  We aim to study the influence of radiative cooling on the standing kink
oscillations of a coronal loop. Using the FLASH code, we solved the 3D ideal
magnetohydrodynamic equations. Our model consists of a straight, density
enhanced and gravitationally stratified magnetic flux tube. We perturbed the
system initially, leading to a transverse oscillation of the structure, and
followed its evolution for a number of periods. A realistic radiative cooling
is implemented. Results are compared to available analytical theory. We find
that in the linear regime (i.e. low amplitude perturbation and slow cooling)
the obtained period and damping time are in good agreement with theory. The
cooling leads to an amplification of the oscillation amplitude. However, the
difference between the cooling and non-cooling cases is small (around 6% after
6 oscillations). In high amplitude runs with realistic cooling, instabilities
deform the loop, leading to increased damping. In this case, the difference
between cooling and non-cooling is still negligible at around 12%. A set of
simulations with higher density loops are also performed, to explore what
happens when the cooling takes place in a very short time (tcool = 100 s). We
strengthen the results of previous analytical studies that state that the
amplification due to cooling is ineffective, and its influence on the
oscillation characteristics is small, at least for the cases shown here.
Furthermore, the presence of a relatively strong damping in the high amplitude
runs even in the fast cooling case indicates that it is unlikely that cooling
could alone account for the observed, flare-related undamped oscillations of
coronal loops. These results may be significant in the field of coronal
seismology, allowing its application to coronal loop oscillations with observed
fading-out or cooling behaviour.
