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

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 $\sim 5\times10^{-3}$, 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, $C_\mathrm{irr} < 1.5 \times10^{-4}$, 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 $(3-6)\times10^{-4}$. 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 $\dot M(t)$.