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arXiv 2211.03082astro-ph.CO
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$i(cm)z$，一个计算星系团热力学性质的半解析模型：质量和红移的校准，以及流体静力学偏差的意义

$i(cm)z$, a semi-analytic model for the thermodynamic properties in galaxy clusters: calibrations with mass and redshift, and implication for the hydrostatic bias

S. Ettori, L. Lovisari, D. Eckert

备注：
15 pages; A&A in press. Updated to match the published version; a few typos were corrected, and a reference added
发表信息：
A&A 669, A133 (2023)
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摘要：

在星系团形成和演化的自相似方案中，X射线发射等离子体的热力学性质可以仅依赖于晕质量和红移来预测。然而，已经观察到与这种简单的自相似场景的几个偏离。我们展示了如何我们的半解析模型$i(cm)z$，它修改了自相似的预测，通过两个温度依赖的量，气体质量分数$f_g=f_0 T^{f_1} E_z^{f_z}$和温度变化$f_T=t_0 T^{t_1} E_z^{t_z}$，可以被校准，将质量和红移的依赖关系。我们使用了一组已发布的17个比例关系来约束模型的参数。随后，我们能够预测任何观测到的标度关系的斜率，其值在中心值的百分之几以内，标称误差约为一个$σ$。在上下文中，这些标度律的演变也被确定，预测在$1.5 σ$和10%的观测约束。依靠这种校准，我们还评估了与一些观测数据集的径向轮廓的预测的一致性。对于高质量数据（X-COP）的样本，我们能够约束模型的另一个参数，流体静力学偏差$b$。通过校准模型，我们确定了（i）温度依赖性的斜率为$f_1=0.403 (\pm0.009)$和$t_1=0.144 (\pm0.017)$ ;（ii）对$E_z$的依赖性被限制为$f_z=-0.004 (\pm 0.023)$和$t_z=0.349 (\pm 0.059)$。这些值允许人们直接估计给定量$Q_Δ$的归一化如何作为质量（或温度）和红移晕的函数以$Q_Δ \sim M^{a_M} E_z^{a_z} \sim T^{a_T} E_z^{a_{Tz}}$的形式变化，与当前的观测约束非常一致。

英文摘要：

In the self-similar scenario for galaxy cluster formation and evolution, the thermodynamic properties of the X-ray emitting plasma can be predicted in their dependencies on the halo mass and redshift only. However, several departures from this simple self-similar scenario have been observed. We show how our semi-analytic model $i(cm)z$, which modifies the self-similar predictions through two temperature-dependent quantities, the gas mass fraction $f_g=f_0 T^{f_1} E_z^{f_z}$ and the temperature variation $f_T=t_0 T^{t_1} E_z^{t_z}$, can be calibrated to incorporate the mass and redshift dependencies. We used a published set of 17 scaling relations to constrain the parameters of the model. We were subsequently able to make predictions as to the slope of any observed scaling relation within a few percent of the central value and about one $σ$ of the nominal error. Contextually, the evolution of these scaling laws was also determined, with predictions within $1.5 σ$ and within 10 percent of the observational constraints. Relying on this calibration, we have also evaluated the consistency of the predictions on the radial profiles with some observational datasets. For a sample of high-quality data (X-COP), we were able to constrain a further parameter of the model, the hydrostatic bias $b$. By calibrating the model, we have determined that (i) the slopes of the temperature dependence are $f_1=0.403 (\pm0.009)$ and $t_1=0.144 (\pm0.017)$; and that (ii) the dependence upon $E_z$ are constrained to be $f_z=-0.004 (\pm 0.023)$ and $t_z=0.349 (\pm 0.059)$. These values permit one to estimate directly how the normalizations of a given quantity $Q_Δ$ changes as a function of the mass (or temperature) and redshift halo in the form $Q_Δ \sim M^{a_M} E_z^{a_z} \sim T^{a_T} E_z^{a_{Tz}}$, in very good agreement with the current observational constraints.

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