H0LiCOW - IX. Cosmographic analysis of the doubly imaged quasar SDSS 1206+4332 and a new measurement of the Hubble constant (1809.01274v3)

Abstract: We present a blind time-delay strong lensing (TDSL) cosmographic analysis of the doubly imaged quasar SDSS 1206+4332. We combine the relative time delay between the quasar images, Hubble Space Telescope imaging, the Keck stellar velocity dispersion of the lensing galaxy, and wide-field photometric and spectroscopic data of the field to constrain two angular diameter distance relations. The combined analysis is performed by forward modelling the individual data sets through a Bayesian hierarchical framework, and it is kept blind until the very end to prevent experimenter bias. After unblinding, the inferred distances imply a Hubble constant $H_0 = 68.8^{+5.4}_{-5.1}$ kms$^{-1}$Mpc$^{-1}$, assuming a flat Lambda cold dark matter cosmology with uniform prior on $\Omega_{\rm m}$ in [0.05, 0.5]. The precision of our cosmographic measurement with the doubly imaged quasar SDSS 1206+4332 is comparable with those of quadruply imaged quasars and opens the path to perform on selected doubles the same analysis as anticipated for quads. Our analysis is based on a completely independent lensing code than our previous three H0LiCOW systems and the new measurement is fully consistent with those. We provide the analysis scripts paired with the publicly available software to facilitate independent analysis. The consistency between blind measurements with independent codes provides an important sanity check on lens modelling systematics. By combining the likelihoods of the four systems under the same prior, we obtain $H_0 = 72.5^{+2.1}_{-2.3}$kms$^{-1}$Mpc$^{-1}$. This measurement is independent of the distance ladder and other cosmological probes.

• The paper demonstrates a blind time-delay lensing analysis of a doubly imaged quasar to measure the Hubble constant with 7.2% precision.
• It employs a Bayesian hierarchical framework integrating HST imaging, Keck spectroscopy, and lenstronomy modeling to estimate key cosmological distances.
• The findings validate doubly lensed quasars as robust, independent cosmological probes, offering an alternative to traditional distance ladder techniques.

Cosmographic Analysis and Hubble Constant Estimation from SDSS 1206+4332

The paper presented explores the cosmological implications of the strongly lensed system SDSS 1206+4332, focusing on the precise determination of the Hubble constant, $H_0$. This research is a continuation of the H0LiCOW project, which examines strong lens systems to measure cosmological distances independently of the traditional distance ladder. The primary focus of this analysis is to explore the time-delay strong lensing (TDSL) technique for the doubly imaged quasar SDSS 1206+4332, and subsequently derive constraints on $H_0$.

Research Methodology

The research employs a blind analysis protocol to mitigate bias, combining multiple datasets in a Bayesian hierarchical framework. Key datasets include:

• Time delay measurements between quasar images
• Hubble Space Telescope (HST) images for high-resolution lensing data
• Keck spectroscopic measurements for the stellar velocity dispersion of the lens galaxy
• Photometric and spectroscopic data for characterizing the field.

A noteworthy aspect is the use of the software lenstronomy, which models the lensing system and extracts the necessary parameters such as angular diameter distances $D_{\Delta t}$ and $D_{\text{d}}$, essential for determining $H_0$.

Findings and Interpretation

Upon unblinding the results, the paper finds:

• A time-delay distance $D_{\Delta t} = 5769_{-457}^{+569}$ Mpc and a lens distance $D_{\text{d}} = 1804_{-386}^{+534}$ Mpc, directly informing cosmography.
• Utilizing a uniform prior in $\Omega_{\text{m}}$, the analysis yields a Hubble constant $H_0 = 68.8_{-5.4}^{+5.4}$ -1, showcasing a 7.2% precision from a single lens system.

The results are consistent with earlier H0LiCOW findings from quadruply lensed systems. Notably, this paper demonstrates the feasibility of using doubly lensed quasars for precise cosmographic measurements, potentially expanding the pool of viable lens systems for future analytics.

Implications and Future Directions

The implications of these findings are multidimensional:

• Precision Cosmology: The ability to use doubles in addition to quads opens new avenues for increasing sample size, thus reducing statistical uncertainties in cosmological parameters.
• Systematic Uncertainty Benchmarking: The agreement between results from lenstronomy and prior studies using other codes highlights robustness against systematic uncertainties in models.
• Independent Cosmological Probes: TDSL provides a measurement of $H_0$ that is independent of Cepheid and supernova distance ladders, pertinent for resolving the ongoing $H_0$ tension.

Moving forward, the extended applicability to doubly lensed systems as shown here paves the way for a more inclusive analysis framework in lensing cosmology. Integrating results from a broader lens sample, including high-cadence monitoring data, will refine constraints on $H_0$ and other parameters like $\Omega_{\text{m}}$ or the curvature $\Omega_{\text{k}}$. The paper concludes on a positive note for TDSL’s utility in current and forthcoming cosmological inquests, particularly in synergy with dark energy and cosmic microwave background studies. By evaluating the constraints on curvature, the paper also illustrates potential enhancements in cosmological model discrimination. Through advancing the methods and expanding the datasets, future research will likely achieve the sub-percent precision that is crucial for contemporary and planned dark energy experiments.