diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml index f78d39c..34ea1d4 100644 --- a/.github/workflows/test.yml +++ b/.github/workflows/test.yml @@ -9,8 +9,10 @@ permissions: contents: read concurrency: - group: ${{ github.workflow }}-${{ github.ref }} - cancel-in-progress: ${{ github.event_name == 'pull_request' }} # a superseded PR run, never a run on main + # A push to main gets a group of its own commit, so no run on main is cancelled or left pending; + # a pull request's runs share one group, and a new push cancels the superseded run. + group: ${{ github.workflow }}-${{ github.event_name == 'pull_request' && github.ref || github.sha }} + cancel-in-progress: ${{ github.event_name == 'pull_request' }} jobs: test: diff --git a/CORRECTIONS.md b/CORRECTIONS.md index c2798e7..85e13fd 100644 --- a/CORRECTIONS.md +++ b/CORRECTIONS.md @@ -55,7 +55,7 @@ Claims made during the exploration that did not survive it, kept so the record s Not fixed: giving molecules a gap and measured spectra would change the buckyball and giant-molecule rows, so it needs a decision. 9. **Joos and Zeh's air entry is 10³⁶, not 10³⁷.** The old check quoted 10³⁷ cm⁻² s⁻¹ (10⁴¹ m⁻² s⁻¹) as Joos and - Zeh's. All four copies of their table checked here (Kiefer and Joos 1998; Joos 1999; Kiefer 1999; Joos 2005) + Zeh's. All four copies of their table checked here (Kiefer and Joos 1999; Joos 2000; Kiefer 2000; Joos 2005) give 10³⁶. The 10³⁷ is Schlosshauer's (his 10⁻³¹ s at Δx = 10⁻³ cm), and it matches the closed-form formula (8.6×10³⁶). The two tables differ by ten; the model follows the formula. 10. **Three disagreements inside the published tables.** Not model errors; recorded so nobody tunes the model to @@ -104,3 +104,14 @@ Claims made during the exploration that did not survive it, kept so the record s to grow, and at its radius the galaxy, not the black hole, holds the particles. Any cloud these black holes can grow within the age of the universe, at any particle mass, peaks within about 0.1 pc. See [notes/bh-lensing.md](notes/bh-lensing.md). + +## 18 October 2026: the black hole lensing note revisited (issue #28) + +16. **SDP.81 as the anomaly lens with a bound on its black hole.** Claimed (notes/bh-lensing.md, issue #1): "Only one + anomaly lens, SDP.81, has even a bound on its black hole". The note paired a 10^(8.96±0.12) M☉ dark lump at + 6.9σ (Hezaveh et al. 2016) with a black hole above 3×10⁸ M☉ from the missing central image. That no longer + holds. Stacey et al. (A&A, 2025) re-analysed the same ALMA data. They find the lump most likely spurious, + produced by poorly fitting multipoles, and no evidence for either previously reported lump, only for extra + angular structure in the lens. Their mock data show they would have found a real 10⁹ M☉ lump (log Bayes factor + 29). The black hole bound stands, so no lens in the note now has both a small-scale anomaly and a bound on its + black hole. Fixed in [notes/bh-lensing.md](notes/bh-lensing.md) (issue #28). diff --git a/README.md b/README.md index 2bad672..fc021a6 100644 --- a/README.md +++ b/README.md @@ -319,43 +319,43 @@ Mistakes found along the way are in [CORRECTIONS.md](CORRECTIONS.md). Open quest - K. Hornberger, L. Hackermüller and M. Arndt, *Influence of molecular temperature on the coherence of fullerenes in a near-field interferometer*, Phys. Rev. A 71, 023601 (2005). https://doi.org/10.1103/PhysRevA.71.023601 (https://arxiv.org/abs/quant-ph/0412003) - M. Schlosshauer, *Decoherence and the Quantum-to-Classical Transition* (Springer, 2007). Not consulted directly; see the next two. https://doi.org/10.1007/978-3-540-35775-9 - M. Schlosshauer, *The quantum-to-classical transition and decoherence* (2014), Table I. https://arxiv.org/abs/1404.2635 -- M. Schlosshauer, *Quantum decoherence*, Phys. Rep. 831, 1 (2019), Table 1 and eqs. 65–70. https://arxiv.org/abs/1911.06282 +- M. Schlosshauer, *Quantum decoherence*, Phys. 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Only the faint central image can. -- **So the test changes shape.** I found no study that tests lensing anomalies against black hole mass or spin. - Only one anomaly lens, SDP.81, has even a bound on its black hole. Masses read off the M–σ relation would only - restate the galaxy's velocity dispersion, which also sets the size of the wave granules. Section 6 gives - testable versions. +- **So the test changes shape.** As of 18 October 2026 I found no study that tests lensing anomalies against the + lens galaxy's black hole mass or spin (section 4). No lens I found has both a small-scale anomaly and a bound on + its black hole. SDP.81 had both until its dark lump was found most likely spurious (Stacey et al. 2025). Masses + read off the M–σ relation would only restate the galaxy's velocity dispersion, which also sets the size of the + wave granules. Section 6 gives testable versions. ## 1. The gravitational atom, step by step @@ -41,7 +42,7 @@ For μ = 10⁻²² eV, λ_c = 2.0×10¹⁵ m, or 0.064 pc. A 10⁸ M☉ black ho | α | 7.5×10⁻⁵ | 7.5×10⁻⁴ | | Spin needed for any growth | above 3×10⁻⁴ | above 3×10⁻³ | | Cloud peak, 4 r_g/α² | 3.4 kpc | 0.34 kpc | -| Bohr speed in the cloud, αc/2 | 11 km/s | 110 km/s | +| n = 2 Bohr speed in the cloud, αc/2 | 11 km/s | 110 km/s | | Growth time (spin 0.99) | 1×10³⁴ years | 1×10²⁶ years | | ... in ages of the universe | 7×10²³ | 7×10¹⁵ | | Velocity dispersion of the host's stars (M–σ) | 150 km/s | 260 km/s | @@ -50,7 +51,7 @@ For μ = 10⁻²² eV, λ_c = 2.0×10¹⁵ m, or 0.064 pc. A 10⁸ M☉ black ho How each row comes out: -- **The window is open.** A cloud grows only while it circles more slowly than the horizon spins (BCP eq. 2.1). +- **The window is open.** A cloud grows only while its pattern turns more slowly than the horizon spins (BCP eq. 2.1). For small α that needs spin above about 4α. With α near 10⁻⁴, almost any spinning black hole qualifies. α sits deep inside the superradiant window. The window is not the problem. - **The size is large because α is small.** The level that grows fastest, |211⟩ (n = 2, one unit of angular @@ -64,7 +65,7 @@ How each row comes out: dominates out to the cloud. It does so only out to GM/σ², the sphere of influence, where σ is the velocity dispersion of the surrounding stars (Kormendy and Ho 2013). Taking σ from their M–σ relation, M = 3.1×10⁸ M☉ (σ / 200 km/s)^4.38 (eq. 7), the sphere of influence is 18 pc for 10⁸ M☉ and 63 pc for 10⁹ M☉: - 5 to 190 times smaller than the would-be cloud. Put another way, the cloud's Bohr speed, 11 to 110 km/s, + 5 to 190 times smaller than the would-be cloud. Put another way, the cloud's n = 2 Bohr speed, 11 to 110 km/s, is below the stars' 150 to 260 km/s. At those radii the galaxy holds the particles: they belong to its wave dark matter core and halo, not to a gravitational atom. @@ -138,44 +139,81 @@ The black hole does not swallow the core either. For a core the black hole domin ## 4. Literature check -Asked: has anyone tested lensing anomalies against the lens galaxy's black hole mass or spin? I found no such -study (web searches covering arXiv, October 2026). The closest work: +Asked: has anyone tested lensing anomalies against the lens galaxy's black hole mass or spin? As of 18 October 2026 +I found no such study. A test here means a study that fits a small-scale anomaly itself (a flux-ratio or +astrometric anomaly, or a detected dark lump) with a model that includes the lens galaxy's own black hole, or +compares such anomalies with that black hole's mass or spin. Models that use the black hole only in the smooth +macro-model or for a central image's flux, as Tamura et al. (2015) and Wong et al. (2015) do for SDP.81, do not +count; the models of SDP.81's lump (Hezaveh et al. 2016; Stacey et al. 2025) do not include its black hole. The +search used the arXiv API, INSPIRE full-text search, citation chasing from this note's sources and web searches; +ADS was not queried. Microlensing and X-ray work on lensed quasars does involve black hole mass and spin, but the +source quasar's, not the lens's: microlensing light curves give accretion disc sizes that scale as M_BH^(0.80±0.17) +(Morgan et al. 2010), and X-ray spectra brightened by lensing give the spin of the quasar in RX J1131−1231, a = +0.87 (Reis et al. 2014). The closest work: - **Oguri and Kubo (2026)**: a soliton whose centre is deepened by a black hole makes a dense, hard-to-strip lump. The 10⁶ M☉ dark lump in JVAS B1938+666 fits a particle of about 4×10⁻²¹ eV with a 4×10⁵ M☉ black hole. That black - hole sits in a small satellite halo, not at the centre of the lens. + hole sits in a small satellite halo, not at the centre of the lens. What every reading of the lump has to explain + is Vegetti et al.'s (2026) measured profile: an unresolved point mass, at most 10 pc in radius, inside an + extended mass of almost constant surface density out to 139 pc, an edge they flag as possibly an artefact of + their model. Oguri and Kubo take the point mass to be the black hole. Other readings need no wave dark matter. + Vegetti et al. note that, if the lump is dark matter, its structure is incompatible with cold dark matter but may + fit a self-interacting halo whose centre has collapsed into a black hole. Zhang and Yu (2026) match instead + Vegetti et al.'s pseudo-Jaffe plus point mass model, which fits less well (Δln E = −30 against the best fit) and + has a 1.9×10⁵ M☉ point mass: with a self-interacting halo deep in collapse, or with the tidally stripped remnant + of a cold dark matter halo hosting a black hole of that mass, the halo having lost about 5 orders of magnitude of + its mass. The two black hole masses, 4×10⁵ and 2×10⁵ M☉, come from different fits to the same data. In Zeng et + al. (2026, a preprint) a black hole seeded by the collapse grows to 5 to 12% of the halo's mass within 2 Gyr and + depletes the inner halo, which matches the lump qualitatively. - **Davies and Mocz (2020)** and **Bar et al. (2019)**: how a black hole squeezes, and may swallow, the core. Bar et al. use Sgr A* and M87* to bound the core's mass. - **Central images** weigh lens-galaxy black holes directly: below 2×10⁸ M☉ in PMN J1632−0033 (Winn, Rusin and Kochanek 2004), above 3×10⁸ M☉ in SDP.81 (Tamura et al. 2015; Wong et al. 2015 find log M ≳ 8.5). The SDP.81 bound trades off against the assumed size of the galaxy's stellar core (Tamura et al. 2015). +- **Two wave dark matter models of the main lens** mention its central black hole, in passing. Chan et al. (2020) + find two small extra critical curves at the edge of a compact, dense core and add, in one sentence, that a black + hole inside a lighter halo's core may make them too; they compute nothing for it. Palencia et al. (2025), whose + cores add a second critical curve near the centre, leave the black hole out: they argue it would add a small + inner critical curve and leave their results effectively unchanged, but call its effect on the core less clear + and defer it. - **Is 10⁻²² eV right at all?** Amruth et al. (2023) and Hou et al. (2026) favour wave dark matter near 10⁻²² eV - from anomalies (Hou et al.: 17 cusp quads, a benchmark of 0.8×10⁻²² eV, and a Bayes factor above 100 against - cold and self-interacting dark matter). - Laroche et al. (2022), with 11 quads, prefer cold dark matter 8 to 1 over 10^−22.5 to 10^−22.25 eV. Powell et al. - (2023) rule out masses up to 4.4×10⁻²¹ eV at 20 to 1 odds from one extended arc. Outside lensing, the Lyman-α - forest gives above 2×10⁻²⁰ eV at 95% (Rogers and Peiris 2021) and ultra-faint dwarf galaxies above 3×10⁻¹⁹ eV at - 99% (Dalal and Kravtsov 2022). If the particle is that heavy, superradiance does work around these black holes - (from 6×10⁻²¹ eV for 10⁹ M☉, 5×10⁻²⁰ eV for 10⁸ M☉), but section 2 shows the clouds are then under 0.1 pc, far - too small for lensing. + from anomalies (Hou et al.: 17 cusp quads, a benchmark of 0.8×10⁻²² eV, and a Bayes factor above 100 against cold + and self-interacting dark matter). For HS 0810+2554, simulated wave halos at 10⁻²² eV match each radio quad to + about 3 mas (a 3σ miss) in the best of 1000 realizations, each optimised over orientation and source position, + against 12 mas for the best-fit smooth NFW model; matching all eight images at once would combine different + realizations (Zhou et al. 2026). Cold dark matter with multipoles of 0.4 to 0.9% also fits the positions: at χ = + 1.6 if the images arrive in an order the authors call unlikely, and at χ = 3.0, which they still call adequate, + in the usual order but with two images assigned to the other source (Miller and Williams 2025). So do cold dark + matter subhalos, in the best of 1000 realizations at the best-fitting host mass (Gong et al. 2026, a preprint). + None of these models includes a black hole. Laroche et al. (2022), with 11 quads, prefer cold dark matter 8 to 1 + over 10^−22.5 to 10^−22.25 eV. Powell et al. (2023) rule out masses up to 4.4×10⁻²¹ eV at 20 to 1 odds from one + extended arc. Outside lensing, the Lyman-α forest gives above 2×10⁻²⁰ eV at 95% (Rogers and Peiris 2021) and + ultra-faint dwarf galaxies above 3×10⁻¹⁹ eV at 99% (Dalal and Kravtsov 2022). If the particle is that heavy, + superradiance does work around these black holes (from 6×10⁻²¹ eV for 10⁹ M☉, 5×10⁻²⁰ eV for 10⁸ M☉), but section + 2 shows the clouds are then under 0.1 pc, far too small for lensing. ## 5. Lens systems: anomalies and black hole masses | System | Anomaly measurement | Wave dark matter analysis | Lens galaxy's black hole | |---|---|---|---| -| HS 0810+2554 | Radio jets with VLBI (Hartley et al. 2019); narrow-line fluxes (Nierenberg et al. 2020) | Amruth et al. 2023: reproduced at ~10⁻²² eV | Not measured. M–σ estimate ~6×10⁸ M☉ (section 3) | -| SDP.81 | A 10^(8.96±0.12) M☉ dark lump at 6.9σ (Hezaveh et al. 2016) | None found | Above 3×10⁸ M☉ from the missing central image (Tamura et al. 2015; Wong et al. 2015) | +| HS 0810+2554 | Radio jets with VLBI (Hartley et al. 2019); narrow-line fluxes (Nierenberg et al. 2020) | Amruth et al. 2023 and Zhou et al. 2026: reproduced at ~10⁻²² eV; cold dark matter also fits (section 4) | Not measured. M–σ estimate ~6×10⁸ M☉ (section 3) | +| SDP.81 | A 10^(8.96±0.12) M☉ dark lump at 6.9σ (Hezaveh et al. 2016), most likely spurious: poorly fitted multipoles (Stacey et al. 2025) | None found | Above 3×10⁸ M☉ from the missing central image (Tamura et al. 2015; Wong et al. 2015) | | PMN J1632−0033 | None found | None found | Below 2×10⁸ M☉ from the central image (Winn, Rusin and Kochanek 2004) | -| JVAS B1938+666 | A 10⁶ M☉ dark lump at 26σ (Powell et al. 2025, as cited by Oguri and Kubo) | Oguri and Kubo 2026: soliton plus a 4×10⁵ M☉ black hole inside the lump | Not measured | +| JVAS B1938+666 | A 10⁶ M☉ dark lump at 26σ (Powell et al. 2025) | Oguri and Kubo 2026: soliton plus a 4×10⁵ M☉ black hole inside the lump; self-interacting and cold dark matter readings too (section 4) | Not measured | | MG J0751+2716 | Extended arc at milliarcsecond resolution | Powell et al. 2023: up to 4.4×10⁻²¹ eV ruled out | Not measured | | B1422+231, HE0435−1223, WGD J0405−3308, RX J0911+0551, PS J1606−2333, WFI 2026−4536, WFI 2033−4723, WGD 2038−4008 | Narrow-line fluxes, as compiled by Gilman et al. 2020 | Laroche et al. 2022 bound the particle mass with an 11-quad sample of this kind | Not measured | | 17 cusp quads, e.g. J1042+1641 | Microlensing-free fluxes, many from JWST | Hou et al. 2026: FDM preferred | Not measured | -SDP.81 is the only system I found with both a small-scale anomaly and a lensing bound on its black hole. "Not -measured" means I found no direct measurement, and none is expected: at these redshifts a black hole's sphere of -influence (18 to 63 pc) spans 2 to 14 milliarcseconds, well inside the 36 milliarcsecond core of the Hubble image -blur that a stellar-dynamical mass must resolve (Kormendy and Ho 2013). Lensing central images are the only route. -I found no spin measurement for any lens galaxy's black hole. +No system I found has both a small-scale anomaly and a bound on its black hole. SDP.81 had both until its dark lump +was found most likely spurious (Stacey et al. 2025). "Not measured" means I found no direct measurement, and none +is expected from stars alone: at these redshifts a black hole's sphere of influence (18 to 63 pc) spans 2 to 14 +milliarcseconds, well inside the 36 milliarcsecond core of the Hubble image blur that a stellar-dynamical mass must +resolve (Kormendy and Ho 2013). Lensing does better. Central images have so far given bounds (the table above); +lensed images near the centre have measured two black holes, of (3.3 ± 2.1)×10¹⁰ M☉ (3σ range) in Abell 1201 at z = +0.17 (Nightingale et al. 2023; one model without a black hole fits comparably, which the authors argue is +unphysical) and 3.6×10¹⁰ M☉ in the Cosmic Horseshoe at z = 0.44, with stellar kinematics (Melo-Carneiro et al. +2025): both about 10¹⁰ M☉, ten times or more heavier than those in section 1. Neither is among the anomaly lenses +above. I found no spin measurement for any lens galaxy's black hole. ## 6. How the question changes shape @@ -185,18 +223,21 @@ I found no spin measurement for any lens galaxy's black hole. nothing. With black hole masses taken from M–σ, testing "anomaly against black hole" is testing "anomaly against σ". A fair test needs masses measured independently of σ, compared at fixed σ. No anomaly lens has one today. 3. **Testable versions.** - - **Central images.** A core squeezed by a black hole of given mass predicts a definite central image. SDP.81 and - PMN J1632−0033 show deep radio and submillimetre imaging can find or bound it. Doing this in quads with + - **Central images.** A core squeezed by a black hole of given mass predicts a definite central image. SDP.81 + and PMN J1632−0033 show deep radio and submillimetre imaging can find or bound it, but SDP.81's small-scale + anomaly is now disputed and none has been reported for PMN J1632−0033 (section 5). Doing this in quads with anomaly data would weigh the black hole and the core in the same lens. - **Lumps with their own black hole.** Oguri and Kubo's reading of JVAS B1938+666 predicts a point mass inside - some dark lumps. Gravitational imaging can test that lump by lump. + some dark lumps. Gravitational imaging can test that lump by lump. A point mass alone does not single out + wave dark matter: the best model of the B1938+666 lump has one (Vegetti et al. 2026), and the self-interacting + and cold dark matter readings in section 4 can hold a black hole too. - **The particle mass.** Anomaly fits and black hole spins constrain the same particle through different objects: lensing through kiloparsec halos, spins through sub-parsec clouds. At 10⁻²² eV only lensing can speak. From a few times 10⁻²¹ eV up both can, and M87*'s spin already excludes 2.9 to 4.6×10⁻²¹ eV. ## The model -`gravAtom(M, muEV, spin)` in `witness-map/model.js` returns α, the |211⟩ cloud size, its Bohr speed, whether it +`gravAtom(M, muEV, spin)` in `witness-map/model.js` returns α, the |211⟩ cloud size, its n = 2 Bohr speed, whether it is inside the superradiant window, and its growth time. `npm test` checks it against published numbers: | Check | Published | Model | @@ -210,7 +251,7 @@ Two more checks guard this note's main claims: the 10⁻²² eV clouds above tak grow, and no cloud that grows within that time around 10⁸ to 10⁹ M☉ peaks beyond 1 pc. 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