# Define tully fisher relationship

### [] The HI Tully-Fisher Relation of Early-Type Galaxies

We explore the Tully-Fisher relation over five decades in stellar mass in with Vc less, similar90 km s-1 fall below the relation defined by brighter galaxies. This equation became known as the Tully-Fisher relation. slope and the galaxies with independently known distances define the zero point. The Tully-Fisher relation is an empirical relationship between the it is important to define the local locus of that relation in the best way.

This sample is unique in that membership is simply defined by the overlap of blind cm, optical and near-infrared catalogues, rather than pre-selecting candidate Tully—Fisher galaxies for which to obtain rotational measurements. Three fundamental questions are considered: Third parameter dependencies are tested by correlating offsets from the derived B- and K-band relations with candidate observed and intrinsic variables.

A strong dependence is found on purely observational parameters such as galaxy inclination and size. Large-scale galaxy flows are also found to increase observed scatter. Correlations of Tully—Fisher offset with physical properties are found to be strongly dependent on the fitted slope of relation, indicating that if real, these dependencies are weak and largely act in parallel to the observed relations.

However, a potential dependence is observed on stellar population as measured by B-R colour and star formation rate measured by far-infrared luminosity. The intrinsic scatter and slope of the Tully—Fisher relation are measured by applying galaxy selection cuts to minimize observational errors. For the B-band relation, a slope of 3. Including the observed H i masses to calculate baryonic relations, a slope of 3.

However, a consensus on the physical basis of the Tully—Fisher relation is yet to be reached. Possible physical origins of the Tully—Fisher relation include cosmological initial conditions e.

One of the difficulties in understanding the Tully—Fisher relation is to account for the large-scale uniformity of galaxy luminosity given the known dependence of star formation on local processes. In particular, time-averaged star formation in galaxies seems to depend on parameters such as gas surface density and velocity dispersion, stellar initial mass function and metallicity kennicutt ; Elmegreen ; Larson The question of why the Tully—Fisher relation exists and is so tight, can thus be rephrased as why star formation is so accurately described by the large-scale properties of a galaxy, and in particular, its rotational velocity?

## The Baryonic Tully-Fisher Relation.

The data set for this study of the Tully—Fisher relation avoids traditional biases that affect many existing samples. Rather, global H i profiles are already available for galaxies selected purely on their H i content.

In particular, this study focuses on the central issues of Tully—Fisher slope and scatter.

The large sample enables detailed subsampling of galaxies, looking at the properties of the Tully—Fisher relation as a function of parameters such as Hubble type, wavelength and environment.

The all-sky data taken with consistent instrumentation avoids the need to make corrections for data observed with different telescopes and different methods, removing resulting scatter. Section 2 describes the data used in this study and the cross-correlation of catalogues. The derivation of Tully—Fisher parameters is then discussed in Section 3 and the selection of basic observables in Section 4.

Recipes convert luminosity into the mass in stars, then the sum of this mass and the mass observed in cold gas gives a parameter called the "baryonic mass". In plots of baryonic mass vs. The slope of the Tully-Fisher relation depends on passband, steepening from the blue toward the infrared. Details depend on how luminosities and the rotation parameter are defined and how the regression that gives the slope is carried out.

Attempts to reduce scatter with added parameters have been unconvincing. There is weak evidence for a surface brightness dependency. The Faber-Jackson relation has a somewhat larger scatter but in this case surface brightness as a third parameter significantly improves the correlation.

The result is a formulation called the "fundamental plane" [5,6]. It is interesting that the fundamental plane transforms considerably more closely into the virial theorem than the Tully-Fisher relation. Distance Measurements In the s the situation regarding the extragalactic distance scale was in a sorry state.

There was a debate over the value of this constant at the level of a factor two. At its core was a critical issue.

### The Tully-Fisher relation in spirals

The standard cosmological model at the time held that the primary constituents of the universe were particles of matter that had been acting since the Big Bang to slow the cosmic expansion.

The "theory of inflation" anticipated that the density of matter amounted to the "critical value" required to give a flat topology. This model implies a specific link between the age of the universe and the expansion scale. The age of the universe was reasonably constrained by the age-dating of stellar populations in globular clusters.

The theoretically preferred model required that the Hubble constant be at the very lowest of the range being seriously discussed at the end of the 20th Century.

Other methodologies emerged, such as the use of the bright end cutoff in the luminosities of planetary nebulae [9] and "surface brightness fluctuations " caused by the distribution of the brightest stars in galaxies dominated by old populations [10]. A paradigm shift came with the evidence from observations of supernovae of type Ia that the universe appears to be accelerating [11,12].

## Tully–Fisher relation

It seems that a repulsive dark energy is dynamically dominant. The relationship between ages and expansion rate is altered. New methods to measure distance become available. The use of supernovae is particularly accurate. If the brightest red giant branch stars are resolved in the image of a galaxy, the known luminosities of these stars gives a good distance [13].

However each of the various methods has a weakness: There is still an important role for the Tully-Fisher relation. It is no longer the most accurate method on a single case basis but since the application is to normal disk systems, with little restriction in range, it enables the determination of distances to many thousands of galaxies in all the environments that galaxies are found [14,15].

Independent of the value of the Hubble Constant, the Tully-Fisher relation can be used to measure peculiar velocities, motions of galaxies that are deviations from the linear Hubble expansion.

### The Local Tully-Fisher Relation

These motions are thought to be due to the gravitational influence of over- and under-densities of matter. There is an extensive literature discussing the relationship between the peculiar velocities of galaxies measured via the Tully-Fisher relation and the large-scale distribution of galaxies. Constraints on Galaxy Evolution The other uses of the Tully-Fisher relation derive from the constraints imposed on ideas of galaxy formation.

Although the general correlation between luminosity and rotation rate was anticipated, it was a surprise to find it to be so tight, with so little spread caused by additional parameters. The dependence need not have been a power law. What defines the slope?