Correlation between the luminosity and spin-period changes during outbursts of 12 Be binary pulsars observed by the MAXI/GSC and the Fermi/GBM

Abstract

To observationally study spin-period changes of accreting pulsars caused by the accretion torque, the present work analyzes X-ray light curves of 12 Be binary pulsars obtained by the MAXI/GSC all-sky survey and their pulse periods measured by the Fermi/GBM pulsar project, both covering more than 6 years from 2009 August to 2016 March. The 12 objects were selected because they are accompanied by clear optical identification, and accurate measurements of surface magnetic fields. The luminosity L and the spin-frequency derivativesν, measured during large outbursts with L > ∼ 1 × 10 37 erg s −1 , were found to approximately follow the theoretical relations in the accretion torque models, represented byν ∝ L α (α ≃ 1), and the coefficient of proportionality betweenν and L α , agrees, within a factor of ∼ 3, with that proposed by Ghosh & Lamb (1979). In the course of the present study, the orbital elements of several sources were refined.

Broad-band X-ray characteristics of the transient pulsar GRO J2058+42

“…The rapid spin up episodes during such outbursts make Be X-ray binaries excellent candidates to establish a quantitative comparison of theoretical predictions with minute observations. The luminosity and the spin frequency derivatives during large outbursts with L X ≥ 1 × 10 37 ergs −1 were found to be related as ν ∝ L α X (α ≃ 1) (Parmar et al 1989;Bildsten et al 1997;Sugizaki et al 2017). This proportionality relation validates the expected theoretical XBP spin up models of magnetospheric interaction with accretion disk.…”

“…11.6keV . For Be XRPs the CRSF is observed within a energy range of 12-76 keV (Sugizaki et al 2017). The energy spectra of GRO J2058+42 does not show any CRSF in 3-78 keV energy band.…”

“…Along with it we also look at the difference in the estimation of the strength of the surface magnetic field from spin-up rate and luminosity relation, and from the observed cyclotron line. We calculated the µ 30 and B 12 from the proportionality factor k in the spin-up rate and luminosity relation in equation 1 provided in Sugizaki et al (2017) for nine transient pulsars for which cyclotron line has been observed. Canonical values of R 6 = 1, M 1.4 = 1, I 45 = 1 for neutron stars have been assumed for the calculation.…”

“…The spin-up rate ( ν s ) and the luminosity L are known to be correlated in transient X-ray pulsars (Sugizaki et al 2017). The disk-magnetosphere interaction model of a rotating neutron star which is spinning up by accreting mass from it's companion via a Keplerian disk, with a moment of inertia I, holds the following relation approximated to the non-relativistic limit (Ghosh & Lamb 1979b;Sugizaki et al 2017).…”

“…According to Ghosh & Lamb (1979a,b) model, under slow-rotator condition n ∼ 1.39 and ζ ∼ 0.52. Therefore, equation (1) reduces to (Sugizaki et al 2017),…”