# Intra-Day Variability Observations of Two Dozens of Blazars at 4.8 GHz
## 2 Observations and Data Reduction  
The IDV observations are carried out in 8 February 2014 05:12-12 February 2014 03:21 (94 h in total) and 7 March 2014 03:52-9 March 2014 17:53 (62 h in total) with the Urumqi 25 m radio telescope. Most of the blazars are selected from the 2014 February and March sessions of RadioAstron space VLBI program [23], with the declination \(>+10^{\circ}\), plus several additional blazars selected from previous IDV observations. The observations were done with the 25 m telescope at the central frequency of 4.8 GHz with the bandwidth of 600 MHz, the lowest system temperature of 24 K, and the antenna sensitivity of \(\sim\)0.12 K/Jy.  
The observations were made with the cross-scans mode consisting of 4 + 4 sub-scans in azimuth and elevation over the source position. After initial calibration of raw data, the intensity profile of each sub-scan is fitted with a baseline and a Gaussian function after subtracting the baseline, and then the data are averaged in 4 azimuth sub-scans and 4 elevation sub-scans respectively. The averaged azimuth amplitude is corrected with the pointing error in elevation direction, and vice verse. The antenna gain curve is applied for the data averaged from the azimuth and elevation scans, the gain curve (including the air-mass effect) is measured from the secondary calibrators in the same observation. A systematic time-dependent effect which is derived from the secondary calibrators is applied. Finally, the amplitude is converted to the absolute flux density with the average scale of the primary calibrators, 3C48, 3C286, and NGC7027 [24; 25] which are included in the observation.  
It takes about 5 min for each source with 4 + 4 observing sub-scans, and about 2 h for nearly 25 sources to complete one cycle of observation, if the sources are up (\(>\)10\({}^{\circ}\) elevation) in the sky, and then we repeat the cycle of observation. So the sampling rate is about 0.5 per hour for each source.  
To analyze the variability, we used the statistical quantities, such as the modulation index \(m\) (a measure of the relative strength of variations), the modified modulation index or fractional variability [26]\(m^{\prime}\) (a parameter that similar to \(m\) but take into account the error of flux density, when the part within the square root is less than 0, we set \(m^{\prime}=0\), which imply that there is no variability), the variability amplitude \(Y\) which is assumed to be unbiased to the systematic noise, and the reduced chi-squared \(\chi^{2}_{r}\), to describe the variability as shown below, also see [27],  
\[m[\%]=100\frac{\sigma_{s}}{<S>}, \tag{1}\]  
\[m^{\prime}[\%]=100\sqrt{\frac{\sigma_{s}^{2}-<\Delta S_{i}^{2}>}{<S>^{2}}}, \tag{2}\]\[Y[\%]=3\sqrt{(m)^{2}-(m_{0})^{2}}, \tag{3}\]  
\[\chi_{r}^{2}=\frac{1}{N-1}\sum(\frac{S_{i}-<S>}{\Delta S_{i}})^{2}, \tag{4}\]  
where \(\sigma_{\rm s}\) is the standard deviation of flux densities from the mean flux density (\(<S>\)) in a light curve, \(m_{0}\) is the mean modulation index of all calibrators in the same observation, \(N\) is the number of measurements in a light curve, \(S_{i}\) and \(\Delta S_{i}\) denote individual flux density and its error.