lambda 1}/{\mathrm{ZMF}}_{\lambda 1}}{{F}_{\lambda 2}/{\mathrm{ZMF}}_{\lambda 2}},\end{eqnarray} \tag{ 1 }$$

where ZMF_λi is the ZMF at a given wavelength (λi; see Table 2).

The reference wavelength for the W3[12] band largely affects the model colors for O-AGB stars because the wavelength is very near the conspicuous 10 μm silicate features of the model SEDs (see Figure 10). For the WISE W3[12] band, the isophotal wavelength is 11.56 μm (Jarrett et al. 2011), and the response function weighted average wavelength is 12.33 μm. The isophotal wavelength (11.56 μm) for the W3[12] band, which was obtained from the observations of Vega (Jarrett et al. 2011), could be too short for dusty AGB stars.

The theoretical model for O-AGB stars used in this work reproduced various spectral and photometric observations of O-AGB stars (e.g., Suh 2002; Suh 2004; González-Lópezlira 2018) in wide wavelength ranges reasonably well. However, the same model produced model colors that show very large deviations from the observed colors of O-AGB stars in our Galaxy (Suh 2018) and the Magellanic Clouds (this work) when we use λ_ref = 11.56 μm for the W3[12] band.

For the WISE W3[12] band, we use the reference wavelength of 12 μm and ZMF of 28.3 Jy (the same values as those for the IRAS [12] band; Beichman et al. 1988) to obtain the theoretical model colors (see Table 2).

Figure 12 shows IR 2CDs using two different reference wavelengths for the W3[12] band compared with the observations of AGB stars in our Galaxy. This small change makes a large difference for the O-AGB model colors. Though the SiC dust feature at 11.3 μm is also affected, the effect is minor for C-AGB models without SiC dust (see Figure 11). With this choice (λ_ref = 12 μm for the W3[12] band), the model colors fit the observed colors much better on all IR 2CDs for AGB stars in our Galaxy and the Magellanic Clouds (see Figures 3–8).

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The theoretical dust shell model used in this work does not consider gas-phase radiation processes (see Section 4). The AGB stars show various gas-phase emission or absorption features in the NIR and MIR bands due to circumstellar molecules such as H₂O, CO, and C₂H₂ (e.g., Lançon & Wood 2000; Le Bertre et al. 2005; Gonneau et al. 2016). The deviations of the theoretical models from the observations would be larger at the wavelength bands where gas-phase radiation processes are more active.

Also, the spherically symmetric dust shell model does not consider nonspherical dust envelopes. The observed colors of AGB stars with nonspherical dust envelopes can show various deviations from the theoretical models at the NIR and MIR bands.

We may compare the number distribution of observed IR colors with the theoretical model. Figure 13 shows the number density distributions of the four observed IR colors for AGB stars in our Galaxy and the Magellanic Clouds. The four IR colors (W2[4.6]–W3[12], K[2.2]–W3[12], S2[4.5]–S4[8.0], and S3[5.8]–S5[24]) are good measures of the dust optical depth (τ₁₀), as we can see on the IR 2CDs (see Figures 4–9).

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We mark the theoretical model colors in Figure 13. For the O-AGB stars, the dust shell (silicate; T_c = 1000 K) model colors for typical LMOA (τ₁₀ = 0.1) and HMOA (τ₁₀ = 7 and 15) stars are indicated. For the C-AGB stars, the dust shell (AMC; T_c = 1000 K) model colors for the thin (τ₁₀ = 0.1) and thick (τ₁₀ = 1) dust shell model colors are indicated. See Section 4.1 for the detailed model parameters.

We may also obtain the percentages of the objects with thin or thick dust shells using the information presented in Figure 13. Table 3 lists the percentages of the objects with thin (O-AGB: τ₁₀ < 0.1; C-AGB: τ₁₀ < 0.1), thick (O-AGB: τ₁₀ > 7; C-AGB: τ₁₀ > 1), and very thick (O-AGB: τ₁₀ > 15) dust shells from the comparison of the observed colors with the theoretical models for the seven IR colors: W2[4.6]–W3[12], K[2.2]–W3[12], S1[3.6]–S4[8.0], S2[4.5]–S4[8.0], S3[5.8]–S5[24], IRAS [12]–[25], and 2MASS–IRAS K–[12]. Though three colors (S1[3.6]–S4[8.0], IRAS [12]–[25], and 2MASS–IRAS K–[12]) were not used for the IR 2CDs presented in this paper, they are also good measures of the dust optical depth. The data for IRAS [12]–[25] and 2MASS–IRAS K–[12] colors are from Suh & Hong (2017), which presented IR properties of AGB stars in our Galaxy.

Table 4 lists the weighted averaged percentages of the objects with thick dust shells (O-AGB: τ₁₀ > 7; C-AGB: τ₁₀ > 1; O-AGB: τ₁₀ > 15) obtained from Table 3. For the AGB stars in our Galaxy, we obtain the weighted averaged percentages from the data for four IR colors: W2[4.6]–W3[12], K[2.2]–W3[12], IRAS [12]–[25], and 2MASS–IRAS K–[12]. We do not use Spitzer colors for our Galaxy because the sample number is small and they show large deviations.

For AGB stars in the Magellanic Clouds, we obtain the weighted averaged percentages from the data for four IR colors: W2[4.6]–W3[12], S1[3.6]–S4[8.0], S2[4.5]–S4[8.0], and S3[5.8]–S5[24]. We do not consider K[2.2]–W3[12] because it shows a "bluing effect" for the Magellanic Clouds (see Section 5.3). In obtaining the weighted averaged percentages for the objects in the Magellanic Clouds, the number of observed objects for SAGE-S samples is multiplied by 100 because the SAGE-S samples are more reliable than the SAGE samples.

Compared with our Galaxy, we find that the LMC and SMC are deficient in O-AGB stars with thick dust shells on any IR 2CDs. The weighted averaged percentages of HMOA stars with thick dust shells (τ₁₀ > 7) for our Galaxy (17.2%) are larger than the ones for the LMC (3.4%) and SMC (1.8%) SAGE sample stars (see Table 4). The percentages of HMOA stars with very thick dust shells (τ₁₀ > 15) for our Galaxy (7.0%) are even larger than the ones for the LMC (0.44%) and SMC (0.348%).

For C-AGB stars in our Galaxy and the LMC, the observations can be reproduced by the C-AGB models in wide ranges of the dust optical depth (τ₁₀ = 0.001–5) on all IR 2CDs except for the 2CD using the K[2.2]–W3[12] color, for which AGB stars in the LMC show the bluing effect (see Section 5.3). The weighted averaged percentages of C-AGB stars with thick dust shells (τ₁₀ > 1) for our Galaxy (17.1%) are larger than the ones for the LMC (9.4%) and SMC (1.3%) (see Table 4).

Compared with our Galaxy, we find that much larger portions of O-AGB stars in the LMC and SMC have thin dust shells with smaller dust optical depths (τ₁₀) on the IR 2CDs (see Figures 4–9 and histograms in Figure 13). The weighted averaged percentages of LMOA stars with thin dust shells (τ₁₀ < 0.1) for the LMC (79.5%) or SMC (82.7%) are much larger than the ones for our Galaxy (27.1%; see Table 4). This could be due to a selection effect. In our Galaxy, it is difficult to identify the optically visible AGB stars (with thin dust shells) using optical or NIR surveys because of the severe extinction by the Galactic disk. Note that the sample of Galactic AGB stars is based on the IRAS PSC (see Section 2.2).

Figure 4 shows WISE 2CDs using W3[12]–W4[22] versus W2[4.6]–W3[12]. The upper panel plots AGB stars in our Galaxy, and the lower panel plots AGB stars in the LMC.

For LMOA stars with thin dust shells in our Galaxy and the LMC, the silicate dust with a mixture of Al₂O₃ and Fe_0.9Mg_0.1O can explain wider regions on the IR 2CDs. Compared with our Galaxy, we find that LMOA stars in the LMC have more detached dust shells (T_c 300 K).

For O-AGB stars, the ratio of HMOA stars with thick dust shells (τ₁₀ > 7) for the LMC (SAGE-S: 5.3%; SAGE: 0.68%) is smaller than the one for our Galaxy (17.5%; see Table 3). Even for the most dusty O-AGB stars (or OH/IR stars) in the LMC, τ₁₀ would be about 1–7, which produces conspicuous emission or shallow self-absorption silicate features at 10 μm (see Figure 10; see Jones et al. 2017 for the Spitzer IRS spectra). On the other hand, τ₁₀ for many O-AGB stars in our Galaxy is about 10–40, which produces deep silicate absorption features at 10 μm (e.g., Suh 1999, 2004).

The C-AGB stars in our Galaxy and the LMC are located in the wide range of the C-AGB model colors (τ₁₀ = 0.001–5) on this 2CD. For C-AGB stars, the ratio of C-AGB stars with thick dust shells (τ₁₀ > 1) for the LMC (SAGE-S: 13.1%; SAGE: 0.6%) is comparable to the one for our Galaxy (12.0%; see Table 3). For C-AGB stars, the effect of the SiC dust feature (at 11.3 μm) on the W3[12]–W4[22] color is conspicuous, while the effect of the Mg_0.9Fe_0.1S dust feature (at 26 μm) is small.

The upper panel of Figure 6 shows the WISE 2CDs for AGB stars in the SMC. For C-AGB stars, the ratio of objects with thick dust shells (τ₁₀ > 1) for the SMC is 0%, which is much smaller than those for the LMC and our Galaxy (see Table 3).

Figure 5 shows WISE–2MASS 2CDs using W3[12]–W4[22] versus K[2.2]–W3[12]. The upper panel plots AGB stars in our Galaxy, and the lower panel plots AGB stars in the LMC.

Unlike the other three IR 2CDs (compare with Figures 4–9), we find that the observed K[2.2]–W3[12] colors on this WISE–2MASS 2CD are bluer than the theoretical model colors. Compared with other IR colors, the observed K[2.2]–W3[12] colors show smaller percentages of thick dust shells for both the O-AGB and C-AGB stars in our Galaxy and the LMC (see Table 3). The effect is much stronger for the AGB stars in the LMC than for those in our Galaxy. For the LMC-SAGE-S sample stars, the ratio of C-AGB stars with thick dust shells (τ₁₀ > 1) for the K[2.2]–W3[12] color (1.6%) is much smaller than that for other colors (13.1%–14.8%), and the ratio of O-AGB stars with thick dust shells (τ₁₀ > 7) for the K[2.2]–W3[12] color (0.0%) is also much smaller than that for other colors (5.3%–29.0%).

The cause of the bluing effect could be some gas-phase emission at the K[2.2] band due to circumstellar (or interstellar) molecules (e.g., CO) and/or inadequate dust opacity for the dust shell model. There have been some studies on the NIR spectra of AGB stars (e.g., Lançon & Wood 2000; Le Bertre et al. 2005), but it is not yet clear whether or not the AGB stars in our Galaxy and the LMC show similar NIR spectra at the K[2.2] band. Though it is not presented in a 2CD in this paper, we have found that the observed S1[3.6]–S4[8.0] color for the LMC does not show the bluing effect (see Table 3).

The lower panel of Figure 6 shows the WISE–2MASS 2CDs for AGB stars in the SMC. Compared with other IR colors, the observed K[2.2]–W3[12] colors show small percentages of AGB stars with thick dust shells in the SMC (see Table 3). But it is not clear whether or not the AGB stars in the SMC show the bluing effect because other IR colors also show small percentages of AGB stars with thick dust shells.

Figures 7 and 8 show Spitzer–WISE 2CDs. Figure 7 shows the 2CDs using S3[5.8]–S5[24] versus W2[4.6]–W3[12] for AGB stars in our Galaxy and the LMC. Figure 8 shows the Spitzer–WISE 2CDs using W3[12]–S5[24] versus S2[4.5]–S4[8.0] for AGB stars in our Galaxy and the LMC. The S5[24] band can be useful to investigate the Mg_0.9Fe_0.1S dust features around 26 μm (see Figure 11) for C-AGB stars.

The upper panels of Figures 7 and 8 show the two WISE–Spitzer 2CDs for our Galaxy, which are less meaningful than other 2CDs because the usable Spitzer data are available only for a minor portion of AGB stars in our Galaxy. For C-AGB stars, the sample number is too small to find any meaning. Though the sample number is small, the observed data points of Galactic O-AGB stars are located in the wide range of O-AGB model colors (τ₁₀ = 0.001–40) on the 2CDs.

The lower panels of Figures 7 and 8 show the two WISE–Spitzer 2CDs for the LMC. The observations of AGB stars in the LMC show similar properties on both 2CDs, though there are more scatters in the W3[12]–S5[24] color. This could be partly because the W3[12] and S5[24] fluxes are obtained at different pulsation phases.

For O-AGB stars, the ratio of HMOA stars with thick dust shells (τ₁₀ > 7) for the LMC (SAGE-S: 8.1%–29.0%; SAGE: 0.1%–0.2%) is smaller than the one for our Galaxy (13.8%–67.6%; see Table 3). Observations of C-AGB stars in the LMC-SAGE-S sample can be reproduced by wide ranges of C-AGB dust model colors (τ₁₀ = 0.001–5) using AMC, SiC, and Mg_0.9Fe_0.1S dust grains. For C-AGB stars, the effect of the Mg_0.9Fe_0.1S and SiC dust, which shows deviations from the pure AMC model, is more conspicuous on the 2CD using the W3[12]–S5[24] color (see Figure 8).

Figure 9 shows the two WISE–Spitzer 2CDs for AGB stars in the SMC. For C-AGB stars, the ratio of C-AGB stars with thick dust shells (τ₁₀ > 1) for the SMC (SAGE-S: 2.5%–2.7%; SAGE: 0.1%–0.2%) is smaller than the one for the LMC (SAGE-S: 13.3%–13.9%; SAGE: 0.6%; see Table 3).

For C-AGB stars, the SiC dust features at 11.3 μm and Mg_0.9Fe_0.1S dust features at 28 μm can be useful to compare the theoretical models with the observations (see the lower panel of Figure 10). For the SiC dust feature at 11.3 μm, the emission feature becomes stronger as τ₁₀ increases up to τ₁₀ = 0.1, then becomes a weaker emission feature, and then becomes an absorption feature for τ₁₀ > 1. On IR 2CDs, the observations of C-AGB stars show similar effects.

Figure 14 shows the strength of SiC and MgS line emission features in the Spitzer IRS spectra versus IR colors (W2[4.6]–W3[12] and S2[4.5]–S4[8.0]) for the C-AGB stars in the (LMC and SMC) SAGE-S samples. The plots in Figure 14 show similar effects: the strength become stronger as the color gets redder up to some point, then it becomes weaker.

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For C-AGB stars, the theoretical models using AMC dust with a mixture of SiC and Mg_0.9Fe_0.1S grains can reproduce the observations in much wider regions on any IR 2CDs (see Figures 4–9).

Figure 15 shows period–color relations. It shows K[2.2]–W3[12] and W2[4.6]–W3[12] colors versus pulsation periods for AGB stars in our Galaxy and the LMC. The left and right panels show the relation for AGB stars in our Galaxy and the LMC, respectively. Though there are large scatters, we find that Mira variables, among all types of variables, show a stronger relationship between IR colors and pulsation periods.

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During the AGB phase, the more evolved stars with longer pulsation periods would have thicker dust envelopes and redder IR colors. Compared with our Galaxy, we find that Mira variables in the LMC show larger coefficients of determination (R²) for both IR colors, which mean a higher strength of the relationship. This could be because most of the Galactic AGB stars with thick dust shells are not listed in the AAVSO catalog (see Section 2.2). The AAVSO catalog is mainly based on optical observations, which suffer severe extinctions due to the Galactic disk.

Compared with AGB stars in our Galaxy, it is easier to study the period–magnitude relations (PMRs) for the AGB stars in the Magellanic Clouds because they share similar distances. Among all types of pulsating variables, it is known that Mira variables show a stronger relationship between the IR fluxes and pulsation periods (e.g., Soszyński et al. 2009).

Figure 16 shows the relation for Miras in the LMC-SAGE sample at the NIR and MIR bands. Though the relation shows very large scatters at the 2MASS bands (J[1.2], H[1.7], and K[2.2]) and shorter wavelengths, the Miras show a strong linear relationship when the wavelength is longer than about 3 μm (W1[3.4], S2[4.5], and S3[5.8]). We find that Mira variables in the LMC show fairly large coefficients of determination (R² = 0.6–0.85) of the linear relationship at the wavelength bands in the range 3–24 μm.

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Figure 17 shows the PMRs at the NIR and MIR bands (W2[4.6], S4[8.0], and W3[12]) for SAGE AGB sample stars in the Magellanic Clouds that are identified as pulsating variables from OGLE3. The plots show objects of different variable types and chemical classifications. Again, we find that the Mira variables in the LMC and SMC show fairly strong linear relationships.

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Figure 18 shows the PMRs at longer-wavelength bands (W4[22] and S5[24]). In the two plots, low-brightness O-AGB stars are relatively deficient compared with the three plots at shorter wavelengths (see Figure 15). This would be because of the lower sensitivity of the detectors (W4[22]: 5.4 mJy, S5[24]: 0.11 mJy; see Section 2.1). Because of the even lower sensitivity, the W4[22] band cannot detect more low-brightness objects (dimmer than about 9.5 mag). Therefore, the upper panel is more deficient in low-brightness O-AGB stars (mostly OSARGs). We expect that there would be as many low-brightness O-AGB stars as those in Figure 18 if we had detectors with higher sensitivities.

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We may obtain the theoretical model magnitude at a given wavelength band from the model SED using the ZMF at the wavelength band (see Table 2). Because the shape of the model SED is independent of the luminosity of the central star when all other parameters are fixed, the DUSTY code (Ivezić & Elitzur 1997) calculates the model SED only in relative scale (see Section 4.1). To calculate the model SED in absolute scale for a given luminosity and distance, we use the RADMC-3D code² in conjunction with the DUSTY code. The RADMC-3D models using the same scheme as Suh & Kwon (2013a) and the same model parameters as the DUSTY model produce almost identical results.

We obtain the model magnitudes from the model SED in absolute scales for a given luminosity of the central star and distance. For the RADMC-3D models, we use the same model parameters as the DUSTY model used in this work (see Section 4.1), except for the luminosity of the central star. Table 5 lists the parameters for six models of typical AGB stars with various luminosities of the central star. Figure 19 shows the model SEDs for the six models for LMOA, C-AGB, and HMOA stars in absolute scales when we use the distance of the LMC. We assume that the distances of the LMC and SMC are 49.97 and 60.6 kpc, respectively.

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In Figures 17 and 18, the horizontal lines indicate the model magnitudes for the six different models for LMOA, C-AGB, and HMOA stars (see Table 5).

Figure 20 shows magnitude distributions at two MIR bands (W3[12] and S5[24]) for all AGB stars in the SAGE samples (LMC and SMC). We choose the two MIR bands (W3[12] and S5[24]) because they can be good measures of the luminosity for the objects with thick dust shells. The vertical lines indicate the model magnitudes for the six different models for LMOA, C-AGB, and HMOA stars (see Table 5).

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Table 6 lists the percentages of bright stars at the MIR bands. The weighted averaged percentages of bright O-AGB stars (brighter than model HM2) in the LMC and SMC are 1.76% and 0.07%, respectively. The weighted averaged percentages of bright C-AGB stars (brighter than model CA2) in the LMC and SMC are 8.33% and 0.97%, respectively.

Based on the magnitudes at the wavelength bands in the range 4–24 μm (see Figures 17–20), we may roughly divide the AGB stars in the LMC and SMC into three groups: (1) a large group of low-brightness O-AGB stars (LMOA stars), including most of the OSARGs; (2) a large group of intermediate-brightness C-AGB stars; and (3) a small group of bright O-AGB stars (HMOA stars), including OH/IR stars. See also Table 7.

We find that the LMC is deficient in the O-AGB stars that are bright at the MIR bands and the SMC is more deficient in those stars. Though it cannot be confirmed in this work because it requires distance information for the large sample of Galactic AGB stars, we expect that there would be abundant O-AGB stars that are bright at the MIR bands in our Galaxy. In our Galaxy, 1520 OH/IR stars are identified (see Section 2.5), of which many are known to be as bright as 3 × 10⁴ L_⊙ at maximum phases (e.g., Suh 2004; Suh & Kwon 2013a). We expect that there would be more bright O-AGB stars, including many extreme OH/IR stars in the third group, if we could make similar plots (see Figures 17–20) for AGB stars in our Galaxy.