Viscous Evolution of Magnetized Clumps: A Source for X-Ray Flares in Gamma-Ray Bursts

X-ray flares may indicate the late-time activity of the central engines of gamma-ray bursts. Such long-term activity has been described through some models, one of which is the viscous evolution of the outer disk's fragments proposed by Perna et al., and developed quantitatively by Dall'Osso et al. Here, we reconstruct the framework of Dall'Osso et al. by taking both small- and large-scale effects of magnetic field into account. To consider the magnetic barrier as a possible mechanism that might govern the accretion process of each magnetized clump, we construct a simple pattern in boundary conditions through which this mechanism might act. Regarding various model parameters, we probe for their influence and follow some key analogies between our model predictions and previous phenomenological estimates, for two different choices of boundary conditions (with and without a magnetic barrier). Our model is remarkably capable of matching the bolometric and X-ray light curves of flares, as well as reproducing their statistical properties, such as the ratios between rise and decay time, width parameter and peak time, and the power-law correlation between peak luminosity and peak time. Combining our results with the conclusions of previous studies, we are led to interpret a magnetic barrier as a less probable mechanism that might control the evolution of these clumps, especially those created later (or viscously evolved ones).