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TDCOSMO. XXIII. Measurement of the Hubble constant from the doubly lensed quasar HE1104-1805

This paper presents the first TDCOSMO analysis of a doubly lensed quasar, HE1104-1805, combining 17 years of time-delay data, stellar kinematics, lens modeling, and external convergence measurements to derive a Hubble constant of $64.2^{+5.8}_{-5.0}$ km s $^{-1}$ Mpc $^{-1}$ (scaled by the internal mass sheet degeneracy parameter), demonstrating that doubly lensed systems can achieve precision comparable to quadruply lensed quasars and serve as a foundation for future large-sample cosmological constraints.

Original authors: Eric Paic, Frédéric Courbin, Christopher D. Fassnacht, Aymeric Galan, Martin Millon, Dominique Sluse, Devon M. Williams, Simon Birrer, Elizabeth J. Buckley-Geer, Michele Cappellari, Frédéric Dux, Xian

Published 2026-03-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Eric Paic, Frédéric Courbin, Christopher D. Fassnacht, Aymeric Galan, Martin Millon, Dominique Sluse, Devon M. Williams, Simon Birrer, Elizabeth J. Buckley-Geer, Michele Cappellari, Frédéric Dux, Xiang-Yu Huang, Shawn Knabel, Cameron Lemon, Anowar J. Shajib, Sherry H. Suyu, Tommaso Treu, Kenneth C. Wong, Lise Christensen, Veronica Motta, Alessandro Sonnenfeld

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Solving the Universe's "Speedometer" Problem

Imagine the Universe is a giant car driving down a highway. Astronomers want to know exactly how fast it is going right now. This speed is called the Hubble Constant ( $H_0$ ).

For a long time, scientists have been arguing about the speed.

Team A looks at the "baby photos" of the Universe (the Cosmic Microwave Background) and calculates the speed should be about 67.
Team B looks at "adult photos" (nearby stars and supernovae) and calculates the speed should be about 73.

They disagree by a significant amount, and this disagreement is a major mystery in physics. To solve it, we need a third, completely independent way to measure the speed, like a radar gun that doesn't rely on the car's history or its current location.

This paper introduces that radar gun: Gravitational Lensing.

The Analogy: The Cosmic Traffic Jam

Imagine a massive truck (a galaxy) driving on the highway. Behind it, a race car (a distant quasar) is trying to pass. The truck's gravity bends the space around it, acting like a giant lens.

Because of this bending, the light from the race car takes two different paths to get to your eyes:

Path A: A slightly shorter, faster route.
Path B: A slightly longer, slower route.

Even though the race car flashes its lights at the exact same moment, you see the flash on Path A arrive before the flash on Path B. This gap in time is called the Time Delay.

By measuring exactly how many days apart the flashes are, and by understanding how much the truck bent the light, we can calculate the distance to the truck and the speed of the Universe.

The Challenge: The "Double" vs. The "Quad"

For years, the TDCOSMO collaboration (the team of scientists who wrote this paper) has been using Quadruply Lensed Quasars.

The Analogy: Imagine the truck creates four different images of the race car. It's like having four different GPS routes to compare. This gives a very precise map of the road.
The Problem: These "four-image" systems are rare. Finding enough of them to get a super-precise measurement is like trying to win the lottery every day.

This paper is a breakthrough because they successfully used a Doubly Lensed Quasar (HE 1104−1805).

The Analogy: This is like having only two GPS routes. It's harder to get a perfect map with fewer routes, but these systems are five times more common than the four-image ones. If they can prove this method works on doubles, they can build a massive sample size and finally nail down the Hubble Constant with 1% precision.

How They Did It: The Four Ingredients

To get the speed of the Universe from this "two-route" system, the team had to mix four specific ingredients, like a chef making a complex stew:

1. The Stopwatch (Time Delay)
They watched the quasar for 17 years using three different telescopes (SMARTS, Euler, and WFI). They tracked the brightness of the two images like a heartbeat.

Result: They found the time delay was 176.3 days. One image arrives about half a year after the other.

2. The Engine Check (Stellar Kinematics)
To know how much the "truck" (the lensing galaxy) weighs, they didn't just guess. They used the MUSE instrument on the Very Large Telescope to measure how fast the stars inside that galaxy are moving.

Analogy: If you see a car swerving wildly, you know the driver is heavy or the car is light. By measuring the "swerving" (speed) of the stars, they calculated the galaxy's mass. They did this in three different rings around the galaxy to get a detailed profile.

3. The Road Map (Lens Modeling)
They used high-resolution images from the Hubble Space Telescope to build a 3D computer model of the galaxy's gravity. They tested two different theories about what the galaxy is made of:

Theory A: A smooth, simple power-law shape.
Theory B: A complex mix of normal matter and dark matter.
Result: The data strongly favored the simpler, smooth shape (Theory A).

4. The Background Noise (Line-of-Sight)
The Universe isn't empty. There are other galaxies and groups of galaxies between us and the lens that might be tugging on the light, too.

Analogy: Imagine trying to hear a whisper in a room, but there are other people talking in the background. The team had to measure how much "background noise" (other galaxies) was affecting the signal and subtract it out. They found the line of sight was actually slightly empty (under-dense), which helped refine the calculation.

The Result: A New Measurement

After mixing all these ingredients together, and doing the math "blindly" (so they wouldn't accidentally bias the result by hoping for a specific number), they got their answer:

The Hubble Constant is $64.2 \pm 5.8$ km/s/Mpc.

What does this mean? It sits right in the middle of the debate between Team A (67) and Team B (73).
How good is it? The precision is about 8.5%. This is comparable to the best measurements they've ever gotten from the rare "four-image" systems.

Why This Matters

This paper is a stepping stone.

Before: They were limited by the rarity of "four-image" quasars.
Now: They have proven that "two-image" quasars work just as well.
The Future: Since "two-image" quasars are much more common, the next big paper will combine data from many of these doubles. This will allow them to shrink that 8.5% error bar down to a tiny 1%, finally solving the mystery of how fast the Universe is expanding.

In short: They took a difficult, rare puzzle piece (the double lens), solved it with incredible precision, and proved that we can now use thousands of similar pieces to solve the biggest mystery in cosmology.

1. Problem and Context

The Hubble constant ( $H_0$ ) tension remains one of the most significant challenges in modern cosmology. Measurements from the Cosmic Microwave Background (CMB) yield $H_0 \approx 67.4$ km s $^{-1}$ Mpc $^{-1}$ , while local distance ladder measurements (Cepheids, Supernovae) yield $H_0 \approx 73.2$ km s $^{-1}$ Mpc $^{-1}$ . This discrepancy exceeds $5\sigma$ .

Time-delay cosmography (TDC) using strongly lensed quasars offers an independent method to measure $H_0$ . While the TDCOSMO collaboration has previously focused on quadruply lensed quasars (quads) due to their abundance in early surveys and additional constraints from image multiplicity, these systems are rare. Doubly lensed quasars (doubles) are far more abundant (representing ~75% of known lenses) and offer precise time delays. However, they have historically been underutilized for $H_0$ measurements due to fewer constraints on mass modeling and the difficulty of breaking the Mass-Sheet Degeneracy (MSD). This paper aims to demonstrate that doubles can achieve precision comparable to quads, serving as a stepping stone toward a 1% precision $H_0$ measurement.

2. Methodology

The authors performed a blind analysis of the doubly imaged quasar HE 1104−1805 ( $z_s = 2.32$ , $z_d = 0.729$ ). The measurement required four independent ingredients:

A. Time-Delay Measurement ( $\Delta t_{AB}$ )

Data: Combined 17 years of photometric monitoring from three telescopes: SMARTS (2003–2016), Euler/ECAM (2013–2018), and WFI (2017).
Technique: Used the PyCS (Python Curve Shifting) package with free-knot spline fitting.
Process:
- Separated intrinsic quasar variability from extrinsic microlensing variability.
- Marginalized over hyperparameters ( $\eta$ for intrinsic splines, $n_{ml}$ for microlensing) to ensure robustness.
- Generated mock light curves to estimate systematic and statistical uncertainties.
Result: $\Delta t_{AB} = 176.3^{+11.4}_{-10.3}$ days (5.8% precision).

B. Stellar Kinematics (Velocity Dispersion, $\sigma_{LOS}$ )

Data: Integral Field Unit (IFU) spectroscopy from MUSE (VLT) with adaptive optics.
Process:
- Subtracted the quasar point sources to isolate the lens galaxy light.
- Divided the lens galaxy into three concentric radial bins (0.53" width).
- Used pPXF (penalized Pixel Fitting) with multiple stellar template libraries (Indo-US, MILES, X-shooter) to measure line-of-sight velocity dispersion.
- Applied corrections for inclination and PSF convolution.
Result: Measured $\sigma_{LOS}$ in three bins with 5–13% precision (e.g., $278 \pm 15$ km s $^{-1}$ in the innermost bin).

C. Lens Modeling (Fermat Potential)

Data: High-resolution HST/WFC3 imaging (F160W filter).
Modeling:
- Modeled the main deflector using two families of mass profiles: Power-Law (PEMD) and Composite (Baryonic + Dark Matter).
- Included 9 perturbers (P1–P9) within 5" and 6 galaxy groups explicitly in the mass model using multi-plane lensing formalism.
- Modeled the Point Spread Function (PSF) iteratively using Lenstronomy.
- Marginalized over different perturber inclusion strategies using Bayesian Information Criterion (BIC) weighting.
Outcome: Derived the Fermat potential difference ( $\Delta \phi$ ) between images A and B.

D. Line-of-Sight (LOS) Convergence ( $\kappa_{ext}$ )

Data: Wide-field imaging from Subaru/SuprimeCam (i-band).
Process:
- Constructed a galaxy number count catalog up to 120" from the lens.
- Compared the density of galaxies along the LOS to reference fields and simulations (Millennium Simulation) to estimate the external convergence contribution from mass not explicitly modeled.
Result: $\kappa_{ext} = -0.019^{+0.058}_{-0.020}$ , indicating a slightly underdense LOS.

E. Cosmographic Inference

Combined the time delay, Fermat potential, $\sigma_{LOS}$ , and $\kappa_{ext}$ to solve for the Time-Delay Distance ( $D_{\Delta t}$ ) and Angular Diameter Distance ( $D_d$ ).
Blind Analysis: The final $H_0$ value was hidden until the analysis chain was complete to prevent experimenter bias.
Assumption: The internal mass-sheet degeneracy parameter was fixed to $\lambda_{int} = 1$ (to be constrained in future hierarchical analyses).

3. Key Contributions

First Doubly Lensed Quasar in TDCOSMO: This is the first TDCOSMO paper to successfully measure $H_0$ using a doubly imaged system, proving that doubles can yield competitive precision.
Robust Time Delay: Provided the most precise time delay measurement for HE 1104−1805 to date, utilizing the longest and highest-cadence dataset available.
Spatially Resolved Kinematics: Successfully extracted high-quality velocity dispersion profiles from a double lens, overcoming the challenge of the bright quasar image A contaminating the lens light.
Model Comparison: Demonstrated that for this specific system, a Power-Law mass model is strongly favored over a Composite model when compared against the observed kinematic data. The composite model failed to fit the inner velocity dispersion bin.
Blind Protocol: Rigorously applied the blind analysis protocol to ensure the integrity of the $H_0$ result.

4. Results

Time Delay: $\Delta t_{AB} = 176.3^{+11.4}_{-10.3}$ days.
Distances:
- Time-delay distance: $D_{\Delta t} = 5083^{+504}_{-487}$ Mpc.
- Angular diameter distance to lens: $D_d = 1921^{+254}_{-236}$ Mpc.
Hubble Constant:
- $H_0 = 64.2^{+5.8}_{-5.0} \times \lambda_{int}$ km s $^{-1}$ Mpc $^{-1}$ .
- Assuming $\lambda_{int} = 1$ , the result is $64.2^{+5.8}_{-5.0}$ km s $^{-1}$ Mpc $^{-1}$ .
- Precision: 8.5% (comparable to the best TDCOSMO quad measurements, which typically achieve 4–6%).
Model Preference: The likelihood-weighted combination assigned 95% of the posterior weight to the Power-Law model, effectively discarding the Composite model due to its inability to match the kinematic data.

5. Significance

Validation of Doubles: This work confirms that doubly lensed quasars are a viable and powerful sample for time-delay cosmography. Given that doubles are ~4 times more abundant than quads, incorporating them can expand the TDCOSMO sample size by a factor of 5.
Path to 1% Precision: By adding doubles to the sample, the statistical noise can be significantly reduced, accelerating the path toward the collaboration's goal of a 1% precision measurement of $H_0$ .
Bias Mitigation: Including doubles helps test for selection biases inherent in quad-only samples (e.g., specific alignment or ellipticity requirements), ensuring the robustness of the $H_0$ measurement across different lens morphologies.
Future Work: The next TDCOSMO milestone will perform a hierarchical analysis of all lenses (including this double) to jointly constrain $\lambda_{int}$ and $H_0$ , which will further reduce uncertainties.

In conclusion, this paper successfully demonstrates that a single doubly lensed quasar, when analyzed with high-quality multi-wavelength data and rigorous modeling, can provide an $H_0$ measurement with precision rivaling that of the most complex quadruply lensed systems.