Lecture 7:Our Universe 1.  Traditional Cosmological tests

–  Theta-z –  Galaxy counts –  Tolman Surface Brightness test

2.  Modern tests –  HST Key Project (Ho) –  Nucleosynthesis (Ωb) –  BBN+Clusters (ΩM) –  SN1a (ΩM & ΩΛ)

–  CMB (Ωk & ΩR)

3.  Latest parameters 4.  Advanced tests (conceptually)

–  CMB Anisotropies –  Galaxy Power Spectrum

Course Text: Chapter 6 & 7 Wikipedia: Dark Energy, Cosmological constant, Age of Universe

Cosmological tests •  The proper distance, dp, is the critical expression to test in

all experiments –  Find a standard candle in luminosity or size. –  Measure that quantity to a large redshift –  Compare distance or angle and redshift to constrain Ωs –  Tests geometry not dynamics

•  Typically we test either: –  Angular size v distance, e.g., cluster size, radio lobes, CMB anisotropy –  Luminosity v distance, e.g., SNIa, Bright Cluster Galaxies –  Number-density v distance, e.g., Space-density of galaxies, galaxy counts

•  Above all test geometric effects not dynamics: –  Test in planning with ELT which will look at dynamics (i.e., re-measure

redshift after a small time interval to measure change with time).

Theta-z •  Assume radio lobes of radio galaxies are constant

in size. –  Popular test in 1960-1980s –  Provided first indication that model makes sense –  Idea:

–  In a Euclidean Universe:

–  In a curved Universe:

! !1d

! !1da

, da = f "M"R"k"#, z( )

Fixed Rod θ

Fixed Rod θ

Curvature

Theta-z relation

Radio lobe data While demonstrating the effect expected the radio lobe data was never accurate enough to distinguish between models. Main concern was evolution of the radio lobes. However test was reborn when CMB anisotropies were discovered.

Quasar Radio Lobes

Current Theta-z •  Recent observations use compact radio sources

Galaxy Number Counts •  In 1936 Hubble proposed using galaxy counts to

measure geometry –  If galaxies uniformly distributed then expect differential number

v magnitude to be different. –  200’’ telescope at Mt Palomar constructed

Apparent magnitude

Num

ber-

coun

ts p

er d

m in

terv

al

FLAT CONTRACTING EUCLIDEAN

FLAT EXPANDING

CLOSED EXPANDING

OPEN EXPANDING

Volumes in expanding space

For very small triangle number of squares is roughly the same. As the triangle grows the number of squares sampled becomes noticeably different:

closed = increase in squares falls off flat = squares increase linearly open=squares increase faster than linear.

Galaxy counts

ΩM=1 ΩΛ=0

EUCLIDEAN

Galaxy Counts

Classificationuncertainty

Neuschaefer et al. G-Based

Casertano et al. HST(WF/PC)

Driver et al. HST(WFPC2)

Fig. 2

Main problem again evolution (Tinsley et al) Attempts made to isolate elliptical Galaxies which should have least evolution but then Errors dominated by ability to identify Ellipticals. Galaxy count work no longer used for Cosmology but to study galaxy evolution

Tolman SB test •  Proposed in 1930s •  In static Euclidean Universe SB is distance independent •  In an expanding Universe it depends on the curvature

–  (1+z)-4 in a flat Universe

•  Results supported notion of expansion but once again test too crude for precision cosmology

Classical tests •  All three tests showed the general effect expected

–  Sizes fall more slowly than expected –  Galaxy counts not linear but drop off –  Surface brightness not distance independent

•  But all were plagued by evolution of the standard candle –  Radio lobes will evolve and grow with time –  Galaxies evolve getting brighter/fainter/more numerous etc. –  Because galaxies get brighter SB is also affected.

•  From 1980s the era of discovery cosmology began powered by new facilities and supercomputers

•  By 2000 the Concordance Model emerged •  But its an odd set of params. in many ways…

Big Bang Nucleosynthesis, Ωb

See Lecture 2. Abundance measurements of the light elements tightly constrain the baryon density. Perhaps more importantly the independent measures of the different light elements all concur.

!bh2 ~ 0.02, h = Ho

100!b ~ 0.04

BBN+Cluster M/L, ΩM

•  If clusters represent a fair sample of the Universe one can derive their Dark-to-baryon mass ratio.

•  The idea is large bound structures will retain their baryons and dark matter. –  Motion of galaxies and/or lensing and/or SZ à DM mass –  X-ray observations of inter-cluster gas à ionised mass –  Optical census of cluster à stellar masses (very small) –  Radio census of cluster à Neutral gas mass (very very small)

–  Typically:

!DM =MDM

Mb

!b

!M = (MDM

Mb

+1)!b

MDM

Mb

~ 5

!M ~ 0.25

Supernova Type Ia, ΩΛ

•  SNIa believed to be standard candles much like Cepheids –  Caused by accretion onto a WD at a specific mass goes SN. –  Happens at fixed mass è fixed luminosity à standard candle.

•  If we can measure peak brightness and the redshift we can use the magnitude-distance relation to measure prams.

•  Only unknowns are: ΩMΩΛΩK but Ωk=0 from CMB •  Just need to find SN and measure light curves

m =M + 5log10[dl (z,Ho,!M!"!K )]+ 25+ Av +K(z)

Apparent mag (can measure)

Absolute mag (calibrate locally)

z via redshift Ho via Cepheids

Can estimate redenning From colours

Can derive from Local SNIa spectra

Nearby SN (Calibrator)

More distant SN

SNIa light curve

SNIa do show some sign of Variation, i.e., not perfect Standard cnadles (top figure) However brighter SNIa have broader light curves (top figure) Once this is taken into account (bottom figure) SNIa look like an ideal standard candle

(Re)discovery of Λ •  Two independent groups competing

–  High-z Supernova Search Team (Reiss et al 1998) –  Supernova cosmology project (Perlmutter et al 1997) –  Both report non-zero Λ

Alternative interpretations •  Result is that galaxies appear fainter by ~20% over

expectation for an EdS Universe. •  Could other effects cause this:

–  Dust attenuation: –  Normal dust reddens light but spectra show no effect

–  Grey dust, e.g., large dust grains > wavelength –  Unphysical

–  Evolution of SNI1, e.g., metallicity –  Models show minimal effect

–  GR wrong/incomplete in some other way (e.g., Tired Light)

•  SN searches gave the first indication •  CMB and LSS studies provided orthogonal support. •  Increased age of Universe from 9Gyrs à 14Gyrs

–  More consistent with GC ages (~13Gyrs).

CMB, ΩR, ΩK •  BB spectrum at z=0 gives ΩR precisely

•  First anisotropy peak gives extreme theta-z test

–  The early Universe was lumpy (see next lecture on inflation) –  Over-densities in the radiation field flow out dragging the

baryons with them at the sound speed.

!"d" =8#hc3

"3

exp(h" / kBT )!1d"

! =8# 5kB

4

15h3c3T 4 = 7.565"10!16 (2.725)4

$R =!c2= 4.5"10!31kgm!3

#R =$R

$Crit~ 0.00002

CMB •  The early Universe was lumpy (see next lecture on

inflation) •  Over-densities in the radiation field flow out

dragging the baryons with them at the sound speed.

•  At decoupling baryons are left behind

•  This gives an over-density on a particular scale.

vs2 =

d!dp

=d 13c2p

!

"#

$

%&

dp=c3

ls = vst =ct3

Eqn of state for radiation

Temp. at which H atom kept ionised by BB photon distribution (nγ/nb) Age at which decoupling occurred dictated only by Ho,ΩM because for most of the time from BB to Decoup matter dominated. Evaluating using current params gives: Valid for similar ΩM Note:

ls =ctdecoup3

(1+ z) = RoRdecoup

=TdecoupTo

=30002.7

=1111

tage =1Ho0

1

! ["M (1+ z)+"R (1+ z)2 +"# (1+ z)

$2 +"k ]$12d 1

(1+ z)

tdecoup ! 380, 000yrs

[tdecoup,EdS = toRdecoup

Ro

"

#$

%

&'

32

=2

3Ho

[1+ z](3

2 ! 230, 000yrs]

CMB theta- test •  BB predicts lumps on scales of 2ls~0.14Mpc at

decoupling (or 0.08Mpc for EdS) •  Can measure anisotropies.

0.14Mpc

da=f(z,ΩM,ΩR,ΩΛ)

θ

da (!M =1.00,!" = 0.00) = 9.3 !(!M =1.00,!" = 0.00) = 0.50

da (!M = 0.25,!" = 0.00) = 27.3 ! = 2 tan#1 lsda

$

%&

'

() !(!M = 0.25,!" = 0.00) = 0.30

da (!M = 0.25,!" = 0.75) =13.2 !(!M = 0.25,!" = 0.75) = 0.60

Peak~10

Results:

Assignment 2 & 3 •  Recent results from WMAP (see

http://letterstonature.wordpress.com/2010/01/29/wmap-7-cosmological-parameter-set/), find:

T = 2.725KHo = 70.2km/s/Mpc!b = 0.0455!dm = 0.227!m = 0.272!" = 0.728zeq = 3196to =13.78Gyr

•  From these parameters derive: i.  The density of radiation today in kg m-3

ii.  The redshift range over which matter dominates the dynamics iii.  The temperature at matter-radiation equilibrium iv.   The age of the Universe at matter-radiation equilibrium (use approximation) v.  The temperature of the Universe 1s after the Big Bang vi.  The radiation, mass, and vacuum densities 1s after the Big Bang (in kgm-3) vii.  The proper distance to an object at z=1 (HINT: find an online cosmology

calculator) viii. The apparent magnitude of a galaxy with M=-20 mag at z=1 (ignore dust

attenuation and the K-correction). ix.   The apparent diameter of a galaxy in arc seconds assuming the galaxy’s

intrinsic radius is 15kpc. x.  What is the minimum size an object 1kpc across can appear on the sky and

how does this compare to the resolution of the Hubble Space Telescope. xi.  Finally relax and watch: http://www.vimeo.com/22956103 and then describe

what you find convincing and what you find unconvincing in the current standard model.

•  Tidy solutions with explanation as necessary to be handed in 11am Friday 20th in person or via email.