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Register a new userMethods of Reverberation Mapping. I. Time-lag Determination by Measures of Randomness
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A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical estimators are considered that do not rely on polynomial interpolations of the light curves nor on their stochastic modeling, and do not require binning in correlation space. Methods based on von Neumanns mean-square successive-difference estimator are found to be superior to those using other estimators. An optimized von Neumann scheme is formulated, which better handles sparsely sampled data and outperforms current implementations of discrete correlation function methods. This scheme is applied to existing reverberation data of varying quality, and consistency with previously reported time delays is found. In particular, the size-luminosity relation of the broad-line region in quasars is recovered with a scatter comparable to that obtained by other works, yet with fewer assumptions made concerning the process underlying the variability. The proposed method for time-lag determination is particularly relevant for irregularly sampled time series, and in cases where the process underlying the variability cannot be adequately modeled.
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The Sloan Digital Sky Survey Reverberation Mapping project (SDSS-RM) is a dedicated multi-object RM experiment that has spectroscopically monitored a sample of 849 broad-line quasars in a single 7 deg$^2$ field with the SDSS-III BOSS spectrograph. The RM quasar sample is flux-limited to i_psf=21.7 mag, and covers a redshift range of 0.1<z<4.5. Optical spectroscopy was performed during 2014 Jan-Jul dark/grey time, with an average cadence of ~4 days, totaling more than 30 epochs. Supporting photometric monitoring in the g and i bands was conducted at multiple facilities including the CFHT and the Steward Observatory Bok telescopes in 2014, with a cadence of ~2 days and covering all lunar phases. The RM field (RA, DEC=14:14:49.00, +53:05:00.0) lies within the CFHT-LS W3 field, and coincides with the Pan-STARRS 1 (PS1) Medium Deep Field MD07, with three prior years of multi-band PS1 light curves. The SDSS-RM 6-month baseline program aims to detect time lags between the quasar continuum and broad line region (BLR) variability on timescales of up to several months (in the observed frame) for ~10% of the sample, and to anchor the time baseline for continued monitoring in the future to detect lags on longer timescales and at higher redshift. SDSS-RM is the first major program to systematically explore the potential of RM for broad-line quasars at z>0.3, and will investigate the prospects of RM with all major broad lines covered in optical spectroscopy. SDSS-RM will provide guidance on future multi-object RM campaigns on larger scales, and is aiming to deliver more than tens of BLR lag detections for a homogeneous sample of quasars. We describe the motivation, design and implementation of this program, and outline the science impact expected from the resulting data for RM and general quasar science.
We broadly explore the effects of systematic errors on reverberation mapping lag uncertainty estimates from {tt JAVELIN} and the interpolated cross-correlation function (ICCF) method. We focus on simulated lightcurves from random realizations of the lightcurves of five intensively monitored AGNs. Both methods generally work well even in the presence of systematic errors, although {tt JAVELIN} generally provides better error estimates. Poorly estimated lightcurve uncertainties have less effect on the ICCF method because, unlike {tt JAVELIN}, it does not explicitly assume Gaussian statistics. Neither method is sensitive to changes in the stochastic process driving the continuum or the transfer function relating the line lightcurve to the continuum. The only systematic error we considered that causes significant problems is if the line lightcurve is not a smoothed and shifted version of the continuum lightcurve but instead contains some additional sources of variability.
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.
We investigate the performance of different methodologies that measure the time lag between broad-line and continuum variations in reverberation mapping data using simulated light curves that probe a range of cadence, time baseline, and signal-to-noise ratio in the flux measurements. We compare three widely-adopted lag measuring methods: the Interpolated Cross-Correlation Function (ICCF), the z-transformed Discrete Correlation Function (ZDCF) and the MCMC code JAVELIN, for mock data with qualities typical of multi-object spectroscopic reverberation mapping (MOS-RM) surveys that simultaneously monitor hundreds of quasars. We quantify the overall lag detection efficiency, the rate of false detections, and the quality of lag measurements for each of these methods and under different survey designs (e.g., observing cadence and depth) using mock quasar light curves. Overall JAVELIN and ICCF outperform ZDCF in essentially all tests performed. Compared with ICCF, JAVELIN produces higher quality lag measurements, is capable of measuring more lags with timescales shorter than the observing cadence, is less susceptible to seasonal gaps and S/N degradation in the light curves, and produces more accurate lag uncertainties. We measure the Hbeta broad-line region size-luminosity (R-L) relation with each method using the simulated light curves to assess the impact of selection effects of the design of MOS-RM surveys. The slope of the R-L relation measured by JAVELIN is the least biased among the three methods, and is consistent across different survey designs. These results demonstrate a clear preference for JAVELIN over the other two non-parametric methods for MOS-RM programs, particularly in the regime of limited light curve quality as expected from most MOS-RM programs.
By using standard broad-band VRI photometry we were able to discriminate the variations of the broad hydrogen alpha line from the continuum variations for the active galaxy Mkn 279. Cross-correlating both light curves enabled us to determine the time lag of the broad line variations behind the continuum and thus to determine the BLR size (about 8 light days). Our preliminary results are rather consistent with the spectroscopic reverberation mapping results (about 12/17 days). This study is a part of an ambitious program to perform photometric reverberation mapping and determine BLR sizes (respectively - the central black hole masses) for more that 100 nearby AGN.
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