REVIEW
TDCOSMO XXVIII. The Hubble constant from the quadruply lensed quasar J1537$-$3010 with precise time delays
Cosmology and Nongalactic Astrophysics · Submitted 31 Aug 2026 · 178 references
Pith's verdict: Solid new H0 measurement from a single lens system, honestly quoted at 10% precision; the load-bearing dynamical assumptions are the soft spot, but the paper is transparent about them.
T0 · AI review
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Referee report
The paper
The paper claims
This paper presents the first Hubble constant measurement from the quadruply lensed quasar J1537–3010, finding H0 = 75.5^{+9.3}_{-5.8} km/s/Mpc (10% precision) in flat ΛCDM by explicitly incorporating the mass-sheet degeneracy into the…
The reading
What carries the argument
The central object is the mass-sheet parameter λ = (1 − κ_ext) λ_int, which encodes the combined effect of the internal mass-sheet transformation and the external convergence. The key relationship is H0 ∝ 1/λ, so constraining λ directly breaks the dominant systematic degeneracy in time-delay cosmography. The machinery that constrains λ_int is the Jeans anisotropic modelling (JAM) framework applied to the MUSE stellar kinematics map, combined with a cored-mass-sheet profile (Eq. 9) that mimics a pure mass sheet over the Einstein-radius region. The external convergence κ_ext is estimated by comparing galaxy counts in a 120″ aperture around the lens to random lines of sight in the Euclid Flagship simulation, using the method described in Wells et al. (2023).
Extended reading notes
Core claim
The central claim is that the Hubble constant can be measured from J1537–3010 with 10% precision by explicitly modelling the internal and external parts of the mass-sheet degeneracy. The internal mass-sheet parameter λ_int is constrained by Jeans anisotropic modelling (JAM) of the MUSE stellar kinematics under the assumption of axisymmetry and a power-law plus cored-mass-sheet density profile. The external convergence κ_ext is constrained from the number counts of galaxies along the line of sight, calibrated against the Euclid Flagship simulation. The total mass-sheet parameter is λ = (1 − κ_ext) λ_int = 0.$89^{{+0.11}}$_{-0.06}, and because H0 ∝ 1/λ, the inferred H0 = 75.$5^{{+9.3}}$_{-5.8} km/s/Mpc. The analysis was performed blindly to H0, distances and the mass slope, and the two independent lens-modelling codes (lenstronomy and glee) produce results that agree after the mass-sheet transformation is applied.
Load-bearing premise
The measurement assumes that the stellar kinematics can be modelled by an axisymmetric Jeans anisotropic model with a radially constant stellar anisotropy, a specific inclination prior derived from MaNGA, and a mass profile that is a power law plus a cored mass-sheet component; any bias in the anisotropy or mass-profile assumption directly translates into a biased H0 because H0 scales as 1/λ_int.
Editorial extensions
If this is right
- If the measurement is correct, J1537–3010 becomes the ninth system in the TDCOSMO sample, providing additional leverage for population-level hierarchical inference of H0 that can approach percent-level precision.
- The posterior distributions of lens model parameters and stellar kinematics will be used in future TDCOSMO analyses, potentially breaking remaining degeneracies between the internal mass-sheet parameter and the stellar anisotropy across the sample.
- Future JWST NIRSpec and NIRCam observations of this system, which are already being gathered, are expected to dramatically reduce the kinematic and imaging uncertainties, so that the current 10% precision on H0 from this single system could shrink toward the few-percent floor set by the time delays.
- The agreement of this single-system H0 with the distance ladder (e.g., Breuval et al. 2024) and its consistency with Planck+SPT+ACT at ∼1σ suggests that the mass-sheet treatment used here does not introduce a large systematic bias; if the tension persists and sharpens with better data, it would strengthen the case for new physics beyond flat ΛCDM.
Reading between the lines
- Editorial inference: The 10% uncertainty is dominated by the kinematic constraint, which reaches only 0.7 arcsec while the Einstein radius is 1.37 arcsec. Deep JWST spectroscopy will map kinematics further out, and if the inferred velocity dispersion profile remains consistent with the current JAM best-fit, the posterior on λ_int should tighten by a factor of ∼2–3, yielding H0 at ∼5% from this sys
- Editorial inference: The paper does not explicitly test whether a more flexible mass profile (e.g., a two-power-law or a composite stars+dark-matter NFW) would change the inference on λ_int. Because the cored-mass-sheet term (Eq. 9) is only an approximation to a true mass sheet, a future analysis that jointly fits a more physically motivated mass model and the kinematics may produce a different λ_
Original abstract
We present the first measurement of the Hubble constant ($H_0$) from the quadruply-lensed quasar J1537$-$3010, which has optically-measured time delays at $\sim2 \%$ precision. We combine these delays with multi-band imaging data from the Hubble Space Telescope (HST) and model the system with two independent software and teams. We adopt a mass profile that is maximally degenerate with $H_0$ to fully incorporate the mass-sheet degeneracy in the error budget, with nuisance parameters constrained by spatially resolved stellar kinematics from the Multi Unit Spectroscopic Explorer (MUSE) and a line-of-sight (LoS) analysis using the Euclid Flagship simulation. The entire analysis is performed blindly to $H_0$, distances and mass density slope of the main deflector. After unblinding, we measure $H_0 = 75.5^{+9.3}_{-5.8}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, corresponding to a $10\%$ precision measurement from a single system. This precision is driven by conservative lens modeling assumptions including differences between lens modeling methods and the limited stellar kinematics constraints, from which we infer a total mass-sheet parameter $\lambda\equiv(1-\kappa_{\rm ext})\lambda_{\rm int} = 0.89^{+0.11}_{-0.06}$ ($\lambda_{\rm int}=0.89^{+0.09}_{-0.07}$) that is consistent with current results for elliptical galaxies ($\lambda \approx 1$). Our lensing constraints, stellar kinematic measurements and LoS characterization will be included in subsequent population-level measurements of $H_0$. Moreover, our lens models combined with future near-infrared spectroscopy and imaging from the James Webb Space Telescope will further reduce the uncertainties on $H_0$ from J1537$-$3010 alone, bringing it closer to the few percents precision of the time delays.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present the first measurement of the Hubble constant ($H_0$) from the quadruply-lensed quasar J1537$-$3010, which has optically-measured time delays at $\sim2 \%$ precision. We combine these delays with multi-band imaging data from the Hubble Space Telescope (HST) and model the system with two independent software and teams. We adopt a mass profile that is maximally degenerate with $H_0$ to fully incorporate the mass-sheet degeneracy in the error budget, with nuisance parameters constrained by spatially resolved stellar kinematics from the Multi Unit Spectroscopic Explorer (MUSE) and a line-of-sight (LoS) analysis using the Euclid Flagship simulation. The entire analysis is performed blindly to $H_0$, distances and mass density slope of the main deflector. After unblinding, we measure $H_0 = 75.5^{+9.3}_{-5.8}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, corresponding to a $10\%$ precision measurement from a single system. This precision is driven by conservative lens modeling assumptions including differences between lens modeling methods and the limited stellar kinematics constraints, from which we infer a total mass-sheet parameter $\lambda\equiv(1-\kappa_{\rm ext})\lambda_{\rm int} = 0.89^{+0.11}_{-0.06}$ ($\lambda_{\rm int}=0.89^{+0.09}_{-0.07}$) that is consistent with current results for elliptical galaxies ($\lambda \approx 1$). Our lensing constraints, stellar kinematic measurements and LoS characterization will be included in subsequent population-level measurements of $H_0$. Moreover, our lens models combined with future near-infrared spectroscopy and imaging from the James Webb Space Telescope will further reduce the uncertainties on $H_0$ from J1537$-$3010 alone, bringing it closer to the few percents precision of the time delays.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present the first measurement of the Hubble constant ($H_0$) from the quadruply-lensed quasar J1537$-$3010, which has optically-measured time delays at $\sim2 \%$ precision. | contribution 0.95 | 0.95 | 0.24 | asserted 1.00 |
| s1 | We combine these delays with multi-band imaging data from the Hubble Space Telescope (HST) and model the system with two independent software and teams. | method 0.99 | 0.94 | 0.02 | asserted 0.99 |
| s2 | We adopt a mass profile that is maximally degenerate with $H_0$ to fully incorporate the mass-sheet degeneracy in the error budget, with nuisance parameters constrained by spatially resolved stellar kinematics from the Multi Unit Spectroscopic Explorer (MUSE) and a line-of-sight (LoS) analysis using the Euclid Flagship simulation. | method 1.00 | 0.87 | 0.02 | asserted 0.99 |
| s3 | The entire analysis is performed blindly to $H_0$, distances and mass density slope of the main deflector. | method 0.99 | 0.94 | 0.02 | asserted 1.00 |
| s4 | After unblinding, we measure $H_0 = 75.5^{+9.3}_{-5.8}\ {\rm km\,s^{-1}\,Mpc^{-1}}$, corresponding to a $10\%$ precision measurement from a single system. | result 1.00 | 0.98 | 0.92 | asserted 1.00 |
| s5 | This precision is driven by conservative lens modeling assumptions including differences between lens modeling methods and the limited stellar kinematics constraints, from which we infer a total mass-sheet parameter $\lambda\equiv(1-\kappa_{\rm ext})\lambda_{\rm int} = 0.89^{+0.11}_{-0.06}$ ($\lambda_{\rm int}=0.89^{+0.09}_{-0.07}$) that is consistent with current results for elliptical galaxies ($\lambda \approx 1$). | result 0.47 | 0.94 | 0.07 | asserted 0.55 |
| s6 | Our lensing constraints, stellar kinematic measurements and LoS characterization will be included in subsequent population-level measurements of $H_0$. | future work 1.00 | 0.77 | 0.03 | asserted 0.87 |
| s7 | Moreover, our lens models combined with future near-infrared spectroscopy and imaging from the James Webb Space Telescope will further reduce the uncertainties on $H_0$ from J1537$-$3010 alone, bringing it closer to the few percents precision of the time delays. | future work 1.00 | 0.36 | 0.03 | hedged possibility 0.78 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:2609.00179 by the authors.
References
Discussion
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