Magnetic accretion flow explains the hysteresis q-diagram seen in outbursts of black hole low-mass X-ray binaries

Black hole low-mass X-ray binaries undergo quiescence-outburst cycles. During the outbursts, they typically go through a q-shaped pattern in the hardness-intensity diagram (HID), known as the hysteresis q-diagram, while the physical nature is still unknown. We argue that the hysteresis q-diagram can be well explained with a recently proposed magnetized accretion disk model. The model takes into account the saturated magnetic pressure and predicts that the standard Shakura-Sunyaev disk (SSD) has an inner truncation at relatively low accretion rates, filled with an optically thin, hot accretion flow that resembles the advection-dominated accretion flow (ADAF) inside. Given a perturbation of accretion rate, the variation of the truncation radius can be derived as a result of thermal equilibrium by comparing the heating and cooling rates. We show that the truncation radius displays a hysteresis effect in response to the variation of mass accretion rate. As a result, the spectral hardness due to competition of the soft SSD and hard ADAF components is also hysteresis along with the rise and decay of the mass accretion rate or source intensity, leading to a q-shaped diagram in the HID.