Lecture 20 - Our Galaxy (4/1/99)

Black Holes --- | --- Galactic Dynamics

Reading:
Chapter 18-2, 14 (ZG4)

Notes:
pages 81-86

	Key Question:	Why do Cepheid stars pulsate?
	Key Principle:	Sound Speed
	Key Problem:	Derive period-density relation for Cepheids.

Investigations:

1. Cepheid Variable Stars
   • What are variable stars?
   • Why are Cepheid and RR Lyrae variables special?
   • What is the instability gap in the H-R diagram?
   • What did Henrietta Leavitt discover about Cepheids?
   • What is the sound speed in a gaseous medium?
   • What kind of pulsations take place in a Cepheid?
   • How does the pulsation period of pressure oscillations scale with density?
   • What is the period for a Cepheid with 50 Rsun and 5 Msun?
   • What is the period-luminosity relation for classical Cepheids?
   • What is the absolute magnitude-period relation for Cepheids?
   • How are observations of Cepheid variables used to determine distances?
   • How far away is Polaris, the nearest Cepheid?
   • What effect does dust extinction have on Cepheid distances?
2. Topology of the Galaxy
   • What is the Milky Way?
   • Why is it a band across the sky?
   • What are galactic coordinates?
   • Why is the galactic pole misaligned with the celestial and ecliptic poles?
   • Which direction is the galactic center?
3. Star Counts
   • What is the volume element at radius r and solid angle w?
   • What are the number counts with magnitude expected for uniform density?
   • Why do we not see that?
   • Are we at the center of the galaxy?
   • Why do open and globular clusters have differing distributions on the sky?
   • How was the center of the galaxy located?
   • What are spiral arms?
   • How should star counts scale with flux for a uniform distribution?
   • Why is this log-log slope called "Euclidean"?
   • Why does the inclusion of a luminosity function not change the slope of the number-flux counts?
   • Why does the slope of galactic star counts fall below Euclidean at faint brightness?
   • What effect does dust extinction have on star counts?
4. Galactic Rotation and Kinematics
   • What is the local standard of rest (LSR)?
   • What is differential rotation?
   • What are the radial and tangential velocities of nearby stars as a function of galactic longitude?
   • What is a rotation curve?
   • What are Keplerian and solid body rotation profiles?

Our Galaxy in Outline:

1. Survey of Our Galaxy
   • The milky way appears of a band of faint stars spanning the sky. It appears that we are in the middle of a disk or wheel of stars.
   • It was only early in this century that the true extent of our galaxy was realized - it is over 30,000 pc in diameter and contains about 100 billion stars!
   • Almost everything we can see with our unaided eyes in the sky is in our galaxy. The exceptions are the faint Andromeda galaxy (M31), and the Large and Small Magellanic Clouds near the south celestial pole.
   • There are a number of questions we would like answered about our galaxy:
     • What does our galaxy look like?
     • What are its physical properties?
     • What does it contain?
     • What is its history?
     • What is its neighborhood like?
2. The Appearance of the Milky Way
   • There are three main components to the Milky Way: disk, bulge, and halo.
   • We measure galactic distances in kiloparsecs, abbreviated kpc, which are thousands of parsecs: 1 kpc = 1000 pc.
   • The galactic disk, in which the Sun is embedded at a distance of about 8.5 kpc from the center, is over 15 kpc in radius.
   • The disk does not have a sharp edge at 15 kpc, but it fades away in luminosity fairly drastically at this radius.
   • The galactic bulge is a slightly flattened sphere of stars centered on the galactic center with a radius of about 2 kpc.
   • The bulge is bright, and has a high star density, but is difficult to see because of the large obscuration by dust in the inner disk of the galaxy.
   • The galactic halo is an extended tenuous assemblage of stars and globular star clusters, that extends out to more than 80 kpc from the center.
   • The disk is rotating, like a protostellar disk. The Sun is moving at a velocity of 220 km/s, which is the rotation velocity of the disk at the Sun's radius of 8.8 kpc.
   • The bulge may be slightly rotating, while the halo is not rotating at all, and the halo stars are moving in elliptical orbits with random orientations about the center.
   • The disk contains large amounts of gas and dust in addition to stars. All the gaseous nebulae are in the disk. The bulge and halo do not contain gas clouds.
   • The dust clouds in the disk are apparent as dark clouds, lanes, and nebulae against the brightness of the Milky Way. They obscure our view in optical wavelengths of most of the galaxy, especially toward the galactic center.
   • It is thus hard to measure the true luminosity of our galaxy, since we cannot just add up all the light. Comparison with other galaxies, and with galactic models lead us to estimate a total luminosity of about 10^11 Lsun for the Milky Way.
   • We can see only about 2 kpc from the Sun in the disk, except in some special "windows" where low dust content lets us see farther than this. Because of this, it was long thought that the galaxy was a wheel centered on the Sun (William Herschel 1785).
   • To find out what the galaxy really looked like, we needed to be able to measure distances.
3. Distance Indicators
   • Distances in the galaxy are too great to use parallax. The parallax of something 100 pc away is 0.01" and thus too small to measure from the ground.
   • We can use apparent and absolute magnitudes (luminosity) to find distances, using the formula for the distance modulus: m_v - M_v = 5 log d - 5
   • Thus, if we had a source of known luminosity, and thus known absolute magnitude, we could find its distance by comparing this to its apparent magnitude.
   • We can get a distance estimate for a main sequence star by using its temperature to find its luminosity on the H-R diagram. This method is called spectroscopic parallax. However, this is not very accurate, since it is hard to determine the effective temperature exactly, and the width of the main sequence in the H-R diagram can be as much as a magnitude.
   • It turns out there are a class of stars for which it is easy to find out their intrinsic luminosity, or absolute magnitude.
   • Certain stars are seen to vary in brightness with a regular pattern and period (not outbursts or novae). When plotted in the H-R diagram, these stars fall in a well-defined band above and to the right of the main sequence.
   • Stellar models predict that stars lying in this instability strip should indeed be variable because of an energy absorbing layer that forms in the envelope of the star. This layer can absorb and emit the energy like a resevoir, causing variations in the radius of the star, which pulsates alternately expanding and contracting.
   • Calculations and observations also show that the period of pulsation is dependent upon how far up the instability strip the star lies. Since the strip is rather narrow, and oriented at an angle to the luminosity-temperature axes, the luminosity of the star can be fixed by observations of the temperature and the period of the variations!
   • There are three varieties of these variable stars. Type I Cepheids are disk stars that lie in this strip, with periods from 1 day to over 100 days. These are the "classical" Cepheids first discovered by Harvard Astronomer Henrietta Leavitt in 1912.
   • The name Cepheid comes from the prototype star in this class: Delta Cepheii.
   • The Type II Cepheids are halo stars that are counterparts to the classical Type I Cepheids. They have similar ranges of periods, but have lower luminosities for a given period. It is easy to tell from the stellar spectra which sort of Cepheid a give star is (Type I have more elements heavier than helium).
   • There are also halo stars with shorter periods and lower luminosities than the Type II Cepheids. These are called RR Lyrae stars, after the first star in the class discovered.
   • If one of these types of variable stars is seen, then the period can be measured and the distance modulus, and thus the distance to the star, can be determined!
   • The astronomer Harlow Shapley used Leavitt's Cepheid relation, and measured the distances to a number of globular clusters in the halo.
   • In a series of papers published from 1915 to 1919, Shapley reported his findings that the system of globular clusters was not centered on the Sun, but on a point in the galactic plane in the direction of the constellation Sagittarius, and was about 15 kpc from the Sun!
   • This was identified as the location of the galactic center, and displaced us once again from the center of things in a post-Copernican revolution.
   • The best current estimates give the distance to the center in the range of 8 - 10 kpc.
   • The scale of our galaxy given above was obtained with the use of Cepheids and RR Lyrae stars as distance indicators.

continued next lecture...

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smyers@nrao.edu Steven T. Myers