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

## TL;DR

This study applies multiple statistical methods to determine the time lag between continuum and emission lines in a distant quasar, confirming the BLR size-luminosity relation and exploring its potential for cosmology.

## Contribution

It demonstrates the application and comparison of various time-lag determination methods on high-redshift quasar data, validating the BLR size-luminosity relation at large distances.

## Key findings

- Quasar follows the BLR size-luminosity power-law scaling.
- Multiple methods yield consistent time-lag estimates.
- Supports using quasars as standard candles for cosmology.

## Abstract

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.