We present the deep homogeneous 𝑈𝐵𝑉𝑅𝐼 photometric data of 135,071 stars down to 𝑉 ∼ 23 mag and 𝐼 ∼ 22 mag toward the Carina Nebula. These stars are cross-matched with those from the previous surveys in the X-ray, near-infrared, and mid-infrared wavelengths as well as the Gaia Early Data Release 3 (EDR3). This master catalog allows us to select reliable members and determine the fundamental parameters distance, size, stellar density of stellar clusters in this star-forming region. We revisit the reddening toward the nebula using the optical and the near-infrared colors of early-type stars. The foreground reddening [𝐸(𝐵 −𝑉) 𝑓 𝑔] is determined to be 0.35 ± 0.02, and it seems to follow the standard reddening law. On the other hand, the total-toselective extinction ratio of the intracluster medium (𝑅𝑉,𝑐𝑙) decreases from the central region (Trumpler 14 and 16, 𝑅𝑉,𝑐𝑙 ∼ 4.5) to the northern region (Trumpler 15, 𝑅𝑉,𝑐𝑙 ∼ 3.4). It implies that the central region is more dusty than the northern region. We find that the distance modulus of the Carina Nebula to be 11.9 ± 0.3 mag (𝑑 = 2.4 ± 0.35 kpc) using a zero-age main-sequence fitting method, which is in good agreement with that derived from the Gaia EDR3 parallaxes. We also present the catalog of 3,331 pre-main-sequence (PMS) members and 14,974 PMS candidates down to 𝑉 ∼ 22 mag based on spectrophotometric properties of young stars at infrared, optical, and X-ray wavelengths. From the spatial distribution of PMS members and PMS candidates, we confirm that the member selection is very reliable down to faint stars. Our data will have a legacy value for follow-up studies with different scientific purposes.

New methods are developed to estimate the effective temperature (Te), surface gravity (log g), and metallicity ([A/H]) simultaneously with the spectral line depth ratios. Using the model atmosphere grids, depth values are calculated for the wavelength range of 4000 A–5600 A for various temperatures, gravities, and metallicities. All possible different combinations of line depth ratios for different pairs of ratios are investigated. A graphical 3D figure is produced with X, Y, and Z axes corresponding to Te, log g, and [A/H], respectively. By reading a cross point of two curves plotted by a connection of three parameters obtained from spectral line depth ratio pairs on each of the three projected planes, Te, log g, and [A/H] are determined simultaneously. In addition, an analytical method is devised based on the similar algorithm developed for the graphical method. Our methods were applied to estimate the fundamental atmospheric parameters of the Sun and Arcturus.

A deep stellar analysis is introduced for the poorly studied open cluster NGC 2509. The Near-IR database of the digital Two Micron All Sky Survey (2MASS) has been used to re-estimate and refine the fundamental parameters of the cluster, i.e. age, reddening, distance, and diameter. As well as, luminosity function, mass function, total mass, relaxation time, and mass segregation of NGC 2509 have been estimated here for the first time.