Cosmology
Distances
- In 1924, Edwin Hubble measured the period of Cepheids in Andromeda. The distance that he
came up with put the object much further away than the edge of our galaxy. The only
conclusion was that there are other galaxies. This was a huge fundamental shift in
our understanding.
- As soon as Hubble realized that these spiral nebulae were external galaxies, Hubble began
measuring the distances to these objects. Another bit of information that he had was
their radial velocity (how fast they are moving away from us).
- It turned out that nearly all of these galaxies are moving away from us and, more than
that, in 1929 Hubble presented one of the most important astronomical discoveries of our
times: The HUBBLE LAW.
- The Hubble Law states that the galaxies distance is directly related to the galaxies
velocity. In other words, the more distant the galaxy was, the faster it is moving away
from us. This means that the universe is expanding. Hubble's Law is written as
velocity = Hubble's Constant times the distance.
- Below is Hubble's original plot:
- The actual value Hubble's constant is extremely important and this was one of the main
missions of the Hubble Space Telescope. The value is known now to about 5% accuracy,
whereas before HST it was known to about 50% accuracy.
Velocity = H0 x Distance (H0 is called Hubble's constant and it is somewhere
around 71). For this equation, we put velocity in km/s and distance in Mpc.
- As well as Cepheids, supernova can act as standard candles. The advantage with supernovas
is that they are extremely bright and we can see them to far distances. In fact, supernovas
are one of our best measurements of the shape of the universe since we can see them so
far back in time.
- Another distance measurement comes from the Tully-Fisher relation. The Tully-Fisher
also uses a correlation (like Cephieds) in that there is a relation between the brightness
of a galaxy and the rate at which is spins. The faster the galaxy is rotating, the
brighter it is. This correlation has been used to measure galaxy distance at the edge
of the observable universe.
- As our most extreme case of a standard candle, gamma-ray bursts may be very important
once we understand them, since they are the brightest objects in the universe.
- The plot below provides a summary of the distance ladder:
Expansion of the Universe
- Hubble showed that the universe is expanding and this has significant consequences.
First, it says that early in the universe galaxies were closer together. Extrapolating
this, we realize that the universe began at an infinite density or a singularity.
This eventually was formulated as the Big Bang.
- Another consequence is that since space is expanding, then distances between all galaxies
is expanding. In other words, the universal expansion is seen by every galaxy.
- If the universe had been expanding since the beginning of the universe, then we can
use the expansion rate (Hubble's constant) as a measure of the age of the universe.
This places the age around 14 billion years. Fortunately, the age of the oldest
globular cluster is around the same age (if it was older we would be in trouble).
- Thus, the fact that the universe is expanding confuses the issue of galaxy velocities.
The question is whether the galaxies themselves are moving that fast or are they
standing still and space is expanding. This expansion of space mimicing as a velocity
is what we can the COSMOLOGICAL REDSHIFT. The wavelength of the emitted light is redshifted,
but that can be due to either a velocity or a expansion.
Basic Structure
- In order for us to understand galaxy formation we must first measure basic
properties of the Universe, for example: age, size, mass.
- There are three underlying principles that govern much of our understanding
of the Universe. These are 1) cosmological constant, 2) the Heisenberg
Uncertainty Principle, and 3) the Anthropic Principle.
Cosmological Constant
- One of the most
important properties that has been realized in the last few years is the
cosmological constant.
- The cosmological constant was invented by Einstein. Based on his GR equations,
he discovered that the Universe could not be standing still since the mutual
gravitational attraction would cause it to collapse in on itself. However,
he firmly believed in a static Universe (unchanging). Thus, he proposed
a repulsive force that counteracted gravity. He simply inserted a fudge
factor into his equations, and this was called the cosmological constant.
- Einstein proposed this in 1915. In 1924, Hubble discovered that Andromeda
was a galaxy significantly far away from us (this was a fundamental breakthrough),
and subsequently measured HUBBLE'S LAW.
- This results instantly showed that the Universe was expanding. This proved
to Einstein that we don't live in a static Universe and that there was no
need at all to include his fudge factor. Einstein calls this his biggest blunder.
- Essentially noone thought that a cosmological constant existed for about 80 years
after Einstein came up with the idea. Now it looks like the cosmological constant is the dominant source
in the Universe! Einstein's blunder may be one of his greastest triumphs.
Recent Supernova Results
- As we discussed earlier, the best way to understand the expansion of the
Universe is to measure distances between objects. Supernovae are one of our
best examples we have in order to do this. Below are a few examples of
supernovae in distant galaxies.
- We measure the brightness of these supernovae and since they are standard
candles, we can get their distances. The plots below demonstrate how we
use these distances to understand the structure of the Universe. In each
of the plots, we are plotting the redshift on the bottom axis and
a distance indicator on the side axis.
- There are two main groups working on this project and the plot below shows
the results from both groups. They are remarkably consistent with each
other which is always a strong sign that something correct.
- All of the results suggest that the
Universe is dominated by the cosmological constant. Today, the cosmological
constant is over twice as important as the matter in the Universe. This
represents a huge step in understanding the structure of the Universe.
- The supernovae at high redshifts are very important. Just the one SN at z=1.7 was
critical for a lot of the dark energy discussion: it is so distant that it puts tight constraints on the
various models. However, there is still a very large uncertainty since we
have to make sure we understand how supernovae evolve, if they do at all.
- Below is the most recent update of the SN data: