Transcript Introduction to Astrophysics, Lecture 3

Introduction to
Astrophysics
Lecture 3: Light
Properties of light
Light propagates as a wave, and corresponds to oscillations of
electric and magnetic fields in the vacuum. It also carries energy.
Almost all our knowledge of the Universe comes from the
detection of light emitted by distant objects.
Light has a fixed speed, the speed of light c, which acts as a
universal speed limit. Nothing can travel faster than light.
A particular wave will have a distance between crests,
known as the wavelength  of the light.

Our eyes respond to light with wavelengths between about
400 and 700 nanometres, with the short wavelength
appearing violet and the long wavelength red.
One nanometre = 10-9 metres

The frequency f is the number of wave crests passing in
each second, and is measured in Hertz.
f 
c

As light travels out from a source, its intensity falls off as it
spreads out. This is a simple consequence of conservation of
energy, and leads to the famous inverse square law for the
intensity of light.
The apparent brightness of an object depends on how
much light arrives at our eyes, and so depends on both the
absolute brightness of the source and on its distance.
The electromagnetic spectrum
The waves between 400nm and 700nm are only a special set of possible waves. In fact
there are waves of all possible wavelengths, and modern astronomy exploits them all.
Name
Wavelength
Subdivisions
Radio waves
106 nm < 
Microwaves
Infrared
700 nm <  < 106 nm
Submillimetre, far infrared,
near infrared
Visible
400 nm <  < 700 nm
Ultraviolet
10 nm <  < 400 nm
Near ultraviolet, far ultraviolet
X-rays
10-2 nm <  < 10 nm
Soft X-rays, hard X-rays
Gamma rays
 < 10-2 nm
Black-bodies
Different types of object radiate at different wavelengths,
and the main thing which governs how much radiation, and
at what frequency, is the temperature. The hotter an object
is, the more energetic will be the radiation it produces.
A useful concept is that of a black-body, which is defined
as a perfect absorber and emitter of light. As it absorbs
energy it heats up, radiating away energy at the same rate as
it is being absorbed.
The hotter a black-body, the greater the amount of radiation
emitted.
Black-bodies
A black-body radiates some energy at every frequency, but there is a
particular frequency where the emission is at a maximum, and that
frequency determines how we perceive the colour of the emitter.
This graph shows
the emission from
a black-body at
5000K.
Black-bodies
The peak frequency changes
with temperature, moving to
shorter wavelengths as the
temperature increases. The
peak wavelength is given by
Wien’s Law, which states
max
2,900,000 nm K

T
where T is measured in Kelvin.
(Kelvin scale reminder)
The Kelvin temperature scale is the one best suited to physics
and astrophysics. You obtain the Kelvin temperature by adding
273 to the temperature in Celsius (Centigrade).
0K
= Absolute zero
273 K = freezing point of water
300 K = approximate room temperature
3K
= present temperature of the Universe!
Colours and temperatures
We perceive the colours of objects according to their temperature.
For example, the Sun has a surface temperature of 5800 K, giving a
peak wavelength of about 500 nm, more or less in the centre of the
visible band.
[This maximum is actually in the green part of the spectrum; however our eyes
have a more efficient response at longer wavelengths and our eyes perceive the Sun
as yellow.]
Cooler objects radiate more towards the red part of the spectrum, for
example a radiator emits most of its energy in the infrared (e.g. at
350K, Wein’s law gives maximum emission at about 104 nm).
Light as energy
The radiation coming from the Sun means that energy is flowing
away from the Sun. The total energy radiated by a black-body
goes as the fourth power of the temperature, known as the
Stefan—Boltzmann Law
E  constant  T
4
This means an object twice as hot as the Sun, but the same
size, would radiate away its energy 16 times faster.
Light as energy
E  constant  T
4
The energy is also proportional to the surface area of the blackbody. If an object has the same temperature as the Sun but twice
the diameter, it will radiate four times as much energy (as the
surface area is proportional to the diameter squared).
When we look at a distant object, its colour gives us some clues
as to its temperature, and hence other properties. Combined with
the temperature, the luminosity lets us estimate the size.
Using the electromagnetic spectrum
Not all forms of electromagnetic
radiation penetrate to the Earth’s
surface. Many are absorbed in the
atmosphere, which is just as well for
us.
2nd degree sunburn from UV
Only visible light and radio waves
reach
reach the Earth’s surface more or less uninterrupted, while UV,
Xrays, gamma-rays and infrared are strongly absorbed.
Some infrared work can be done in high-altitude observatories, but for
the others the only way to proceed is to get above the atmosphere
using rocket, balloon or satellite technology.
Permanent room change.
All Thursday lectures, including this
week’s, will now take place in
Pevensey 2A12.
[This is the same room as the
Friday workshop sessions.]