  We argue that a crucial determinant of the acceptance dependence of
fluctuation measures in heavy-ion collisions is the range of correlations in
the momentum space, e.g., in rapidity, $\Delta y_{\rm corr}$. The value of
$\Delta y_{\rm corr}\sim1$ for critical thermal fluctuations is determined by
the thermal rapidity spread of the particles at freezeout, and has little to do
with position space correlations, even near the critical point where the
spatial correlation length $\xi$ becomes as large as $2-3$ fm (this is in
contrast to the magnitudes of the cumulants, which are sensitive to $\xi$).
When the acceptance window is large, $\Delta y\gg\Delta y_{\rm corr}$, the
cumulants of a given particle multiplicity, $\kappa_k$, scale linearly with
$\Delta y$, or mean multiplicity in acceptance, $\langle N\rangle$, and
cumulant ratios are acceptance independent. While in the opposite regime,
$\Delta y\ll\Delta y_{\rm corr}$, the factorial cumulants, $\hat\kappa_k$,
scale as $(\Delta y)^k$, or $\langle N\rangle^k$. We demonstrate this general
behavior quantitatively in a model for critical point fluctuations, which also
shows that the dependence on transverse momentum acceptance is very
significant. We conclude that extension of rapidity coverage proposed by STAR
should significantly increase the magnitude of the critical point fluctuation
signatures.
