Tullyfisher RelationEdit

The Tully-Fisher relation is a foundational empirical link in extragalactic astronomy that connects how bright a spiral galaxy is with how fast it rotates. Described in 1977 by R. Brent Tully and J. Richard Fisher, this relation quickly became a cornerstone for measuring distances in the local universe and for testing ideas about how galaxies form and sit inside their surrounding dark matter halos. In its standard form, brighter galaxies tend to have higher rotation speeds, a correlation that has proven remarkably robust across a wide range of spiral and irregular systems, especially when the rotation velocity is inferred from the width of the neutral hydrogen line at 21 cm or from detailed optical rotation curves. The Tully-Fisher relation is a practical tool, but it also encodes deep physical connections between luminous matter, dark matter, and the dynamics of disk galaxies.

## History and formulation - The original observation linked absolute luminosity to a measure of rotational speed, establishing a tight, nearly power-law relation between the two quantities. The empirical formula is often written as L ∝ V^α, where L is a galaxy’s luminosity and V is a characteristic rotation velocity. The precise slope α depends on the wavelength band used and on the sample selection. - Early calibrations relied on galaxies with independently determined distances, such as those anchored by standard candles like Cepheid variables or other distance indicators, to fix the zero point of the relation. This made the Tully-Fisher relation a practical rung on the distance ladder for estimating distances to farther systems. - The physical interpretation rests on the coupling between the baryonic components (stars and gas) and the dark matter halos that set the gravitational potential. A simple intuition is that more massive disks, with more rapid rotation, shine more brightly, though the mass-to-light ratio, gas fraction, and halo structure all add complexity to the full picture. - In practice, observers measure V using the width of the 21 cm line from neutral hydrogen or by constructing an optical rotation curve from emission lines such as Hα. Corrections for inclination, extinction, and bandpass are important, and the scatter of the relation reflects both intrinsic variations and measurement/systematic uncertainties.

## Observational form and calibrations - Band dependence: the relation is tighter in the near-infrared, where dust extinction and the mass-to-light ratio are more stable, than in bluer bands. This makes the infrared Tully-Fisher relation a preferred tool for distance work in many surveys. - Rotation velocity: V is typically derived from the HI line width or from detailed velocity profiles of ionized gas in the disk. Properly accounting for projection effects (inclination) is essential to avoid biases. - Scatter and systematics: while the relation is tight, there is always some intrinsic scatter, influenced by factors such as the galaxy’s morphology, star formation history, gas content, and environment. Selection biases—such as preferentially including brighter or more easily measurable galaxies—can skew the inferred slope and zero point if not carefully controlled. - Applications to the distance ladder: by calibrating the zero point with galaxies at known distances, the Tully-Fisher relation provides distance estimates to external galaxies and informs measurements of the local peculiar velocity field and, more broadly, the Hubble constant.

## Applications and significance - Distance measurements: the relation remains a workhorse for estimating distances to spiral galaxies beyond the reach of primary distance indicators, complementing other methods on the cosmic distance ladder. - Tests of galaxy formation: the persistence of the Tully-Fisher relation across cosmic time offers a constraint on models of disk formation within dark matter halos and on how baryons settle into rotating disks. - Cosmological context: in the standard cosmological framework, the relation reflects baryon-to-halo connections and the physics of angular momentum acquisition during halo formation. It has been a touchstone for simulations and semi-analytic models of galaxy formation. - Baryonic comparisons: a variant known as the baryonic Tully-Fisher relation links total baryonic mass (stars plus gas) to rotation velocity, often reducing scatter and offering insights into the role of gas-rich systems in the relation.

## The baryonic Tully-Fisher relation - In some studies, replacing luminosity with total baryonic mass M_b (the sum of stellar mass and gas mass) tightens the correlation with rotation velocity. This formulation highlights a more direct link between the dynamics of the disk and the total normal matter it harbors. - Gas mass, particularly in late-type and irregular galaxies, contributes significantly to M_b, making the baryonic version especially relevant for understanding the role of gas in the mass budget of star-forming systems. - The baryonic relation is often discussed in tandem with stellar mass estimates and measurements of gas mass in galaxies, including their neutral hydrogen content and molecular gas when available.

## Controversies and debates - Dark matter versus alternative theories: in the standard view, the Tully-Fisher relation emerges from the coupling between baryons and their surrounding dark matter halos within the framework of ΛCDM cosmology. Proponents of alternative gravity theories, such as Modified Newtonian Dynamics, have emphasized the strong predictive power of the Tully-Fisher relation (and the related baryonic form) in describing rotation curves without invoking dark matter. Supporters of the mainstream cosmology counter that while MOND can explain certain rotation-curve phenomena, it faces challenges at larger scales, galaxy clusters, and in literature on gravitational lensing and cosmic structure formation. The ongoing dialogue reflects a broader tension between simulating complex baryonic physics in a dark-matter framework and seeking simpler, testable alternatives to gravity. - Universality and evolution: while the Tully-Fisher relation is robust for nearby galaxies, questions persist about its universality across redshift and environment. At higher lookback times, galaxies undergo structural and dynamical changes, and the slope and zero point can evolve—an area of active observational and theoretical work that tests models of galaxy formation and merger histories. - Systematics and biases: critics point to potential biases from inclination corrections, selection effects, and internal extinction corrections, as well as uncertainties in distance anchors. Supporters stress that careful calibrations, multi-wavelength data, and consistent methodologies mitigate many of these concerns, preserving the reliability of the relation as a distance indicator and a physical link.

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Tullyfisher RelationEdit

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