Study Guide for Test #4

Dr. J. R. Webb

Stellar Astronomy

Chapter 23. Our Galaxy

• Galaxy – A collection of stars, gas and dust that are gravitationally bound together.
• Milky Way – The galaxy that we are located in, a spiral galaxy. All of the stars we see in the night sky are members of the Milky Way galaxy.
• Galileo- was the first person to see that the milky white band that stretches across the night sky is actually made up of myriads of stars.
• 1780’s – William Herschel started counting stars in 683 regions of the Milky Way. He determined we were in the center! Wrong! But why?
• He didn’t take into account the gas and dust in the galactic plane that blocks out light from distant stars.

• Harlow Shapley – studied globular clusters, tightly bound clusters of stars, that happened to contain RR Lyrae type variables which can be used to determine distance to the clusters.
• RR Lyrae variables are pulsating stars which have a period-luminosity relationship, the period of pulsation depends on the absolute magnitude M. You then measure the apparent magnitude m. Using: M = m-5log(d) + 5. Where, d is the distance in parsecs!
• Plotted the direction and distances to the star clusters

• 1930’s Trumpler discovered interstellar gas and dust.

Conclusions

The Milky Way Galaxy is a flattened disk with the Sun 25,000 ly from the center and Globular star clusters “clustered” around the galactic center. We live in the disk which contains gas and dust that obscures our view of the galactic center. See Figure 25-8 in the book.

• Stellar Populations –
• Population 1 – O and B stars, open clusters, high metal content, type 1 Cepheid variables.
• Population II.- low mass stars, globular clusters, low metal content, type II Cepheids.

• Stellar Motions and Galactic Rotation
• Proper motion – m is the angular change in position due to stellar motion (seconds of arc per second).
• Tangential velocity – the speed of a star across the line-of-sight. It is related to the proper motion and depends on the distance to the star.

T = 4.7 m d km/sec where d is the distance in parsecs.

Radial Velocity –The speed along the line-of-sight measured using the

Doppler shift of spectral lines R = Dl/l₀.

• Space Velocity is the sum of Tangential and Radial velocities. V² = T² + R².
• Local Standard of Rest – The LSR is defined as a point in space that has a velocity equal to the average velocity of all stars including the Sun lying within 100 parsecs of the Sun. The velocity of the LSR is around 230 km/sec.

The Mass of the Galaxy

Once we determine the Sun’s distance from the galactic center r_Sun and the orbital speed, we can calculate the orbital period. Period (P) = 2 p r / v_LSR, where v_LSR is the velocity of the LSR, and r_Sun = 25,000 ly. The period T works out to be around 200,000 years.

Now use Kepler’s third law (yes again!!) to estimate the mass.

P² = 4p²a³/G(M) or M = 4p²a³/GP²

The Mass of the Galaxy is: M_gal ~ 9.4x10¹⁰ M_Sun

• Galactic Rotation Curves – we can measure the speed of objects around the galactic center at different radii, this is called the galactic rotation curve. One must use the 21-cm line of hydrogen (Doppler shifts!).
• Missing mass problem #1 – The measured rotation curve of our galaxy and other galaxies do not agree with models of the galaxies based on stars, gas and dust actually seen. Solution: Small brown Dwarf stars in the galactic Halo now seen by Hubble’s space telescope!
• We live in a spiral galaxy, we are located in the galactic disk between spiral arms!

Galactic Center

The galactic center is highly obscured by gas and dust which absorbs visible light. However, gamma-rays and radio waves penetrate the gas and dust and we are able to study the galactic center. We see two expanding arms of gas, one on this side of the center expanding toward us, the other on the far side expanding away. We believe there is at least 2,000,000 M_Sun within 2 light years of the galactic center. A massive black hole????

CHAPTER 24. The Universe of Galaxies.

· Immanual Kant speculated about the diffuse nebula astronomers saw as being “Island Universes” in 1755.

· 1845 Lord Rosse – observed spiral structure in some nebula.

· 1900’s - Herschel and son catalogued more than 10,000 nebula

· 1920 The Great Debate – features Harlow Shapley as the champion for the spiral nebula being members of our galaxy, while Heber Curtis argued they were isolated star systems, i.e. external galaxies.

· Edwin Hubble – used the new 100-inch telescope to observe Cepheid variables in the Andromeda spiral nebula. He determined Andromeda was about 2.25 million light years away, i.e. an external galaxy.

Types of Galaxies

Spiral Galaxies	Sa	Tightly wound arms	Prominent nuclei	Gas/dust in disk
	Sb	Moderately wound arms	Moderate nucleus	Gas/dust
	Sc	Loosely wound arms	Small nucleus	Gas/Dust
Barred Spirals	SBa	Tightly wound arms	Prominent nuclei	Gas/dust in disk
	SBb	Moderately wound arms	Moderate nucleus	Gas/dust in disk
	SBc	Loosely wound arms	Small nucleus	Gas/dust in disk
Ellipticals	EO – E7			Very little gas and dust
Irregulars	-------	--------	------	Gas and dust

· Hubble Tuning Fork Diagram – a way of classifying galaxies, but it is not an evolutionary sequence.

· Irregulars have no location on the tuning fork diagram.

· Spiral Arms – Gravitational density waves caused by gravitational instabilities. As the stars, gas and dust move through a spiral shock location, they get compressed and induce further star formation. We understand how the shocks persist, but not t=how they form originally!

· Rotational Curves of Galaxies – a plot of rotational speed as a function of distance from the center of the galaxy. In Keplerian orbits, the rotational speed decreases as you go out, but galaxies rotational curves flatten out suggesting “missing mass” (see missing mass problem #1 above).

Masses and Sizes of Galaxies

TYPE	MASS (MSun)	SIZE (LY)
Spirals	10^9 to 4x10^11	20,000 to 50,000
Ellipticals	5x10^5 to 10^13	2,000 to 500,000
Irregulars	10^6 to 3x10^10	2,000 to 30,000

· Clusters of Galaxies – galaxies tend to be found in clusters. Rich clusters have 1000’s of members while poor clusters have a few dozen members. Member galaxies are gravitationally bound to each other.

· Local Group – Out Galaxy the Milky Way is a member of the “Local Group”, out local galactic cluster.

Distances to Galaxies and Hubble’s Law

• Slipher took spectra of “spiral Nebula” and 11 of 15 turned out to show redshifted spectral lines – they were receding from us!
• Hubble and Humason took spectra of hundreds of galaxies and all had redshifted lines – All galaxies except those very close to us are moving away from us.
• Hubble found a direct correlation between the distance to the galaxy and its motion or recessional velocity. This is called Hubble’s Law.

V = H_o D

Where V is the recessional velocity (V = cDl/l_o) in units of km/sec, D is the distance in megaparsecs (10⁶parsecs) and H_o is Hubbles constant in units of km/sec-Mpc.

• To determine the value of Hubble’s constant, H_o, Hubble needed to determine the distance to a large number for galaxies for which he had spectra (thus velocities). He then would plot recessional velocity versus distance, and the slope of a line fit to the data is the value of H_o. PROBLEM – How do you determine distances to distant galaxies???
• Methods of determination the distance of galaxies
1. The sizes galaxies appear. The smaller they look, the further they must be.
2. The brightness galaxies appear – The brighter they appear, the closer they are.
3. The sizes of HII regions. (See 1 above).
4. Supernova – the most accurate one!

• Space telescopes primary mission was to determine reliable values for Hubble’s constant. (It is now at ~ 65 km/sec/Mpc).

Chaper 26. The Big Bang Theory and the History and Future of the Universe

• 1/H_o = the age of the universe ~ 15 Billion Years old
• Big Bang theory – the universe started as an infinitely small point 15 byrs ago and space-time expanded out, carrying galaxies, gas and dust, along with it. This theory predicts the 3^oKelvin background radiation that was observed by Penzias and Wilson.
• Einsteins equations – Solutions of Einsteins equations of General Relativity for a homogeneous and isotropic universe, allows for the universe to have 3 possible shapes: Spherical, Hyperbolic (saddle–shaped), Flat.
1. Spherical – the universe will eventally collapse back on itself, parallel lines will eventually intersect, sum of angles in a triangle are greater than 180 degrees (over many mega parsecs!).
2. Flat – The universe will expand forever, but not accelerate. Parallel lines remain parallel; angles in a triangle always equal 180^o.
3. Hyperbolic – The universe accelerates outward. Parallel lines eventually diverge, interior angles in a triangle add to less than 180^o.

• History of the Universe – Regardless of the shape, the history of the universe back to the moment of the big bang goes as follows:

T =0 Big Bang	Universe, space, time, matter and energy are all contained in an infinitesimally small point.
0 to 10^-43 sec	Planck Era – need quantized gravity to know what happened here.
10^-43 to 10^-35 sec	Grand Unified Field Era, no normal atoms, strong force, weak force and electromagnetic force are all one force here!
10^-35 to 10^-10sec	Electro-weak era – The strong force splits off, so there are now 3 fundamental forces: gravity, strong and electro-weak. Elementary particles form.
10^-10 to 0.001	Electromagnetic and weak forces separate. Particle era.
0.001 to 3 minutes	Era of nucleosynthesis –protons, neutrons form first atoms and H forms helium during the early part of this era.
3 min – 300,000 years	Atoms now form and radiation (photons) become free from the matter, they decouple. The radiation cools as the universe expands, and the atoms are free to pick up electrons, form complete atoms, and start forming stars and galaxies.
300,000 years to 1 billion years	First galaxies from during this period.
1 billion years –present	Stars, galaxies evolve and life evolves on Earth!

• Inflationary Epoch – There was a time early on (10^-35 sec) when the universe expanded faster than the speed of light. This is necessary to explain observations of the background radiation (mapped by NASA satellite COBE). An energy field (called the Higgs field) decayed out of the false vacuum and powered the rapid expansion. This put us out of causal contact with distant regions of the universe (i.e. light from distant regions moving only at the speed of light c, has not had time and will never have enough time to reach us!).
• The future fate of the Universe – New observations indicate the universe is accelerating! Therefore, we actually live in a hyperbolic universe and the universe will expand forever!