A silicate carbon star is a carbon star which shows circumstellar silicate dust features. We collect a sample of 44 silicate carbon stars from the literature and investigate the validity of the classification. For some objects, it is uncertain whether the central star is a carbon star. We confirm that 29 objects are verified silicate carbon stars. We classify the confirmed objects into three subclasses based on the evolution phase of the central star. To investigate the effect of the chemical transition phase from O to C, we use the radiative transfer models for the detached silicate dust shells. The spectral energy distributions and the infrared two-color diagrams of the silicate carbon stars are compared with the theoretical model results. For the chemical transition model without considering the effect of a disk, we find that the life time of the silicate feature is about 50 to 400 years depending on the initial dust optical depth. A silicate carbon star (hereafter; SCS) is a carbon star which shows circumstellar silicate dust features. They were discovered by the IRAS observations (Little- Marenin 1986; Willems & de Jong 1986). So far, about 35 SCSs have been identified in our Galaxy (e.g., Suh & Kwon 2011). As stars evolve into the thermal pulsing asymptotic giant branch (AGB) phase, the abundances of some elements in the stellar atmosphere may change by the episodic third dredge-up process after each thermal pulse. The stepwise increase of the carbon abundance is related to the formation of a carbon star because the C/O abundance ratio can change from C/O < 1 to C/O > 1 (e.g., Busso et al. 1999). These stars may experience the S star phase before they become carbon stars when the C/O ratio is close to 1. When AGB stars of intermediate mass range go through carbon dredge-up processes, the abundance of carbon becomes larger than that of oxygen, O-rich dust grain formation ceases, and the stars become visual carbon stars. After that phase, C-rich dust grains start forming (Iben 1981; Chan & Kwok 1990; Groenewegen et al. 1995; Suh 2000). Willems & de Jong (1986) and Chan & Kwok (1991) suggested that SCSs are in transition from O-rich AGB stars to carbon stars. Many of the SCSs are fairly well fitted with a simple detached silicate dust shell model. However, this scenario could be unlikely because the time scale for such a transitional object to be observed as a SCS is predicted to be too short. A more promising scenario suggests that SCSs have a low-luminosity companion, possibly a dwarf star (e.g., Morris 1987; Lloyd Evans 1990; Yamamura et al. 2000). A relatively long-lived disk of silicate dust is supposed to be formed when the primary was still an O-rich AGB star. When the primary star was an M-type giant and O-rich materials were supposed to be used to form a cir-cumbinary (or circum-companion) disk. The disk may serve as a reservoir of O-rich material even after the star undergoes thermal pulses and evolves into a carbon star. For a large sample of AGB stars, infrared observational data are available from the Infrared Astronomical Satellite (IRAS), Infrared Space Observatory (ISO), Midcourse Space Experiment (MSX), USNO-B1.0 (Monet et al. 2003), Two-Micron All-Sky Survey (2MASS), Wide-field Infrared Survey Explorer (WISE) and AKARI. The IRAS point source catalog (PSC) version 2.1 contains useful photometric data in four bands (12, 25, 50 and 100 μ m). The MSX (Egan et al. 2003) PSC provides useful photometric data in 8.28, 12.13, 14.65, 21.34 μ m wavelength bands. The 2MASS (Cutri et al. 2003) PSC contains accurate positions and fluxes for about 470 million stars and other unresolved objects in J (1.25 μ m), H (1.65 μ m) and K (2.17 μ m) bands. The WISE (Wright et al. 2010) surveyed the entire sky with much higher sensitivity than previous missions. The AKARI space telescope (Murakami et al. 2007) made an all sky survey with the infrared camera (IRC) and far infrared surveyor (FIS). We may use the AKARI PSC data in two bands (9 and 18 μ m) obtained by the IRC and the bright-source catalogue (BSC) data in four bands (65, 90, 140 and 160 μ m) obtained by the FIS. The IRAS Low Resolution Spectrograph (LRS; λ = 8.22 μ m) data are useful to identify important dust features of SCSs. Kwok et al. (1997) used IRAS LRS to identify the class E (the 10 μ m silicate feature in emission) and class A (the 10 μ m silicate feature in absorption) objects. The ISO Short Wavelength Spec- trometer (SWS; λ = 2.4.45.4 μ m) and Spitzer Infrared Spectrograph (IRS; λ = 5.2.38 μ m) provided high resolution spectra for some SCSs. In this paper, we present a new catalog of SCSs. We confirm the C-rich nature of central stars and O-rich nature of circumstellar envelopes for the sample SCSs. To investigate the effect of the chemical transition phase from O to C, we use radiative transfer models for the detached silicate dust shells. We compare the spectral energy distributions and infrared two color diagrams of the SCSs with the theoretical model results and estimate the evolutionary time scales for SCSs. Suh & Kwon (2011, hereafter SK11) listed 35 SCSs. We have used the 35 objects in SK11 to construct the initial sample of stars to be verified in this paper. Chen & Shan (2011, hereafter CS11) presented 5 new SCSs which were verified from 17 new candidate objects as well as 34 previously known SCSs. The 12 candidate objects which were not verified to be SCSs by CS11 are regarded as unconfirmed objects (see Section 3). The two objects (IRAS 06176−1036 and 13198−6224) listed in CS11 as previously known SCSs were not listed in SK11. We add those 7 objects to the sample stars (the 5 new SCSs and 2 previously known objects presented in CS11). We add two more objects: IRAS 19163+2745 (EP Lyr) and IRAS 20451+4552 (CY Cyg). EP Lyr is a post-AGB star which shows both polycyclic aromatic hydrocarbon (PAH) and crystalline silicate features like the Red Rectangle (Gielen et al. 2008, 2009). CY Cyg is a SC type star with silicate emission feature. According to Kwok et al. (1997), there are 4 SC type stars (W Cas, VX Aql, S Lyr and CY Cyg) and a CS type star (IRAS 09083−5158) which are in LRS class E. Finally, the 44 objects are selected for the sample of SCSs to be verified in this paper and they are listed in Table 1 . Because the AKARI PSC measures the flux of the peak emission with a much smaller aperture (9 arcsec beam size) than IRAS PSC, we use the AKARI PSC position for further identification. For the 44 objects, we cross-identify the AKARI PSC counterpart by finding the nearest source within 30′′ using the position information of the IRAS PSC (version 2.1). For each sample star, we have found an AKARI source within 30′′ except for IRAS 16070−4359 which has two AKARI sources. For the IRAS 16070−4359, the counterpart is selected by comparing the flux data with the IRAS PSC. We use the counterpart of the General Catalog of Galactic Carbon stars (Alksnis et al. 2001, hereafter CGCS) based on the position information of the AKARI PSC as well as the available spectral evidences in optical, infrared and radio regions. In Table 1 , we present the IRAS PSC number, AKARI PSC counterpart, position information from the AKARI PSC counterpart, CGCS counterpart, and IRAS LRS class. For the 44 sample objects, we investigate the validity of the classification. To confirm the nature of the SCS, we investigate the signatures of the C-rich nature of central star and O-rich nature of circumstellar envelope. We identify the CGCS counterparts for which the position difference between the AKARI PSC and CGCS is less than 2′. For the 44 sample stars, we find that 35 objects have the CGCS counterparts and they are listed in Table 1 . The position differences (Δr) between the AKARI PSC and CGCS are also listed in Table 1 . For the 35 CGCS counterparts, only 3 sources have position differences larger than 30′′ (IRAS 12364−6539, 16070−4359 and 18252−1011). For the three sources, the AKARI, MSX and 2MASS counterparts based on the IRAS PSC and CGCS positions are different. These objects seem to be different sources. We mark those objects with the asterisk symbol in Table 1 . We list the 3 objects as unconfirmed objects in Table 2 . These 3 stars with large position differences need more reliable observation data to confirm their nature. The O-rich nature of the outer shells can be easily recognized by IRAS LRS class by Kwok et al. (1997). Among the 35 stars, 33 stars with silicate emission features are classified as E class, and 2 stars (IRAS 07204−1032 and 12364−6539) as F class. For IRAS 07204−1032, Engels (1994) detected H ₂ O maser. H ₂ O maser occurs only in the dusty O-rich environments. The spectral type of the last one, IRAS 12364−6539, is M9 according to Skiff (2014). Note that this is one of the unconfirmed objects with the large position differ- ence between the AKARI and CGCS. As mentioned in Section 2.1, 9 stars do not have CGCS counterparts within 3′. We check these stars using the available optical and infrared spectral information from the literature. C ₂ H ₂ +HCN absorption features around 3.0 μ m observed by the ISO SWS are clear evidences of the central carbon star. There are obvious C ₂ H ₂ +HCN absorption features for three stars: IRAS 03201+5459, 09425−6040 and 19111+2555 (e.g., Molster et al. 2001). These three stars show amorphous or crystalline silicate features. IRAS 06176−1036 and 19163+2745 (Red Rectangle and EP Lyr) show the PAH and crystalline silicate features detected by ISO-SWS or Spitzer-IRS (e.g., Gielen et al. 2008, 2009). Drew et al. (2005) observed the optical spectrum toward IRAS 22146+6111 and identified this star as a carbon star. IRAS 20451+4552 (CY Cyg) is classified as an SC star by Keenan & Boeshaar (1980). Kwok et al. (1997) classified IRAS 21135+5200 as a carbon star. All the 3 stars show a silicate emission feature at 10 μ m detected from the IRAS LRS. However, the remaining one object, IRAS 21444+5053 has no direct evidence of a carbon star. We list it as an unconfirmed object in Table 2 . We present a detailed discussion for all of the unconfirmed objects in Section 3. For some sample stars having the CGCS number, they are classified to be carbon stars by the method based on the color index. This method classifies the stars based on their location in a two-color diagram (2CD). Epchtein et al. (1987, 1990) showed that the 2CD using [12]-[25] versus K-L allows to distinguish carbon stars from O-rich stars with some reliability. In the 2CD using [12]-[25] versus K-L , carbon stars are located in the lower region and O-rich stars appear in the upper region. However, it is well known that the position of an AGB star on a 2CD varies widely depending on the phase of pulsation (e.g., Suh 2004). The variation of the positions on 2CDs could lead to mis-classifications especially for the stars near the border. Therefore, the color index method is not sufficient to reveal the C-rich nature of the central star. For the 10 objects, for which the C-rich nature is solely determined from the 2CD method, we need further verifications. We list these as unconfirmed objects in Table 2 . Through the investigations described in Section 2, we confirm that 29 objects are real SCSs. But for 15 objects, it is not clear whether the central star is a real carbon star. We list the 15 unconfirmed objects in Table 2 . CS11 presented 12 candidate objects (5 candidates in table 2; 7 probable candidates in Table 3 ) which were not verified to be real SCSs. In Table 3 , we list the 12 candidate objects presented by CS11 which can also be regarded as unconfirmed objects. For all of the 15 unconfirmed objects, the silicate emission feature at 10 μ m is detected in the IRAS LRS spectrum. Kwok et al. (1997) classified them as the IRAS LRS class E. IRAS 06194+1635 (CGCS 6139): Guglelmo et al. (1993) identified it as a carbon star based on the 2CD using [12]-[25] versus K-L . Althogh the object is in the region of carbon stars, its C-rich nature is not clear (see Section 2.3). IRAS 09411-5933 (CGCS 6337): This star was identified to be a carbon star by Fouque et al. (1992) using the [12]-[25] and K-L color indices. However, Skiff (2014) identified its spectral type as M2/3. OH maser emission at 1612 MHz was not detected in OH maser survey of te Lintel Hekkert (1991). IRAS 11311-6355 (CGCS 6450): Guglielmo et al. (1993) first identified it as a carbon star from the 2CD using [12]-[25] versus K-L . Kwok et al. (1997) classified this star as LRS class E with self-absorption. As mentioned above, the color index method is not enough for revealing the C-rich nature of the central star. IRAS 12364-6539: This star has a large position difference from CGCS 3264 (Δr = 51′′). Skiff (2014) identified the spectral type as M9. The AKARI, MSX and 2MASS counterparts based on the IRAS PSC position and CGCS position are different. IRAS 12364-6539 seems to be an O-rich star rather than an SCS. IRAS 12569-6105 (CGCS 6503): Epchtein et al. (1990) classified it as a carbon star using a 2CD. Mac- Connell (2000) and Skiff (2014) classified this star as an S star. IRAS 13198-6224 (CGCS 6610): Aaronson et al. (1989) classified it as a carbon star, but Lloyd Evans (1991) argued that the spectral type is M2. IRAS 14286-4706 (CGCS 6559): Fouque et al. (1992) firstly identified this object as a carbon star using the [12]-[25] versus K-L 2CD. It is seen near the border region between O-rich AGB stars and carbon stars on the 2CD. IRAS 16001-4851 (CGCS 6612): Epchtein et al. (1990) identified it as a carbon star using the color index method. Its C-rich nature is not clear IRAS 16070-4359: Guglielmo et al. (1993) identified it as a carbon star from the 2CD using [12]-[25] versus K-L . However, this star has a large position difference between the AKARI and CGCS positions (Δr = 101′′). The AKARI, MSX and 2MASS counterparts based on the IRAS PSC position and CGCS position are different. Therefore, IRAS 16070-4359 and CGCS 3668 seem to be different objects. IRAS 16103-4929 (CGCS 6624): Epchtein et al. (1990) classified this star as carbon star based on the color index method. Skiff (2014) revealed that the spectral type is M4,M6. Therefore, this star could be a O-rich star with large interstellar extinction. IRAS 16328-4656 (CGCS 6650): Although Epchtein et al. (1987) first identified this star as a carbon star based on the color index method, it is necessary to confirm the C-rich nature of the central star. IRAS 17291-3401 (CGCS 3841): Chan & Kwok (1991) first identified it as an SCS based on the CGCS. However, MacConnell (2006) reported it as a M3 star by the NIR spectral observation. This star seems to be misclassified as a carbon star. IRAS 18252-1011: The C-rich nature is not certain. This star has a large position difference between the AKARI and CGCS positions (Δr = 107′′). The AKARI, MSX and 2MASS counterparts based on the IRAS PSC position and CGCS position are different. IRAS 20476+4422 (CGCS 4993): Although this object has a CGCS counterpart and shows the silicate emission feature at 10 μ m, its C-rich nature is not clear. IRAS 21444+5053: This object is not listed in CGCS and there is no available spectral information to confirm its nature. Jiang et al. (1997) identified this star as a carbon star based on the J-H versus H-K 2CD. However, it was classified as an O-rich star based on the color index method by Guglielmo et al. (1997). Groenewegen et al. (2002) detected CO emission but did not detect HCN and SiO emission. For this object, further investigations are necessary. For the 29 confirmed SCSs, we classify them into three subclasses based on the evolutionary stage of the central star. The objects in subclass 1 are five SC/CS stars showing weak silicate emission features. The objects in subclass 2 are 22 carbon stars showing silicate features. In subclass 3, there are two C-rich post-AGB stars showing crystalline silicate features. We list them in Table 4 . The general catalogue of variable stars (GCVS: Samus et al. 2011) contains the list of LPVs for different variable types. LPVs in AGB phase are classified according to the amplitude and regularity of the period into Miras (M), semi-regulars (SR), irregular (L), and RV Tauri type (RV) variables. The GCVS variability type is also listed in Table 4 . In Figure 1 , we present the relative spectral energy distributions (SEDs) for the 29 objects. The SEDs show the observational data of USNO-B, 2MASS, WISE, AKARI, IRAS and ISO which cover the wavelength range from 0.9 μ m to 100 μ m. They show the relative fluxes based on the K band data. The five objects in subclass 1 are SC/CS stars showing weak silicate emission features. The SC/CS stars (Keenan & Boeshaar 1980) form a continuous spectral sequence intermediate between the S and C stars. They show very strong sodium D-lines, and strong CN bands, and either weak ZrO bands (SC stars) or C ₂ bands (CS stars). The molecular abundances indicate a C/O number ratio very close to unity, so that CO formation leaves little C or O for the other molecules. SC or CS stars are likely to be in a transitional phase from an S star to a carbon star. For lower metallicity, starsmay go from being O-rich to being carbon stars without any S-type star phase, depending on the dredge-up efficiency and the initial mass of the star (e.g., Iben 1981; Chan and Kwok 1990; Groenewegen et al. 1995). Generally, dust formation in envelopes of S stars is less efficient because of the lack of free O or C to form dust. This could easily explain the weak silicate emission features generally observed in this subclass. Most stars in subclass 2 show silicate emission features. However, IRAS 03201+5459 shows the silicate absorption feature at 10 μ m. And crystalline silicate emission features are observed from IRAS 09425−6040. 11 objects in this subclass are J-type carbon stars (see, e.g., Chen et al. 2007). Groenewegen et al. (1995) argued that the C/O abundance ratio for the star of low initial masses increases in a few and rather larger steps and they probably skip the intermediate state of an S star (C/O∼1) in most cases. The stars in subclass 2 could be in this case. The rich silicate features (see Section 4.1) may indicate that the silicate dust formation phase in the previous O-rich atmosphere was relatively recent. There are two objects in subclass 3. They are C-rich post-AGB stars with crystalline silicate features. These stars show PAH and crystalline silicate features. HD 44179, the central star of the Red Rectangle (IRAS 06176-1036), is known as a spectroscopic binary with a period of 298 days (Van Winckel et al. 1995). EP Lyr (IRAS 19163+2745) is a post-AGB star which is a RV Tau variable with the period of P = 83.46 days (Zsoldos 1995; Gonzalez et al. 1997). RV Tauri stars are luminous evolved stars crossing the instability strip. EP Lyr shows unusually low infrared excess that means a lower dust mass compared to the Red Rectangle. In order to measure the characteristics of a silicate feature at 10 μ m, we assume that the local continuum is a simple power law as follows: where the λ F _λ,cont is the assumed local continuum, K and P are constants to determine. The simple power law was fit to the continuum in the ∼8 μ m and ∼13.5 μ m region. The used spectral data for the continuum fitting are IRAS LRS or ISO SWS. After the continuum fitting, we obtain the normalized spectra, where λ F _λ,obs is the observed spectrum. Figure 2 shows the normalized spectra of some SCSs with good quality data. All of the objects are in subclass 2 except S Lyr (subclass 1) and Red Rectangle (subclass 3). They show various shapes of the silicate feature at 10 μ m. For S Lyr (subclass 1), the 10 μ m feature is very weak. For Red Rectangle (subclass 3), no evident silicate feature at 10 μ m is seen but PAH features at 7.7, 8.6 and 11.3 μ m as well as crystalline silicate features at longer wavelengths are evident. For most of the objects in subclass 2, the silicate feature at 10 μ m is easily detectable. The dominant feature appears in two objects: V778 Cyg and BM Gem. The 10 μ m amorphous silicate feature is less prominent for Hen 38 and IRAS 23138+6204. The feature is weak and flat for IRAS 09425-6040, IRAS 10170-6205. The 10 μ m absorption feature of amorphous silicate is identified for IRAS 03201+5459. The 11.3 μ m emission feature seen in spectra of IRAS 03201+5459 and 09425-6040 (subclass 2) can be caused by SiC, PAH or crystalline forsterite. However, 11.3 μ m emission features due to PAH or crystalline forsterite are narrower and involve other features at other wavelengths. There is no other conspicuous features indicating PAH or crystalline silicate in the spectra of IRAS 03201+5459 and 09425-6040. Therefore, the emission feature at 11.3 μ m is likely to be caused by SiC grains. For some of the SCSs in subclass 2 (e.g., IRAS 10171-6205 and Hen 38), the silicate feature at 10 μ m is weak and flat. Kessler-Silacci et al. (2006) argued the weak and flat features of amorphous silicate can be interpreted as grain growth (from 0.1 to 1.0 μ m in radius). The unusual silicate features in the SCSs indicate that the dust grains experience significant chemical and physical processing in their environment. Generally, a suitable site for grain growth is believed to be a stationary disk rather than an expanding shell. The weak and flat silicate feature may imply dust processing in a long lived reservoir such as a disk. To investigate the effect of the chemical transition phase from O to C, we use simple radiative transfer models for the detached silicate dust shells. The spectral energy distributions and infrared color-color diagrams of SCSs are compared with the theoretical model results. In this work, we use the radiative transfer code RADMC-3D (http://www.ita.uni-heidelberg.de/∼dullemond/software/radmc-3d/) to calculate the model SEDs. RADMC-3D is the three-dimensional version of the code for investigating dust continuum radiative transfer processes based on the Monte Carlo simulation method of Bjorkman & Wood (2001). For this work, we consider the geometry of one-dimensional grid only. Given spherically symmetric density structures, the code calculates the dust temperature and scattering source function at every geometric point in the model. Model SEDs can be calculated by integrating the intensity inside synthetic observing apertures at each wavelength. In this paper, we assume a spherically symmetric dust shell around a single star. We use similar schemes for dust density distribution as those used by Suh & Kwon (2013). Although AGB stars are pulsating, the overall continuous density distribution is believed to be maintained for a time scale larger than the pulsation period (e.g., Suh 1999; Suh 2004). In this paper, we assume that the dust density distribution is continuous (𝜌 ∝ r ^-2 ) from the inner radius ( R_in ) to the outer radius ( R_out ) for each dust shell. For the dust density distribution of a spherically symmetric dust shell, we use the simple power law equation where 𝜌 _in is the density at R_in of the dust shell. The inner shell dust temperature ( T_c ) is the dust temperature at R_in . In model calculations, we may find R_in at which the dust temperature ( T_c ) becomes the desired one after a few trials. The model SEDs are sensitively dependent on T_c . We may roughly regard the temperature T_c as the dust formation (or condensation) temperature. However, T_c is not necessarily the same as the dust formation temperature, depending on the physical conditions of pulsating OH/IR stars (see Suh 2004). For the central star, we assume that the luminosity is 1 × 10 ⁴ L _⊙ and a stellar blackbody temperature is 2500 K. We investigate the time scales for the appearance of the silicate feature after the chemical transition of the central star from O to C which is characterized by a sudden cessation of the O-rich mass-loss. Because the central star does not provide O-rich material after the chemical transition, the silicate dust shell will be detached gradually from the central star and the silicate dust features will become weaker. The transition object with a C-rich central star can be classified to be a SCS until the silicate dust feature completely disappears. Previously estimated time scale for the transitional object as a SCS is predicted to last only a few decades (e.g., Little-Marenin et al. 1988). The initial inner radius ( R ₀ ) of dust shell is chosen by the radius where the dust temperature is 1000 K. As the dust shell expands, the inner radius (R _in ) of the dust shell increases with time ( R_in = R ₀ + V_expt ) after the chemical transition begins (or the O-rich mass-loss stops at R ₀ ). We use spherically symmetric O-rich dust shells with four different dust optical depths of 𝜏 _10,int = 0.01, 0.1, 1 and 7 as the initial conditions. For all of the models, we assume that the stellar wind velocity V_exp is constant. We use the dust opacity functions of warm (𝜏 _10,int = 0.01, 0.1 and 1) and cold (𝜏 _10,int = 7) amorphous silicate derived by Suh (1999). We assume that all dust grains are spherical with a uniform radius of 0.1 μ m and the scattering is assumed to be isotropic. For each model, the dust temperature (T _c ) at the R _in decreases as the O-rich dust shell expands. We fixed the outer radius (R _out ) of the dust shell to 10 ⁵ AU (∼0.5 pc). For the all of the models, dust temperatures at R _out are lower than 30 K which is comparable to the temperature of interstellar medium. In Figure 3 , we present the profile lines of the silicate feature at 10 μ m obtained from the model SEDs of the transitional dust shells explained in Section 5.3. As explained in Section 3.1, the normalized model spectra are obtained using the local continuum Equation (1). As the dust shell expands, the strength of the silicate emission feature becomes weak and the peak of the feature moves slightly to longer wavelengths. We may claim that the silicate feature disappears when the following condition is satisfied around 10 μ m: where F _cal,λ is the calculated flux. We find that the silicate emission feature for the expanding O-rich shell is retained only for a short time and fade away rapidly. We assume that the shell expands outward with a constant velocity of 10 km/sec (e.g., Loup et al. 1993) thereby moving 210 AU in 100 years. The life time scales for the silicate emission feature for the models of 𝜏 _10,int = 0.01, 0.1, 1 and 7 are about 50, 140, 380 and 400 years, respectively. As the O-rich dust shell expands, silicate emission features disappear due to fast dilution of silicate dust density and/or cooling of dust temperature (< 150 K) (See Table 4 ) . For the model of 𝜏 _10,int = 7, the silicate absorption feature at 10 μ m is retained only for a short time scale (∼28 years). Then the silicate emission feature lasts for about 380 years. Though the transition models reproduce various shapes of the silicate feature, they can not reproduce the flat silicate features seen in some of the SCSs (e.g., IRAS 10171-6205). Other theoretical models (e.g., a disk model) could be more useful. We present the IRAS 2CDs for AGB stars using [25]-[60] versus [12]-[25] in Figure 4 and the NIR-IRAS 2CD using [12]-[25] versus K-L in Figure 5 . See Suh & Kwon (2011) for detailed explanations about the color indices. We use available NIR data in K and L bands obtained from ground-based observations as explained in Suh & Kwon 2011. We plot the observed colors of 29 SCSs verified in this paper and 15 unconfirmed objects and 12 candidate objects presented by CS11. We also plot the observed colors of 3373 O-rich AGB stars listed in Kwon & Suh (2012) and 1168 C-rich AGB stars for comparison. For any 2CD, we use only objects with a good photometric quality flag (q = 3) to plot at any wavelength. We also plot the results of model calculations for the spherical dust shell models presented in Section 5 for comparison. Each model track on the 2CD is composed of 24 points of different inner radii of dust shell from r ₁ to r ₁ +15000 AU. The amount of shell detachment (Δ r = V_expt) corresponds to the time steps from 0 to about 10000 years under the condition of V_exp = 10 km/s. We examine the shape of the silicate feature at 10 μ m to determine the silicate emission or absorption phases as explained in Section 5.4. We represent the silicate absorption phases by red filed squares and the emission phases by blue filled cicles on the 2CDs. In Table 5 , we list the model parameters of 𝜏 ₁₀ = 0.01, 0.1, 1 and 7 for six time step points which are also labeled in the 2CDs. The inner radius(R _in ) of the dust shell, dust density (𝜌 _in ) at the inner radius, dust temperature (T _c ) at the inner radius and 𝜏 ₁₀ of each model are listed. The points labeled with number 1 indicate the initial points for normal O-rich AGB stars. The points labeled as 2, 3 and 4 refer to the end point of silicate emission phase for the model of 𝜏 ₁₀ = 0.01, 0.1 and 1, respectively. The points 5 and 6 are the model points for the expansion times of ∼1000 and ∼10 ⁴ years, respectively. The loop-like shape of evolutionary tracks on the [25]-[60] versus [12]-[25] diagram ( Figure 4 ) resemble the works of Willems & de Jong (1988) and Chan & Kwok (1988). The model tracks show that the silicate emission feature remains toward higher values of [12]-[25] color but disappears for higher values of [25]-[60] color. Although some SCSs are located around the model track on the [25]-[60] versus [12]-[25] diagram, the model can not cover the wide distributions of observed SCSs. Although it takes less time to show silicate features in the transition model, the expanding shell can contribute to far-IR continuum emission for a much longer time scale. As we can see in Figure 4 , the flux excesses at 60 μ m relative to O-rich AGB stars are due to the cooling dust remnants ejected at least ∼100 and 1000 years ago for the models of 𝜏 ₁₀ = 0.01 and 7, respectively. These model tracks for later stages are particularly successful in explaining the SCSs in the upper-left region of the 2CD where optical carbon stars are located. In the [12]-[25] versus K-L diagram ( Figure 5 ), the model tracks develop toward the upper left region to converge quickly (less than 500 years) to the vertical line of K-L ≃ 0.6. Many of the SCSs are outside the regions of the transition model tracks. This is because carbon stars show strong photospheric molecular bands in K and L which can skew the K-L color value away from what is expected for a blackbody of 2500 K. Note that the time scale for the model tracks is relatively short (∼1000 years from the label point 1 to point 5). Contrary to previous works (Willems & de Jong 1988; Chan & Kwok 1988), our results show that the life time of the silicate feature can be much longer (up to 400 years depending on the initial dust optical depth; see Section 5.4). This is because we use higher initial dust optical depths (𝜏 ₁₀ = 1 and 7) which are appropriate for some observed SCSs (e.g., the IRAS 03201+5459 shows the 10 μ m silicate feature in absorption) as well as smaller ones (𝜏 ₁₀ = 0.01 and 0.1). The previous works considered only the SCSs with the initial 10 μ m silicate feature in emission (𝜏 ₁₀ < 1). As explained in Sections 5.4 and 6, we find that the detached silicate dust shell models can not explain the observed SEDs for the whole sample of SCSs. We may need a more complicated geometry for the dust distribution. A more sophisticated theoretical model using a circumbinary or circumstellar dust disk as well as the dust shell would be more useful. There are some observational evidences for the presence of a disk in some SCSs. For BM Gem and EU And, the variations of radial velocity are detected due to motions in a binary system by Barnbaum et al. (1991). And Kahane et al. (1998) and Jura & Kahane (1999) observed the narrow CO emission lines supporting the presence of long-lived reservoirs of orbiting gas in the two stars. Izumiura et al. (2008) found the P Cygni-type profile in the violet spectra of BM Gem which indicates the presence of an outflow with at least 400 km / s . Ohnaka et al. (2008) made mid-IR interferometry observations toward BM Gem which suggested a circum-companion disk. And VLBA H ₂ O maser observations toward EU And supported the circum-companion disk (Ohnaka & Boboltz 2008). For V778 Cyg, Szczerba et al. (2006) obtained high resolution H ₂ O maser maps at 22 GHz and they concluded that the object is composed of a C-rich star and a companion that stores an O-rich disk. Those observations are strong evidences for presence of an O-rich disk around a SCS which is actually a binary system. We expect that most SCS are likely to be binary systems rather than single stars. We have collected 44 SCSs from the literature and verified their classification. We have confirmed that 29 objects are real SCSs and 15 objects are unconfirmed. For some objects, it is doubtful whether the central star is a carbon star. Other objects seem to be contaminated by interstellar clouds. For the confirmed 29 SCSs, we have classified them into three subclasses based on the evolution phase of the central star: SC/CS stars with silicate emission features, carbon stars with silicate features and C-rich post-AGB stars with crystalline silicate. The shapes of the silicate emission feature at 10 μ m for various SCSs have been investigated. We have made radiative transfer model calculations for the transitional dust shell models of SCSs with detached O-rich dust shells. We have compared the theoretical model results with the observations of SCSs on different 2CDs. The life time of the silicate emission feature at 10 μ m has been estimated to be 50-400 years depending on the thickness of the dust shell in the O-rich phase. For model of 𝜏 _10,ini = 7, silicate absorption phase appears only for a short time scale. The transitional dust shell models presented in this paper may provide only a partial explanation for the origin of SCSs because the models do not reproduce all of the observations. For the chemical transition model without considering the effect of a disk, the life time of the silicate feature is too short. We expect that a more sophisticated theoretical model using a circumbinary or circumstellar dust disk as well as the dust shell would be useful.