Formation and Evolution of [Wolf-Rayet] Planetary Nebulae through a Late Thermal Pulse

The gist: The first radiation-hydrodynamical simulations of the formation of a born-again planetary nebula (PN) triggered by a late thermal pulse (LTP) show that H-deficient LTP ejecta forms a transient double-shell structure which, after ∼1000 yr, becomes fully mixed with the H-rich PN <ref:2603.26536#pg12>.

Stellar Evolution Model and Input Physics

The research utilizes a stellar evolution model computed with the modules for experiments in stellar astrophysics (mesa) code to simulate a low-mass star experiencing a born-again event, specifically an LTP <ref:2603.26536#pg3>. This model incorporates two key improvements over previous works: (i) after the LTP event, we activated updated opacity tables for H-deficient, C-rich material – specifically those used for R Coronae Borealis stars – that provides a better match to the expected abundances of the LTP phase; (ii) we adopted a massloss prescription during the post-LTP phase tailored for H-deficient [WR]-type winds <ref:2603.26536#pg4>. The stellar model reproduces the nearly complete depletion of H expected after an LTP event, while matching the observed abundances and spectral types of iconic [WR]-type central stars of PNe <ref:2603.26536#pg5>.

Hydrodynamical Simulations and Structure Formation

The 2D radiation-hydrodynamic simulations were performed using the pluto code with a finite-volume formulation and a Godunov-type solver using an HLLC Rieman solver, covering a radial extent (r) of 0.6 pc <ref:2603.26536#pg6>. The simulations are evolved into an initial medium with density of nISM = 1 cm−3 and initial temperature of TISM = 100 K <ref:2603.26536#pg6>. The impact of the ionising flux is included in the simulations through the Sedna module, a hydrogen photoionisation solver developed by Kuiper et al. (2020) <ref:2603.26536#pg6>. The simulations illustrate that after roughly 1000 yr of post-LTP evolution, the H-deficient ejecta will mix with the clumps and filaments formed in the innermost nebular rim <ref:2603.26536#pg9>.

Mixing and Observational Implications

The total mass ejected predicted by the born-again event is M LTP = 3.4 × 10−4 M⊙, a relatively small amount compared to that of the ionised nebula <ref:2603.26536#pg9>. Consequently, once mixing occurs, it becomes impossible to disentangle or identify the presence of the H-deficient ejecta. The combination of these effects is probably the explanation why PNe hosting [WR] CSPN do not exhibit significant abundance differences when compared with PNe with H-rich CSPN, both cases showing abundances consistent with models of H-rich post-AGB stars. This high degree of turbulent mixing can also be used to explain why [WR] PNe are more easily detected by X-ray instruments.

Spectral Signatures and Classification

A synthetic optical spectrum computed 4500 yr after the LTP event predicts that after the born-again event the H-deficient CSPN will evolve extremely fast into a [WO]-type star. The model predicts a carbon-to-oxygen abundance ratio X C/X O ≳ 1.0 at late stages of the LTP evolution, which can be expected to lead to the formation of large amounts of C-rich dust during this short phase. The results unambiguously confirm previous suggestions that [WR] CSPNe can be produced through a born-again event.

Conclusion on Event Type

The nitrogen abundance of NGC 5189 stands out because of its larger N abundance (XN = 0.01) compared to the values reported for other [WR] CSPN (XN ⩽ 3 × 10−3), which are more consistent with the predictions of LTP models – including the one presented in this work. Such differences seem to suggest that XN can be used to discern between an LTP and a VLTP event. The authors note that the stellar evolution model is not intended to reproduce all PNe hosting [WR] CSPN.

Summary of Key Findings

**- Our stellar evolution model predicts abundances slightly different from previous LTP models. However, these new predictions are very similar to those of [WR] CSPN reported in the literature. In particular, a virtually zero H abundance is reached as the result of the strong mass-loss rate during the post-LTP phase. Overall, our model reproduces well the observed abundances of H-deficient [WR] CSPN. Our predictions compare very favourably with the properties of the [WR] CSPNe of NGC 40, NGC 1501, NGC 2371, NGC 5189, NGC 6905, and PC 22. **

**- A synthetic optical spectrum computed 4500 yr after the LTP event predicts that after the born-again event the H-deficient CSPN will evolve extremely fast into a [WO]-type star. **

**- The stellar evolution model predicts a carbon-to-oxygen abundance ratio X C/X O ≳ 1.0 at late stages of the LTP evolution. In conjunction with the star evolution to low Teff, it can be expected the formation of large amounts of C-rich dust during this short phase. **

**- Our radiation-hydrodynamical simulations show that a star forming a PN and subsequently undergoing an LTP event develops a short-lived double-shell structure. Our model indicates that, after roughly 1000 yr of post-LTP evolution, the H-deficient ejecta will mix with the clumps and filaments formed in the innermost nebular rim. **

**- The LTP event produces a layer of enhance turbulence inside the H-rich nebula. This is inline with previous observational evidence that [WR] PNe exhibit larger expansion velocities and turbulence than PNe hosting H-rich CSPN. **

The combination of the born-again ejecta and the high mechanical luminosity of the post-LTP [WR] wind produces a high degree of turbulence. By comparing the predictions of our LTP model with an upcoming grid of born-again stellar models (including both LTP and VLTP events), together with results from stellar atmosphere analyses, we will be able to probe the origins of PNe surrounding [WR] CSPN. The authors thank the anonymous referee for comments and suggestions that improved the presentation of our results. J.B.R.G., R.O.D., and J.A.T. acknowledge support from the UNAM PAPIIT project IN102324. J.A.T thanks the staff of Facultad de Ciencias de la Tierra y el Espacio of Universidad Autónoma de Sinaloa (FACITEUAS, Mexico) for their support during a research visit. J.B.R.G. and M.A.G acknowledge financial support from grants CEX2021-001131-S funded by MCIN/AEI/10. M3B acknowledges support by the CONICET-DAAD 2022 bilateral cooperation grant number 80726, and grants PIP-2971 and PICT 2020-03316 by CONICET. R.K. acknowledges financial support via the Heisenberg Research Grant funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant no. KU 2849/9, project no. 445783058 <ref:2603.

1. Bold header: Enhanced stellar evolution modeling for born-again events

The improved AI system can accurately predict the nearly complete depletion of H expected after an LTP event by utilizing updated opacity tables for H-deficient, C-rich mixtures during the LTP, which is crucial for matching observed abundances.

2. Bold header: Improved radiation-hydrodynamic simulation capabilities

The system can now perform axially symmetric (2D) and midplanesymmetric simulations in spherical coordinates using a finite-volume formulation with a Godunov-type solver using a HLLC Rieman solver, allowing it to model the formation of a transient double-shell structure.

3. Bold header: Detailed temporal evolution tracing of mixing

The AI can track the fate of ejecta by including an advected passive scalar (s) where intermediate values informs on the mixing of H-deficient and H-rich material, enabling it to predict when the LTP material is considerably mixed with the turbulent medium at the outer edge of the first hot bubble.

4. Bold header: Discrimination between LTP and VLTP events

The system can differentiate between progenitor scenarios by analyzing key abundance ratios, as the nitrogen abundance of NGC 5189 seems to be more consistent with a VLTP event compared to LTP models.