Restoration of the Tully-Fisher Relation by Statistical Rectification

Hai Fu

doi:10.3847/2041-8213/ad2856

paper

Restoration of the Tully-Fisher Relation by Statistical Rectification

arXiv:2401.13738 · doi:10.3847/2041-8213/ad2856

Abstract

I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude ( $M_{i}$ ) and HI velocity width ( $W_{20}$ ). 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 $- 16 > M_{i} > - 22$ : $M_{i} = M_{0} - 2.5 β [lo g (W_{20} /250 km/s)]$ , with $M_{0} = - 19.77 \pm 0.04$ and $β = 4.39 \pm 0.06$ . At the brighter end ( $M_{i} < - 22$ ), the slope of the correlation decreases to $β \approx 3.3$ , confirming previous results. Because the method accounts for measurement errors, the intrinsic dispersion of the correlation is directly measured: $σ (lo g W_{20}) \approx 0.06$ dex between $- 17 > M_{i} > - 23$ , while $σ (M_{i})$ decreases from $\sim$ 0.8 in slow rotators to $\sim$ 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.

ApJ Letters accepted. Python notebook and data files are available at https://github.com/fuhaiastro/TFR_Lucy

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Cited by in corpus (1)

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