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Reverberation-mapping of distant quasars: time-lag determination using different methods

By applying different statistically robust methods, we analyze the time-lag between the continuum and ionized line-emission (Mg II line) light curves for the distant bright quasar CTS C$30.10$ (redshift $z \sim 0.9$). The data were obtained by the 10-meter SALT telescope in South Africa. In detail, we demonstrate the application of several methods using interpolated cross-correlation function (ICCF), discrete correlation function (DCF), z-transformed discrete correlation function (zDCF), von Neumann estimator, and the JAVELIN code package. In particular, we discuss the uncertainties of these methods. In conclusion, we find that the quasar lies on the broad-line region (BLR) size -- monochromatic luminosity power-law scaling, $R_{\rm BLR}\propto L_{5100}^{1/2}$, which was already confirmed for low-redshift sources. In case the BLR size-luminosity relation holds for other distant sources, quasars could be used for probing cosmological models as ``standard candles'' complementary to supernovae Ia.