## Why the Galaxy isnt bumpy twobody relaxation

Given enough time, molecules of air or scent, or small particles of smoke, will spread themselves out evenly within a room. This happens because particles can exchange energy and momentum during 'collisions' two of them come so close that the forces between them are much stronger than the force that each feels from all the other molecules together. At an average room temperature and normal atmospheric pressure, each molecule of oxygen or nitrogen has about 1011 such encounters every second....

## DpG M r

We write the average mass m of a gas particle as m mp for fully ionized hydrogen 0.5, whereas & 0.6 for gas of solar composition. For a perfect gas at temperature T and density p, we have p kBT, so M(< r) -(-pT). (7.4) Problem 7.4 Suppose that the hot gas of a group has a uniform temperature TX, and outside the very center the surface brightness in X-rays drops with radius R as IX a R Y .Writing the gas density p (r) a r, use Equation 7.2 to show that the luminosity per cubic centimeter...

## K

Earth-rotation synthesis during a day's observation, as seen from the source, the baseline vectors from dishes 2 and 3 to dish 1 sweep out an ellipse. 'telescope' is smaller in the north-south direction than in the east-west direction, by a factor of sin S . To speed up the observations, radio telescopes like the Very Large Array (VLA) in New Mexico place the dishes in a large 'Y'. A four-hour observation then includes baselines at a full range of angles, and even a brief 'snapshot'...

## Info

Merrifield, 1998, Galactic Astronomy, 3rd edition (Princeton University Press, Princeton, New Jersey). These are both graduate texts. 6.2.2 The Faber-Jackson relation and the fundamental plane The range in the velocity dispersion a for elliptical galaxies is close to what we saw in Section 5.3 for the peak rotation speed of disk galaxies. Just as for spirals, the stars move faster in more luminous galaxies. At the centers of bright ellipticals, the dispersion can reach 500...

## Bulges and centers of disk galaxies

Bulges, along with the centers of small elliptical galaxies, are some of the densest known stellar systems (see Figure 4.18). The Milky Way's bulge is largely hidden from us by dust but when we look at M31 through a small telescope or binoculars, or at an 'underexposed' optical image of a disk galaxy, only the bright bulge is visible. In Figure 5.4, the surface brightness at the center of NGC 7331 rises to fifty times that of the inward-extrapolated exponential disk. The bulge is the 'big city'...

## Bibliography

We have drawn for our presentation on the following graduate texts J. Binney & S. Tremaine, 1987, Galactic Dynamics (Princeton University Press, Princeton, New Jersey), on the dynamics of galaxies and star clusters F. Combes, P. Boisse, A. Mazure, & A. Blanchard, Galaxies and Cosmology, 2nd edition (English translation, 2002 Springer, Heidelberg, Germany), covering similar ground to our text and J. Binney & M. Merrifield, 1998, Galactic Astronomy, 3rd edition (Princeton University...

## The pregalactic era a brief history of matter

Here, we sketch what we know of the history of matter in the Universe before the galaxies formed. When a gas is compressed, as in filling a bicycle tire, it heats up when it is allowed to expand, as in using a pressurized spray can, its temperature drops. The gas of the early Universe was extremely hot and dense, and it has been cooling off during its expansion. This is the Big Bang model for the origin of the Universe the cosmos came into existence with matter at a very high temperature, and...

## The past and future of the Local Group

The galaxies of the Local Group are no longer expanding away from each other according to Hubble's law. Their mutual gravitational attraction, and that of any matter present between the galaxies, has been strong enough to pull the group members back toward each other. The Milky Way and M31 are now approaching each other these two galaxies will probably come near to a head-on collision within a few gigayears. We can use the orbits to make an estimate of the total mass within the Local Group....

## The orbits of the stars

Stars travel around the Galaxy, and galaxies orbit within their groups and clusters, under the force of gravity. Stars are so much denser than the interstellar gas through which they move that neither gas pressure nor the forces from embedded magnetic fields can deflect them from their paths. If we know how mass is distributed, we can find the resulting gravitational force, and from this we can calculate how the positions and velocities of stars and galaxies will change over time. But we can...

## How did the Local Group galaxies form

We can now sketch a picture for the formation of the Milky Way and the other galaxies of the Local Group, starting from the hot dense early Universe that we discussed in Section 1.5. Roughly 350 000 years after the brilliant beginning of the Big Bang, photons of the cosmic fireball no longer had enough energy to ionize Fig. 4.12. Small galaxies form near large ones the density of matter (wavy solid line) is a combination of small clumps within a large region that is denser than average (dashed...

## T T V T

The ratio of measured peak rotation speed Vmax to central velocity dispersion a for elliptical galaxies, plotted against apparent ellipticity filled circles show bright galaxies (Mb < -19.5) open circles are dimmer galaxies. Points with downward-extending bars indicate upper limits on Vmax. The dashed line gives (V a )iso, the fastest rotation expected for a given flattening - R. Bender. We cannot measure the true flattening B A for a galaxy, but only the apparent axis ratio b a....

## Contents

Preface to the second edition page vii 1.4 Galaxies in the expanding Universe 46 1.5 The pregalactic era a brief history of matter 50 2 Mapping our Milky Way 58 2.1 The solar neighborhood 59 2.2 The stars in the Galaxy 67 2.4 Milky Way meteorology the interstellar gas 95 3 The orbits of the stars 110 3.1 Motion under gravity weighing the Galaxy 111 3.2 Why the Galaxy isn't bumpy two-body relaxation 124 3.3 Orbits of disk stars epicycles 133 3.4 The collisionless Boltzmann equation 140 4 Our...

## Satellites of the Milky

The most prominent companion galaxies to the Milky Way are the two Magellanic Clouds in the southern sky, they are easily visible to the naked eye, even among city lights. These gas-rich galaxies are forming new stars and star clusters in abundance. John Herschel, who extended his father William's nebula-hunting to the southern skies, noted in 1851 that 'there are nebulae in abundance, both regular and irregular globular clusters in every state of condensation and objects of a nebulous...

## Dark matter and black holes

Following near-circular orbits, along with Equation 3.20 for the gravitational force. Generally, the mass of these galaxies is more spread out than the luminous stars the mass-to-light ratio M L is larger when measured further from the center. Most of whatever makes up the outer parts of a spiral emits very little light we call it dark matter. Do elliptical galaxies also contain dark matter To answer this question, we must estimate the mass within a given region, from measurements of the...

## Other galaxies

This section introduces the study of galaxies other than our own Milky Way. We discuss how to classify galaxies according to their appearance in optical light, and how to measure the amount of light that they give out. Although big galaxies emit most of the light, the most common type of galaxy is a tiny dim dwarf. The existence of other galaxies was established only in the 1920s. Before that, they were listed in catalogues of nebulae objects that appeared fuzzy in a telescope and were...

## The stars in the Galaxy

Most stars do not have measurable parallaxes, which tells us that the Galaxy is much larger than 500 pc across. To estimate distances of stars further away, we rely on the cosmic distance ladder we measure their distances relative to stars that are close enough to show parallaxes. Occasionally we can use information from velocities to obtain distances without this intermediate step. In this section, we first explore some of these opportunities, then discuss the distribution of stars and star...

## L

Often, we do not know the distance d very well, and must remember in subsequent calculations that our estimated luminosity L is proportional to d2. The Sun's total or bolometric luminosity is LG 3-86 x 1026W, or 3-86 x 1033ergs-1. Stars differ enormously in their luminosity the brightest are over a million times more luminous than the Sun, while we observe stars as faint as 10-4LG. Lengths in astronomy are usually measured using the small-angle formula. If, for example, two stars in a binary...