Hierarchically modelling many stars to improve inference with asteroseismology

Lyttle, Alexander J. ORCID: 0000-0001-8355-8082 (2023). Hierarchically modelling many stars to improve inference with asteroseismology. University of Birmingham. Ph.D.

Preview

Lyttle2023PhD.pdf
Text - Accepted Version
Available under License Creative Commons Attribution.
Download (14MB) | Preview

Abstract

Astronomers want accurate physical properties of stars like age, mass, and radius. We can estimate these by comparing observable parameters to those from models of stellar evolution. This has been made possible on a large-scale with recent astronomical surveys and the field of asteroseismology probing inside stars. In the first chapter of this thesis, I introduce asteroseismology --- the study of stellar oscillations. I choose to focus on stars which oscillate like the Sun with masses from 0.8 to 1.2 \(\mathrm{M}_{\odot}\) undergoing their main sequence and subgiant phases of evolution. To date, we have observed oscillations in hundreds of these stars. With the upcoming space-based PLATO mission, we anticipate observations of \(\sim 10^4\) more solar-like oscillators. In this thesis, I aim to develop probabilistic modelling methods which can quickly and easily scale to such huge numbers of stars. Furthermore, we know our stellar models are wrong. It is important to accurately quantify this uncertainty if we are to use stellar parameters to understand stellar populations. In Chapters 2 and 3, I present a novel approach for improving the inference of fundamental stellar parameters using a hierarchical Bayesian model. I introduce a statistical treatment which 'pools' helium abundance (\(Y\)) and the mixing-length theory parameter (\(\alpha_\mathrm{MLT}\)) to incorporate information about their distributions in the population. Specifically, I model \(Y\) as a distribution centred on a linear enrichment law parametrised by \(\Delta Y/\Delta Z\). I test our method on a sample of dwarfs and subgiants observed by Kepler with \(0.8 < M/\mathrm{M}_{\odot} < 1.2\). Exploring various levels of pooling parameters, with and without the Sun as a calibrator, I report \(\Delta Y/\Delta Z = 1.05^{+0.28}_{-0.25}\) when the Sun is included in the sample. Despite marginalising over uncertainties in \(Y\) and \(\alpha_\mathrm{MLT}\), I am able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Moreover, my approach can be extended to larger samples. This will enable further uncertainty reduction in fundamental parameters and data-driven insight into population-level distributions.

There is additional information on \(Y\) to be gained from detailed asteroseismology. Acoustic glitches, which arise from rapid changes in stellar structure (e.g. from helium ionisation), leave a periodic signature in the mode frequencies (\(\nu_{nl}\)) of solar-like oscillators. I explore the theoretical background behind this effect in Chapter 4. Then, in Chapter 5, I present a new method for modelling glitch signatures in the radial mode frequencies using a Gaussian Process (GP). The GP provides a statistical treatment of uncertainty in the functional form of our model for \(\nu_{nl}\). Using a model star and 16 Cyg A, I compare this approach to another method which models the smooth component of the function using a 4th-order polynomial. My results show that the GP method accurately determines the strength and location of glitches caused by He II ionisation and the base of the convective zone. I find that using a prior to inform the glitch parameters in my method reduces the occurrence of extreme, unrealistic solutions in the posterior. Furthermore, I demonstrate that the GP approach outperforms the polynomial by marginalising over the lesser signature of He I ionisation. However, inclusion of the He I ionisation glitch in the model remains a question. Overall, my results suggest that the GP method should be further tested on more solar-like oscillators and then integrated into the hierarchical model presented in this work.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):