Maximizing Ariel's Survey Leverage for Population-Level Studies of Exoplanets

TL;DR

The paper addresses how to optimally select Ariel's exoplanet targets to maximize population-level trend precision in atmospheric properties. It introduces the leverage metric $L = \sqrt{N}\,\mathrm{stdev}(x)$ and shows that the slope uncertainty $\sigma_m$ scales as $\sigma_y / L$, turning target selection into a combinatorial problem of maximizing leverage under fixed observing time. Through notional three-axis diversity (radius, equilibrium temperature, and host-star temperature) and class-based schemes, the study finds that while adding diversity increases sample heterogeneity, it often reduces the number of observable targets; the one-room schoolhouse (single class) scheme frequently yields the highest leverage, with periodic schemes offering modest gains at the cost of fewer targets. Including planet candidates significantly boosts both target counts and leverage, underscoring the importance of vetting and weighing candidates before finalizing the Ariel target list. The results provide practical guidance for prioritizing easy-to-observe targets to maximize population-level scientific return, while acknowledging scheduling and observational-equity tradeoffs.

Abstract

ESA's Ariel mission will be uniquely suited to performing population-level studies of exoplanets. Most of these studies consist of quantifying trends between an Ariel-measured quantity, y, and an a priori planetary property, x; for example, atmospheric metallicity as inferred from Ariel transit spectroscopy vs. planetary mass. The precision with which we can quantify such trends depends on the number of targets in the survey and their variance in the a priori parameter. We define the leverage of a survey with N targets as L = sqrt(N)stdev(x) and show that it quantitatively predicts the precision of population-level trends. The target selection challenge of Ariel can therefore be summarized as maximizing L along some axes of diversity for a given cumulative observing time. To this end, we consider different schemes to select the mission reference sample for a notional three year transit spectroscopy survey with Ariel. We divide the exoplanets in the mission candidate sample into logarithmic classes based on radius, equilibrium temperature and host star temperature. We then construct a target list by cyclically choosing the easiest remaining target in each class. We find that the leverage on a single axis of diversity can be increased by dividing that axis into many classes, but this sacrifices leverage along other axes of diversity. We conclude that a modest number of classes, possibly only one, should be defined when selecting Ariel targets. Lastly, we note that the statistical leverage of the Ariel transit survey would be significantly increased if current candidate planets were confirmed. This highlights the urgency of vetting and confirming the easiest transmission and emission spectroscopy targets in the Ariel mission candidate sample.

Figures (5)

• Figure 1: Example science case for the Ariel transit spectroscopy survey. Each black dot represents a hypothetical planet with a precisely measured equilibrium temperature and uniform uncertainties on the retrieved atmospheric metallicity (motivated by the uniform signal-to-noise of Ariel Tier 2 transit spectra). The gray line and band shows the best-fit linear trend and its $1\sigma$ confidence interval. The Ariel target-selection problem for this science case amounts to choosing the planets that minimize the uncertainty on the slope of the trend line, for a given amount of cumulative observing time.
• Figure 2: An example $3\times3$ logarithmic class structure for two axes of diversity: planetary radius, $R_{\rm p}$, and equilibrium temperature, $T_{\rm eq}$. Gray dots show the Ariel mission candidate sample from 2022AJ....164...15E, while gray dotted lines denote the extrema of the sample. The dashed red lines show the class boundaries for the regular classes (equally dividing the parameter space bounded by the extrema), while the blue dashed lines show the boundaries between percentile classes (equally dividing the planets based on a ranked list).
• Figure 3: Number of observed planets (top), standard deviation of the population (middle), and leverage on equilibrium temperature (bottom) as a function of total observing time. From left to right we consider an increasing number of axes of diversity: only equilibrium temperature (left), also planet radius (middle), and also stellar effective temperature (right), always with three classes per axis. The central column corresponds to the $3\times 3$ logarithmic class system shown in Figure \ref{['fig: classes']}. Surveys using only confirmed planets (dashed lines) observe 44% to 71% fewer targets and provide 15% to 27% less leverage. Dividing planets into regular classes improves leverage when only considering one axis of diversity (left column), but this advantage disappears ---and becomes a disadvantage--- when considering more axes.
• Figure 4: Leverage in equilibrium temperature (left) and planetary radius (right) for 2D regular classes in log space. For each panel the leverage is normalized to that of the one-room schoolhouse (bottom left corner of each panel). The green star in each panel highlights the class system yielding greatest leverage in that axis. The sum of the normalized leverages in both$T_{\rm eq}$ and $R_{\rm p}$ is shown by a white star. The $3\times 3$ class structure used in previous figures is highlighted by a black box. The best leverages achievable are $\sim$25% better than that of the one-room schoolhouse (light blue), but most class structures lead to somewhat worse leverage (shades of red).
• Figure 5: Number of planets observed (left) and resulting Gini coefficient (right) for a notional 3 year Ariel transit survey. The white star highlights the best overall leverage. The one-room schoolhouse yields the most targets, with other scenarios resulting in 30--60% fewer planets and Gini coefficients 50--100% worse. The one-room schoolhouse is the most equitable option and in general the Gini coefficient is lower for class structures that lead to more planets being observed.