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Balancing Variety and Sample Size: Optimal Parameter Sampling for Ariel Target Selection

Emilie Panek, Alexander Roman, Katia Matcheva, Konstantin T. Matchev, Nicolas B. Cowan

TL;DR

This work addresses how to optimally select exoplanet targets for Ariel within a finite observing budget by comparing time-, variance-, and leverage-based criteria. It introduces a leverage-based objective that balances sample size and diversity and evaluates multiple algorithms, including leverage-greedy, simulated annealing, class-based binning, and clustering, across one to three axes of planetary diversity. The results show leverage-based strategies, particularly leverage-greedy, achieve higher population-leverage than time- or variance-focused methods, while maintaining substantial target counts; simulated annealing provides competitive performance with larger samples. The approach provides a practical framework for mission planning, enabling diverse and scientifically valuable atmospheric samples within mission constraints and setting up future work on population-level trends and scheduling considerations for Ariel.

Abstract

Targeted astrophysical surveys are limited by the amount of telescope time available, which makes it impossible to observe every single object of interest. In order to maximize the scientific return, we need a well thought strategy for selecting the observational targets, in our case exoplanets. This study evaluates various strategies for selecting exoplanet targets within limited observation windows, focusing specifically on the selection of exoplanet targets for Tier 2 transit spectroscopy with ESA's upcoming Ariel mission. We define three distinct selection criteria -- sample size, variance, and leverage -- and translate them into objective functions compatible with modern optimization algorithms. Specifically, we test five heuristics for maximizing sample leverage: leverage greedy, simulated annealing, K-means clustering, regular classes, and quantile classes. The performance of these methods is demonstrated through three practical exercises across one, two, and three parameters of diversity. Each criterion represents a unique trade-off between sample size, diversity, and total observation time. While a time-greedy approach maximizes the quantity of planets, it fails to capture diversity. Conversely, variance-greedy selection prioritizes diversity but introduces significant drawbacks: it oversamples rare cases and undersamples typical planets, ultimately reducing the total number of targets observed. Leverage-based selections emerge as the most effective middle ground, successfully balancing sample diversity with a robust sample size. This work supports the broader community effort to ensure that Ariel delivers the most diverse and scientifically valuable sample of exoplanet atmospheres within mission limits.

Balancing Variety and Sample Size: Optimal Parameter Sampling for Ariel Target Selection

TL;DR

This work addresses how to optimally select exoplanet targets for Ariel within a finite observing budget by comparing time-, variance-, and leverage-based criteria. It introduces a leverage-based objective that balances sample size and diversity and evaluates multiple algorithms, including leverage-greedy, simulated annealing, class-based binning, and clustering, across one to three axes of planetary diversity. The results show leverage-based strategies, particularly leverage-greedy, achieve higher population-leverage than time- or variance-focused methods, while maintaining substantial target counts; simulated annealing provides competitive performance with larger samples. The approach provides a practical framework for mission planning, enabling diverse and scientifically valuable atmospheric samples within mission constraints and setting up future work on population-level trends and scheduling considerations for Ariel.

Abstract

Targeted astrophysical surveys are limited by the amount of telescope time available, which makes it impossible to observe every single object of interest. In order to maximize the scientific return, we need a well thought strategy for selecting the observational targets, in our case exoplanets. This study evaluates various strategies for selecting exoplanet targets within limited observation windows, focusing specifically on the selection of exoplanet targets for Tier 2 transit spectroscopy with ESA's upcoming Ariel mission. We define three distinct selection criteria -- sample size, variance, and leverage -- and translate them into objective functions compatible with modern optimization algorithms. Specifically, we test five heuristics for maximizing sample leverage: leverage greedy, simulated annealing, K-means clustering, regular classes, and quantile classes. The performance of these methods is demonstrated through three practical exercises across one, two, and three parameters of diversity. Each criterion represents a unique trade-off between sample size, diversity, and total observation time. While a time-greedy approach maximizes the quantity of planets, it fails to capture diversity. Conversely, variance-greedy selection prioritizes diversity but introduces significant drawbacks: it oversamples rare cases and undersamples typical planets, ultimately reducing the total number of targets observed. Leverage-based selections emerge as the most effective middle ground, successfully balancing sample diversity with a robust sample size. This work supports the broader community effort to ensure that Ariel delivers the most diverse and scientifically valuable sample of exoplanet atmospheres within mission limits.
Paper Structure (15 sections, 18 equations, 5 figures, 1 table)

This paper contains 15 sections, 18 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data
  3. Methods
  4. Sample size (time greedy selection)
  5. Sample variety (variance greedy selection)
  6. Sample leverage
  7. Regular classes
  8. Quantile classes
  9. K-means clustering
  10. Leverage greedy selection
  11. Simulated annealing
  12. Random selection
  13. Multiple axes of diversity
  14. Results
  15. Summary and conclusions

Figures (5)

  • Figure 1: Total observing time required to reach an Ariel Tier 2 SNR versus the planet radius (left panel), the planet equilibrium temperature (middle panel) or the effective temperature of the star (right panel).
  • Figure 2: One-parameter exercise. Subpopulation of selected planets (in orange) using different selection objectives: sample size (eq. (\ref{['eq:ft']}), top panel), sample variety (eq. (\ref{['eq:fv']}), middle panel) and sample leverage (eq. (\ref{['eq:fL']}), bottom panel). The color-coding indicated on the colorbar represents the contribution of an individual planet to the total time budget $T$ (top panel) or to the objective function (middle and lower panels).
  • Figure 3: One-parameter exercise. Subpopulations of selected planets (in orange) for the leverage objective function (\ref{['eq:fL']}), using alternative heuristics for maximizing the objective function: regular classes (Section \ref{['sec:regular_classes']}, top left panel), quantile classes (Section \ref{['sec:quantile_classes']}, top right panel), K-means clustering (Section \ref{['sec:Kmeans']}, bottom left panel) and simulated annealing (Section \ref{['sec:simulated_annealing']}, bottom right panel). The selection using the leverage-greedy algorithm of Section \ref{['sec:leverage_greedy']} was already shown in the bottom panel of Figure \ref{['fig:comparison_planet_greedy_selections']}.
  • Figure 4: A summary plot of the performance of all the different selection methods discussed in the paper for the one-parameter exercise. Colored circles correspond to the seven selection strategies shown in Table \ref{['tab:heuristics']}, while black dots represent randomly chosen subsets. The background is shaded according to the leverage of the selected subset.
  • Figure 5: Comparison of cumulative curves for each of the seven selection strategies discussed in the paper. The top row is showing the number of planets selected as a function of observation time in days. The bottom row is similarly showing the sample leverage as a function of observation time. The left (middle, right) columns represent the results for the one- (two-, three-) parameter exercise, respectively.