最小浴缸玩具模型的解析解：高z星系恒星形成历史的挑战
An analytic solution for the minimal bathtub toy model: challenges in the star-formation history of high-z galaxies
摘要：
我们研究最小的“浴缸”玩具模型作为一种分析工具，捕捉星系演化的关键过程，并确定强大的成功和挑战，在高红移再现观测。气体和恒星连续性方程的源项和汇项由第一性原理用简单的项表示。假设恒星形成率（SFR）对气体质量的依赖性自调节系统到一个唯一的渐近行为，这是近似的解析准稳态解（QSS）。我们解决的QSS在不同的时代独立的早期条件的有效性。在高z时，假设吸积仅由气体组成，比SFR被稳健地预测为sSFR = [（1+z）/3]^{5/2} Gyr^{-1}，略高于宇宙学比吸积率，与z=3-8时的观测结果一致。预计气体分数将缓慢下降，并且观测结果将每动态时间的SFR效率限制为λ =0.02。恒星-维里质量比f_sv在时间上是恒定的，观测值需要一个流出质量装载因子eta=1-3，取决于气体进入星系的穿透效率。然而，在z=2时，恒星也通过合并吸积，最简单的模型在匹配观测时有明显的困难。使sSFR最大化的模型，流出物完全再循环，在sSFR中不足3倍，并且高估了f_sv。在强流出的情况下，模型可以重现观测到的fsv，但代价是低估了一个数量级的sSFR。我们讨论了潜在的补救措施，包括由于排除淬火星系的偏见。
英文摘要：
We study the minimal ``bathtub" toy model as an analytic tool for capturing key processes of galaxy evolution and identifying robust successes and challenges in reproducing observations at high redshift. The source and sink terms of the continuity equations for gas and stars are expressed in simple terms from first principles. The assumed dependence of star-formation rate (SFR) on gas mass self-regulates the system into a unique asymptotic behavior, which is approximated by an analytic quasi-steady-state solution (QSS). We address the validity of the QSS at different epochs independent of earlier conditions. At high z, where the accretion is assumed to consist of gas only, the specific SFR is robustly predicted to be sSFR = [(1+z)/3]^{5/2} Gyr^{-1}, slightly higher than the cosmological specific accretion rate, in agreement with observations at z=3-8. The gas fraction is expected to decline slowly, and the observations constrain the SFR efficiency per dynamical time to epsilon=0.02. The stellar-to-virial mass ratio f_sv is predicted to be constant in time, and the observed value requires an outflow mass-lading factor of eta=1-3, depending on the penetration efficiency of gas into the galaxy. However, at z=2, where stars are also accreted through mergers, the simplest model has an apparent difficulty in matching observations. The model that maximizes the sSFR, with the outflows fully recycled, falls short by a factor 3 in sSFR, and overestimates f_sv. With strong outflows, the model can reproduce the observed f_sv but at the expense of underestimating the sSFR by an order of magnitude. We discuss potential remedies including a bias due to the exclusion of quenched galaxies.
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