Galaxies Lecture 08

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The Tully-Fischer Relationship

he Tully-Fisher relationship says that if we plot the luminosity of a (spiral) galaxy as a function of the circular velocity (), which is the (constant) rotational velocity of a galaxy with effects of projection removed by assuming the galaxy is circular, we find that grows linearly with , and that morphologically, increasing luminosities go like . This is very useful because it tells us the inherent luminosity of a galaxy based on measurements we can take. This tells us the distance to a galaxy, has can be used for cosmology. This relationship can be tightened by removing the effects of dust extinction–by measuring in infrared. Doing this, the relationship tightens to instrumental error. Therefore, something fundamental is being indicated in this relationship.\

Looking at slides about the Local Group, we find that around the Milky Way and Andromeda, are clustered a bunch of dwarf spheroidals. We then look at a plot of galaxies outside the Local Group. Some of them aren’t so far away, but they aren’t included in the Local Group. This is because, measuring their velocities, we find that they are not bound gravitationally to us. When we measure velocity of M31 (Andromeda), it is approaching us. By the way, Andromeda outweighs the Milky Way, but they together account for 90% of the mass of the Local Group. We define the Local Group to be all galaxies within 1200 kpc, which is the distance to the surface of 0 velocity where infall balances Hubble recession.\

Historically, we’ve known of the “missing mass” problem since Zwicky measured the luminous mass of galaxies, and compared that to the gravitational mass required for stable rotation. The confirmation of this problem came when we try to account for the infall of the Milky Way and Andromeda by the luminous mass of each. Even lower bounds which assume radial infall and this being the first approach of the two galaxies give mass estimates which are an order of magnitude above what we observe.\

The Seeing problem is the problem of the Airy disc (beam) of the telescope being scattered as a result of the index of refraction through the atmosphere changing along different paths as a result of density disturbances caused by turbulence. This turbulence has a power law, and is a problem on all scales.