TD-CARMA: Painless, accurate, and scalable estimates of gravitational-lens time delays with flexible CARMA processes

Abstract

Cosmological parameters encoding our understanding of the expansion history of the Universe can be constrained by the accurate estimation of time delays arising in gravitationally lensed systems. We propose TD-CARMA, a Bayesian method to estimate cosmological time delays by modelling the observed and irregularly sampled light curves as realizations of a Continuous Auto-Regressive Moving Average (CARMA) process. Our model accounts for heteroskedastic measurement errors and microlensing, an additional source of independent extrinsic long-term variability in the source brightness. The semi-separable structure of the CARMA covariance matrix allows for fast and scalable likelihood computation using Gaussian Process modeling. We obtain a sample from the joint posterior distribution of the model parameters using a nested sampling approach. This allows for ``painless'' Bayesian Computation, dealing with the expected multi-modality of the posterior distribution in a straightforward manner and not requiring the specification of starting values or an initial guess for the time delay, unlike existing methods. In addition, the proposed sampling procedure automatically evaluates the Bayesian evidence, allowing us to perform principled Bayesian model selection. TD-CARMA is parsimonious, and typically includes no more than a dozen unknown parameters. We apply TD-CARMA to six doubly lensed quasars HS 2209+1914, SDSS J1001+5027, SDSS J1206+4332, SDSS J1515+1511, SDSS J1455+1447, SDSS J1349+1227, estimating their time delays as $-21.96\pm 1.448$, $120.93\pm 1.015$, $111.51\pm 1.452$, $210.80\pm 2.18$, $45.36\pm 1.93$ and $432.05\pm 1.950$ respectively. These estimates are consistent with those derived in the relevant literature, but are typically two to four times more precise.

References in corpus (18)

• Modeling the Time Variability of SDSS Stripe 82 Quasars as a Damped Random Walk
• H0LiCOW V. New COSMOGRAIL time delays of HE0435-1223: $H_0$ to 3.8% precision from strong lensing in a flat $\Lambda$CDM model
• Is Quasar Optical Variability a Damped Random Walk?
• A buyer's guide to the Hubble Constant
• Strong Lens Time Delay Challenge: II. Results of TDC1
• Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?
• COSMOGRAIL XVI: Time delays for the quadruply imaged quasar DES J0408-5354 with high-cadence photometric monitoring
• Limitations on the recovery of the true AGN variability parameters using Damped Random Walk modeling
• Strong lensing time-delay cosmography in the 2020s
• Optical Variability of Quasars with 20-Year Photometric Light Curves
• Examining AGN UV/optical Variability Beyond the Simple Damped Random Walk
• TDCOSMO II: 6 new time delays in lensed quasars from high-cadence monitoring at the MPIA 2.2m telescope
• Bayesian Analysis of Quasar Lightcurves with a Running Optimal Average: New Time Delay Measurements of COSMOGRAIL Gravitationally Lensed Quasars
• Modeling Stochastic Variability in Multi-Band Time Series Data
• Doubly imaged quasar SDSS J1515+1511: time delay and lensing galaxies
• Be It Unresolved: Measuring Time Delays from Lensed Supernovae
• Fast and Reliable Time Delay Estimation of Strong Lens Systems Using Method of Smoothing and Cross-Correlation
• Identifying lensed quasars and measuring their time-delays from unresolved light curves

Cited by in corpus (4)

• GausSN: Bayesian Time-Delay Estimation for Strongly Lensed Supernovae
• Six Maxims of Statistical Acumen for Astronomical Data Analysis
• Semi-Supervised Learning for Lensed Quasar Detection
• A Robust Bayesian Meta-Analysis for Estimating the Hubble Constant via Time Delay Cosmography