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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 L X- L rotrelationship of 22 magnetars with persistent soft X-ray luminosities and obtain two new fitting formulas on L X- L rot. We find that for the magnetars with L X< L rot, 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 L X> L rot, 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. 434123), 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
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] -
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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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. DownLoad:
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T= 1 × 108K T= 2 × 108K T= 3 × 108K $Q = 1$ $Q = 5$ $Q = 10$ $Q = 1$ $Q = 5$ $Q = 10$ $Q = 1$ $Q = 5$ $Q = 10$ $\rho $/g·cm–3 Z A $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 $\sigma $/1023s–1 Bp= 5 × 1014G 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 × 1015G 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 DownLoad:
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$\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 DownLoad:
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Source P/s $\dot{ P}$/10–11s–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] DownLoad:
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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. DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102]
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