Methods: ISL Reproducibility & Fit Verification

by

Subject: Quantitative verification of the NGC 3198 rotation curve fit.

1. Dataset Selection

The fit utilizes data from the SPARC (Spitzer Photometry & Accurate Rotation Curves) database and Begeman (1989).

  • Target: NGC 3198 (Spiral Galaxy)
  • Input Data: Radial distance (kpc), Observed circular velocity V_{obs} (km/s), Stellar disk component V_{disk} (M/L=1), and Gas component V_{gas}.

2. Model Functional Form

The ISL gravity model assumes an effective gravitational coupling that runs linearly with distance:

V_{model}^2(r) = \left[ \Upsilon_* V_{disk}^2(r) + V_{gas}^2(r) \right] \cdot \left( 1 + \frac{r}{r_{mod}} \right)

Where:

  • \Upsilon_* is the stellar mass-to-light ratio (free parameter).
  • r_{mod} is the Universal Modularity Radius (free parameter).

3. Optimization Parameters

  • Algorithm: Grid search / Least Squares minimization.
  • Stellar M/L Range: [0.5, 1.5]
  • Modularity Radius Range: [5.0 kpc, 50.0 kpc]

4. Best Fit Results

  • Stellar M/L: 0.847
  • r_{mod}: 13.27 kpc
  • Reduced \chi^2 (9 points, 2 DOF free): 0.999

5. Raw Data Package

The complete residuals and prediction table is available in [NGC3198_REPRODUCIBILITY.json](./reports/NGC3198_REPRODUCIBILITY.json).

| Radius (kpc) | V_{obs} | V_{pred} | Residual | Error |
|————–|———–|———–|———-|——-|
| 2.0 | 62.2 | 56.63 | 5.57 | 5.0 |
| 4.0 | 115.7 | 108.80 | 6.90 | 5.0 |
| 8.0 | 144.8 | 152.24 | -7.44 | 5.0 |
| 12.0 | 152.8 | 157.14 | -4.34 | 5.0 |
| 16.0 | 155.1 | 156.60 | -1.50 | 5.0 |
| 20.0 | 156.9 | 154.87 | 2.03 | 5.0 |
| 24.0 | 157.0 | 154.03 | 2.97 | 5.0 |
| 28.0 | 155.0 | 155.31 | -0.31 | 5.0 |
| 30.0 | 154.0 | 156.57 | -2.57 | 5.0 |

Verification Verdict: The fit accurately captures the kinematic plateau beyond 10 kpc, where Newtonian dynamics typically fail.

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