This Set of Slides
• This set of material starts “the big(gest) picture”.
• Cosmology – the study of the structure and
evolution of the universe.
• This set of slides deals mostly with galactic
motion, evidence of black holes, expansion of the
universe, evidence of dark matter.
• It includes material from Units 70, 73, 74, 75, 78,
79.
Our Galaxy, the Milky Way
• A galaxy is a large
collection of billions of
stars.
• The galaxy in which the
Sun and our solar
system is located is
called the Milky Way.
• From our vantage point
inside the galaxy, the
Milky Way looks like a
band of stars across the
night sky, with dark dust
lanes obscuring the
center of the band.
Rotation in the Milky Way
• The Milky Way does not rotate
like a solid disk.
– Inner parts rotate about the center
faster than outer parts.
– Similar to the way planets rotate
around the Sun.
– This is called differential rotation.
• A plot of rotation speed vs.
distance is a rotation curve.
• A star is held in orbit around the
galactic center by the gravity of
all matter within its orbit.
Calculating the Mass of the Galaxy
• The rotational velocity of the
Sun around the center of the
galaxy can be used to estimate
the galaxy’s mass.
• The combined gravitational
effect of all mass within the
Sun’s orbit is equivalent to one
large lump of mass at the
center of the galaxy.
• Newton’s Law of Gravitation
shows that the mass of all matter
within the Sun’s orbit is 91010
solar masses.
• We can estimate the mass of the
entire galaxy by measuring the
orbital velocity of small satellite
galaxies in orbit around the Milky
Way (21012 solar masses).
The Galactic Center and Edge
• Despite the appearance of being
closely spaced, stars in the Milky
Way are very far apart.
– At the Sun’s distance from the
center, stellar density is around 1 star
per 10 cubic parsecs.
• Density is much higher at the core
– Exceeds 100,000 stars per cubic
parsec.
• X-ray and gamma ray telescopes
reveal a supermassive black hole at
the Milky Way’s core.
– Called Sag A*
– 5 million solar masses!
Detecting Black Holes – 2nd Way
Sag A* - Our Galactic Center Black Hole
Distances to other galaxies
• We can use Cepheid variable
stars to measure the distance
to other galaxies.
• A Cepheid’s luminosity is
proportional to its period, so if
we know how rapidly it
brightens and dims, we know
much energy it emits.
• If we see a Cepheid in another
galaxy, we measure its period,
determine its luminosity, and
calculate its distance.
• Distance between galaxies is
huge.
– M100 is 17 million parsecs
away.
The Redshift and Expansion of the Universe
• Early 20th century
astronomers noted that the
spectra from most galaxies
were shifted towards red
wavelengths.
• Edwin Hubble (and others)
discovered that galaxies
that were farther away had
even more pronounced
redshifts.
• This redshift was
interpreted as a measure of
radial velocity, and it
became clear that the more
distant a galaxy is, the
faster it is receding.
The Hubble Law
• In 1920, Edwin Hubble
developed a simple
expression relating the
distance of a galaxy to its
recessional speed.
• V=Hd
– V is the recessional
velocity.
– D is the distance to the
galaxy.
– H is the Hubble Constant
(70 km/sec per Mpc)
• This was our first clue that
the universe is expanding.
The Tuning Fork
• Edwin Hubble organized these
different galaxy types into a
tuning fork shaped diagram.
• Ellipticals are labeled E0-E7.
– E0 is almost perfectly spherical,
E7 is quite flattened.
• Spirals are labeled Sa – Sd
– Sa galaxies have tightly wound
arms and a large central bulge.
– Sd galaxies are loosely wound
and have a small central bulge.
• Barred Spirals are labeled
SBa – SBd
– Same pattern as the spirals
The Tuning Fork, continued
• Hubble viewed this tuning fork model as an
“evolutionary” model. Galaxies evolved from left to right,
forking in the middle for whatever reason (likely
gravitational.)
• Astronomers today do not believe galaxies evolve along
this “tuning fork”.
• Still, the model is used for classification.
Galactic Collisions
• Galaxies can collide, though not in the sense of a car accident.
• The galaxies pass through one another, and their immense
gravitational pull can tear both galaxies apart.
• This can occur with no stars actually colliding! (The space is so
enormous!)
• Eventually, a new elliptical galaxy will form…
Galaxy collision and merger
Current galactic evolutionary model.
Galactic Rotation Curves
• Like a planetary system,
galaxies rotate as non-solid
disks. (Because they ARE
non-solid disks.)
• Rotation curve for galaxy is
not the same as for a solar
system.
• It’s flat. But it shouldn’t be.
• The outer stars are rotating
too rapidly based on visible
matter within their orbits.
Missing Mass
• We can calculate the mass of the
Milky Way by measuring the
orbital velocities of dwarf galaxies
in orbit around our galaxy.
• We can also count the number of
stars in the galaxy, and estimate the
galactic mass. The two numbers do
not agree. By a factor of 10!
• Rotation curves do not show the
expected decrease in stars’ orbital
velocities with distance; there must
be much more mass present in our
galaxy. By a factor of 10!
• Astronomers cannot find or see this
mass!
• We call the missing mass dark
matter.
Many galaxies have flat rotation curves
Dark matter is not unique to the Milky Way.
Spiral Galaxy Rotation Curve
• 99 percent of the stars in a galaxy are
within 20 kpc of the center.
• Gas extends far out into the disk, but
is not very massive.
• Galaxies are now thought to be
embedded in a dark-matter halo that
surrounds the entire galaxy.
• Unfortunately, dark matter cannot be
detected directly.
Dark Matter Distribution
• “Halo” can be misleading – not a ring.
• Density of visible matter (stars, dust) in a galaxy is
highest in the center but falls off rapidly with
distance from center.
• Density of dark matter is highest in center of
galaxy but falls off gradually and even exists
between galaxies.
Dark Matter in Clusters of Galaxies
• Missing mass is also a
problem in clusters of
galaxies.
Once again, dark matter
seems to be the solution –
10 times as much mass as
the visible matter.
– Not enough visible mass
to hold the clusters
together by gravitation,
and to keep hot gas in
their vicinity.
– Cluster mass must be 100
times greater than the
combined stars.
– Gases previously unseen
accounts for a tenth.
Gravitational Lensing
• Dark matter warps space just like ordinary
matter does. (General Relativity.)
• The path of light rays bends in the
presence of mass.
• A galaxy or other massive object can bend
and distort the light from objects located
behind it, producing multiple images.
• This is called gravitational lensing.
Galactic Cluster Gravitational Lens
Amount of matter needed to provided lens effect is 10 times the
amount of matter visible (at any wavelength.)
90% of the universe is not detectable to us!
What IS Dark Matter?
• Unknown. All known matter interacts with SOME
wavelength of electromagnetic radiation.
• Perhaps small, cold, planet-sized bodies? Cold, dead
white dwarfs? Non-rotating neutron stars? Black holes?
• MACHOs! Massive, Compact Halo Objects.
• Not enough of such things have been detected to make up
the quantity of dark matter needed.
• Perhaps neutrino-like particles, except massive?
• WIMPs! Weakly Interacting Massive Particles.
Neutrolinos!
• So far? Dark Matter is entirely unlike any matter we are
familiar with.
The Recession of Galaxies
• Recall from Hubble’s Law that the
farther away a galaxy is, the faster it
is receding from the Milky Way.
– V=Hd
• This gives the appearance that the
Milky Way is at the center of the
Universe, and all galaxies are
moving away from us, perhaps due
to some large explosion (The Big
Bang.)
• However, Hubble’s Law can be
applied to any observer in any galaxy
• No matter where you are, an
expanding Universe will give this
appearance.
• This lack of a preferred location in
the Universe is called the
cosmological principle.
An Expanding Universe
• The expansion of the Universe is not
like the explosion of a bomb sending
fragments in all directions through
space.
• The space itself is expanding!
• We can detect photons that appear to
have moved at different speeds
through space.
•
•
Rather, the speed of light is constant, and
it is space that was moving relative to the
photon.
If each galaxy is like a button attached to
a rubber band, an ant walking along the
band as it is stretched will appear to have
a velocity slower than it really does. The
buttons (galaxies) are fixed relative to
space, but space itself is moving.
Another Analogy
• The expansion of the universe and the
increasing distance between galaxies is
similar to the increase in distance
between raisins in a rising loaf of raisin
bread.
• The raisins are fixed relative to the
dough, but the dough expands, increasing
the space between them.
• Problem with these analogies – loaves
and rubber bands have edges.
– We have seen no ‘edge’ to the Universe;
there are an equal number of galaxies in
every direction.
– Also, galaxies can move relative to space,
as gravity can accelerate one galaxy
toward another faster than space expands.
The Age of the Universe
• Thanks to the Hubble Law, we can
estimate the age of the universe.
• At some point in the distant past,
matter in the universe must have
been densely packed.
• From this point, the universe would
have expanded at some high speed
to become today’s universe.
• Assuming a constant expansion over
time, we find that the age of the
universe is around 14 billion years.