A large oxygen-dominated core from the seismic cartography of a pulsating white dwarf

Abstract

White-dwarf stars are the end product of stellar evolution for most stars in the Universe1. Their interiors bear the imprint of fundamental mechanisms that occur during stellar evolution2,3. Moreover, they are important chronometers for dating galactic stellar populations, and their mergers with other white dwarfs now appear to be responsible for producing the type Ia supernovae that are used as standard cosmological candles4. However, the internal structure of white-dwarf stars—in particular their oxygen content and the stratification of their cores—is still poorly known, because of remaining uncertainties in the physics involved in stellar modelling codes5,6. Here we report a measurement of the radial chemical stratification (of oxygen, carbon and helium) in the hydrogen-deficient white-dwarf star KIC08626021 (J192904.6+444708), independently of stellar-evolution calculations. We use archival data7,8 coupled with asteroseismic sounding techniques9,10 to determine the internal constitution of this star. We find that the oxygen content and extent of its core exceed the predictions of existing models of stellar evolution. The central homogeneous core has a mass of 0.45 solar masses, and is composed of about 86 per cent oxygen by mass. These values are respectively 40 per cent and 15 per cent greater than those expected from typical white-dwarf models. These findings challenge present theories of stellar evolution and their constitutive physics, and open up an avenue for calibrating white-dwarf cosmochronology11.

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Figure 1: Segments of the Lomb–Scargle periodogram for KIC08626021.
Figure 2: Derived chemical stratification.

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Acknowledgements

S.C., N.G. and W.Z. acknowledge financial support from Programme National de Physique Stellaire (PNPS) of CNRS/INSU, France, and from the Centre National d'Études Spatiales (CNES, France). We also acknowledge support from the Agence Nationale de la Recherche (ANR, France) under grant ANR-17-CE31-0018, funding the INSIDE project. This work was granted access to the high-performance-computing resources of the CALMIP computing centre under allocation number 2017-p0205. This work was supported by the Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT, Canada) through a postdoctoral fellowship awarded to N.G. G.F. also acknowledges the contribution of the Canada Research Chair Program, and W.Z. the LAMOST fellowship as a young researcher, supported by the Special Funding for Advanced Users, budgeted and administrated by the Center for Astronomical Mega-Science, Chinese Academy of Sciences. V.V.G. is an F.R.S.-FNRS Research Associate. The authors acknowledge the Kepler team and everyone who has contributed to making this mission possible. Funding for the Kepler mission is provided by NASA’s Science Mission Directorate.

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Authors

Contributions

N.G. wrote the manuscript and performed the seismic analysis of KIC08626021. S.C. and G.F. contributed to the writing of the manuscript. S.C., P.Br. and N.G. contributed to the development of the numerical codes used in this analysis. E.M.G. obtained the spectroscopic data for KIC08626021. P.Be. and G.F. performed the model atmospheric analysis. W.Z. provided Fig. 1. V.V.G., G.F. and M.A.D. performed non-adiabatic complementary analysis. All authors discussed the results and contributed to their interpretation.

Corresponding author

Correspondence to N. Giammichele.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks M. Salaris, O. Straniero and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Model fit to the spectrum of KIC08626021 (catalogued as J1929+4447).

The model fit is shown in black, the observed spectrum in red. Our estimates indicate that KIC08626021 is the second hottest of the known pulsators of the V777 Her type. The quoted uncertainties are only the formal errors of the fit.

Extended Data Figure 2 Parameterization of the helium profile in the envelope of a typical DB white dwarf model.

The figure shows the local helium mass fraction, X(He), as a function of the fractional mass depth, log(q)?≡log[1−M(r)/M]. Along with the three quantities depicted in the plot—log(q1), log(q2) and X(He)env, as defined previously—there are two other hidden parameters that are related to the shape of the helium profile in the descent centred on log(q1) and in the descent centred on log(q2) (see text for details).

Extended Data Figure 3 Map of the 15-dimensional merit function S2 projected onto the log(g)–Teff plane for models of KIC08626021.

The merit function is shown on a logarithmic colour scale (base 10).The location of the optimal model in this plane is indicated by a white cross. The white dotted curves delimit the regions where the merit function has values within the 1σ, 2σ and 3σ confidence levels relative to the best-fitting solution. The black cross surrounded by the solid black box indicates the independent spectroscopic solution and its 1σ uncertainties.

Extended Data Figure 4 Results of the statistical analysis carried out in parameter space about the optimal seismic model for KIC08626021.

Only the most interesting parameters are illustrated here. Each histogram shows the derived probability-density function for a given model parameter. The orange hatched region between the two vertical solid red lines defines the?±1σ range, containing 68.3% of the distribution. The green curve defines the Gaussian fit applied to the distribution, which gives the?±1σ range. The blue vertical dashed line indicates the value of the parameter of the optimal model solution. The mean, median and mode values are also indicated. The estimate of the parameter of interest, indicated in red, is the statistical value (not the optimal one) and corresponds to the central value of the?±1σ interval. The various panels correspond to the following model parameters: a, effective temperature; b, surface gravity; c, central mass fraction of oxygen; d, total mass fraction of helium; e, total mass; and f, total radius of the star (in logarithmic units).

Extended Data Figure 5 Derived probability-distribution functions, normalized to 1, for the oxygen, carbon and helium profiles.

Extended Data Figure 6 Various properties of our optimal model.

a, Normalized weight function plotted against the normalized radius. Each individual weight function for the eight gravity modes of interest from the optimal model of KIC08626021 is normalized to a maximum value of 1.0. The weight function of a mode indicates the layers contributing most to the integral, giving the frequency (period) of the mode according to a well known variational principle in linear pulsation theory. The middle panel illustrates the chemical stratification of the model. All of the identified modes are useful probes of the core composition. b, Internal rotation profile. Contour map of the two-dimensional merit function that optimizes the match between the observed spacings in the three frequency multiplets with computed spacings on the basis of our seismic model. This is shown in terms of depth (expressed as the normalized radius) and in terms of the local rotation period of the inner region in the two-zone approach of ref. 45. The best-fitting solution is illustrated by the nearly vertical white curve about the solid-body solution (vertical dot-dashed white line). The dotted white curves on both sides of the solution depict its associated 1σ, 2σ and 3σ uncertainty contours. The fact that these contours diverge out at the greater depths considered here indicates that the rotationally split gravity modes available here lose their capacity to measure the local rotation rate at greater depths (indeed, their rotation kernels have negligible amplitudes at such depths). The horizontal white dot-dashed lines indicate the layer below which there is 99%, 90% and 10% of the mass of the star, from top to bottom. c, Comparison between the ranges of detected and excited periods in KIC08626021. The panel shows the detected periods (thick lines) with the bands of excited periods (thin lines) in two models similar to the optimal seismic model, but computed with the higher convective efficiency of ML2/α?=?1.5 (above) and ML2/α?=?1.6 (below). The reduced period is used as the abcissa in order to have comparable values for both dipole mode (in red) and quadrupole mode (in blue). The radial order k is indicated at both ends of each range.

Extended Data Table 1 Mode identification and details of the frequency fit obtained for the optimal solution
Extended Data Table 2 Defining parameters of the optimal seismic model found for KIC08626021
Extended Data Table 3 Observed periods, mode identification and normalized merit functions for past seismic studies of KIC08626021 compared with this work
Extended Data Table 4 Main inferred parameters from past seismic studies of KIC08626021 in comparison with this work

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Giammichele, N., Charpinet, S., Fontaine, G. et al. A large oxygen-dominated core from the seismic cartography of a pulsating white dwarf. Nature 554, 73–76 (2018). https://doi.org/10.1038/nature25136

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