Time Delay in QSO 0957+561 From 1984–1999 Optical Data

Abstract

Photometric optical data of QSO 0957+561 covering the period 1984-99 are analyzed to discern between the two values of the time delay (417 and 424 days) mostly accepted in the recent literature. The observations, performed by groups from three different institutions-Princeton University, Harvard-Smithsonian Center for Astrophysics, and Instituto de Astrofísica de Canarias-and including new unpublished 1998-9 data from the IAC80 Telescope, were obtained in five filters (V , R, I, g, and r). The different light curves have been divided into observational seasons and two restriction have been applied to better calculate the time delay: (i) points with a strange photometric behavior have been removed; and (ii) data sets without large gaps have been selected. Simulated data were generated to test several numerical methods intended to compute the time delay (∆τ AB ). The methods giving the best results-the discrete correlation function, δ-square, z-transformed discrete correlation function, and linear interpolation-were then applied to real data. A first analysis of the 23 different time delays derived from each technique shows that ∆τ AB must be into the interval 420-424 days. From our statistical study, a most probable value of ∆τ AB = 422.6 ± 0.6 days is inferred.

Long-Term Monitoring, Time Delay, and Microlensing in the Gravitational Lens System Q0142-100

“…There are several "classical ways" of obtaining the time delay between the components of a variable quasar from discrete, unevenly sampled temporary series: the discrete correlation function (Edelson & Krolik 1988), dispersion spectra (Pelt et al 1996), linear interpolation (Kundić et al 1997), and the z-transformed discrete correlation function (Alexander 1997), etc (see Oscoz et al 2001 and references therein for a brief description of all these methods). In this paper, we will use the δ 2 method (Serra-Ricart et al 1999) to calculate the time delay of Q0142-100, as it offers very good results even with large gaps (Oscoz et al 2001) and small variations in the flux of the components.…”

“…In this paper, we will use the δ 2 method (Serra-Ricart et al 1999) to calculate the time delay of Q0142-100, as it offers very good results even with large gaps (Oscoz et al 2001) and small variations in the flux of the components.…”

“…This second order technique helps to improve the estimation of the time delay, as was stated in Oscoz et al (2001), where a comparison of the results obtained with several statistical methods is made. Oscoz et al (2001) demonstrate, with simulated and real data obtained from different telescopes, that the δ 2 method offers the best results without interpolating data, even when large gaps are present.…”

COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses

“…Lovell et al 1998), SDSS J1004+4112 (Fohlmeister et al 2007(Fohlmeister et al , 2008, QSO 0957+561 (e.g. Oscoz et al 2001;Shalyapin et al 2008;Fadely et al 2010). Two other systems are not presented here because we already published improved astrometry and time delays: WFI J2033-4723 (Vuissoz et al 2008) and HE 0435-1223 (Courbin et al 2011).…”

How accurate are the time delay estimates in gravitational lensing?

“…However, SOLA differs from our approach in several (Haarsma et al 1999), c) optical data at g-band (Kundic et al 1997), and d) optical data at r-band (Ovaldsen et al 2003). Kundic et al (1997) -Linear 417 ± 3 -Cross correlation -PRH -Dispersion Oscoz et al (1997) -Cross correlation 427 ± 3 -Dispersion Pijpers (1997) -SOLA 425 ± 17 Pelt et al (1998b) -Dispersion 416.3 ± 1.7 Haarsma et al (1999) -PRH 409 ± 30 -Dispersion Oscoz et al (2001) -Linear 422.6 ± 0.6 -Cross correlation -Dispersion Burud et al (2001) -χ 2 algorithm 423 ± 9 Colley et al (2003) -PRH 417.09 ± 0.07 Ovaldsen et al (2003) -Dispersion 424.9 ± 1.2 -χ 2 algorithm respects: (i) SOLA does a symmetric treatment of the two estimated fluxes (flux A is fixed and flux B is varied to match A and vice versa); (ii) the reported time delay is the mean of the estimated time delays in the two symmetric cases; (iii) a free parameter is used to adjust the relative weighting of the errors in the variance-covariance matrix. We also note that parameter estimation in SOLA is problematic (Larsen & Hansen 1997;Rabello-Soares et al 1999) and this method has been rarely used.…”