Distribution of magnetic fields in the quiet-Sun internetwork areas has been affected by weak polarization (in particular Stokes Q and U) signals. To improve the signal-to-noise ratio (SNR) of the weak polarization signals, several approaches, including temporal integrations, have been proposed in the literature. In this study, we aim to investigate a proper temporal-integration time with which an optimum SNR maintained physical properties is obtained. We use magnetographs of Zeeman sensitive Fe I 5250.2 Ǻ line recorded by Sunrise/IMaX to determine fraction of areas with significant polarization signals after temporal integrations with different durations. We examine several thresholds for the noise level. We also perform simple numerical simulations to explore the effect of size and lifetime of the magnetic features in obtaining the proper integration time. We find that the maximum fraction of pixels with real detectable linear polarization signals in the quiet-Sun internetwork is achieved with a maximum integration time about 8 minutes. Variation of polarization signals with integration time is strongly dependent on lifetime and size of magnetic patches. The temporal integration should be performed with great caution since in the presence of relatively long-lived magnetic features (such as network patches) SNR increases monotonically by increasing the integration time. This monotonic increase does not necessarily correspond to the internetwork areas where the linear magnetic features are relatively short-lived.
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