In classical supergiant X-ray binaries (SgXBs), the Bondi-Hoyle-Lyttleton wind accretion was usually assumed, and the angular momentum transport to the accretors is inefficient. The observed spin-up/spin-down behavior of the neutron star in SgXBs is not well understood. In this paper, we report an extended low state of Vela X-1 (at orbital phases 0.16-0.2), lasting for at least 30 ks, observed with Chandra during the onset of an unusual spin-up period. During this low state, the continuum fluxes dropped by a factor of 10 compared to the preceding flare period, and the continuum pulsation almost disappeared. Meanwhile, the Fe K$alpha$ fluxes of the low state were similar to the preceding flare period, leading to an Fe K$alpha$ equivalent width (EW) of 0.6 keV, as high as the Fe K$alpha$ EW during the eclipse phase of Vela X-1. Both the pulsation cessation and the high Fe K$alpha$ EW indicate an axisymmetric structure with a column density larger than $10^{24}rm cm^{-2}$ on a spatial scale of the accretion radius of Vela X-1. These phenomena are consistent with the existence of an accretion disk that leads to the following spin-up of Vela X-1. It indicates that disk accretion, although not always, does occur in classical wind-fed SgXBs.
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