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The mysterious age invariance of the planetary nebula luminosity function bright cut-off


Planetary nebulae mark the end of the active life of 90% of all stars. They trace the transition from a red giant to a degenerate white dwarf. Stellar models1,2 predicted that only stars above approximately twice the solar mass could form a bright nebula. But the ubiquitous presence of bright planetary nebulae in old stellar populations, such as elliptical galaxies, contradicts this: such high-mass stars are not present in old systems. The planetary nebula luminosity function, and especially its bright cut-off, is almost invariant between young spiral galaxies, with high-mass stars, and old elliptical galaxies, with only low-mass stars. Here, we show that new evolutionary tracks of low-mass stars are capable of explaining in a simple manner this decades-old mystery. The agreement between the observed luminosity function and computed stellar evolution validates the latest theoretical modelling. With these models, the planetary nebula luminosity function provides a powerful diagnostic to derive star formation histories of intermediate-age stars. The new models predict that the Sun at the end of its life will also form a planetary nebula, but it will be faint.

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Fig. 1: Stellar evolution sequences and timescales.
Fig. 2: Evolution of [O iii] 5007 Å fluxes against logarithmic time for the maximum-nebula hypothesis.
Fig. 3: The synthesized PNLF for the intermediate-nebula and minimum-nebula hypothesis, for different SFHs.


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A.A.Z. and K.G. acknowledge the financial support by The University of Manchester and by Nicolaus Copernicus University. A.A.Z. is supported by the UK Science and Technology Facility Council (STFC) under grant ST/P000649/1. M.M.M.B. is partially suported by ANPCyT and CONICET through grants PICT-2 014-2708 and PIP 112-200801-00940 and also by a Return Fellowship from the Alexander von Humboldt Foundation.

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A.A.Z. and K.G. developed the concept. M.M.M.B. provided the post-AGB evolutionary sequences obtained with LPCODE and computed the supplementary data. K.G. adopted the Torun codes for the present work, performed the photoionization calculations and synthesized the PNLF. All authors participated in discussions of the results, in their presentations in figures and descriptions in manuscript and in pinpointing the conclusions.

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Correspondence to K. Gesicki.

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Supplementary Figure 1, Supplementary Text, Supplementary References

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Gesicki, K., Zijlstra, A.A. & Miller Bertolami, M.M. The mysterious age invariance of the planetary nebula luminosity function bright cut-off. Nat Astron 2, 580–584 (2018).

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