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磁星是指主要由磁场提供辐射能量的一类脉冲星. 部分宁静状态下的磁星X射线有热起源, 对应的温度kT为0.2—0.6 keV (1 eV = 1.602 × 10–19 J), 这比转动供能的脉冲星的典型温度值高很多, 并且可以用黑体谱来拟合. 对磁星的观测和理论研究是当前脉冲星领域一个重要的热点. 结合物态方程, 本文首先计算了在超强磁场下壳层的电导率; 从统计上研究了由于环向磁场衰变, 磁场能释放率与磁星软X射线光度之间的关系. 通过分类和数值拟合, 所得到的新的拟合公式能较好地反映磁星软X射线光度和旋转能损率之间的关系. 研究发现, 对于绝大多数高X射线光度的磁星, 环向磁场欧姆衰变足够提供其观测的软X射线辐射; 对于低X射线光度的暂变磁星, 其软X射线辐射可能来源于旋转能损率、磁层流或粒子星风. 随着对磁星理论和观测研究的深入, 本文模型也会得到进一步的改进, 理论结果将更好地符合磁星的软X射线观测.
Magnetar is a kind of pulsar powered by magnetic field energy. Part of the X-ray luminosities of magnetars in quiescence have a thermal origin and can be fitted by a blackbody spectrum with temperature kT ～ 0.2－0.6 keV, much higher than the typical values for rotation-powered pulsars. The observation and theoretical study of magnetar are one of hot topics in the field of pulsar research. The activity and emission characteristics of magnetar can be attributed to internal superhigh magnetic field. According to the work of WGW19 and combining with the equation of state, we first calculate the electric conductivity of the crust under a strong magnetic field, and then calculate the toroidal magnetic field decay rate and magnetic energy decay rate by using an eigenvalue equation of toroidal magnetic field decay and considering the effect of general relativity. We reinvestigate the LX-Lrot relationship of 22 magnetars with persistent soft X-ray luminosities and obtain two new fitting formulas on LX-Lrot. We find that for the magnetars with LX < Lrot, the soft X-ray radiations may originate from their rotational energy loss rate, or from magneto-sphere flow and particle wind heating. For the magnetars with LX > Lrot, the Ohmic decay of crustal toroidal magnetic fields can provide their observed isotropic soft X-ray radiation and maintain higher thermal temperature. As for the initial dipole magnetic fields of magnetars, we mainly refer to the rersearch by Viganò et al. (Viganò D, Rea N, Pons J A, Perna R, Aguilera D N, Miralles J A 2013 Mon. Not. R. Astron. Soc. 434 123), because they first proposed the up-dated neutron star magneto-thermal evolution model, which can successfully explain the X-ray radiation and cooling mechanism of young pulsars including magnetars and high-magnetic field pulsars. Objectively speaking, as to the decay of toroidal magnetic fields, there are some differences between our theoretical calculations of magnetic energy release rates and the actual situation of magnetic field decay in magnetars, this is because the estimate of initial dipolar magnetic field, true age and the thickness of inner crust of a magnetar are somewhat uncertain. In addition, due to the interstellar-medium’s absorptions to soft X-ray and the uncertainties of distance estimations, the observed soft X-ray luminosities of magnetars have certain deviations. With the continuous improvement of observation, equipment and methods, as well as the in-depth development of theoretical research, our model will be further improved, and the theoretical results are better accordant with the high-energy observation of magnetars. We also discuss other possible anisotropy origins of soft X-ray fluxes of magnetars, such as the formation of magnetic spots and thermoplastic flow wave heating in the polar cap. Although anisotropic heating mechanisms are different from Ohmic decay, all of them require that there exist strong toroidal magnetic fields inside a magnetar. However, the anisotropic heating mechanisms require higher toroidal multipole fields inside a magnetar (such as magnetic octupole field) and are related to complex Hall drift: these may be our research subjects in the future. -
Keywords:
- superhigh magnetic field /
- magnetar /
- Ohmic decay /
- luminosity
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图 1 在NL3, GM1和TMA模型下中子星的质量和半径的关系
Fig. 1. Relationships between mass and radius of neutron stars in NL3, GM1 and TMA model.
图 2 在TMA模型中磁星的转动惯量I随质量m和半径R的关系
Fig. 2. Relationship of moment of inertial I to mass M and radius R for magnetars in TMA models.
图 3 在无力磁场结构位型下壳层归一化磁场分量
${{{B_r}}/{\left( {B\cos \theta } \right)}}$ (红线),${{{B_\theta }}/{\left( {B\sin \theta } \right)}}$ (蓝线), 及${{{B_\phi }}/{\left( {B\sin \phi } \right)}}$ (黄线)与归一化径向坐标x的关系(选取μ = 1.676, 对应在TMA模型下的M = 1.45M⊙, R = 11.77 km及I = 1.45 × 1045 g·cm2)Fig. 3. Normalized magnetic field components of the crustal confined for the force-free field:
${{{B_r}}/{\left( {B\cos \theta } \right)}}$ (red line),${{{B_\theta }}/{\left( {B\sin \theta } \right)}}$ (blue line), and${{{B_\phi }}/{\left( {B\sin \phi } \right)}}$ (yellow line) vs. normalized radial coordinate x. Here we assume the parameter μ = 1.676, corresponding to M = 1.45M⊙, R = 11.77 km and I = 1.45 × 1045 g·cm2 in the TMA model.
图 4 磁星壳层电导率随密度、温度及不纯净度参数的变化 (a)电导率由电子-声子散射主导; (b)电导率由电子-杂质散射主导; 物态方程一律采用BBP 模型
Fig. 4. Relationship of σ to ρ, Τ and Q in the inner crust for magnetar: (a) The conductivity due to electron-phonon scattering; (b) the conductivity due to electron-impurity scattering. The EOS of BBP model is used.
图 5 磁星磁场欧姆衰变的数值模拟 (a) 在x = 1处极向磁场Bp随时间t的变化; (b) 在x = 1处极向磁场Bt随时间t的变化; (c) 在x = 1处极向磁场衰减率dBp/dt, 随时间t的变化; (d) 在x = 1处环向磁场衰减率dBt/dt, 随时间t的变化; (e) 极化磁场的能量衰减率Lp随时间t的变化; (e) 环向磁场的能量衰减率Lt随时间t的变化; 在(a)−(f)图中红色和蓝颜色的线分别表示
$\sigma = 2.52 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ 和$\sigma = 8.75 \times {10^{24}} \;{{\rm{s}}^{{\rm{ - 1}}}}$ Fig. 5. Numerical fitting of Ohmic decay for magnetars: (a) The poloidal magnetic field, Bp, as a function of t at x = 1; (b) the toroidal magnetic field, Bt, as a function of t when at x = 1; (c) the poloidal magnetic field decay rate, dBp/dt, as a function of t when at x = 1; (d) the toroidal field decay rate, dBt/dt, as a function of t when at x = 1; (e) the poloidal field energy decay rate, Lp, as a function of t; (f) the toroidal filed energy decay rate, Lt, as a function of t. The red and blue lines in (a)−(f) indicate
$\sigma = 2.52 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ and$\sigma = 8.75 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ , respectively.
图 6 在各向同性加热模型下磁星及相关致密天体
$L_{\rm{X}}^\infty $ -${L_{{\rm{rot}}}}$ 的关系图Fig. 6. The
$L_{\rm{X}}^\infty $ -${L_{{\rm{rot}}}}$ plot for our magnetars and selected objects in isotropic heating models.
图 7 在各向同性加热模型下拟合得到的磁星的旋转能损率与软X射线光度的关系
Fig. 7. Fitting relationship between the soft X-ray luminosity and rotational energy loss rate of magnetars in the isotropic heating model.
表 1 在NL3, GM1和TMA模型下饱和核物质特性.
Table 1. Saturation properties of nuclear matter in the parameterizations for NL3, GM1 and TMA models.
RMF模型 ${\rho _0}$/fm–3 ${E_0}$/MeV ${K_0}$/MeV m* K′/MeV J/MeV ${L_0}$/MeV $K_{{\rm{sym}}}^0$/MeV $Q_{{\rm{sym}}}^0$/MeV $K_{\tau ,V}^0$/MeV NL3 0.148 –16.24 271.53 0.60 –202.91 37.40 118.53 100.88 181.31 –698.85 TMA 0.147 –16.33 318.15 0.635 572.12 30.66 90.14 10.75 –108.74 –367.99 GM1 0.153 –16.02 300.50 0.70 215.66 32.52 94.02 17.98 25.01 –478.64 
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表 2 在TMA模型中磁星的m, R, Rcore/R, μ和I的部分值
Table 2. Partial values of m, R, Rcore/R, μ and I for magnetars in TMA model.
m/M⊙ R/km Rcore/R $\mu $ I/g·cm2 1.20 11.42 0.915 1.678 1.03(1) × 1045 1.45 11.77 0.917 1.676 1.47(2) × 1045 1.72 12.05 0.919 1.675 1.87(2) × 1045 2.03* 11.25 0.914 1.679 2.09(2) × 1045 注: *在TMA模型下由物态方程给出的最大中子星质量.
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表 3 在不同温度和不同纯净度参数下磁星壳层电导率的部分值(采用BBP模型)
Table 3. Partial values of electrical conductivity for different temperatures and impurity parameters in the crust of magnetars. Here we use the equation of station (EOS) of BBP model.
T = 1 × 108 K T = 2 × 108 K T = 3 × 108 K $Q = 1$ $Q = 5$ $Q = 10$ $Q = 1$ $Q = 5$ $Q = 10$ $Q = 1$ $Q = 5$ $Q = 10$ $\rho $/g·cm–3 Z A $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 $\sigma $/1023 s–1 Bp = 5 × 1014 G 4.66 × 1011 40 127 0.455 2.15 0.752 1.69 1.15 0.591 0.998 0.821 0.490 6.61 × 1011 40 130 0.641 2.58 0.865 2.24 1.45 0.703 1.18 0.982 0.592 8.79 × 1011 41 134 0.928 3.22 0.991 2.97 1.54 0.822 1.31 1.20 0.702 1.20 × 1012 42 137 1.26 3.72 1.15 3.88 2.21 0.953 2.08 1.49 0.787 1.47 × 1012 42 140 1.97 4.63 1.23 4.89 2.50 1.04 2.43 1.69 0.867 2.00 × 1012 43 144 2.62 4.78 1.42 6.31 3.10 1.22 3.18 2.11 1.03 2.67 × 1012 44 149 2.67 5.59 1.68 7.82 3.75 1.41 4.08 2.59 1.29 3.51 × 1012 45 154 3.42 6.41 1.85 10.30 4.52 1.62 5.20 3.14 1.40 4.54 × 1012 46 161 4.20 7.26 2.08 15.60 5.24 1.89 6.53 3.78 1.65 6.25 × 1012 48 170 5.58 8.56 2.37 17.50 6.42 2.18 8.60 4.68 1.96 8.38 × 1012 49 181 6.95 9.67 2.66 22.20 7.46 2.49 10.90 5.55 2.23 1.10 × 1013 51 193 8.58 11.40 2.99 27.90 8.75 2.81 13.70 6.60 2.55 1.50 × 1013 54 211 10.80 12.90 3.45 35.60 10.40 3.24 17.30 7.95 2.95 1.99 × 1013 57 232 13.00 14.90 3.95 43.60 12.10 3.73 21.20 9.37 3.12 2.58 × 1013 60 257 15.20 16.90 4.46 51.20 13.80 4.22 24.90 10.80 3.88 3.44 × 1013 65 296 17.70 19.70 5.22 59.60 16.20 4.93 28.90 12.50 4.53 4.68 × 1013 72 354 20.40 23.50 6.23 67.70 19.10 5.87 32.60 14.60 5.37 5.96 × 1013 78 421 21.70 26.50 7.08 69.00 21.10 6.63 33.80 15.90 6.02 8.01 × 1013 89 548 22.10 31.20 8.48 69.80 23.80 7.82 34.70 17.20 6.95 9.83 × 1013 100 683 23.20 35.30 9.78 69.80 25.40 8.83 36.00 17.50 7.64 1.30 × 1014 120 990 25.50 40.30 11.80 70.80 26.50 10.10 38.20 18.10 8.20 Bp = 3 × 1015 G 4.66 × 1011 40 127 0.463 2.21 0.764 1.70 1.18 0.603 1.04 0.830 0.505 6.61 × 1011 40 130 0.649 2.67 0.873 2.29 1.50 0.721 1.36 1.04 0.605 8.79 × 1011 41 134 0.943 3.30 1.09 3.05 1.71 0.842 1.42 1.29 0.723 1.20 × 1012 42 137 1.32 3.77 1.19 3.98 2.32 1.01 2.21 1.59 0.854 1.47 × 1012 42 140 1.70 4.76 1.36 5.09 2.84 1.19 2.66 1.87 0.937 2.00 × 1012 43 144 2.00 4.85 1.65 6.41 3.29 1.30 3.40 2.28 1.12 2.67 × 1012 44 149 2.66 5.66 1.81 7.99 3.79 1.43 4.18 2.65 1.31 3.51 × 1012 45 154 3.48 6.49 1.91 11.30 4.58 1.64 5.20 3.17 1.45 4.54 × 1012 46 161 4.20 7.32 2.11 15.80 5.31 1.92 6.56 3.81 1.69 6.25 × 1012 48 170 5.58 8.64 2.44 17.90 6.49 2.24 8.65 4.74 1.99 8.38 × 1012 49 181 6.94 9.74 2.69 23.10 7.53 2.52 11.20 5.61 2.27 1.10 × 1013 51 193 8.58 12.00 3.06 28.80 8.80 2.86 13.80 6.65 2.68 1.50 × 1013 54 211 10.90 13.20 3.50 35.70 10.80 3.29 17.40 7.98 2.97 1.99 × 1013 57 232 13.10 15.10 3.98 43.70 12.60 3.77 21.30 9.40 3.45 2.58 × 1013 60 257 15.30 17.00 4.48 51.30 14.00 4.24 25.00 11.10 3.90 3.44 × 1013 65 296 17.70 19.90 5.25 59.70 16.40 4.95 28.90 12.70 4.55 4.68 × 1013 72 354 20.50 23.70 6.25 67.70 19.30 5.89 32.70 14.70 5.38 5.96 × 1013 78 421 21.80 26.70 7.10 69.00 21.30 6.65 33.80 16.00 6.03 8.01 × 1013 89 548 22.10 31.30 8.49 69.80 23.90 7.83 34.70 17.30 6.96 9.83 × 1013 100 683 23.20 35.40 9.79 70.30 25.50 8.85 36.10 17.70 7.65 1.30 × 1014 120 990 25.50 40.30 11.80 70.80 25.50 10.10 28.20 18.10 8.20
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表 4 当Bp(0) = 2.0 × 1015 G时Bp, dBp/dt, Lp, Bt, dBt/dt, Lt和LB的部分值(假定一个中等质量的磁星M = 1.45M⊙, R = 11.77 km, Rc = 0.98 km, 对应着I = 1.47I45和
$\mu = 1.676$ ; 表格上和下半部分分别对应着$\sigma = 8.75 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ 和$\sigma = 2.52 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ )Table 4. Partial values of Bp, dBp/dt, Lp, Bt, dBt/dt, Lt and LB when Bp(0) = 2.0 × 1015 G. Here we assume a medium-mass magnetar M = 1.45M⊙, R = 11.77 km, Rc = 0.97 km, corresponding to I = 1.47I45 and
$\mu = 1.676$ , respectively. The top and bottom parts correspond to$\sigma = 8.75 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ and$\sigma = 2.52 \times {10^{24}}\; {{\rm{s}}^{{\rm{ - 1}}}}$ , respectively.$\sigma $/s–1 t/a ${B_{\rm{p}}}$/G ${{{\rm{d}}B_{\rm{p}}^{}}/{{\rm{d}}t}}$/G·a–1 ${L_{\rm{p}}}$/erg·s–1 ${B_{\rm{t}}}$/G ${{{\rm{d}}B_{\rm{t}}^{}}/{{\rm{d}}t}}$/G·a–1 ${L_{\rm{t}}}$/erg·s–1 ${L_B}$/erg·s–1 8.75 × 1024 5.0 × 102 1.995 × 1015 –5.92 × 109 1.57 × 1034 1.965 × 1016 –5.84 × 1010 6.28 × 1035 6.44 × 1035 2.0 × 103 1.981 × 1015 –4.65 × 109 1.15 × 1034 1.953 × 1016 –4.58 × 1010 4.59 × 1035 4.70 × 1035 2.0 × 104 1.954 × 1015 –1.37 × 108 3.61 × 1033 1.927 × 1016 –1.35 × 1010 1.44 × 1035 1.48 × 1035 2.0 × 105 1.844 × 1015 –5.91 × 108 1.63 × 1033 1.818 × 1016 –5.84 × 1010 6.52 × 1034 6.68 × 1034 2.0 × 106 1.373 × 1015 –8.61 × 107 1.56 × 1032 1.354 × 1016 –8.48 × 108 6.24 × 1033 6.40 × 1033 2.0 × 107 6.865 × 1014 –4.36 × 107 7.85 × 1031 6.772 × 1015 –4.29 × 108 3.14 × 1033 3.22 × 1033 2.52 × 1024 5.0 × 102 1.990 × 1015 –1.51 × 1010 3.98 × 1034 1.96 × 1016 –1.49 × 1011 1.59 × 1036 1.63 × 1036 2.0 × 103 1.977 × 1015 –5.43 × 1010 1.65 × 1034 1.95 × 1016 –5.36 × 1010 6.61 × 1035 6.77 × 1035 2.0 × 104 1.931 × 1015- –1.86 × 109 4.74 × 1033 1.905 × 1016 –1.83 × 1010 1.90 × 1035 1.94 × 1035 2.0 × 105 1.745 × 1015 –7.21 × 109 1.69 × 1033 1.721 × 1016 –7.11 × 1010 6.76 × 1034 6.93 × 1034 2.0 × 106 8.712 × 1014 –3.87 × 109 4.46 × 1032 8.592 × 1015 –3.82 × 1010 1.78 × 1034 1.83 × 1034 2.0 × 107 2.749 × 1013 –1.33 × 107 4.82 × 1029 2.711 × 1014 –1.31 × 108 1.93 × 1031 1.98 × 1031
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表 5 具有软X射线辐射的22颗磁星的到达时间及其辐射特性
Table 5. The persistent timing, ages and emission characteristics for 22 magnetars with observed soft X-ray flux.
Source P/s $\dot{ P}$/10–11 s–1 ${\tau _{\rm{c}}}$/ka Age Est/ka Associa. Method $L_{\rm{X}}^\infty $/erg·s–1 Lrot./erg·s–1 Refs. SGR 0418+5729 9.07839 0.0004(1) 36000 550 SMC 磁热模拟 9.60 × 1029 3.1 × 1029 [46,48,49] 1E 2259+586 6.97904 0.04837 230.0 10—20 SNR CTB109 SNR年龄 1.70 × 1034 7.37 × 1031 [50—52] 4U 0142+61 8.68870 0.2022(4) 68.0 68.0 SMC 特征年龄 1.05 × 1035 1.85 × 1032 [49,50,53] CXOU J164710 10.61 < 0.04 > 420.0 > 420 Cluster Wdl 特征年龄 4.50 × 1032 < 1.88 × 1031 [54,55] 1E 1048–5937 6.45787 2.250 4.5 4.5 GSH 288.3–0.5–28 特征年龄 4.90 × 1034 4.65 × 1033 [56—58] CXOU J010043 8.02039 1.88(8) 6.8 6.8 SMC 特征年龄 6.50 × 1034 2.33 × 1033 [49,59] 1RXS J170849 11.00502 1.9455(13) 9.0 9.0 MC 13A 特征年龄 4.20 × 1034 7.37 × 1032 [50,55] 1E 1841–045 11.78898 4.092(15) 4.70 0.5—1.0 SNR Kes73 SNR年龄 1.84 × 1035 1.47 × 1033 [50,60] SGR 0501+4516 5.76206 0.594(2) 16.00 4—6 SNR HB9 SNR年龄 8.10 × 1032 1.85 × 1033 [61—63] SGR 0526–66 8.054(2) 3.8(1) 3.400 4.8 SNR N49 SNR年龄 1.89 × 1035 4.22 × 1033 [64,65] SGR 1900+14 5.19987 9.2(4) 0.900 3.98—7.9 Massive star Cluster 自行年龄 9.00 × 1034 3.79 × 1034 [66—68] SGR 1806–20 7.54773 49.5000 0.240 0.63—1.0 W31, MC13A 自行年龄 1.63 × 1035 6.68 × 1034 [68,69] XTE J1810–197 5.54035 0.777(3) 11 11 W31, MC13A 特征年龄 4.3 × 1031 2.93 × 1035 [69,70] IE 1547–5408 2.07212 4.77 0.69 0.63 SNR G327.24–013 SNR年龄 1.3 × 1033 3.11 × 1035 [71,72] 3XXMJ185246 11.5587 < 0.014 > 1300 5—7 SNR Kes 79 SNR年龄 < 4.0 × 1038 < 4.8 × 1038 [73,74] CXOU J171405 3.82535 6.40 0.95 5 CTB 37B SNR年龄 5.6 × 1034 6.13 × 1034 [45,75] SGR 1627–41 2.59458 1.9(4) 2.2 5.0 SNR G337.0–0.1 SNR年龄 3.6 × 1033 5.87 × 1034 [76,77] Swift J1822–1606 8.43772 0.0021(2) 6300 6300 HII region 特征年龄 < 4.0 × 1029 2.0 × 1030 [78,79] Swift J1834–0864 2.4823 0.796(12) 4.9 60200 SNR W41 SNR年龄 < 8.4 × 1030 3.1 × 1034 [80,81] PSR J1622–4950 4.326(1) 1.7(1) 4.0 ≤ 6.0 SNR G33.9+0.0 SNR年龄 4.40 × 1032 1.18 × 1034 [63,82] SGR J1745–2900 3.7636 1.385(15) 4.30 4.30 Galaxy Center 特征年龄 1.10 × 1032 1.47 × 1034 [83,84] PSR J1846–0258 0.32657 0.71070 0.73 0.9-4.3 SNR Kes75 SNR年龄 1.90 × 1034 8.10 × 1036 [49,85]
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表 6 12颗旋转能损率远小于软X射线光度的磁星的辐射特性及磁场能衰变率
Table 6. The X-ray emission characteristics and magnetic field energy decay rates of 12 magnetars with rotational energy loss rates less than their soft X-ray luminosities.
Source Bp(0)/G PL Ind. $T_{BB}^{\infty} $/keV D/kpc $F_{\rm{X}}^\infty $/erg·s–1·cm2 $L_{\rm{X}}^\infty $/erg·s–1 $L_B^{\rm{a}}$/erg·s–1 $\eta _{}^{\rm{a}}$/% $L_B^{\rm{b}}$/erg·s–1 $\eta _{}^{\rm{b}}$/% Ref. SGR 0418–5729 3.0 × 1014 — 0.30 2.0 2.0 × 10–11 9.60 × 1029 5.35 × 1032 0.31 2.26 × 1032 0.74 [48,49,50] 1E 2259+586 5.0 × 1014 3.75(4) 0.37(1) 3.2(2) 1.41 × 10–11 1.70 × 1034 6.5(1.0) × 1035 22(6) 1.4(3) × 1035 47(8) [50—52] CXOU J164710 3.0 × 1014 3.86(22) 0.59(6) 3.9(7) 2.54 × 10–11 4.50 × 1032 8.65 × 1033 9 3.62 × 1033 21 [50,54,95] 3XXMJ185246 3.0 × 1014 — 0.6 7.1 1.0 × 10–15 4.0 × 1033 3.53 × 1034 3.11 × 1035 [73,74] 4U 0142+61 3.0 × 1015 3.88(1) 0.41 3.6(4) 6.97 × 10–11 1.0 × 1035 1.14 × 1036 15 4.85 × 1035 37 [50,53,96] 1E1048–5937 1.0 × 1015 3.14(11) 0.56(1) 9.0(1.7) 5.11 × 10–11 4.90 × 1034 7.19 × 1035 12 3.08 × 1035 27 [50,57,58] CXOU J010043 1.0 × 1015 — 0.30(2) 62.4(1.6) 1.40 × 10–11 6.50 × 1034 6.82 × 1035 16 3.22 × 1035 34 [50,97] IRXS J170849 1.0 × 1015 2.79(1) 0.456 3.8(5) 2.43 × 10–11 4.20 × 1034 7.65 × 1035 9 3.23 × 1035 21 [50,53,96] 1E1841–045 1.0 × 1015 1.9(2) 0.45(3) 8.6(1.1) 2.13 × 10–11 1.84 × 1035 1.2(2) × 1036 26(4) 5.9(7) × 1035 46(4) [50,98,99] SGR 0526–66 3.0 × 1015 $2.5_{ - 0.12}^{ + 0.11}$ 0.44(2) 53.6(1.2) 5.50 × 10–11 1.89 × 1035 2.28 × 1036 8 7.11 × 1035 26 [50,65] SGR1900+14 3.0 × 1015 1.9(1) 0.47(2) 13.0(1.2) 4.82 × 10–12 9.0 × 1034 2.2(6) × 1036 7(1) 7.8(8) × 1035 19(2) [50,66] SGR1806–20 3.0 × 1015 1.6(1) 0.55(7) 8.8(1.6) 1.81 × 10–12 1.63 × 1035 3.8(4) × 1036 7.4(8) 8.9(9) × 1035 26(2) [50,69] 注: a表示$\sigma = 2.52 \times {10^{24} }\; { {\rm{s} }^{ {\rm{ - 1} } } }$的情况; b表示$\sigma = 8.75 \times {10^{24} } \;{ {\rm{s} }^{ {\rm{ - 1} } } }$的情况; PL Ind. 表示幂率指数.
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