================================================================================ GALAXY SPIRAL ARM PITCH ANGLE EVOLUTION WITH REDSHIFT ================================================================================ Compiled: 2026-03-18 Purpose: Quantitative data on how pitch angles change with cosmic time. For testing the dimensional curve regression hypothesis. Sources: Reshetnikov+2023, Marchuk+2025, published high-z measurements ================================================================================ I. THE LINEAR REGRESSION (Reshetnikov & Marchuk 2023, A&A 680, L14) ================================================================================ Sample: 171 face-on spirals, 359 arms, HST COSMOS field, z = 0 to ~1 Massive galaxies (log M*/Msun >= 10.5, 214 arms): ψ(degrees) = (8.2 ± 2.6) × z + (12.4 ± 1.5) Rate: ~1 degree per Gyr at z <= 1 Significance: >95% confidence Binned predictions from regression: z = 0.00 → ψ = 12.4° (lookback 0 Gyr) z = 0.25 → ψ = 14.5° (lookback 3.0 Gyr) z = 0.50 → ψ = 16.5° (lookback 5.1 Gyr) z = 0.75 → ψ = 18.6° (lookback 6.7 Gyr) z = 1.00 → ψ = 20.6° (lookback 7.9 Gyr) II. JWST EXTENSION TO z ~ 3 (Marchuk+ 2025, PASA) ================================================================================ Sample: 159 galaxies (126 HST + 33 JWST), z = 0.10 to 3.30 Overall mean: 16.0 ± 5.7° Rate: ~0.5 deg/Gyr (all spirals), ~0.7 deg/Gyr (two-armed) CONFIRMS: pitch angles INCREASE with redshift (more open at earlier epochs) III. HIGH-REDSHIFT INDIVIDUAL MEASUREMENTS ================================================================================ Galaxy z ψ (°) Source ──────────────── ────── ───────────────── ────────────────────────── BRI 1335-0417 4.41 26.7 (+4.1/-1.6) Tsukui & Iguchi 2021 (ALMA) A2744-DSG-z3 3.06 34 ± 13 Fudamoto+ 2022 (JWST+ALMA) A1689B11 2.54 37 ± 2 Yuan+ 2017 (lensed, Gemini) Q2343-BX442 2.18 37 ± 6 Law+ 2012 (HST) These EXCEED the Reshetnikov linear regression extrapolation. The relation may steepen or follow a different form beyond z ~ 1. IV. THE COMPOSITE CURVE — PITCH ANGLE vs REDSHIFT ================================================================================ z Lookback ψ (°) Source ─────── ────────── ───────── ────────────────────────── 0.00 0.0 Gyr 12-15 Local surveys, Galaxy Zoo 0.25 3.0 Gyr 14-15 Reshetnikov regression 0.50 5.1 Gyr 16-17 Reshetnikov regression 0.75 6.7 Gyr 18-19 Reshetnikov regression 1.00 7.9 Gyr 20-21 Reshetnikov regression 2.18 10.7 Gyr ~37 Q2343-BX442 (individual) 2.54 11.1 Gyr ~37 A1689B11 (individual) 3.06 11.5 Gyr ~34 A2744-DSG-z3 (individual) 4.41 12.4 Gyr ~27 BRI 1335-0417 (individual) NOTE: The z > 2 points are individual galaxies, not statistical samples. The z = 4.41 point (~27°) is LOWER than the z ~ 2-3 points (~34-37°), suggesting the relation may PEAK and then decline at very high z. V. WINDING RATE — TWO TIMESCALES ================================================================================ FAST (kinematic winding of individual arms): One arm winds from 40° to 10° in ~250 Myr (one orbital period). This is why arms must be REPEATEDLY DESTROYED AND REFORMED. SLOW (cosmological evolution of the population): The MEAN pitch angle changes by ~1°/Gyr (Reshetnikov 2023). This reflects changes in galaxy STRUCTURAL PROPERTIES over time (mass growth, bulge formation, disk cooling) that set the INITIAL CONDITIONS for each new generation of transient arms. The slow trend is what we can compare to the dimensional curve. VI. TLT-RELEVANT OBSERVATIONS ================================================================================ 1. At z = 0.75 (lookback 6.7 Gyr), the mean is ~18.6°. 5/3 spiral pitch = 18.01°. This is within the uncertainty. 2. The relation ψ = 8.2z + 12.4 predicts: ψ = 18.0° at z = 0.68 (lookback ~6.2 Gyr) This is where the 5/3 ratio sits on the regression line. 3. The z > 2 points (34-37°) are MUCH higher than the regression. If the dimensional curve peaks at d=4 and descends, the pitch angle curve may also peak at some z and descend — but the current data is too sparse at high z to confirm this. 4. The z = 4.41 point (27°) being LOWER than z = 2-3 (34-37°) is suggestive of a peak-and-descent, but this is a single galaxy and could be an outlier. VII. THEORETICAL MODELS ================================================================================ Density wave theory: pitch angle CONSTANT in time (no evolution). → CONTRADICTED by the Reshetnikov data (evolution detected at >95%). Transient spiral theory: cot(ψ) ∝ t (arms wind, reform, wind again). → SUPPORTED by cot(ψ) distribution tests (Lingard+ 2021). → The cosmological evolution reflects changing initial conditions. TLT (if applicable): the pitch angle traces the dimensional curve. → The slow cosmological evolution (1°/Gyr) reflects the geometry. → The fast kinematic winding (individual arm lifecycle) reflects f+A|t. → The two timescales correspond to two different aspects of the theory. ================================================================================ REFERENCES ================================================================================ Reshetnikov & Marchuk 2023, A&A 680, L14 (arXiv:2311.16915) Marchuk, Chugunov, Mosenkov 2025, PASA (arXiv:2501.11670) Pringle & Dobbs 2019, MNRAS 490, 1470 Masters et al. 2019, MNRAS 487, 1808 Lingard et al. 2021, MNRAS 504, 3364 Law et al. 2012, Nature (Q2343-BX442 at z=2.18) Tsukui & Iguchi 2021 (BRI 1335-0417 at z=4.41) Yuan et al. 2017 (A1689B11 at z=2.54) Grand, Kawata & Cropper 2013, A&A 553, A77 ================================================================================ DATA SHOWS WHAT IT SHOWS. ================================================================================