# What is the tully fisher relationship and how it used to measure distances

### [] Derivation of Distances with the Tully-Fisher Relation: The Antlia Cluster

Independent of the value of the Hubble Constant, the Tully-Fisher relation can be used to measure peculiar velocities. It is used to derive galaxy distances in the interval 7 to Mpc. are luminous objects still available for distance measurement purposes. With the Tully Fisher relation, the inclination angle is determined the angle to the rotational velocity because the measure is based on our line.

The amplitude of the linewidth is approximately twice the maximum rotation velocity since the linewidth includes components of the motion toward and away from the viewer.

The small symbols of various shapes and colors represent galaxies drawn from 5 separate clusters of galaxies and the large open symbols represent nearby galaxies with accurate independently known distances. The straight line is a regression to the data with errors in linewidth. The 5 cluster sample defines the slope and the galaxies with independently known distances define the zero point.

The Tully-Fisher relation Here are some of the properties of the relationship. The scatter diminishes toward near-infrared passbands.

It may slightly degrade at passbands beyond 1 micron although that may only be a consequence of competition from airglow, reducing the accuracy of the galaxy photometry.

The relationship holds for disk dominated systems. It seriously breaks down for S0 types, with greatly increased scatter and a zero point offset. A few percent of disk systems are strongly deviant, especially those affected by strong starbursts or mergers.

Observational uncertainties enter into measurements of apparent luminosity, including adjustments for internal dust obscuration, inclinations, and the estimator of galactic rotation. It is possible that most of the scatter arises from observational uncertainties and the intrinsic scatter is much less than the observed scatter.

## Astrophysics

The power law relationship has been observed to break at low luminosities but this might only be because much of the baryonic mass in low mass galaxies is in gas rather than stars. 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 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].

### Distant galaxies: geometry, Tully-Fisher, and the fundamental plane

It seems that a repulsive dark energy is dynamically dominant. The relationship between ages and expansion rate is altered. Both the orbital radius r and the central mass M depend linearly on the distance to the galaxy d.

**Astronomy - Measuring Distance, Size, and Luminosity (12 of 30) Luminosity and Size**

Suppose we could measure the acceleration a of this little cloud of gas? If we could observe the acceleration, we could break the degeneracy and solve for the distance to the galaxy. Where should we look? Here are the locations of the masing clouds again, as observed by radio interferometers: Which of these clouds might be the best choice to detect the acceleration?

Just how big is this acceleration? Can we really measure it? Well, let's find out. Use your values to fill in the acceleration column of your table. How could we measure such tiny accelerations? Well, the good thing about accelerations is that they can accumulate over time into large changes in velocity. Suppose we measure the velocity of one cloud now, and then again after one year has passed.

How large would the change in velocity be? My estimate Radio astronomers have patiently monitored this galaxy for many years, watching for exactly these expected changes in velocity of the individual clouds.

Below is a small sample of their results; the numbers in the upper-right corner of each panel refer to the number of days since Apr Each cloud is drawn in a different color to help you follow the evolution of its velocity. Modified from Figure 5 of Humphreys et al. Pick one cloud and compute its acceleration.

So, as you can see, we CAN measure accelerations of the size produced by orbital motion around the central black hole. In theory, then, we can solve for the distance to the galaxy. In practice, this is complicated because the clouds are all at different distances from the center, because the disk is not perfectly edge-on, and because it appears to be warped slightly. But some astronomers have done all that work and conclude: Abstract from Humpheys et al.