midterm exam 2 tuesday april 20
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Midterm Exam #2 Tuesday, April 20. Closed book Will cover Lecture 15 (Stellar Evolution) through Lecture 21 (Galaxy Evolution) only If a topic is in the book, but was not covered in class, it will not be on the exam! Some combination of multiple choice, short answer, short calculation

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midterm exam 2 tuesday april 20
Midterm Exam #2Tuesday, April 20
  • Closed book
  • Will cover Lecture 15 (Stellar Evolution) through Lecture 21 (Galaxy Evolution) only
  • If a topic is in the book, but was not covered in class, it will not be on the exam!
  • Some combination of multiple choice, short answer, short calculation
  • Equations, constants will all be given
  • Standard calculators allowed (but not provided)
  • Cell phones, PDAs, computers not allowed
what s the ultimate fate of the universe will it expand forever
What’s the Ultimate Fate of the Universe?Will it expand forever?

To answer, we need to know:

How much energy is in the form of mass (including dark matter)

How much energy is in the form of light

How much “weird” energy (not mass, not light) is there

fate of the universe
Fate of the Universe

If there’s nothing especially weird about the energy components to the universe, then the fate of the universe will depend on the balance of Kinetic Energy and (Gravitational) Potential Energy

Kinetic Energy: energy of motion (due to big bang)

(Gravitational) Potential Energy: energy that is stored when two massive objects are located at some distance from each other (after about 10 sec the universe has substantial amounts of mass in it; objects with mass attract each other)

What happens if you throw a ball upwards?

What happens if you fire a rocket at 11 km/s?

gravity as brakes
Gravity as “Brakes”
  • just like ball and rocket, gravity should slow down the universe’s expansion
  • should expect a deceleration over time if there is nothing weird about the energy components to the universe

No mass = universe has no brakes! (constant expansion rate)

“Little bit” of mass = universe has weak brakes (weak deceleration)

“Lots of mass” = universe has strong brakes (strong deceleration)

Depending on how much mass there is in the universe you (naively) expect 3 possible fates for the universe…

Theoretical “Fates” for the Universe(plot of distance between galaxies as a function of time since Big Bang)

halt, no collapse

high mass

theoretical fates for the universe3
Theoretical “Fates” for the Universe


weird: initially decelerating

what s the future of our universe
What’s the future of OUR universe?
  • More than 15 years ago:
  • the observers were reasonably sure that we lived in a low mass, coasting universe that would expand forever at a rate that’s roughly constant
  • the theorists were positive that the observers hadn’t managed to count up all the mass in the universe (Dark Matter) and that we actually lived in a “critical mass” universe that would come to a halt after an infinite length of time but would not re-collapse on itself


  • the observers are reasonably sure that we live in an accelerating universe and that the universe will continue to expand at an ever faster rate forever!
  • the theorists are reasonably sure that the observers have done their jobs right, but they aren’t positive what’s causing the acceleration!(Dark Energy)
humble truths science is a process
Humble Truths(science is a process…)
  • Assuming that all of the observations (and interpretations) are correct, then we appear to live in a very weird universe. At the present day we think:
  • 27% of the energy density is in the form of mass (at present the energy density in light is negligible)
  • 73% of the energy density is in the form of dark energy, the nature of which is unknown
  • only 15% of the mass is in the form of ordinary chemical elements, the rest is in some type of unknown material that emits no light whatsoever (dark matter)

What’s the evidence for Dark Matter and Dark Energy - should you take this stuff seriously????

evidence for dark matter
Evidence for Dark Matter

The stars and gas in the outer parts of the disks of spiral galaxies are moving too quickly to be explained by the amount of mass contained in the luminous material of the galaxies, therefore the majority of the mass in galaxies must be “dark”.

v = (GM / r)1/2 is the rotation speed

G is Newton’s constant, M is the mass contained within a radius r

Rotation speeds, v, of planets in solar system decrease, proportional to (1/r)1/2

Implication: “M” above is a constant in our solar system = Msun

rotation of spiral galaxies
Rotation of Spiral Galaxies

Measure rotation speed from the Doppler shift

Rotation looks nothing like we see in the solar system!

In spiral galaxies, v isapproximately constant at all radii


Rearrange the previous formula and you’ll get:

M = (v2 r) / G

If v = constant, then we must have that the total mass contained within a radius r, M increases with radius:

M( r ) = constant x r

BUT, the star light decreases sharply with radius!!!!


Dark Matter in Elliptical Galaxies: NGC 4649



Some elliptical galaxies have hot, X-ray gas in them. The gas is so hot (i.e., it’s moving so quickly) that the only way it can be bound to the galaxy by gravity is for the mass of the galaxy to be mostly DARK MATTER.

In a typical galaxy (like our own) there is at 50 to 100 times more dark matter than luminous matter.

still more evidence for dark matter
Still more evidence for dark matter…
  • galaxies in “clusters” of galaxies are moving too quickly to be explained by the luminous material; the majority of the mass in clusters of galaxies must be “dark”

A large galaxy cluster

still more evidence for dark matter in galaxy clusters
Still more evidence for dark matter in galaxy clusters

Hot X-ray gas in galaxy clusters and gravitational lensing by galaxy clusters leads to the conclusion that galaxy clusters contain a great deal of dark matter.

In a typical big galaxy cluster there is 500 to 800 times more dark matter than luminous matter.

what is the dark matter
What is the dark matter????

Turns out that it cannot be made up of the ordinary chemical elements (not enough time to make it in the Big Bang).

Best candidate is a type of particle called a WIMP (Weakly Interacting Massive Particle).

Pros of WIMPs:

Computer models show excellent agreement with observations

Grows the right number of galaxies, galaxy clusters and gives right “structure” to the universe

Cons of WIMPs:

Nobody has (yet) seen a WIMP - they are currently hypothetical particles (it’s possible they may be detected for the first time within 5 years)

The 400,00 Brightest Galaxies in the Northern Sky(galaxies don’t live in random locations in the universe)

“frothy”, “lacework” pattern to the observed galaxy distribution

a wimp universe
A WIMP Universe

WIMP universes reproduce the observed “structure” to the universe, grows the right number of galaxies of the right size, and grows the right number of galaxy clusters of the right size (big success).

Big problem is that WIMPS are currently hypothetical particles!

dark matter vs alternative gravity
Dark Matter vs. “Alternative Gravity”

Fair Question: Do we really understand how gravity should behave in the limit of very weak gravity?

Einstein showed us that Newton was wrong in the limit of very strong gravity. Maybe Newton was also wrong in the limit of very weak gravity (i.e., maybe Newton’s law of gravity only works in the “middle range”).

should you believe in dark energy
Should you believe in dark energy??
  • Two Independent Lines of Evidence for Dark Energy:
  • white dwarfsupernovae in extremely distant galaxies (lookback times of 7 billion years or so) are too faint to be explained by a universe in which the expansion rate has been decelerating for all time (i.e., the galaxies are much farther away than they ought to be)
  • “lumps and bumps” in temperature of the leftover light from the Big Bang (called the CMBR) have a distinct, measurable pattern, and the details of the pattern give us precise measurements of the amount of energy in the form of mass versus the amount of energy in the form of “dark energy”

At its peak brightness, a supernova is typically as bright as the whole galaxy in which it lives.

White Dwarf Supernovae (known as a Type-Ia supernova) can be used to make very accurate measurements of the distances to galaxies.

Type-Ia supernovae are easily identified from details in their spectra and light curves.

HST image of a supernova in a nearby spiral galaxy


before supernova

during supernova

HST images, before and during supernova in an extremely distant galaxy

Who’s awake out there?

Why is the big spiral galaxy in this picture ORANGE?

The spirals we saw in other classes were more blue in color.

dark energy from supernova measurements
Dark Energy from Supernova Measurements
  • measurements of distances to supernovae in many different galaxies (measure “Hubble Law” at different times in the history of the universe)
  • expansion rate of the universe decelerated for the first 9.5 billion years after the big bang
  • for the past 4.5 billion years the expansion rate of the universe has been accelerating (and will continue to accelerate forever)

Fair question: Do we really understand supernovae well enough to make this statement?

Maybe stars blew up very differently in the past than they do today. Maybe something else (not accelerating universe) is causing the distant supernovae to look fainter than we expect.

where are the fossil photons from the big bang
Where are the “fossil photons” from the Big Bang?

Answer: Everywhere! (they make up about 90% of the radiant energy of the universe at the present day, but you can’t see them with your eyes…)

MICROWAVE photons (very long wavelength, very low energy)

cosmic microwave background radiation cmbr
Cosmic Microwave Background Radiation (CMBR)
  • If the universe began in an extremely hot, extremely dense state:
  • universe would have been opaque initially
  • primordial light would have had a continuous, black body spectrum
  • primordial light would have been very high energy ( very short wavelength)
  • Expansion of the Universe:
  • stretches the wavelengths of the primordial photons
  • does not change the shape of the spectrum (i.e., it remains a black body but with a different temperature than it had early on)
  • after roughly 14 billion years, the high energy photons will have stretched so much that they will have become microwave photons!

The CMBR should appear as a (nearly) uniform “hiss” of microwave radiation on the sky, and it should have a black body spectrum.

observations of the cmbr
Observations of the CMBR
  • 1964, Arno Penzias & Bob Wilson
  • discovered serendipitously
  • unable to measure spectrum
  • awarded Nobel Prize in Physics (1978)
  • 1992, COBE Satellite
  • measured shape of spectrum, nearly perfect black body with T = 2.73 Kelvin
  • detected extremely tiny “fluctuations” in the temperature (deviation of only 1 part in 100,000); best proof that the universe is isotropic!
  • made low-resolution map of temperature on the sky
  • George Smoot & John Mather awarded Nobel Prize in Physics (2006)
  • 2003 to 2005, WMAP Satellite
  • made extremely high-resolution map of temperature of CMBR on the sky
temperatures on the earth
Temperatures on the Earth

blue = “cold”,red = “hot”

Note the big temperature range! (100o C)


CMBR Temperature “Fluctuations”MicroKelvin (10-6 K) deviations from universal average temperatureColor scale goes from -3x10-6K (blue) to +3x10-6K (red)

cmbr temperature fluctuations
CMBR Temperature Fluctuations

The “lumps and bumps” in the CMBR aren’t random. They’re correlated and the pattern tells us that there is dark energy in the universe.

Neither the CMBR nor the supernovae have anything to do with each other, but they both give the same value of the amount of dark energy in our universe!!