Introduction to Astrophysics

1. Introduction to Astrophysics Lecture 3: Light

2. 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.

3.  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

4.  The frequency f is the number of wave crests passing in each second, and is measured in Hertz.

5. 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.

6. 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.

8. 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.

9. This graph shows the emission from a black-body at 5000K. 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.

10. 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 where T is measured in Kelvin.

11. (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). 0 K = Absolute zero 273 K = freezing point of water 300 K = approximate room temperature 3 K = present temperature of the Universe!

12. 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).

13. 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 This means an object twice as hot as the Sun, but the same size, would radiate away its energy 16 times faster.

14. Light as energy The energy is also proportional to the surface area of the black-body. 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.

15. 2nd degree sunburn from UV 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. Only visible light and radio waves reach reach the Earth’s surface more or less uninterrupted, while UV, X-rays, 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.

16. 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.]