Multiband Studies of the Optical Periodic Modulation in the X-Ray Binary SAX~J1808.4-3658 during Its Quiescence and 2008 Outburst

We report on time-resolved optical imaging of the X-ray binary SAX J1808.4-3658 during its quiescent state and 2008 outburst. The binary, containing an accretion-powered millisecond pulsar, has a large sinusoidal-like modulation in its quiescent optical emission. We employ a Markov chain Monte Carlo technique to fit our multi-band light curve data in quiescence with an irradiated star model, and derive a tight constraint of $50^{+6}_{-5}$ deg on the inclination angle $i$ of the binary system. The pulsar and its companion are constrained to have masses of $0.97^{+0.31}_{-0.22} M_{\sun}$ and $0.04^{+0.02}_{-0.01} M_{\sun}$ (both 1$σ$ ranges), respectively. The dependence of these results on the measurements of the companion's projected radial velocity is discussed. We also find that the accretion disk had nearly constant optical fluxes over a $\sim$500 day period in the quiescent state our data covered, but started brightening 1.5 months before the 2008 outburst. Variations in modulation during the outburst were detected in our four observations made 7-12 days after the start of the outburst, and a sinusoidal-like modulation with 0.2 mag amplitude changed to have a smaller amplitude of 0.1 mag. The modulation variations are discussed. We estimate the albedo of the companion during its quiescence and the outburst, which was approximately 0 and 0.8 (for isotropic emission), respectively. This large difference probably provides additional evidence that the neutron star in the binary turns on as a radio pulsar in quiescence.