ASTROPHYSICS

Introduction

Stars are the building blocks of the visible Universe, which drive the galactic chemical evolution and act as observational tracers of the evolution of the cosmos as a whole. Yet models of stellar structure and evolution rely on parametric models of multi-dimensional phenomena, because many multi-dimensional processes operate on timescales that are up to 10 orders of magnitude smaller than the nuclear timescale, which is dominating stellar evolution during most of a stars' lifetime. The parametrizations of multi-dimensional processes are often based on simplistic assumptions and include free parameters that are adjusted to match observational properties of stars. In this project, we performed three-dimensional simulations of convective core hydrogen burning in main sequence stars, which allow us to test parametrized models and assumptions of two important stellar phenomena.

The most stringent tests of solar models are derived from helioseismology, which has been used to investigate the internal structure of the Sun for decades by observing tiny brightness fluctuations on the stellar surface. Therefore, the free parameters of convection are rather well known for the Sun. This, however, is not the case for most other stars. While the advancement in space-born observations has allowed us to use similar techniques to investigate the structure of distant stars, the seismological data is missing many details due to the larger distance.

Recent systematic observations, e.g., show a power excess in low oscillations (red noise) of inter-mediate to high mass stars on the main sequence. This feature cannot be explained by coherent oscillations, which indicates that it is driven by a stochastic excitation mechanism. The fact that red noise is seen in stars with and without convective envelopes strongly suggests that it is caused by internal waves created at the boundary of the convective core. This is an intrinsically multi-dimensional process, which cannot be captured by standard 1D stellar evolution models. The shape of the wave excitation spectrum is, hence, highly uncertain. Theoretical predictions of the excitation spectrum from convective regions predict a steep power law. Other simulations using 3D spherical geometry, on the other hand, find excitation spectra significantly shallower than predicted. However, the results of these simulations are likely affected by the high viscosity and artificially increased luminosity of the numerical setup in addition to the anelastic approximation.

We also found shallow excitation spectra in our fully compressible 2D simulations of a star with three times the mass of the Sun without any explicit viscosity but with an increased luminosity [2]. The simulations performed in this project aim to confirm this result in a fully compressible 3D simulation at the nominal stellar luminosity.

The other aspect we were investigating is the mixing of material across the convective boundary of convective cores, which is arguably the free parameter with the largest uncertainty in 1D stellar models. The evolution of stars more massive than the Sun is largely determined by the mass of their convectively mixed core, such that a more massive star with a smaller mixing parameter can have the same observable surface properties as a less massive star with larger mixing values. However, the respective age of these stars will be different. The degeneracy of mass and age has far-reaching consequences for other fields like the characterization of exoplanets and galactic archaeology.

Furthermore, the mixing during the early stages of stellar evolution, like hydrogen burning on the main sequence, has a huge impact throughout the remaining evolution up until the death of the star. The question if a star will eventually explode as a supernova is to a large extent determined by the size of the helium core at the end of the hydrogen burning phase.

Ongoing Research / Outlook

We are currently in the process of comparing excitation spectra generated from both two- and three-dimensional simulations. By analyzing these spectra and interpreting them based on theoretical models, we aim to make predictions for the excitation spectrum of stars with different masses, which can then be tested with further simulations. We are also working on a paper draft about these results, which we plan to submit to a peer-reviewed journal.

In the future, we would also like to assess the observability of certain features in the spectra. This requires an equilibrium state between the excitation and dissipation of the internal waves. Due to the long travel times of internal waves this would take 10 to 100 times longer simulations than we performed here, which is not achievable with current computing systems. However, studies showed that non-linear wave features do not play a significant role in the observed spectra, i.e. the current practice of using linear stellar oscillation codes to extract oscillation frequencies from one-dimensional stellar models can hardly be improved by multi-dimensional simulations. However, oscillation codes cannot predict the expected amplitudes of standing waves without additional information about the driving mechanism. The excitation spectra we extract from our simulations can be used exactly for that purpose, which will give us more insight into ways of detecting signatures of convection in asteroseismic observations.

References and Links

[1] www.h-its.org

[2] Horst, L., et al. 2020, A&A, 641, 18.

[3] Horst, L., et al. 2021, A&A, 653, 55.