Astro 105: Our Place in the Universe

1
Astro 105 Our Place in the Universe
Lecture 12

• Lecturers
• J.P.Ostriker
• A.E.Shapley
• J.E. Gunn
• P. Steinhardt

2
Reading

• Chapters 8-11 in Rees, Just Six Numbers
• Scientific American article, The Cosmic
  Symphony by Hu and White
• Scientific American article, Misconceptions
  about the Big Bang by Lineweaver and Davis
• Problem set 5 is due next Thursday, November
  17th
• Midterm solution set available on course website
  and on Blackboard (under syllabus)

3
Overview

• What stuff is the Universe made of?
• How much of it is there?
• The total amount of stuff (mass and energy)
  determines the the expansion history (future) of
  the Universe and the overall geometry of
  spacetime.
• A major goal of observational cosmology in the
  last half century has been to determine the
  cosmological parameters of the Universe (i.e.
  nature and amount of the stuff)
• Very important parts of current picture are
  Dark Matter and Dark Energy

4
Review

• Distances (check the one for the edge of the
  observable Universe)
• The critical density and the dynamics of
  expansion
• Matter and the geometry of the Universe
• Estimates of Wm baryonic, non-baryonic
• Dark Matter
• Today Review estimates of Wm the nature of
  Dark Matter Cosmological Redshift Evidence for
  Dark Energy The Cosmic Microwave Background

5
Distances in the Universe
Think of natural units for each problem.
Distance
Light Travel Time
c3x1010 cm/s, speed of light
6
Escape velocity and the critical density

• A few important cases
• Wm forever, and have an open infinite geometry
• Wm1, rrcrit, and the Universal expansion
  assymptotes to zero at infinity (with no other
  energy sources), and the Universe has a flat
  infinite geometry (called Einstein-de Sitter
  Universe)
• Wm 1, rrcrit, and the Universal expansion
  stops, turns around, and the Universe collapses
  back on itself, with a closed finite geometry
  (sometimes called the Big Crunch)

7
Matter and the Geometry of Space
Reminder Closed Universe recollapses Flat
universe (no dark energy) is just balanced Open
universe expands forever The geometry and
expansion history are both determined by the
overall density.
8
Matter and the Geometry of Space
W1, closed rrcrit
W1, flat rrcrit
W 9
Escape velocity and the critical density

• A few questions came up last time
• What does it mean that the flat (matter-only)
  Universe assymptotes to zero expansion rate at
  t8? Maybe an easier way to think about it is
  just that if you compare the change in expansion
  rate for an open and flat universe (both infinite
  in extent), you find that the flat universe slows
  down a little more than the open one. If the time
  since the Big Bang is t, then the size goes as
  t2/3 power. The rate of change of that size goes
  as t-1/3 power, so as t gets really big, the rate
  of change goes to zero.

10
Escape velocity and the critical density

• A few questions came up last time
• (contd). In fact, the Hubble Expansion rate is
  defined as the rate of change in the size of the
  Universe divided by the size of the universe
  (v / d). So, in a flat Wm1 Universe, H(t) is
  proportional to 1/t. So as t approaches 8, H(t)
  approaches zero.

11
Escape velocity and the critical density
A few questions came up last time 2. How are the
expansion dynamics related to the whole geometry
(and finite vs. infinite nature) of space. Well,
lets consider a closed universe. If a beam of
light is emitted, it traces the geometry of
space. At some point, when the Universe contracts
in the Big Crunch, the light beam is going to
have to curve back on itself. This example should
illustrate both the finite and closed nature of
the Wm1 Universe.
12
Matter and the Geometry of Space
Reminder Closed Universe recollapses Flat
universe (no dark energy) is just balanced Open
universe expands forever The geometry and
expansion history are both determined by the
overall density.
13
What is the Matter in Wm?

• One way is to directly estimate it
• Count up all the ordinary matter
• Stars only make up W
• Gas atomic, molecular, hot (ionized)
• -galaxies contain gas (molecular clouds,
  neutral atomic gas, warm ionized gas, hot gas)
• -clusters of galaxies contain hot gas
• -there is ionized and neutral gas in the
  intergalactic medium
• Current best estimate is Wb0.04-0.05

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What is the Matter in Wm?

• 1933, Fritz Zwicky notes that galaxies in the
  Coma cluster move much faster than mass
  calculated for visible galaxies would indicate.

Zwicky, abrasive Swiss astronomer, professor at
Caltech, known for calling people spherical
bastards because they were bastards every way
he looked at them. Known to accost unfamiliar
students in the hallway of the astro building
with Who the hell are you??? Many other
discoveries supernovae, gravitational lensing
15
What is the Matter in Wm?

• 1970s, Vera Rubin showed that stars in the
  outer parts of galaxies rotate just as fast as
  stars in the inner parts of galaxies
• According to Newtons laws, if there were only
  visible matter, the stars in the outer parts
  should rotate more slowly

16
Measuring Wm

• Many different techniques for measuring Wm
• Two fairly simple methods
• Mass-to-light method
• Baryon-fraction method

17
Measuring Wm

• Mass-to-light method
• 1. Determine average ratio of total mass
  (luminous and dark) to emitted light in largest
  systems possible.
• 2. Multiply this ratio by luminosity density
  of the universe (determine this from adding up
  the light from statistical samples of galaxies)
• Clusters of galaxies are ideal for
  determining this Mtot/L ratio 1-2 Mpc in radius,
  2x1014-10x1014 Msun (10s -100s of galaxies).
  Appears valid up to the regime of superclusters,
  10 Mpc scales.
• Measure cluster mass 3 different ways galaxy
  motions, X-ray gas temperature, gravitational
  lensing
• Mtot/L20070 (if you measure the luminosity of 1
  Sun, there is the mass of 200 suns)
• Yields Wm0.2 0.1

18
Measuring Wm

• Mass-to-light method (1970s, 1990s, Ostriker,
  Bahcall)
• 1. Determine average ratio of total mass
  (luminous and dark) to emitted light in largest
  systems possible.
• 2. Multiply this ratio by luminosity density
  of the universe (determine this from adding up
  the light from statistical samples of galaxies)
• Clusters of galaxies are ideal for
  determining this Mtot/L ratio 1-2 Mpc in radius,
  2x1014-10x1014 Msun (10s -100s of galaxies).
  Appears valid up to the regime of superclusters,
  10 Mpc scales.
• Measure cluster mass 3 different ways galaxy
  motions, X-ray gas temperature, gravitational
  lensing
• Mtot/L20070 (if you measure the luminosity of 1
  Sun, there is the mass of 200 suns)
• Yields Wm0.2 0.1 (after calculating luminosity
  density)

19
Measuring Wm

• Baryon fraction method (1990s)
• Again, use clusters, which scoop up mass from
  large volume of space, so should be
  representative of baryon to total matter density
• Measure ratio of baryonic cluster mass (mass of
  hot gas plus stars) to total cluster mass
  fWb/Wm
• Then we independently know Wb from other methods
  (the Deuterium to Hydrogen ratio in the early
  Universe)
• So, Wm Wb / f f is measured to be 0.15. So,
  given Wb0.045, Wm0.3 (less than rcrit)
• Other methods for determining Wm Evolution of
  cluster number density out to high redshift, weak
  lensing, shape of matter power spectrum, CMB

20
What is Dark Matter?

• WIMPS Weakly Interacting Massive Particles
  (non-baryonic). Exotic sub-atomic particles like
  axions, photinos, neutralinos, produced in the
  early Universe only interact through gravity (no
  charge or other forces) however, try to detect
  rare WIMP interaction with ordinary matter No
  definitive detection yet.
• Neutrinos with mass (no charge), produced in
  the early Universe, in fusion reactions in the
  centers of stars, and in supernova explosions
  detected, apparently have mass, but not massive
  enough to make up Wm
• MACHOS Massive Compact Halo Objects (baryonic)
  these would be low-mass stars like Black Holes,
  Brown Dwarfs, and planets, that are very hard to
  detect. Try to detect though gravitational
  microlensing events. Not enough to make up Wm.

21
Another possibility

• What if theres no dark matter, but actually
  the gravitational force doesnt behave like 1/r2?
  This idea is known as MOND (Modified Newtonian
  Dynamics).
• The idea is that Newtons laws were demonstrated
  for the solar system. What if they dont work on
  galaxy scales?
• MOND reduces to Newtonian dynamics for high
  accelerations, but
• MOND has some problems. If the Universe has no
  Dark Matter, there are other observables that are
  not explained (clusters, fluctuations in the
  microwave background)
• Scientific method! Model must explain the
  observations!

22
Wm Summary

• Baryonic matter density corresponds to
  Wb0.04-0.05
• Dark Matter density corresponds to WDM0.23
• Total matter density corresponds to Wm0.3

Ordinary matter

• Our current estimate is that ordinary matter
  (protons and neutrons), only makes up a small
  fraction of the total matter density in the
  universe.

23
Complications

• Things are now going to get a little harder.
• We need to discuss the cosmological
  interpretation of redshift.
• Also, so far we have only been talking about the
  density associated with matter (baryonic and
  non-baryonic). Actually we also need to include
  the effects of Dark Energy (the largest fraction
  of that pie chart), which has an impact on the
  overall expansion history and geometry of the
  Universe.
• Thats why some of the preceding slides dealing
  with matter density specifically say
  matter-only when talking about the expansion
  and geometry of the Universe.

24
Cosmological Redshift
25
Redshift/Doppler Shift
Redshifts/blueshifts described as due to
recessional/approaching velocities That model
works okay for things near us, like objects
moving in our galaxy, and M31, which is actually
falling towards us (Milky Way and M31 might merge)
26
Redshift/Doppler Shift

• c3x1010 cm/s
• Speed of light frequency x wavelength
  constant
• So longer wavelengths mean lower frequency.
• Shorter wavelengths mean higher freqency.
• Photon energy proportional to frequency, inverse
  of wavelength

27
Redshift/Doppler Shift
We said that zv/c, which is an approximation of
the Doppler formula for small v. The exact
formula is actually 1z (1v/c)/(1-v/c)1/2
which reduces to above formula for vz, v approaches c, according to this formula.
Cant have vc.
28
Redshift/Doppler Shift

• According to the Doppler shift model, the
  galaxies are moving through space.
• At some point Hubbles Law, vH0xd, would have to
  break down, because v could not be greater than
  the speed of light.
• But, in fact, the galaxies are NOT moving through
  space. Rather, space itself is expanding. At
  large distances, the Doppler formula is an
  INCORRECT way of interpreting redshifts!
• Remember the picture of the chessboard

Space at a later time -- its expanded
Space at an earlier time
29
Cosmological Redshift
If the balloon is space, and the coins (??)
taped to the surface of the balloon are galaxies,
you can see that as space expands, the
separations between the coins (galaxies) grow
larger. This picture is analogous to the galaxies
tracing the expansion of the Universe.
Also, the coins themselves dont expand, just
like the radii of galaxies dont expand with the
Universes expansion
30
Cosmological Redshift
So then what does cosmological redshift
mean? Redshift is due to the expansion of the
universe, which stretches the wavelength of light
passing between galaxies. Light from more distant
objects travels for a greater time (because light
has a finite speed), the Universe expands more
while the light travels to us, and the
wavelengths get more stretched.
Size of the Universe when the light was emitted
Size of the Universe now, when we observe the
light
31
Matter and the Geometry of Space
Reminder Closed Universe recollapses Flat
universe (no dark energy) is just balanced Open
universe expands forever The geometry and
expansion history are both determined by the
overall density.
32
Cosmological Redshift
The important formula is observed
wavelength/emitted wavelength (size of the
Universe now)/(size when the light was
emitted) lobs observed wavelength, lememitted
wavelength rnowsize of the Universe now remsize
of Universe when light was emitted lobs/lem
rnow/rem Remember, lobs/lem 1z, so 1z
rnow/rem For any given object, z is easy to
measure (remember redshifts are the easy part).
Now were saying that the redshift tells you by
how much the Universe has expanded in the time
its taken for the light to get to us.
33
Cosmological Redshift Example
Quasars are galaxies that host supermassive
black-holes in their centers. The energy from
the matter falling onto the BH makes the quasar
much brighter than normal galaxies, so you can
see them out to GREAT distances.
Question Why does this spectrum show emission
lines? What do they mean?
34
Cosmological Redshift Example
Lya emission line observed at lobs4042Å Rest
wavelength is lem1216 Å CIV emission line
observed at lobs5150Å Rest wavelength is
lem1549Å
What is the redshift? How much has the Universe
expanded since the light was emitted?
35
Cosmological Redshift Example
Object is far enough away that you cant apply
simple Hubbles Law to get distance based on
redshift. Why is this????
What is the redshift? How much has the Universe
expanded since the light was emitted?
36
Dark Energy, WL
37
Expansion History

• We had a simple picture for Hubbles law vH0xd.
• This holds in the nearby Universe.
• However, it turns out that H0 is just the value
  of the expansion rate today (the current change
  in size per unit time divided by the current size
  of the Universe). At earlier times, the expansion
  rate was different (depending on the matter and
  energy density in the Universe). At earlier
  times, t, HH(t)?H0.
• Even if we interpret redshifts as the expansion
  factor of the Universe since the light was
  emitted some distance from us (rather than as
  recession velocities), we can still use redshifts
  and distances to probe how H(t) evolves.

38
Expansion History

• Even if we interpret redshifts as the expansion
  factor of the Universe since the light was
  emitted some distance from us (rather than as
  recession velocities), we can still use redshifts
  and distances to probe how H(t) evolves.

Because light has finite speed, measuring objects
at large distances allows us to probe earlier
times (x-axis). Distancect. Redshift allows us
to probe the relative size of the universe at the
time the light was emitted to its current size
(y-axis). So, a redshift vs. distance plot is
equivalent to an stretch-factor vs. time plot.
Now
Earlier
39
The Rubber Band Analogy
Stretch factor of rubber band is like expansion
factor of Universe, or redshift. Distance is a
proxy for time. The point is that the
relationship between distance and redshift
(observed) depends on the nature of the expansion
history.
Redshift
40
The Rubber Band Analogy
So far, we have only talked about cases in which
the expansion rate decelerates. In all of the
closed, flat, and open matter only models weve
looked at, the expansion rate is decreasing.
This plot shows another option.
Redshift
41
The Rubber Band Analogy
It is possible to distinguish between the case of
an accelerating and decelerating Universe. You
start being able to tell the difference at
zseveral tenths.
Redshift
42
The Supernova Story
What are Type Ia Supernovae? Explosion when dead
star (white dwarf) becomes a natural
thermonuclear bomb. Progenitor is probably normal
star when star uses up its fuel, it evolves into
a white dwarf (size of the earth), which
cools. Type Ia SNe occur when a white dwarf has a
companion star, which dumps material onto the WD,
causing the WD to become denser and denser, until
a major explosion results when the WD crosses a
certain mass and density threshold.
White Dwarf
43
The Supernova Story
What are Type Ia Supernovae? Explosion (expanding
fireball) reaches maximum luminosity in about 3
weeks, and then declines in brightness over a
period of months It turns out that the
intrinsically brighter explosions also last
longer than the intrinsically fainter ones. Once
this relationship was well calibrated, Type Ia
SNe became great distance indicators!
White Dwarf
44
The Supernova Story
What are Type Ia Supernovae? Measure light
curve shape of supernova. Determine intrinsic
peak luminosity. Compare with apparent magnitude
-- Distance Type Ia Supernovae are very very
bright (as bright as a billion suns) so you can
observe them out to really large distances,
probing the expansion history by comparing their
distances and redshifts.
White Dwarf
45
The Supernova Story

• Two independent teams High-Z Team (started in
  1995 and led by Brian Schmidt of Mt Stromlo and
  Siding Spring Observatories in Australia), and
  the Supernova Cosmology Project (started in
  1988 and led by Saul Perlmutter of Berkeley)
• Both teams are trying to measure distances and
  redshifts to Type Ia Supernovae
• A Type Ia Supernova goes off once every 300 years
  in a typical galaxy. So, they need to survey
  thousands to find about one per month.

46
The Supernova Story
This shows the technique of finding the Type Ia
supernova explosions. Image the same galaxy
separated by several days, take the difference.
Then do follow-up imaging and spectroscopy of SNe
candidates (get distances and redshifts).
47
The Supernova Story
It is possible to distinguish between the case of
an accelerating and decelerating Universe. If the
Universe is accelerating, supernovae at a given
redshift will look fainter than if the Universe
is decelerating (because they are further away).
Redshift
48
The Supernova Story
If the Universe is accelerating, supernovae at a
given redshift will look fainter than if the
Universe is decelerating (because they are
further away).
Big result In 1998, both teams found that the
Universe is accelerating!!!
49
The Supernova Story
Remember x-axis is time, which is equivalent to
distance. Objects that are farther away tell us
about the Universe at earlier times. Y-axis is
redshift (or inverse redshift) size of Universe
at earlier times compared to size now. At tNow,
all models have the same size and H0 (expansion
rate). But look at how they start to diverge at
earlier times (more distant obj).
Different colors are models with different
amounts of stuff
50
The Supernova Story
The point is that the red curve (which is for an
accelerating Universe) has a smaller redshift at
a given distance (time in the past) than the
green curve. Lets look at 10 billion years in
the past. See how the red curve is higher than
the green curve. That means that the Universe
stretches less between 10 billion years ago and
tnow, for the red curve. Equivalent to other
plot.
51
The Supernova Story
The red curve is our current best estimate of
what the Universes expansion history looks
like. It is not decelerating, but actually
starting to ACCELERATE!! We attribute this
acceleration to DARK ENERGY, or the COSMOLOGICAL
CONSTANT
52
The Supernova Story
In fact, the Hi-Z team describes it as a cosmic
jerk that took place 5 billion years ago. Funny
moment when NY Times article appeared in 2003
called A Cosmic Jerk that reversed the
Universe (showing a picture of the astronomer
Adam Riess) Science Magazines Discovery of the
Year in 1998
Side note notice how the age of the Universe is
different for the different models
53
Cosmological Constant

• If its true that the Universe is accelerating
  (though read caveats in Scientific American
  article), what makes it do so?
• Einsteins equations for general relativity
  imply that expansion can speed up if exotic form
  of repulsive energy exists
• Einstein didnt know about Hubble Expansion
  (derived equations for dynamics of Universe in
  1917, 10 years before expansion was discovered),
  and believed Universe was static.
• Couldnt find static solution to his equations,
  so introduced a constant fudge factor which
  balanced gravity and kept the Universe static,
  (allowed for other solutions to equations of
  motion)

54
Cosmological Constant

• Then expansion of the Universe was discovered,
  and equations without cosmological constant
  seemed to describe them very well.
• Einstein declared the Cosmological constant, L,
  the biggest blunder of his scientific career.
• However, now it appears that the Cosmological
  Constant may be the best way to describe the
  accelerating Universe.
• This universe is spatially flat (remember our
  definitions), but is accelerating.
• So, clearly our different cases of Wm1,
  are not the only ones to consider

55
Cosmological Constant

• There is a density associated with L. We can
  then define WL, the ratio of the density in this
  Cosmological Constant form to the critical
  density.
• As we will discuss next, the combination of the
  supernova and CMB observations suggest Wm0.3
  (less than critical matter density) and WL0.7.
  The sum of Wm and WL is 1, leading us to believe
  that the total W1, which is the description of a
  flat overall geometry.
• The Microwave background offers independent
  evidence for the cosmological constant. So well
  talk about that next.(plus its historical
  background).