[Paper Review] COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses I. How to sample the light curves of gravitationally lensed quasars to measure accurate time delays

A. Eigenbrod, F. Courbin+4 more|ArXiv.org|Mar 1, 2005

Adaptive optics and wavefront sensing13 references3 citations

TL;DR

This paper proposes an optimized observational strategy for measuring time delays in gravitationally lensed quasars using photometric monitoring, employing numerical simulations to test temporal sampling schemes. It finds that logarithmic sampling significantly improves accuracy when the time delay is comparable to the annual visibility window, while microlensing increases random errors but not systematic ones, enabling 1–2% accuracy with optimal targets and sampling.

ABSTRACT

We use numerical simulations to test a broad range of plausible observational strategies designed to measure the time delay between the images of gravitationally lensed quasars. Artificial quasar light curves are created along with Monte-Carlo simulations in order to determine the best temporal sampling to adopt when monitoring the photometric variations of systems with time delays between 5 and 120 days, i.e., always shorter than the visibility window across the year. Few and realistic assumptions are necessary on the quasar photometric variations (peak-to-peak amplitude and time-scale of the variations) and on the accuracy of the individual photometric points. The output of the simulations is the (statistical) relative error made on the time delay measurement, as a function of 1- the object visibility over the year, 2- the temporal sampling of the light curves and 3- the time delay. Also investigated is the effect of long term microlensing variations which must be below the 5 % level (either intrinsically or by subtraction) if the goal is to measure time delays with an accuracy of 1-2 %. However, while microlensing increases the random error on the time delay, it does not significantly increase the systematic error, which is always a factor 5 to 10 smaller than the random error. Finally, it is shown that, when the time delay is comparable to the visibility window of the object, a logarithmic sampling can significantly improve the time delay determination. All results are presented in the form of compact plots to be used to optimize the observational strategy of future monitoring programs.

Motivation & Objective

• To determine the optimal temporal sampling strategy for photometric monitoring of gravitationally lensed quasars to minimize time delay measurement errors.
• To assess the impact of microlensing variations (≤5%) on time delay accuracy and distinguish between random and systematic errors.
• To evaluate whether logarithmic sampling improves time delay estimation, especially when the time delay is near the visibility window length.
• To provide a decision framework for selecting lensed quasar targets with the highest potential for 1–2% time delay accuracy.
• To support the COSMOGRAIL project in maximizing Hubble constant precision with limited telescope time.

Proposed method

• Numerical simulations generate artificial quasar light curves with realistic photometric noise and variability timescales (peak-to-peak amplitude and timescale).
• Monte Carlo simulations vary key parameters: time delay (5–120 days), visibility window (1–12 months), and temporal sampling (regular and logarithmic).
• Time delays are extracted using cross-correlation techniques on simulated light curves with added observational noise (±0.4 days).
• Microlensing effects are modeled as intrinsic or subtractable variations at the 5% level to assess their impact on error budgets.
• Statistical error on time delay is computed as a function of sampling strategy, visibility, and time delay, with systematic error measured as |Δt_in - Δt_out|.
• Results are visualized in compact plots to guide observational planning for future monitoring programs.

Experimental results

Research questions

• RQ1 What temporal sampling strategy minimizes statistical error in time delay measurements for lensed quasars with time delays between 5 and 120 days?
• RQ2 How does the visibility window of a lensed quasar over the year affect the achievable accuracy of time delay measurements?
• RQ3 To what extent does microlensing at the 5% level increase random or systematic errors in time delay estimation?
• RQ4 Can logarithmic sampling improve time delay accuracy when the time delay is comparable to the visibility window?
• RQ5 Which combinations of time delay, visibility, and sampling yield time delay measurements accurate to 1–2%?

Key findings

• Time delays between 40 and 100 days are optimal for achieving 2% accuracy, especially for circumpolar objects with visibility >8 months.
• For equatorial objects with only 5–6 months of visibility, time delays of 80 days yield twice the error of circumpolar counterparts with the same sampling.
• Logarithmic sampling significantly improves time delay accuracy when the time delay is comparable to the visibility window, but degrades results for shorter delays.
• Microlensing at the 5% level doubles the random error on time delay measurements but increases systematic error by only a factor of 5–10, remaining negligible in comparison.
• Even with 0.3 mag amplitude variability, time delays shorter than 10 days cannot be measured with better than 10% accuracy using 3-day sampling.
• With 0.2 mag amplitude and 5% microlensing, 2% accuracy on time delay remains achievable for long-delay systems with visibility >8 months.