The neutron excess of 22Ne, relative to the matter composing the white dwarf core that has equal number of protons and neutrons, results in a net downward gravitational force and a slow settling of 22Ne in the liquid regions towards the centre of the white dwarf 26,27. 22Ne sedimentation process releases substantial energy to appreciably modify the cooling of white dwarfs, causing delays in their evolution 28. The occurrence of this process in average-mass white dwarfs has been shown to be a key factor in solving the long-standing age discrepancy of the metal-rich cluster NGC 6791 29 and to understand the cutoff regions of the local white dwarf luminosity function 30.
The diffusion coefficient of 22Ne in the liquid core of white dwarfs has a strong dependence on the atomic charge Z of the background matter 31, 32. Therefore, 22Ne sedimentation turns out to be more efficient in a CO-core white dwarf than in a ONe-core white dwarf, thus resulting in a selective effect that produces strong delays in the cooling times of CO-core white dwarfs, but not in ONe-core white dwarfs. In Fig. 2, we show the effect of ²²Ne diffusion process on the evolution of selected 1.10 Mo ultra-massive white dwarf sequences with different core chemical compositions, i. e., CO-core and ONe-core white dwarfs. All these white dwarf sequences consider the energy released by latent heat and phase separation due to crystallization process. The white dwarf sequences displayed with dashed lines consider also the energy released by ²²Ne sedimentation process. This process was computed using the diffusion coefficients provided by 32, which are the result of molecular dynamic simulations. The strong dependence of the diffusion coefficients on the core chemical composition results evident by inspecting this Figure. For the CO-core white dwarf considering ²²Ne diffusion, the time delay compared to the ONe-core white dwarf sequence that disregards ²²Ne sedimentation is on average ~ 5 Gyr. For the ONe-core white dwarf sequence, the time delay caused by ²²Ne sedimentation process is negligible. Although ultra-massive white dwarfs are affected by 22Ne sedimentation quite early in their evolution due to their large characteristic gravities, this process is abruptly interrupted in the crystallized core, and the energy released is reduced when crystallization process sets in. Coulomb interactions are weaker in nuclei with lower atomic charge, and thus, crystallization occurs at lower luminosities in CO-core white dwarfs than in their ONe-core counterparts, allowing ²²Ne diffusion to operate for a longer period of time. Furthermore, the total thermal content of a white dwarf is higher for lower atomic-mass chemical compositions. Hence, the thermal energy stored in the ions is higher in CO-core white dwarfs than in ONe-core white dwarfs, reducing their cooling rate. This fact is reflected in the long cooling times experienced by the CO-core white dwarf model that does not consider ²²Ne sedimentation process in Fig. 2. However, the delays induced only by considering CO-core chemical composition and not including ²²Ne diffusion are not high enough to account for the new observations revealed by the Gaia space mission.
It is important to remark that the real C to O proportion in the core of ultra-massive white dwarfs is still unclear due to the high uncertainties on the C + α nuclear rate and due to the uncertainties in their past merger evolutionary history. Therefore, a C-enhanced chemical composition would provide even larger cooling delays induced by ²²Ne sedimentation process than the standard C-O proportions. Moreover, possible uncertainties in the 22Ne diffusion coefficients could also enlarge the cooling delays induced by this process in CO-core white dwarfs.
To correctly assess the white dwarf cooling delays induced by 22Ne sedimentation, the exact amount of 22Ne content in these stars is crucial, as higher ²²Ne abundances will lead to larger delays in the cooling times 33. In the single-star evolution scenario, the abundance of 22Ne expected in a white dwarf star is roughly equal to the initial stellar metallicity, and is created during the helium core burning phase from helium captures on 14N, via the reactions 14N(α, γ)18F(β+)18O(α, γ)22Ne. 14N is left from hydrogen burning via the CNO cycle. Hence, ²²Ne sedimentation will be more effective in those white dwarfs that result from high-metallicity progenitors 29, due to their larger 22Ne content. On the contrary, the amount of ²²Ne remaining in the CO-core of a white dwarf that results of a merger event could be larger, depending on the hydrogen content of the binary components at the moment of merger. The study of 34 shows that the abundance in a merger episode of two white dwarfs could be as high as ~ 0.06. Therefore, we have also explored the 22Ne sedimentation process considering a higher 22Ne abundance (X²²Ne=0.06), and we confirmed the strong dependence of the cooling delays of CO-core ultra-massive white dwarfs on the 22Ne content. The impact of ²²Ne sedimentation process on the evolution of CO core ultra-massive white dwarfs is particularly strong for high 22Ne content, where the delays in the cooling times reach 8 Gyrs at the Q branch, and 11 Gyrs by the faint end of the cooling sequence, when compared with the ONe-core cooling sequence (see Fig. 3). On the other hand, due to the larger mean atomic number in their core chemical composition, the cooling of ONe core ultra-massive white dwarfs is not substantially altered by ²²Ne sedimentation process, regardless of their 22Ne content. The cooling age of a 1.10 Mo ultra-massive ONe white dwarf in the Q branch is of 2 Gyrs, whereas a CO-core white dwarf with X²²Ne=0.06 of the same mass amounts to 10 Gyrs (see Fig. 3). These strong delays in the cooling times of CO-core ultra-massive white dwarfs imply that these stars will remain in the Q branch for longer periods of time, when compared with their ONe counterparts, that will rapidly age towards fainter absolute magnitudes.
In order to demonstrate the possible existence of these eternal youth ultra-massive CO-core white dwarfs, we have analyzed the effect of ²²Ne sedimentation on the local white dwarf population revealed by Gaia observations by means of an up-to-date population synthesis code. The code, based on Monte Carlo techniques, incorporates the different theoretical white dwarf cooling sequences under study, as well as an accurate modeling of the local white dwarf population and observational biases.
We have performed a population synthesis analysis of the Galactic thin disk white dwarf population within 100 pc from the Sun under different input models. In order to minimize the selection effects, we chose the 100 pc sample, given that it represents the maximum size that the sample can be considered volume-limited and thus practically complete sample 4.
First, we considered that all the ultra-massive white dwarfs in the simulated sample have ONe core composition. This first synthetic population is shown in the Gaia HR diagram in the upper left panel of Fig. 4. The histogram of this synthetic population is shown in the upper right panel (black steps), together with the Gaia 100 pc white dwarf sample (red steps). The Q branch can easily be regarded as the main peak in the histogram of the Gaia 100 pc white dwarf sample, between z = 13.0 and z = 13.4. A first glance at these three histograms reveals that ultra-massive ONe white dwarfs fail to account for the pile-up in the Q branch, even though the ONe white dwarf sequences used include all the energy sources resulting from the crystallization process. A quantitative statistical reduced x2-test analysis of the synthetic population distribution in the Q branch reveals a value of 11.18 when compared to the observed distribution.
The middle left panel of Fig. 4 illustrates the HR diagram of a typical synthetic white dwarf population realization, considering that 20% of the ultra-massive white dwarfs come from merger events. That is, 20% of the ultra-massive white dwarfs harbour a CO-core. In this model we also have assumed white dwarfs with high ²²Ne abundance, X²²Ne=0.06. The histogram of this synthetic population, shown in black steps in the middle right panel, reveals that, although a mixed white dwarf population with both CO-core and ONe-core white dwarfs is in better agreement with the observations, the pile-up is still not fully reproduced. The reduced x2 value of this synthetic population is 2.60.
Finally, we have also performed a population synthesis realization in which 50% of the ultra-massive white dwarfs have a merger origin and their core-chemical composition is CO. As in the previous model, the ²²Ne content of the white dwarf sequences with merger origin was set to X²²Ne=0.06. The results of this synthetic population are shown in the lower panels of Fig. 4. We found that this simulation is in perfect agreement with the observed white dwarf sample, being its reduced x2-test value 1.36.
The better agreement with the observations revealed by Gaia of the synthetic populations that include CO-core ultra-massive white dwarf sequences is in line with the longer cooling times that characterize these stars due to ²²Ne sedimentation process. We have also simulated a synthetic population that considers a fraction of merger of 50% and a ²²Ne abundance of 0.02, finding a better agreement when compared to simulations computed with only ONe-core white dwarfs, but not as good as the agreement we found for a population with high ²²Ne content (The reduced x2 value of this synthetic population is 4.86). We have also generated synthetic populations considering different ²²Ne abundances in the white dwarf models and found that the best fit models are obtained for a high ²²Ne abundance (X²²Ne=0.06), as the one shown in the middle and lower panels of Fig. 4. Such a high ²²Ne abundance is not consistent with the isolated standard evolutionary history channel, because it would imply that these white dwarfs come from high-metallicity progenitors. However, merger events provide a possible scenario to create such a high ²²Ne abundance. If H were burnt in C-rich layers during the merger event, it would create a high amount of 14N that could later capture He ions, creating a high ²²Ne abundance before the ultra-massive white dwarf is born.
The analysis of the ultra-massive white dwarf population revealed by Gaia shows that ONe-core white dwarfs alone are not able to account for the pile-up in the ultra-massive Q branch. Indeed, energy sources as latent heat and phase separation process due to crystallization, and ²²Ne sedimentation can not prevent the fast cooling of these stars. According to our study, the Q branch is the observational evidence of the presence of white dwarfs with CO core, that experience a stronger delay in their cooling due to the combination of three effects: crystallization, ²²Ne sedimentation and higher thermal content.