# Infrared properties of carbon stars in our Galaxy

Kyung-Won Suh Department of Astronomy and Space Science, Chungbuk National
University, Cheongju-City, 28644, Republic of Korea

###### Abstract

In this study, we explore the characteristics of carbon stars within our
Galaxy through a comprehensive analysis of observational data spanning visual
and infrared (IR) bands. Leveraging datasets from IRAS, ISO, Akari, MSX,
2MASS, WISE, Gaia DR3, AAVSO, and the SIMBAD object database, we conduct a
detailed comparison between the observational data and theoretical models. To
facilitate this comparison, we introduce various IR two-color diagrams (2CDs),
IR color-magnitude diagrams (CMDs), and spectral energy distributions (SEDs).
We find that the CMDs, which utilize the latest distance and extinction data
from Gaia DR3 for a substantial number of carbon stars, are very useful to
distinguish carbon-rich asymptotic giant branch (CAGB) stars from extrinsic
carbon stars that are not in the AGB phase. To enhance the accuracy of our
analysis, we employ theoretical radiative transfer models for dust shells
around CAGB stars. These theoretical dust shell models demonstrate a
commendable ability to approximate the observations of CAGB stars across
various SEDs, 2CDs, and CMDs. We present the infrared properties of known
pulsating variables and explore the infrared variability of the sample stars
by analyzing WISE photometric data spanning the last 14 yr. Additionally, we
present a novel catalog of CAGB stars, offering enhanced reliability and a
wealth of additional information.

Asymptotic giant branch stars (2100); Carbon stars (199); Circumstellar dust
(236); Long period variable stars (935); Infrared astronomy (786); Radiative
transfer (1335)

revtex4-1.clsrevtex4-2.cls

##  1 Introduction

The asymptotic giant branch (AGB) phase is divided into the early AGB (E-AGB)
and the thermally pulsing AGB (TP-AGB) phases (e.g., Iben & Renzini 1983).
Carbon-rich AGB (CAGB) stars are generally believed to be the evolutionary
successors of M-type oxygen-rich AGB (OAGB) stars that are in the E-AGB phase.
When the OAGB stars of intermediate mass range (1.55 $M_{\odot}$ $\leq$ M $<$
4 $M_{\odot}$: for solar metallicity) go through third dredge-up processes,
which occurs due to thermal pulses in the AGB phase, the C/O ratio can become
larger than one and thus O-rich dust formation ceases and the stars become
visual CAGB stars (Groenewegen et al. 1995), which are now CAGB stars in the
TP-AGB phase. After that phase, C-rich dust grains start forming and the stars
evolve into infrared carbon stars, which are CAGB stars with thick C-rich dust
envelopes and high mass-loss rates (e.g., Suh 2000). More evolved or massive
OAGB stars also undergo the TP-AGB phase. Almost all AGB stars are long-period
variables (LPVs) with large amplitude pulsations (e.g., Höfner & Olofsson
2018).

A carbon star is typically a CAGB star but there are other types of carbon
stars. Generally, a classical (or intrinsic or type C-N) carbon star is known
as a CAGB star. And there are non-classical or extrinsic carbon stars that are
not in the AGB phase: Barium (Ba) stars, CH (or C-H) stars, dwarf carbon (dC)
stars, J-type (or C-J) stars, and early R (R-hot or RH) type stars (e.g.,
Green 2013; Abia et al. 2020).

Extrinsic carbon stars of the Ba, CH, and dC types are hypothesized to be
binary systems, featuring one giant (or dwarf) star and another in the form of
a white dwarf. The white dwarf was once a CAGB star involved in a mass
transfer process, providing C-rich material (Lü 1991; Li et al. 2018; Abia et
al. 2022). While these stars exhibit carbon enhancement, the C/O ratio in the
envelope is not necessarily greater than one. CH stars, identified as
Population II stars, share similarities in evolutionary state, spectral
peculiarities, and orbital statistics with Ba stars. They are considered the
older, metal-poor analogs of the latter (Escorza et al. 2017).

The nature of J-type or R type extrinsic carbon stars are not yet clearly
known. Late R-type stars are known to be similar to CAGB stars (Zamora et al.
2009). On the other hand, early R-type (R-hot or RH) stars are believed to be
single stars that were merged from binary stars that consist of a red giant
and a white dwarf (Zhang & Jeffery 2013; Abia et al. 2020). The anomalous He-
flash after the red giant star’s merging has been suggested as a cause of the
carbon enhancement for the RH stars (Zhang & Jeffery 2013). J-type carbon
stars are suspected to represent a short and luminous stage in the evolution
of a R-hot star (Zhang & Jeffery 2013; Abia et al. 2020).

Various IR observational data are available from the Infrared Astronomical
Satellite (IRAS), Infrared Space Observatory (ISO), Midcourse Space Experiment
(MSX), AKARI, Two-Micron All-Sky Survey (2MASS), Wide-field Infrared Survey
Explorer (WISE). These data have been very useful to identify carbon stars and
understand the nature of them. Additionally, the Near-Earth Object WISE
Reactivation (NEOWISE-R) mission (Mainzer et al. 2014) has conducted
photometric observations at 3.4 and 4.6 $\mu$m since 2013.

Recently, the Gaia Data Release 3 (DR3) provided useful data at visual bands
for more than one billion stars (Rimoldini et al. 2023). The newly obtained
distance (Bailer-Jones et al. 2021) and extinction (e.g., Lallement et al.
2022) data derived from the Gaia DR3 data can be useful to find the absolute
luminosity for a large number of carbon stars in our Galaxy.

In this study, we explore the properties of carbon stars within our Galaxy. In
Section 2, we furnish lists of known carbon stars across various subclasses.
For the sample of carbon stars, we conduct cross-identifications with
counterparts from IRAS, AKARI, MSX, 2MASS, WISE, Gaia Data Release 3 (DR3),
and American Association of Variable Star Observers (AAVSO; international
variable star index; version 2023 December 12; Watson et al. 2023).

Section 3 presents diverse infrared two-color diagrams (2CDs) and color-
magnitude diagrams (CMDs) for distinct subclasses of carbon stars, juxtaposed
with theoretical models of CAGB stars. This comparison aims to unveil
potential differences in their infrared properties. Section 4 outlines the
theoretical radiative transfer models for dust shells enveloping CAGB stars.

In Section 5, we compare observed spectral energy distributions (SEDs) of CAGB
stars with theoretical models, exploring the properties of CAGB stars in
depth. Section 6 details the spatial distributions of carbon stars across
various subclasses throughout our Galaxy. In Section 7, we present the
infrared properties of known Mira variables among the CAGB stars and
investigate the infrared variability of all sample stars. This analysis is
carried out by scrutinizing WISE photometric data at the W1 and W2 bands
spanning the last 14 yr. In Section 8, we present a new catalog of CAGB stars.
Finally, Section 9 consolidates and summarizes the key findings and results of
this paper.

##  2 Carbon stars in our Galaxy

In this section, we compile lists of known carbon stars spanning various
subclasses, drawing from diverse literature sources and the Strasbourg
Astronomical Data Centre (CDS) SIMBAD astronomical database. For the recently
acquired sample of carbon stars, we perform cross-identifications with
counterparts from IRAS, AKARI, MSX, 2MASS, WISE, Gaia DR3, and AAVSO.

Suh (2022) presented a catalog of CAGB stars within our Galaxy, divided into
two parts: one based on the IRAS PSC (4118 objects) and the other on the
AllWISE source catalog (5366 objects). However, this catalog includes
(extrinsic) carbon stars not in the AGB phase (refer to Section 1) and objects
with uncertain chemistry. To enhance the catalog’s reliability, we utilize a
fresh sample of carbon stars in our Galaxy, discerning CAGB stars from other
subclasses of carbon stars. The inclusion of distance and extinction
information from the new Gaia DR3 data proves beneficial for this purpose.

Table 1: Sample of carbon stars (CS) with IRAS counterparts (CS_IC)

Subclass | Reference | Number | Selected | IRAS | Ba-CH_IC | RH_IC | J-type_IC | RCB_IC | CAGB_IC
---|---|---|---|---|---|---|---|---|---
CAGB-IRAS | Suh (2022) | 4118 | 4118 | 4118 | 4 | 3 | 78 | 35 | 3523a
CS | Alksnis et al. (2001) | 6891 | 6817b | 3799 | 6 | 4 | 98 | 26 | 3574
CAGB | Chen & Yang (2012) | 974 | 963c | 962 | 0 | 0 | 2 | 4 | 938
J-type | Chen et al. (2007) | 113 | 112d | 103 | 1 | 1 | 97 | 1 | 6
CS | Abia et al. (2022) | 827 | 818b | 574 | 0 | 5 | 78 | 0 | 292
CS | Li et al. (2018) | 2650 | 2624b | 349 | 0 | 0 | 13 | 1 | 328
Ba | Lü (1991) | 389 | 389 | 168 | 166 | 1 | 0 | 0 | 0
Ba (mostly) | Escorza et al. (2017) | 437 | 437 | 176 | 167 | 2 | 2 | 0 | 1
dC (mostly) | Green (2013) | 1211 | 1211 | 1 | 0 | 0 | 0 | 0 | 1
CS | SIMBAD CS | 21,743 | 7541e | 3641 | 0 | 4 | 95 | 5 | 3511
CS | Gaia DR3 CS | 30023f | 19863g | 4498 | 0 | 0 | 89 | 6 | 4132
Totalh | - | - | - | - | 181 | 5 | 100 | 39 | 4909

acolor-selected objects without any other evidences are excluded bsources of
duplicate SIMBAD identifers are excluded. cwrongly classified objects are
excluded. dIRAS 18006-3213 is an OH/IR star eCDS SIMBAD main type C* in our
Galaxy. fC-rich stars from Gaia DR3 spectra for LPVs (Lebzelter et al. 2023).
gobjects in our Galaxy. hduplicate objects are excluded.

Table 2: Sample of carbon stars (CS) without IRAS counterparts (CS_NI; AllWISE
or Gaia DR3 sources)

Subclass | Reference | Number | Selected | non-IRAS | Ba-CH_NI | dC_NI | RH_NI | J-type_NI | CAGB_NI
---|---|---|---|---|---|---|---|---|---
CAGB-WISE | Suh (2022) | 5366 | 2440a | 2440 | 24 | 2 | 28 | 69 | 1663
CS | Alksnis et al. (2001) | 6891 | 6817b | 3018 | 28 | 2 | 31 | 75 | 2022
CAGB | Chen & Yang (2012) | 974 | 963c | 1 | 0 | 0 | 0 | 0 | 1
J-type | Chen et al. (2007) | 113 | 112d | 9 | 0 | 0 | 0 | 8 | 0
CS | Abia et al. (2022) | 827 | 818b | 244 | 0 | 0 | 230 | 1 | 3
CS | Li et al. (2018) | 2650 | 2624b | 2275 | 1442 | 6 | 204 | 124 | 75
Ba | Lü (1991) | 389 | 389 | 221 | 221 | 0 | 0 | 0 | 0
Ba (mostly) | Escorza et al. (2017) | 437 | 437 | 261 | 244 | 0 | 1 | 0 | 0
dC (mostly) | Green (2013) | 1211 | 1211 | 1210 | 25 | 1086 | 0 | 2 | 2
CS | SIMBAD CS | 21,743 | 7541e | 3901 | 80 | 448 | 203 | 78 | 1789
CS | Gaia DR3 CS | 30023f | 19863g | 15365h | 2 | 2 | 0 | 66 | 1857 + (7470)i
Totalj | - | - | - | - | 1707 | 1087 | 230 | 131 | 2254 + (7470)i

acolor-selected objects without any other evidences are excluded bsources of
duplicate SIMBAD identifers are excluded. cwrongly classified objects are
excluded. dIRAS 18006-3213 is an OH/IR star. eCDS SIMBAD main type C* in our
Galaxy. fC-rich stars from Gaia DR3 spectra for LPVs (Lebzelter et al. 2023).
gobjects in our Galaxy. hdenoted by GC(all)_NI. icandidate objects for new
CAGB stars solely identified from Gaia DR3 spectra and absolute magnitudes
(denoted by GC-CAGB_NI; see Section 3.6). jduplicate objects are excluded.

###  2.1 Sample stars

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.

R Coronae Borealis (RCB) variables, which are a class of Hydrogen-deficient
Carbon (HdC) stars, are believed to be formed via the merger of two white
dwarf (WD) 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 at IR[12] or W3[12] (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 2023-12-12;
Watson et al. 2023), and the CDS SIMBAD object database.

###  2.2 Infrared Photometric Data

2MASS (Cutri et al., 2003) provided fluxes at J (1.25 $\mu$m), H (1.65
$\mu$m), and K (2.16 $\mu$m) bands. The WISE (Jarrett et al., 2011) mapped the
sky at four bands (3.4, 4.6, 12, and 22 $\mu$m; W1, W2, W3, and W4). The FOV
pixel sizes of the IRAS, MSX, AKARI PSC, AKARI BSC, 2MASS, and WISE images are
0$\farcm$75x(4$\farcm$5-4$\farcm$6), 18$\farcs$3, 10$\arcsec$, 30$\arcsec$,
2$\arcsec$, and 2$\farcs$75, respectively.

Table 3 list IR bands used in this work for 2CDs and CMDs. For each band, the
reference wavelength ($\lambda_{ref}$) and zero magnitude flux (ZMF) value,
which are useful to obtain theoretical models 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 at 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).

Table 3: IR bands and zero magnitude flux values

Band |  $\lambda_{ref}$ ($\mu$m) | ZMF (Jy) | Telescope | Reference
---|---|---|---|---
K[2.2] | 2.159 | 666.7 | 2MASS | Cohen et al. (2003)
W1[3.4] | 3.35 | 306.682 | WISE | Jarrett et al. (2011)
W2[4.6] | 4.60 | 170.663 | WISE | Jarrett et al. (2011)
IR[12] | 12 | 28.3 | IRAS | Beichman et al. (1988)
W3[12]a | 12 | 28.3 | WISE | Jarrett et al. (2011)
W4[22] | 22.08 | 8.284 | WISE | Jarrett et al. (2011)
IR[25] | 25 | 6.73 | IRAS | Beichman et al. (1988)
IR[60] | 60 | 1.19 | IRAS | Beichman et al. (1988)

aFor W3[12], we use a new reference wavelength and zero magnitude flux for
theoretical models (see section 4.2 in Suh 2020).

###  2.3 The IRAS Data

Given the considerably 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).

In the IRAS Point Source Catalog (PSC), there are 245,889 sources, and in the
Faint Source Catalog (FSC), there are 173,044 sources. 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 $\mu$m fainter than the average FSC flux. For the brighter
41,690 associated sources, PSC data is preferred, as it yields 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$\arcsec$, 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.

###  2.4 Spectroscopic data

The SIMBAD astronomical database provides useful information on the optical
and IR spectra for the sample stars. AAVSO (Watson et al. 2023) also provides
spectrocopic information for a major portion of sample stars.

In identifying important dust features for AGB stars, IRAS Low Resolution
Spectrograph (LRS; $\lambda$ = 8$-$22 $\mu$m) data are useful (Kwok et al.
1997). The class E (the 10 $\mu$m silicate feature in emission) and class A
(the 10 $\mu$m silicate feature in absorption) objects are typically OAGB
stars. Class C (the 11.3 $\mu$m 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: $\lambda$=2.4–45.4
$\mu$m) data can be employed for analysis (see Section 5.1). The ISO SWS
catalogue by Sloan et al. (2003) encompasses high-resolution spectral data
from 1271 observations.

Carbon stars exhibit diverse gas-phase emission or absorption features at the
NIR and MIR bands, attributable to circumstellar molecules like 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
(IRTS) 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 $\mu$m. 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 RP
spectra at 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 Spectroscopy
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 GBP $<$ 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).

Figure 1: IRAS-2MASS 2CDs for various subclasses of CS_IC objects (see Table
1) and special subgroups of CAGB stars (see Section 3) compared with
theoretical models (see Section 4). For CAGB models (AMC $T_{c}$ = 1000 K):
$\tau_{10}$ = 0.0001, 0.01, 0.1, 0.5, 1, 2, and 4 from left to right. For each
subclass, the number of objects is shown. The number in parentheses denotes
the number of the plotted objects on the 2CD with good-quality observed
colors. See Section 3.1.

Figure 2: WISE-2MASS 2CDs for CS_IC and CS_NI objects (see Tables 1 and 2)
compared with theoretical models (see Section 4). For CAGB models (AMC $T_{c}$
= 1000 K): $\tau_{10}$ = 0.0001, 0.01, 0.1, 0.5, 1, 2, and 4 from left to
right. For each subclass, the number of objects is shown. The number in
parentheses denotes the number of the plotted objects on the 2CD with good-
quality observed colors. See Section 3.3. Figure 3: Error bar plot of the
WISE-2MASS 2CD for all carbon stars (CS_IC and CS_NI objects; see Figure 4).
See Section 3.3. Figure 4: Histograms of the K[2.2]$-$W3[12] colors for CAGB
stars (CAGB_IC objects) with thick dust shells. CAGB stars that can be
classified as C-rich stars based on the Gaia DR3 spectra are compared with all
CAGB stars. See Section 3.3.

Figure 5: IRAS-2MASS CMDs for carbon stars with IRAS counterparts spanning
various subclasses (see Table 1). For CAGB models (AMC $T_{c}$ = 1000 K):
$\tau_{10}$ = 0.0001, 0.01, 0.1, 0.5, 1, 2, and 4 from left to right (see
Section 4). For each subclass, the number of objects is shown. The number in
parenthesis denotes the number of the plotted objects with good quality
observed data. See Section 3.4.

Figure 6: WISE-2MASS CMDs for carbon stars spanning various subclasses (see
Tables 1 and 2). For CAGB models (AMC $T_{c}$ = 1000 K): $\tau_{10}$ = 0.0001,
0.01, 0.1, 0.5, 1, 2, and 4 from left to right (see Section 4). For each
subclass, the number of objects is shown. The number in parenthesis denotes
the number of the plotted objects with good quality observed data. See Section
3.4.

###  2.5 Distances and Galactic extinction

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 ($A_{V}$) at the visual band from the data server provided
by Lallement et al. (2022). Expanding our analysis, we can calculate
extinction values at 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.

##  3 Infrared properties of carbon stars

In this section, we investigate IR properties of known carbon stars in our
Galaxy presented in Section 2. Using various observational data, we present
useful IR 2CDs and CMDs for the large sample of the carbon stars compared with
the theoretical models for CAGB stars (see Section 4) and distinguish CAGB
stars from other subclasses of carbon stars. Table 3 lists the IR bands used
for the IR 2CDs and CMDs presented in this work (see Section 2.2).

Although the photometric fluxes are less useful than a full SED, the large
number of observations at various wavelength bands can be used to form a 2CD,
which can be compared with theoretical models. IR 2CDs are useful to
statistically distinguish various properties of AGB stars and post-AGB stars
(e.g., Epchtein et al. 1990; Suh & Kwon 2011; Suh 2015).

Figures 1 and 2 show various IR 2CDs using different combinations of observed
IR colors for various subclasses of carbon stars (see Tables 1and 2). For
comparison, we also plot OAGB stars from Suh (2022). We juxtapose the
observations on the IR 2CDs with the theoretical dust shell models for CAGB
stars (refer to Section 4). Generally, the theoretical dust shell models for
both OAGB and CAGB stars demonstrate a commendable ability to reproduce the
observed points. However, certain objects deviate significantly from the
theoretical models. This discrepancy may arise from AGB stars with non-
spherical dust envelopes, which are not accurately represented by the
theoretical dust shell models. Additionally, the substantial effects on IR
colors caused by the large amplitude pulsations of AGB stars, along with
instances of thermal pulses (superwinds), may contribute to the observed
deviations.

Figures 5 and 6 show CMDs using IR bands. We find that the CMDs, which utilize
the latest distance and extinction data from Gaia DR3 for a substantial number
of carbon stars, are very useful to distinguish CAGB stars from extrinsic
carbon stars that are not in the AGB phase.

A specific subset of well-known 152 CAGB stars are notably highlighted on all
the 2CDs and CMDs, encompassing 51 visual-CAGB_IC objects and 101 IR-CAGB_IC
objects, for which detailed SEDs are compared with theoretical models (see
Section 5.1). Among the 152 CAGB stars, a simple single dust shell model
incorporating amorphous carbon (AMC) and SiC dust effectively reproduces the
observed SEDs for the majority of objects. However, certain objects require
more intricate models, such as detached or double shells, or non-spherical
dust envelopes (refer to Section 5.2). The twelve objects necessitating more
complex models, as indicated exclusively in Figure 1, consist of two visual-
CAGB_IC (detached shell) objects and ten CAGB_IC (double shell) objects.

###  3.1 The IRAS 2CD

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 the 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, exhibiting excessive flux at 60
$\mu$m due to remnants of an earlier phase when the stars were OAGB stars (see
e.g., Chan & Kwok 1990). Notably, the twelve 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
ten 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). Especially,
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 no carbon stars in our sample.

###  3.2 IRAS and 2MASS 2CDs

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 compared to others. Specifically, extrinsic
carbon stars of Ba and CH types are notably concentrated in the far-left
region.

###  3.3 WISE and 2MASS 2CDs

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 carbon stars without IRAS counterparts (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 at 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.

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 illustrates 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.

Figure 7: Error-bar plots of averaged colors and magnitudes for various
subclasses of carbon stars. For each subclass, the number of objects is shown.
The number in parenthesis denotes the number of the plotted objects with good
quality observed data. See Section 3.5.

Figure 8: Histograms of observed absolute magnitudes for various subclasses of
carbon stars. The vertical lines indicate theoretical magnitudes for CAGB
models CA1 and CA7 (see Table 4). See Section 3.5.

###  3.4 IR CMDs

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. 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. Galactic extinction is taken into account when determining the
K[2.2]$-$IR[12] and K[2.2]$-$IR[12] colors, as well as the absolute magnitude
at the K[2.2] band.

Figure 5 displays CMDs using K[2.2]$-$IR[12] color and absolute magnitudes at
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.

Extrinsic carbon stars of subclasses Ba, CH, and RH are notably
distinguishable from CAGB stars on these CMDs, displaying dimmer absolute
magnitudes at 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 at K[2.2], W3[12], and W4[22] bands for various
subclasses of carbon stars (CS_IC and CS_NI) objects. The left panels display
CMDs for CS_IC objects, exhibiting similar characteristics as depicted in
Figure 5, while the right panels feature CS_NI objects.

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 compared to 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 at 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 at the W4[22] band are brighter than -5. CS_IC objects are
distributed across a limited range 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).

###  3.5 Different subclasses of carbon stars

The CMDs (see Figures 5 and 6) prove valuable in distinguishing CAGB
(intrinsic carbon) stars from extrinsic carbon stars, particularly when
comparing magnitudes at MIR bands (IR[12], W3[12], and W3[22]). We find that
the absolute magnitudes at 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 at 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.

Figure 8 presents histograms depicting the observed absolute magnitudes at
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 at the W3[12] band
(-5 mag at 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.

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 a RGB or a red dwarf) star, and the mass
transfer process enhances the 13C content.

###  3.6 Carbon stars from Gaia DR3 spectra

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 at the W3[12] band are brighter than -6.
There are 7470 candidate objects for new CAGB stars solely identified 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 AGB
stars, we calculated theoretical distances assuming that the absolute
magnitudes at 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.

Table 4: Models for typical AGB stars

Model | Class | Dust1 | $\tau_{10}$ |  $T_{*}$ (K) |  $L_{*}(10^{3}L_{\odot}$)
---|---|---|---|---|---
LM1 | OAGB | silicate | 0.001 | 3000 | 1
LM2 | OAGB | silicate | 0.01 | 3000 | 2
LM3 | OAGB | silicate | 0.1 | 3000 | 3
CA1 | CAGB | AMC | 0.0001 | 3000 | 5
CA2 | CAGB | AMC | 0.01 | 2700 | 5
CA3 | CAGB | AMC | 0.1 | 2500 | 5
CA4 | CAGB | AMC | 0.5 | 2500 | 7
CA5 | CAGB | AMC | 1 | 2200 | 8
CA6 | CAGB | AMC | 2 | 2000 | 10
CA7 | CAGB | AMC | 4 | 2000 | 10
HM4 | OAGB | silicate | 7 | 2000 | 10
HM5 | OAGB | silicate | 15 | 2000 | 20
HM6 | OAGB | silicate | 30 | 2000 | 20

1See Section 4 for details. For all models, $T_{c}$ = 1000 K.

##  4 Theoretical Dust Shell Models

On all of the 2CDs and CMDs in Figures 1 through 8, theoretical models for AGB
stars are plotted to be compared with the observations. To compute theoretical
model SEDs for CAGB stars, we employ radiative transfer models for spherically
symmetric dust shells around central stars. The radiative transfer code
RADMC-3D (http://www.ita.uni-heidelberg.de/~dullemond/software/radmc-3d/),
following the same methodologies as utilized by Suh & Kwon (2013a), Suh
(2015), and Suh (2020), is employed. Refer to Suh (2020) for details about the
theoretical models and their limitations.

Table 4 details the parameters for seven models representing typical CAGB
stars and six models representing typical OAGB stars. We assume a continuous
power-law ($\rho\propto r^{-2}$) dust density distribution with a dust
formation temperature ($T_{c}$) of 1000 K. The inner radius of the dust shell
is determined by $T_{c}$, and the outer radius is set at the point where the
dust temperature reaches 30 K. Spherical dust grains with a uniform radius of
0.1 $\mu$m are assumed. The dust optical depth ($\tau_{10}$) is taken at 10
$\mu$m as the fiducial wavelength. We assume a stellar blackbody temperature
($T_{*}$) in the range of 2000-3000 K and a stellar luminosity ($L_{*}$) in
the range of 1x$10^{3}$ \- 2x$10^{4}$ $L_{\odot}$.

For OAGB stars, we use optical constants of warm and cold silicate dust from
Suh (1999). We use warm silicate for OAGB stars with thin dust shells (3
models with $\tau_{10}$ $\leq 3$) and cold silicate for OAGB stars with thick
dust shells (3 models $\tau_{10}$ $>3$).

For CAGB stars, the optical constants of amorphous carbon (AMC) and SiC dust
grains are sourced from Suh (2000) and Pégourié (1988), respectively.
Additionally, for MgS dust, we utilize the optical constants of Mg0.9Fe0.1S, a
composition close to pure MgS, as provided by Begemann et al. (1994). We adopt
three distinct dust opacity models: a simple mixture of AMC and Mg0.9Fe0.1S
(30% by mass), a simple mixture of AMC and SiC (30% by mass), and pure AMC.

##  5 CAGB stars in our Galaxy

We have selected CAGB stars from the sample of carbon stars spanning various
subclasses (see Section 3). In this section, we compare observed SEDs of the
CAGB stars with theoretical models (see Section 4), exploring the properties
of CAGB stars in depth.

Figure 9: Observed SEDs compared with simple dust shell models: eight visual
CAGB stars (visual-CAGB_IC). See Section 5.1.

Figure 10: Observed SEDs compared with simple dust shell models: eight IR CAGB
stars (IR-CAGB_IC). See Section 5.1.

Figure 11: Observed SEDs compared with more complex models (detached or double
dust shell models): two CAGB stars in upper panels with detached (O-rich) dust
shell models and other four CAGB stars with double (C-rich and O-rich) dust
shell models. See Section 5.2.

###  5.1 Model SEDs for CAGB stars

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 relatively
well known 152 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 ($\tau_{10}$ $<$ 0.5) and
101 IR-CAGB_IC objects featuring thick dust shells ($\tau_{10}$ $\geq$ 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. Sub-millimeter observational data
from JCMT (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
at visual and NIR bands in detail. In many cases, distinguishing whether the
extinction (or emission) at 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 sixteen selected objects from the CAGB
star sample. These are juxtaposed with theoretical model SEDs arranged in
ascending order of dust optical depths ($\tau_{10}$). $\tau_{10}$ 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
$\tau_{10}$ $<$ 0.5). On the other hand, Figure 8 illustrates SEDs of eight IR
CAGB stars (selected from 101 IR-CAGB_IC objects with $\tau_{10}$ $\geq$ 0.5).

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

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 non-spherical dust envelopes
(refer to Section 5.2).

###  5.2 Objects that show complex SEDs

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

Figure 11 showcases the SEDs for six objects selected from the aforementioned
twelve 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 $\mu$m. 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 $\mu$m as well as in other
wavelength bands. However, achieving a more detailed replication would
necessitate more advanced models, such as those incorporating multiple non-
spherical dust envelopes. Nevertheless, exploring such intricacies is beyond
the scope of this work.

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 $\mu$m 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, potentially
not displaying 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.

Figure 12: Comparison of distances obtained from observations (Gaia DR3 and
Hipparcos) and the ones obtained from theoretical model SEDs (See Section
5.3). Figure 13: Spacial distributions AGB stars (CAGB_IC and CAGB_NI) in
Galactic coordinate.

Figure 14: Distances from the Galactic plane for various subclasses of carbon
stares. (See Section 6).

###  5.3 Distances obtained from CAGB Model SEDs

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 through 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 5 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 2 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 ($R^{2}$) is larger than 0.79, indicating
the reliability of the theoretical models.

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 at the W3[12] band were found to be
dimmer than -6 for three objects based on Gaia DR3 distances. Since Miras can
be considered 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.

Figure 15: Period-Color and period-magnitude relations for Mira variables in
the CAGB sample. For each subclass, the number of objects is shown. The number
in parenthesis denotes the number of the plotted objects with good quality
observed data. See Section 7.1.

Figure 16: Period-magnitude relations for Mira variables and candidates for
Mira variable found from WISE data. See Sections 7.2 and 7.3.

##  6 Spacial distribution of carbon stars

Figure 13 illustrates the spatial distributions of carbon stars in Galactic
coordinates. Notably, we observe a higher concentration of CAGB stars toward
the Galactic plane compared to most extrinsic carbon stars (only CAGB stars,
CH stars, and dC stars are depicted in this diagram).

In Figure 14, the number distributions of Galactic latitudes and distances
from the Galactic plane are presented for various subclasses of carbon stars.
Mean values and standard deviations are provided alongside each subclass name.
Once again, our analysis reveals that CAGB stars exhibit a pronounced
concentration toward the Galactic plane compared to the majority of extrinsic
carbon stars.

As previously discussed in Section 1, CH stars are regarded as the older,
metal-poor analogs to Ba stars (Escorza et al. 2017). The histograms presented
in the lower panels of Figure 14 illustrate the distribution of distances from
the Galactic plane for both Ba stars and CH stars. It is evident that the
distances for CH stars are notably greater than those for Ba stars, providing
clear confirmation that CH stars indeed serve as older, metal-poor analogs to
Ba stars.

##  7 Infrared properties of pulsating variables

Most AGB stars are commonly considered to be LPVs featuring outer dust
envelopes (e.g., Suh 2021). LPVs are categorized into small-amplitude red
giants (SARGs), semiregular variables (SRVs), and Mira variables (e.g.,
Soszyński et al. 2013). While majority of SRVs and a significant proportion of
SARGs may also be in the AGB phase, it is established that all Mira variables
are in the AGB phase (e.g., Höfner & Olofsson 2018).

The consensus in the scientific community holds that more evolved (or more
massive) AGB stars tend to display larger pulsation amplitudes, longer
pulsation periods, and higher mass-loss rates (De Beck et al. 2010; Suh & Kwon
2013b; Groenewegen 2022).

###  7.1 Period-color and Period-magnitude relations

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, solely
identified 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 scatters, a meaningful relationship
between IR color and pulsation periods is discernible among Mira variables.

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
periods for CAGB stars. The primary cause of the scatters 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 scatters when the wavelength exceeds
about 3 $\mu$m (Suh 2020). The study finds that Mira variables in the
Magellanic clouds demonstrate relatively large coefficients of determination
($R^{2}$=0.6-0.85) in the linear relationship across wavelength bands in the
range of 3-24 $\mu$m. This phenomenon is attributed to the objects being at
similar distances and experiencing less extinctions.

Figure 17: Lomb-Scargle periodograms for six CAGB stars with known periods
(AAVSO Miras). The top panels display OGLE4 ($I$ band) light curves for two
selected CAGB stars. Subsequently, the following six panels present WISE light
curves for all six CAGB stars. The corresponding AAVSO periods for these six
CAGB stars are as follows: 413, 365, 1060, 445, 442, and 302 days. See
Sections 7.2 and 7.3.

Figure 18: Lomb-Scargle periodograms using WISE light curves for eight CAGB
stars with unknown periods (AAVSO). They could be candidates for new Mira
variables. Note that the secondary period was used for the last two objects.
See Section 7.3.

###  7.2 Finding IR variations of CAGB stars from WISE data

Suh (2021) investigated the variability of AGB stars at 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 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 at W1[3.4] and W2[4.6] bands over the past 14
yr. 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 portion of AGB stars in our Galaxy, primarily bright stars, are
either saturated or exhibit significant scatters, rendering variation
parameters unreliable. To ensure robust results, we selected objects with over
200 observed points, $R^{2}$ larger than 0.6, and Lomb-Scargle power exceeding
0.6.

Only for 227 objects, pulsation parameters are 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 scatters compared
to those obtained from AAVSO data.

The upper two panels of Figure 17 display Lomb-Scargle periodograms using
OGLE4 light curves at the $I$ (0.8 $\mu$m) band (Iwanek et al. 2022) and WISE
light curves at 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 at $I$ (0.8 $\mu$m) 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 six months).

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.

###  7.3 Candidates for new Mira variables found from WISE data

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) deviating significantly from the general
trends of Miras. The revised PMRs based on WISE light curves display
considerably fewer scatters. Out of the 227 CAGB stars with determined
pulsation periods 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.

##  8 A new catalog of CAGB stars in our Galaxy

In this study, we have assembled a novel sample of CAGB stars drawn from known
carbon stars, exploring various properties associated with them. We introduce
a new catalog comprising 7,163 CAGB stars (4909 CAGB_IC and 2254 CAGB_NI
objects; see Tables 1 and 2) in our Galaxy.

For the 4909 CAGB_IC objects (see Table 1), Table 5 lists the CAGB_IC number,
IRAS identifier, CDS SIMBAD main identifier, Gaia identifier, position (RA and
DEC; right ascension and declination J2000), source of the position (SP),
AllWISE identifier, variable type from AAVSO, period (in days) from AAVSO,
period (in days) from WISE data (see Section 7.2), distance in pc (dist_pc),
and source of the distance (SD). The sources of the position (SP) are
categorized into two groups: 1) G3: Gaia DR3 2) AP: Akari PSC.

For the 2254 CAGB_NI objects (see Table 2), Table 6 lists the CAGB_NI number,
CDS SIMBAD main identifier, Gaia identifier, position (RA and DEC; right
ascension and declination J2000 from Gaia DR3), AllWISE identifier, variable
type from AAVSO, period (in days) from AAVSO, period (in days) from WISE data
(see Section 7.2), distance in pc (dist_pc), and source of the distance (SD).

The source of the distance information (SD; see Section 5.3) in Tables 5 and 6
is categorized into five groups: 1) G: Gaia DR3 2) GS: Gaia DR3 and CAGB model
SED (mean value) 3) H: Hipparcos 4) HS: Hipparcos and CAGB model SED (mean
value) 5) S: CAGB model SED.

In Tables 5 and 6, only 21 rows of the catalogs are shown. The full catalogs
are available in machine-readable format.

Table 5: CAGB_IC objectsa (13 columns; 4909 rows)

No. | IRAS | SIMBAD_id | Gaia_id | RA | DEC |  SPb | AllWISE_id | A_Type | A_Period | WISE_period | dist_pc |  SDc
---|---|---|---|---|---|---|---|---|---|---|---|---
1 | 19118+1020 | IRAS 19118+1020 | DR3 4309357708491415552 | 288.54703101 | 10.43097188 | G3 | J191411.33+102551.5 |  |  |  | 3911.8 | G
2 | 21458+4539 | Case 662 | DR3 1974364515721462656 | 326.93394427 | 45.89813167 | G3 | J214744.15+455353.1 | SRA | 514.0 |  | 2101.7 | G
3 | 21458+5244 | [ABC90] cyc 27 | DR3 2173236138784903296 | 326.89962901 | 52.97894764 | G3 | J214735.90+525844.1 | SR | 386.0 |  | 5046.6 | G
4 | 00533+5503 | IRAS 00533+5503 | DR3 423450072786302208 | 14.05721350 | 55.33304974 | G3 | J005613.76+551958.9 | M | 344.5 |  | 8051.5 | G
5 | 00535+5923 | V* V721 Cas | DR3 426094260814792576 | 14.13762143 | 59.66223355 | G3 | J005633.03+593943.9 | M | 585.9 |  | 2769.3 | G
6 | 00538+6410 | V* V881 Cas | DR3 524221378626364160 | 14.23383979 | 64.45034263 | G3 | J005656.16+642701.2 | SR: |  |  | 5456.5 | G
7 | 00539+5621 | IRAS 00539+5621 | DR3 423994365404423040 | 14.22248683 | 56.62959076 | G3 | J005653.41+563746.1 | SR | 306.0 |  | 4954.7 | G
8 | 17552-2814 | PN H 1-45 | DR3 4062646712567004416 | 269.59108375 | -28.24784676 | G3 | J175821.90-281452.7 | ZAND+M | 416.2 |  | 1770.1 | G
9 | 13078-5828 | IRAS 13078-5828 | DR3 6062228557472426880 | 197.72661782 | -58.74670061 | G3 | J131054.41-584447.8 | M | 444.3 | 460.3 | 8262.7 | G
10 | 13078-6012 | IRAS 13078-6012 | DR3 6055840669782220544 | 197.75262618 | -60.47458390 | G3 | J131100.64-602828.2 | M | 433.9 |  | 8036.3 | G
11 | 06344-1656 | V* V368 CMa | DR3 2946796410619430144 | 99.16446215 | -16.99285239 | G3 | J063639.49-165934.1 | SRB | 194.0 |  | 4091.6 | G
12 | 06344-0124 | IRAS 06344-0124 |  | 99.25662000 | -1.45002000 | AP | J063701.62-012701.7 |  |  | 839.8 | 4000.0 | S
13 | 06347-1203 | IRC -10133 | DR3 2953571120234692736 | 99.26478306 | -12.09544908 | G3 | J063703.56-120543.5 | MISC | 160.0 |  | 1574.7 | G
14 | 06348+3114 | IRAS 06348+3114 | DR3 3435862859142788352 | 99.52239512 | 31.19535495 | G3 | J063805.33+311143.6 | L |  |  | 2212.8 | G
15 | 06349+2250 | C* 3277 | DR3 3379346655806590208 | 99.49454391 | 22.80064937 | G3 | J063758.71+224802.3 | LB | 172.5 |  | 3033.4 | G
16 | 20176-1458 | IRAS 20176-1458 | DR3 6875984878440208512 | 305.11527656 | -14.82426347 | G3 | J202027.67-144926.9 | SR | 354.0 | 374.2 | 13527.4 | GS
17 | 05185+0718 | LEE 18 | DR3 3241334169578902656 | 80.30572294 | 7.35537774 | G3 | J052113.38+072119.4 | SRB | 277.2 |  | 957.1 | G
18 | 05186+1551 | IRAS 05186+1551 | DR3 3394034241365927936 | 80.36858711 | 15.90941185 | G3 | J052128.46+155433.8 | M | 298.7 |  | 9326.0 | G
19 | 19122+1830 | Case 185 | DR3 4516021020719021440 | 288.60342816 | 18.59832942 | G3 |  | MISC | 215.0 |  | 2152.6 | G
20 | 19122+2318 | IRAS 19122+2318 | DR3 2022495667287340800 | 288.59025215 | 23.39755057 | G3 |  | SR | 176.0 |  | 2414.6 | G
21 | 21468+5747 | V* V493 Cep | DR3 2202334748365238144 | 327.10479972 | 58.01428062 | G3 | J214825.15+580051.2 | SRB | 390.0 |  | 6170.8 | G

aSee Table 1 and Section 8. The full catalog is available in machine-readable
format. bThe source of the position: 1) G3: Gaia DR3 2) AP: Akari PSC. cThe
source of the distance: 1) G: Gaia DR3 2) GS: Gaia DR3 and model SED (mean
value) 3) H: Hipparcos 4) HS: Hipparcos and CAGB model SED (mean value) 5) S:
model SED.

Table 6: CAGB_NI objectsa (11 columns; 2254 rows)

No. | SIMBAD_id | Gaia_id | RA | DEC | AllWISE_id | A_Type | A_Period | WISE_period | dist_pc |  SDb
---|---|---|---|---|---|---|---|---|---|---
1 | Kiso C1-38 | DR3 432154116070047232 | 0.37424664 | 64.91885902 | J000129.81+645507.8 | SR | 253.6 |  | 8629.5 | G
2 | [TI98] 0000+3021 | DR3 2861332746177405696 | 0.75359455 | 30.63984305 | J000300.86+303823.4 | M | 253.2 |  | 11740.0 | G
3 | NIKC 1-28 | DR3 423280885436848128 | 0.92486743 | 59.73694096 | J000341.96+594413.0 | M | 259.0 | 246.3 | 4809.5 | G
4 | Kiso C1-46 | DR3 432237129193547392 | 1.43538322 | 65.51587342 | J000544.48+653057.1 | SR | 121.6 |  | 4350.8 | G
5 | Kiso C1-47 | DR3 423227524761428480 | 1.43800744 | 59.49667112 | J000545.12+592948.0 | SR | 274.4 |  | 5385.3 | G
6 | CGCS 11 | DR3 432115255205278208 | 2.29989983 | 65.02399643 | J000911.97+650126.3 |  |  |  | 6730.9 | G
7 | Kiso C1-53 | DR3 431355664475998976 | 2.89769938 | 63.30855466 | J001135.45+631830.8 | SR | 310.7 |  | 5892.5 | G
8 | [I81] C 3 | DR3 429650768615042560 | 3.01956677 | 61.54713277 | J001204.70+613249.6 | SR | 192.3 |  | 5332.3 | G
9 | [I81] C 5 | DR3 431338617735738240 | 3.31931379 | 63.03340946 | J001316.63+630200.3 | SR | 255.5 |  | 5554.2 | G
10 | BC 110 | DR3 528876019357498112 | 3.44344370 | 68.29170688 | J001346.40+681730.2 | SR: | 130.0 |  | 4655.8 | G
11 | [I81] C 4 | DR3 429556004454036480 | 3.62955399 | 60.92529709 | J001431.09+605531.0 | SR | 152.9 |  | 8384.2 | G
12 | [I81] M 67 | DR3 429135887932964992 | 3.77838467 | 60.14894424 | J001506.82+600856.1 | LPV | 278.0 |  | 5998.7 | G
13 | Kiso C1-65 | DR3 431374871565656320 | 4.46342775 | 63.06836065 | J001751.22+630406.1 | SR | 103.9 |  | 6861.2 | G
14 | CGCS 38 | DR3 430469973497669632 | 5.02739175 | 61.98879143 | J002006.57+615919.6 | SR | 209.4 |  | 8237.9 | G
15 | Kiso C1-70 | DR3 431035294271577088 | 5.50380093 | 63.49398185 | J002200.91+632938.3 |  |  |  | 4568.3 | G
16 | Kiso C1-75 | DR3 430400498104743808 | 6.02907819 | 61.70314714 | J002406.97+614211.3 | SR | 364.3 |  | 5600.7 | G
17 | BC 79 | DR3 421752628690357632 | 6.07930817 | 56.88220974 | J002419.04+565255.9 | L |  |  | 7893.4 | G
18 | Kiso C1-78 | DR3 431011345534262784 | 6.16820049 | 63.23646455 | J002440.36+631411.2 | SR | 55.6 |  | 6756.6 | G
19 | Kiso C1-81 | DR3 428878499133379840 | 6.59766229 | 61.30082116 | J002623.44+611803.0 | SR | 153.0 |  | 7797.5 | G
20 | C* 3222 | DR3 2793301598079856512 | 6.72477116 | 17.55777751 | J002653.94+173328.0 | LB |  |  | 7080.7 | G
21 | Kiso C1-83 | DR3 527881893347020672 | 6.84269872 | 66.76993732 | J002722.25+664611.8 | SR | 269.5 |  | 7180.3 | G

aSee Table 2 and Section 8. The full catalog is available in machine-readable
format. bThe source of the distance: 1) G: Gaia DR3 2) GS: Gaia DR3 and model
SED (mean value).

##  9 summary

We have made an in-depth investigation into the infrared properties of carbon
stars within our Galaxy, employing a comprehensive analysis of observational
data across visual and IR bands. Utilizing datasets from IRAS, Akari, MSX,
2MASS, WISE, and Gaia DR3, we conductd an extensive comparison between
observational data and theoretical models. The comparison involve the use of
various 2CDs, CMDs, and SEDs.

We have found that the CMDs, which utilize the latest distance and extinction
data from Gaia DR3 for a substantial number of carbon stars, are very useful
to distinguish CAGB stars from extrinsic carbon stars that are not in the AGB
phase. In the case of all CAGB stars, the absolute magnitudes at the IR[12] or
W3[12] bands are brighter than -6. In contrast, extrinsic carbon stars of Ba,
CH, dC, and RH types are notably distinguishable from CAGB stars on various
CMDs, displaying dimmer absolute magnitudes at the MIR bands. However, J-type
stars, constituting another subclass of extrinsic carbon stars, demonstrate
properties shared with both CAGB stars and other extrinsic carbon stars.

We have performed radiative transfer model calculations for CAGB stars,
exploring various parameters of central stars and spherically symmetric dust
shells. A comprehensive comparison of theoretical models with observations on
various IR 2CDs, CMDs, and SEDs reveals a notable agreement.

For selected CAGB stars, the observed SEDs are compared with theoretical
models, with a simple single dust shell model of AMC and SiC dust reproducing
SEDs effectively for most objects. Some objects require more complex models,
such as detached or double shells or non-spherical dust envelopes.

We have established theoretical distances for 152 CAGB stars, optimizing the
fit to the observed SED by comparing it with the corresponding CAGB model SED.
A comparison between distances derived from observations and those obtained
from theoretical model SEDs reveals a significantly strong correlation,
affirming the reliability of the theoretical models.

We have studied the IR properties of known variable stars, revealing that for
Mira variables, IR colors intensify in reddish hues, and absolute magnitudes
brighten with longer pulsation periods. Furthermore, we investigated the IR
variability of carbon stars by analyzing WISE photometric data spanning the
last 14 yr. Through a detailed examination of WISE light curves for all
sampled stars, we have identified useful variation parameters for 227 CAGB
stars.

We have presented a novel catalog of CAGB stars, offering enhanced reliability
and a wealth of additional information, including distances obtained from Gaia
DR3 and model SEDs, and variational parameters from AAVSO and WISE light
curves. We have identified CAGB stars from a substantial sample of carbon
stars spanning various subclasses, leveraging information from diverse
literature sources, the SIMBAD database, and examining their IR properties
through 2CDs, CMDs, SEDs, and variations. The resulting catalog introduces
7163 CAGB stars, categorized as 4909 CAGB_IC and 2254 CAGB_NI objects within
our Galaxy.

I thank the anonymous referee for constructive comments and suggestions. This
work was supported by a funding for the academic research program of Chungbuk
National University in 2023. This research was supported by Basic Science
Research Program through the National Research Foundation of Korea (NRF)
funded by the Ministry of Education (2022R1I1A3055131). This research has made
use of the SIMBAD database and VizieR catalogue access tool, operated at CDS,
Strasbourg, France. This research has made use of the NASA/IPAC Infrared
Science Archive, which is operated by the Jet Propulsion Laboratory,
California Institute of Technology, under contract with the National
Aeronautics and Space Administration.

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