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# Slowly cooling white dwarfs in M13 from stable hydrogen burning

## Abstract

White dwarfs (WDs) are the final evolutionary product of the vast majority of stars in the Universe. They are electron-degenerate structures characterized by no stable thermonuclear activity, and their evolution is generally described as a pure cooling process. Their cooling rate is adopted as cosmic chronometer to constrain the age of several Galactic populations, including the disk, globular and open clusters. By analysing high-resolution photometric data of two very similar Galactic globular clusters (M3 and M13), we find a clear-cut and unexpected overabundance of bright WDs in M13. Theoretical models suggest that, consistent with the horizontal branch morphology, this overabundance is due to a slowing down of the cooling process in ~70% of the WDs in M13, caused by stable thermonuclear burning in their residual hydrogen-rich envelope. The presented observational evidence of quiescent thermonuclear activity occurring in cooling WDs brings new attention on the use of the WD cooling rate as cosmic chronometer for low-metallicity environments.

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## Data availability

The photometric data that support the plots and other findings of this study are available from the corresponding author upon reasonable request. The catalogues are also publicly downloadable from the web site of the Cosmic-Lab project (http://www.cosmic-lab.eu/Cosmic-Lab/Home.html). All the HST images are publicly available from the Mikulski Archive for Space Telescopes (https://archive.stsci.edu/).

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## Acknowledgements

This research is part of the Cosmic-Lab project at the Physics and Astronomy Department of the University of Bologna (see http://www.cosmic-lab.eu/Cosmic-Lab/Home.html). The research has been funded by project Light-on-Dark, granted by the Italian MIUR through contract no. PRIN-2017K7REXT (F.R.F., M.C., B.L., C.P. and E.D.). J.C. acknowledges the financial support from the China Scholarship Council. The research is based on data acquired with the NASA/ESA HST under projects GO12605 and GO10775 at the Space Telescope Science Institute, which is operated by Aura Inc. under NASA contract no. NAS5-26555.

## Author information

Authors

### Contributions

J.C. analysed the photometric data sets, F.R.F. designed the study and coordinated the activity. M.S. performed the Monte Carlo simulations, and M.S. and L.G.A. were in charge of the theoretical model development. J.C., M.C., C.P. and E.D. contributed to the data analysis and the computation of the artificial star analysis. J.C., F.R.F. and B.L. wrote the first draft of the paper. M.S., L.G.A. and M.C. critically contributed to the paper presentation. All the authors contributed to the discussion of the results and commented on the manuscript.

### Corresponding author

Correspondence to Francesco R. Ferraro.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Astronomy thanks Pier-Emmanuel Tremblay and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 The effect of stable H-burning on a low mass WD.

a, Contribution of stable H-burning15,16 (via PP and CNO chain) to the global luminosity of a low metallicity (Z = 0.001), low mass (0.54 M) WD as a function of its decreasing luminosity. H-burning provides a relevant contribution (larger than 40%) to the WD luminosity in the brightest portion of the cooling sequence, becoming negligible at log(L/L) ≈ −4 and log(Te) ≈ 3.7 (see the temperature scale in the top axis). b, Delay15,16 in the cooling time induced by stable H-burning, with respect to a model without burning. The time delay keeps increasing during the phase of active H-burning and reaches a value as large as ~760 Myr, which then remains constant during the entire subsequent evolution.

### Extended Data Fig. 2 Physical parameters of M3 and M13.

From top to bottom, the listed parameters are: metallicity, age, V-band absolute integrated magnitude, logarithm of the central luminosity density (in units of L pc-3), logarithm of the central relaxation time (in years).

### Extended Data Fig. 3 The completeness distribution of the WD populations of M13 and M3.

a, Completeness parameter as a function of the F275W magnitude and colour-coded in terms of the distance from the cluster centre (see colour bars) for each WD detected in M13. b, The same for M3. The mean error (1 s.e.m.) is also reported.

### Extended Data Fig. 4 The RGB reference population.

Selection box (red shaded area) adopted to define the RGB ‘reference population’ in the observed and realigned CMDs of M13 and M3. The number of red giants counted in each cluster is also marked. The mean errors (1 s.e.m.) are also marked.

### Extended Data Fig. 5 WD cooling time for models with and without hydrogen burning.

Comparison between the cooling times of a low metallicity, 0.54 M WD with and without hydrogen-burning16 (solid and dashed lines, respectively). The red segment marks the difference in the cooling time at the luminosity of the faintest WD considered in this study, log(L/L) = – 1.7 and reports the absolute difference between the two cooling time values (60 Myr), corresponding to a 75% increase if hydrogen-burning is active, with respect to the ‘standard’ (no-burning) case.

### Extended Data Fig. 6 HB and AGB populations in M3 and M13.

a, UV-CMD of M13 zoomed in the HB region. The extreme-HB (E-HB) and the 7 candidate AGB-manqué stars are highlighted as blue circles. b, AGB and HB selection boxes in the optical- and UV-CMD (top and bottom panels, respectively) for the two clusters. The population star counts are also marked in each panel. The mean photometric errors (1 s.e.m.) are also marked in all panels.

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Chen, J., Ferraro, F.R., Cadelano, M. et al. Slowly cooling white dwarfs in M13 from stable hydrogen burning. Nat Astron 5, 1170–1177 (2021). https://doi.org/10.1038/s41550-021-01445-6

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• DOI: https://doi.org/10.1038/s41550-021-01445-6