  Hydrogen-dominated atmospheres of hot exoplanets expand and escape due to the
intense heating by the X-ray and extreme ultraviolet (XUV) irradiation of their
host stars. Excess absorption of neutral hydrogen has been observed in the
Ly$\alpha$ line during transits of several close-in exoplanets, indicating such
extended atmospheres. For the hot Jupiter HD 189733b, this absorption shows
temporal variability. Variations in stellar XUV emission and/or stellar wind
conditions have been invoked to explain this effect. We apply a 1D hydrodynamic
upper atmosphere model and a 3D MHD stellar wind flow model to study the effect
of variations of the stellar XUV and wind conditions on the neutral hydrogen
distribution, including the production of energetic neutral atoms (ENAs), and
the related Ly$\alpha$ transit signature. We obtain comparable, albeit slightly
higher Ly$\alpha$ absorption as observed in 2011 with a stellar XUV flux of
$1.8\times10^4$ erg cm$^{-2}$ s$^{-1}$, rather typical activity conditions for
this star. Flares similar to the one observed 8 h before the transit are
unlikely to have caused a significant modulation of the transit signature. The
resulting Ly$\alpha$ absorption is dominated by atmospheric broadening, whereas
the contribution of ENAs is negligible, as they are formed inside the bow shock
from decelerated wind ions that are heated to high temperatures. Thus, within
our modeling framework and assumptions, we find an insignificant dependence on
the stellar wind parameters. Since the transit absorption can be modeled with
typical stellar XUV and wind conditions, it is possible that the non-detection
of the absorption in 2010 was affected by less typical stellar activity
conditions, such as a very different magnitude and/or shape of the star's
spectral XUV emission, or temporal/spatial variations in Ly$\alpha$ affecting
the determination of the transit absorption.
