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Time-dependent corrections to the Ly?$lpha$ escape probability during cosmological recombination

机译：宇宙重组过程中对Ly？$ alpha $逃逸概率的时间依赖性校正

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We consider the effects connected with the detailed radiative transfer during the epoch of cosmological recombination on the ionization history of our Universe.We focus on the escape of photons from the hydrogen Lymanresonanceat redshifts ,one of two key mechanismsdefining the rate of cosmological recombination. We approach this problem within the standard formulation, and corrections due to two-photon interactions are deferred to another paper.As a main result we show here that within a non-stationary approach to theescape problem, the resulting correction in the free electron fraction, ,is about 1.6-1.8% in the redshift range .Therefore the discussed process results in one of the largest modifications tothe ionization history close to the maximum of Thomson-visibility function atconsidered so far.We prove our results both numerically and analytically, deriving the escapeprobability, and considering both Lymanline emission and line absorption in a way different from the Sobolev approximation.In particular, we give a detailed derivation of the Sobolev escape probability during hydrogen recombination, and explain the underlying assumptions. We then discuss the escape of photons for the case of coherent scattering in the lab frame, solving this problem analytically in the quasi-stationary approximation and also in the time-dependent case.We show here that during hydrogen recombination the Sobolev approximation forthe escape probability is not valid at the level of -10%.This is because during recombination the ionization degree changessignificantly over a characteristic time ,so that atpercent level accuracy the photon distribution is not evolving along asequence of quasi-stationary stages.Non-stationary corrections increase the effective escape by at ,and decrease it by close tothe maximum of the Thomson-visibility function.We also demonstrate the crucial role of line emission and absorption indistant wings (hundreds and thousands of Doppler widths from the resonance) for this effect, and argue that the final answer probably can only be given within a more rigorous formulation ofthe problem using a two- or multi-photon description.Key words: radiative transfer - cosmology: cosmic microwave background - cosmology: early Universe - cosmology: theory - atomic processes - cosmology: cosmological parameters
机译：我们考虑了宇宙重组时期与详细辐射转移相关的影响，对我们宇宙的电离历史。我们着重研究了氢从里曼共振红移中的光子逸出，这是定义宇宙重组速率的两个关键机制之一。我们在标准公式中解决了这个问题，并且由于两光子相互作用而产生的校正被推迟到了另一篇论文中。作为主要结果，我们在这里表明，在非平稳方法中的逸出问题中，所得的自由电子分数校正， ，在红移范围内约为1.6-1.8％。因此，所讨论的过程导致了迄今为止所考虑的接近于汤姆森可见度函数最大值的最大电离历史变化之一。我们通过数值和分析证明了我们的结果，得出逃逸概率，并以不同于Sobolev近似的方式同时考虑Lymanline发射和线吸收。特别是，我们给出了氢重组过程中Sobolev逃逸概率的详细推导，并解释了基本假设。然后我们讨论了在实验室框架中相干散射情况下光子的逸出情况，在准平稳逼近以及时间相关情况下解析地解决了这个问题。在此我们证明了在氢重组过程中，Sobolev逼近的逸出概率不能在-10％的水平上有效。这是因为在重组过程中，电离度会在一个特征时间内发生显着变化，因此，在水平精度上，光子分布不会沿着准平稳阶段的顺序演化。非平稳校正会增加有效逃逸，并使其降低到接近汤姆森可见度函数的最大值。我们还证明了这种效应在距离较远的机翼（共振产生数百和数千个多普勒宽度）的线发射和吸收中的关键作用，并指出最终答案可能只能在使用两光子或多光子设计的更严格的问题表述中给出关键词：辐射传递-宇宙学：宇宙微波背景-宇宙学：早期宇宙-宇宙学：理论-原子过程-宇宙学：宇宙学参数

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