The Hubble Constant from the Gravitational Lens B1608+6561
Bibliographic record
Abstract
We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (1) the three independent time delays and flux ratios from Very Large Array observations, (2) the radio-image positions from Very Large Baseline Array observations, (3) the shape of the deconvolved Einstein ring from optical and infrared Hubble Space Telescope images, (4) the extinction-corrected lens-galaxy centroids and structural parameters, and (5) a stellar velocity dispersion, ap 247 AE 35 km s 1 , of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck II Telescope. The lens-mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes that are the key parameters for determining the value of H 0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum-2 model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein ring. A combined gravitational lens and stellar dynamical analysis leads to a value of the Hubble constant of H 0 75 7 6 km s 1 Mpc 1 (68% CL; m 0:3, 0:7). The nonlinear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H 0 . The lens galaxy G1 is $5 times more massive than the secondary lens galaxy (G2) and has a mass density slope of 0 G1 2:03 0:14 0:14 AE 0:03 (68% CL) for / r 0 , very close to isothermal ( 0 2). After extinction correction, G1 exhibits a smooth surface brightness distribution with an R 1/4 profile and no apparent evidence for tidal disruption by interactions with G2. Given the scope of the observational constraints and the gravitational lens models, as well as the careful corrections to the data, we believe this value of H 0 to be little affected by known systematic errors (d5%).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".