Refinement of the timing-based estimator of pulsar magnetic fields

Abstract

Numerical simulations of realistic non-vacuum magnetospheres of isolated neutron stars have shown that pulsar spin-down luminosities depend weakly on the magnetic obliquity. This result provides the opportunity to estimate the surface magnetic field for a given radiopulsar with quite a high accuracy. In the current work, we present a refinement of the classical `magneto-dipolar' formula for pulsar magnetic fields $B_{\rm md} = (3.2\times 10^{19}\mbox{ G})\sqrt{P\dot P}$, where $P$ is the neutron star spin period. The new, robust timing-based estimator is introduced as $\log B=\log B_{\mathrm{md}}+{\Delta }_{\mathrm{B}}(M,\alpha )$, where the correction ${\Delta }_{\mathrm{B}}$ depends on the equation of state (EOS) of dense matter, the individual pulsar obliquity $\alpha$ and the mass $M$. Adopting state-of-the-art statistics for $M$ and $\alpha$ we calculate the distributions of ${\Delta }_{\mathrm{B}}$ for a representative subset of 22 EOSs that do not contradict observations. It has been found that ${\Delta }_{\mathrm{B}}$ is distributed nearly normally, with the average in the range -0.5 to -0.25 dex and standard deviation $\sigma [{\Delta }_{\mathrm{B}}]\approx$ 0.06 to 0.09 dex, depending on the adopted EOS. The latter quantity represents a formal uncertainty of the corrected estimation of $\log B$ because ${\Delta }_{\mathrm{B}}$ is weakly correlated with $\log B_{\mathrm{md}}$. At the same time, if it is assumed that every considered EOS has the same chance of occurring in nature, then another, more generalized, estimator $B^{\ast }\approx 3B_{\mathrm{md}}/7$ can be introduced providing an unbiased value of the pulsar surface magnetic field with $\sim$30 per cent uncertainty with 68 per cent confidence. Finally, we discuss the possible impact of pulsar timing irregularities on the timing-based estimation of $B$ and review the astrophysical applications of the obtained results.

13 pages, 5 figures; accepted for publication in MNRAS

References in corpus (29)

• Shapiro delay measurement of a two solar mass neutron star
• A Massive Pulsar in a Compact Relativistic Binary
• The ATNF Pulsar Catalogue
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XII: Stiffness and stability of neutron-star matter
• Switched magnetospheric regulation of pulsar spin-down
• A periodically active pulsar giving insight into magnetospheric physics
• The Evolution of Compact Binary Star Systems
• Signals of the QCD phase transition in core-collapse supernovae
• Symmetry Energy I: Semi-Infinite Matter
• New Hyperon Equations of State for Supernovae and Neutron Stars in Density-dependent Hadron Field Theory
• Inner crust of neutron stars with mass-fitted Skyrme functionals
• On the birthrates of Galactic neutron stars
• Three-dimensional numerical simulations of the pulsar magentoshere: Preliminary results
• Equation of state and thickness of the inner crust of neutron stars
• Population synthesis of isolated Neutron Stars with magneto--rotational evolution
• The population of pulsars with interpulses and the implications for beam evolution
• Evidence for Heating of Neutron Stars by Magnetic Field Decay
• 30 Glitches in slow pulsars
• Rotational evolution of the Crab pulsar in the wind braking model
• Braking Index of Isolated Pulsars
• Magnetic fields of neutron stars in X-ray binaries
• A strong $\ddot{\nu }-\dot{\nu }$ correlation in radio pulsars with implications for torque variations
• On the role of the current loss in radio pulsar evolution
• A New, Low Braking Index For the LMC Pulsar B0540-69
• Statistics of interpulse radio pulsars - the key to solving the alignment/counter-alignment problem
• Braking Index of Isolated Pulsars II: A novel two-dipole model of pulsar magnetism
• A note on the cyclic evolution of the pulsar magnetosphere
• Evidence of longterm cyclic evolution of radio pulsar periods
• A novel look at the pulsar force-free magnetosphere

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• Magnetic angle evolution in accreting neutron stars
• XMM-Newton observations of a gamma-ray pulsar J0633+0632: pulsations, cooling and large-scale emission
• The apparent decay of pulsar magnetic fields
• Imprint of magnetic obliquity in apparent spin-down of radio pulsars
• Investigating the neutron star physics through observations of several young pulsars in the dipole-field re-emergence scenario
• Evidence for the spin-kick alignment of pulsars from the statistics of their magnetic inclinations