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Mapping the Universe
Measuring Distances with Standard Candles
Imagine that you find a star with an unknown distance, but you
notice that it has a distinctive characteristic that tells you that it
is a specific type of star. And let’s imagine that all stars of that
type have the same luminosity, and you happen to know the
value of that luminosity. You can then estimate the distance for
the star you found from the inverse square law of light:
b = L / d2 where
b is the brightness seen from Earth
L is the luminosity that all stars of
this type are known to have
d is the distance.
Objects that are distinctive and
have known luminosities are
standard candles.
Estimating distance
with a standard candle
measured expected
value
from Earth
L
b 2
solve for
d
The Distances to Galaxies with Cepheids
In the lecture on the Milky Way, we used RR Lyrae stars as
standard candles for measuring distances in our galaxy, but
most galaxies are too far away for telescopes to detect RR Lyrae
stars within them.
Like RR Lyrae stars, Cepheid stars
also pulsate in a regular fashion,
which makes them easy to
identify,
and
have
known
luminosities, so they too act as
standard
candles.
Because
Cepheids are brighter than RR
Lyrae stars, they can be detected
at larger distances, even in other
galaxies.
The Cepheid Period-Luminosity Relation
Unlike RR Lyraes, Cepheids have a wide range of luminosities.
But brighter Cepheids have longer pulsation periods, so if we
measure how fast a Cepheid pulsates, we can deduce its
luminosity from the relation shown below.
The Distance Ladder
Cepheids
100 milllion ly
RR Lyrae
10 million ly
parallax
1000 ly
Earth
Distance
Using Cepheids as a
standard candle, we can
measure distances to
galaxies out to 100
million light years (ly).
If we want to reach
galaxies beyond that
limit, we will need
additional methods of
measuring distances.
The Tully-Fisher Relation
The rotation speed of a galaxy
depends on its mass (as we
found when discussing dark
matter). Galaxies with higher
masses generally have higher
luminosities. So the luminosities
and rotation speeds of galaxies
are correlated, which is know as
the Tully-Fisher relation.
So using the Tully-Fisher relation,
we can estimate a galaxy’s
luminosity by measuring its
rotation speed, and then use that
luminosity to estimate the
distance of the galaxy.
The Distance Ladder
Tully-Fisher
600 million ly
Cepheids
100 million ly
parallax
1000 ly
Earth
Distance
RR Lyrae
10 million ly
Type Ia Supernovae
If a white dwarf gains enough matter from another star so that
its mass exceeds 1.4 M, it experiences a Type Ia supernova,
which is bright enough to be seen in distant parts of the
universe. These supernova always have the same luminosities,
and therefore can be used as standard candles for measuring
distances to the most distant galaxies.
The Distance Ladder
Type Ia Supernovae
3 billion ly
Tully-Fisher
600 million ly
Cepheids
100 million ly
parallax
1000 ly
Earth
Distance
RR Lyrae
10 million ly
Mapping Galaxies in the Universe
Galaxies are not scattered randomly in space. Most galaxies
are in groups and clusters. These clusters are arranged in walls
and filaments that are separated by huge voids.
Mapping Galaxies in the Universe
Mapping Galaxies in the Universe
The Origin of Structure in the Universe
Stars form from the gravitational collapse of ripples and
clumps in gas and dust clouds. Galaxy clusters formed in a
similar manner after the Big Bang, but on a far larger scale.
100 Mly
Age of universe = 0.2 billion years
The Origin of Structure in the Universe
Because it makes up most of the mass in the universe, dark
matter played a crucial role in this process. Clumps of dark
matter acted as the seeds that led to the formation of galaxies.
100 Mly
Age of universe = 1.0 billion years
The Origin of Structure in the Universe
The formation of galaxies probably would not have occurred
without the presence of dark matter.
100 Mly
Age of universe = 4.7 billion years
The Velocities of Galaxies
In 1912, Vesto Slipher obtained spectra of galaxies, which
he used to measure their velocities through the Doppler
shift of absorption lines.
The Velocities of Galaxies
Moving Toward Us
(blueshifted)
Moving Away From Us (redshifted)
The Hubble Law
Edwin Hubble measured distances to Slipher’s galaxies. He found
that galaxies with higher velocities away from us (higher
redshifts) have larger distances from us. This correlation between
distance and velocity is known as the Hubble Law.
But it’s very unlikely that we
are at the center of the
universe, so why are all of the
galaxies moving away from us?
1.5
3
(billion light years)
The Expanding Universe
At any location in a universe that is expanding, galaxies that are
farther away will appear to be moving away faster. In other
words, the Hubble Law would be observed by everyone in an
expanding universe. Rather than indicating that we are at the
center of the universe, the Hubble Law tells us that the universe is
expanding.
So galaxies are not flying
apart into the universe.
The universe itself is
expanding. The galaxies
are simply riding along
as the fabric of space
expands.
The Expanding Universe
The expansion of the universe also causes light to get stretched
to longer wavelengths, or redshifted.
So the redshifts that we measure for galaxies are not due to their
velocities away from us, but instead result from the expansion of
the space itself.
The Cosmological Constant
Einstein believed that the universe was static and unchanging.
However, gravity should eventually cause a static universe to
collapse. He didn’t like this idea, so he proposed the existence of
anti-gravity, which he called the Cosmological Constant, that
would prevent the universe from collapsing.
The Cosmological Constant
Shortly after Einstein developed the Cosmological Constant,
Hubble discovered that the universe isn’t static, and instead is
expanding. So Einstein was wrong to assume the universe is
static, and it wasn’t necessary to invent anti-gravity to
maintain a static universe. He referred to the Cosmological
Constant has his “greatest blunder”.
1.5
3
(billion light years)