I treated the 15 power columns as the merged spectra. For each, I fit the dominant peak near 1.33 eV with a Lorentzian plus a linear local baseline. “Intensity” is the fitted Lorentzian amplitude above that baseline. The allometric fits use \(y=aP^b\), fitted by linear regression in log space; uncertainties are 1σ standard errors.

| Power (µW) | Peak intensity (counts) | \(x_c\) (eV) |
|---:|---:|---:|
| 5 | 140.5 | 1.31624 |
| 10 | 242.4 | 1.32183 |
| 15 | 346.9 | 1.32407 |
| 20 | 440.6 | 1.32591 |
| 25 | 537.6 | 1.32720 |
| 30 | 646.8 | 1.32818 |
| 35 | 721.4 | 1.32885 |
| 40 | 850.5 | 1.33023 |
| 45 | 918.4 | 1.33044 |
| 50 | 1023.1 | 1.33156 |
| 60 | 1232.2 | 1.33207 |
| 70 | 1443.3 | 1.33350 |
| 80 | 1641.2 | 1.33363 |
| 90 | 1879.7 | 1.33432 |
| 100 | 2162.2 | 1.33496 |

The intensity fit gives \(b=0.9126\pm0.0140\) (\(R^2_{\log}=0.9969\)). The peak-position fit gives \(b=0.004573\pm0.000101\) (\(R^2_{\log}=0.9937\)).

- [Peak intensity vs power plot](peak_intensity_vs_power.png)
- [Peak position vs power plot](peak_position_vs_power.png)
- [Per-power fit results CSV](lorentzian_peak_results.csv)
- [Allometric fit summary](allometric_fit_summary.txt)

RESULT: b = 0.9126 ± 0.0140