Is it possible to model observed active region coronal emission simultaneously in EUV and X-ray filters?

Aims. We investigate the possibility of modeling the active region coronal emission in the EUV and X-ray filters using one, universal, steady heating function, tied to the properties of the magnetic field. Methods. We employ a simple, static model to compute the temperature and density distributions in the active region corona. The model allows us to explore a wide range of parameters of the heating function. The predicted EUV and X-ray emission in the filters of EIT/SOHO and XRT/Hinode are calculated and compared with observations. Using the combined improved filter-ratio (CIFR) method, a temperature diagnostic is employed to compare the modeled temperature structure of the active region with the temperature structure derived from the observations. Results. The global properties of the observations are most closely matched for heating functions scaling as B-0(0.7-0.8)/L-0(0.5) that depend on the spatially variable heating scale-length. The modeled X-ray emission originates from locations where large heating scale-lengths are found. However, the majority of the loops observed in the 171 and 195 filters can be modeled only by loops with very short heating scale-lengths. These loops are known to be thermally unstable. We are unable to find a model that both matches the observations in all EUV and X-ray filters, and contains only stable loops. As a result, although our model with a steady heating function can explain some of the emission properties of the 171 and 195 loops, it cannot explain their observed lifetimes. Thus, the model does not lead to a self-consistent solution. The performance of the CIFR method is evaluated and we find that the diagnosed temperature can be approximated with a geometric mean of the emission-measure weighted and maximum temperature along the line of sight. Conclusions. We conclude that if one universal heating function exists, it should be at least partially time-dependent.