基于随机森林回归器的IRAS 13224-3809和1H 0707-495日冕高度约束
Coronal height constraint in IRAS 13224-3809 and 1H 0707-495 by the random forest regressor
AI总结：
本研究开发随机森林回归器模型，利用X射线回响的PSD特征约束两个活动星系核的日冕高度，验证了模型抗噪性与参数敏感性，支持光弯曲情景下日冕高度与光度相关的结论。
摘要：
我们开发了一种随机森林回归器（random forest regressor，RFR）机器学习模型，通过探测印在其功率谱密度（power spectral density，PSD）轮廓上的X射线回响特征，追踪XMM-牛顿卫星观测到的两个高变活动星系核（active galactic nuclei，AGNs）IRAS 13224-3809和1H 0707-495的日冕演化。我们生成了幂律形式的模拟PSD，其频率范围和频率分箱与观测数据相似。随后，这些模拟PSD与来自灯柱源的相对论性盘响应函数进行卷积，再用于训练和测试模型以预测日冕高度。我们移除了一些以泊松噪声为主的分箱，发现模型最多可容忍移除约10个频率分箱，仍能维持$R^{2} > 0.9$的预测精度。黑洞质量和倾角需保持固定，这样源高度的预测精度仍能>0.9。精度还随反射分数的增加而提升。随后，我们利用由模拟PSD开发的RFR模型预测了两个活动星系核的日冕高度，这些模拟PSD的频率范围和分箱经过专门调整，以匹配每次单独观测的对应参数。模型显示，两个活动星系核的日冕高度在$\boldsymbol{\tilde{} 5 - 18~r_{\rm g}}$之间变化，所有观测的$R^{2}$均>0.9。即使真实质量与训练值的差异$\boldsymbol{\tilde{}< 10 \text{（原符号为}\boldsymbol{\tilde{<}}\text{，即小于等于约10}\boldsymbol{\textit{）}}}$，仍能获得如此高的精度。最后，该模型支持光弯曲情景下的高度变化日冕模型，即在IRAS 13224-3809和1H 0707-495中，日冕高度与源光度相关。
英文摘要：
We develop a random forest regressor (RFR) machine learning model to trace the coronal evolution in two highly variable active galactic nuclei (AGNs) IRAS 13224-3809 and 1H 0707-495 observed with XMM-Newton, by probing the X-ray reverberation features imprinted on their power spectral density (PSD) profiles. Simulated PSDs in the form of a power-law, with similar frequency range and bins to the observed data, are produced. Then, they are convolved with relativistic disc-response functions from a lamp-post source before being used to train and test the model to predict the coronal height. We remove some bins that are dominated by Poisson noise and find that the model can tolerate the frequency-bin removal up to $\sim 10$ bins to maintain a prediction accuracy of $R^{2} > 0.9$. The black hole mass and inclination should be fixed so that the accuracy in predicting the source height is still $> 0.9$. The accuracy also increases with the reflection fraction. The corona heights for both AGN are then predicted using the RFR model developed from the simulated PSDs whose frequency range and bins are specifically adjusted to match those from each individual observation. The model suggests that their corona varies between $\sim~5 - 18~r_{\rm g}$, with $R^{2} > 0.9$ for all observations. Such high accuracy can still be obtained if the difference between the true mass and the trained value is $\lesssim 10\%$. Finally, the model supports the height-changing corona under the light-bending scenario where the height is correlated to source luminosity in both IRAS 13224-3809 and 1H 0707-495.
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