Midterm exam:

• datedate: March 17, 2006, 8:15 a.m.: March 17, 2006, 8:15 a.m.• locationlocation: Conrad Naber Hall: Conrad Naber Hall• bring bring pocket calculatorpocket calculator• NO text books, notes laptops etc.NO text books, notes laptops etc.• do NOT bring your own paperdo NOT bring your own paper• write on exam sheets directlywrite on exam sheets directly

astrophysicsastrophysics

Spacephysics: see web sitesee web site

Sir Isaac Newton:(1643-1727)

Cosmology as a Science

• Mathematical description Mathematical description of the Universeof the Universe

• The same physical lawsThe same physical laws apply to earth and Universeapply to earth and Universe

Newton: Fundamental contributions

•MathematicsMathematics: - series expansions: - series expansions - differential calculus- differential calculus - approximation methods- approximation methods - …- …• OpticsOptics: - spectral analysis of white light: - spectral analysis of white light• PhysicsPhysics: - ‘Principia mathematica…’: - ‘Principia mathematica…’• AstronomyAstronomy: - : - derivederive Kepler’s laws from Kepler’s laws from gravitational forcesgravitational forces• … …....

A toy universe

According to Newton, what is going to happen ?According to Newton, what is going to happen ? The model Universe is going to collapse under The model Universe is going to collapse under

its own gravityits own gravity

boundaryboundary

constant densityconstant density

(homogeneous)(homogeneous)

Newton’s Conclusion:

In order to avoid collapseIn order to avoid collapse homogeneoushomogeneous isotropicisotropic infinite sizeinfinite size no centerno center

infinite in timeinfinite in time has always beenhas always been will always bewill always be

perfect cosmological principleperfect cosmological principle

The perfect cosmological principle

homogeneous: homogeneous: the universe looks the same the universe looks the same

everywhere on large scaleseverywhere on large scales there is there is no special placeno special place (center) (center)

isotropic:isotropic: the universe looks the same in the universe looks the same in

all directions on the sky all directions on the sky

there is there is no special directionno special direction unchanging: unchanging: The universe looks the same atThe universe looks the same at

all timesall times there is there is no special epochno special epoch

Olber’s Paradox

• If the universe is i) If the universe is i) eternaleternal ii) ii) (more or less)(more or less) uniformly filleduniformly filled with stars with stars iii) iii) infiniteinfinite

• then there is a star along each line of sightthen there is a star along each line of sight

so: so: Why is the night sky dark ?Why is the night sky dark ?

Shell of radius rShell of radius r11::

Surface: SSurface: S11=4=4 r r1122

Volume: VVolume: V11=4=4 r r1122xx

# of stars: N# of stars: N11= 4= 4 r r1122xx

luminosity per star: lluminosity per star: l**

luminosity of shell:luminosity of shell:

LL11 = 4 = 4 r r1122x lx l**

Shell of radius rShell of radius r2 2 = 2r= 2r1 1 ::

Surface: SSurface: S22=4=4 (2r (2r11))22

Volume: VVolume: V22=4=4 (2r (2r11))22xx

# of stars: N# of stars: N22= 4= 4 (2r (2r11))22xx

luminosity per star: lluminosity per star: l**/4/4

luminosity of shell:luminosity of shell:

LL22 = 4 = 4 (2r (2r11))22x lx l**/4/4

= 4= 4 r r1122x lx l* * = L= L11

Shell of radius rShell of radius r3 3 = 4r= 4r1 1 ::

Surface: SSurface: S33=4=4 (4r (4r11))22

Volume: VVolume: V33=4=4 (4r (4r11))22xx

# of stars: N# of stars: N33= 4= 4 (4r (4r11))22xx

luminosity per star: lluminosity per star: l**/16/16

luminosity of shell:luminosity of shell:

LL33 = 4 = 4 (4r (4r11))22x lx l**/16/16

= 4= 4 r r1122x lx l* * = L= L11

Problems with an infinite universe Olber’s Paradox: Why is the night sky Olber’s Paradox: Why is the night sky

dark?dark?

Olber’s Paradox:

Each shell contributesEach shell contributes

LL11 = 4 = 4 r r1122x lx l**

infinite number of shellsinfinite number of shells

infinite luminosityinfinite luminosity

(at least) one of the (at least) one of the assumptions must be wrong !assumptions must be wrong !

How to solve Olber’s paradox ?

Universe is finiteUniverse is finite Universe has finite ageUniverse has finite age The distribution of stars throughout space is The distribution of stars throughout space is

not uniformnot uniform The wavelength of radiation increases with The wavelength of radiation increases with

timetime

Note:Note: for the big bang model, all thesefor the big bang model, all these conditions are satisfied conditions are satisfied

Einstein:• speed of light = constspeed of light = const relativity of relativity of simultaneity,simultaneity, special relativityspecial relativity

• general relativity:general relativity: space-time is curvedspace-time is curved

• prediction of prediction of black holesblack holes• prediction of prediction of gravitational wavesgravitational waves

Einstein• Universe Universe has to be static!has to be static!• only possible if extra-term is included in only possible if extra-term is included in equations to counter-balance attractionequations to counter-balance attraction cosmological constantcosmological constant

• Einstein’s Einstein’s “biggest blunder”“biggest blunder”

Edwin Hubble (1889-1953)Four major accomplishments Four major accomplishments in extragalactic astronomyin extragalactic astronomy The establishment of the The establishment of the

Hubble Hubble classification classification scheme of galaxiesscheme of galaxies

The convincing The convincing proof that galaxies are islandproof that galaxies are island “universes”“universes”

The distribution of galaxies in spaceThe distribution of galaxies in space The discovery thatThe discovery that the universe is expandingthe universe is expanding

Doppler effect (for light)

The light of an approaching source is shifted to the The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the blue, the light of a receding source is shifted to the redred

Doppler effect

red shiftred shiftblue shiftblue shift

The light of an approaching source is shifted to the blue, The light of an approaching source is shifted to the blue,

the light of a receding source is shifted to the red.the light of a receding source is shifted to the red.

Doppler effect

redshift:redshift:

zz=0: not moving=0: not moving

zz=2: =2: vv=0.8=0.8cc

zz==: : vv==cc

em

emobsz

em

emobsz

The redshift-distance relation

Key results Most Most galaxiesgalaxies are moving are moving away from usaway from us The recession The recession speed vspeed v is is larger for morelarger for more distant distant

galaxiesgalaxies. The relation between recess velocity. The relation between recess velocity vv and distanceand distance dd fulfills a linear relation: fulfills a linear relation: v = Hv = H0 0 d d

Hubble’s measurement of the constantHubble’s measurement of the constant HH00::

HH00 = 500 km/s/Mpc = 500 km/s/Mpc

today’s best fit value of the constant:today’s best fit value of the constant: HH00 = 71 km/s/Mpc = 71 km/s/Mpc (WMAP)(WMAP)

Question:If all galaxies are moving away from us,If all galaxies are moving away from us,

does this imply that we are at the center?does this imply that we are at the center?

Answer:Not necessarily, it also can indicate that the Not necessarily, it also can indicate that the universe is expanding and that we are at no universe is expanding and that we are at no special place.special place.

Einstein’s General Relativity +Einstein’s General Relativity +observation of expanding Universe:observation of expanding Universe:

Universe started from a point:Universe started from a point:

““Big Bang Model”Big Bang Model”

Big Bang Model

Big Bang in a nutshell:

Cosmological redshift

While a photon travels from a distant source While a photon travels from a distant source to an observer on Earth, the Universe to an observer on Earth, the Universe expands in size fromexpands in size from RRthen then toto RRnownow..

Not only the Universe itself expands, but Not only the Universe itself expands, but also the wavelength of the photonalso the wavelength of the photon ..

emittedthen

nowreceived R

R emittedthen

nowreceived R

R

Cosmological redshift

General definition of redshift:General definition of redshift:

for cosmological redshift: for cosmological redshift:

emitted

emittedreceivedz

emitted

emittedreceivedz

then

now

emitted

received

R

Rz

1then

now

emitted

received

R

Rz

1

A large redshift z implies ...

The The spectrumspectrum is strongly is strongly shiftedshifted toward red toward red or even infrared colorsor even infrared colors

The object is very The object is very far awayfar away We We see the objectsee the object at an epoch when the at an epoch when the

universe was much universe was much youngeryounger than the than the present day universepresent day universe

most distant astrophysical object discovered most distant astrophysical object discovered so far: z= 6.3 (in 2005)so far: z= 6.3 (in 2005)

z>5.8: “dark ages”z>5.8: “dark ages”

Are there any indications that this picture is correct?

Yes !Yes !

Primordial NucleosynthesisPrimordial Nucleosynthesis

Cosmic Microwave backgroundCosmic Microwave background

Primordial NucleosynthesisGeorgy Gamov (1904-1968)

If the universe is expanding, then If the universe is expanding, then there has been a big bangthere has been a big bang

Therefore, the early universe must Therefore, the early universe must have been very dense and hothave been very dense and hot

Optimum environment to breed the elements by Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)nuclear fusion (Alpher, Bethe & Gamow, 1948) success: predicted that helium abundance is 25%success: predicted that helium abundance is 25% failure: could not reproduce elements more massive failure: could not reproduce elements more massive

than lithium and beryllium (than lithium and beryllium ( formed in stars) formed in stars)

The Cosmic Microwave Background (CMB)

Last scattering surface transparenttransparent

opaqueopaque

Penzias and Wilson 1965

Working at Bell labsWorking at Bell labs Used a satellite dish to measure radio Used a satellite dish to measure radio

emission of the Milky Wayemission of the Milky Way They found some extra noise in the They found some extra noise in the

receiver, but couldn’t explain itreceiver, but couldn’t explain it discovery of the background radiation discovery of the background radiation

Most significant cosmological observation Most significant cosmological observation since Hubblesince Hubble

Nobel prize for physics 1978Nobel prize for physics 1978

The cosmic microwave background radiation (CMB)

Temperature of Temperature of 2.728±0.004 K2.728±0.004 K

isotropic to isotropic to 1 part in 100 0001 part in 100 000

perfect black bodyperfect black body 1990ies: CMB is 1990ies: CMB is

one of the major tools to study cosmologyone of the major tools to study cosmology Note: ~1% of the noise in your TV is from Note: ~1% of the noise in your TV is from

the big bangthe big bang

More results from the CMB

The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift

The emission of the The emission of the GalaxyGalaxy

Fluctuations in the Fluctuations in the CMBCMB

•Fluctuations in CMB responsible for structure formation in the universe

Cosmic Structure formation

New developments:Science discovery of the year 1998

qq00 = 0 = 0qq00 = 0.5 = 0.5

more distantmore distant

fain

ter

fain

ter

Data indicates:Data indicates:

qq00 < 0 < 0

Expansion Expansion

is acceleratingis accelerating

From Supernova observations:

The expansion of theThe expansion of the universe is universe is accelerating !!!accelerating !!!

But gravity is always attractive, so it only But gravity is always attractive, so it only can deceleratecan decelerate

Revival of the cosmological constant Revival of the cosmological constant

k=+1

=0

>0

The fate of the Universe for >0

Wilkinson Microwave Anisotropy Probe (WMAP) (2003)

COBE COBE (1992)(1992) WMAP WMAP (2003)(2003)

Summary of most important results of

WMAP

• Age of the UniverseAge of the Universe: : 13.7 billion13.7 billion years years• First starsFirst stars: : 200 million200 million years years after Big Bangafter Big Bang• CMBCMB: decoupled : decoupled 379 000379 000 years years after Big Bangafter Big Bang• Hubble constant: HHubble constant: H00= 71 (km/s)/Mpc= 71 (km/s)/Mpc• Content of the UniverseContent of the Universe:: -- 4% Atoms 4% Atoms - 23 % cold, dark matter- 23 % cold, dark matter - 73 % ‘Dark Energy’- 73 % ‘Dark Energy’