Introduction to Astrophysics

Lecture 4: Light as particles

Emission and absorption lines

A black-body is a continuous spectrum with light at all wavelengths. However a real spectrum (meaning the intensity of light plotted against wavelength) may show either bright or dark lines, or maybe even both.

These are known as emission and absorption because of the quantum nature of atoms.

lines, and they arise

Atoms

Atoms consist of a nucleus, made from protons and neutrons, plus a set of electrons in orbit around them. Because of electromagnetic attraction, the locations of electrons correspond to different energy levels.

Electron Niels Bohr showed that interactions between atoms and radiation can be explained if electrons can only occupy certain energy levels.

Energy levels Nucleus

Atoms

An electron can only change energy level by either absorbing or emitting energy. This energy is in the form of a discrete package called a photon . According to quantum theory, at a microscopic level light is made up of these photons, with its wavelike nature apparent only when vast numbers of photons are present.

Whether it is more convenient to describe light as a wave or a particle depends on circumstances.

Atoms

The energy of a photon is related to its frequency by

E



hf

where

h

is Planck’s constant,

h

= 6.63 x 10 -34 J s .

If an electron drops to a lower energy level, it emits a photon with frequency given by this relation. Alternatively, a photon with the correct frequency can be absorbed, raising the electron to a higher level. Such processes favour the emission or absorption of light at particular frequencies.

Atoms

Each type of atom has a characteristic set of energy levels. That means these atoms can absorb or emit photons only at a characteristic set of energies, corresponding to the transitions between those levels.

For example, the energy pattern of hydrogen is completely different from oxygen.

Study of these energies is known as spectroscopy . It is an invaluable astronomical tool as it can tell us about the types of atoms present in distant objects. Each type of atom has a distinct fingerprint.

Absorption lines

Absorption lines arise when the material we are interested in lies between a source of continuum radiation and ourselves.

Source Dust cloud A classic example is the Sun, where radiation originating deep within the Sun is absorbed by material in the surface regions.

Note re-emission is in random directions and so doesn’t “fill in” absorption lines.

Emission lines

Emission lines arise when it is possible to see the photons emitted when the electrons fall to lower energy levels within atoms.

In the case of hydrogen, there are accurate formulae giving the wavelengths at which radiation is emitted or absorbed, for example the Balmer lines arise in transitions to or from the second energy level and are at wavelengths 1   1 91 .

18 nm 1 2 2  1

n

2

n

 2 For example,

n

= 3 gives  = 656 nm, in the red part of the visible spectrum, while higher values of

n

give shorter wavelength light.

Emission lines

Rydberg devised a more general version of this formula, written

1

 

R R

  

1

m

2 

1

n

2 

1 .

097



10

7   

n



metres

 1

m R

is the Rydberg constant, and different values of the integer

m

correspond to different series of atomic lines of hydrogen (Lyman, Balmer, Paschen etc).

Ionization

Extremely high energy radiation can do more than just raise electrons to higher energy levels – it can knock electrons completely out of atoms in a process known as ionization . You may have encountered this as the photoelectric effect.

Atoms with many electrons can be in different ionization states, depending how many electrons have been lost. It becomes progressively harder to remove electrons as the excess positive charge will attract them back more strongly.

Ionization changes the energy levels of the remaining electrons, and so different ionization states have their own unique spectral fingerprints.

Detecting photons

For most forms of astronomy, the idea that light comes in individual photons is not very relevant as so many photons are present that the behaviour is like a wave.

The exception is the very high energies of X-ray and gamma-ray astronomy; an X-ray telescope might spend a day collecting only a few thousand photons to build up an image.

X-ray image of young stars taken by the XMM-Newton satellite

Doppler shifts

Another piece of evidence that light can carry to us is the motion of the source. With sound we are familiar with the idea that something coming towards us, e.g. a fire engine, has the pitch of its siren raised as the waves are crowded up.

Light also experiences the same phenomenon; if an object moves towards us the crests of the light waves are crowded together and the light is shifted to the blue end of the spectrum. If the object is moving away, we talk about a

redshift

.

Doppler shifts

The shift in wavelength is related to the velocity of the object being studied, and can often be measured accurately from the well-defined spectral lines. The shift in wavelength is related to the velocity by 

observed



lab

 

lab



v c

where  lab is the wavelength measured in the laboratory, and the speed of light (equation valid only for

v

≪

c

).

c

is

Doppler shifts

If an object has a well-defined shift of spectral lines (for instance this is commonly seen in distant galaxies), then the velocity

v

measured is the component along the line-of-sight. Doppler shifts tell us nothing about the velocity at right angles to our view.

Actual velocity Us Line-of sight velocity Moving object

Doppler shifts

If instead we see an object which has lots of motion (eg turbulent motion of hot gas), then light coming from different parts of the gas will have different amounts of redshifting and blueshifting.

Instead of shifting the line in one particular direction, the net effect can be to smear out the line, known as Doppler line broadening . This can sometimes be used to measure quantities such as the temperature of particular elements.