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arXiv 2006.05041astro-ph.HE
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中子星低质量X射线双星中X射线光子指数与X射线光度反相关的平流主导吸积流

The advection-dominated accretion flow for the anti-correlation between the X-ray photon index and the X-ray luminosity in neutron star low-mass X-ray binaries

Erlin Qiao, B. F. Liu

备注：
12 pages, 12 figures. Accepted for publication by MNRAS
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摘要：

观测发现，在中子星低质量X射线双星（NS-LMXB）中，X射线光子指数$Γ$（用单一幂律拟合0.5 ~ 10 keV的X射线能谱得到）与X射线光度$L_{\rm 0.5-10keV}$在$L_{\rm 0.5-10keV}\sim 10^{34}-10^{36}\ \rm erg\ s^{-1}$范围内存在反相关.在本文中，我们解释了观测到的反相关$Γ$和$L_{\rm 0.5-10keV}$的框架内的对流为主的吸积流（ADAF）的弱磁化NS的自相似解决方案。ADAF模型固有地预测$Γ$和$L_{\rm 0.5-10keV}$之间的反相关性。在ADAF模型中，有一个关键参数，$f_{\rm th}$，它描述了在NS表面释放的ADAF能量的分数，作为在ADAF中散射的热发射。我们测试了$f_{\rm th}$对$Γ$和$L_{\rm 0.5-10keV}$之间的反相关性的影响。发现$f_{\rm th}$的值可以显著影响$Γ$和$L_{\rm 0.5-10keV}$之间的反相关性。具体地，当分别采用$f_{\rm th}=0.1, 0.03, 0.01, 0.005$、$0.003$和$0$时，随着$f_{\rm th}$的减小，$Γ$和$L_{\rm 0.5-10keV}$之间的反相关变得更平坦。通过与具有良好测量的$Γ$和$L_{\rm 0.5-10keV}$的非脉动NS-LMXB的样本进行比较，我们发现实际上仅需要小的$0.003\lesssim f_{\rm th}\lesssim 0.1$值来匹配所观察到的$Γ$和$L_{\rm 0.5-10keV}$之间的反相关。最后，我们认为，本文中导出的小$f_{\rm th}\lesssim 0.1$值进一步证实了我们以前的结论，即具有ADAF吸积的NS的辐射效率可能不如$ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$高。

英文摘要：

Observationally, an anti-correlation between the X-ray photon index $Γ$ (obtained by fitting the X-ray spectrum between 0.5 and 10 keV with a single power law) and the X-ray luminosity $L_{\rm 0.5-10keV}$, is found in neutron star low-mass X-ray binaries (NS-LMXBs) in the range of $L_{\rm 0.5-10keV}\sim 10^{34}-10^{36}\ \rm erg\ s^{-1}$. In this paper, we explain the observed anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$ within the framework of the self-similar solution of the advection-dominated accretion flow (ADAF) around a weakly magnetized NS. The ADAF model intrinsically predicts an anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. In the ADAF model, there is a key parameter, $f_{\rm th}$, which describes the fraction of the ADAF energy released at the surface of the NS as thermal emission to be scattered in the ADAF. We test the effect of $f_{\rm th}$ on the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. It is found that the value of $f_{\rm th}$ can significantly affect the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. Specifically, the anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$ becomes flatter with decreasing $f_{\rm th}$ as taking $f_{\rm th}=0.1, 0.03, 0.01, 0.005$, $0.003$ and $0$ respectively. By comparing with a sample of non-pulsating NS-LMXBs with well measured $Γ$ and $L_{\rm 0.5-10keV}$, we find that indeed only a small value of $0.003\lesssim f_{\rm th}\lesssim 0.1$ is needed to match the observed anti-correlation between $Γ$ and $L_{\rm 0.5-10keV}$. Finally, we argue that the small value of $f_{\rm th}\lesssim 0.1$ derived in this paper further confirms our previous conclusion that the radiative efficiency of NSs with an ADAF accretion may not be as high as $ε\sim {\dot M GM\over R_{*}}/{\dot M c^2}\sim 0.2$.

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