SIMBAD references

We conduct a detailed study of the planetary nebula (PN) DdDm 1 in the Galactic halo field. DdDm 1 is a metal-deficient and the most carbon-poor PN (${\rm C/O} =0.11 \pm 0.02$) identified in the Galaxy. We aim to verify whether it evolved into a PN without experiencing the third dredge-up (TDU) during the thermal pulse asymptotic giant branch (AGB) phase and to investigate its origin and evolution through accurate measurements of the physical parameters of the nebula and its central star. We perform a comprehensive investigation of DdDm 1 using multiwavelength spectra. The KOOLS-IFU emission-line images achieve $\sim$${0^{\prime \prime }_{.}9}$ resolution, resolving the elliptical nebula and revealing a compact spatial distribution of the [Fe III] line compared to the [O III] line, despite their similar volume emissivities. This indicates that iron, with its higher condensation temperature than oxygen, is easily incorporated into dust grains such as silicate, making the iron abundance prone to underestimation. Using a fully data-driven approach, we directly derive 10 elemental abundances, the gas-to-dust mass ratio, and the gas and dust masses based on our own heliocentric distance scale (19.4 kpc) and the emitting volumes of gas and dust. Our analysis reveals that DdDm 1 is a unique PN evolved from a single star with an initial mass of $\sim 1.0\, M_{\odot }$ and a metallicity $Z$ of 0.18$\, Z_{\odot }$. Thus, DdDm 1 is the only known PN that is confirmed to have evolved without experiencing TDUs. The photoionization model reproduces all observed quantities in excellent agreement with predictions from AGB nucleosynthesis, post-AGB evolution, and AGB dust production models. Our study provides new insights into the internal evolution of low-mass and metal-deficient stars like DdDm 1 and highlights the role of PN progenitors in the chemical enrichment of the Galaxy.