Reverberation mapping of distant quasars: Time lag determination using different methods

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 C30.10 (redshift z∼0.9). The data were obtained by the 10-meter South African Large Telescope (SALT) telescope in South Africa. In detail, we demonstrate the application of several methods using the 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, BLR ∝ 1∕2 5100 , which was already confirmed for low-redshift sources. In case, the BLR size-luminosity relation holds for other distant sources, quasars could be used to probe cosmological models as "standard candles" complementary to supernovae Ia.

Do reverberation-measured H$β$ quasars provide a useful test of cosmology?

“…17 It is possible that this discrepancy of the H𝛽 cosmological constraints is just a statistical fluctuation. We also note that reverberation mapping of H𝛽 sources were performed by several groups that used different methods to determine the time delay and different arguments to determine how reliable and significant their measurements were, see Zajaček et al (2019). Also, for the H𝛽 analyses, the spectroscopic fitting was performed using a variety of different routines and Fe templates.…”

Current and Future Applications of Reverberation-Mapped Quasars in Cosmology

“…A special attention should be paid to realistic estimates of the uncertainties of different time-lag methods (ICCF, DCF, zDCF, JAVELIN, χ 2 , regularity measures-von Neumann estimator, see Zajaček et al, 2019, for a general overview and the comparison) since this is one of the main sources of the scatter of the radius-luminosity relation. The effect of systematic errors on the time-lag uncertainty was analyzed by Yu et al (2019), who compared JAVELIN and ICCF methods using simulated light curves, with JAVELIN performing better in terms of uncertainty determination.…”

“…The delay measurements used here are a compilation of the results from the literature, and each group uses different criteria and methods, which also introduces an error when different samples are compared. In particular, Czerny et al (2019) and Zajaček et al (2019) applied six different methods to determine the time-lag between the continuum and MgII line response. These included cross-correlation based techniques ICCF, DCF, zDCF, χ 2 -based method (Czerny et al, 2013(Czerny et al, , 2019, the measure of data regularity (von Neumann's estimator; Chelouche et al, 2017), and the JAVELIN code (Just Another Vehicle for Estimating Lags In Nuclei, formerly SPEAR; Zu et al, 2011Zu et al, , 2013Zu et al, , 2016.…”

Standardizing reverberation-measured Mg II time-lag quasars, by using the radius-luminosity relation, and constraining cosmological model parameters

“…The sample is relatively homogeneous, with ∼ 83% of the sources coming from the most recent SDSS-RM sample and ∼ 9% of the sources from the previous SDSS-RM sample. This means that for most of the sources a consistent approach was used to infer the significant time-delay, mostly using the JAVELIN method that makes use of the damped random walk approach in fitting the continuum light curve (Kelly et al 2009;MacLeod et al 2010;Kozłowski et al 2010;Zu et al 2011Zu et al , 2013Zu et al , 2016, while the remaining sources were analyzed typically by a combination of other methods, including a standard interpolation and discrete cross-correlation functions, the 𝜒 2 method, and measures of data randomness/regularity (see Czerny et al 2013;Chelouche et al 2017;Zajaček et al 2019Zajaček et al , 2021, for overviews and applications to data).…”