Introduction

Fitting stellar models to observations

Suppose you’ve observed some isolated star (i.e. not a binary or multiple) in the sky. Perhaps you’ve recorded its brightness in a number of passbands. Perhaps you’ve recorded a spectrum at optical wavelengths. How old is this star? One way to estimate the star’s age is to compare these observations to a collection of models computed using a stellar evolution code, which solves a set of equations, derived with some physical assumptions and approximations.

For single stars, however, there are generally more free parameters than we can constrain using our observations. The degeneracy is usually solved by making strict assumptions about the parameters. e.g. convection’s length-scale is the same as whatever gives us a good fit to the Sun, for which we do have enough information to constrain all the free parameters. 1 Even then, age estimates in particular can be quite uncertain.

The situation changes for solar-like oscillators. With high-quality data, one can at measure the frequencies and identify the angular degrees of multiple individual modes, which leaves us with more observables than unknowns. Even if we can’t reliably detect individual mode frequencies, we can often detect the characteristic spacing between modes of the same angular degree (the large separation) and the frequency at which the modes have the greatest power.

AIMS3 is a Python library that provides components for pipelines to fit pre-computed stellar models to observations that includes data from oscillations (seismic data) and other sources, like optical spectra (nonseismic data). The principal components of this process are:

  1. some sort of function that takes stellar model parameters (e.g. mass and age) and returns predicted observables,

  2. a function that defines how well a given set of predicted (or theoretical) observables matches actual observations, and

  3. a function that combines these functions to estimate the true distribution of the model parameters.

Following the original AIMS implementation, the core methods that AIMS3 uses for each of these steps are:

  1. linear interpolation in a pre-computed grid of stellar models,

  2. a configurable posterior function, and

  3. Markov Chain Monte Carlo (MCMC) sampling.

The rest of the user guide describes the concepts behined each of these components. For the details of the interfaces, see the API documentation.

1

Unless you start adding more free parameters, like for convective overshooting.