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Cepheids are the key link
One primary justification for the Hubble Space Telescope was to
resolve Cepheids
in galaxies far
enough away to
measure the
Hubble flow
properly, and thus
obtain the age of
the Universe.
Along with other
methods, this
gives about
14 billion years.
Distances to Nearby Galaxies
The distance to…
Is measured by…
Which gives you…
Venus
Radar echoes
Astronomical Unit
Nearby Stars
Parallax
Main sequence
luminosities
Star Clusters
Main sequence fitting
Luminosities of
Cepheids
Nearby Galaxies
Apparent brightness
of Cepheids
Relation of distance
to redshift
There is a chain of links which get us out
to the distances of galaxies.
Errors in any one affect all the further
ones.
Galactic Redshifts
The relation is given by D=v/H ; D is distance, v is redshift velocity,
and H is the “Hubble constant”. H is about 25 (km/s)/(million ly).
The redshift is called “z”, where z = Dl/l ~ v/c. Remember, these
are only apparent velocities, caused by the expansion of space.
Distances deep into the Universe
You must use nearby galaxies to calibrate distance indicators that can be seen
across the Universe.
1) brightest star (hypergiants), brightest HII regions (star formation)
2)“Tully-Fisher” relation:
Luminosity in red or infrared correlated with 21-cm broadening
(number of stars)
(rotation rate)
3) largest spiral in cluster
4) brightest galaxy in cluster
5) Hubble expansion: distance is correlated with redshift
Assigning a distance by redshift
The Hubble law lets us use a simple spectrum of a galaxy to figure out
where it is along the
line-of-sight. Higher
redshifts indeed go with
smaller and fainter
looking galaxies.
Redshift takes us from 2-D to 3-D
Huge surveys are ongoing to
get redshifts for hundreds of
thousands of galaxies. These
give us the large-scale
structure of the Universe.
Quasar Spectra and the “Lyman-alpha Forest”
Redshifts tell us where
everything is…
us
Galaxy “Filaments”
QSO
Probing the Cosmic Foam
Gravity acting on dark matter gives the basic layout of matter in space.
Quasar absorption lines allow us to map out the gas not collected into
galaxies. Clusters will continue to collect, but the space between them
will continue to expand.
Hubble Expansion – what it is NOT
In an explosion, the stuff that is
moving faster will have gotten
further, so you would see what
Hubble saw. Despite the term “Big
Bang” to describe the expanding
Universe, that is NOT what is going
on!
The motion is only “apparent”
Galaxies stay fixed on the “co-moving” grid.
Their separation only increases because
the amount of space between them
increases. The scale of the Universe
increases, but not the scale of particles,
galaxies, or even clusters (anything
bound).
The expansion is only apparent on scales
of millions of light years.
Hubble Expansion – what it IS
Space itself is expanding… into the future…
The apparent increase of velocity with distance is due to the increase
in the amount of space that has expanded in a given amount of time.
There is no spatial center of expansion…
The center is the beginning…
There is no edge (except the present)
Local structure interferes with Hubble flow
We have to be careful in determining the expansion rate.
“Local” flow field
Supercluster density field
The Hubble Constant and the Age of the Universe
If you plot the scale of the Universe vs time, the Hubble constant is the
slope of the line now. If it’s really constant, then the age of the
Universe is just 1/H [since H=v/D=(d/t)/d].
That’s because if you know how fast we are expanding, you can run
the movie backwards and see when everything crunches together.
If the Universe is slowing its expansion, you get a younger age.
You can compare the age gotten
this way with the oldest globular
cluster, or other independent
methods. Recently they have all
come into agreement.
Density is Destiny
The shape depends on the curvature of spacetime.
The curvature of spacetime depends on density.
“Flat” corresponds to the “critical density”
~10-29 gm/cc, beyond which the
Universe would recollapse.
Curvature of the Universe
Since gravity is spacetime
curvature, the density sets the
geometry. Only in a “flat”
Universe do parallel lines stay
next to each other. In a
“closed” Universe, in
principle a beam of light
eventually comes back upon
itself.
In principle, we can measure
the geometry of spacetime
through geometrical tests. For
example, you can count the
number of galaxies in a given
patch of sky as you go further
out. These tell us our ultimate
fate.
Spacetime Diagrams
In order to picture spacetime
(which is 4-dimensional), it
helps to get rid of some
spatial dimensions, and
keep time as a shown
dimension.
Here is a diagram with only
2 dimensions, one space and
one time. Light is the fastest
thing in it, and marks out
“lightcones” which
determine what can be seen,
and when. An object’s
existence is a “worldline”.
The Spacetime
Diagram of an
Expanding Universe
If space expands with time,
a 2-D spacetime diagram
looks like this. All spatial
points converge at the
beginning. The Universe is
opaque for a time, so you
see the fireball in the
distant past in all
directions. You see more
distant objects as they
were in the more distant
past. Beyond a horizon, the
rest is unobservable (now).
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