2 – Expanding Horizons

Asking the big question

• Today’s scientific knowledge is a real challenge to traditional ideas

• What questions can we hope to answer?• We know a lot more about the Universe

Hubble Space Telescope, courtesy NASA

Hubble’s lawEdwin Hubble (1889 – 1953)

The law

• v is velocity of galaxy• r is distance away• Hubble’s law

– H0 is Hubble’s constant

• Hubble’s 1929 data didn’t extend very deeply into space

rH v 0=Mt Wilson 100 inch telescope; Courtesy http://www.mtwilson.edu/vir/100/100_int.jpg

The evidence

• Galaxies have velocities relative to their neighbours ~few hundred km s-1

– called peculiar velocity– Andromeda galaxy is coming towards us– light is blue-shifted

Andromeda galaxy, M31: courtesy http://seds.lpl.arizona.edu/messier/Jpg/m31.jpg

Receding galaxies are red-shifted

• Red-shifted light is recognised from the wavelength of characteristic spectral lines

↑ ↑ ↑ ↑ dark absorption lines ↑

HαHβHγHδ

Red-shift z = 0.07

Red-shift parameter z

• z is calculated from the observed wavelength λobs and the emitted wavelength λem

• e.g. λem = 486 nm; λobs = 520 nm– Z = 34/486 = 0.07– λem is cyan; λobs = green

em

emobszλ

λλ −=

Speed of recession

• Using the standard Doppler effect

– v is the velocity of recession

• E.g. z = 0.07; c = 3×105 km s-1

gives v = 21,000 km s-1

– for today’s value of H0, then r ≈ 300 Mpc

• For z >0.1, need to use relativistic Doppler formula

v = cz

Cepheid variables

• Cepheids– brightness deduced

from variable light curve

– distances deduced from faintness

– velocity deduced from red-shift

– NGC4603 @ 33 Mpc

NGC4603 →

Cepheids in NGC4603; Courtesy NASA

HUDF images galaxies with z ≈ 6

• Very distant galaxies appear wholly red

Today’s value of H0

• 2 converging answers– analysis of fluctuations in the

cosmic microwave background• H0 = 71 (+4, – 3) km s-1 Mpc-1

• Cosmology texts use h– H0 = h × 100 km s-1 Mpc-1

• h = 0.71

• Hubble flow describes cosmological red-shift– cause of red shift for galaxies >100 Mpc

↑The Coma cluster

Expansion of the Universe

• Concept implicit in Einstein’s General Theory of Relativity

• Realised by Willem de Sitter• Range of possibilities pointed out by

Alexander Friedmann

Willem de Sitter (1872 – 1934) at St Andrews in 1934

Alexander Friedmann (1888 – 1925)

Hubble time & Hubble radius

• Hubble time: estimate of age of Universe– r radius of Universe; v expansion rate– TH = r/v = 1/H0 = 9.78 h-1 billion years

• 13.8 × 109 yr

• Hubble radius rH

• rH is distance to a notional horizon– rH = c/H0 = 3000 h-1 Mpc = 4200 Mpc

Meaning of the expanding Universe

• Every point moves away from every other point

• Every point sees itself as the centre of the expansion

• All points are equivalent• Hubble constant is the

same in all directions

Local Matters

• Expansion affects the Universe as a whole, not bound systems

• Density Universe ~10-26 kg m-3

– ~few protons m-3

Cosmic scale factor

• x is position of object relative to a reference grid– co-moving coordinate

• Expansion by a factor of a(t)– coord r = a(t)x

• a(t) is the cosmic scale factor

x

r = a(t)x

Universe expanded

• Vel v of a galaxy = = =• Since in general v = Hr

• Hubble constant generally depends on time, not space– H(t)

• Using subscript 0 to represent ‘now’

Expansion velocity

r&

r& x(t)a& )(/)( tarta&

a(t)(t)a

H&

=

0

00 a

aH

&=

Cosmological red-shift

• Red-shift is due to the stretching of space as the light travels to us

• Applied to ‘now’: 1 + z = a0/a(tem)• z can be used to determine the size of

the Universe in the past– z = 6 gives a(tem) = a0/7

)a(t)a(t

λλ

z1em

obs

em

obs ==+

z11

a)a(t

0

em

+=

Olbers’ paradox

• Why is the sky dark at night?• If the Universe is static and infinite, you

would expect to see stars in every direction– dust is not the answer

• Finite life of Universe and finite life of stars

Contributions to starlight• Stars in successive shells

make approximately equal contributions of light– number of stars in a shell

at distance ‘d’ ∝ d2

– light from individual stars ∝ 1/d2

– hence light from each shell is constant

• Finite life of Universe and stars limits the number of shells