Download II Light

II
Light
http://sgoodwin.staff.shef.ac.uk/phy111.html
0. Light
Light is the main tool we have in astronomy.
We detect light from distant objects and can determine the
temperature, density, composition, kinematics etc. of the
body that emitted that light.
If the light passes through any intervening material (e.g.
gas and dust) it can tell us about the properties of that
material as well.
0. Light
‘Light’ is shorthand for electromagnetic radiation and it is
both a wave and a particle.
Light can be thought of as a wave with a particular
frequency or wavelength.
Light can be thought of as a particle – a photon – with a
particular energy that corresponds to a particular
frequency/wavelength.
0. Light
Light can be described by its wavelength (λ) or frequency
(f), and speed (c=3x108 m s-1)
λf = c
And the energy of a photon is
E = hf = hc/λ
(where h is Planck’s constant = 6.6x10-34 J s-1).
1. Blackbodies
Temperature is a measure of the thermal energy (random
kinetic energy) of a system.
Hot bodies contain more thermal energy so compared to a
cold body we would expect them to
a)  Give-out more energy (higher luminosity)
b)  Give-out higher-energy light (shorter wavelengths)
And this is what they do – emitting as a ‘blackbody’.
1. Blackbodies
These are the blackbody curves of objects at T=3500K to
5500K (y-axis is energy per unit wavelength)
1. Blackbodies
The luminosity (L – energy emitted per unit time) depends
on the temperature (T) and the surface area (for a sphere
4πr2):
L = 4πr2 σSB T4
Where σSB is the Steffan-Boltzmann constant=5.67x10-8 W
m-2 K-4.
Hotter objects give out more energy, and larger objects give
out more energy. So a small, hot star can be as luminous
as a large, cool star.
1. Blackbodies
The peak wavelength of the light emitted by a blackbody is
given by Wein’s Law:
λmax = 0.29 cm / T
Where T is in K.
So hotter bodies have peaks at shorter wavelengths.
1. Blackbodies
The Sun has T=5800K, so λmax~500nm – the middle of the
visible (and why it is the visible to our eyes).
The Earth has T~300K, so λmax~10µm – everything in this
room is emitting radiation at about 10µm.
The coldest gas in the Universe is at about 10K, so
λmax~100µm.
Note: you might see wavelengths given in Ångströms (units
of 10-10m), so 1nm=10Å.
2. Atoms and lines
An atom has a nucleus of protons and neutrons with
electrons ‘orbiting’ the nucleus (the Bohr model).
The electrons have specific energy levels they can inhabit,
and they cannot have energies in-between.
If an atom absorbs a photon of exactly the right energy it
can cause an electron to ‘jump’ to a higher energy level.
Electrons in higher levels can ‘fall’ to a lower level emitting
a photon with the energy difference.
2. Atoms and lines
The energy differences between levels change from
element to element (or molecule).
So particular energy differences are a ‘finger print’ of the
particular atom that caused them.
Atoms can gain energy by
a)  Absorbing a photon of exactly the right energy.
b)  Being hit by another atom and extracting energy from
the impact.
Once the electron is ‘excited’ it will want to ‘de-excite’ by
emitting a photon in a random direction.
2. Atoms and lines
The most common element is hydrogen. Energy levels are
always numbered from n=1 (ground state) to n=2,3…
Transitions to-and-from
n=1 have high energy (UV)
and are Lyman series lines.
Tranisitions to-and-from
n=2 are Balmer series lines
in the visible.
And for n=3 they are the
Paschen series in the IR.
2. Ionisation
If you give an electron enough energy you can unbind it
from its atom – ionisation.
The bigger the atom, generally the easier this is to do. So
as temperature increases first metals like iron become
more-and-more ionised, then atoms like carbon and
oxygen, then hydrogen, and finally helium.
Astronomers tend to use roman numerals to denote
ionisation levels: so FeVI is 5x ionised Fe. HI is neutral
hydrogen, HII is singly (the most it can be) ionised H.
2. Atoms and lines
Electrons do not have to de-excite to the ground state at
once.
An electron could be excited from n=1 to n=4 by a collision,
and then dexcite from n=4 to n=2 (emitting a Balmer series
photon), and then from n=2 to n=1 (Lyman series).
3. `Types’ of light
Solid bodies tend to emit as blackbodies giving out all
wavelengths of light according to their BB curve.
But if that light passes through gas, atoms and molecules in
the gas can absorb or emit various ‘lines.’
Almost all of our understanding of astronomy comes from
analysing the light we see, looking at BB curves and lines.
3. Blackbodies
If a body is at high density light will scatter internally and
become ‘thermalised’ and we will see a continuum (light of
all wavelengths/energies).
The distribution of energies will be a blackbody spectrum
that depends on the temperature (to the power 4) of the
object.
[Technically this is cavity emission, but this explanation will
do for now.]
3. Emission lines
A low-density gas will excite atoms inside it by collisions.
The atoms will then emit light at particular wavelengths so
we see a few bright emission lines.
Which lines depend on the temperature and composition of
the gas.
3. Absorption lines
A low-density gas with a background source will absorb
light of particular energies and then re-emit it randomly. So
we see less light at particular wavelengths – absorption
lines.
Which lines depend on the temperature and composition of
the gas.
4. Light from the Sun
Light from the Sun as seen from the Earth is roughly a
blackbody with T~5800K, but with absorption lines due to
(a) the Sun’s atmosphere, and (b) the Earth’s atmosphere.
Summary
Dense bodies will emit blackbody radiation. The total
luminosity depends on r2 and T4. The peak wavelength
depends on T.
Atoms have ‘quantised’ electron energy levels. Lowdensity gas can absorb lines of background light, or emit
lines from themselves. The energy of those lines tells us
the atoms that are present (as well as their temperature
and density).
So the light we see can be a mixture of any or all of three
sources: blackbody (continuum), emission lines, absorption
lines.
Key points
Know that f, λ, and E for light are equivalent.
Know the relationships between L, r, T and λmax for a
blackbody (the Steffan-Boltzmann law, and Wein’s law).
Be able to describe if and why something will show a
blackbody continuum, emission line, or absorption line
spectrum.
Quickies
The luminosity of the Sun is 7.0x1026 W, and its surface temperature is 5800K.
What is the radius of the Sun?
What type of spectrum would the following sources show:
a)  Sodium street light?
b)  Tungsten filament lightbulb?
c)  A star?
d)  A neon sign?
e)  An energy-saving lightbulb? (Not obvious.)
What would the luminosity of a 10000km diameter ‘star’ of temperature 105K
be? What strikes you as odd about this? (We’ll see what it is later.)
Star A and Star B have the same temperature, but star B is 25 times more
luminous. How much bigger is star B than star A?
A cold molecular cloud is observed. What type of spectrum will it show and
why?
Notes
The reason for most of the behavior of light and atoms is ‘quantum’. The
quantum world is very strange, but at very small scales things like electrons
and photons show both wave- and particle-like behavior. Experiments show
they act like this and quantum mechanics seems to be an extremely good
description of the microscopic world.
Electrons don’t really ‘orbit’ the nucelus, rather there is a messy and undefined
‘electron cloud’, but this orbital picture is OK for understanding the energy
levels. Understanding blackbodies was impossible before quantum mechanics
(and it was a problem wrestled-with by many scientists).
Physicists and chemists will get to do quantum mechanics in great detail from
second year, but there is a fairly serious level of maths needed to solve the
equations.
Notes
Rather annoyingly H2 (molecular hydrogen) and HII (ionised hydrogen) and
both said out-loud the same way ‘aitch-two’.
This can get confusing in molecular cloud which have a massive star because
they contain both types of ‘aitch-two’.
Depending on the part of the electromagnetic spectrum being observed
astronomers work in frequency, wavelength or energy. In the X- and γ-ray
energy is used (keV or MeV usually where ‘eV’ is an electronvolt – a useful
measure of energy in particle physics). In the visible and IR people tend to
work in wavelength (nm, micron or sub-mm for example). In the radio people
tend to talk about frequency (MHz of GHz for example).