[Paper Review] A time-delay determination from VLA light curves of the CLASS gravitational lens B1600+434

L. V. E. Koopmans, A. G. de Bruyn+2 more|University of Groningen research database (University of Groningen / Centre for Information Technology)|Jan 31, 2000

Galaxies: Formation, Evolution, Phenomena1 references7 citations

TL;DR

This study presents a time-delay measurement of 47⁺¹²₋₉ days (95% confidence) between the two images of the gravitational lens B1600+434 using 8.5-GHz VLA light curves from February to October 1998. The analysis attributes short-term flux variability in image A to microlensing rather than intrinsic source variability, enabling a Hubble parameter estimate of H₀ = 57⁺¹⁴₋₁₁ km s⁻¹ Mpc⁻¹ (isothermal model), though systematic uncertainties limit precision due to degeneracy in the lens mass profile slope.

ABSTRACT

We present Very Large Array (VLA) 8.5-GHz light curves of the two lens images of the Cosmic Lens All Sky Survey (CLASS) gravitational lens B1600+434. We find a nearly linear decrease of 18-19% in the flux densities of both lens images over a period of eight months (February-October) in 1998. Additionally, the brightest image A shows modulations up to 11% peak-to-peak on scales of days to weeks over a large part of the observing period. Image B varies significantly less on this time scale. We conclude that most of the short-term variability in image A is not intrinsic source variability, but is most likely caused by microlensing in the lens galaxy. The alternative, scintillation by the ionized Galactic ISM, is shown to be implausible based on its strong opposite frequency dependent behavior compared with results from multi-frequency WSRT monitoring observations (Koopmans & de Bruyn 1999). From these VLA light curves we determine a median time delay between the lens images of 47^{+5}_{-6} d (68%) or 47^{+12}_{-9} d (95%). We use two different methods to derive the time delay; both give the same result within the errors. We estimate an additional systematic error between -8 and +7 d. If the mass distribution of lens galaxy can be described by an isothermal model (Koopmans, de Bruyn & Jackson 1998), this time delay would give a value for the Hubble parameter, H_0=57^{+14}_{-11} (95% statistical) ^{+26}_{-15} (systematic) km/s/Mpc (Omega_m=1 and Omega_Lambda=0). Similarly, the Modified-Hubble-Profile mass model would give H_0=74^{+18}_{-15} (95% statistical) ^{+22}_{-22} (systematic) km/s/Mpc. For Omega_m=0.3 and Omega_Lambda=0.7, these values increase by 5.4%. ... (ABRIDGED)

Motivation & Objective

• To determine the time delay between the two lensed images of the CLASS gravitational lens B1600+434 using radio light curves.
• To distinguish between intrinsic source variability and external causes (microlensing or scintillation) for observed short-term flux variations.
• To estimate the Hubble parameter H₀ using the measured time delay and lens mass models, while accounting for degeneracies in the mass profile slope.
• To assess the viability of microlensing versus interstellar scintillation as the origin of rapid flux variations in image A.
• To evaluate the potential of this system for constraining the radial mass profile of the lens galaxy's dark matter halo once H₀ is independently known.

Proposed method

• Conducted a multi-epoch 8.5-GHz monitoring campaign of B1600+434 using the Very Large Array (VLA) in A- and B-arrays over 8 months (February–October 1998), resulting in 75 observing epochs with a median cadence of 3.3 days.
• Applied the minimum dispersion method (Pelt et al. 1996) and the PRH method (Press et al. 1992) to cross-correlate the light curves of the two lens images to determine the time delay.
• Used multi-frequency WSRT data at 1.4 and 5 GHz to test the frequency dependence of variability, rejecting the ionized Galactic ISM scintillation hypothesis due to mismatched frequency scaling.
• Modeled the lens galaxy's mass distribution using both isothermal and Modified-Hubble-Profile (MHP) models to derive H₀ values from the time delay.
• Quantified systematic errors in the time delay and H₀ estimates by considering uncertainties in the mass model slope and cosmological parameters.
• Combined statistical and systematic error estimates to report 95% confidence intervals for the time delay and H₀.

Experimental results

Research questions

• RQ1 What is the time delay between the two lensed images of B1600+434 as measured from 8.5-GHz VLA light curves?
• RQ2 What is the dominant physical origin of the short-term flux variability observed in image A—microlensing or interstellar scintillation?
• RQ3 How does the uncertainty in the radial slope of the lens galaxy’s mass profile affect the derived Hubble parameter?
• RQ4 Can the time delay measurement be used to constrain the dark matter halo structure of the lens galaxy if H₀ is known independently?
• RQ5 How do the results from two independent time-delay estimation methods (minimum dispersion and PRH) compare in consistency and precision?

Key findings

• The VLA light curves show a nearly linear flux decrease of 18–19% in both lens images over eight months, with no significant time delay in the long-term trend.
• Image A exhibits short-term variability of up to 11% peak-to-peak on timescales of days to weeks, while image B varies by at most 6% on the same timescales.
• The short-term variability in image A is most likely due to microlensing by compact objects in the lens galaxy, as the ionized Galactic ISM scintillation hypothesis is ruled out by multi-frequency WSRT data.
• The time delay between the lens images is measured as 47⁺¹²₋₉ days at 95% confidence, with two independent methods yielding consistent results.
• Using an isothermal mass model, the Hubble parameter is estimated at H₀ = 57⁺¹⁴₋₁₁ km s⁻¹ Mpc⁻¹ (95% statistical), with a systematic uncertainty of ±15 to +26 km s⁻¹ Mpc⁻¹.
• For the Modified-Hubble-Profile mass model, H₀ is estimated at 74⁺¹⁸₋₁⁵ km s⁻¹ Mpc⁻¹ (95% statistical), with a symmetric systematic error range of ±22 km s⁻¹ Mpc⁻¹.