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The Role for the Inner Disk in Mass Accretion to the Star in the Early Phase of Star Formation

A physical mechanism that drives FU Orionis-type outbursts is reconsidered. We study the effect of inner part of a circumstellar disk covering a region from near the central star to the radius of approximately $5$ AU (hereafter, the inner disk). Using the fluctuated mass accretion rate onto the inner disk $\dot{M}_{\rm out}$, we consider the viscous evolution of the inner disk and the time variability of the mass accretion rate onto the central star $\dot{M}_{\rm in}$ by means of numerical calculation of an unsteady viscous accretion disk in a one-dimensional axisymmetric model. First, we calculate the evolution of the inner disk assuming an oscillating $\dot{M}_{\rm out}$. It is shown that the time variability of $\dot{M}_{\rm in}$ does not coincide with $\dot{M}_{\rm out}$ due to viscous diffusion. Second, we investigate the properties of spontaneous outbursts with temporally constant $\dot{M}_{\rm out}$. Outburst occur only in a limited range of mass accretion rates onto the inner disk $10^{-10}<\dot{M}_{\rm out}< 3\times 10^{-6}~{\rm M}_{\odot} {\rm yr}^{-1}$ due to gravo-magneto limit cycle (GML). Finally, we discuss the case with a combination of episodic $\dot{M}_{\rm out}$ and accretion outbursts cause by the GML in the inner disk. The GML can drive accretion outbursts onto the star even for the case of fluctuating $\dot{M}_{\rm out}$, although fluctuations of $\dot{M}$ decay during transmitting the inner disk inwards. We newly identified two modes of outburst which are spontaneous one and stimulated one. In a stimulated mode of outburst, $\dot{M}_{\rm out}$ does appear directly in $\dot{M}_{\rm in}$ (the latter defining the stellar accretion luminosity). In a spontaneous mode of outburst, $\dot{M}_{\rm out}$ appears as the interval between outbursts.