Tully-Fisher Relation Estimator
Tully-Fisher Estimator calculates galaxy magnitude, luminosity from rotation speed, plots data.
Tully-Fisher Relation Overview
The Tully-Fisher relation estimates a spiral galaxy’s absolute magnitude from its rotational velocity:
Absolute Magnitude:
\\[ M = a \log_{10} v_{\text{rot}} + b \\]Luminosity:
\\[ L = L_\odot \cdot 10^{-0.4 (M – M_\odot)} \\]Where:
- \\(M\\): Absolute magnitude in B-band
- \\(v_{\text{rot}}\\): Rotational velocity (km/s)
- \\(a, b\\): Coefficients (e.g., for Sb: \\(a = -7.5\\), \\(b = -3.5\\))
- \\(L\\): Luminosity (solar units, \\(L_\odot\\))
- \\(M_\odot\\): Solar absolute magnitude in B-band (\\(\approx 5.48\\))
Example Calculation
Example: Sb galaxy, \\(v_{\text{rot}} = 200 \, \text{km/s}\\)
\\[
M = -7.5 \cdot \log_{10} 200 – 3.5 \approx -19.36
\\]
\\[
L = 10^{-0.4 (-19.36 – 5.48)} \approx 9.12 \times 10^9 \, L_\odot
\\]