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tokens: variability, although this is also consistent with the calibration error. The future simultaneous, multi-frequency ALMA observations at the 300 GHz bands, are still required to provide better constraints on the instantaneous spectral energy distributions. The detailed analysis the Stokes flux variability, and the analytical modeling of the spectral energy distribution, are beyond the scope of this paper. They will be elaborated in forthcoming papers. 3.2. Polarization fitting, intrinsic polarization angle, and rotation measure During the observations, the target source is rotated with respected to the receiver frame, owing to the alt-azimuth mount of the ALMA antennae. If the polarization position angle and the polarization percentage do not vary significantly in a shorter timescale than the durations of our observing tracks (1–2 h, typically), then the polarization percentage and the polarization position angle can be fitted according to the following formula by definition: where denotes the observed Stokes flux, ( offset, hereafter) is an assumed constant normalized offset of observed Stokes as a result of the amplitude calibration errors or polarization leakage; is the polarization percentage; , , and are the polarization position angle in the sky (e.g. right ascension/declination) frame, the parallactic angle, and the Evector (Sect. 2 , Table 2 ), respectively (see also Hildebrand et al. 2000 ; Li et al. 2005 ). The application to the interferometric observations of point sources is straightforward since the visibility amplitude does not vary with uv distance. A generalized formulation for extended sources is given in Martí-Vidal et al. ( 2016 ). In practice, we determine our fitting results and errors using an iterative process. First, for each epoch of observations at each frequency, we perform a prior fitting of , and , based on XX and YY observed at various . From all data points, we then derive the standard deviation () of the difference between the observed and the priori fit. Finally, we disturb each data point of with a Gaussian random number of which the standard deviation is , and then re-fit , , and . In the end, , , and and their errors are determined by mean and standard deviations of fittings to 1000 independent realizations of the perturbed . We checked that those means converged to the values close to a priori fittings. We reject records which present poor signal-to-noise ratios with the measurements of Stokes fluxes, which could be observations at low elevation, or with poor weather conditions, or are observations of mosaic fields of which the pointing centers are far away from Sgr A* (e.g. outside of the central seven fields, see Figs. 1 , 2 ). Table 4 Polarization properties of Sgr A*. Notes. (1) Polarization position angle. (2) Measurements made from combining all ACA observations of B9-a and B9-b setups. We note that the extended emission surrounding Sgr A* is dominated by the unpolarized, free-free emission of the