AI 中文总结
本研究基于质量连续性方程提出统一物理框架，结合最小化宇宙学气体流动模型与控制实验，揭示了基本金属丰度关系（FMR）的物理起源，证明气态FMR更具根本性，为利用金属丰度标度关系探测宇宙重子循环提供理论基础。
AI 中文摘要
我们基于质量连续性方程，提出了一个用于解释基本金属丰度关系（FMR）的统一物理框架。FMR并非仅仅是固定恒星质量（$M_\star$）下恒星形成率（SFR）与气体金属丰度（$Z_{\rm g}$）之间的反相关关系；它是$(M_\star, {\rm SFR}, Z_{\rm g})$空间中一个不随红移变化的曲面。我们构建了一个最小化宇宙学气体流动模型，经校准后可重现$z=0-3$时的质量-金属丰度关系、恒星形成主序以及恒星-晕质量关系，并证明FMR是该校准物理模型的自然预测结果。通过逐步简化模型的控制实验，我们揭示出在恒星形成效率（$ε$）和质量负载因子（$η$）均为常数的宇宙中，FMR会简化为$Z_{\rm g}$与$M_\star/{\rm SFR}$之间的普适标度关系，其形态反映了从流入驱动区向平衡态的转变。观测到的FMR的具体参数化形式并非一种基本对称性，而是$ε$和$η$依赖于恒星质量与红移的偶然结果。我们表明，定义在$(M_\star, M_{\rm g}, Z_{\rm g})$空间中的气态FMR（gFMR）比标准FMR更具根本性：在流入驱动极限下，$Z_{\rm g}$与$M_\star/M_{\rm g}$成正比，且向平衡态的趋近仅由$M_\star/M_{\rm g}$和$η$决定。我们推导了模型理想化版本的解析解，给出了关联$Z_{\rm g}$、$M_{\rm g}/M_\star$和$η$的闭合形式表达式，并证明该框架能准确复现宇宙学气体流动模型的结果。通过明确FMR的物理起源及其与更根本的gFMR的联系，我们为将金属丰度标度关系转化为探测宇宙历史中重子循环的精密工具提供了理论基础。
英文摘要
We present a unified physical framework for the fundamental metallicity relation (FMR), based on the mass-continuity equations. The FMR is not merely the anti-correlation between star formation rate (SFR) and gas metallicity ($Z_{\rm g}$) at fixed stellar mass ($M_\star$); it is a redshift-invariant surface in the $(M_\star,{\rm SFR},Z_{\rm g})$ space. We construct a minimal cosmological gas flow model, calibrated to reproduce the mass-metallicity relation, star-forming main sequence, and stellar-to-halo mass relation at $z=0-3$, and show that the FMR emerges as a prediction of the calibrated physics. Through controlled experiments that progressively simplify the model, we reveal that in a universe where both the star formation efficiency ($ε$) and mass-loading factor ($η$) are constants, the FMR reduces to a universal scaling between $Z_{\rm g}$ and $M_\star/$SFR, whose shape traces the transition from inflow-driven regime to equilibrium. The specific parameterisation of the observed FMR is not a fundamental symmetry but a contingent consequence of how $ε$ and $η$ depend on stellar mass and redshift. We show that the gaseous FMR (gFMR), defined in the $(M_\star,M_{\rm g},Z_{\rm g})$ space, is more fundamental than the standard FMR: in the inflow-driven limit, $Z_{\rm g}$ is proportional to $M_\star/M_{\rm g}$, and the approach to equilibrium is governed by $M_\star/M_{\rm g}$ and $η$ alone. We derive an analytic solution for an idealised version of the model that provides closed-form expressions relating $Z_{\rm g}$, $M_{\rm g}/M_\star$, and $η$, and show this framework accurately reproduces the cosmological gas flow model. By establishing the physical origin of the FMR and its connection to the more fundamental gFMR, we provide the theoretical foundation to turn metallicity scaling relations into precision probes of the baryon cycle over cosmic history.
Comments29 pages, 17 + 2 figures. Presents a unified framework for the fundamental metallicity relation, with a physical picture in Sec. 3, an analytic derivation in Sec. 4, and a comparison to previous models and observations in Sec. 5
