  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.
