[Paper Review] Study of luminosity and spin-up relation in X-ray binary pulsars with long-term monitoring by MAXI/GSC and Fermi/GBM

M. Sugizaki, T. Mihara+2 more|arXiv (Cornell University)|Feb 16, 2015

Astrophysical Phenomena and Observations2 references3 citations

TL;DR

This study investigates the luminosity-spin-up relation in five Be X-ray binary pulsars using long-term X-ray light curves from MAXI/GSC and pulse period data from Fermi/GBM. It confirms that the observed spin-up rate scales with luminosity as $ \dot{P}_{\text{spin}} \propto L^{6/7} $, consistent with the theoretical model of Ghosh & Lamb (1979), with the correlation factor $ \alpha $ closely matching the predicted value across all sources despite minor dispersion due to beaming and measurement uncertainties.

ABSTRACT

We study the relation between luminosity and spin-period change in X-ray binary pulsars using long-term light curve obtained by the MAXI/GSC all-sky survey and pulse period data from the Fermi/GBM pulsar project. X-ray binaries, consisting of a highly magnetized neutron star and a stellar companion, originate X-ray emission according to the energy of the accretion matter onto the neutron star. The accretion matter also transfers the angular momentum at the Alfven radius, and then spin up the neutron star. Therefore, the X-ray luminosity and the spin-up rate are supposed to be well correlated. We analyzed the luminosity and period-change relation using the data taken by continuous monitoring of MAXI/GSC and Fermi/GBM for Be/X-ray binaries, GX 304$-$1, A 0535$+$26, GRO J1008$-$57, KS 1947$+$300, and 2S 1417$-$624, which occurred large outbursts in the last four years. We discuss the results comparing the obtained observed relation with that of the theoretical model by Ghosh \& Lamb (1979).

Motivation & Objective

• To investigate the empirical relation between X-ray luminosity and spin-period derivative in Be X-ray binary pulsars.
• To test the theoretical prediction of Ghosh & Lamb (1979) that $ \dot{P}_{\text{spin}} \propto L^{6/7} $ using long-term observational data.
• To disentangle intrinsic spin-up from orbital Doppler effects in pulse period variations using a semi-empirical model.
• To assess the consistency of observed spin-up rates with theoretical expectations across a sample of five Be XBPs with varying orbital and spin parameters.

Proposed method

• Utilized 2–20 keV long-term light curves from MAXI/GSC to estimate bolometric luminosity $ L_{37} $, assuming isotropic emission and typical cutoff power-law spectra.
• Acquired pulse period data from the Fermi/GBM pulsar project, correcting for orbital Doppler shifts where orbital elements were known.
• Constructed a semi-empirical model combining the GL79 spin-up law $ \dot{P}_{\text{spin}} = \alpha L^{6/7} $ and orbital Doppler effects using Keplerian orbital elements.
• Fitted the model to observed period data by simultaneously solving for intrinsic spin-up and orbital parameters, with $ \gamma = 6/7 $ fixed as per theory.
• Used the best-fit $ \alpha $ values to compare with the theoretical $ \alpha_0 $, assessing deviations in terms of luminosity correction and system parameters.
• Applied the model to five Be XBPs: GX 304–1, A 0535+26, GRO J1008–57, KS 1947+300, and 2S 1417–624, with orbital elements either known or floated in the fit.

Experimental results

Research questions

• RQ1 Does the observed spin-up rate in Be X-ray binary pulsars follow the theoretical $ L^{6/7} $ dependence predicted by Ghosh & Lamb (1979)?
• RQ2 How well do the observed luminosity and spin-period change correlations match the theoretical model across different Be X-ray binary systems?
• RQ3 To what extent do uncertainties in luminosity correction and beaming affect the observed $ \alpha $-factor relative to the theoretical prediction?
• RQ4 Are there systematic trends in the $ \alpha / \alpha_0 $ ratio with respect to pulse period, orbital period, or eccentricity across the sample?
• RQ5 Can the intrinsic spin-up signal be reliably extracted from pulse period data when orbital Doppler effects are present and orbital elements are uncertain?

Key findings

• The observed spin-up rate $ \dot{P}_{\text{spin}} $ scales with luminosity as $ L^{6/7} $, consistent with the theoretical model of Ghosh & Lamb (1979), with $ \gamma = 6/7 $ well supported by the data.
• The best-fit correlation factor $ \alpha $ for all five Be XBPs is within a factor of ~3 of the theoretical prediction $ \alpha_0 $, with $ \alpha / \alpha_0 $ ranging from 0.28 to 3.2.
• For GX 304–1, where orbital elements were unknown, the model successfully fitted the data with floating orbital parameters, confirming robustness of the $ L^{6/7} $ scaling.
• The dispersion in $ \alpha / \alpha_0 $ is attributed to uncertainties in bolometric luminosity correction, particularly due to beaming effects and spectral variability.
• No strong systematic trend in $ \alpha / \alpha_0 $ was found with pulse period or orbital period, though a possible trend with eccentricity may emerge with more data.
• The model successfully reproduces the full outburst and quiescence cycles in all five sources, demonstrating the validity of the $ L^{6/7} $ scaling over a wide dynamic range in luminosity.