## 5. ConclusionsIn this paper we have developed a model for the rising phase of some radio flares observed on the active binary system UX Arietis. Positive spectral indexes, lower than the canonical self-absorbed value (Eq. (2)), characterize the observed spectra for GHz. These spectra can be explained in terms of gyrosynchrotron emission from a dipolar magnetic loop, where the lower regions, near the photosphere, contribute to the emission around 10 GHz, while the low-frequency part of the spectrum comes from the extended regions, upper in the corona, near the loop top. In this way the periodical minimum observed in the high frequency emission is easily explained as the shadowing of the compact part of the loop by the rotation of the system. In addition to the loop-like geometry, in order to reproduce the observed spectral shape, both a continuous supply of relativistic electrons and loss mechanisms (synchrotron and collision energy losses and the effect of the loss-cone) must be taken into account. Among the eight parameters which must be defined to compute the emission three have been fixed in the correct range and have not been changed to improve the fit; two of them, namely and are determined by the less intense spectrum available for each flare; the three left parameters (, and ) are chosen to fit the spectrum at the following time. This means that for each flare two spectra determine all the parameters of the model and that any subsequent time evolution of the flare spectrum is forecasted. Hence, for all the flares for which three spectra are available, the third one, i.e. the last one, is a prediction of the model. The good agreement of the model results with the observed data confirms the interpretation of the flaring emission in terms of gyrosynchrotron emission from relativistic electrons continuously injected in a bipolar magnetic loop. How long this continuous supply of accelerated electrons lasts cannot be determined exactly. In the case of flare 3, for example, the data show that the emission increases for hours; however our model, in which the number of injected electrons is constant in time, can reproduce only part of this evolution, namely 2 hours. This fact implies that the injection rate is not constant, but varies in time, and that the observed 23 hours growth is probably due to a succession of unresolved strong bursts, instead of a single event. In the case of flares 2 and 4, for which it is possible to follow the evolution starting from the "quiescent" ground level of emission, our model derives 4 and 13 hours respectively of constant injection. In any case, it is possible to conclude that the observed flare rising phases imply a continuous supply of relativistic electrons at least for some hours. The observations are however too sparse in time to allow a definite real comprehension of the process. As Figs. 3 - 6 show, the model is able to reproduce flares having different spectral shapes and observed at different phases of their evolution. This large applicability of the model is assured by the complex interplay of radiative losses and continuous injection of fresh relativistic electrons. The very different values deduced for and reported in Table 1 confirm the flexibility of the model. Flares observed near the peak of the rising phase (flares 1 and 3) have an almost vanishing injection rate while those observed in an earlier phase need higher values of to be reproduced. Despite the interest and the originality of the data and the good results of the model reported in this paper, a deeper insight in the injection mechanism and hence in the physics of flares will be possible only with a model where the injection rate of accelerated electrons varies in time and is allowed to end at a certain time. However a more detailed model can give useful informations only if more complete data sets become available, with a better time coverage of the evolution of the flaring spectrum from its onset to the end of its decay. © European Southern Observatory (ESO) 1998 Online publication: April 28, 1998 |