Abstract
We present a novel and efficient method for fitting dynamical models of stellar kinematic data for dwarf spheroidal galaxies (dSph). Our approach is based on Gaussian-process emulation (GPE), which is a sophisticated form of curve fitting that requires fewer training data than alternative methods. We use a set of validation tests and diagnostic criteria to assess the performance of the emulation procedure. We have implemented an algorithm in which both the GPE procedure and its validation are fully automated. Applying this method to synthetic data, with fewer than 100 model evaluations we are able to recover a robust confidence region for the three-dimensional parameter vector of a toy model of the phase-space distribution function of a dSph. Although the dynamical model presented in this paper is low-dimensional and static, we emphasize that the algorithm is applicable to any scheme that involves the evaluation of computationally expensive models. It therefore has the potential to render tractable previously intractable problems, for example, the modelling of individual dSphs using high-dimensional, time-dependent N-body simulations.
Highlights
In the cold dark matter ( CDM) model of cosmology, galaxies form by hierachical growth, with large galaxies being formed by the agglomeration of smaller ones
Dark-matter-only N-body simulations of halo-formation using CDM cosmology predict cusps in the dark-matter density profile of the dwarf spheroidal galaxies (dSph), the literature on the modelling of observed dSphs contains claims of both cusps and cores (Battaglia et al 2008, Strigari, Frenk & White 2010, Breddels & Helmi 2013, and Read & Steger 2018)
We wish better to understand the evolution of dSphs and as such require robust dynamical modelling of their end-states to act as targets for evolutionary simulations
Summary
In the cold dark matter ( CDM) model of cosmology, galaxies form by hierachical growth, with large galaxies being formed by the agglomeration of smaller ones. We perform a small number of runs, each using a different parameter, and use the resulting data to estimate the output for a parameter that we have not explicitly computed, along with a confidence interval for that estimate. We do this without needing to make an additional simulation run or model evaluation. We focus on DF-based models of the internal dynamics of a galaxy in order to illustrate the value of the GPE approach by emulating the likelihood of the DF parameter.
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