Papers › Restoration of the Tully-Fisher Relation by Statistical Rectification
Restoration of the Tully-Fisher Relation by Statistical Rectification
Hai Fu
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I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude (Mᵢ) and HI velocity width (W₂₀). By considering the inclination angle as a random variable with a known probability distribution, the novel approach eliminates one major source of uncertainty in studies of the Tully-Fisher relation: inclination angle estimation from axial ratio. Leveraging the statistical strength derived from the entire sample of 28,264 HI-selected disk galaxies at z < 0.06 from the Arecibo Legacy Fast ALFA (ALFALFA) survey, I show that the restored distribution follows a sharp correlation that is approximately a power law between -16 > Mᵢ > -22: Mᵢ = M₀ - 2.5β [log(W₂₀/250 km/s)], with M₀ = -19.77±0.04 and β= 4.39±0.06. At the brighter end (Mᵢ < -22), the slope of the correlation decreases to β≈3.3, confirming previous results. Because the method accounts for measurement errors, the intrinsic dispersion of the correlation is directly measured: σ(logW₂₀) ≈0.06 dex between -17 > Mᵢ > -23, while σ(Mᵢ) decreases from ∼0.8 in slow rotators to ∼0.4 in fast rotators. The statistical rectification method holds significant potential, especially in the studies of intermediate-to-high-redshift samples, where limited spatial resolution hinders precise measurements of inclination angles.
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