# Time Delay Cosmography: Analysis of Quadruply Lensed QSO SDSSJ1433 from Wendelstein Observatory

**Authors:** G. Queirolo, S. Seitz, A. Riffeser, M. Kluge, R. Bender, C. Gössl, U. Hopp, C. Ries, M. Schmidt, R. Zöller  
**arXiv:** [2312.09311](https://arxiv.org/abs/2312.09311)  
**Date:** 2023-12-14  
**Summary page:** https://www.summarizepaper.com/en/paper/2312.09311v1/

## Key points

- Primary objective: Derive Hubble constant estimate using quadruply lensed, variable QSO SDSSJ1433+6007
- Combine multi-filter, archival $\textit{HST}$ data for lens modeling
- Conduct dedicated time delay monitoring campaign at the 2.1m Fraunhofer telescope at the $\textit{Wendelstein Observatory}$
- Discovery of light contaminant in F160W filter that could bias lensing potentials and cosmological inferences if unaddressed
- Precise posterior estimates for Fermat potential differences obtained from lens modeling in remaining filters (F475X, F814W, F105W, F140W) with approximately 6% precision
- Analysis of Wendelstein light curve data using free-knot spline fitting method in Python tools to determine time delays between QSO images (7.5% to 9.8% range)
- Derived Hubble parameter estimate of $H_0=76.6^{+7.7}_{-7.0}\frac{\mathrm{km}}{\mathrm{Mpc\;s}}$ with uncertainty as low as 9.6%
- Comparison with study by Schmidt et al. (2022) showing tensions in certain parameters due to differences in modeling approach and contaminants present in specific filters
- Contribution to addressing Hubble tension through independent verification via Time Delay Cosmography (TDC) for QSOs like SDSSJ1433+6007
- Emphasis on importance of 2-meter ground-based telescopes for high cadence observational campaigns essential for following up on strong lenses identified through large-scale surveys
- Significance of meticulous data analysis and observation techniques in deriving accurate cosmological parameters such as the Hubble constant within acceptable uncertainties

## Summary

In this work, the primary objective was to derive a Hubble constant estimate utilizing the quadruply lensed, variable QSO SDSSJ1433+6007. The methodology involved combining multi-filter, archival $\textit{HST}$ data for lens modeling with a dedicated time delay monitoring campaign conducted at the 2.1m Fraunhofer telescope at the $\textit{Wendelstein Observatory}$. Notably, it was discovered that one of the $\textit{HST}$ filters (F160W) contained a light contaminant that could have significantly biased the lensing potentials and subsequent cosmological inferences if left unaddressed. After excluding these problematic data points, precise posterior estimates for the Fermat potential differences were obtained from lens modeling in the remaining filters (F475X, F814W, F105W, and F140W), achieving an impressive precision of approximately $6\%$. Furthermore, analysis of the $\textit{g'}$-band Wendelstein light curve data was carried out using a free-knot spline fitting method implemented in Python tools. The resulting time delays between the QSO images exhibited a range of 7.5% to 9.8% depending on image brightness and time delay duration. By combining the posteriors for Fermat potential differences and time delays under assumptions of a flat $\Lambda$CDM cosmology, a Hubble parameter estimate of $H_0=76.6^{+7.7}_{-7.0}\frac{\mathrm{km}}{\mathrm{Mpc\;s}}$ was derived with an uncertainty as low as $9.6\%$ for this single system. Moreover, comparisons were made with a study by Schmidt et al. (2022) that utilized similar HST data but differed in modeling approach and scope. Tensions were observed in certain parameters between their analysis and this study due to differences in axis ratio estimations potentially influenced by contaminants present in specific filters. Additionally, this research contributes to addressing the Hubble tension by providing an independent verification through implementing Time Delay Cosmography (TDC) for QSOs like SDSSJ1433+6007. Furthermore, it highlights the importance of 2-meter ground-based telescopes for conducting high cadence observational campaigns essential for following up on strong lenses identified through large-scale surveys expected to increase significantly in number with upcoming astrophysical projects. Overall, this study not only refines our understanding of gravitational lensing systems like SDSSJ1433+6007 but also underscores the significance of meticulous data analysis and observation techniques in deriving accurate cosmological parameters such as the Hubble constant within acceptable uncertainties.