Updated gravitational-wave upper limits on the internal magnetic field strength of recycled pulsars
📝 Abstract
Recent calculations of the hydromagnetic deformation of a stratified, non-barotropic neutron star are generalized to describe objects with superconducting interiors, whose magnetic permeability \mu is much smaller than the vacuum value \mu_0. It is found that the star remains oblate if the poloidal magnetic field energy is \gtrsim 40% of total magnetic field energy, that the toroidal field is confined to a torus which shrinks as \mu decreases, and that the deformation is much larger (by a factor \sim \mu_0/\mu) than in a non-superconducting object. The results are applied to the latest direct and indirect upper limits on gravitational-wave emission from Laser Interferometer Gravitational Wave Observatory (LIGO) and radio pulse timing (spin-down) observations of 81 millisecond pulsars, to show how one can use these observations to infer the internal field strength. It is found that the indirect spin-down limits already imply astrophysically interesting constraints on the poloidal-toroidal field ratio and diamagnetic shielding factor (by which accretion reduces the observable external magnetic field, e.g. by burial). These constraints will improve following gravitational-wave detections, with implications for accretion-driven magnetic field evolution in recycled pulsars and the hydromagnetic stability of these objects’ interiors.
💡 Analysis
Recent calculations of the hydromagnetic deformation of a stratified, non-barotropic neutron star are generalized to describe objects with superconducting interiors, whose magnetic permeability \mu is much smaller than the vacuum value \mu_0. It is found that the star remains oblate if the poloidal magnetic field energy is \gtrsim 40% of total magnetic field energy, that the toroidal field is confined to a torus which shrinks as \mu decreases, and that the deformation is much larger (by a factor \sim \mu_0/\mu) than in a non-superconducting object. The results are applied to the latest direct and indirect upper limits on gravitational-wave emission from Laser Interferometer Gravitational Wave Observatory (LIGO) and radio pulse timing (spin-down) observations of 81 millisecond pulsars, to show how one can use these observations to infer the internal field strength. It is found that the indirect spin-down limits already imply astrophysically interesting constraints on the poloidal-toroidal field ratio and diamagnetic shielding factor (by which accretion reduces the observable external magnetic field, e.g. by burial). These constraints will improve following gravitational-wave detections, with implications for accretion-driven magnetic field evolution in recycled pulsars and the hydromagnetic stability of these objects’ interiors.
📄 Content
arXiv:1112.1542v1 [astro-ph.HE] 7 Dec 2011 Mon. Not. R. Astron. Soc. 000, 1–10 (?) Printed 31 August 2018 (MN LATEX style file v2.2) Updated gravitational-wave upper limits on the internal magnetic field strength of recycled pulsars A. Mastrano1⋆and A. Melatos1† 1School of Physics, University of Melbourne, Parkville VIC 3010, Australia Accepted ?. Received ?; in original form ? ABSTRACT Recent calculations of the hydromagnetic deformation of a stratified, non-barotropic neutron star are generalized to describe objects with superconducting interiors, whose magnetic permeability µ is much smaller than the vacuum value µ0. It is found that the star remains oblate if the poloidal magnetic field energy is ≳40% of total mag- netic field energy, that the toroidal field is confined to a torus which shrinks as µ decreases, and that the deformation is much larger (by a factor ∼µ0/µ) than in a non-superconducting object. The results are applied to the latest direct and indirect upper limits on gravitational-wave emission from Laser Interferometer Gravitational Wave Observatory (LIGO) and radio pulse timing (spin-down) observations of 81 mil- lisecond pulsars, to show how one can use these observations to infer the internal field strength. It is found that the indirect spin-down limits already imply astrophysically interesting constraints on the poloidal-toroidal field ratio and diamagnetic shielding factor (by which accretion reduces the observable external magnetic field, e.g. by burial). These constraints will improve following gravitational-wave detections, with implications for accretion-driven magnetic field evolution in recycled pulsars and the hydromagnetic stability of these objects’ interiors. Key words: MHD – stars: magnetic field – stars: interiors – stars: neutron – gravi- tational waves 1 INTRODUCTION The external magnetic field of a neutron star is (relatively) easily inferred from its spin-down rate, but its internal magnetic field is not directly observable. The main clue suggesting the existence of strong internal neutron star fields comes from the 1998 August 27 giant flare from the soft gamma-ray repeater (SGR) 1900+14 (Feroci et al. 1999; Hurley et al. 1999; Mazets et al. 1999). The giant flare, which released ∼1037 J of energy as X-rays, was accompanied by a 2.3-fold increase in the spin-down rate (Mazets et al. 1999; Woods et al. 1999; Thompson et al. 2000). To explain this, Ioka (2001) proposed that the flare and the enhanced spin down were caused by a global reconfiguration of the internal magnetic field of ∼1013 T, well above the external dipole field of 6.4 × 1010 T1. Corsi & Owen (2011) generalised the Ioka (2001) calculation (by allowing the toroidal field strength to change, as well as the moment of inertia) and concluded that an internal field strength of ∼1012 T gave rise to the 1998 August 27 event, lower than the first estimate by Ioka (2001), but still significantly higher than the observed external field. Stellar ellipticity can also be used to constrain the strength of a star’s internal field (Cutler 2002; Dall’Osso et al. 2009; Abbott et al. 2010; Pitkin 2011). It is well known that a strong magnetic field can deform a star (Chandrasekhar & Fermi 1953; Ferraro 1954; Goosens 1972; Katz 1989; Payne & Melatos 2004; Haskell et al. 2008; Mastrano et al. 2011). The ellipticity ǫ is roughly proportional to the magnetic energy (Cutler 2002; Haskell et al. 2008; Dall’Osso et al. 2009). Neutron stars, with ⋆E-mail: alpham@unimelb.edu.au † E-mail: amelatos@unimelb.edu.au 1 Throughout this paper, we use SI units: 1 T = 104 G. c⃝? RAS 2 A. Mastrano and A. Melatos their intense magnetic fields, possess significant ellipticities, making them good candidates for gravitational wave sources (Bonazzola & Gourgoulhon 1996; Melatos & Payne 2005; Stella et al. 2005; Haskell et al. 2008; Dall’Osso et al. 2009). Recent data from the fifth Laser Interferometer Gravitational Wave Observatory (LIGO) Science Run set an upper limit of ǫ ≲ 1.4 × 10−4 on the Crab Pulsar (Abbott et al. 2008, 2010), translating into an internal magnetic field of ≲1012 T under standard assumptions. LIGO non-detections of the central compact object (CCO) in the supernova remnant Cassiopeia A (Cas A) have constrained its ellipticity as well. The Cas A CCO has not been detected electromagnetically, making it impossible to infer its external magnetic field from the spin-down rate. However, Wette et al. (2008) and Wette (2010) constrained its ellipticity as a function of gravitational wave frequency (e.g., ǫ ≲3.6 × 10−4 for 100 Hz, ǫ ≲0.6 × 10−4 for 200 Hz, and ǫ ≲0.38 × 10−4 for 300 Hz), implying an internal magnetic field ≲1014 T. Lastly, Chung et al. (2011) showed that it will be possible to use future data from LIGO to set a lower limit of 107 T on the magnetic field (ǫ ≲10−4) of the putative 24-year-old neutron star in the supernova remnant SNR 1987A. Gravitational waves are generated by a rotating star when it is not spherically symmetric and when its ‘wobble ang
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