Download Power Point of Slides I never Got to

Next Topic, Brute Force
Let’s go measure a lot of redshifts, assume z tells
us the distance, and see what we can see. => The
“z machine of Huchra and Geller
Degrees
across the
sky
Velocity
The
Coma
cluster
Great
wall
void
Latest and Greatest
“Blow up” of Great Wall
http://www.angelfire.com/id/jsredshift/grtwall.htm
Sloan Survey Image
The Next Great Leap Forward:
Sloan
Goal to really tie down how the light is
distributed. A million redshifts @$80/redshift!
[Make no small plans No results from this yet,
but lots of other neat stuff which we won’t talk
about.]
Generate is a “Power Spectrum”
Do with galaxies just by “blindly assuming”
redshift gives distance and all galaxies “created
equal,” i.e no correction for galaxy mass.
http://astro.estec.esa.nl/Planck/report/redbook/146.htm
We generate the “power spectrum” by measuring the
apparent (based on redshift and trigonometry), the
distance to the next galaxy, the next and the next. We
build up the information on the probability of finding
the next galaxy and the next galaxy at a certain
distance.
Number of Objects
Concept:
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Separation distance
=>
CMB
over
laid
Galaxies
“shape
parameter” is
needed to go
from
fluctuations in
“brick wall” to
galaxies
See that G = 0.25 is
not consistent with
Wb =0.05, Wm =1, h =
0.5; more reason for
us to assume L > 0
to have a flat
universe.
G = Wmh exp[-Wb(1 + sqrt(2h)/Wm)]n; JP, page 481
As of a few years ago; the CMB
derived values are the boxes
CDM
model
doesn’t
fit all!
Fits
CBM
<= larger scales this way
The galaxy “power” data are the
vertical lines
Figure 1.13: The boxes in the left hand panel show constraints on the power spectrum P(k) of the
matter distribution in an universe implied by observations of the microwave background
anisotropies (adapted from White et al. 1994). The points show the power spectrum of the galaxy
distribution determined from various galaxy surveys (see Efstathiou 1996). The right hand panel
illustrates the accuracy with which PLANCK will be able to determine the power spectrum. The
solid curve shows the matter power spectrum expected in an inflationary cold dark matter (CDM)
universe. The dotted curve shows a theoretical prediction for a `mixed dark matter' (MDM)
universe consisting of a mixture of CDM (60%), massive neutrinos (30%) and baryons (10%).
but not
galaxies
Update: 2001
Real space galaxy power spectrum of
PSCz.
Data: correlated power spectrum (version of October
2001).
Data: decorrelated linear power spectrum.
The dashed line is the flat LCDM concordance model
power spectrum from Tegmark, Zaldarriaga & Hamilton
(2001), nonlinearly evolved according to the
prescription of Peacock & Dodds (1996). The model fits
well at linear scales, but fails dismally at nonlinear
scales. The PSCz power spectrum requires scaledependent bias: all unbiased Dark Matter models
(Eisenstein & Hu 1998, 1999; Ma 2000) are ruled out
with high confidence. Real space correlation function of
PSCz. Data: correlation function (version of October
2001). The dashed line is a power law (r / 4.27 h-1Mpc)1.55.
Prewhitened power spectrum of PSCz. Data:
prewhitened power spectrum.
The solid line is the (unprewhitened) power spectrum.
The dashed line is the linear LCDM concordance model
power spectrum from Tegmark, Zaldarriaga & Hamilton
(2001). The prewhitened nonlinear power spectrum
appears intriguingly similar to the linear power
spectrum, as remarked by Hamilton (2000). It is not
clear whether the similarity has some physical cause, or
whether is is merely coincidental.
Basic point of the previous slide is that in theory
the measurements of the density fluctuations in
the CMB and galaxies are tied together and one
model needs to fit all.
And it is difficult to measure both on an
overlapping length scale. Galaxies are easier to
measure on the relatively small scales, CMB on
large ones. For the CMB, the z = 1000 means
that today the CBM scale as been stretched by
1000 => That’s the problem.
Bottom line:
Power spectrum of galaxies is difficult to
measure and harder to simulate.
So far, we have no good answers.
Walls,voids, and power spectra of galaxies
require theorists to “fine tune” (dare we say
“fudge”?) their models, but there seems no
way out for now. And getting CMB, Wb , Wt,
and galaxies to all fit is difficult.
Using H0 and distance indicators,
the classic tests
(1) Number of objects versus redshift
(2) Luminosity distance versus redshift
(3) Angular size versus redshift
Number of objects versus z
The name this goes by is “logN logS”, this is
because the range is so large we need to use
logs for our ; and which reduces to a straight
line if plotted as logS and “S” because this
was the way radio people labeled the
apparent brightness.
LogN LogS
For a Euclidean universe the total number see
out to a certain limiting sensitivity ( lowest
possible value of S) goes as S-(3/2), easy to
show for standard candle case. Without the
details, S goes as L/4pD2 for a fixed L and the
Volume we are observing to goes as D3 => our
exponent [solve for D in terms of S and
substitute in to the N = density x (4/3) p D3
equation] is then -3/2
This never worked until recently
Because of: “Evolution”. The number of objects per
unit volume and the intrinsic luminosity changes.
This test failed when we used radio sources. (Because
radio is relatively cheap and easy we used radio
first.) Rich clusters of galaxies are so “simple” we
think we can calculate the evolution, however, and
we’ve done this. (cf. The first third of the course)
To do the test correctly you have to be sure that you
are always comparing the objects with the same
intrinsic brightness (implies they are the same
physically = size and mass) => be careful
Apparent brightness versus z
This has apparently been worked out, i.e.
supernovae! But nothing else because the distant
objects are different from nearby ones and we can’t
predict (model) how. Some math details
For L = 0 it is relatively easy to derive a
relationship between dL and Omega and z
dL= (4c/H0W02)x[zW0/2 + (W0/2-1)(-1 sqrt(W0z+1)]
dL is called the Luminosity Distance and
clearly depends of W and z and scales as H0
Apparent brightness versus z
The one key point is that 4pdL2 is what we divide the
luminosity by to predict a flux,F and then we assume
we have a standard candle and we know L and then
we compare predicted F with observed F.
Abundances:
Why is this important for Cosmology?
Because He/H, D/H, and Li/H are all
predicted by BB nucleosynthesis
The values of these ratios that we
measure can then be used to infer Wb
which we can use to infer there must
be WIMPs
Key Concepts
Need to be sure the region we observe is close to
“primodial” = the initial stuff left over form the BB.
The reason we can’t use measurement of abundaces
here on Earth.. There have been too many changes. No
need for you to know them all.
Need to be sure you are counting all the atoms which
can be “hidden”: for example , ionized, atomic, and
molecular H all give different “finger prints”
Key Concepts, cont.
Atoms can absorb (absorption lines) and re-radiate
light (emission lines). Only certain kinetic energy
values are allowed (this is Quantum Mechanics; take it
as given here) for the electrons circling the nucleus.
Cool Atom model
We use both absorption and
emission line studies
Emission lines are generally harder to come by
because the gas has to supply the light were as we
can look for a bright “light bulb” that shines
through cooler (means there are atoms with
electrons in orbits that are low enough to absorb
the light and make “lines”
Real live examples: Stars
Hotter interior
Cooler
atmosphere
Absorption lines are the darker regions
MK Types
White
O5V
B1V
A1V
F3V
G2V
K0V
M0V
Key to inferring the element type is the spacing of
the lines.
Key to inferring the amount is the darkness
(and width) of the lines.
Key to interpretation: must assume atoms
haven’t been created or destroyed.
Helium
Two places to look: star atmospheres and the
interstellar medium.
He is nice because it is chemically inert, so we
don’t have to worry about it’s being bound up.
Helium is also nice because it has a very stable
nucleus and is not likely to be destroyed.
It might be created, however since H is burned
into He in stars. => look for the lowest values we
can find
How low can you go? Part I
Concept is that Oxygen was made
after the BB, so the presence of O
is a measure of contamination
Make a measure of He/H versus O/H
and “extrapolate to “zero” O.
And look at stellar atmospheres
A delicate measurement
SN
only go
to here
“How low can you go?”, Part II
He/H is
defined as
Y
More on definition of Y
There are 2 ways to measure ratio, by mass and
by number. When astronomers measure by
mass, they call the ratio Y, and for all the
elements heavier than He, astronomers call
these elements “metals” and call the ratio of
metals/H = Z.
How do we convert from mass to number for He?
More on definition of Y
Y= mass of He/(mass of He + mass of H + mass
of metals) ; assume metals are negligible
Or Y = mHex NHe/(mHex NHe+mH x NH)
Take mHe = 4mH, and mH =1, and substitute in,
then do algebra. Find that if Y = 0.25 = 1/4,
that NHe/NH = 1/12 or about 8% => 25% by
mass is equivalent to 8% by number =>
Always be sure to ask, by mass or by number
Deuterium
What is it? It is chemically just like ordinary H.
It is an “isotope” of H which means D has the
same number of protons in its nucleus, but a
different number of neutrons. In this case, just
one neutron for D, and zero for H.
Deuterium
D/H has proven very difficult to measure. Why?
Three reasons at least:
(1) D is rare (D/H about 0.01% by number,
because not much was left over from BB
(2) D is easily destroyed in stellar
atmospheres so we can’t use stars or our very
own ISM.
(3) The spectral “finger print” is only very
slightly shifted with respect to H.
Deuterium
The finger print is almost the same because the
only difference is one neutron in the nucleus,
and this has no charge. Remember D and H both
have one electron orbiting the nucleus.
The only effect is with mass, not charge.
The electron’s orbital distance from the
nucleus is slightly different (about 1 part in
1000 smaller)
Deuterium
How to see this without too much math?
Concept is “center of mass”, and the more massive
the nucleus, the closer the center of mass will be to it.
This means for the same separation, since both orbit
the center of mass, the electron will go faster for the
heavier nucleus case since the nucleus travels a
smaller circle to follow around. This means it needs
to get closer to the nucleus so the electrical force can
hold it to balance the centrifugal force (higher v =
higher centrifugal force for a given radius). Means
stronger electric pull, means bluer (more energetic
line)
Round
‘n
Round
Electron must always be exactly opposite the nucleus along the Center of mass
line, by definition . The H nucleus (proton) is over 1000 times more massive
than the electron, so even doubling the mass of the nucleus isn’t going to move
the nucleus in much closer to the center of mass. Therefore the effect is
SMALL.
Center of mass
Proton motion
Proton + neutron nucleus motion
Electron motion
Electron motion
H exaggerated
D, exaggerated
Consequence of small effect:
Need a very good prism and a very strong “light
bulb” behind the absorbing material. And star
atmospheres can’t work because D can be
destroyed there.Also, Interstellar medium D
comes from stars => also depressed below
primoridal values.
Furthermore, the main effect is only slight shift,
not a real change in the pattern. => Deuterium
lines look like “blue shifted” H, and we have to
hope we have made the right identification.
Deuterium, OK where to look?
Find distant ( highs z = > 1) bright light bulbs =
QSOs, that through clouds of gas in between
galaxies that we think are “primodial” and
therefore have not had D reduced by star
processing
First try looked good, but they seem to have
been wrong!
data
Models in blue
models
D/H = 0
Better result?
D/H = 3.4 x10-5
D/H = 25 x10-5
data
Location of D line center if no H present
Li
Lithium is so rare we can only look for it
in stars, but it is easily destroyed so the
results are uncertain
Predictions and results
(Ratio of baryons/photons)
(Ratio of baryons/photons)
Agreement?
There results barely agree within errors
(uncertainties), but we still think Big Bang
Nucleuosynthesis is OK
Star cluster dating
Assume all the stars in a cluster
formed at the same time
Assume we know how stars evolve,
know how long they spend as stable
stars such as our sun does.
Star cluster dating
Assume all the stars in a cluster
formed at the same time
Assume we know how stars evolve,
so we know how long they spend as
stable stars such as our sun does.
Star Cluster Dating
The keys is that L is proportional to M and also
proportional to the surface T, so that we know that
kind of star we are looking at by either measuring
it’s color (or if dust messes us up, the lines for the
gases that will be different depending on the T; more
later)
Star Cluster Dating
Log(L)
See page 128 of book
Stars here live the
shortest time
The lower this point,
the older the cluster
“Main
sequence”
Log(T)
Analogy
Assuming no re-seeding but that it started with
marigolds ( an annual) and roses (a perennial) and we
find one garden with marigolds we know it is less than
1 year old, and conversely, one without is at least 1
year old.
Star type, so
we know what
we’re looking
at, lines tell
MK Types
White
O5V
B1V
A1V
F3V
G2V
K0V
M0V
Where RR
Lyrae stars go
Asymptotic giant branch
Brightness
Red GB
Horizontal
branch
Turn off point
Main sequence
Color (bluer to the left)
Concept: Look at Star Clusters:
Look for the cluster with the reddest end
to the main sequence = the oldest
Globular cluster
We don’t need distance to the cluster to
make the plot, but we do need the
distance to match with theory
This is because our theory is for the “life time” of
star on the main sequence is complicated. Ignoring
the complication at first,
Concept: Look at Star Clusters:
Life time goes with mass (higher mass lives
shorter time). And we can infer the mass from the
luminosity which we can derive from the color.
Results and Interpretation
For stars, the more massive, the more quickly they use
up their fuel so the most massive stars only live about
1 million years on the main sequence and are
therefore “young” on star time scales => 12-15 billion
is good number but uncertainty is enough with a low
H0 to fit even L = 0 models. Remember previous slide.
Also see book, page 346. Also remember this
method requires a good theory of stellar evolution.
But life is not easy!
So to derive the life time you have to know the true
luminosity, or distance, directly.