Observations of the Lyman-α forest in distant quasar spectra with upcoming surveys are expected to provide significantly larger and higher-quality datasets. To interpret these datasets, it is imperative to develop efficient simulations. One such approach is based on the assumption that baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. We extend our earlier work to assess the robustness of the lognormal model of the Lyman-α forest in recovering the parameters characterizing IGM state, namely, the mean-density IGM temperature (T ₀), the slope of the temperature-density relation (γ), and the hydrogen photoionization rate (Γ₁₂), by comparing with high-resolution Sherwood SPH simulations across the redshift range 2 ≤ z ≤ 2.7. These parameters are estimated through a Markov Chain Monte Carlo (MCMC) technique, using the mean and power spectrum of the transmitted flux. We find that the usual lognormal distribution of IGM densities cannot recover the parameters of the SPH simulations. This limitation arises from the fact that the SPH baryonic density distribution cannot be described by a simple lognormal form. To address this, we extend the model by scaling the linear density contrast by a parameter ν. While the resulting baryonic density is still lognormal, the additional parameter gives us extra freedom in setting the variance of density fluctuations. With this extension, values of T ₀ and γ implied in the SPH simulations are recovered at ∼ 1 - σ (≲ 10%) of the median (best-fit) values for most redshifts bins. However, this extended lognormal model cannot recover Γ₁₂ reliably, with the best-fit value discrepant by ≳ 3 - σ for z > 2.2. Despite this limitation in the recovery of Γ₁₂, whose origins we explain, we argue that the model remains useful for constraining cosmological parameters.

中文翻译：

---

Lyman-α 森林的改进对数正态近似：与 2 ≤ z ≤ 2.7 时的完整流体动力学模拟进行比较

莱曼河的观察-α遥远类星体光谱中的森林以及即将进行的调查预计将提供更大、质量更高的数据集。为了解释这些数据集，必须开发有效的模拟。其中一种方法基于这样的假设：星系间介质（IGM）中的重子密度遵循对数正态分布。我们扩展了我们早期的工作来评估莱曼对数正态模型的稳健性α森林恢复表征 IGM 状态的参数，即平均密度 IGM 温度（时间 ₀ ), 温度-密度关系的斜率 (γ) 和氢光电离率 (Γ ₁₂ )，通过与红移范围 2 ≤ 的高分辨率 Sherwood SPH 模拟进行比较z≤2.7。这些参数通过马尔可夫链蒙特卡罗 (MCMC) 技术使用传输通量的平均值和功率谱进行估计。我们发现 IGM 密度的通常对数正态分布无法恢复 SPH 模拟的参数。这种限制是由于 SPH 重子密度分布不​​能用简单的对数正态形式来描述。为了解决这个问题，我们通过参数缩放线性密度对比度来扩展模型ν。虽然最终的重子密度仍然是对数正态分布，但附加参数为我们提供了额外的自由度来设置密度波动的方差。通过此扩展，值时间 ₀和γSPH 模拟中隐含的值在 ∼ 1 - 处恢复σ大多数红移箱的中值（最佳拟合）的 (≲ 10%)。然而，这种扩展的对数正态模型无法可靠地恢复 Γ ₁₂，最佳拟合值相差 ≳ 3 -σ为了z> 2.2。尽管我们解释了 Γ ₁₂的恢复的局限性（我们解释了其起源），但我们认为该模型对于约束宇宙学参数仍然有用。