We have estimated elemental abundances of the planetary nebula (PN) Hen2-436 in the Sagittarius (Sgr) spheroidal dwarf galaxy using ESO/VLT FORS2, Magellan/MMIRS, and Spitzer /IRS spectra. We have detected candidates of fluorine [F ii ] λ4790, krypton [Kr iii ] λ6826, and phosphorus [P ii ] λ7875 lines and successfully estimated the abundances of these elements ([F/H] = +1.23, [Kr/H] = +0.26, [P/H] = +0.26) for the first time. These elements are known to be synthesized by the neutron capture process in the He-rich intershell during the thermally pulsing asymptotic giant branch (AGB) phase. We present a relation between C, F, P, and Kr abundances among PNe and C-rich stars. The detections of these elements in Hen2-436 support the idea that F, P, Kr together with C are synthesized in the same layer and brought to the surface by the third dredge-up. We have detected N ii and O ii optical recombination lines (ORLs) and derived the N 2+ and O 2+ abundances. The discrepancy between the abundance derived from the oxygen ORL and that derived from the collisionally excited line is >1 dex. To investigate the status of the central star of the PN, nebula condition, and dust properties, we construct a theoretical spectral energy distribution (SED) model to match the observed SED with Cloudy . By comparing the derived luminosity and temperature of the central star with theoretical evolutionary tracks, we conclude that the initial mass of the progenitor is likely to be ∼1.5–2.0 M ☉ and the age is ∼3000 yr after the AGB phase. The observed elemental abundances of Hen2-436 can be explained by a theoretical nucleosynthesis model with a star of initial mass 2.25 M ☉ , Z = 0.008, and LMC compositions. We have estimated the dust mass to be 2.9 × 10 −4 M ☉ (amorphous carbon only) or 4.0 × 10 −4 M ☉ (amorphous carbon and polycyclic aromatic hydrocarbon). Based on the assumption that most of the observed dust is formed during the last two thermal pulses and the dust-to-gas mass ratio is 5.58 × 10 −3 , the dust mass-loss rate and the total mass-loss rate are <3.1 × 10 −8 M ☉ yr −1 and <5.5 × 10 −6 M ☉ yr −1 , respectively. Our estimated dust mass-loss rate is comparable to a Sgr dwarf galaxy AGB star with similar metallicity and luminosity.
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