TDCOSMO: XIX. Measuring stellar velocity dispersion with sub-percent accuracy for cosmography
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Abstract
The stellar velocity dispersion ( σ ) of massive elliptical galaxies is a key ingredient in breaking the mass-sheet degeneracy and obtaining precise and accurate cosmography from gravitational time delays. The relative uncertainty on the Hubble constant H 0 is double the relative error on σ . Therefore, time-delay cosmography imposes much more demanding requirements on the precision and accuracy of σ than galaxy studies. While precision can be achieved with an adequate signal-to-noise ratio (S/N), the accuracy critically depends on key factors such as the elemental abundance and temperature of stellar templates, flux calibration, and wavelength ranges. We carried out a detailed study of the problem using multiple sets of galaxy spectra of massive elliptical galaxies with S/N ∼ 30–160 Å −1 , along with state-of-the-art empirical and semi-empirical stellar libraries and stellar population synthesis templates. We show that the choice of stellar library is generally the dominant source of residual systematic errors. We propose a general recipe for mitigating and accounting for residual uncertainties. We show that a sub-percent level of accuracy can be achieved on individual spectra with our data quality, which we subsequently validated with simulated mock datasets. The covariance between velocity dispersions measured for a sample of spectra can also be reduced to sub-percent levels. We recommend this recipe for all applications that require high precision and accurate stellar kinematics. Thus, we have made all the software publicly available to facilitate its implementation. This recipe will also be used in future TDCOSMO collaboration papers.
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The same paper demonstrated such an effect on measurements using MUSE spectra was typically of order approximately 3-4%, well below the statistical uncertainty in this work, and of similar scale to the systematic uncertainty we observe.
“However, the same paper demonstrated such an effect on measurements using MUSE spectra was typically of order ≈ 3 -4%, well below the statistical uncertainty in this work, and of similar scale to the systematic uncertainty we observe.”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as [64]
Section 6.1 (p. 15) reports about 2% average statistical uncertainty for MUSE measurements, sub-percent systematic error from template choice, and other potential errors of 0.2–0.5%. Section 6.4 (p. 16) assigns the 3–4% average random errors to SDSS, not MUSE. The comparison with uncertainties in the citing authors’ own work is their assessment, not a result this source could establish. (LLM, conf=0.84)
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Experimental — accuracy not yet measuredKnabel et al. demonstrated that the leading systematic uncertainty comes from the choice of template library, and that this uncertainty is at most O(3-4%) in fits to MUSE spectra.
“Note that while Knabel et al. [64] have demonstrated the leading systematic uncertainty comes from the choice of template library, and advocate comparing a wide array of such libraries, they demonstrate this uncertainty is at most O (3-4%) in fits to MUSE spectra.”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as Knabel et al. [64]
Section 4.4.1 (p. 9) identifies template choice as the dominant potential systematic error, and the Summary (p. 17) recommends comparing all three clean libraries. The claimed 3–4% ceiling does not describe the MUSE results: Section 6.1 (p. 15) reports a template-choice error well below 1% with BIC weighting, while Section 4.3 (p. 9) says differences between full and clean libraries for some MUSE fits reach 5% or more. (LLM, conf=0.88)
Experimental — accuracy not yet measuredOur statistical uncertainty is large compared to [62, 64] in part because we use a less stringent SNR target inspired by [21].
“However, our statistical uncertainty is large compared to [62, 64] in part because we use a less stringent SNR target inspired by [21].”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as [64]
Knabel et al. [64] demonstrated that the choice of stellar template library is often the dominant source of systematic uncertainty in similar measurements.
“Knabel et al. [64] has rigorously explored systematic uncertainty in similar measurements with the goal of subpercent precision σ v measurements, and demonstrated that the choice of stellar template library is often the dominant source of systematic uncertainty.”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as Knabel et al. [64]
Measurements of stellar kinematics can be highly sensitive to analysis choices, and we have drawn on recent work, particularly [62, 64], to ensure our measurements are as robust as possible.
“Measurements of stellar kinematics can be highly sensitive to analysis choices, and we have drawn on recent work, particularly [62, 64], to ensure our measurements are as robust as possible.”
From Constraint on dark matter self-interaction from combined strong lensing and stellar kinematics in MACS J0138-2155 (2026) · cites this paper as [64]
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Cites
Suyu, S. H., Marshall, P. J., Auger, M. W., Hilbert, S., Blandford, R. D., Koopmans, L. V. E., Fassnacht, C. D., & Treu, T. (2010) · The Astrophysical Journal · doi:10.1088/0004-637x/711/1/201 · Cited by 454 · see citing works
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Research works printed but not linked: 7
- Bacon, R., Accardo, M., Adjali, L., et al. 2010, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 773508
- Bacon, R., Accardo, M., Adjali, L., et al. 2010, in SPIE Conference Series, Vol. 7735, Ground-based and Airborne Instrumentation for Astronomy III, ed. I. S. McLean, S. K. Ramsay, & H. Takami, 8
- Huang, X.-Y., Birrer, S., Cappellari, M., et al. 2025, A&A, submitted; arXiv eprints, arXiv:2503.00235 · arXiv
- Knabel, S., Treu, T., Cappellari, M., et al. 2024, arXiv e-prints, arXiv:2409.10631 · arXiv
- Mozumdar, P., Cappellari, M., Fassnacht, C. D., & Treu, T. 2025, arXiv e-prints, arXiv:2510.23863 · arXiv
- Schwarz, G. 1978, The Annals of Statistics, 6
- Shajib, A. J., Treu, T., Suyu, S. H., et al. 2025, A&A, submitted; arXiv e-prints, arXiv:2506.21665 · arXiv
Cited by
Sorted by citations
O’Donnell, J. H., Jeltema, T. E., Roberts, M. G., Nightingale, J., Flowers, A., & Aldas, D. (2026) · Physical Review D · doi:10.1103/hfgd-245k · Cited by 5 · see citing works
- Authors
- Knabel, S., Mozumdar, P., Shajib, A. J., Treu, T., Cappellari, M., Spiniello, C., & Birrer, S.
- Affiliations
- Department of Physics and Astronomy, University of California
- Independent University, Bangladesh (BD)
- University of Oxford (GB)
- Stony Brook University (US)
- ORCID
- Venue
- Astronomy & Astrophysics
- Publisher
- EDP Sciences
- Published
- 2025-11
- Volume
- 703
- Pages
- A117
- ISSN
- 0004-6361 (ISSN-L)
- 1432-0746
- OpenAlex
- W4414150293
- Cited by
- 14
- References
- 1
- Citations by year
- 2026: 8 · 2025: 6
- FWCI
- 6.24
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Astronomy and Astrophysics (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Keywords
- stellar velocity dispersion, giant elliptical galaxies, time-delay cosmography, mass-sheet degeneracy, Hubble constant, stellar libraries, stellar kinematics, systematic errors
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