The observation of varying broad iron lines during the state transition of
the black hole X-ray binaries (BHXBs) have been accumulating.In this work, the
relation between the normalized intensity and the width of iron lines is
investigated, in order to understand better the variation of iron lines and
possibly its connection to state transition. Considering the uncertainties due
to ionization and illuminating X-rays, only the effects of geometry and gravity
are taken into account. Three scenarios were studied, i.e., the continuous disk
model, innermost annulus model, and the cloud model. As shown by our
calculations, at given iron width, the line flux of the cloud model is smaller
than that of the continuous disk model; while for the innermost annulus model,
the width is almost unrelated with the flux. The range of the line strength
depends on both the BH spin and the inclination of the disk. We then apply to
the observation of MAXI J1631-479 by NuSTAR during its decay from the soft
state to the intermediate state. We estimated the relative line strength and
width according to the spectral fitting results by Xu et al.(2020), and then
compared with our theoretical width-flux relation. It was found that the cloud
model was more favored. We further modeled the iron line profiles, and found
that the cloud model can explain both the line profile and its variation with
reasonable parameters.Comment: 7 figures, 12 pages, accepted for publication in RA