of 406
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Seb Oliver
Lecture 1: Introduction
Distant Universe
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Todays Topics
Course Document
Brief Introduction to Some of the Topics
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Course Aims
The aim of this course is to introduce the
student to studies of the Universe at high
redshift
In particular the student will become
familiar with the observable properties of
the Universe and learn how these can beused to improve our physical understanding
of cosmology
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Course ObjectivesBy the end of the course
the student should:
Understand the standard
cosmological tests
Appreciate the
dependence of these on
our understanding of
galaxy evolution
Be familiar with and be
able to manipulate some
of the fundamental
ingredients of our
theoretical models of
structure/galaxy formation
Understand many of the
basic principles of
observational cosmology Have had exposure to
some of the latest results
and debates in
observational cosmology.
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Work & Assessment
Teaching activities:
18 lectures
~8 weekly discussion/exercise class Teaching and learning materials:
Textbooks
Problem sheets
Exercise sheets, model answers, lecture notes
Available on WWW
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Work & Assessment
Student activities: Students are asked to hand in answers to selected
problems most weeks
to participate in classroom discussions
normal lecture attendance
To read around the subject as necessary
Feedback: Marked exercises, usually one per week. Model answers to problem sheets will be made
available for consultation via the WWW.
Student questionnaires at the end of term.
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Work & Assessment
AssessmentThe assessment is based on a combination
of continuous assessment and exams asfollows:40% weekly problem sheets
60% end-of-year exam
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Lecturers Contact Details
Seb Oliver
Arundel 216
http://astronomy.sussex.ac.uk/~sjo/
http://astronomy.sussex.ac.uk/~sjo/teach/dist.html
(01273-67) 8852 Office Hours
TBD
mailto:[email protected]://astronomy.sussex.ac.uk/~sjo/index.htmlhttp://astronomy.sussex.ac.uk/~sjo/teach/dist.htmlhttp://astronomy.sussex.ac.uk/~sjo/teach/dist.htmlhttp://astronomy.sussex.ac.uk/~sjo/index.htmlmailto:[email protected]8/8/2019 3191214 Distant Universe Lecture
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light Structure Formation
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Equations of State
Geometry and fate of the Universe
The Early Universe
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Model of theUniverse
Observational
Tests of model
Theorist
Observ
Lets Have
a look?
Spanner in the works?
Galaxies evolve.
But we alsowant to know
how galaxies
evolve
Is this how
the universe
works?
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Standard Hot Big Bang Model
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Classical Observational
Cosmology Observable Parameters
Distances
Classical Tests
The microwave background and Primordial
Abundances
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Galaxy Evolution
K-Corrections
Luminosity Functions
V/Vmax test of Evolution
Passive Stellar Evolution
Number Counts The Global History of Star-Formation
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Why Study Galaxy Evolution?
Initial Conditions
in the Early
Universe
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The Hunt for the First Galaxies
Searches for Lyman a emitting galaxies
Photometric Redshifts & the UV-drop-out
technique
Distant Absorption Systems
Dusty Galaxies
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The Hunt for the First Galaxies
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The Background Light
Olbers Paradox
Background Light Components
The Extra-Galactic Source Background
The Cosmic Microwave Background
Radiation (CMBR)
Contributions to the background light
across the e/m spectrum
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Background Light
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Structure Formation
Gravitational Instability
Primordial Fluctuations
Modification of Fluctuations
Linear evolution
Non-Linear Evolution
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Structure Formation
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Seb Oliver
Lecture 2: Homogeneity & Isotropy
Distant Universe
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Equations of State
Geometry and fate of the Universe
The Early Universe
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Copernican Principle
The earth does not occupy a special position
in the universe
This principal was possibly first formulatedby Giordano Bruno and not Copernicus, but
in any case it was a rather radical
proposition with profound implications forthe thinking of the universe at the time
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Definitions
Afundamental observeris someone who is at rest with
respect to the rest of the Universe in their locality
Homogeneous: at any given time the Universe appears the
same to fundamental observers, e.g. the observers will
measure the same mean density or any other scalar
quantity
Isotropic: the Universe appears the same in all directions
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Homogeneity
Homogeneous Not homogeneous
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Isotropy
Isotropic at Not isotropic
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Homogeneous Isotropic
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Isotropy + Copernican Principal
Homogeneity
Isotropy about A
Isotropy about B
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Cosmological Principle
The cosmological principle is that the
universe is isotropic and homogeneous
Equivalently is isotropic for everyfundamental observer
The cosmological principle alone can tell us
some very useful things
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Cosmological Principle implies a
cosmological time The Cosmological Principal implies a
cosmologicaltime.
Since the Universe appears the same to allfundamental observers at any given time,
they can all synchronise their watches to
some event which occurs in the history ofthe Universe, thereafter all the watches
measure the same cosmological time
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Cosmological Principle &
Hubbles Law
a
r r
v (a)
v (r)
P
O
1
)()()'(' avrvrv = 2
)(')'(' arvrv = 3
)()('arvarv
= 4
2,3,4 )()()( avrvarv = 5
1
CP
-v (a)
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Cosmological Principle &
Hubbles Law
)()()( avrvarv = 5
Solution is
=
3
2
1
333231
232221
131211
)(
r
r
r
bbb
bbb
bbb
rvi.e.
which you could check by substituting e.g. 1131121111 rbrbrbv ++= into 5
including a tdependence rBrv )(),( tt = 6
now isotropy implies equation 6 must be invariant under rotation
rrv )(),( tHt = 7
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Simply assuming that the universe ishomogeneous & isotropic has lead us to theconclusion that
i.e. the universe is either: Static h(t) = v = 0
Uniformly expanding h(t) > 0 Uniformly contracting h(t) < 0
Cosmological Principle &
Hubbles Law
rrv )(),( tHt =
H(t) is
Hubble parameter
7
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Cosmological Principle &
Hubbles Law
rrv )(),( tHt =
x = 0 321
x = 0 21
x = 0 321
r
r
r
comoving position
proper position
scale factor
trial solution
8
9
aa
t
a
t
rx
r ==
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We have gone a
long way with verylittle
to go any further we needsome physics ....
but how do we
know howH(ora)
varies with time?
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Equations of State
Geometry and fate of the Universe
The Early Universe
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Seb Oliver
Lecture 3: Nearly-NewtonianCosmology
Distant Universe
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Geometry again
Equations of State
Fate of the Universe
The Early Universe
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Nearly-Newtonian Cosmology
Friedman Equation
Fluid Equation
Acceleration Equation
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Friedman Equation
Birkhoffs Theorum
which states that the
gravitational fieldwithin a spherical hole
embedded within an
otherwise infinite
medium is zero
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Friedman Equation
Thus in a homogenous Universe we can ignore the
matter outside a small sphere
m
r
Grav.
Pot.
Kin.
Energy.
Conservation of Energy
Mass in sphere
mGrrmU 22
3
4
2
1-= & 2
1
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Friedman Equation
mGrrmU 22
3
4
2
1-= &2 6
mxGaxamU 2222382 -= &
I dont change
with time
mGxxa
am
a
U 222
2 3
82-
=
&
222
22
3
8
a
UmGxx
a
am +=
&
/a2
rearrange
22
22
3
8
amx
UG
a
a+=
&
const, -kc2
Friedman Equation
2
22
3
8
a
kcG
a
a=
&
3
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Nearly-Newtonian Cosmology
Friedman Equation
Fluid Equation
Acceleration Equation
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Fluid / Conservation Equation
1st Law of
Thermodynamics
Reverseable
Einsteins
4
233232
3
44 cxacxaa
t
E && +=
5
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Fluid Equation
0
32
232 =++
&&&
rr
6
Fluid Equation
TdSPdVdE =+
=
=
=
&& +=
0=
+
t
VP
t
E4
5
6
465 + into
032
=
++
&&*3/a3
Fluid
Equatio
7
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Acceleration / Differential
Friedman EquationFriedman Equation
2
22
3
8
a
kcG
a
a=
&3
( )
2
2
2a
aaa
a
a &&&&3
2
23
8
a
akcG&+=
032
=
++
&&7
Fluid
Equation
( ) 22
22
2
4a
kccpG
aaaa +
+-=
- rp&&&
2
2
2
2
4a
kc
c
pG
a
a
a
a+
+=
&&&
Gc
pG
a
a
3
84
2+
+-=
&&
+=
23
34
c
pG
a
arp&&
Acceleration
Equation
8
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We derived the acceleration equation from
the Friedman and fluid equations
The acceleration equation has no newphysics
Thus only 2 of those 3 are independent
The acceleration equation is interesting as it
is independent of k
+=
23
3
4
c
pG
a
arp
&&
Acceleration / Differential
Friedman Equation
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The Geometry of the Universe
From our Newtonian derivation wefound
We need some more GeneralRelativity to explore k more
The Geometry in GR is described bymetrics
Metrics determine the separation ofpoints
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Euclidean 2-D Metrics
dx
dy
dsdsrd
dr
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Euclidean 3-D Metrics
(dx2+dy2)1/2
dz
dsdsrd
dr
( ) 2222222 sin fqq drdrdrds ++=1
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Minkowski metric
(dx2+dy2+dz2)1/2
dt2
ds
(222222 dzdydxdtcds ++-=
dsrd
dr
( )222222 jdrdrdtcds +-=2
3
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Robertson Walker Metric
( ) 2222222 )( jdrSdrtRdtcds k+-= ( )
=
==
=
0)(k,
1)(k,sinh
1)(k,sin
r
r
r
rSk
+
= 22
2
22222
1)( jdr
kr
drtadtcds
++
= 2222
2
22222 sin
1)( fqq drdr
kr
drtadtcds
Various alternative forms
N.B. definitions
ofr are not
equivalent
between these
two forms
4a
5
64 5/6
4b
4c
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Hand-waving derivation of
Robertson Walker Metric
r
( )22222 sin jrddrRds +=
i.e. spatial part of k=1 solution
Represent 3-D spatial co-ordinates r, , by r, and thesetwo as angular spherical co-ordinates
7
4a
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Hand-waving Derivation of
Robertson Walker Metric
i.e. spatial part of k=-1 solution
To go to negative curvature set
( 22222 sin jrddrRds +=
(22222 sinh jrddrRds +=
7
8
4b
spatial part of k=0 solution is Minkowski4c
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Hand-waving Derivation of
Robertson Walker MetricTo get alternative form 5 apply the co-ordinate transforms
Subs. into 7 gives k = +1 part of 5
gives k = -1 part of 5
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Geometries
k = 0k = -1k = +1
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Seb Oliver
Lecture 4: Equations of state andcosmological models
Distant Universe
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Geometry again
Equations of State
Fate of the Universe
The Early Universe
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Models of the Universe
Three main things we can play with
Geometry
Density
Equation of State
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Equation of State
Equation of state relates P and
Some simple equations of state we can
consider Matter, dust, galaxies
Radiation
Cosmological Constant
1
2
3
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Question
[ yznzzyz
nn
n&&
11 -+=
1
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Equation of State
We need to put these into the Fluid equation
032
=
++
&& Fluid
Equation
7
1
2
3
1 ( ) 01 33
=
a
tar 4
2 ( ) 01 44 =
ata
r 5
3 6
Critical Density
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Critical Density
( )2
22
2
3
8
a
kcGtH
a
a-==
rp
&
3
set k = 0
( )
2
c 3
8
tH
G==W
Define
density
parameter
Friedman Equation
Critical density
22
2
23
81
aH
kc
H
G=
If > 1 then k >0If < 1 then k
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Some definitions
Hubble Constant
Current time i.e.
age of the universe:
Current Density
Current Density
parameter
matter densities
radiation densities
cosmological constant
equivalent densities
Current scale
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Specific Models
k= 0, matter dominated, Einstein de Sitter
k= 0, radiation dominated
k< 0,= 0, Milne Model
k< 0,> 0
k> 0
dominated
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k= 0, matter dominated
Einstein de Sitter
Ga
a
3
82
=
&
3 Friedman Equation
with k= 0
3
0
2
3
8 =
&
10
2
38 = &
21
03
8 =
= dtGdaa 38
0
21 rp
tGa 3
82 0
23 =
3/2
1/3
0 382 tGa =
i.e.
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k= 0, radiation dominated
Ga
a
3
82
=
&
3 Friedman Equation
with k= 0
4
0
2
3
8=
&
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k= < 0, = 0
Milne Model
2
22
a
kc
a
a=
&
3 Friedman Equation
2
21
aa
a +
&
with = 0
since k< 0
k< 0, >0
2
22
3
8
a
kcG
a
a=
&
3 Friedman Equation
either matter or radiation
dominated models tend to
Milne model
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k= +1, P>0
2
22
3
8
a
kcG
a
a=
&
3 Friedman Equation
222
3
8caGa = &
c2
0
c2
at some point and since
therefor collapse is
inevitable
+=
23
3
4
c
PG
a
arp
&&
Acceleration
Equation
8
if or then decreases
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Matter dominated
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dominated
2
22
3
8
a
kcG
a
a=
&
3 Friedman Equation
assuming is allowed to grow then eventually
dominates over
Universe expands for ever
no matter what value ofk
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Models with both matter &
radiationFluid equation is modified with
( ) ( ) 011 4
4
3
m3 =
+
ataata grr
Assuming negligible conversion of
mass to radiation,
both terms must separately be zero
4 5
log
now
Matter
Domination
Rad
iationDomination
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Models with both matter &
radiationHarder to solve for (t)
4
log
now
Matter
Domination
Rad
iationDomination
However we can assume that
k= 0 and either Radiation ormatter dominate
5
-dom m-dom
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Combination of materials
( 40,30,m0,203
8 --L W+W+W= aaH
Gg
rp
matter dominated
radiation dominated
combination
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Seb Oliver
Lecture 5: The Early Universe
Distant Universe
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
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Standard Hot Big Bang Model
Assumptions of Homogeneity and Isotropy
Nearly-Newton Cosmology
Geometry again
Equations of State
Fate of the Universe
The Early Universe
Bl k B d
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Black Body
Radiation
If the radiation is in in
thermal equilibrium
with a body theradiation exhibits a
black body spectrum
on
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Black Body Radiation
de
v
c
hd
kTh 1
8)(
/
3
3 -=Planck Spectrum
Stephans Law
i.e.
We know
log
no
w
MatterDomination
RadiationDominati
log
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The Hot Big Bang
It can be shown that as the Universe expands or
contracts a Planck spectrum remains a Planck Spectrum
COBE has been shown that the microwave backgroundradiation has a Planck Spectrum to an extraordinary high
degree of accuracy
It is likely therefore that the radiation had a black body
profile over the evolution of the Universe and by
implication the radiation was in thermal equilibrium with
the matter at some time in the past
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COBE Background
De-coupling and Recombination
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De coupling and Recombination
At some point in the past the matter (H, He)
was in thermal equilibrium with the
radiation. How?
If the gas is ionised into a plasma p & e- then
Thompson scattering would allow the
photons and electrons to interact
If susequently the temperature drops then
p+e-H (confusingly called recombination)and the interactions stop allowing the
photons to escape (de-coupling)
De-coupling and Recombination
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De coupling and Recombination
p
e-
p pp
e-
e- e-
HH
H
H
H
zT
t arecombination
de-coupling
Temperature of Recombination
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Temperature of Recombination
Mean energy of
Ionisation energy of H
Photo-Ionisation
Temperature
In fact as there are many more g than p, the T
can be lower and enough g have high enough
energies to ionize
>
TkEEn
B
exp)(gBoltzmann distribution
( )K2500
10ln93
eV6.13==
Bk
T
Temperature of Recombination
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Temperature of Recombination
Detailed calculations give recombination at
Thus recombination occurred when Universe smaller by what factor
Current Temperature of the radiation in the Universe is
a b c d10
n
nation
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Prior to recombination
As T drops such that pair creation processes
no longer occur then non-stable species disappear
Early in the Universe all sorts of exotic species exist
At these times photons dominate and thus i.e.
in fact
MeV2~
t
sec12/1
TkB
log n
o
w
MatterD
omination
Radiat
ionDomin
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Standard Hot Big Bang Model
The Early Universe
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t < 10-10
s T > 1015
K GUT
10
-10
< t T>10
12
Ke
+, e
-,quarks,,
+> ,
,
> ,
A t i N t / P t
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Asymmetry in Neutron / Proton
RatioMass difference between n and p causes an asymmetry via
slightly easier
(requires less
energy) to
producep than n
once e+, e- annihilation occurs only neutron can decay
+=
s1013exp16.0~
t
NN
NX
pn
nn until nucleosynthesis
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Nucleosynthesis
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y
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
Classical Observational
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Classical Observational
Cosmology Observable Parameters
Distances
Classical Tests
The microwave background and Primordial
Abundances
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Observable Parameters
Redshift
Hubble Constant and Hubble Parameter
Deceleration (acceleration?) parameter
Redshift z
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Redshift --- z
maintaining convention that x0 is now
How do we relate z to scale factor?
Three ways
Redshift
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Redshift
Redshift Balloon analogy
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Redshift --- Balloon analogy
( )( )tata
z00
01 =+ l
l
n
n
Redshift R W metric
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Redshift --- R-W metric
+
= 22
2
22222
1)( jdr
kr
drtadtcds5
Photons travel along paths with ds = 0
Consider a photon travelling along a path which we
choose to have d = 0
= 2
2
2
22
1
1)( kr
dr
ctadt
all constant, since dr is
co-moving coordinate
( )
( )ta
taz 00
0
1 =+l
l
n
n
R d hift E
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Redshift --- Energy
Number density of particles:
in thermal equilibrium or where no interactions
photon numbers are conserved
( )( )tata
z 00
0
1 =+l
l
n
n
Energy density of particles
Hubble Constant and
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Hubble Constant and
Hubble Parameter
( )
( )tata
tH&
=)(
( )( )0
00
ta
taH
&= Hubble constant can be observed
locally as we shall see later e.g. below
Hubble parameter
more difficult.....
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Deceleration parameter
( )( ) [ ] [ ]
2
0
2
00
00
0 21 ttH
qttH
ta
ta---+
Taylor expansion
( ) ( )[ ] ( )[ ] ...2
1)(
2
0000 +-+-+= tttatttatata &&&
defining a deceleration parameterq0
( )( ) 200
00
1
Hta
taq
&&
( )( ) 2
00
1taq
&&
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Deceleration parameter ( )2
00
0Hta
q
Recall acceleration equation
+=
23
3
4
c
pG
a
arp
&&
If p = 0
8
( )
2
c 3
8
tH
G==Wrecall too
in this case measuring q0 would thusgive us 0
( )( ) 2
00
1taq
&&
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Deceleration parameter ( )2
00
0Hta
q
if we have a Cosmological Constant term
if we can assume the Universe to be flat i.e.
So in the presence of a measurement ofq0 alone is insufficient
to determine some additional theoretical or observationconstraint is required
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Seb Oliver
Lecture 6: Observable Parameters
Distance Measures
Distant Universe
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
Classical Observational
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Classical Observational
Cosmology Observable Parameters
Distances
Classical Tests The microwave background and Primordial
Abundances
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Observable Parameters
Redshift
Hubble Constant and Hubble Parameter
Deceleration (acceleration?) parameter
Redshift --- z
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Redshift --- z
maintaining convention that x0 is now
How do we relate z to scale factor?
Three ways
Redshift
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Redshift
Redshift --- Balloon analogy
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Redshift --- Balloon analogy
( )( )tata
z00
01 =+ l
l
n
n
Redshift --- R-W metric
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Redshift R W metric
+
= 22
2
22222
1)( jdr
kr
drtadtcds5
Photons travel along paths with ds = 0
Consider a photon travelling along a path which we
choose to have d = 0
= 2
2
2
22
1
1)( kr
dr
ctadt
all constant, since dr is
co-moving coordinate
( )
( )ta
taz 00
0
1 =+l
l
n
n
Redshift Energy
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Redshift --- Energy
Number density of particles:
in thermal equilibrium or where no interactions
photon numbers are conserved
( )( )tata
z 00
0
1 =+l
l
n
n
Energy density of particles
Hubble Constant and
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Hubble Constant and
Hubble Parameter
( )
( )tata
tH&
=)(
( )( )0
00
ta
taH
&= Hubble constant can be observed
locally as we shall see later e.g. below
Hubble parameter
more difficult.....
l i
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Deceleration parameter
( )( ) [ ] [ ]
2
0
2
00
00
0 21 ttH
qttH
ta
ta---+
Taylor expansion
( ) ( )[ ] ( )[ ] ...2
1)(
2
0000 +-+-+= tttatttatata &&&
defining a deceleration parameterq0
( )( ) 200
00
1
Hta
taq
&&
l i
( )( ) 2
00
1
Ht
taq
&&
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Deceleration parameter ( )2
00 Hta
Recall acceleration equation
+=
23
3
4
c
pG
a
arp
&&
If p = 0
8
( )
2
c 38
tHG==Wrecall too
in this case measuring q0 would thusgive us 0
D l i
( )( ) 2
00
1
Ht
taq
&&
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Deceleration parameter ( )2
00 Hta
if we have a Cosmological Constant term
if we can assume the Universe to be flat i.e.
So in the presence of a measurement ofq0 alone is insufficient
to determine some additional theoretical or observationconstraint is required
Classical Observational
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Classical Observational
Cosmology Observable Parameters Distances
Classical Tests The microwave background and Primordial
Abundances
Di
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Distances
Redshift
Co-Moving Distance
Proper Distance Luminosity Distance
Angular-Diameter Distance
R d hif
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Redshift z=0 z=z1 z=z2 z=z3
z=0
z=z1z=z
2
z=z3
C M i Di / i
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Co-Moving Distance/separation
Much the easiest to work with
Once you have defined your co-movingpositions separations etc. they stay fixed!
Not directly related to measurable quantities
Since redshift is an important measure ofdistance from us to objects it is important to
see how co-moving separation relates to z
R b t W lk M t i
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Robertson Walker Metric
( ) 2222222 )( jdrSdrtRdtcds k+-= ( )
=
==
=
0)(k,
1)(k,sinh
1)(k,sin
r
r
r
rSk
+
= 22
2
22222
1)( jdr
kr
drtadtcds
++
= 2222
2
22222 sin
1)( fqq drdr
kr
drtadtcds
Various alternative forms
N.B. definitions
ofr are not
equivalentbetween these
two forms
4a
5
64 5/6
4b
4c
C i di t
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Co-moving distance vsz
If we know the cosmology we can relate the
co-moving distance to the redshift using the
Robertson-Walker metric
( ) 2222222 )( jdrSdrtRdtcds k+-=
( )( )z
zz
H
cSR k
+W
-W+-W+W
=
1
11222
0
0
( )zz
dz
H
cdrR
W++
=
110
0Differential form
Intergal form
Matterdominatedmodels
P Di t
Cosmological Principle &Hubbles Law
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Proper Distances
Proper sizes are related to co-
moving sizes by the scale
factor
It can be confusing to
talk ofproper distance
meaning the distancefrom us to an object
because the Universe
has expanding while the
photon travelled
The co-moving system is defined to be such that co-moving separations today are proper separations
rrv )(),( tHt =
=
=
=
=
( )zt +D
=D1
)(x
r
Warning
Distances vs Cosmologies
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Proper distanceR0Skas a function of
cosmology Matter dominated, = 0
Matter & Radiation, = 0
0
Distances vs Cosmologies
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It can be shown from consideration of the
derivation of redshift in the R-W metric andconsideration of the Friedman Equation formatter dominated Universes (=0)
Hence also luminosity and angular-diameterdistances (DL, DA)
Ideally measuring distances would givecosmology
( )( )zzz
HcSR k
+W-W+-W+W=
11122
2
0
000
0
0
Distances vs Cosmologies
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A similar (equally nasty) expression can be
derived if radiation is also present, seehand-out sheets
If 0 an analytical expression for R0Sk is
not possible, must be determinednumerically
However
+ 20
0
02
1z
qz
H
cSR k
to second order
Again we see that geometric measures can give q0 but will not
give , unless we assume an equation of state
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Luminosity Distance
Bolometric Luminosity
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A major goal of astrophysics will be to explain
the energy (E) that celestial bodies emit
In physics the rate at which energy is emitted is
calledpower, P
Most of this energy is emitted as light
The rate at which celestial bodies emit energy via
lightis called bolometric luminosity (L)
Joules, J
Watts, W = J s-1
Watts, W = J s-1
Flux (Euclidean)
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When one is somedistance away from a
source which emits
isotropically the
bolometric luminosityLis distributed over a
sphere
Fluxis the amount of energy per
second passing through a unit area
A E/tWatts / metre2, W m-2
Flux (Cosmological)
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photons loose energy
interval between photons increases
N.B. using the co-moving distance as
we want the size of the sphere today
Luminosity Distance
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Luminosity Distance
Cosmological Flux
Want this to look Euclidean
DefinedLuminosity Distance DL
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Angular Diameter Distance
Angular Diameter DistanceP i f bj t
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d
Proper size of an object
N.B.R(t)SknotR0Sk as we want
separation when photon emitted
( )kSR zdld 01+= jdl
Angular Diameter Distance( )
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( )kSR
zdld
0
1+= j
ddlBy analogy with Euclidean
Where we have defined the angular diameter distance
Surface BrightnessW ld lik f
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Surface brightness (B): Flux
per unit solid angle
independent
of distance
W m-2 sr-1B
Would like a measure of
energy per unit area on the sky
Surface Brightness and Olbers
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paradox In an infinite Universe every line of sight
will eventually end on a star
Since in a Euclidean Universe the surfacebrightness is constant the night sky shouldbe as bright as a typical star e.g. the sun
However, the night sky is dark!
Possible resolution ...
Surface Brightness
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Surface brightness is flux perunit solid angle
( ) 422
2
21
-+== z
dl
L
D
D
dl
LB
L
A
Independent of cosmology!
Surface Brightness and Olbers
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paradox
Possible resolution ...
The surface brightness is not constant, but
decreases as (1+z)4
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Seb Oliver
Lecture 7 & 8: Classic Cosmological
Tests
Distant Universe
Main Topics
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Main Topics
Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution The Hunt for the First Galaxies
Background Light
Structure Formation
Classical Observational
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Cosmology
Observable Parameters
Distances
Classical Tests The microwave background and Primordial
Abundances
Classic Cosmological Tests
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Classic Cosmological Tests
Hubble Diagram
Number Counts
Tolman Test
Angular-Diameter Distance Test
Age of the Universe
The microwave Background and Primordial
Abundances
Hubble Diagram
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Cosmological model 1
Cosmological model 3
Cosmological model 2
Ideally choose astandard candle, i.e. a class of object
whose Luminosities do not change over cosmological time
flux(f)
Redshift (z)
Predictf(z) from DL in
cosmological model
Hubble Diagram Plots
Same information can be(m)
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Same information can be
plotted in a variety of ways
flux(f)
Redshift (z)
magni
tude
Redshift (z)
DL
v=cz
Measure Dl from
ratio of flux to
Luminosity
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Hubble Diagram Not possible to find a class of fixed luminosity
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Not possible to find a class of fixed luminosityobject
Usually choose a class whose luminosity in thelocal Universe depends in a known way on alimited number of other parameters
( )L+++= 321 aaaLL So measuring 1,etc. giveL
The stronger the correlation with andsmaller the dispersion the better
Hubble Diagram Measurement of reduces
the spread in standard candle
luminosities but a residual
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L
uminosity(L
)
(z)
L()
luminosities, but a residual
dispersion re mains
UncertaintyinL
Uncertai
ntyinL,
knowing
Local calibration
What makes a good candle?
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What makes a good candle?
Small range of luminosities
High Luminosities
Few calibration parameters Low dispersion of calibration relation
Doesnt evolve
Hubble Diagram
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Hubble Diagram
Cephid variables: is period
Spiral galaxies: is rotational velocity
Elliptical galaxies: is velocity dispersion Brightest Cluster Galaxy (BCG): iscluster X-ray temperature
Super Novae Ia: is time-constant of lightcurve
See. The Cosmological Distance Ladder (Rowan-Robinson)
or 5.3, 5.4 & 5.5 Cosmological Physics Peacock
Supernovae Hubble Diagram
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Supernovae Hubble Diagram
We will discuss this on Friday
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Number Counts
Euclidean Number Counts
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r
Assume a class of objects with
L which with a sensitivity farevisible to a distance r
Euclidean Number Counts
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L
++=
2
3
2,0
23
1,0 fNfNN
r
Cosmological
Number counts
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Number counts
( )3
0
0
=
R
Rtnn
Co-moving volume element (all-sky):
( )[ ] ==drRzSRndVnN
k 0
2
000
4p
since we know:
we can deduceN(f)
Assume co-moving density is constant
( )[ ]3max003
4zSRn kp=
Co-moving volume
Cosmological Number counts
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Cosmological Number counts
Number density of sources:
( )3
00
3
0
0
=
=
-
R
Rn
R
Rntn
Proper volume element: ( ) 2/1223
1 kr
drdrRdV
-=
j
( ) ( ) ===0
02/12
23
002/12
23
00141
r
kr
drr
Rnkr
drdr
RndVnN p
j
since we know:
we can deduceN(f)
Assume co-moving density is constant
Measuring Number Counts
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Measuring Number Counts
N (f2)
N (f1)
redsh
ift,
z
timesinc
ebeginofUniverse
Number Counts
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Cosmological model 1
Cosmological model 3
Cosmological model 2
Perform a surveys often
at different deeper fluxlimits
Log(N
>f)
Log (f)
All matter-dominated,
P=0 models have
Euclidean
Olbers Paradox again
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Olber s Paradox again
Another statement of Olbers paradox says
that the Sky should be infinitely bright as in
an infinite Universe
=== dfdfdN
ffdNB
fmax
0
4p
True in a Euclidean Universe, but not in other cosmological models with
(4 converts from surfacebrightness to flux over
whole sky, f max is
brightest object in the sky)
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Tolman Test
Surface Brightness
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Surface brightness is flux perunit solid angle
( ) 422
2
21
-+== z
dl
L
D
D
dl
LB
L
A
Independent of cosmology!
Surface Brightness / Tolman Test
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Gregory D. Wirth
Last modified: Sat Apr 19 13:13:18 1997
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Angular-Diameter Distance Test
Angular Diameter Distance Test
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g
Virtually identical to the Hubble diagram
Except instead of flux the observed
parameter is angular diameter of object Instead of luminosity the true quantity is
length, so astandard rodrather than
standard candle is required
What makes a good rod?
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g
Small range of sizes
Sizes at frequencies that are observable with high
resolution
Large sizes!
Few calibration parameters
Low dispersion of calibration relation
Doesnt evolve
Angular-Diameter Distance Test
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g
Angular - Diameter test
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g
Angular - Diameter Distance test
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g
Using Clusters
Angular - Diameter Distance Test
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g
UsingRadio
galaxies
Angular - Diameter Distance Test
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g
UsingRadio
galaxies
Age of the Universe
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Age of the Universe
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Age can be measure by Age of globular clusters
age of Universe > age of stars
Nuclear Cosmo-chronologyAge of Universe > age of chemicals
g
e.g. Peacock Chapter 5.
( ) ( ) ( )1
6.01
2
11
--
W+ zzHzt half way between
empty
critical
Cosmic Microwave Background
and Nucleosynthesis
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and Nucleosynthesis
Nucleosynthesis
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Summary Black-body CMBR and nucleosynthesis confirm big
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picture but dont constrain models
Hubble Diagram assumes Luminosity of standard candle
does not depend on redshift
Number counts diagram assumes co-moving number
density of sources is constant
Angular-diameter distance assumes rods dont change
length (plus large scatter)
Age of the Universe assumes we can measure the age
accurately
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Seb Oliver
Lecture 8: Classic Cosmological
Tests See Lecture 7
Distant Universe
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Seb Oliver
Lecture 9: K-corrections
Distant Universe
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Main Topics
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Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution The Hunt for the First Galaxies
Background Light
Structure Formation
Galaxy Evolution
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Historically the classic tests were designed
to tell us about the cosmological models
To do so they assume populations do notevolve
Early applications of the tests to galaxies
soon showed that galaxies do evolve .
Why Study Galaxy Evolution?
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Initial Conditions
in the Early
Universe
Galaxy Evolution
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K-Corrections
Luminosity Functions
V/Vmax test of Evolution Passive Stellar Evolution
Number Counts
The Global History of Star-Formation
K-Correction
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The emission from a galaxy is observed at a
different wavelength from the one that at which it
was emitted - due to the cosmological redshift
In general one wants to compare the emissionproperties of galaxies at the same (emitted)
wavelength
The K-correction is an additional term in the fluxdensity to luminosity relationship which accounts
for this difference
Luminosities Important to draw a distinction betweenB l t i L i it
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Bolometric Luminosity
LBol, Total luminosity of a galaxy, measured in W or L (or absolute
magnitudes)
Line Luminosity
e.g. LH, Total luminosity of an emission line, measured in W or L
In band power
e.g. luminosity emitted in a given wavelength interval measured in W or L (or
absolute magnitudes)
Luminosity (density)
Luminosity per unit frequency, measured in WHz-1, often quoted asLmeasured in W
LuminosityAstrophysical objects tend to emit their light
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energy over a range of different frequencies, ,it is thus useful to define theLuminosity(L) to
be the energy per unit time per unit frequency
intervalWatts / Hertz, W Hz-1
Spectrum of a narrow line
Seyfert Galaxy
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Seyfert Galaxy
Flux densityFlux density (f) to be the energy per unit time
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per unit area per unit frequency interval
Both are often simply called flux :-(
Common to see ... Flux density (f) the energy per unit time perunit area per unit wavelength interval
Watts / metre2 / Hertz, W m-2 Hz-1
Watts / metre2 / metre, W m-3
Jansky: 1Jy = 10-26 W m-2 Hz-1
Flux density
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negative because increases as decreases
Flux (Cosmological)
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N.B.R0SknotRSk as photons are
distributed on a sphere with radius at
todays scales
Can be used to relates Bolometric luminosities and lineluminosities but notluminosity densities and flux densities
M82 a star forming galaxy
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log
Lum
inosity
10 1001
Efstathiou et al. MNRAS submitted
Wavelength /m
Galaxies at Higher-zwavelength
If the sameobject is
seen further
away
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Observed band
emitted feature
We see the
light
redshifted
at a fixed we seelight emitted from
bluer parts
Observed Frame Emitted or Rest Frame
galaxies at higher-z
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Usually what we want to do is to know about the
objects properties at the emitted wavelength
[ ] ( )[ ]01 nn zLL e +=
galaxies at higher-z
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Emitted
band ~ 1014 Hz
Observed
Band ~ 1013 Hz
Given rest-frame frequency band is
observed in a narrower band thusenergy per unit frequency increases
K-CorrectionWe want to relate the observed light to the light emitted at the
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rest-frame frequencies
( )2
2
22
0 41
4 Lk D
Lz
SR
Lf
pp=+=
-
( ) ( )200 4 L
ee
D
dLdf
p
nnnn nn =
Using the same arguments
as we used to derive
We can see
we know ( ) ( ) 00 11 nnnn dzdz ee +=+=
( ) ( )[ ]( )2
0000
4
11
LD
dzzLdf
p
nnnn nn
++=
K-Correction
shift of spectrum
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( ) ( )[ ]( )2
00
4
11
LD
zzLf
p
nn nn
++=
Band pass
Observed Frame Emitted or Rest Frame
galaxies at higher-z
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Usually what we want to do is
to compare objects at the same
emitted wavelength
We can do this by assuming we
know what the spectrum of
Spectral Energy Distribution
SED i
[ ] ( )[ 01 nn zLL e +=
K-Correction
( ) ( )[ ]( )200 411
LD
zzLfp
nn nn++=
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e.g. ( ) ( ) = 00LL
( )[ ] ( )
( )
+=+
0
000
11
zLzL
( ) ( )( )2
10
0 41
LD
zLf
p
nn
an
n
-+=K-correction
K-Correction in band fluxes and
magnitudesTransmission of band
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g
( )zKDMm L +
+=
pc10log5
If fluxes and luminosities are expressed in magnitudes
Shape of spectrum
and band-pass
correction
Hence name:K-correction
( ) ( )[ ] ( ) dTzLDzL ++= 1
41
02
K-Correction in magnitudes
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E.g.
( ) ( ) ( )zzK +--= 1log15.2 a
( ) ( )
=
0
0LL
( ) ( ) ( )[ ] ( )( ) ( )
++=
dTL
dTzLzzK
11log5.2
0
K-Correction in magnitudes
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K-correction for galaxies in the
optical is usually positive
i.e. galaxies are fainter because
of this effect
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Seb Oliver
Lecture 10: Luminosity Functions
Distant Universe
Main Topics
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Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution The Hunt for the First Galaxies
Background Light
Structure Formation
Galaxy Evolution
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K-Corrections
Luminosity Functions
V/Vmax test of Evolution Passive Stellar Evolution
Number Counts
The Global History of Star-Formation
The Luminosity Functions
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To study galaxy evolution we need to compare
galaxies today with galaxies in the past
To perform a fair comparison we need to compare
the emitted power at the same wavelengths, henceK-corrections (Lect. 9)
We cannot observe thesame galaxy at different
times, so we must look at the statistical properties
of galaxies as populations, hence we study
luminosity functions
Luminosity FunctionsThe luminosity function characterises the number density ofgalaxies as a function of the luminosityL
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Num
berDens
ity
Luminosity
Luminosity function,
usually written (L), is
defined as the co-movingnumber density (number
of objects per co-moving
volume) in some range of
luminosity (usually
logarithmic)
Luminosity Functions:
1/VA Estimator Object Too Faint
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A
( ) ( )minmax11
zVzVVn
A
X-
==
Given a single object, X, visible
within some volume, VAObject
Detectable
j
1
For a number of objects i:
This 1/VA estimator is a
maximum likelihood estimator
Too
Big
Luminosity Functions:
1/VA Estimator
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A
1
21
21
3
2121
11
VVnn
V
NNn +=+=
+=+
Luminosity Functions:
1/VA Estimator: zmaxObserve f and z over some area 2down to some flux
( )[ ] ( ) ( )02
01
41 n
pn nn f
z
DzL L
+=+
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aObservef
andzover some area down to some flux
density limit,f,min
( )
( ) ( )
( )[ ]
++
=
zL
Lf
z
DL Li
11
4
0
00
2
n
nn
p
n
nn
can be estimated for
different galaxy
types
i.e.
&
calculated
numerically
likewise using Tfor type and for cosmology
Luminosity Functions:
1/VA Estimator: Vmax
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( )dzdz
dzd
dVdVV 2
2
jj
==
=max
0
2
2
max
z
dzdzd
dVV
jj
Assume for simplicity that the zmax is constant acrossthe survey area, and that the survey is only limited at
zmax i.e. zmin=0, though generalisations not difficult
( )[ ] 2020 jdrdRrSRdV k=
( ) zzdz
H
cdrR
W++
=
1100
co-moving volume
Matter
dominated
Luminosity Functions
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Luminosity functionsare different andshould be estimatedseparately fordifferent:
Galaxy Types Ellipticals
Spirals
AGNs
Dwarfs
Emission Wavelengths -/X-ray through radio
Environments
Clusters Field
Redshifts
Evolution
Normal galaxy Types
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Environment
Cluster
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Environment
Field
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Luminosity Functions
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In order to allow easy comparison between
different determinations of luminosity functions
and luminosity functions of different types it is
usual to use simple parameterisations Schecter - common for galaxies
Two-Power-Law - common for AGN
Power - Law with exponential cut-off - infraredgalaxies
Luminosity Functions
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Schecter Function - common for galaxies
( )***
* expL
dL
L
L
L
LLd
-
F=
a
f
Log (Luminosity)
Log((L))
*
L*
Exponential Cut-off
Power-Law slope
Luminosity Functions
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L
og
[(L)]
Log Luminosity
SDSS Luminosity Function
Blanton et al. 2001 AJ 121, 2358
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www.sdss.org
SDSS Luminosity Function
Blanton et al. 2001 AJ 121, 2358
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Parametric Evolution of
Luminosity Functions
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Log (Luminosity)
Log((L))
*
L*
Luminosity
Evolution
Density
Evolution
( ) ( ) ( )0,, == zLzfzL f
( ) ( )
== 0,, zzg
LzL f
Pure density evolution
Pure Luminosity
evolution
Parametric Evolution of
Luminosity Functions
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Log (Luminosity)
Log((L))
*
L*
Luminosity
Evolution
Density
Evolution
( ) ( )
== 0,, z
zg
LzL f
typical estimate of
Luminosity Function from 2dF
Quasar Survey
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www.2dfquasar.org
Luminosity Function from 2dF
Quasar Survey
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Luminosity Function from 2dF
Quasar Survey
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Luminosity Function from 2dF
Quasar Survey
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For objects of fixed luminosity, L, in a
V/Vmax Evolution Test
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j y, ,
redshift survey there is a maximum
volume in which the object could have
been seen, Vmax(zmax)
We can compare this to the volumein which the object actually was
seen: V(z)
Thus Vcould be
between 0 and Vmax
V(z) z
Vmax(zmax)
zmax
V/Vmax Evolution TestIf there was no change in co-moving
Vmax
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number density V(z)
(f)
(e)
(d)(c)
(b)
(a)
05.0
5050
50
1
3
23
32
max/
/
.
.
.
VV =
Since the number density does
not change theprobability of
an object appearing in a
survey volume V, P(
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V(z)
( ) 2/1max
125.0-
= nV
V
max
y
and it can be shown that in the absence of evolution
Thus a measured value of that differed significantly
from 0.5 demonstrates that evolution has occurred
galaxies more numerous in past
galaxies less numerous in past
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Seb Oliver
Lecture 11: Luminosity Functions
V/Vmax & Morphological Evolution
Distant Universe
Main Topics
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Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
Galaxy Evolution
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K-Corrections
Luminosity Functions
V/Vmax test of Evolution
Morphological Evolution
Passive Stellar Evolution
Number Counts The Global History of Star-Formation
Luminosity Functions
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L
og
[(L)]
Log Luminosity
Parametric Evolution of
Luminosity Functions
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Log (Luminosity)
Log((L))
*
L*
Luminosity
Evolution
Density
Evolution
( ) ( ) ( )0,, == zLzfzL f
( ) ( )
== 0,, zzg
LzL f
Pure density evolution
Pure Luminosity
evolution
Parametric Evolution of
Luminosity Functions
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Log (Luminosity)
Log((L))
*
L*
Luminosity
Evolution
Density
Evolution
( ) ( )
== 0,, zzg
LzL f
typical estimate of
Luminosity Function from 2dF
Quasar Survey
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www.2dfquasar.org
Luminosity Function from 2dF
Quasar Survey
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Luminosity Function from 2dF
Quasar Survey
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Luminosity Function from 2dF
Quasar Survey
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For objects of fixed luminosity, L, in a
V/Vmax Evolution Test
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redshift survey there is a maximum
volume in which the object could have
been seen, Vmax(zmax)
We can compare this to the volumein which the object actually was
seen: V(z)
Thus Vcould be
between 0 and Vmax
V(z) z
Vmax(zmax)
zmax
V/Vmax Evolution TestIf there was no change in co-moving
b d i
Vmax
V(z)
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number density
(f)
(e)
(d)(c)
(b)
(a)
05.0
5050
50
1
3
23
32
max/
/
.
.
.
VV =
Since the number density does
not change theprobability of
an object appearing in a
survey volume V, P(
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( ) 2/1max
125.0-
= nV
V
and it can be shown that in the absence of evolution
Thus a measured value of that differed significantly
from 0.5 demonstrates that evolution has occurred
galaxies more numerous in past
galaxies less numerous in past
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MorphologicalEvolution
http://star-www.st-and.ac.uk/~spd3/hdf/hdf.html
Morphological Evolution z~0.09
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Morphological Evolution 0.36
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Morphological Evolution z~0.5
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Morphological Evolution z~0.63
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Morphological Evolution z~0.75
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Morphological Evolution z~0.89
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Morphological Evolution z~0.96
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Morphological Evolution z~1.16
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Morphological Evolution z~1.28
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Morphological Evolution z~1.4
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Morphological Evolution z~1.57
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Morphological Evolution z~1.65
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Morphological Evolution z~1.79
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Morphological Evolution z~2.07
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Morphological Evolution z~2.50
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Morphological Evolution z~3.21
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MorphologicalEvolution
Summary
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Summary
Morphological Evolution
Summary
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Morphological
redshift distributions
are shown for
I=22.5,23.5,24.5,25.
5. the panels from
left to
right are: Total,
E/S0, Sabc, Sd/Irr
Morphological Evolution
The Butcher Oemler Effect
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The Butcher Oemler EffectClusters at low redshift have many more red
galaxies than blue galaxies, at higher redshiftsthe clusters have a higher fraction of bluegalaxies
The morphology Density RelationshipThe denser regions of clusters have a higher
proportion of red galaxies than the less denseregions
Environment
Cluster
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Morphological Evolution
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Morphological Evolution
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Morphological Evolution
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Morphological Evolution
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Morphological Evolution
Read Dressler et al 1997 ApJ 490 677 (D) use ADS or
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Read Dressler et al. 1997 ApJ 490, 677 (D), use ADS or
astro-ph/9707232
How does morphology density relationship evolve?
Is this paper consistent with Butcher Oemler effect?
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Seb Oliver
Lecture 12: Passive Evolution,
Number counts
Distant Universe
Main Topics
Standard Hot Big Bang Model
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Standard Hot Big Bang Model
Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
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Passive Evolution
Galaxy Evolution
K-Corrections
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K Corrections
Luminosity Functions
V/Vmax test of Evolution
Morphological Evolution
Passive Stellar Evolution
Number Counts The Global History of Star-Formation
Passive Evolution
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Passive Evolution
Stellar evolution is relatively well
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Stellar evolution is relatively well
understood both observationally and
theoretically
Massive stars are very hot and blue
Massive stars are very luminous
Massive stars have very short lives
Live fast die young!
Passive Evolution - Stellar Synthesis
Stellar theory predicts the evolution or (stellar
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Stellar theory predicts the evolution or (stellatracks) or stars of a given mass
Observations give us libraries of stellar spectra asa function of age, mass etc.
If we know the distribution star masses producedwhen star-formation occurs - the initial mass
function - we can predict the evolution and finalspectrum and colours of the whole region or
galaxy
Passive Evolution - Stellar Synthesis
N(m)
Initial Mass-function
SFR(t)
Star-formation Rate
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m
N
t
SF
Stellar Tracks
Spectral Libraries
t
SFR(t)
Star-formation RateEvolution of light froma collection of stars
born in a single burst
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Wavelength / nm
Lum
inosityperu
nitmass
Ultra Violet Optical
t
Passive Evolution - Single Burst
Single Burst of Star-formation
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g Galaxy starts of very blue as the light is dominated by the
massive hot blue stars
After the burst the massive stars live only a short time and
soon the light of the galaxy as a whole is dominated by thered light of the less massive, longer lived stars
Galaxy gets redder with age
Even a nave picture of the evolution of the Universe inwhich galaxies switched on at some early epoch would
predict some evolution of galaxies (all galaxies would nowbe red)
Passive Evolution More complicated star formation histories
can be imagined as a series of instantanious
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can be imagined as a series of instantaniousbursts
An exponential star-formation rate fits
many galaxies wellt
S
FR(t)
Star-formation Rate
t
t
Mexp
t is time since start of star-formation
is time-scale
Passive EvolutionThe spectra of present day
elliptical galaxies are well fit
with
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t
t
Mexp
t ~ 15 Gyr and ~ 1Gyr
The spectra of present day
spiral galaxies are well fit witht ~ 15 Gyr and ~ 3-10 Gyr
Irregular galaxies are often well fit by constant star-formation rates
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Number Count Models
Galaxy Evolution
K-Corrections
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Luminosity Functions
V/Vmax test of Evolution
Morphological Evolution
Passive Stellar Evolution
Number Counts The Global History of Star-Formation
Number Counts
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Current thinking on the basis of
number counts is that bluer
galaxies with an intrinsically
lower luminosity were more
numerous in the past
Euclidean Number CountsAssume a class of objects with
L which with a sensitivity fare
visible to a distance r
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r
Euclidean Number Counts
L++=
23
2,02
3
1,0 fNfNN
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r
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Number counts as a test of
Cosmology
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Modelling Number CountsIngredients:
REvolutionary rate
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z
SFR
Num
be
rDens
ity
Luminosity
Wavelength
Lum
inos
ity
Luminosity Functions
Spectral Energy Distributions
Evolutionary rate
Modelling Number Counts
( ) ( ) =>L
z
dLdVLfNmax
f
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( ) ( ) => LdVLfN0 0
f
( ) ( ) => T:Types 0 0maxL z
TL
dL
dVLfN f
recall
Thus can predictN(f) at various wavelengths
aim is to find a model that fits all observed counts
A no-evolution model would have (L) constant
Sophisticated models might include passive
Number Counts
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Current thinking on the basis of
number counts is that bluer
galaxies with an intrinsically
lower luminosity were more
numerous in the past
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ISO 15micron counts
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Number of galaxies
15m
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Serjeant, Oliver et al. 2000 MNRAS
Different components to models
include:starburst galaxies
normal galaxies
Seyfert galaxies
Proto-spheroidsetc....
15 micron counts
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Mid IR surveys
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NoEvo
lutionr
ange
Elbaz et al 1999, A&A 351L, 37
Open Stars: Lens fields
Open circles: HDF North field
Filled circles: HDF south field
Open squares/cross: IGTES ultra-deep
Stars/open triangles: IGTES, Deep
Filled triangles: IGTES, shallow
Radio Counts
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Modelling Number Counts
Currently there is no single models thatsuccessfully predict the number counts across all
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successfully predict the number counts across allwavelengths
Even over limited wavelength regions optical and
Near Infrared Mid Infrared
Far Infrared
Radio
Xray
There is no consensus on a best model
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Main Topics
Standard Hot Big Bang Model
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Classical Observational Cosmology
Galaxy Evolution
The Hunt for the First Galaxies
Background Light
Structure Formation
Galaxy Evolution
K-Corrections
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306/405
Luminosity Functions
V/Vmax test of Evolution
Morphological Evolution
Passive Stellar Evolution
Number Counts The Global History of Star-Formation
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Global History of Star-formation
Galaxy Evolution
K-corrections
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Luminosity functions
V/Vmax test of evolution
Morphological evolution
Passive stellar evolution
Number counts The global history of star-formation
Global History of Star-formation
The hot topic in observational cosmologyover the last few years
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over the last few years
Galaxies evolve
Galaxies produce stars Stars produce elements
These elements are essential for us
The global history of SF is the history of theproduction of elements and our history
Evolution of Light From aCollection of Stars Born in a
Single Burst
s
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Wavelength / nm
Lum
inosityperu
nitmass
Ultra Violet Optical
Live Fast Die Young Massive stars are short lived
Massive stars are very bright in UV
Number born similar to the number that die (c.F.
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(Newspapers & books)
Death of massive stars produces super novae
Death of massive stars produces elements Star birth rate proportional to UV luminosity
Star birth rate proportional to death rate (SN rate)
Star birth rate proportional to element production
Global History of Star Formation
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( ) ( )ttdNtdN D-= BornstarsBO,DeathstarsBO,
m
N(m) Initial
Mass-function
*BornstarBornstarsBO, & dNdN via IMF
Global History of Star FormationGlobal Star-formation rate is star formation rate per
unit volume
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( )
L
dLLL
dVUV
* fr
c&
HII Regions
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The trapezium regionwithin the Orion Nebula
Molecular Clouds
Reflection nebula within Orion
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A Local Star Forming Region in
Our Galaxy
The Trifid Nebula
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Cernicharo et al.
Interactions Between
Different Components
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Star Formation
IR
Dust
UV
IR
G
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H
Dust
UV
IR
IR
Gas
Gas
SN
e-e-
e-e-
Radio
DustUV
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M33 in H, OIII, 555nm
M82 a Star Forming Galaxy
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Wavelength /m
logLum
inosity
10 1001
Efstathiou et al. MNRAS
submitted
Star Formation Rate Measures
SFR = -1 CuvLuv
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SFR = -1 CHLH
SFR = C1.4GHz
L1.4GHz
SFR = (1-)-1CFIRLFIRCuv = 4.2 kg s
-1 / WHz-1
CH = 4.2X10-12 kg s-1 / W
C1.4GHz = 15.75
kg s
-1 / WHz-1
CFIR =0.12 kg s-1 / WHz-1
Comparison of
Star Formation
Rate Measures
SF
Rinfrare
d
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Star formation rates in the radio
Solar masses per yearCram et al 1999
SFRUV
SFRH
Summary
Star formation activity dominated by short-lived massive stars
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lived massive stars
Their UV light absorbed by dust and re-
emitted in FIR High z objects observed in sub-mm
Surveys in FIR and sub-mm required totrace obscured SFR history
Current Star
Formation Rate
FR/kg
s-1m-3
]
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IR
Radio Oliver, Gruppioni & Serjeant 1999 MNRAS Submitted
Serjeant, Gruppio