<trans-title xml:lang="en">Conductivity of neutron star crust under superhigh magnetic fields and Ohmic decay of toroidal magnetic field of magnetar</trans-title>

Jian-Ling Chen; Hui Wang; Huan-Yu Jia; Zi-Wei Ma; Yong-Hong Li; Jun Tan

doi:10.7498/aps.68.20190760

Acta Physica Sinica, Volume. 68, Issue 18, 180401-1(2019)

Conductivity of neutron star crust under superhigh magnetic fields and Ohmic decay of toroidal magnetic field of magnetar

Jian-Ling Chen^1、*, Hui Wang², Huan-Yu Jia², Zi-Wei Ma¹, Yong-Hong Li¹, and Jun Tan³

Author Affiliations

¹Department of Physics and Electronic Engineering, Yuncheng University, Yuncheng 044000, China

²School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China

³Maths and Information Technology School, Yuncheng University, Yuncheng 044000, China

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Figures & Tables(13)

Fig. 1. Relationships between mass and radius of neutron stars in NL3, GM1 and TMA model.在NL3, GM1和TMA模型下中子星的质量和半径的关系

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Fig. 2. Relationship of moment of inertial I to mass M and radius R for magnetars in TMA models. 在TMA模型中磁星的转动惯量I随质量m和半径R的关系

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Fig. 3. Normalized magnetic field components of the crustal confined for the force-free field: (red line), (blue line), and (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. 在无力磁场结构位型下壳层归一化磁场分量 (红线), (蓝线), 及 (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)

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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. 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

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Fig. 5. Numerical fitting of Ohmic decay for magnetars: (a) The poloidal magnetic field, B_p, as a function of t at x = 1; (b) the toroidal magnetic field, B_t, as a function of t when at x = 1; (c) the poloidal magnetic field decay rate, dB_p/dt, as a function of t when at x = 1; (d) the toroidal field decay rate, dB_t/dt, as a function of t when at x = 1; (e) the poloidal field energy decay rate, L_p, as a function of t; (f) the toroidal filed energy decay rate, L_t, as a function of t. The red and blue lines in (a)−(f) indicate and , respectively. 磁星磁场欧姆衰变的数值模拟　(a) 在x = 1处极向磁场B_p随时间t的变化; (b) 在x = 1处极向磁场B_t随时间t的变化; (c) 在x = 1处极向磁场衰减率dB_p/dt, 随时间t的变化; (d) 在x = 1处环向磁场衰减率dB_t/dt, 随时间t的变化; (e) 极化磁场的能量衰减率L_p随时间t的变化; (e) 环向磁场的能量衰减率L_t随时间t的变化; 在(a)−(f)图中红色和蓝颜色的线分别表示和

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Fig. 6. The - plot for our magnetars and selected objects in isotropic heating models. 在各向同性加热模型下磁星及相关致密天体 - 的关系图

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Fig. 7. Fitting relationship between the soft X-ray luminosity and rotational energy loss rate of magnetars in the isotropic heating model.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

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Table 1.
Saturation properties of nuclear matter in the parameterizations for NL3, GM1 and TMA models.
在NL3, GM1和TMA模型下饱和核物质特性.

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Table 1.
Saturation properties of nuclear matter in the parameterizations for NL3, GM1 and TMA models.
在NL3, GM1和TMA模型下饱和核物质特性.

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

Table 2.
Partial values of m, R, R_core/R, μ and I for magnetars in TMA model.
在TMA模型中磁星的m, R, R_core/R, μ和I的部分值

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Table 2.
Partial values of m, R, R_core/R, μ and I for magnetars in TMA model.
在TMA模型中磁星的m, R, R_core/R, μ和I的部分值

m/M_⊙	R/km	R_core/R	$\mu $	I/g·cm²
注: *在TMA模型下由物态方程给出的最大中子星质量.
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

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.
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)

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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.
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)

				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
B_p = 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

B_p = 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

Table 4. Partial values of B_p, dB_p/dt, L_p, B_t, dB_t/dt, L_t and L_B when B_p(0) = 2.0 × 10¹⁵ G. Here we assume a medium-mass magnetar M = 1.45M_⊙, R = 11.77 km, R_c = 0.97 km, corresponding to I = 1.47I₄₅ and , respectively. The top and bottom parts correspond to and , respectively. 当B_p(0) = 2.0 × 10¹⁵ G时B_p, dB_p/dt, L_p, B_t, dB_t/dt, L_t和L_B的部分值(假定一个中等质量的磁星M = 1.45M_⊙, R = 11.77 km, R_c = 0.98 km, 对应着I = 1.47I₄₅和 ; 表格上和下半部分分别对应着和 )

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Table 4. Partial values of B_p, dB_p/dt, L_p, B_t, dB_t/dt, L_t and L_B when B_p(0) = 2.0 × 10¹⁵ G. Here we assume a medium-mass magnetar M = 1.45M_⊙, R = 11.77 km, R_c = 0.97 km, corresponding to I = 1.47I₄₅ and , respectively. The top and bottom parts correspond to and , respectively. 当B_p(0) = 2.0 × 10¹⁵ G时B_p, dB_p/dt, L_p, B_t, dB_t/dt, L_t和L_B的部分值(假定一个中等质量的磁星M = 1.45M_⊙, R = 11.77 km, R_c = 0.98 km, 对应着I = 1.47I₄₅和 ; 表格上和下半部分分别对应着和 )

$\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 × 10^15-	–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

Table 5.
The persistent timing, ages and emission characteristics for 22 magnetars with observed soft X-ray flux.
具有软X射线辐射的22颗磁星的到达时间及其辐射特性

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Table 5.
The persistent timing, ages and emission characteristics for 22 magnetars with observed soft X-ray flux.
具有软X射线辐射的22颗磁星的到达时间及其辐射特性

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	L_rot./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]

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.
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

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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.
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

Source	B_p(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.
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.
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]

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Jian-Ling Chen, Hui Wang, Huan-Yu Jia, Zi-Wei Ma, Yong-Hong Li, Jun Tan. Conductivity of neutron star crust under superhigh magnetic fields and Ohmic decay of toroidal magnetic field of magnetar[J]. Acta Physica Sinica, 2019, 68(18): 180401-1

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Paper Information

Received: May. 19, 2019

Accepted: --

Published Online: Jun. 28, 2020

The Author Email:

DOI:10.7498/aps.68.20190760

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. Saturation properties of nuclear matter in the parameterizations for NL3, GM1 and TMA models.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.在NL3, GM1和TMA模型下饱和核物质特性.

Table 2. Partial values of m, R, Rcore/R, μ and I for magnetars in TMA model. 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. 在TMA模型中磁星的m, R, Rcore/R, μ和I的部分值

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.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.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 5. The persistent timing, ages and emission characteristics for 22 magnetars with observed soft X-ray flux.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.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 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.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.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 1.
Saturation properties of nuclear matter in the parameterizations for NL3, GM1 and TMA models.
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.
在NL3, GM1和TMA模型下饱和核物质特性.

Table 2.
Partial values of m, R, R_core/R, μ and I for magnetars in TMA model.
在TMA模型中磁星的m, R, R_core/R, μ和I的部分值

Table 2.
Partial values of m, R, R_core/R, μ and I for magnetars in TMA model.
在TMA模型中磁星的m, R, R_core/R, μ和I的部分值

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.
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.
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 5.
The persistent timing, ages and emission characteristics for 22 magnetars with observed soft X-ray flux.
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.
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 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.
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.
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