论文标题
部分可观测时空混沌系统的无模型预测
The Hardness-intensity Correlation of Photospheric Emission from a Structured Jet for Gamma-Ray Bursts
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
For many gamma-ray bursts (GRBs), hardness-intensity correlation (HIC) can be described by a power-law function, $E_{\rm p}\propto F^κ$, where $E_{\rm p}$ is the peak energy of $νF_ν$ spectrum, and $F$ is the instantaneous energy flux. In this paper, HIC of the non-dissipative photospheric emission from a structured jet is studied in different regimes. An intermediate photosphere, which contains both of unsaturated and saturated emissions is introduced, and we find positive $κ<1/4$ in this case. The same conclusion could be generalized to the photospheric emission from a hybrid jet without magnetic dissipations, or that with sub-photospheric magnetic dissipations and fully thermalized. This may imply that the contribution peaking at $\sim1/2$ in the distribution of observed $κ$ are mainly from the prompt emission of GRBs with synchrotron origin. Besides, emissions of the intermediate photosphere could give a smaller low-energy photon index $α$ than that in the unsaturated regime, and naturally reproduce anti-correlation in $α-E_{\rm p}$ in a GRB pulse.
