Determination of the turbulent parameter in the accretion disks: effects of self-irradiation in 4U 1543-47 during the 2002 outburst

Abstract

We investigate the viscous evolution of the accretion disk in 4U 1543-47, a black hole binary system, during the first 30 days after the peak of the 2002 burst by comparing the observed and theoretical accretion rate evolution $\dot{M}(t)$. The observed $\dot{M}(t)$ is obtained from spectral modelling of the archival RXTE/PCA data. Different scenarios of disk decay evolution are possible depending on a degree of self-irradiation of the disk by the emission from its centre. If the self-irradiation, which is parametrized by factor $C_{\mathrm{irr}}$, had been as high as $\sim 5\times 10^{-3}$, then the disk would have been completely ionized up to the tidal radius and the short time of the decay would have required the turbulent parameter $\alpha \sim 3$. We find that the shape of the $\dot{M}(t)$ curve is much better explained in a model with a shrinking high-viscosity zone. If $C_{\mathrm{irr}}\approx (2-3)\times 10^{-4}$, the resulting $\alpha$ lie in the interval $0.5-1.5$ for the black hole masses in the range $6-10{\mathrm{M}}_{\odot }$, while the radius of the ionized disk is variable and controlled by irradiation. For very weak irradiation, $C_{\mathrm{irr}}<1.5\times 10^{-4}$, the burst decline develops as in normal outbursts of dwarf novae with $\alpha \sim 0.08-0.32$. The optical data indicate that $C_{\mathrm{irr}}$ in 4U 1543-47 (2002) was not greater than approximately $(3-6)\times 10^{-4}$. Generally, modelling of an X-ray nova burst allows one to estimate $\alpha$ that depends on the black hole parameters. We present the public 1-D code Freddi to model the viscous evolution of an accretion disk. Analytic approximations are derived to estimate $\alpha$ in X-ray novae using $\dot{M}(t)$.

13 pages, 14 figures. Accepted for publication in MNRAS. Code Freddi is publicly available at http://xray.sai.msu.ru/~malanchev/freddi/ V3 fixes a typo in an equation on page 3, we thank Ankit Mishra for pointing it out to us

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