Abstract
The lack of isolated X-ray pulsars with spin periods longer than 12 s raises the question of where the population of evolved high-magnetic-field neutron stars has gone. Unlike canonical radiopulsars, X-ray pulsars are not subject to physical limits to the emission mechanism nor observational biases against the detection of sources with longer periods. Here we show that a highly resistive layer in the innermost part of the crust of neutron stars naturally limits the spin period to a maximum value of about 10–20 s. This highly resistive layer is expected if the inner crust is amorphous and heterogeneous in nuclear charge, possibly owing to the existence of a nuclear ‘pasta’ phase. Our findings suggest that the maximum period of isolated X-ray pulsars may be the first observational evidence for an amorphous inner crust, whose properties can be further constrained by future X-ray timing missions combined with more detailed models.
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References
Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts, M. S. E. & Hessels, J. W. T. A two-solar-mass neutron star measured using Shapiro delay. Nature 467, 1081–1083 (2010).
Van Kerkwijk, M. H., Breton, R. P. & Kulkarni, S. R. Evidence for a massive neutron star from a radial-velocity study of the companion to the black-widow pulsar PSR B1957+20. Astrophys. J. 728, 95–102 (2011).
Shternin, P. S., Yakovlev, D. G., Heinke, C. O., Ho, W. C. G. & Patnaude, D. J. Cooling neutron star in the Cassiopeia A supernova remnant: Evidence for superfluidity in the core. Mon. Not. R. Astron. Soc. 412, L108–L112 (2011).
Steiner, A. W., Lattimer, J. M. & Brown, E. F. The equation of state from observed masses and radii of neutron stars. Astrophys. J. 722, 33–54 (2010).
Mereghetti, S. The strongest cosmic magnets: Soft γ-ray repeaters and anomalous X-ray pulsars. Astronom. Astrophys. Rev. 15, 225–287 (2008).
Gavriil, F. P., Kaspi, V. M. & Woods, P.M. Magnetar-like X-ray bursts from an anomalous X-ray pulsar. Nature 419, 142–144 (2002).
Palmer, D. M. et al. A giant γ-ray flare from the magnetar SGR 1806-20. Nature 434, 1107–1109 (2005).
Camilo, F. et al. Transient pulsed radio emission from a magnetar. Nature 442, 892–895 (2006).
Duncan, R. C. & Thompson, C. Formation of very strongly magnetized neutron stars—Implications for γ-ray bursts. Astrophys. J. 392, L9–L13 (1992).
Kaspi, V. M. Grand unification of neutron stars. Proc. Natl Acad. Sci. USA 107, 7147–7152 (2010).
Psaltis, D. & Miller, M. C. Implications of the narrow period distribution of anomalous X-Ray pulsars and soft γ-ray repeaters. Astrophys. J. 578, 325–329 (2002).
Colpi, M., Geppert, U. & Page, D. Period clustering of the anomalous X-Ray pulsars and magnetic field decay in magnetars. Astrophys. J. 529, L29–L32 (2000).
Rea, N. et al. A low-magnetic-field soft γ repeater. Science 330, 944–946 (2010).
Turolla, R., Zane, S., Pons, J. A., Esposito, P. & Rea, N. Is SGR 0418+5729 indeed a waning magnetar? Astrophys. J. 740, 105–111 (2011).
Rea, N. et al. A new low magnetic field magnetar: The 2011 outburst of swift J1822.3-1606. Astrophys. J. 754, 27–40 (2012).
Goldreich, P. & Reisenegger, A. Magnetic field decay in isolated neutron stars. Astrophys. J. 395, 250–258 (1992).
Cumming, A., Arras, P. & Zweibel, E. Magnetic field evolution in neutron star crusts due to the hall effect and ohmic decay. Astrophys. J. 609, 999–1017 (2004).
Chamel, N. & Haensel, P. Physics of neutron star crusts. Living Rev. Relat. 11, 10 (2008).
Anderson, P. W. & Itoh, N. Pulsar glitches and restlessness as a hard superfluidity phenomenon. Nature 256, 25–27 (1975).
Strohmayer, T. E. & Watts, A. L. The 2004 hyperflare from SGR 1806-20: Further evidence for global torsional vibrations. Astrophys. J. 653, 593–601 (2006).
Brown, E. F. & Cumming, A. Mapping crustal heating with the cooling light curves of quasi-persistent transients. Astrophys. J. 698, 1020–1032 (2009).
Pons, J. A. & Geppert, U. Magnetic field dissipation in neutron star crusts: From magnetars to isolated neutron stars. Astron. Astrophys. 470, 303–315 (2007).
Viganò, D., Pons, J. A. & Miralles, J. A. A new code for the Hall-driven magnetic evolution of neutron stars. Comput. Phys. Comm. 183, 2042–2053 (2012).
Ravenhall, D. G., Pethick, C. J. & Wilson, J. R. Structure of matter below nuclear saturation density. Phys. Rev. Lett. 50, 2066–2069 (1983).
Horowitz, C. J., Pérez-Garcı´a, M. A., Berry, D. K. & Piekarewicz, J. Dynamical response of the nuclear pasta in neutron star crusts. Phys. Rev. C 72, 035801 (2005).
Horowitz, C. J. & Berry, D. K. Shear viscosity and thermal conductivity of nuclear pasta. Phys. Rev. C 78, 035806 (2008).
Watanabe, G., Iida, K. & Sato, K. Thermodynamic properties of nuclear pasta in neutron star crusts. Nucl. Phys. A 676, 455–473 (2000).
Sotani, H. Constraints on pasta structure of neutron stars from oscillations in giant flares. Mon. Not. R. Astron. Soc. 417, L70–L73 (2011).
Gearheart, M., Newton, W.G., Hooker, J. & Li, B-An. Upper limits on the observational effects of nuclear pasta in neutron stars. Mon. Not. R. Astron. Soc. 418, 2343–2349 (2011).
Jones, P. B. Disorder resistivity of solid neutron-star matter. Phys. Rev. Lett. 93, 221101 (2004).
Jones, P. B. Heterogeneity of solid neutron-star matter: Transport coefficients and neutrino emissivity. Mon. Not. R. Astron. Soc. 351, 956–966 (2004).
Magierski, P. & Heenen, P. H. Structure of the inner crust of neutron stars: Crystal lattice or disordered phase? Phys. Rev. C 65, 045804 (2002).
Horowitz, C. J. & Berry, D. K. Structure of accreted neutron star crust. Phys. Rev. C 79, 065803 (2009).
Horowitz, C. J., Caballero, O. L. & Berry, D. K. Thermal conductivity and phase separation of the crust of accreting neutron stars. Phys. Rev. E 79, 026103 (2009).
Hughto, J., Schneider, A. S., Horowitz, C. J. & Berry, D. K. Diffusion in Coulomb crystals. Phys. Rev. E 84, 016401 (2011).
Daligault, J. & Gupta, S. Electron-ion scattering in dense multi-component plasmas: Application to the outer crust of an accreting neutron star. Astrophys. J. 703, 994–1011 (2009).
Pons, J. A., Miralles, J. A. & Geppert, U. Magneto-thermal evolution of neutron stars. Astron. Astrophys. 496, 207–216 (2009).
Aguilera, D. N., Pons, J. A. & Miralles, J. A. The impact of magnetic field on the thermal evolution of neutron stars. Astrophys. J. 673, L167–L170 (2008).
Li, J., Spitkovsky, A. & Tchekhovskoy, A. Resistive solutions for pulsar magnetospheres. Astrophys. J. 746, 60 (2012).
Ho, W. C. G & Andersson, N. Rotational evolution of young pulsars due to superfluid decoupling. Nature Phys. 8, 787–789 (2012).
Feroci, M. et al. The large observatory for X-ray timing (LOFT). Exp. Astronom. 34, 415–444 (2012).
Acknowledgements
This work has been supported by the grants AYA 2010-21097-C03-02, AYA2012-39303, SGR2009-811, TW2010005 and iLINK 2011-0303. N.R. is supported by a Ramon y Cajal Research Fellowship and D.V. by the Prometeo/2009/103 grant.
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J.A.P. and D.V. contributed to developing the model, performed the calculations and wrote the manuscript. N.R. contributed to writing the manuscript and selected and checked the observational data.
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Pons, J., Viganò, D. & Rea, N. A highly resistive layer within the crust of X-ray pulsars limits their spin periods. Nature Phys 9, 431–434 (2013). https://doi.org/10.1038/nphys2640
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DOI: https://doi.org/10.1038/nphys2640
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