All the Stars in the Sky: Our Galaxy!

These flashcards cover essential terms and concepts about galaxies, specifically the Milky Way, and important notions related to stellar populations and motions.

Galaxy

A collection of stars, gas, and dust gravitationally bound together.

Milky Way galaxy

The galaxy that contains our Solar System.

Proper motion

The angular rate of change in position of a star due to its motion through space.

Population I stars

O and B stars, open clusters, high metal content, type 1 Cepheid variables.

Young stars, often found in open clusters

Population II stars

low mass stars, globular clusters, low metal content, type II Cepheids.

Older stars, usually found in globular clusters

Globular clusters

Collections of thousands of stars that appear to be concentrated in specific regions of the sky.

RR Lyrae variables

Pulsating variable stars found in globular clusters, used to measure distances.

Interstellar gas and dust

Matter in between stars that can obstruct our view of distant stars.

Local Standard of Rest (LSR)

A point in space moving with the average velocity of nearby stars, including the Sun.

Galactic rotation curve

A plot showing the observed rotational velocity of stars in the galaxy compared to predictions.

big bang

really happened

• all space-time, matter and energy emerged from a single point in space-time.

• If you run time backwards, all of space-time, matter and energy emerge from a single point!  ]

  universe evolves and expands according to Einstein’s equations.  

• physics is fairly well known down to

• about 10^-43 seconds (the Planck time).

dark energy

Must evenly spread out in space time, a ubiquitous field like a non-zero cosmological constant.; have negative pressure, drive universal acceleration, similar to inflation but much more gradual and much longer lasting; no theoretical candidate fields.

Quintessence

in the right-hand side of Einstein’s equation (the stress-energy tensor) and would represent a new type of matter.'; must have negative pressure, but much weaker than Higgs fields.; Lightweight and large (size of superclusters of galaxies); evolve spatially, while background energy doesn’t!

Age of the Universe

13.7 billion years

COBE Microwave Background Radiation Results

avg temp-2.78 kelvins

order temp differnce-3.353mK

second order differnces- 18

Measuring Ω₀

Ω₀  = 1 +/- 0.2 from Cosmic background measurements.; Weighing matter in galaxies and clusters   Ω_m = 0.4 +/-0.1

Inflation

If the universe in its early history expanded out very rapidly, then the distant regions of the universe are no longer in causal contact with the rest of the universe.  Horizon problem and flatness problems are solved (we can only see small region of the universe!).

Expansion was driven by Higgs bosons condensing out of the false vacuum. (time dependant cosmological constant!)

Problems With the Big Bang Cosmology

horzion and flatness

• Horizon Problem

The background radiation from the universe is too homogeneous and isotropic that the initial conditions would have to be too fine-tuned.

Flatness problem

The universe is too flat for the amount of mass we see in space.

Ancient Cosmologies were based on

the Sun, Moon and stars, but instead of natural mechanisms, Gods were created to explain the universe around them.

Philosophical Foundations of Newton’s Laws

Calculus as a mathematical foundation.

Gravity is a “Force” (Causes acceleration).

Time ticks off at a constant rate regardless of motion of observer.

Force is propagated by “Action at a distance”.

Only mass causes gravity and responds to gravity, energy is not involved!.

Gravity is propagated at infinite speed?

Philosophical Underpinnings of Special Relativity

• The universe is a 4-dimensional space-time continuum (no accelerations).

• The speed of light is constant.

• The laws of physics are the same in all inertial frames.

Consequences of Philosophical Underpinnings of Special Relativity

• • Time ticks off at a different rate depending on velocity. T’ = t(1/(1+v²/c²))^1/2

  • Mass increases with velocity

  • Length decreases with velocity

  • E=mc²

The Principles of General Relativity

Matter and energy warp space-time, and a projectile must follow the curvature of space-time; Principle of Equivalence ; General Relativity is couched in terms of differential geometry.  Einstein’s equations are:

Principle of Equivalence

In any small region of space, you can’t tell whether you are being accelerated by gravity, or by any other force, i.e. inertial mass is identical to gravitational mass. 

The Einsteinian Universe

Makes an analogy between a gas and a cloud of stars: an isolated system cannot be in equilibrium without modification of  Boltzmann’s distribution laws (Newtonian concept).; never considered the universe isn’t stable, so: added a correction/stability factor.

Relativity 

Stabilize the universe Einstein introduced a cosmological constant into his “pure” equations” Λ. 

What was Einstein’s Motivation for Believing in a Static Universe¹?

Observations did not require a static universe!

No strong apparent religious motivations.

Guesses: static cosmology is simpler than an evolving one?

Friedmann 1922

found non-static solutions for the universe to solve Einsteins equations and pointed out that Einsteins assumption of a static universe is only an assumption!

Einstein said what about Friedmann

had erred in his calculations!  Einstein was wrong!; Einstein then admitted Friedmanns work was correct, but didn’t think his solutions had any physical meaning!; Einstein rejected any possibility of a non-static universe.

Observational Cosmology

• All but the nearest galaxies have red-shifted spectral lines.

• H_o = 71.0 +/-2 km/sec/Mpc

• V = (Δλ/λ) c = z c (non-relativistic)

• Relativistic case: V = [(z+1)²-1] c / [(z-1)²-1]

Edwin Hubble derived what

the relationship between the distances to galaxies and the redshift of their spectral lines:  Hubble’s Law!  V = H d.  H = Hubble’s Constant.

Competing Theories

Steady State Theory + The Big Bang 

steady State Theory

As the universe expands, matter and energy spontaneously comes into being to fill gaps, i.e. the average density of the universe is constant over time. 

• Penzias and Wilson

• unwittingly found the background radiation indicating the universe has a temperature of about 3^oK

Calculations involving the synthesis of elements in the early universe indicate what

the universe should still have a temperature.  Calculations indicate that if the big bang is correct, the universal temperature should be around 3^oK.

discovery killed the steady state theory since it did not predict the background radiation.

Possible Solutions of Einstein’s Equations

• Spherical Universe :

  • Universe is closed

  • Cyclic (expands, then contracts

• Flat Universe:

  • Critical density

  • Expands forever with a constant velocity

• Saddle-shaped:

  • Universe is closed

  • Less than critical desnsity

  • Universe accelerates forever

Immanuel Kant thought what?

the diffuse nebula were island universes, i.e. other Galaxies of stars. (1755)

Charles Messier

1758-1782 catalogued many of these “Nebula”

Astronomer William Parsons (Lord Rosse)

1845 examined many nebula and observed spiral structure in some of them.

Herschel and his son

1900’s; catalogued more than 10,000 nebula.

William Herschel drawing

galaxy M51

made looking through the 1.8 meter mirror telescope, the most powerful of its time. Mid 1800’s!

National Academy of sciences

1920

held a famous debate in Washington D.C to try and determine the nature of these spiral nebula. (Harlow Shapley, Heber Curtis)

No one won because no one knew the DISTANCE to these objects! No one could resolve individual stars in any of the nebula.

Harlow Shapley

in our Galaxy, i.e. part of the milky Way

Heber Curtis

external galaxies, Island Universes.

Period

luminosity relationship for Cepheid variables – then use distance modulus and apparent magnitude to calculate distance

Hubble showed what

M87 (Andromeda Galaxy) is ~2.5 million light years away i.e. an external star system far beyond the limits of the Milky Way.

Spiral Galaxies

Regular; Sa –tightly wound w/prominent nucleus • Sb – moderately wound with moderate nucleus • Sc – loosley wound with small nucleus

Barred

Sa-sightly wound w/prominent nucleus • Sb – moderately wound with moderate nucleus • Sc – loosley wound with small nucleus

Elliptical Galaxies

E0 (round) – E7 (highly elliptical)

Exhibit a large range in sizes. Are among the largest and smallest galaxies ever seen.;Virtually devoid of gas and dust; No evidence of young stars

Galaxy Clusters

Galaxies tend to live in clusters in space

Our Milky Way galaxy lives in

THE LOCAL GROUP- The Milky Way galaxy, 9 smaller dwarf elliptical galaxies, the Andromeda Nebula, and 8 satellite galaxies, Large and small Magellenic clouds.

Virgo cluster of Galaxies

1000 galaxiesm 500 million light years across

Hercules Cluster

200 galaxies 500 million light years from earth

Slipher

1914 took spectra of “spiral nebula”, 11 of 15 spiral nebula had redshifted spectral lines.

Hubble and Humason:

1020’s took spectra of hundreds of galaxies, all had redshifted lines.'; galaxies except those very close to us are moving away from us.

• Distant clusters • Supernova

8 billion light years • Largest galaxy in cluster or brightest galaxy in cluster

Measuring galaxy distances (standard candles)

Nearby galaxies

Cepheid variables ~20 million light years • Luminous supergiant stars ~80 million light years

Separating cosmological redshifts from cluster motion

Redshift z = v/c z total = z cosmological + z cluster motion

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

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.

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

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!

Hyperbolic

The universe accelerates outward.  Parallel lines eventually diverge, interior angles in a triangle add to less than 180^o.

flat

The universe will expand forever, but not accelerate.  Parallel lines remain parallel; angles in a triangle always equal 180^o.

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

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.

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).

Hubble Tuning Fork Diagram

 a way of classifying galaxies, but it is not an evolutionary sequence.

History of the Universe

Regardless of the shape, the history of the universe back to the moment of the big bang goes as follows

1/H_o

=the age of the universe

15 Billion Years old

V = H_o D

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.

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!

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. 

Space telescopes primary mission

determine reliable values for Hubble’s constant.  (It is now at ~ 65 km/sec/Mpc).

Hubble’s Law.

a direct correlation between the distance to the galaxy and its motion or recessional velocity. 

Irregulars

have no location on the tuning fork diagram.

Trumpler discovered

1930; interstellar gas and dust.

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.

Missing mass problem #1

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!

galactic center

highly obscured by gas and dust which absorbs visible light. 

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. 

Once we determine the Sun’s distance from the galactic center r_Sun  and the orbital speed

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.  

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.

Lord Rosse

1845 observed spiral structure in some nebula.

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.

 

William Herschel

1780’s counting stars in 683 regions of the Milky Way.  He determined we were in the center!  Wrong! But why?

didn’t take into account the gas and dust in the galactic plane that blocks out light from distant stars.