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Register a new userChromatic Microlensing Time Delays
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Kai Liao
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Due to the finite size of the disk and the temperature fluctuations producing the variability, microlensing changes the actual time delays between images of strongly lensed AGN on the $sim$day(s) light-crossing time scale of the emission region. This microlensing-induced time delay depends on the disk model, primarily the disk size $R_mathrm{disk}$ which has been found to be larger than predicted by the thin-disk model. In this work, we propose that light curves measured in different bands will give different time delays since $R_mathrm{disk}$ is a function of wavelength, and by measuring the time delay differences between bands, one can 1) directly verify such an new effect; 2) test the thin-disk model of quasars. For the second goal, our method can avoid the potential inconsistency between multi-band light curves that may bias the results by continuum reverberation mapping. We conduct a simulation based on a PG 1115+080-like lensed quasar, calculating the theoretical distributions of time delay differences between two bands: u and i centered around 354nm and 780nm, under and beyond the thin-disk model, respectively. Assuming the disk size is twice larger than the standard one, we find that with a precision of 2 days in the time delay difference measurements, the microlensing time delay effect can be verified with $sim4$ measurements while with $sim35$ measurements the standard model can be excluded. This approach could be realized in the ongoing and upcoming multi-band wide-field surveys with follow-up observations.
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Time-delay strong lensing provides a unique way to directly measure the Hubble constant ($H_{0}$). The precision of the $H_{0}$ measurement depends on the uncertainties in the time-delay measurements, the mass distribution of the main deflector(s), and the mass distribution along the line of sight. Tie and Kochanek (2018) have proposed a new microlensing effect on time delays based on differential magnification of the coherent accretion disc variability of the lensed quasar. If real, this effect could significantly broaden the uncertainty on the time delay measurements by up to $30%$ for lens systems such as PG1115+080, which have relatively short time delays and monitoring over several different epochs. In this paper we develop a new technique that uses the time-delay ratios and simulated microlensing maps within a Bayesian framework in order to limit the allowed combinations of microlensing delays and thus to lessen the uncertainties due to the proposed effect. We show that, under the assumption of Tie and Kochanek (2018), the uncertainty on the time-delay distance ($D_{Delta t}$, which is proportional to 1/$H_{0}$) of short time-delay ($sim18$ days) lens, PG1115+080, increases from $sim7%$ to $sim10%$ by simultaneously fitting the three time-delay measurements from the three different datasets across twenty years, while in the case of long time-delay ($sim90$ days) lens, the microlensing effect on time delays is negligible as the uncertainty on $D_{Delta t}$ of RXJ1131-1231 only increases from $sim2.5%$ to $sim2.6%$.
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.
Owing to the advent of large area photometric surveys, the possibility to use broad band photometric data, instead of spectra, to measure the size of the broad line region of active galactic nuclei, has raised a large interest. We describe here a new method using time-delay lensed quasars where one or several images are affected by microlensing due to stars in the lensing galaxy. Because microlensing decreases (or increases) the flux of the continuum compared to the broad line region, it changes the contrast between these two emission components. We show that this effect can be used to effectively disentangle the intrinsic variability of those two regions, offering the opportunity to perform reverberation mapping based on single band photometric data. Based on simulated light curves generated using a damped random walk model of quasar variability, we show that measurement of the size of the broad line region can be achieved using this method, provided one spectrum has been obtained independently during the monitoring. This method is complementary to photometric reverberation mapping and could also be extended to multi-band data. Because the effect described above produces a variability pattern in difference light curves between pairs of lensed images which is correlated with the time-lagged continuum variability, it can potentially produce systematic errors in measurement of time delays between pairs of lensed images. Simple simulations indicate that time-delay measurement techniques which use a sufficiently flexible model for the extrinsic variability are not affected by this effect and produce accurate time delays.
The Hubble constant value is currently known to 10% accuracy unless assumptions are made for the cosmology (Sandage et al. 2006). Gravitational lens systems provide another probe of the Hubble constant using time delay measurements. However, current investigations of ~20 time delay lenses, albeit of varying levels of sophistication, have resulted in different values of the Hubble constant ranging from 50-80 km/s/Mpc. In order to reduce uncertainties, more time delay measurements are essential together with better determined mass models (Oguri 2007, Saha et al. 2006). We propose a more efficient technique for measuring time delays which does not require regular monitoring with a high-resolution interferometer array. The method uses double image and long-axis quadruple lens systems in which the brighter component varies first and dominates the total flux density. Monitoring the total flux density with low-resolution but high sensitivity radio telescopes provides the variation of the brighter image and is used to trigger high-resolution observations which can then be used to see the variation in the fainter image. We present simulations of this method together with a pilot project using the WSRT (Westerbork Radio Synthesis Telescope) to trigger VLA (Very Large Array) observations. This new method is promising for measuring time delays because it uses relatively small amounts of time on high-resolution telescopes. This will be important because many SKA pathfinder telescopes, such as MeerKAT (Karoo Array Telescope) and ASKAP (Australian Square Kilometre Array Pathfinder), have high sensitivity but limited resolution.
In principle, the most straightforward method of estimating the Hubble constant relies on time delays between mirage images of strongly-lensed sources. It is a puzzle, then, that the values of H0 obtained with this method span a range from 50 - 100 km/s/Mpc. Quasars monitored to measure these time delays, are multi-component objects. The variability may arise from different components of the quasar or may even originate from a jet. Misidentifying a variable emitting region in a jet with emission from the core region may introduce an error in the Hubble constant derived from a time delay. Here, we investigate the complex structure of sources as the underlying physical explanation of the widespread in values of the Hubble constant based on gravitational lensing. Our Monte Carlo simulations demonstrate that the derived value of the Hubble constant is very sensitive to the offset between the center of the emission and the center of the variable emitting region. Thus, we propose using the value of H0 known from other techniques to spatially resolve the origin of the variable emission once the time delay is measured. We advocate this method particularly for gamma-ray astronomy, where the angular resolution of detectors reaches approximately 0.1 degree; lensed blazars offer the only route for identify the origin of gamma-ray flares. Large future samples of gravitationally lensed sources identified with Euclid, SKA, and LSST will enable a statistical determination of H0.
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