Restoration of the Tully-Fisher Relation by Statistical Rectification
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916135051460608 |
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| author | Fu, Hai |
| author_facet | Fu, Hai |
| contents | 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 $-16 > M_i > -22$: $M_i = M_0 - 2.5β\ [\log(W_{\rm 20}/250 {\rm km/s})]$, with $M_0 = -19.77\pm0.04$ and $β= 4.39\pm0.06$. 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: $σ(\log W_{20}) \approx 0.06$ dex between $-17 > M_i > -23$, while $σ(M_i)$ decreases from $\sim$0.8 in slow rotators to $\sim$0.4 in fast rotators. The statistical rectification method holds significant potential, especially in the studies of intermediate-to-high-redshift samples, where limited spatial resolution hinders precise measurements of inclination angles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13738 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restoration of the Tully-Fisher Relation by Statistical Rectification Fu, Hai Astrophysics of Galaxies Instrumentation and Methods for Astrophysics I employ the Lucy rectification algorithm to recover the inclination-corrected distribution of local disk galaxies in the plane of absolute magnitude ($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 $-16 > M_i > -22$: $M_i = M_0 - 2.5β\ [\log(W_{\rm 20}/250 {\rm km/s})]$, with $M_0 = -19.77\pm0.04$ and $β= 4.39\pm0.06$. 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: $σ(\log W_{20}) \approx 0.06$ 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. |
| title | Restoration of the Tully-Fisher Relation by Statistical Rectification |
| topic | Astrophysics of Galaxies Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2401.13738 |