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Christopher W. Morgan
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We expand our Bayesian Monte Carlo method for analyzing the light curves of gravitationally lensed quasars to simultaneously estimate time delays and quasar structure including their mutual uncertainties. We apply the method to HE1104-1805 and QJ0158-4325, two doubly-imaged quasars with microlensing and intrinsic variability on comparable time scales. For HE1104-1805 the resulting time delay of (Delta t_AB) = t_A - t_B = 162.2 -5.9/+6.3 days and accretion disk size estimate of log(r_s/cm) = 15.7 -0.5/+0.4 at 0.2 micron in the rest frame are consistent with earlier estimates but suggest that existing methods for estimating time delays in the presence of microlensing underestimate the uncertainties. We are unable to measure a time delay for QJ0158-4325, but the accretion disk size is log(r_s/cm) = 14.9 +/- 0.3 at 0.3 micron in the rest frame.
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Aims. The main purpose of this paper is to study time delays between the light variations in different wavebands for a sample of quasars. Measuring a reliable time delay for a large number of quasars may help constraint the models of their central engines. The standard accretion disk irradiation model predicts a delay of the longer wavelengths behind the shorter ones, a delay that depends on the fundamental quasar parameters. Since the black hole masses and the accretion rates are approximately known for the sample we use, one can compare the observed time delays with the expected ones. Methods. We applied the interpolation cross-correlation function (ICCF) method to the Giveon et al. sample of 42 quasars, monitored in two (B and R) colors, to find the time lags represented by the ICCF peaks. Different tests were performed to assess the influence of photometric errors, sampling, etc., on the final result. Results. We found that most of the objects show a delay in the red light curve behind the blue one (a positive lag), which on average for the sample is about +4 days (+3 for the median), although the scatter is significant. These results are broadly consistent with the reprocessing model, especially for the well-sampled objects. The normalized time-lag deviations do not seem to correlate significantly with other quasar properties, including optical, radio, or X-ray measurables. On the other hand, many objects show a clear negative lag, which, if real, may have important consequences for the variability models.
We present new measurements of the time delays of WFI2033-4723. The data sets used in this work include 14 years of data taken at the 1.2m Leonhard Euler Swiss telescope, 13 years of data from the SMARTS 1.3m telescope at Las Campanas Observatory and a single year of high-cadence and high-precision monitoring at the MPIA 2.2m telescope. The time delays measured from these different data sets, all taken in the R-band, are in good agreement with each other and with previous measurements from the literature. Combining all the time-delay estimates from our data sets results in Dt_AB = 36.2-0.8+0.7 days (2.1% precision), Dt_AC = -23.3-1.4+1.2 days (5.6%) and Dt_BC = -59.4-1.3+1.3 days (2.2%). In addition, the close image pair A1-A2 of the lensed quasars can be resolved in the MPIA 2.2m data. We measure a time delay consistent with zero in this pair of images. We also explore the prior distributions of microlensing time-delay potentially affecting the cosmological time-delay measurements of WFI2033-4723. There is however no strong indication in our measurements that microlensing time delay is neither present nor absent. This work is part of a H0LiCOW series focusing on measuring the Hubble constant from WFI2033-4723.
We present time-delay estimates for the quadruply imaged quasar PG 1115+080. Our resuls are based on almost daily observations for seven months at the ESO MPIA 2.2m telescope at La Silla Observatory, reaching a signal-to-noise ratio of about 1000 per quasar image. In addition, we re-analyse existing light curves from the literature that we complete with an additional three seasons of monitoring with the Mercator telescope at La Palma Observatory. When exploring the possible source of bias we consider the so-called microlensing time delay, a potential source of systematic error so far never directly accounted for in previous time-delay publications. In fifteen years of data on PG 1115+080, we find no strong evidence of microlensing time delay. Therefore not accounting for this effect, our time-delay estimates on the individual data sets are in good agreement with each other and with the literature. Combining the data sets, we obtain the most precise time-delay estimates to date on PG 1115+080, with Dt(AB) = 8.3+1.5-1.6 days (18.7% precision), Dt(AC) = 9.9+1.1-1.1 days (11.1%) and Dt(BC) = 18.8+1.6-1.6 days (8.5%). Turning these time delays into cosmological constraints is done in a companion paper that makes use of ground-based Adaptive Optics (AO) with the Keck telescope.
We present 13 seasons of $R$-band photometry of the quadruply-lensed quasar WFI 2033-4723 from the 1.3m SMARTS telescope at CTIO and the 1.2m Euler Swiss Telescope at La Silla, in which we detect microlensing variability of $sim0.2$ mags on a timescale of $sim$6 years. Using a Bayesian Monte Carlo technique, we analyze the microlensing signal to obtain a measurement of the size of this systems accretion disk of $log (r_s/{rm cm}) = 15.86^{+0.25}_{-0.27}$ at $lambda_{rest} = 2481{rm AA}$, assuming a $60^circ$ inclination angle. We confirm previous measurements of the BC and AB time delays, and we obtain a tentative measurement of the delay between the closely spaced A1 and A2 images of $Delta t_{A1A2} = t_{A1} - t_{A2} = -3.9^{+3.4}_{-2.2}$ days. We conclude with an update to the Quasar Accretion Disk Size - Black Hole Mass Relation, in which we confirm that the accretion disk size predictions from simple thin disk theory are too small.
Classical distributed estimation scenarios typically assume timely and reliable exchanges of information over the sensor network. This paper, in contrast, considers single time-scale distributed estimation via a sensor network subject to transmission time-delays. The proposed discrete-time networked estimator consists of two steps: (i) consensus on (delayed) a-priori estimates, and (ii) measurement update. The sensors only share their a-priori estimates with their out-neighbors over (possibly) time-delayed transmission links. The delays are assumed to be fixed over time, heterogeneous, and known. We assume distributed observability instead of local observability, which significantly reduces the communication/sensing loads on sensors. Using the notions of augmented matrices and Kronecker product, the convergence of the proposed estimator over strongly-connected networks is proved for a specific upper-bound on the time-delay.
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