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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 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
[1] Goldreich P, Julian W H 1969 Astrophys. J. 157 869
Google Scholar
[2] Goldreich P, Reisenegger A 1992 Astrophys. J. 395 250
Google Scholar
[3] Gao Z F, Wang N, Xu Y, Shan H, Li X D 2015 Astron. Nachr. 336 866
Google Scholar
[4] Gao Z F, Li X D, Wang N, Yuan J P, Wang P, Peng Q H, Du Y J 2016 Mon. Not. R. Astron. Soc. 456 55
Google Scholar
[5] Gao Z F, Shan H, Wang W, Wang N 2017 Astron. Nachr. 338 1066
Google Scholar
[6] Gao Z F, Wang N, Shan H 2017 Astron. Nachr. 338 1060
Google Scholar
[7] Gao Z F, Wang N, Shan H, Li X D, Wang W 2017 Astrophys. J. 849 19
Google Scholar
[8] Mereghetti S, Pons J A, Melatos A 2015 Space Sci. Rev. 191 315
Google Scholar
[9] Kaspi V M, Beloborodov A M 2017 Annu. Rev. Astron. Astr. 55 261
Google Scholar
[10] Gao Z F, Peng Q H, Wang N, Chou C K 2012 Chin. Phys. B 21 057109
Google Scholar
[11] Gao Z F, Peng Q H, Wang N, Yuan J P 2012 Astrophys. Space Sci. 342 55
Google Scholar
[12] Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett. A 28 1350138
[13] Yuan J P, Manchester R N, Wang N, Zhou X, Liu Z Y, Gao Z F 2010 Astrophys. J. Lett. 719 L111
Google Scholar
[14] Olausen S A, Kaspi V M 2014 Astrophys. J. Suppl. S. 212 6
Google Scholar
[15] Gao Z F, Peng Q H, Wang N, Chou C K, Huo W S 2011 Astrophys. Space Sci. 336 427
Google Scholar
[16] Flowers E, Ruderman M A 1977 Astrophys. J. 215 302
Google Scholar
[17] Yan W M, Wang N, Manchester R N, Wen Z G, Yuan J P 2018 Mon. Not. R. Astron. Soc. 476 3677
[18] Gourgouliatos K N, Cumming A 2014 Mon. Not. R. Astron. Soc. 438 1618
Google Scholar
[19] Gourgouliatos K N, Cumming A 2014 Phys. Rev. Lett. 112 171101
Google Scholar
[20] Thompson C, Murray N 2001 Astrophys. J. 560 339
Google Scholar
[21] Tiengo A, Esposito P, Mereghetti S, Turolla R, Nobili L, Gastaldello F, Götz D, Israel G, Rea N, Stella L, Zane S, Bignami G 2013 Nature 500 312
Google Scholar
[22] Gao Z F, Wang N, Yuan J P, Jiang L, Song D L, 2011 Astrophys. Space Sci. 332 129
Google Scholar
[23] Urpin V A, Chanmugam G, Sang Y 1994 Astrophys. J. 433 780
Google Scholar
[24] Urpin V A, Muslimov A G 1992 Mon. Not. R. Astron. Soc. 256 261
Google Scholar
[25] Muslimov A, Page D 1996 Astrophys. J. 458 347
Google Scholar
[26] Mitra D, Konar S, Bhattacharya D 1999 Mon. Not. R. Astron. Soc. 307 459
Google Scholar
[27] Geppert U, Urpin V 1994 Mon. Not. R. Astron. Soc. 271 490
Google Scholar
[28] Konar S, Bhattacharya D 1997 Mon. Not. R. Astron. Soc. 284 311
Google Scholar
[29] Geppert U, Page D, Zannias T 2000 Phys. Rev. D 61 123004
Google Scholar
[30] Aguilera D N, Pons J A, Miralles J A 2008 Astron. Astrophys. 486 255
Google Scholar
[31] Beloborodov A M, Li X 2016 Astrophys. J. 833 261
Google Scholar
[32] Wald R M 1984 General Relativity (Chicago: University of Chicago Press)p 504
[33] Wang H, Gao Z F, Wang N, Jia H Y, Li X D, Zhi Q J 2019 Publ. Astron. Soc. Pac. 131 054201
Google Scholar
[34] Esposito P, Rea N, Israel G L 2018 arXiv: 1803.057167
[35] Li X H, Gao Z F, Li X D, Xu Y, Wang P, Wang N, Peng Q H 2016 Int. J. Mod. Phys. D 25 1650002
[36] Baym G, Bethe H A, Pethick C J 1971 Nucl. Phys. A. 175 225
Google Scholar
[37] Baym G, Pethick C, Sutherland P 1971 Astrophys. J. 170 299
Google Scholar
[38] Lalazissis G A, König J, Ring P 1997 Phys. Rev. C. 55 540
Google Scholar
[39] Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414
Google Scholar
[40] Geng L, Toki H, Meng J 2005 Prog. Theor. Phys. 113 785
Google Scholar
[41] Singh D, Saxena G 2012 Int. J. Mod. Phys. E 21 1250076
[42] Demorest P B, Pennucci T, Ransom S M, Roberts M S E, Hessels J W T 2010 Nature 467 1081
Google Scholar
[43] Shapiro S L, Teukolsky S A 1983 Black Holes, White Drarfs, and Neutron Stars (New: YorkJohn Wiley & Sons)
[44] Potekhin A Y, Chabrier G 2013 Astron. Astrophys. 550 16
Google Scholar
[45] Sato T, Bamba A, Nakamura R, Ishida M 2010 Pub. Astron. Soc. J. 62 L33
Google Scholar
[46] Viganò D, Rea N, Pons J A, Perna R, Aguilera D N, Miralles J A 2013 Mon. Not. R. Astron. Soc. 434 123
Google Scholar
[47] Torii K, Kinugasa K, Katayama K, Tsunemi H, Yamauchi S 1998 Astrophys. J. 503 843
Google Scholar
[48] Rea N, Israel G L, Pons J A, Turolla R, Viganò D, Zane S, Esposito P, Perna R, Papitto A, Terreran G, Tiengo A, Salvetti D, Girart J M, Palau A, Possenti A, Götz D, Mignani R P, Ratti E, Stella L 2013 Astrophys. J. 770 65
Google Scholar
[49] Lamb R C, Fox D N, Macomb D J, Prince J A 2002 Astrophys. J. 574 L29
Google Scholar
[50] Dib R, Kaspi V M 2014 Astrophys. J. 784 37
Google Scholar
[51] Zhu W W, Kaspi V M, Dib R, Woods P M, Gavriil F P, Archibald A M 2008 Astrophys. J. 686 520
[52] Fahlman G G, Gregory P C 1981 Nature 293 202
[53] Rea N, Nichelli E, Israel G L, Perna R, Oosterbroek T, Parmar A N, Turolla R, Campana S, Stella L, Zane S, Angelini L 2007 Mon. Not. R. Astron. Soc. 381 293
Google Scholar
[54] An H, Kaspi V M, Archibald R, Cumming A, 2013 Astrophys. J. 763 82
Google Scholar
[55] Muno M P, Clark J S, Crowther P A, Dougherty S M, de Grijs R, Law C, McMillan S L W, Morris M R, Negueruela I, Pooley D, Portegies Z S, Yusef-Zadeh F 2006 Astrophys. J. Lett. 636 L41
Google Scholar
[56] Dib R, Kaspi V M, Gavriil F P 2009 Astrophys. J. 702 614
Google Scholar
[57] Tam C R, Gavriil F P, Dib R, Kaspi V M, Woods P M, Bassa C 2008 Astrophys. J. 677 503
Google Scholar
[58] Gaensler B M, McClure-Griffiths N M, Oey M S, Haverkorm M, Dickey J M, Green A J 2005 Astrophys. J. 620 L95
Google Scholar
[59] McGarry M B, Gaensler B M, Ransom S M, Kaspi V M, Veljkovik S 2005 Astrophys. J. 627 L137
Google Scholar
[60] Vasisht G, Gotthelf E V 1997 Astrophys. J. 486 L129
Google Scholar
[61] Camero A, Papitto A, Rea N, Viganò D, Pons J A, Tiengo A, Mereghetti S, Turolla R, Esposito P, Zane S, Israel G L, Götz D 2014 Mon. Not. R. Astron. Soc. 438 3291
Google Scholar
[62] Lin L, Kouveliotou C, Baring M G 2011 Astrophys. J. 739 87
Google Scholar
[63] Anderson G E, Gaensler B M, Slane P O, Rea N, Kaplan D L, Posselt B, Levin L, Johnston S, Murray S, Brogan C L, Bailes M, Bates S, Benjamin R A, Bhat N D R, Burgay M, Burke-Spolaor S, Chakrabarty D, D'Amico N, Drake J J, Esposito P, Grindlay J E, Hong J, Israel G L, Keith M J, Kramer M, Lazio T J W, Lee J C, Mauerhan J C, Milia S, Possenti A, Stappers B, Steeghs D T H 2012 Astrophys. J. 751 53
Google Scholar
[64] Tiengo A, Esposito P, Mereghetti S, Israel G L, Stella L, Turolla R, Zane S, Rea N, Götz D, Feroci M 2009 Mon. Not. R. Astron. Soc. 399 L74
Google Scholar
[65] Park S, Hughes J P, Slane P O, Burrows D N, Lee J J, Mori K 2012 Astrophys. J. 748 117
Google Scholar
[66] Mereghetti S, Esposito P, Tiengo A, Zane S, Turolla R, Stella L, Israel G L, Götz D, Feroci M 2006 Astrophys. J. 653 1423
Google Scholar
[67] Vrba F J, Henden A A, Luginbuhl C B, Guetter H H, Hartmann D H, Klose S 2000 Astrophys. J. 533 L17
Google Scholar
[68] Tendulkar S P, Cameron P, Brian K, Shrinivas R 2012 Astrophys. J. 761 76
Google Scholar
[69] Woods, Peter M, Kouveliotou C, Finger M H, Göǧüş E, Wilson, C A, Patel S K, Hurley K, Swank J H 2007 Astrophys. J. 654 470
Google Scholar
[70] Camilo F, Cognard I, Ransom S M, Halpern J P, Reynolds J, Zimmerman N, Gotthelf E V, Helfand D J, Demorest P, Theureau G, Backer D C 2007 Astrophys. J. 663 497
Google Scholar
[71] Dib R, Kaspi V M, Scholz P, Gavriil F P 2012 Astrophys. J. 748 3
Google Scholar
[72] Bernardini F, Israel G L, Stella L, Turolla R, Esposito P, Rea N, Zane S, Tiengo A, Campana S, Götz D, Mereghetti S, Romano P 2011 Astron. Astrophys. 529 A19
Google Scholar
[73] Rea N, Vigano D, Israel G L, Pons J A, Torres D F 2014 Astrophys. J. Lett. 781 L17
Google Scholar
[74] Zhou P, Chen Y, Li X D, Safi-Harb S, Mendez M, Terada Y, Sun W, Ge M Y 2014 Astrophys. J. Lett. 781 L16
Google Scholar
[75] Halpern J P, Gotthelf E V 2010 Astrophys. J. 710 941
Google Scholar
[76] Esposito P, Burgay M, Possenti A, Turolla R, Zane S, de Luca A, Tiengo A, Israel G, Mattana F, Mereghetti S, Bailes M, Romano P, Götz D, Rea N 2009 Mon. Not. R. Astron. Soc. 399 L44
Google Scholar
[77] Corbel S, Chapuis C, Dame T M, Durouchoux P 1999 Astrophys. J. 526 L29
Google Scholar
[78] Scholz P, Ng C Y, Livingstone M A, Kaspi V M, Cumming A, Archibald R F 2012 Astrophys. J. 761 66
Google Scholar
[79] Scholz P, Kaspi V M, Cumming A 2014 Astrophys. J. 786 62
Google Scholar
[80] Kargaltsev O, Kouveliotou C, Pavlov G G, Göǧüş E, Lin L, Wachter S, Griffith R L, Kaneko Y, Younes G 2012 Astrophys. J. 748 26
Google Scholar
[81] Leahy D A, Tian W W 2008 Astrophys. J. 135 167
[82] Levin L, Bailes M, Bates S, Bhat N D R, Burgay Marta, Burke-Spolaor S, D'Amico N, Johnston S, Keith M, Kramer M, Milia S, Possenti A, Rea N, Stappers B, van Straten W 2010 Astrophys. J. Lett. 721 L33
Google Scholar
[83] Kaspi V M, Archibald R F, Bhalerao V, Dufour F, Gotthelf E V, An H J, Bachetti M, Beloborodov A M, Boggs S E, Christensen F E, Craig W W, Grefenstette B W, Hailey C J, Harrison F A, Kennea J A, Kouveliotou C, Madsen K K, Mori K, Markwardt C B, Stern D, Vogel J K, Zhang W W 2014 Astrophys. J. 786 84
Google Scholar
[84] Mori K, Gotthelf E V, Zhang S, An H J, Baganoff F K, Barrière N M, Beloborodov A M, Boggs S E, Christensen F E, Craig, W W, Dufour F, Grefenstette B W, Hailey C J, Harrison F A, Hong J, Kaspi V M, Kennea J A, Madsen K K, Markwardt C B, Nynka M, Stern D, Tomsick J A, Zhang W W 2013 Astrophys. J. Lett. 770 L23
Google Scholar
[85] Gotthelf E V, Vasisht G, Boylan-Kolchin M, Torii K 2000 Astrophys. J. 542 L37
Google Scholar
[86] Tong H, Xu R X 2013 Res. Astron. Astrophy. 13 1207
Google Scholar
[87] Livingstone Margaret A, Ng C Y, Kaspi Victoria A 2011 Astrophys. J. 730 66
Google Scholar
[88] Becker W, Truemper J 1997 Astron. Astrophys. 326 682
[89] Shibata S, Watanabe E, Yatsu Y, Enoto T, Bamba A 2016 Astrophys. J. 833 14
Google Scholar
[90] Kaplan D L, van Kerkwijk M H 2009 Astrophys. J. 705 798
Google Scholar
[91] Haberl F 2007 Astrophys. Space Sci. 308 181
Google Scholar
[92] Bogdanov S, Ng C Y, Kaspi V M 2014 Astrophys. J. Lett. 792 L36
[93] Coelho J G, Cáceres D L, de Lima R C R, Malheiro M, Rueda J A, Ruffini R 2017 Astrono. Astrophys. 599 A87
Google Scholar
[94] Gonzalaz D, Reisenegger A 2010 Astrono. Astrophys. 522 A16
Google Scholar
[95] Kothes R, Dougherty S M 2007 Astron. Astrophys. 468 993
Google Scholar
[96] Durant M, van Kerkwijk, Marten H 2006 Astrophys. J. 652 576
Google Scholar
[97] Tiengo A, Esposito P, Mereghetti S 2008 Astrophys. J. 680 L133
Google Scholar
[98] Kumar H S, Safi-Harb S 2010 Astrophys. J. Lett. 725 L191
Google Scholar
[99] Tian W W, Leahy D A 2008 Astrophys. J. 677 292
Google Scholar
[100] Gourgouliatos K N, Hollerbach R 2018 Astrophys. J. 852 21
[101] Beloborodov A M 2011 High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings (Berlin: Springer-Verlag Berlin Heidelberg) p299
[102] Beloborodov A M, Levin Y 2014 Astrophys. J. Lett. 794 L24
Google Scholar
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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
Figure 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
Figure 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)Figure 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
Figure 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$\sigma = 8.75 \times {10^{24}} \;{{\rm{s}}^{{\rm{ - 1}}}}$ Figure 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Figure 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
Figure 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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[1] Goldreich P, Julian W H 1969 Astrophys. J. 157 869
Google Scholar
[2] Goldreich P, Reisenegger A 1992 Astrophys. J. 395 250
Google Scholar
[3] Gao Z F, Wang N, Xu Y, Shan H, Li X D 2015 Astron. Nachr. 336 866
Google Scholar
[4] Gao Z F, Li X D, Wang N, Yuan J P, Wang P, Peng Q H, Du Y J 2016 Mon. Not. R. Astron. Soc. 456 55
Google Scholar
[5] Gao Z F, Shan H, Wang W, Wang N 2017 Astron. Nachr. 338 1066
Google Scholar
[6] Gao Z F, Wang N, Shan H 2017 Astron. Nachr. 338 1060
Google Scholar
[7] Gao Z F, Wang N, Shan H, Li X D, Wang W 2017 Astrophys. J. 849 19
Google Scholar
[8] Mereghetti S, Pons J A, Melatos A 2015 Space Sci. Rev. 191 315
Google Scholar
[9] Kaspi V M, Beloborodov A M 2017 Annu. Rev. Astron. Astr. 55 261
Google Scholar
[10] Gao Z F, Peng Q H, Wang N, Chou C K 2012 Chin. Phys. B 21 057109
Google Scholar
[11] Gao Z F, Peng Q H, Wang N, Yuan J P 2012 Astrophys. Space Sci. 342 55
Google Scholar
[12] Gao Z F, Wang N, Peng Q H, Li X D, Du Y J 2013 Mod. Phys. Lett. A 28 1350138
[13] Yuan J P, Manchester R N, Wang N, Zhou X, Liu Z Y, Gao Z F 2010 Astrophys. J. Lett. 719 L111
Google Scholar
[14] Olausen S A, Kaspi V M 2014 Astrophys. J. Suppl. S. 212 6
Google Scholar
[15] Gao Z F, Peng Q H, Wang N, Chou C K, Huo W S 2011 Astrophys. Space Sci. 336 427
Google Scholar
[16] Flowers E, Ruderman M A 1977 Astrophys. J. 215 302
Google Scholar
[17] Yan W M, Wang N, Manchester R N, Wen Z G, Yuan J P 2018 Mon. Not. R. Astron. Soc. 476 3677
[18] Gourgouliatos K N, Cumming A 2014 Mon. Not. R. Astron. Soc. 438 1618
Google Scholar
[19] Gourgouliatos K N, Cumming A 2014 Phys. Rev. Lett. 112 171101
Google Scholar
[20] Thompson C, Murray N 2001 Astrophys. J. 560 339
Google Scholar
[21] Tiengo A, Esposito P, Mereghetti S, Turolla R, Nobili L, Gastaldello F, Götz D, Israel G, Rea N, Stella L, Zane S, Bignami G 2013 Nature 500 312
Google Scholar
[22] Gao Z F, Wang N, Yuan J P, Jiang L, Song D L, 2011 Astrophys. Space Sci. 332 129
Google Scholar
[23] Urpin V A, Chanmugam G, Sang Y 1994 Astrophys. J. 433 780
Google Scholar
[24] Urpin V A, Muslimov A G 1992 Mon. Not. R. Astron. Soc. 256 261
Google Scholar
[25] Muslimov A, Page D 1996 Astrophys. J. 458 347
Google Scholar
[26] Mitra D, Konar S, Bhattacharya D 1999 Mon. Not. R. Astron. Soc. 307 459
Google Scholar
[27] Geppert U, Urpin V 1994 Mon. Not. R. Astron. Soc. 271 490
Google Scholar
[28] Konar S, Bhattacharya D 1997 Mon. Not. R. Astron. Soc. 284 311
Google Scholar
[29] Geppert U, Page D, Zannias T 2000 Phys. Rev. D 61 123004
Google Scholar
[30] Aguilera D N, Pons J A, Miralles J A 2008 Astron. Astrophys. 486 255
Google Scholar
[31] Beloborodov A M, Li X 2016 Astrophys. J. 833 261
Google Scholar
[32] Wald R M 1984 General Relativity (Chicago: University of Chicago Press)p 504
[33] Wang H, Gao Z F, Wang N, Jia H Y, Li X D, Zhi Q J 2019 Publ. Astron. Soc. Pac. 131 054201
Google Scholar
[34] Esposito P, Rea N, Israel G L 2018 arXiv: 1803.057167
[35] Li X H, Gao Z F, Li X D, Xu Y, Wang P, Wang N, Peng Q H 2016 Int. J. Mod. Phys. D 25 1650002
[36] Baym G, Bethe H A, Pethick C J 1971 Nucl. Phys. A. 175 225
Google Scholar
[37] Baym G, Pethick C, Sutherland P 1971 Astrophys. J. 170 299
Google Scholar
[38] Lalazissis G A, König J, Ring P 1997 Phys. Rev. C. 55 540
Google Scholar
[39] Glendenning N K, Moszkowski S A 1991 Phys. Rev. Lett. 67 2414
Google Scholar
[40] Geng L, Toki H, Meng J 2005 Prog. Theor. Phys. 113 785
Google Scholar
[41] Singh D, Saxena G 2012 Int. J. Mod. Phys. E 21 1250076
[42] Demorest P B, Pennucci T, Ransom S M, Roberts M S E, Hessels J W T 2010 Nature 467 1081
Google Scholar
[43] Shapiro S L, Teukolsky S A 1983 Black Holes, White Drarfs, and Neutron Stars (New: YorkJohn Wiley & Sons)
[44] Potekhin A Y, Chabrier G 2013 Astron. Astrophys. 550 16
Google Scholar
[45] Sato T, Bamba A, Nakamura R, Ishida M 2010 Pub. Astron. Soc. J. 62 L33
Google Scholar
[46] Viganò D, Rea N, Pons J A, Perna R, Aguilera D N, Miralles J A 2013 Mon. Not. R. Astron. Soc. 434 123
Google Scholar
[47] Torii K, Kinugasa K, Katayama K, Tsunemi H, Yamauchi S 1998 Astrophys. J. 503 843
Google Scholar
[48] Rea N, Israel G L, Pons J A, Turolla R, Viganò D, Zane S, Esposito P, Perna R, Papitto A, Terreran G, Tiengo A, Salvetti D, Girart J M, Palau A, Possenti A, Götz D, Mignani R P, Ratti E, Stella L 2013 Astrophys. J. 770 65
Google Scholar
[49] Lamb R C, Fox D N, Macomb D J, Prince J A 2002 Astrophys. J. 574 L29
Google Scholar
[50] Dib R, Kaspi V M 2014 Astrophys. J. 784 37
Google Scholar
[51] Zhu W W, Kaspi V M, Dib R, Woods P M, Gavriil F P, Archibald A M 2008 Astrophys. J. 686 520
[52] Fahlman G G, Gregory P C 1981 Nature 293 202
[53] Rea N, Nichelli E, Israel G L, Perna R, Oosterbroek T, Parmar A N, Turolla R, Campana S, Stella L, Zane S, Angelini L 2007 Mon. Not. R. Astron. Soc. 381 293
Google Scholar
[54] An H, Kaspi V M, Archibald R, Cumming A, 2013 Astrophys. J. 763 82
Google Scholar
[55] Muno M P, Clark J S, Crowther P A, Dougherty S M, de Grijs R, Law C, McMillan S L W, Morris M R, Negueruela I, Pooley D, Portegies Z S, Yusef-Zadeh F 2006 Astrophys. J. Lett. 636 L41
Google Scholar
[56] Dib R, Kaspi V M, Gavriil F P 2009 Astrophys. J. 702 614
Google Scholar
[57] Tam C R, Gavriil F P, Dib R, Kaspi V M, Woods P M, Bassa C 2008 Astrophys. J. 677 503
Google Scholar
[58] Gaensler B M, McClure-Griffiths N M, Oey M S, Haverkorm M, Dickey J M, Green A J 2005 Astrophys. J. 620 L95
Google Scholar
[59] McGarry M B, Gaensler B M, Ransom S M, Kaspi V M, Veljkovik S 2005 Astrophys. J. 627 L137
Google Scholar
[60] Vasisht G, Gotthelf E V 1997 Astrophys. J. 486 L129
Google Scholar
[61] Camero A, Papitto A, Rea N, Viganò D, Pons J A, Tiengo A, Mereghetti S, Turolla R, Esposito P, Zane S, Israel G L, Götz D 2014 Mon. Not. R. Astron. Soc. 438 3291
Google Scholar
[62] Lin L, Kouveliotou C, Baring M G 2011 Astrophys. J. 739 87
Google Scholar
[63] Anderson G E, Gaensler B M, Slane P O, Rea N, Kaplan D L, Posselt B, Levin L, Johnston S, Murray S, Brogan C L, Bailes M, Bates S, Benjamin R A, Bhat N D R, Burgay M, Burke-Spolaor S, Chakrabarty D, D'Amico N, Drake J J, Esposito P, Grindlay J E, Hong J, Israel G L, Keith M J, Kramer M, Lazio T J W, Lee J C, Mauerhan J C, Milia S, Possenti A, Stappers B, Steeghs D T H 2012 Astrophys. J. 751 53
Google Scholar
[64] Tiengo A, Esposito P, Mereghetti S, Israel G L, Stella L, Turolla R, Zane S, Rea N, Götz D, Feroci M 2009 Mon. Not. R. Astron. Soc. 399 L74
Google Scholar
[65] Park S, Hughes J P, Slane P O, Burrows D N, Lee J J, Mori K 2012 Astrophys. J. 748 117
Google Scholar
[66] Mereghetti S, Esposito P, Tiengo A, Zane S, Turolla R, Stella L, Israel G L, Götz D, Feroci M 2006 Astrophys. J. 653 1423
Google Scholar
[67] Vrba F J, Henden A A, Luginbuhl C B, Guetter H H, Hartmann D H, Klose S 2000 Astrophys. J. 533 L17
Google Scholar
[68] Tendulkar S P, Cameron P, Brian K, Shrinivas R 2012 Astrophys. J. 761 76
Google Scholar
[69] Woods, Peter M, Kouveliotou C, Finger M H, Göǧüş E, Wilson, C A, Patel S K, Hurley K, Swank J H 2007 Astrophys. J. 654 470
Google Scholar
[70] Camilo F, Cognard I, Ransom S M, Halpern J P, Reynolds J, Zimmerman N, Gotthelf E V, Helfand D J, Demorest P, Theureau G, Backer D C 2007 Astrophys. J. 663 497
Google Scholar
[71] Dib R, Kaspi V M, Scholz P, Gavriil F P 2012 Astrophys. J. 748 3
Google Scholar
[72] Bernardini F, Israel G L, Stella L, Turolla R, Esposito P, Rea N, Zane S, Tiengo A, Campana S, Götz D, Mereghetti S, Romano P 2011 Astron. Astrophys. 529 A19
Google Scholar
[73] Rea N, Vigano D, Israel G L, Pons J A, Torres D F 2014 Astrophys. J. Lett. 781 L17
Google Scholar
[74] Zhou P, Chen Y, Li X D, Safi-Harb S, Mendez M, Terada Y, Sun W, Ge M Y 2014 Astrophys. J. Lett. 781 L16
Google Scholar
[75] Halpern J P, Gotthelf E V 2010 Astrophys. J. 710 941
Google Scholar
[76] Esposito P, Burgay M, Possenti A, Turolla R, Zane S, de Luca A, Tiengo A, Israel G, Mattana F, Mereghetti S, Bailes M, Romano P, Götz D, Rea N 2009 Mon. Not. R. Astron. Soc. 399 L44
Google Scholar
[77] Corbel S, Chapuis C, Dame T M, Durouchoux P 1999 Astrophys. J. 526 L29
Google Scholar
[78] Scholz P, Ng C Y, Livingstone M A, Kaspi V M, Cumming A, Archibald R F 2012 Astrophys. J. 761 66
Google Scholar
[79] Scholz P, Kaspi V M, Cumming A 2014 Astrophys. J. 786 62
Google Scholar
[80] Kargaltsev O, Kouveliotou C, Pavlov G G, Göǧüş E, Lin L, Wachter S, Griffith R L, Kaneko Y, Younes G 2012 Astrophys. J. 748 26
Google Scholar
[81] Leahy D A, Tian W W 2008 Astrophys. J. 135 167
[82] Levin L, Bailes M, Bates S, Bhat N D R, Burgay Marta, Burke-Spolaor S, D'Amico N, Johnston S, Keith M, Kramer M, Milia S, Possenti A, Rea N, Stappers B, van Straten W 2010 Astrophys. J. Lett. 721 L33
Google Scholar
[83] Kaspi V M, Archibald R F, Bhalerao V, Dufour F, Gotthelf E V, An H J, Bachetti M, Beloborodov A M, Boggs S E, Christensen F E, Craig W W, Grefenstette B W, Hailey C J, Harrison F A, Kennea J A, Kouveliotou C, Madsen K K, Mori K, Markwardt C B, Stern D, Vogel J K, Zhang W W 2014 Astrophys. J. 786 84
Google Scholar
[84] Mori K, Gotthelf E V, Zhang S, An H J, Baganoff F K, Barrière N M, Beloborodov A M, Boggs S E, Christensen F E, Craig, W W, Dufour F, Grefenstette B W, Hailey C J, Harrison F A, Hong J, Kaspi V M, Kennea J A, Madsen K K, Markwardt C B, Nynka M, Stern D, Tomsick J A, Zhang W W 2013 Astrophys. J. Lett. 770 L23
Google Scholar
[85] Gotthelf E V, Vasisht G, Boylan-Kolchin M, Torii K 2000 Astrophys. J. 542 L37
Google Scholar
[86] Tong H, Xu R X 2013 Res. Astron. Astrophy. 13 1207
Google Scholar
[87] Livingstone Margaret A, Ng C Y, Kaspi Victoria A 2011 Astrophys. J. 730 66
Google Scholar
[88] Becker W, Truemper J 1997 Astron. Astrophys. 326 682
[89] Shibata S, Watanabe E, Yatsu Y, Enoto T, Bamba A 2016 Astrophys. J. 833 14
Google Scholar
[90] Kaplan D L, van Kerkwijk M H 2009 Astrophys. J. 705 798
Google Scholar
[91] Haberl F 2007 Astrophys. Space Sci. 308 181
Google Scholar
[92] Bogdanov S, Ng C Y, Kaspi V M 2014 Astrophys. J. Lett. 792 L36
[93] Coelho J G, Cáceres D L, de Lima R C R, Malheiro M, Rueda J A, Ruffini R 2017 Astrono. Astrophys. 599 A87
Google Scholar
[94] Gonzalaz D, Reisenegger A 2010 Astrono. Astrophys. 522 A16
Google Scholar
[95] Kothes R, Dougherty S M 2007 Astron. Astrophys. 468 993
Google Scholar
[96] Durant M, van Kerkwijk, Marten H 2006 Astrophys. J. 652 576
Google Scholar
[97] Tiengo A, Esposito P, Mereghetti S 2008 Astrophys. J. 680 L133
Google Scholar
[98] Kumar H S, Safi-Harb S 2010 Astrophys. J. Lett. 725 L191
Google Scholar
[99] Tian W W, Leahy D A 2008 Astrophys. J. 677 292
Google Scholar
[100] Gourgouliatos K N, Hollerbach R 2018 Astrophys. J. 852 21
[101] Beloborodov A M 2011 High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings (Berlin: Springer-Verlag Berlin Heidelberg) p299
[102] Beloborodov A M, Levin Y 2014 Astrophys. J. Lett. 794 L24
Google Scholar
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