Our Place Our Place in in the the Cosmos Cosmos and that the - - PDF document

Our Our Place Place in in the the Cosmos Cosmos

Lecture 17 The Expanding Universe

The Cosmological Principle

• Contradicting early beliefs that the Earth is at the

centre of the Universe, the cosmological principle posits that there is nothing special about our location and that the same rules of physics apply everywhere

• We now known that the Earth orbits the Sun, one of

hundreds of billions of stars forming the Milky Way

• The Milky Way itself is just one of hundreds of

billions of galaxies scattered throughout a Universe vastly larger than our ancestors might have imagined

Cosmology

• Cosmology is the study of the entire Universe,

including its structure, history, origins and fate

• The cosmological principle makes the testable

prediction that any conclusions we reach about the Universe are independent of our location

• In other words observers everywhere should see the

same Universe

• This implies that the Universe must be homogeneous

and isotropic - that is that it has the same properties from place to place and that it should look roughly the same in whatever direction we look

Cosmology

• Clearly the Universe is neither homogeneous nor

isotropic on scales the size of galaxies or smaller

• By homogeneity, we mean that the stars and galaxies

in our vicinity are similar to the stars and galaxies elsewhere in the Universe - the Universe is homogeneous on large scales

• We can test the predictions of homogeneity and

isotropy by counting galaxies as a function of distance and position on the sky

• Such observations are indeed consistent with the

cosmological principle

Galaxy Spectra

• Galaxy spectra look like the spectra of

ensembles of stars with the addition of interstellar gas

• The gas gives rise to a series of emission or

absorption lines on top of the continuum radiation provided by the stars

• These lines are due to electron transitions

within atoms and have well-defined energies and hence wavelengths

The Redshift

• Vesto Slipher used the Lowell Observatory

24-inch telescope to record galaxy spectra

• He noticed that the emission and absorption

lines were shifted to shorter or longer wavelengths than was measured in the laboratory

• The first galaxy Slipher observed, M31, in 1912,

showed a shift to shorter wavelengths (a blueshift)

• Most galaxies however showed redshifts, that

is shifts to longer wavelengths

Redshift

• Redshift z is defined by
• It is independent of which line is used
• According to the Doppler shift, the redshift is also

equal to the recession velocity vr divided by the speed

• f light c: z = vr/c
• Comparing galaxy redshifts with their distances, as

estimated from Cepheid stars, Edwin Hubble and Milton Humason noticed in 1929 that a galaxy’s recession velocity is proportional to its distance d: vr = H0 x d

• A more distant galaxy is receding from us faster than

a nearby galaxy - the Hubble law

Hubble’s Law

• At first glance, Hubble’s law appears to indicate that

we are at a special place in the Universe and that everything is racing away from us

• In fact, Hubble’s law says that the Universe is

expanding uniformly and the expansion appears the same no matter where you are in the Universe

• The key is to think not of galaxies moving through

space, but of the Universe itself as expanding with the galaxies being carried along with it

• The Hubble law vr = H0 x d is in fact the only

relation between velocity and distance consistent with a homogeneous and isotropic Universe

Hubble’s Law

• A 2d analogue is flat “houses” on the surface
• f an expanding balloon

Hubble’s Law

Determining H0

• Hubble’s law tells us that the Universe is

expanding

• To determine the rate of expansion we need

to measure the Hubble constant H0

• This requires measuring distances and

redshifts to distant galaxies in order to

• vercome deviations from the Hubble

expansion known as peculiar velocities

• These are typically a few hundred km/s and

are due to gravitational forces between galaxies

Determining H0

• On small scales peculiar velocities can

dominate over the Hubble flow and so we need to measure distances to galaxies that are receding from us with velocities of several thousand km/s or more (z > 0.01)

• This is far too distant to apply the distance

estimators we have discussed so far (parallax, Cepheid or RR Lyrae stars)

• We need to find distance indicators in a series
• f steps known as the distance ladder

Cosmic Distance Ladder

David Darling Encyclopaedia

Note uncertainties increase cumulatively with each rung of the ladder

Cosmic Distance Ladder

• In distant galaxies, too far away to resolve

Cepheid variable stars, Type I supernovae provide a valuable distance indicator

• These supernovae result from the accretion of

matter onto a white dwarf from a companion star

• When the white dwarf mass exceeds the

Chandrasekhar limit it implodes, resulting in a Type I supernova

• Because all Type I supernovae progenitors

have the same mass, the resulting supernovae have approximately the same peak brightness, and thus act as standard candles

Supernovae

• With a peak luminosity comparable to

entire galaxies, supernovae can be seen to redshifts z = 1 and beyond

= 72 km/s/Mpc

Look-back Time

• Because light has a finite travel speed

(c 300,000 km/s) when we look at distant galaxies, we see them as they were in the past

• Look-back time is the time taken for light to

reach us from a distant object

• For an object at redshift z = 0.1, the look-

back time is about 1.4 billion years

• At z = 0.2, it is 2.7 billion years
• By observing differences between objects at

high and low redshift we can determine how the Universe evolves

The Big Bang

• Since all galaxies are now moving away from each
• ther, they must have been much closer together in

the past

• According to Hubble’s law, two galaxies separated by

100 Mly from each other are moving apart at vr = H0 x d = 2,200 km/s

• Travelling at this speed, the galaxies would have

taken about 13.6 billion years to travel the 100 Mly that separates them

• Assuming the expansion velocity remains constant, one

arrives at the same time for any two galaxies to have travelled the distance that separates them

The Big Bang

• Since time equals distance divided by velocity, and

velocity is the Hubble constant times distance, one can easily see that 1/H0 has dimensions of time

• Furthermore at a time 1/H0 ago all galaxies were in

the same place and the Universe had zero size!

• 1/H0 is known as the Hubble time and provides an

estimate of the time since the Big Bang and hence the age of the Universe

The Expanding Universe

• The Big Bang should not be thought of an

explosion in the normal sense

• It did not occur at any particular location -

the question “Where did the Big Bang take place?” makes no sense

• Instead the Big Bang created the Universe as

we know it, and set the whole of space expanding, carrying the galaxies along with it, like currants in a fruit cake which is rising in the oven

Redshift and Expansion

• Redshifts are not due to velocity-induced Doppler

shifts but result from the wavelength of light being stretched out by the expansion of the Universe

• In the time the light from a distant object at

redshift z has been travelling to us, the Universe, and the wavelength of the light, has expanded by a factor of (1 + z)

Summary

• Galaxies are moving apart from each other at

a velocity proportional to their separation - the Hubble law

• This observation is consistent with the

Universe being homogeneous and isotropic

• Space itself is expanding - the galaxies are

carried along with this expansion, and redshift results from expansion of the light wave

• Assuming a constant expansion rate, we see

that the Universe had zero size about 13.6 billion years ago - the Big Bang

The classical redshift-velocity relation v = cz is an approximation only valid at low redshifts z << 1