The Conspiracy

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The Conspiracy
That the dark matter conspire to just make the
rotation curves nearly flat
Remember we got about 300 for clusters! And
500-1000 for GA !! gt Larger scale, larger M/L
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For Comparison (rcWm)/rL 450h MO/LO or
290 MO/LO for h 0.65, and Wm 0.3
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.
.
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Where rL is based on adding up all the light from
galaxies out to z 0.25 , MNRAS, VOL 336, pp
907-931, (2002)
Before Lambda was taken as fact, we needed
bias. What? Why?
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M/L from galaxies gives us Wm of 0.3, then if Wm
1, there must have been a great deal of matter
not associated with galaxies or clusters gt
Lots of mass were there is no light at all gt
CDM was thought to be more uniformly distributed
than galaxies and clusters gt We invented a
bais parameter (b) to describe this! With Wm
now 0.3 no general problem (b 1.07-1.24 or
close to 1 now), but GA, weird as has M/L so high
almost high enough to devive of Wm 1, but we
want Wm 0.3!!
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For stars that make most of light(massive, young
stars)
M/L is less than 1 MO/LO gt more evidence for
dark matter and lots of it! For, were seeing M/L
gtgt MO/LO
. .
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Summary
Measure velocities and distances to infer masses
and M/Ls. The keys are distance plus velocity
plus modeling
Results GA (v 4350 km/sec, M 5 x 1016 M )
using T-F and J-F plus Fund Plane, M/L for GA
?? Good guess is 500-1000 MO/LO local galaxy
value is about M/L 5 MO/LO




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rotation curve for our galaxy gt M/L 20, and
for external galaxies, M/L of about 40. gt From
direct measurements we infer the Universe
contains a great deal of dark matter. Within
factor of 2 consistent with indirect method of
determining M/L
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Before we leave this subject, though
Hard core M/L values all are scaled with h.
What have I been assuming? Why doesnt h matter
for our galaxy?
Ive been assuming h 0.5 or H0 50
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Epilogue H0 vs Wm0
rc 3H02/8pG Omega r/rc , but r M/Volume
and we know M goes as h-1 and V does as D3 means
h-3 gt M/V goes as h2 and the hs cancel out so
Wm0 is independent of H0 (or h).
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The Math
r q D
q
D
The concept, mv2/r GMm/r2 gtM depends on r, but
r depends on h-1, since we determine r from an
angle and as calculated distance to the galaxy,
smaller h for fixed angular extent, the larger
the linear size h-1 Remember D vrec/H0 and
r qD where q the observed angular radius gt r
qD qvrec/H0
L F/4pD2, and D depends on h-1 gt M/L scales as
h-1/h-2 h
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Angular distance test
Several key points
(1) the apparent size goes through a
minimum. (2)We see evolution effects that we
dont know how to calculate because our long
bright rulers are complicated
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Angular distance test Lambda 0
See that size goes through minimum
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Angular distance test
See that objects are complicated (but neat)
Blobs of radio emitting plasma, sep. about 1 Mpc
Galaxy, 100 kpc in diameter
Radio false color, red brightest, blue next to
faintest, black faintest
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The Hubble Constant and Age
Another classic test Measure the age of the
universe very carefully and compare with the
model dependent predictions.
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Details suppose find t0 15 billion years, and
H0 75 gt 1/H0 3x1024/(75 x105 x p x 107)
12.7 billion gt t0/H0-1 1.17
Look at t0/H0-1 versus Wm gt next slide
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The Hubble Constant and Age
Too high for any Wm, L 0
L 0
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How do we measure age?
Count tree rings ) .. Only gives us very bad
lower limit to the age
Radioactive dating
Gives another bound, age of the earth. (4.5
billion years)
Look at star clusters use theory gt get age of
our galaxy
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Radio Active Dating
Concept of 1/2 life. Every 1/2 life, one half of
the total number of atoms in our sample decay.
Uranium decays into lead. Assume a Uranium
sample started out pure Uranium, Examine ore
sample and judge its age. Oldest samples give
us an age of about 4.5 x109 yrs
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Math N N0 x exp(-0.69t/t1/2) where t1/2
1/2 life N0 the initial number of atoms
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Little more math
Example Uranium 1/2 life 4.5 billion years, we
find and ore that is 1/2 U and 1/2 Pb gt 4.5
billion year old. Now suppose we have 1/4 of the
(pure) U we started with and therefore 3/4 of the
sample must be Pb (lead), the how old would this
sample be? Would we expect to find any samples
like this?
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Next Topic Evolution of galaxies
Questions
When did the first galaxies appear?
What came first, the galaxies or the stars?
Did all galaxies start from a black hole seed?
Do ellipticals start out as spirals?
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Old Philosophy The study of shapes (Morphology)
tells all!
gt Photograph galaxies, (1) look for common
shapes and features. (2) classify (3) imply
evolution (4) use redshift measurements to tell
distance (5) look for changes in population
versus redshift
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Modern Version
Need to add spectral and color measurements to
extend reach as when z gets high, features become
difficult to distinguish, plus you need physics!
First the naïve model by Hubble
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So called barred spirals
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Implied is that ellipticals evolve into spirals.
And from that day to this, weve been stuck
with calling ellipticals early type and
spirals late type.
But Hubble was WRONG!
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Classification scheme
Ellipticals no gas or dust and no young
million year old stars no current star
formation, and no disks
Spirals amounts of gas and dust such that there
is active star formation and there are young
stars
SOs are galaxies with a disk similar to spirals,
but no gas or dust in the disk
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SMC
LMC
Andromeda and 2 dwarf (size of LMC/SMC) galaxies