Fig. 3: The probability observed exoplanets will accidentally match a log-uniform distribution for pCO₂ in the HZ if the true pCO₂ distribution is regulated by the carbonate–silicate weathering cycle, as shown in Fig. 1.

This probability is shown on the vertical axis. The horizontal axis shows the number of observed Earth-like exoplanets. The solid gray curve and corresponding shaded gray region show the mean probability and 2σ uncertainty, respectively, that the observed planets, sampled from the planets shown in Fig. 1, match a log-uniform pCO₂ distribution in the HZ. This curve is calculated from 10,000 two-dimensional Kolmogorov–Smirnov tests (see Results, subsection “Observational uncertainty for pCO₂ in the HZ”). The solid, horizontal black line highlights the 5% probability line. At the bottom of the figure, the labeled points and error bars show the number of Earth-like exoplanets the next generation of proposed space telescopes are expected to observe (telescope data in Table 2). The vertical scaling of the telescope points is arbitrary, only the horizontal position and extent of the 1σ error bars is significant. To rule out a log-uniform pCO₂ distribution with 95% confidence, future telescopes would need to observe at least 83 Earth-like planets.