  The extremely hot and tenuous accretion flow in the immediate vicinity of Sgr
A* is believed to be invisible (too dim) in the X-ray band, except for short
X-ray flares. Here we point out that during pericenter passages, close
brightest stars irradiate the inner region of the accretion flow, providing a
plenty of optical/UV photons. These seed photons are Compton up-scattered by
the hot electrons of the accretion flow to higher frequencies, some into the
X-ray band, potentially making the innermost accretion flow much brighter in
X-rays than usual. We propose to use coordinated near infra-red and X-ray
observations of close star passages to put constraints onto Sgr A* accretion
theories. The absence of a noticeable change in the steady emission of Sgr A*
as observed by Chandra in the year 2002, when the star named S2 passed through
a pericenter of its orbit, already rules out the hotter of the ``standard''
Advection-Dominated Accretion Flows. The less dense accretion flows, in
particular the model of Yuan et al. (2003), passes the test and is constrained
to accretion rates no larger than $\sim 10^{-7}$ Solar masses per year.
