  The aging part $R_{ag}(t,s)$ of the impulsive response function of the two
dimensional ferromagnetic Ising model, quenched below the critical point, is
studied numerically employing a new algorithm without the imposition of the
external field. We find that the simple scaling form
$R_{ag}(t,s)=s^{-(1+a)}f(t/s)$, which is usually believed to hold in the aging
regime, is not obeyed. We analyse the data assuming the existence of a
correction to scaling. We find $a=0.273 \pm 0.006$, in agreement with previous
numerical results obtained from the zero field cooled magnetization. We
investigate in detail also the scaling function $f(t/s)$ and we compare the
results with the predictions of analytical theories. We make an ansatz for the
correction to scaling, deriving an analytical expression for $R_{ag}(t,s)$.
This gives a satisfactory qualitative agreement with the numerical data for
$R_{ag}(t,s)$ and for the integrated response functions. With the analytical
model we explore the overall behavior, extrapolating beyond the time regime
accessible with the simulations. We explain why the data for the zero field
cooled susceptibility are not too sensitive to the existence of the correction
to scaling in $R_{ag}(t,s)$, making this quantity the most convenient for the
study of the asymptotic scaling properties.
