Next Topic, Brute Force

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Next Topic, Brute Force
Lets go measure a lot of redshifts, assume z
tells us the distance, and see what we can see.
gt The z machine of Huchra and Geller
Degrees across the sky
Velocity
Great wall
The Coma cluster
void
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Latest and Greatest
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Blow up of Great Wall
http//www.angelfire.com/id/jsredshift/grtwall.htm
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Sloan Survey Image
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The Next Great Leap Forward Sloan
Goal to really tie down how the light is
distributed. A million redshifts _at_80/redshift!
Make no small plans No results from this yet,
but lots of other neat stuff which we wont talk
about.
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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/redb
ook/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.
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Concept
xxxxxxxxx
Number of Objects
xxxxxx
gt
xxxxx
xx
Separation distance
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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 gt 0 to have a flat universe.
G Wmh exp-Wb(1 sqrt(2h)/Wm)n JP, page 481
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As of a few years ago the CMB derived values are
the boxes
The galaxy power data are the vertical lines
CDM model doesnt fit all! Fits CBM but not
galaxies
lt larger scales this way
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).
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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 scale-dependent
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.
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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 gt
Thats the problem.
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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.
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Using H0 and distance indicators, the classic
tests
(1) Number of objects versus redshift
(2) Luminosity distance versus redshift
(3) Angular size versus redshift
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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.
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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 gt 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
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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 weve 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) gt be careful
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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
cant 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)xzW0/2 (W0/2-1)(-1 sqrt(W0z1)
dL is called the Luminosity Distance and clearly
depends of W and z and scales as H0
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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.
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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
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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 cant 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
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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
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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
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Real live examples Stars
Hotter interior
Cooler atmosphere
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Absorption lines are the darker regions
MK Types White O5V B1V A1V F3V G2V K0V M0V
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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 havent
been created or destroyed.
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Helium
Two places to look star atmospheres and the
interstellar medium.
He is nice because it is chemically inert, so we
dont have to worry about its 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. gt look for the lowest values
we can find
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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
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A delicate measurement
SN only go to here
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How low can you go?, Part II
He/H is defined as Y
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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?
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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 NHemH 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 gt 25 by mass is
equivalent to 8 by number gt Always be sure to
ask, by mass or by number
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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.
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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 cant use stars or our very own ISM.
(3) The spectral finger print is only very
slightly shifted with respect to H.
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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
electrons orbital distance from the nucleus is
slightly different (about 1 part in 1000 smaller)
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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)
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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 isnt going to
move the nucleus in much closer to the center of
mass. Therefore the effect is SMALL.
Center of mass
Proton neutron nucleus motion
Proton motion
Electron motion
Electron motion
H exaggerated
D, exaggerated
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Consequence of small effect
Need a very good prism and a very strong light
bulb behind the absorbing material. And star
atmospheres cant work because D can be destroyed
there.Also, Interstellar medium D comes from
stars gt also depressed below primoridal values.
Furthermore, the main effect is only slight
shift, not a real change in the pattern. gt
Deuterium lines look like blue shifted H, and
we have to hope we have made the right
identification.
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Deuterium, OK where to look?
Find distant ( highs z gt 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!
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data
Models in blue
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Better result?
models
D/H 0 D/H 3.4 x10-5 D/H 25 x10-5
data
Location of D line center if no H present
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Li
Lithium is so rare we can only look for it in
stars, but it is easily destroyed so the results
are uncertain
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Predictions and results
(Ratio of baryons/photons)
(Ratio of baryons/photons)
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Agreement?
There results barely agree within errors
(uncertainties), but we still think Big Bang
Nucleuosynthesis is OK
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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.
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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.
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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 its color (or if dust messes us up,
the lines for the gases that will be different
depending on the T more later)
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Star Cluster Dating
See page 128 of book
Stars here live the shortest time
Log(L)
The lower this point, the older the cluster
Main sequence
Log(T)
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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.
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Star type, so we know what were looking at,
lines tell
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MK Types White O5V B1V A1V F3V G2V K0V M0V
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Where RR Lyrae stars go
Asymptotic giant branch
Red GB
Brightness
Horizontal branch
Turn off point
Main sequence
Color (bluer to the left)
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Concept Look at Star Clusters
Look for the cluster with the reddest end to the
main sequence the oldest Globular cluster
We dont 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,
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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.
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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 gt 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.
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