Infrared Properties of Carbon Stars in Our Galaxy

We have compiled lists of known carbon stars in our Galaxy from both the literature and CDS SIMBAD astronomical database, as detailed in Tables 1 and 2. Table 1 comprises the sample stars with corresponding IRAS counterparts (CS_IC), while Table 2 lists stars without IRAS counterparts (CS_NI). The tables provide references and the numbers of selected objects for each subclass of carbon stars.

We present the sample of carbon stars in two parts: one (CS_IC) based on the IRAS source catalog for brighter or more isolated objects (Table 1), and the other (CS_NI) based on the AllWISE or Gaia DR3 source catalog for less bright objects or those in crowded regions (Table 2). While most CS_IC objects have AllWISE or Gaia DR3 counterparts, CS_NI objects lack IRAS counterparts.

For each carbon star outlined in Tables 1 and 2, we meticulously assigned specific subclasses by referencing pertinent literature and the CDS SIMBAD database. The subclasses include Ba or CH stars (Ba-CH_IC and Ba-CH_NI), dC stars (dC_NI; relevant only for non-IRAS objects), R-hot stars (RH_IC and RH_NI), J-type stars (J-type_IC and J-type_NI), R Coronae Borealis (RCB) stars (RCB_IC; considered only for IRAS objects), and CAGB stars (CAGB_IC and CAGB_NI). Ambiguous cases, where the carbon-rich nature was unclear due to conflicting information (e.g., certain C-type objects identified as OAGB stars), were omitted from the selection.

RCB variables, which are a class of hydrogen-deficient carbon (HdC) stars, are believed to be formed via the merger of two white dwarf stars. Some RCB stars were known to be CAGB stars or J-type carbon stars in previous studies.

While the IR color-selection method using a 2CD is beneficial for distinguishing between CAGB and OAGB stars (e.g., Suh & Hong 2017; Suh 2022), we acknowledge its potential unreliability for a significant proportion of AGB stars compared to spectroscopic or spectrophotometric methods. To enhance the reliability of our carbon star sample, we excluded objects solely classified based on the IR color-selection method without additional supporting evidence.

In this study, we have identified CAGB stars from a substantial sample of carbon stars spanning various subclasses (refer to Tables 1 and 2), leveraging information from diverse literature sources, the CDS SIMBAD database, and examining their IR properties through 2CDs, CMDs, and SEDs (refer to Sections 3 and 5).

The criteria for classifying CAGB stars can be summarized as follows: (1) they exhibit characteristics indicative of being carbon-rich stars from the spectroscopic information (see Section 2.4); (2) their IR properties (2CDs, CMDs, and SEDs) align with those of known CAGB stars; (3) their absolute magnitudes are brighter than −6 mag in the IR[12] or W3[12] bands (refer to Section 3); (4) there is no conclusive evidence of J-type or complex binary star characteristics; (5) Mira variables can be considered as AGB stars (refer to Section 7).

For all the sample stars, we carefully cross-identified available counterparts from IRAS, Akari, MSX, 2MASS, WISE, Gaia DR3, AAVSO (version 2023 December 12; Watson et al. 2022), and the CDS SIMBAD object database.

2MASS (Cutri et al. 2003) provided fluxes in the J (1.25 μm), H (1.65 μm), and K (2.16 μm) bands. WISE (Jarrett et al. 2011) mapped the sky in four bands (3.4, 4.6, 12, and 22 μm; W1, W2, W3, and W4). The field-of-view pixel sizes of the IRAS, MSX, AKARI PSC, AKARI Bright Source Catalog (BSC), 2MASS, and WISE images are 075 × (45–46), 183, 10'', 30'', 2'', and 275, respectively.

Table 3 lists IR bands used in this work for 2CDs and CMDs. For each band, the reference wavelength (λ_ref) and zero-magnitude flux (ZMF) value, which are useful for obtaining theoretical model colors (see Section 4) and SEDs, are also shown. For more detailed description of IR photometric data and ZMF, refer to Section 2.1 in Suh (2021).

In this work, we use only good-quality observational data in all wavelength bands for the photometric data (quality better than 1 for the IRAS, AKARI, and MSX data; quality better than U for the WISE data).

Given the low angular resolution of IRAS, utilizing AllWISE or 2MASS counterparts derived from the positions of cross-matched AKARI or MSX sources (which possess higher angular resolution, as discussed in Section 2.2) improves the reliability of the data (e.g., Suh 2021).

There are 245,889 sources in the IRAS PSC and 173,044 in the Faint Source Catalog (FSC). This study utilizes the combined source catalog of IRAS, as presented by Abrahamyan et al. (2015), consisting of 345,163 sources with 73,770 associated sources from the PSC and FSC. A correction is applied, acknowledging that IRAS PSC 17501-0333 is distinct from IRAS FSC F17499-0334 due to differing Akari PSC counterparts with distinct flux values. Consequently, a combined source catalog of 345,164 sources with 73,769 associated sources is employed.

In contrast to the approach taken by Abrahamyan et al. (2015), this study utilizes FSC data (position and flux) only for the 32,079 associated sources with FSC flux at 12 μm fainter than the average FSC flux. For the brighter 41,690 associated sources, PSC data are preferred, as they yield higher-quality data.

For all 345,164 IRAS sources, AKARI, MSX, AllWISE, 2MASS, OGLE4, Gaia DR3, and AAVSO counterparts are identified using the following method. The AKARI PSC, MSX, and AKARI BSC counterparts are cross-identified by selecting the nearest source within 60'', utilizing the position provided in the IRAS PSC or FSC. Subsequently, the AllWISE, 2MASS, Gaia DR3, and AAVSO counterparts are cross-identified using the best position among the available AKARI PSC, MSX, or AKARI BSC counterparts. The position of the IRAS source is employed only in cases where there is no AKARI or MSX counterpart. When a Gaia DR3 counterpart is present, the Gaia position can be used as the best position for the IRAS source.

Due to the substantial beam size of IRAS, some sources represent multiple objects. Notably, certain IRAS objects recognized as CAGB stars (e.g., IRAS 17209-3318 and 10151-6008) are now identified as multiple objects. These particular objects are excluded from the CS_IC list. The majority of these objects find inclusion in the CS_NI list, with consideration given to SIMBAD information and their counterparts in AKARI, WISE, and Gaia DR3. It is important to note that there are no duplicate objects in the CS_IC and CS_NI lists.

The SIMBAD astronomical database provides useful information on the optical and IR spectra for the sample stars. AAVSO (Watson et al. 2022) also provides spectroscopic information for a large proportion of sample stars.

In identifying important dust features for AGB stars, IRAS Low Resolution Spectrograph (LRS; λ = 8–22 μm) data are useful (Kwok et al. 1997). The class E (the 10 μm silicate feature in emission) and class A (the 10 μm silicate feature in absorption) objects are typically OAGB stars. Class C (the 11.3 μm SiC feature in emission) objects are generally carbon stars.

Among the 715 IRAS LRS sources identified as class C, 713 were initially categorized as CAGB stars by Suh (2022), with only two exceptions (IRAS 13136-4426: S-type star; IRAS 22306+5918: composite object). However, further examination reveals that 23 objects (9 J-type stars, 3 OAGB stars, 11 others) deviate from the CAGB classification, leaving a total of 690 confirmed CAGB stars.

Additionally, the ISO Short Wavelength Spectrometer (SWS: λ = 2.4–45.4 μm) data can be employed for analysis (see Section 5.1). The ISO SWS catalog by Sloan et al. (2003) encompasses high-resolution spectral data from 1271 observations.

Carbon stars exhibit diverse gas-phase emission or absorption features in the near-IR (NIR) and mid-IR (MIR) bands, attributable to circumstellar molecules such as C₂, CO, CN, HCN, and C₂H₂ (e.g., Lançon & Wood 2000). Identification of 139 cool carbon stars in the NIR spectrophotometric survey of the Infrared Telescope in Space was conducted by Le Bertre et al. (2005), based on the conspicuous presence of molecular absorption bands at 1.8, 3.1, and 3.8 μm. These objects were duly considered in the CAGB lists presented by Suh & Kwon (2011) and Suh (2022).

The Gaia DR3 LPV (Lebzelter et al. 2023) data provided the low-resolution Red Photometric (RP) spectra in visual wavelength bands to identify carbon stars for the 1,720,558 LPV candidates. Li et al. (2018) presented a catalog of 2651 carbon stars from the optical spectra of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). While these spectra in the visual bands may exhibit limitations for objects with thick dust envelopes or those experiencing significant extinction (e.g., Suh 2022), they remain valuable for identifying visual carbon stars within a substantial sample of observed objects.

Using Gaia RP spectral data for the LPV candidates, 30,023 objects can be classified as carbon stars (Suh 2022) using the selection criteria (7 < median_delta_wl_rp < 11 and G_BP < 19 mag) outlined in Section 2.4 of Lebzelter et al. (2023). Among these, 19,863 objects are located in our Galaxy. From these 19,863 objects, 4498 have IRAS counterparts and 15,365 do not. It is noteworthy that most of the 4498 objects with IRAS counterparts are already well known as carbon stars in various literature sources and SIMBAD. Among them, we identify 4132 objects as CAGB_IC objects.

The 15,365 objects without IRAS counterparts are considered candidate carbon stars identified from Gaia DR3 spectra (denoted as GC(all)_NI; refer to Table 2) without any additional evidence. From this group of 15,365 GC(all)_NI objects, we select candidates for CAGB stars (GC-CAGB_NI objects) based on their IR properties (refer to Section 3.6).

The recently obtained distance information (Bailer-Jones et al. 2021) and extinction data from Lallement et al. (2022), derived from Gaia DR3 data, play a crucial role in determining the absolute luminosity of a significant number of carbon stars in our Galaxy.

For the majority of carbon stars, distances derived from Gaia DR3 data are readily available. In instances where Gaia DR3 distances are absent, we turn to distances from SIMBAD (mainly obtained from Hipparcos) when accessible. In cases where such information is unavailable for CAGB stars, we determine the distance through a comparative analysis between the observed SED and the theoretical CAGB model SED, as elaborated in Section 5.3.

Having established the distance and position of each object, we obtained extinction values (A_V ) in the visual band from the data server provided by Lallement et al. (2022). Expanding our analysis, we can calculate extinction values in Gaia, 2MASS, and other bands, employing the optical-to-MIR extinction law presented by Wang & Chen (2019).

The obtained distance and extinction data are used in the construction of various IR 2CDs and CMDs, as detailed in Section 3. Note that the extinction data are applied to the colors and magnitudes using the K[2.2] band data for the IR 2CDs and CMDs presented in Section 3.

The upper panel of Figure 1 illustrates an IRAS 2CD using IR[25]−IR[60] versus IR[12]−IR[25]. We observe that the basic theoretical model tracks can provide a rough explanation for the observed points. This 2CD has been extensively utilized since van der Veen & Habing (1988; note that those authors did not perform zero-magnitude calibrations for their 2CD), who divided it into eight regions representing different classes of celestial bodies. Building on theoretical dust shell models for AGB stars and post-AGB stars, Suh (2015) presented potential evolutionary tracks from AGB stars to post-AGB stars and ultimately to planetary nebulae on this 2CD. In our work, we categorize this 2CD into four regions (from R1 to R4) to enhance the classification of carbon stars.

On the IRAS 2CD, CAGB stars trace a "C"-shaped curve, with visual CAGB stars and extrinsic carbon stars primarily located in the lower left region (R1) and extending to the right side (R2). IR CAGB stars, or infrared carbon stars, situated on the right side (R2), exhibit thicker dust envelopes with larger dust optical depths (see Section 1 for the evolution of CAGB stars). Among them, 51 visual-CAGB_IC objects are positioned in R1 and R4, while all 101 IR-CAGB_IC objects are in R2 (with only one object located in R4 requiring a complex model).

A group of stars in the upper left region (R4) comprises visual carbon stars, including the early phase of CAGB stars, which exhibit excessive flux at 60 μm due to remnants of an earlier phase when the stars were OAGB stars (see, e.g., Chan & Kwok 1990). Notably, the 12 objects requiring more complex models, such as detached or double shell models, are located in region R4 on the 2CD. This subset includes two visual-CAGB_IC (detached shell) objects and 10 CAGB_IC (double shell) objects (refer to Section 5.2).

Furthermore, the region R4 hosts various subclasses of extrinsic carbon stars, primarily binary stars, and some CAGB stars with intricate dust envelopes, potentially arising from binary interactions or the presence of substantial planets.

Most extrinsic carbon stars (Ba, CH, and RH stars) in regions R1 and R4 are not found in R2, while J-type extrinsic carbon stars that may exhibit CAGB-like nature are scattered across all regions (R1, R2, and R4). In particular, extrinsic carbon stars of Ba and CH types are notably concentrated in the far left region.

On the far right side (R3), where most post-AGB stars and planetary nebulae are distributed (e.g., Suh 2015), there are only three CAGB stars in our sample.

The lower panel of Figure 1 displays an IRAS–2MASS 2CD using IR[12]−IR[60] versus K[2.2]−IR[12]. Galactic extinction is taken into account for the K[2.2]−IR[12] color, as explained in Section 2.5. On this 2CD, the differentiation between OAGB and CAGB stars becomes more distinct. Visual carbon stars occupy the lower left region of this 2CD due to their relatively bluer K[2.2]−IR[12] colors than others. Specifically, extrinsic carbon stars of Ba and CH types are notably concentrated in the far left region.

Figure 2 shows 2CDs using W3[12]−W4[22] versus K[2.2]−W3[12]. Galactic extinction is taken into account for the K[2.2]−W3[12] color. The upper panel shows carbon stars with IRAS counterparts (CS_IC) while the lower panel shows those without (CS_NI). In general, the theoretical dust shell models for both OAGB and CAGB stars demonstrate a satisfactory ability to replicate the observed points on these IR 2CDs. Noticeable differences emerge between CS_IC and CS_NI objects. CS_IC objects, being more evolved and brighter in the MIR bands, exhibit much redder K[2.2]−W3[12] colors.

A distinctive group of CS_NI objects deviates from other carbon stars in the upper left region of the 2CD. These objects display bluer K[2.2]−W3[12] colors but redder W3[12]−W4[22] colors, and the reason for this phenomenon remains unclear. Given that many known extrinsic carbon stars (binary stars) are situated in this region, there could be a potential connection with the binary nature of extrinsic carbon stars, such as radiation from white dwarfs.

Figure 3 displays error-bar plots for W3[12]−W4[22] versus K[2.2]−W3[12] for all carbon stars. In this diagram, we present averaged colors and their errors (standard deviations) for all sample stars across various subclasses. We find that CS_NI objects consistently exhibit redder W3[12]−W4[22] colors for extrinsic carbon stars of Ba, CH, dC, and RH types.

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Out of the 4909 CAGB stars, 4132 (84%) can be classified as C-rich stars based on the Gaia DR3 spectra (see Section 2.4). However, when focusing on CAGB stars with thick dust shells (K[2.2]−W3[12] > 4), the percentage drops to 34%. Figure 4 shows histograms of the K[2.2]−W3[12] colors for CAGB stars (CAGB_IC objects) with thick dust shells. This affirms that the Gaia DR3 spectral data can be more effective for stars characterized by thinner dust shells.

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Utilizing the recently acquired distance (Bailer-Jones et al. 2021) and extinction data from Lallement et al. (2022), derived from the Gaia DR3 data, facilitates the determination of absolute magnitudes and unreddened colors across a broad spectrum (see Section 2.5). Leveraging this information for a significant number of carbon stars in our Galaxy, we present various CMDs that prove instrumental in distinguishing between CAGB (or intrinsic carbon) stars and extrinsic carbon stars.

Figure 5 displays CMDs using K[2.2]−IR[12] color and absolute magnitudes in K[2.2] and IR[12] bands for various subclasses of carbon stars with IRAS counterparts (CS_IC objects). Since objects with thicker dust shells exhibit redder K[2.2]−IR[12] colors, most CAGB stars are characterized by colors that are redder than those of extrinsic carbon stars. The distinction between CAGB stars and extrinsic carbon stars is apparent on these IR CMDs.

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Extrinsic carbon stars of subclasses Ba, CH, and RH are notably distinguishable from CAGB stars on these CMDs, displaying dimmer absolute magnitudes in the IR[12] and K[2.2] bands and bluer K[2.2]–W3[12] colors. However, J-type stars, representing another subclass of extrinsic carbon stars, demonstrate properties shared with both CAGB stars and other extrinsic carbon stars. Remarkably, we find that RCB stars exhibit very similar properties to CAGB stars, making it challenging to distinguish them on these CMDs.

The left panel of Figure 5 displays a CMD using K[2.2]−IR[12] color and magnitudes at K[2.2]. CAGB stars exhibit brighter absolute magnitudes at K[2.2] only in bluer K[2.2]−W3[12] color ranges, because more evolved CAGB stars with redder K[2.2]−IR[12] colors have thicker circumstellar dust shells. These dense dust shells absorb radiation at shorter wavelengths (e.g., K[2.2]) and emit at longer wavelengths.

The right panel of Figure 5 illustrates a CMD using K[2.2]−IR[12] color and magnitudes at IR[12]. CAGB stars exhibit brighter absolute magnitudes at IR[12] across all K[2.2]–W3[12] color ranges. We find that the absolute magnitudes at the IR[12] band are brighter than −6 for all CAGB stars.

Figure 6 presents CMDs utilizing K[2.2]−W3[12] and W3[12]−W4[22] colors, along with absolute magnitudes in K[2.2], W3[12], and W4[22] bands for various subclasses of carbon stars (CS_IC and CS_NI). The left panels display CMDs for CS_IC objects, which exhibit similar characteristics to those depicted in Figure 5, while the right panels feature CS_NI objects.

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In the upper four panels of Figure 6, CMDs are presented using the K[2.2]−W3[12] color. Given that objects with thicker dust shells manifest redder K[2.2]−W3[12] colors, the majority of CAGB stars exhibit colors that are redder than those of extrinsic carbon stars. More evolved CAGB stars exhibit redder K[2.2]−W3[12] colors but dimmer absolute magnitudes at K[2.2] due to their thicker circumstellar dust shells.

Notably, CAGB_IC objects are distributed across a wide range of K[2.2]−W3[12] colors, whereas CAGB_NI objects tend to concentrate in bluer K[2.2]−W3[12] colors. This distinction arises from the general trend of CAGB_IC objects being brighter or more evolved than CAGB_NI objects. Conversely, extrinsic carbon stars, whether CS_IC or CS_NI objects, tend to cluster in bluer K[2.2]−W3[12] colors and dimmer absolute magnitudes.

For all CAGB stars, we consistently observe absolute magnitudes in the W3[12] band that are brighter than −6, mirroring our findings in the case of the IR[12] band.

In the lower two panels of Figure 6, CMDs are shown using the W3[12]−W4[22] color and absolute magnitudes at W4[22]. For nearly all CAGB stars, the absolute magnitudes in the W4[22] band are brighter than −5. CS_IC objects are distributed across a limited range of W3[12]−W4[22] colors, while CS_NI objects are distributed across a much wider range into the bluer and redder spectrum. The reason for this phenomenon remains unclear (see Section 3.3).

The CMDs (see Figures 5 and 6) prove valuable in distinguishing CAGB (intrinsic carbon) stars from extrinsic carbon stars, particularly when comparing magnitudes in MIR bands (IR[12], W3[12], and W3[22]). We find that the absolute magnitudes in the IR[12] or W3[12] band are brighter than −6 for all CAGB stars. In contrast, extrinsic carbon stars of Ba, CH, dC, and RH types consistently exhibit dimmer magnitudes than CAGB stars in the MIR bands. J-type stars, constituting another subclass of extrinsic carbon stars, are distributed across a broader range of magnitudes, demonstrating properties that are shared with both CAGB stars and other extrinsic carbon stars.

Figure 7 displays error-bar plots for CMDs using W3[12] versus K[2.2]−W3[12] and W4[22] versus W3[12]−W4[22]. These diagrams present averaged colors and magnitudes and their errors (standard deviations) for all sample stars across various subclasses.

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Figure 8 presents histograms depicting the observed absolute magnitudes in W3[12] and W3[22] bands for different subclasses of carbon stars. The plots clearly delineate the distinction between CAGB stars and extrinsic carbon stars, with CAGB stars consistently brighter than −6 mag in the W3[12] band (−5 mag in the W4[22] band). Conversely, most Ba, CH, dC, and RH type extrinsic carbon stars exhibit dimmer magnitudes. Some J-type carbon stars are as faint as other extrinsic carbon stars, while others are as bright as CAGB stars.

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In contrast to typical extrinsic carbon stars, certain J-type carbon stars, such as IRAS 20166+3717 and IRAS 21566+5309, are recognized as Mira variables (AGB stars). This observation may be attributed to their binary nature, wherein one star is an AGB (not an RGB or a red dwarf) star, and the mass transfer process enhances the ¹³C content.

As discussed in Section 2.4, there are 15,365 candidate objects for carbon stars identified from Gaia DR3 spectra (denoted by GC(all)_NI; refer to Table 2) without any other evidence. We selected candidate objects for new CAGB stars when their absolute magnitudes in the W3[12] band are brighter than −6. There are 7470 candidate objects for new CAGB stars identified solely from Gaia DR3 spectra and absolute magnitudes (denoted by GC-CAGB_NI; see Table 2).

When selecting the 7470 GC-CAGB_NI objects, special considerations were given to Mira variables (597 Miras are identified through AAVSO). Among these 597 Miras, the absolute magnitudes at the W3[12] band were dimmer than −6.5 for 43 objects according to the Gaia DR3 distances. Since Miras can be considered as AGB stars, we calculated theoretical distances assuming that the absolute magnitudes in the W3[12] band are −6. We found that the Gaia DR3 distances were too small compared to the theoretical distances for the 43 objects. By using the mean distances from Gaia DR3 and theoretical distances, the absolute magnitudes for the 43 objects became brighter than −6. Therefore, we have used the mean distances for the 43 Mira variables.

From the sample of 4909 CAGB stars with IRAS counterparts (referred to as CAGB_IC objects; see Table 1), we have selected a subset comprising 152 relatively well-known CAGB objects (e.g., Suh 2000; Groenewegen et al. 2002; Chen & Yang 2012; Groenewegen 2022). Within this subset, encompassing 51 visual-CAGB_IC objects characterized by thin dust shells (τ₁₀ < 0.5) and 101 IR-CAGB_IC objects featuring thick dust shells (τ₁₀ ≥ 0.5), we have meticulously computed detailed theoretical model SEDs (see Section 4) that demonstrate a commendable ability to replicate the observations.

The photometric data utilized for this analysis encompass observations from IRAS, AKARI, MSX, 2MASS, WISE, and Gaia DR3. Submillimeter observational data from the James Clerk Maxwell Telescope (Groenewegen et al. 1993) are also incorporated where available. And IR spectral data from IRAS LRS (Kwok et al. 1997) and ISO SWS (Sloan et al. 2003) are used when accessible.

It is important to note that the theoretical dust shell model used in this work does not consider gas-phase radiation processes (see Section 4). Consequently, the CAGB model SEDs may not accurately reproduce observed SEDs in the visual and NIR bands in detail. In many cases, distinguishing whether the extinction (or emission) in the visual and NIR bands is of circumstellar or interstellar origin proves challenging. Therefore, Galactic extinction is not considered in SED plots.

Figures 9 and 10 showcase the SEDs for 16 selected objects from the CAGB star sample. These are juxtaposed with theoretical model SEDs arranged in ascending order of dust optical depths (τ₁₀). τ₁₀ is indicated in the lower right corner of the respective SED diagram. The theoretical models employ a simple mixture of AMC and SiC (20%–30% by mass) as well as pure AMC for dust (refer to Section 4). Specifically, Figure 7 displays SEDs of eight visual CAGB stars (chosen from 51 visual-CAGB_IC objects with τ₁₀ < 0.5). On the other hand, Figure 8 illustrates SEDs of eight IR CAGB stars (selected from 101 IR-CAGB_IC objects with τ₁₀ ≥ 0.5).

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For objects with available ISO SWS spectra (Sloan et al. 2003), the target dedicated time number is indicated in parenthesis next to each object's name. Moreover, for objects identified as Mira variables by AAVSO, it is explicitly mentioned that they are Miras, and the pulsation period is given in parenthesis.

For the 152 selected CAGB stars, a simple single dust shell model incorporating AMC and SiC dust effectively reproduces the observed SEDs for the majority of objects. However, some objects necessitate more complex models, such as detached or double shells, or nonspherical dust envelopes (refer to Section 5.2).

Among the 152 CAGB stars whose detailed SEDs are compared with theoretical models (see Section 5.1), 12 stars exhibit complex SEDs that may necessitate more sophisticated models, including detached or multiple shells or nonspherical dust envelopes.

Figure 11 showcases the SEDs for six objects selected from the aforementioned 12 stars, for which relatively simple detached or double dust shell models can provide a rough reproduction of the SEDs. In the top panels, for the two displayed objects, we employ detached (T_c = 130 K) silicate dust shells to reproduce the excessive emission at 30–200 μm. For the next four objects displayed in the middle and bottom panels, we utilize double shell models: AMC dust shell and detached (T_c = 80–116 K) silicate dust shell, replicating the excessive emission at 30–200 μm as well as in other wavelength bands. However, achieving a more detailed replication would necessitate more advanced models, such as those incorporating multiple nonspherical dust envelopes. Exploring such intricacies is beyond the scope of this work.

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In Section 3.1, we discussed visual carbon stars (objects in region R4 on the IRAS 2CD; see Figure 1) that exhibit excessive flux at 60 μm due to remnants from an earlier phase when the stars were OAGB stars. This suggests the existence of CAGB stars with detached silicate dust shells, which potentially do not display silicate dust features due to significant detachments. These objects may share characteristics with single-star-type silicate carbon stars that do exhibit silicate dust features (Kwon & Suh 2014), although it is worth noting that most known silicate carbon stars are believed to be binary systems.

When comparing the observed SED with the corresponding theoretical model SED for CAGB stars, we can determine the distance that best fits the observed SED. The theoretical distance for each object is indicated in the lower right corner of the respective SED diagrams in Figures 9–11. Subsequently, these theoretical distances can be compared with the observed distances obtained from Gaia DR3 (Bailer-Jones et al. 2021).

Out of 4909 CAGB_IC objects, distances for 4839 objects are available from observations (4834 from Gaia DR3 and five objects from Hipparcos), and distances for 152 objects are determined using theoretical model SEDs. Among the 152 objects with theoretical distances, 82 objects have both theoretical and observed distances (80 from Gaia and two from Hipparcos), while 70 objects have only the distance derived from model SEDs.

In Figure 12, a comparison is presented between distances obtained from observations and those obtained from theoretical model SEDs for the 82 objects with both sets of distances. The diagram reveals a notably strong correlation: the coefficients of determination (R²) is larger than 0.79, indicating the reliability of the theoretical models.

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Therefore, we employed the mean values of distances obtained from observations (Gaia DR3 or Hipparcos) and distances derived from model SEDs for the 82 objects possessing both sets of distances. For the remaining 70 objects lacking observed distances, we utilized the distances derived from model SEDs.

Out of the 2254 CAGB_NI objects, distances for all objects are accessible from Gaia DR3, and 117 Mira variables have been identified through AAVSO. Among these 117 Miras, the absolute magnitudes in the W3[12] band were found to be dimmer than −6 for three objects based on Gaia DR3 distances. Since Miras can be considered as AGB stars, we compared the observed SEDs with the CAGB model SEDs, despite their simplicity due to fewer observed points.

Our analysis revealed that Gaia DR3 distances for the three Miras were underestimated compared to the distances obtained from the CAGB model SEDs. Utilizing the mean values of distances from Gaia DR3 and theoretical model distances, the absolute magnitudes for the three Mira variables became brighter than −6. Consequently, we have chosen to use the mean distances for these three Mira variables.

Within the sample of 7163 CAGB stars (4909 CAGB_IC and 2254 CAGB_NI objects; see Section 2), 1154 Mira variables have been identified through AAVSO. Additionally, among the 7470 candidate objects for new CAGB stars, identified solely from Gaia DR3 spectra and absolute magnitudes (GC-CAGB_NI objects), 597 Miras have been identified through AAVSO.

The left panels of Figure 15 depict period–color relations for the Mira variables. The plot illustrates the K[2.2]–W3[12] color versus pulsation periods for CAGB stars. Despite noticeable scatter, a meaningful relationship between IR color and pulsation period is discernible among Mira variables.

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On the right panels of Figure 15, period–magnitude relations (PMRs) for the Mira variables are presented. The plot illustrates M (W3[12]) versus pulsation period for CAGB stars. The primary cause of the scatter appears to be uncertainties in distances.

In contrast to Miras in our Galaxy, those in the Magellanic Clouds exhibit robust linear-like PMRs with minimal scatter when the wavelength exceeds about 3 μm (Suh 2020). The study finds that Mira variables in the Magellanic Clouds demonstrate relatively large coefficients of determination (R² = 0.6–0.85) in the linear relationship across wavelength bands in the range 3–24 μm. This phenomenon is attributed to the objects being at similar distances and experiencing less extinction.

Suh (2021) investigated the variability of AGB stars in the W1[3.4] and W2[4.6] bands using WISE data. Additionally, Groenewegen (2022) studied the variation of a sample of AGB stars in our Galaxy and the Magellanic Clouds using WISE data. This paper further explores the variability of carbon stars with a new sample of stars and updated NEOWISE-R data.

Our focus is on all known extrinsic carbon stars (refer to Tables 1 and 2) and 7163 CAGB stars (CAGB_IC and CAGB_NI objects, excluding GC-AGB_NI objects). We investigate their variability in the W1[3.4] and W2[4.6] bands over the past 14 years. For this analysis, we use the AllWISE multiepoch photometry table acquired in 2009–2010 and the NEOWISE-R data (the 2023 data release), providing 18 epochs with two observations annually between 2014 and 2022.

Our analysis aims to identify Mira-like variations in the WISE light curves using a simple sinusoidal light-curve model. The Lomb–Scargle periodogram, a widely used statistical algorithm for detecting periodic signals (Zechmeister & Kürster 2009; VanderPlas 2018), is employed. The periodograms are computed using the AstroPy implementation. Additional details about the algorithm can be found in VanderPlas (2018) and Suh (2021).

For all the sample stars, we generated light curves using WISE data and produced Lomb–Scargle periodograms. As emphasized by Suh (2021), WISE data for a substantial proportion of AGB stars in our Galaxy, primarily bright stars, are either saturated or exhibit significant scatter, rendering variation parameters unreliable. To ensure robust results, we selected objects with over 200 observed points, R² larger than 0.6, and Lomb–Scargle power exceeding 0.6.

Only for 227 objects are pulsation parameters reliably obtained from WISE light curves. As anticipated, no extrinsic carbon stars exhibit Mira-like variations in the WISE light curves. All 227 objects are identified as CAGB stars, comprising 129 CAGB_IC objects and 98 CAGB_NI objects. Among these CAGB stars, 87 are recognized AAVSO Mira variables with identified periods; the remaining 140 objects are not identified as Mira variables by AAVSO.

In the left panels of Figure 16, we present PMRs for known Mira variables from AAVSO and the 227 objects with obtained pulsation periods from WISE data. PMRs derived from WISE light curves exhibit significantly larger scatter than those obtained from AAVSO data.

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The upper two panels of Figure 17 display Lomb–Scargle periodograms using OGLE4 light curves in the I (0.8 μm) band (Iwanek et al. 2022) and WISE light curves in the W2[4.6] band (this work) for two CAGB stars, namely Mira variables IRAS 18010–2626 and [M2003b] dj10, according to AAVSO. While the light curves in the I (0.8 μm) and W2[4.6] bands share similar characteristics, the W2[4.6] band shows a smaller amplitude. In contrast to the OGLE4 periodogram, the Lomb–Scargle periodogram from the WISE light curve exhibits multiple peaks with similar power values due to the regular interval of WISE data acquisition (every 6 months).

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Due to the existence of multiple peaks with similar Lomb–Scargle power values, the precise determination of periods using only WISE data is challenging. As emphasized by Suh (2021), secondary or tertiary periods might represent the true periodicity for specific objects, potentially overshadowing the primary period.

In the right panels of Figure 16, we again present the PMRs, but for those 227 objects based on WISE light curves, we prioritize secondary (or tertiary) periods for 44 objects (red symbols) that deviate significantly from the general trends of Miras. The revised PMRs based on WISE light curves display considerably less scatter. Out of the 227 CAGB stars with pulsation periods determined from WISE light curves, 140 objects (lime symbols) are not identified as Mira variables by AAVSO.

Figure 17 presents Lomb–Scargle periodograms for six selected CAGB stars from the group of 87 objects identified as Mira variables by AAVSO. The obtained pulsation periods from WISE data are similar to the periods from AAVSO.

Figure 18 showcases Lomb–Scargle periodograms for eight selected CAGB stars from the group of 140 objects not identified as Mira variables by AAVSO. It is important to note that for the last two objects, the secondary period was selected. These 140 objects could potentially be candidates for newly discovered Mira variables.

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