Astronomy 101

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Astronomy 101
Lecture 26, Apr. 30 2003
Cosmology the Expanding Universe (Chapter 26.1
26.4 in text)
Our exploration of astronomy from the small scale
solar system to the vast reaches occupied by
galaxies and quasars has revealed a tremendous
range of

• structures clumping of matter into planets,
  stars, gas clouds, galaxies, galactic clusters
  and superclusters.
• What if we look on even larger scales of the
  entire observable universe?
• What is the structure of the universe at the
  largest distance scales?
• How did the universe begin? What laws governed
  it?
• How will it evolve with time?
• This is the branch of astronomy and physics
  called Cosmology. In the past decade, there
  has been enormous progress in understanding the
  universe as a whole.

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north
Galactic maps out to 750 Mpc - about 10 of the
way to the most distant quasars show clumpings
corresponding superclusters out to about 500
Mpc. The amount of structure diminishes beyond
500 Mpc and universe becomes smoother. (Though
we now think the universe had small variations in
density even at the beginning). But on the
largest distance scales beyond 500 Mpc, the
universe looks the pretty much the same
everywhere.
We are here
distance
south
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Cosmology Assumptions
On the largest scale, we see no qualitative
differences when we look out in different
directions. The number of galaxies within a
given area on the sky, and the types and
clustering of galaxies we see are essentially the
same in all directions. The universe appears to
be isotropic. Similarly, the number of galaxies
we see in any given large volume of space is the
same as in any other similar volume at a fixed
time providing we take a big enough region,
larger than the size of superclusters. The
universe appears to be homogeneous at a given
time (but not unchanging in time). The
Cosmological Principle is the assumption that the
universe on the large scale is homogeneous and
isotropic so it is as good to study one large
region as any other. The cosmological
principle then implies that there is no edge to
the universe. And that there is no center to it
either! What we know of the universe is based
solely on the radiation light, radio waves,
X-rays, gamma rays etc. that come to us from a
distance. We interpret what these signals mean
using the laws of physics, deduced from earthly
labs. We assume that the Laws of Physics are the
same everywhere in the universe.
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Olbers Paradox
IF the universe were infinite in size and
unchanging with time then The night sky would be
as bright as the sun, everywhere ! The reason is
that any line outward from earth would ultimately
intersect a star thus that ray and all others
would report the brightness of a star.
(Think of being in a huge forest no matter
where you look, your line of sight ends on a
tree.)
Since the night sky is not bright, the
assumptions are wrong and indeed both are
wrong. The visible universe is limited in extent
by the time available for light to reach us.
There are parts we cannot see. The universe is
changing with time due to the Hubble expansion,
so we cant see infinitely far back in time.
Also, distant objects are not as bright, due to
the cosmological red shift. (And there is
extinction of light due to intervening dust and
gas.)
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We see more of the universe as time goes on.
Speed of light c 300,000 km/s is a constant
we can only see things that were close enough for
light to reach us. (See objects within the
light cone)
time
now
earlier
distance
Galaxy A
Galaxy B
Slope of line fixed by speed of light distance
over time. Range of universe we can receive
light from at an earlier time is less than now.
Now we can see Galaxy A and galaxy B, but earlier
we could not.
time
Us now
At the earlier time, galaxy A cannot see galaxy B
and vice versa. And they could not see us
either.
Us earlier
Galaxy A
Galaxy B
distance
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The cosmological red shift is key to our
observation of distant objects. Distant objects
are viewed as they were when the light started on
its journey so looking at highly red-shifted
objects is like time travel back to the earliest
days of the universe. z Dl/l is the red
shift and tells us the velocity of the object at
time of emission (Doppler effect). Through the
Hubble Law, v H0 d, we get its distance. And
since the time taken by light to reach us is t
d/c (cspeed of light3x105 km/s), the red shift
can be thought of as a cosmic clock, ticking as
the universe ages.
z (red shift) ? v (velocity) ? d
(distance) ? t (lookback time)
Doppler Hubble
speed of light
This sequence of galaxy photographs from the
Sloan Digital Sky Survey at increasing red shift
show the increasingly red appearance of more
distant (and fainter) objects.
z0.05
z0.1
z0.2
z0.3
z0.4
z0.5
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The Big Bang
We see distant galaxies receding with v H0 d ,
and the Hubble constant H0 is presently about 71
(km/sec)/Mpc (the best recent determination).
We can estimate where they were in the past If
the galaxies moved in past with the same velocity
we observe now, and continued along the same
line, we can project them back to calculate their
distance from us at an earlier time.
velocity v
distance d
galaxy
earth
The time T when this galaxy was on top of us is
given by d v T (distance rate x time), so T
d/v.
But the Hubble Law says v H0 d, based on
observation. Then the time T when the galaxy was
on top of us is (substitute v from Hubble Law
into Td/v) T d/v d/(H0 d) 1/H0 around
13 billion years ago
Notice that the calculation does NOT depend on
the distance of the galaxy now all galaxies
were apparently on top of each other 15 x 109
years ago. the BIG BANG -- beginning of the
observable universe
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Are we special because we see all galaxies
rushing away from us?
If there is just one place from which all things
expand and where the Big Bang occurred, it would
violate the cosmological principle, since that
place would be special. In fact residents of
every galaxy would see all the others receding in
proportion to their distance Top row of the
figure shows speeds of 5 galaxies separated by
100 Mpc, seen to obey Hubbles law by observer in
galaxy 3. We can compute what would be seen for
observer in galaxy 2 (middle row) or galaxy 1
(bottom row). All see Hubbles Law with all
galaxies receding from them !
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If observers everywhere see Hubble expansion, it
would seem that there is no true center of the
universe. And indeed since all matter was at the
same point at the Big Bang, we can say that the
center now is everywhere ! The proper way to
view the Hubble expansion and the cosmological
principle is to say that the universe itself is
expanding the space in which stars and galaxies
and light reside is getting larger with
time. Analogy with a spotted balloon as the
balloon the universe is blown up, the distances
between the spots the galaxies all increase and
the velocity with which any particular spot
recedes from another grows with
the separation distance of the spots. The whole
universe, like the balloon, is expanding,
carrying the galaxies apart with it. In this
analogy, the balloon is 2 dimensional, but the
universe is 3 dimensional.
(Galaxies dont grow with time they are
gravitationally bound)
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Interpretation of the cosmological red shift
When we described Hubbles Law based on the
increasing red shift with distance, we
interpreted this as a Doppler shift due to the
velocity of distant galaxies. A better
interpretation now is to say that the universe as
a whole including the space coordinates
describing up/down, left/right, in/out are
stretching with the expanding universe. Then a
wave of light with a certain wavelength in the
past is transformed into a wave with longer
wavelength with the expanding universe. A wave
emitted early in the history of the universe as
blue light is stretched to a longer red wave now.
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The future of the universe.
We see the universe is expanding (more properly,
we see that in the past, galaxies were receding
from each other). Will this expansion go on
forever? We need general relativity to really
work this out. General relativity says that the
presence of matter warps space (and time), and
matter follows curved trajectories in the warped
space. But Newtons mechanics works pretty well
to give us the picture, so lets use that. In
Newtons mechanics, the motion of a rocket shot
upwards can be predicted. consider a rocket shot
with the same speed from two planets of different
masses
On the larger planet, the rocket rises to a
maximum and falls back
On the smaller planet, the rocket slows down but
is able to escape the planet altogether
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We can plot the distance from the planet versus
time in the two cases.
For the more massive planet, the rocket rises to
a maximum height and returns. The d vs. t plot
is an inverted parabola.
For the less massive planet, the rocket continues
to rise forever, but it slows down, so the d vs.
t curve still bends downward with time.
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For the universe as a whole, the same principle
applies. The matter in the universe attracts the
expanding galaxies and would tend to slow the
expansion down. (Providing that there is only
gravity,due to the matter, is operating not
necessarily a good assumption!! See later!
) There is a critical density of matter (kg/m3)
above which gravity will ultimately win and the
galaxies will someday stop expanding and fall
back toward each other. If the density is less
than the critical value, the expansion of the
universe will continue forever. The critical
density (in the present epoch) is very small
about 8 x 10-27 kg/m3 . That corresponds to on
average just 5 hydrogen atoms per cubic meter.
Universe expands forever with finite velocity if
less than critical density
Fate of universe if greater than critical density
recollapse to Big Crunch
Or expands with velocity that ultimately goes to
zero if equal to critical density
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Not only does the future fate of the universe
depend on the density being greater or less than
the critical density, so also does the past
history. At present, we know that a galaxy at 1
Mpc is receding at v 71 km/s (Hubbles Law).
If the matter density is large, there is more
slowing down than if density is small, and
lookback time to the Big Bang is shorter. So
our estimate of the age of the universe also
depends on the matter density.
Actual age of universe is less in bound than
unbound case
Define the ratio of density to the critical
density as W0 W0 gt 1 means a bound or CLOSED
universe. W0 lt 1 means an unbound or OPEN universe
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Measuring the mass density of the universe is
hard to do experimentally. The visible matter
in stars and galaxies however seems to contribute
less than 1 of the critical density. Adding in
the matter in the great interstellar clouds of
gas dust and burned out stars brings the
density up to about 4 of critical. But remember
the dark matter! We see something like 5 times
as much dark matter influencing the rotatation of
stars around galaxies, and galaxies around
galaxies as there is matter associated with
atoms. If that is true, then we are up to about
27 of the critical density. But we are pretty
ignorant of the amount of dark matter, and really
dont know much about it in the furthest reaches
of the universe. We would like a more direct
measure of what the deceleration/ acceleration of
the universe is, and of the density. Recently,
studies of Type Ia supernovae have given us a
direct measurement of the deceleration.
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Supernova Project
Special telescopes scan the sky at new moon and 3
weeks later. A supernova is found if, in that
time, a new bright star has appeared. The big
telescopes like Hubble are then trained on the
supernova to measure its spectrum and time
dependence to determine its type, and if Type Ia,
its peak luminosity.
Type Ia supernovae are standard candles we know
their absolute peak luminosity. Measuring the
apparent brightness tells us their distance,
independent of the Hubble Law
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From the spectral lines red shift, we can get the
velocity. Thus for such a supernovae, we have
distance and velocity (without using the Hubble
Law), so we can check whether the expansion
velocity is really just what Hubble predicts.
If the velocity is smaller in the past than
expected from the Hubble Law, then v is
increasing and the universe is accelerating. If
velocity was larger in past, then universe is
decelerating (as we would expect from the
gravitational attraction slowing things down.
If universe is accelerating we see distant SNs
on the blue curve
If universe is decelerating (velocity is greater
at some fixed distance)we see distant SNs on the
red curve
SN distance
SN velocity
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distance
The data show a smaller velocity than predicted
from v H0 x d for the most distant galaxies
(around red shift 1). Apparently the universe is
actually accelerating. Contrary to expectations!
velocity
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Even if the matter density is less than critical,
it would still tend to slow the expansion of
matter, so acceleration is a real puzzle !
It looks like there is another ingredient besides
matter with gravitational attraction to the
universe one that is counteracting the effect
of gravity from the matter and is trying to push
the universe apart.
Call it Dark Energy! Dark energy exerts an
outward force on the universe, counteracting the
effect of gravity due to the mass, and tending
to accelerate the universe. About 73 of the
stuff in the universe is Dark Energy! We have no
clue what it is!