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$\begin{figure} { \psfig{silent=,figure=fig01ms5308.eps,width=7.5cm} } \end{figure}$ Figure 1: Time sequence of the X-ray flares $\delta \zeta /\zeta _0$ . The perturbation is periodic in time with a periodicity $\tau _{\rm X}^{} = 7 \ \rm days$ while the width of a single perturbation is $t_{\sigma }^{} = 12 \rm\ h$ .
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In the text

$\begin{figure} \par\mbox{\psfig{silent=,figure=fig02lms5308.eps,width=7.5cm}\hspace*{7mm} \psfig{silent=,figure=fig02rms5308.eps,width=7.5cm} }\end{figure}$ Figure 2: Model1 - column densities of the whole disk (solid line) and of the active zones (dashed and dotted lines) - corresponding to magnetic Reynolds numbers ${\rm Re}_{\rm m}$ greater than 100 - for two different heavy metal abundances $x_{{\rm M}^{}}$ . The left panel is for $x_{\rm M}=0$ and the right panel is for $x_{\rm M}=10^{-12}$ . The upper and lower dashed lines refer to simulations with constant ionisation rate $\zeta = \zeta _0$ and $\zeta = 100 \times \zeta _0$ while the long-dashed line refers to simulation with $\zeta = \zeta _{\rm eff}$ . The dotted line refers to the column density of the active zone at $t = 10~ 000 \ \rm yr$ obtained by assuming a time-dependent ionisation rate $\zeta (t) = \zeta _0^{} + \delta \zeta (t)$ . The time of the plot is at the mid-point between two X-ray flares.
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In the text

$\begin{figure} \par\mbox{% \psfig{silent=,figure=fig03lms5308.eps,width=7.5cm}\hspace*{4mm} \psfig{silent=,figure=fig03rms5308.eps,width=7.5cm} } %\end{figure}$ Figure 3: Model3 - column densities of the whole disk (solid line) and of the active zones (dashed and dotted lines) - refering to magnetic Reynolds numbers ${\rm Re}_{\rm m}$ greater than 100 - for two different elemental abundances $x_{{\rm Mg}^{}}$ . The left panel is for $x_{\rm Mg}=0$ and the right panel is for $x_{\rm Mg}=10^{-8}$ . The upper and the lower dashed lines refer to simulations assuming a constant ionisation rate $\zeta = \zeta _0$ and $\zeta = 100 \times \zeta _0$ , while the long-dashed dotted line refers to simulation with $\zeta = \zeta _{\rm eff}$ . The dotted line shows the column density of the active zone at $t = 10~ 000 \ \rm yr$ assuming a time-dependent ionisation rate $\zeta (t) = \zeta _0^{} + \delta \zeta (t)$ . The amplitude $\lambda$ of the perturbation $\delta \zeta /\zeta _0$ is $\lambda = 100$ caused by increasing the X-ray luminosity $L_{\rm X}^{P} = 100 \times L_{\rm X}^{0}$ at the flare peak.
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In the text

$\begin{figure} \par\mbox{% \psfig{silent=,figure=fig04lms5308.eps,width=7.5cm}\hspace*{.6cm} \psfig{silent=,figure=fig04rms5308.eps,width=7cm} } %\end{figure}$ Figure 4: Model1 - the change in the ionisation fraction $x[\rm e_{}^{-}]/x_{\rm crit}[ e_{}^{-}]$ is plotted against the relative change in the ionisation rate $(\zeta _0 + \delta \zeta )/\zeta _0$ at different radial positions R along the transition zone assuming $x_{\rm M}=0$ . It is a limit cycle since the orbit is closed (the arrow points forward in time). In addition, the equlibrium values $x_{\infty }[\rm e_{}^{-}]$ are shown obtained for the unperturbed models with $\zeta = \zeta _0$ , and $\zeta = 100 \times \zeta _0$ .
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In the text

$\begin{figure} \mbox{% \psfig{silent=,figure=fig05lms5308.eps,width=7.5cm}\hspace*{.6cm} \psfig{silent=,figure=fig05rms5308.eps,width=7cm} }\end{figure}$ Figure 5: Model3 - the change in the ionisation fraction $x[\rm e_{}^{-}]/x_{\rm crit}[ e_{}^{-}]$ is plotted against the relative change in the ionisation rate $(\zeta _0 + \delta \zeta )/\zeta _0$ near the transition zone at $R = 1 \ \rm AU$ for different elemental abundances $x_{\rm Mg}$ . The left panel is for $x_{\rm Mg}=0$ and the right panel is for $x_{\rm Mg}=10^{-8}$ . It is a limit cycle since the orbit is closed (the arrow points forward in time). Note that $x[\rm e_{}^{-}]/x_{\rm crit}[ e_{}^{-}]$ is slightly less than unity when $\zeta = \zeta _0$ because the position of the transition zone does not coincide precisely with a grid cell in this model.
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In the text

$\begin{figure} \mbox{% \psfig{silent=,figure=fig06lms5308.eps,width=7.5cm}\hspace*{.6cm} \psfig{silent=,figure=fig06rms5308.eps,width=7.2cm} }\end{figure}$ Figure 6: Model1 - column densities of the whole disk (solid line) and of the active zones (dashed and dotted lines) - refering to magnetic Reynolds numbers ${\rm Re}_{\rm m} > 100$ - for $x_{\rm {M}^{}} = 0$ . The dashed lines refer to simulations obtained by assuming unchanging ionisation rates $\zeta = \zeta _0$ for different plasma temperatures. Left panel: the dotted line refers to the column density of the active zone at $t = 10~ 000 \ \rm yr$ obtained by assuming a time-dependent ionisation rate caused by periodic variation of the plasma temperature between $k_{\rm B} T_{\rm cool}=3$ keV and $k_{\rm B} T_{\rm hot}=7$ keV. Right panel: the dotted line refers to the column density of the active zone at $t = 10~ 000 \ \rm yr$ obtained by assuming a time-dependent ionisation rate $\zeta (t)$ caused by both the X-ray luminosity and the plasma temperature increasing during flares. The disk becomes entirely active when the X-ray luminosity is increased by a factor of 100 and the plasma temperature is maintained at a constant value of $k_{\rm B} T=7$ keV.
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In the text

$\begin{figure} { \psfig{silent=,figure=fig07ms5308.eps,width=8.0cm} }\end{figure}$ Figure 7: The ratio of the effective X-ray ionisation rates $\zeta_{0 ,7~{\rm keV}}/\zeta_{0 ,3~{\rm keV}}$ . $\zeta_{0 ,3~{\rm keV}}$ and $\zeta_{0 ,7~{\rm keV}}$ refer to local ionisation rates for plasma temperatures $k_{\rm B}^{}T = 3~{\rm keV}$ and $k_{\rm B}^{}T = 7~{\rm~keV}$ , respectively. The disk parameter are $\alpha = 10^{-2}$ and ${\dot M} = 10^{-7}$ $M_{\odot }$ yr^-1. The contour lines refer to values of $\zeta_{0 ,7~{\rm keV}}/\zeta_{0 ,3~{\rm keV}}$ : 10, 10², and 10³.
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In the text

$\begin{figure} \mbox{% \psfig{silent=,figure=fig08lms5308.eps,width=7.5cm}\hspace*{.6cm} \psfig{silent=,figure=fig08rms5308.eps,width=7.0cm} }\end{figure}$ Figure 8: model1 - the change in the ionisation fraction $x[{\rm e}_{}^{-}]/x_{\rm crit}[ {\rm e}_{}^{-}]$ is plotted against the relative change in the ionisation rate $(\zeta _0 + \delta \zeta )/\zeta _0$ at different radial positions R with z/R = 0 (midplane). $x_{\rm crit}[ {\rm e}_{}^{-}]$ denotes the ionisation fraction at the transition layer. Each graph describes a limit cycle since the orbit is closed (the arrow points forward in time). The perturbation $\delta \zeta /\zeta _0$ in the ionisation rate is based on the assumption that both the X-ray peak luminosity $L_{\rm X}^{P} = 100 \times L_{\rm X}^{0}$ and the temperature of the hot plasma component $k_{\rm B}^{}T_{\rm hot}^{} = 7 \ \rm~keV$ at the flare peaks.
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In the text

$\begin{figure} { \psfig{silent=,figure=fig01ms5308.eps,width=7.5cm} } \end{figure}$	Figure 1: Time sequence of the X-ray flares $\delta \zeta /\zeta _0$ . The perturbation is periodic in time with a periodicity $\tau _{\rm X}^{} = 7 \ \rm days$ while the width of a single perturbation is $t_{\sigma }^{} = 12 \rm\ h$ .
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