This is a condensed summary of key ideas discussed in Cedric Champeau’s blog post of the same name, found at https://melix.github.io/blog/, and where further detailed information on this subject can be found.
1. The Core Idea
The Solar differential rotation means the Sun spins faster at the equator (~25 days) than near the poles (~35 days). This behaviour is fundamental to solar magnetism and the solar cycle.
2. How It’s Measured
The method relies on the Doppler effect:
- Light shifts blue when approaching, red when receding
- The Sun’s شرق (east) limb moves toward us, west limb away
- Measuring wavelength differences between these limbs gives rotation speed
Importantly, Earth’s motion cancels out because it shifts the entire spectrum equally.
3. Key Innovation in JSol’Ex
Despite very small shifts (~0.04 Å), JSol’Ex achieves sub-pixel precision using:
- Spectral line fitting (Voigt profiles)
- Differential measurements (East vs West), which cancel systematic errors
- Multiple sampling points to reduce noise
4. Measurement Method (Simplified)
For each latitude:
- Select matching points on East and West limbs
- Measure spectral line position
- Compute difference → gives velocity
Then:
- Correct for viewing geometry
- Convert to true rotation speed
5. Why It Works
Absolute wavelength measurements are impossible due to optical distortions (“smile” effect), but JSol’Ex:
- Models this distortion with a polynomial
- Measures deviations from it, isolating Doppler shifts
This enables detection of tiny velocity signals (~2 km/s).
6. Data Processing
Two-stage refinement:
- Longitude averaging → removes outliers
- Latitude smoothing → enforces physically smooth rotation curve
7. Results
- Rotation profile matches expected trend: fast equator, slow poles
- Typical equatorial speed ≈ 2 km/s
- Results vary depending on spectral line (e.g. H-alpha vs Fe I)
Differences likely arise from:
- Formation height in solar atmosphere
- Seeing conditions
- Line properties
- Instrumental/systematic effects
8. Practical Considerations
Best results require:
- Excellent seeing
- High spectral resolution
- Strong, well-defined absorption lines
Avoid:
- Very broad lines (e.g. Ca II K)
9. Critical Insight: Scan Direction Matters
- RA scanning (East–West) → preserves Doppler signal ✔️
- DEC scanning (North–South) → suppresses it ❌
Thus, RA scanning is essential for rotation measurements.
10. Bottom Line
JSol’Ex makes it possible for amateurs to measure solar differential rotation using spectroheliograph data by:
- Leveraging Doppler shifts
- Using differential comparisons
- Applying precise spectral fitting
It’s a powerful but experimental technique—accurate enough for exploration, but not yet a substitute for professional measurements.