In the conventional habitable zone (HZ) concept, a CO₂-H₂O greenhouse maintains surface liquid water. Through the water-mediated carbonate-silicate weathering cycle, atmospheric CO₂ partial pressure (pCO₂) responds to changes in surface temperature, stabilizing the climate over geologic timescales. We show that this weathering feedback ought to produce a log-linear relationship between pCO₂ and incident flux on Earth-like planets in the HZ. However, this trend has scatter because geophysical and physicochemical parameters can vary, such as land area for weathering and CO₂ outgassing fluxes. Using a coupled climate and carbonate-silicate weathering model, we quantify the likely scatter in pCO₂ with orbital distance throughout the HZ. From this dispersion, we predict a two-dimensional relationship between incident flux and pCO₂ in the HZ and show that it could be detected from at least 83 (2σ) Earth-like exoplanet observations. If fewer Earth-like exoplanets are observed, testing the HZ hypothesis from this relationship could be difficult.

在传统的可居住区（HZ）概念中，CO ₂ -H ₂ O温室维持地表液态水。通过水介导的碳酸盐-硅酸盐风化循环，大气中的CO ₂分压（pCO ₂）响应表面温度的变化，在地质时标上稳定了气候。我们表明，这种风化反馈应该在pZ ₂和HZ中类地行星的入射通量之间产生对数线性关系。但是，由于地球物理和理化参数会发生变化，例如风化的土地面积和CO ₂除气通量。使用气候和碳酸盐-硅酸盐风化耦合模型，我们量化了沿整个HZ轨道距离的pCO _2中可能的散射。根据这种弥散，我们预测了HZ中入射通量与pCO ₂之间的二维关系，并表明可以从至少83（2σ）个类似地球的系外行星观测中检测到。如果观测到的地球状系外行星较少，则从这种关系检验HZ假设可能很困难。