Astrophysics

E4 Cosmology

+ E6 Galaxies and the expanding universe

Cosmology

Newton’s Model

Newton suggested...

- the universe is infinite with no beginning or end

- the universe is in static equilibrium, with equal gravitational forces either side of any stellar body.

- the stars in the universe are uniformly distributed, resulting in the equal gravitational forces described above.

However... his own laws explained bodies with elliptical orbits. This could lead to instability in one region, causing the whole delicate balance to collapse.

Olbers’ Paradox

Another problem with Newton’s model is that an infinite universe would result in an infinite number of stars in the sky. Thus the night sky would be uniformly bright, not dark! This is Olbers’ paradox.

d t

Consider the light received from a ‘shell’ of thickness t at distance d from Earth:

Olbers’ paradox assumptions...

- the number of stars per unit volume (n) is constant

- each star has luminosity L

So energy per shell is uniform and constant, irrespective of d.

If shells are infinite then the total energy received per second must also be infinite, resulting in a uniform, infinitely bright sky!

(Note... In answering exam questions you can simply say that the energy per star is given by an inverse square law while the number of stars per shell is given by a square law. Thus they cancel, resulting in a constant amount of energy per shell, irrespective of distance).

Energy per second received on earth for all stars from the shell = (L / 4 π d2) x number of stars in shell

= (L / 4 π d2) x (n x 4 π d2 x t)

= Lnt

We conclude that Newton was probably wrong, the universe is probably finite. So the sky at night is dark because...

- time is finite (it started with a Big Bang!), so the light from the furthest stars hasn’t reached us yet (and by the time it does, light from other stars may have stopped)

- there isn’t an infinite number of stars

The Expanding Universe

We have already seen that Doppler shift can result in light from stars moving away from us or towards us experiencing ‘red shift’ or ‘blue shift’. This is observable from movement of absorption spectra:

Edwin Hubble showed that light from all distant galaxies exhibits red shift

He also showed...

• the further they are, the more the shift.

• so the further they are, the faster they move.

• this means all distant galaxies are moving away from ours (and from each other). i.e.The universe is expanding.

Calculations Involving Red Shift

The change in frequency Δf or wavelength Δλ is related to the recessional velocity v of the galaxy emitting the light...

Note: The original wavelength of an absorption band is known from laboratory values on earth for the corresponding element.

Q. A galaxy is moving away from earth at 1.2 x 107 ms-1. Determine the apparent wavelength in light from this galaxy of a spectral line whose normal wavelength is 410.2 nm.

Δf Δλ v f λ c

= =

Where...f = original frequency (Hz)λ = original wavelength (m)c = speed of light

The Big Bang You tube link (2mins)

Red shift of light from distant galaxies implies that at some point all matter must have originated at the same point in space!

- Space and time began with the Big Bang.

- Before the Big Bang, there was no time or space.

- Space is constantly being created in the universe. This is why galaxies appear to be moving apart with increasing speed.

Evidence for the Big Bang Model

1. The universe is expanding (as seen from red shift of light from more distant galaxies being greater).

2. The current amount of Helium in the universe is as predicted by the Big Bang model (about 25%).

3. Cosmic Microwave Background Radiation (CMB)

Cosmic Background Radiation

Hubble’s Law

H0 = Recessional velocityDistance from earth

The Age of the Universe

For a galaxy moving with constant velocity v for a time t since the big bang across distance d in space...

t = d / v

But from Hubble’s law we know that

v = H0 d

so...

i.e. 1/H0 gives a rough approximation for the age of the universe.

t = d H0 d

t = 1 H0

Q. a. Using a value of H0 = 75 kms-1 Mpc-1 determine a value for the age of the universe in seconds and years.

- 4.13 x 1017s

- 1.3 x 1010 years

b. Give two reasons why this is only an estimate.

- we are assuming constant velocity / constant rate of expansion

- Hubble’s constant has a large uncertainty

Limitations of Hubble’s Law

- Large uncertainties in the distances (less in the velocities – why?) of galaxies and stars.

- If the acceleration of the universe is not constant then H0 would not be constant either. E.g. One theory suggests that H0 has decreased over time.

Future Development of the Universe

The universe does not expand at a constant rate as suggested in our earlier estimation of the age of the universe. There are three possibilities...

Closed Universe - average density above a ‘critical’ value therefore gravity causes collapse.

Open Universe- average density below a ‘critical’ value therefore expands at a barely decreasing rate. Flat Universe- average density at critical value therefore stops expanding at time infinity.

Dark Energy and Dark Matter

Text

Subtitle

Text