Filters

Although we might sometimes want to know the total amount of light that a star emits (called the bolometric magnitude), this is very difficult to calculate, partly because of absorption in the Earth's atmosphere, but also because telescopes and detectors are not equally sensitive across all wavelengths - a telescope designed to look at infra-red radiation would be useless for studying X-rays and vice versa!

Any observation that we make therefore only detects a fraction of the total flux. The most common technique at optical wavelengths involves the use of pieces of coloured glass, known as filters, which are designed to isolate light in particular colours. These filters come in two types:

• broad-band filters allow light through of wavelengths which are about 100 nanometres (nm) wide. The commonest system of broad-band filters, devised by Johnson and Morgan, is the system of UBV filters (see Figure 1). Typically, there are 5 filters which cover the whole range of optical light from U (near the boundary between violet and ultraviolet) to I (near the boundary between red and infrared). In this activity, we will only use data taken with B and V filters.
• narrow-band filters have typical wavelength ranges of about 5 nm usually centred around the wavelengths of specific electronic transitions such as hydrogen alpha and hydrogen beta.

A V-band magnitude is then referred to as mV or just V, for an apparent magnitude, and MV for an absolute magnitude. V stands for visual, B for blue and U for ultraviolet. Central  wavelengths are:

• U 360 nm (or 3600 Angstroms)
• B 440 nm
• V 550 nm
• R 700 nm
• I 900 nm

As examples, the bright star Vega (in the constellation of Lyra) is defined as having mB = mV = 0. Our Sun has MB = 5.48 and MV = 4.83. So in fact, our Sun is not a particularly bright star; it's just that it appears very bright to us since it is so near.

The colour of a star can be given a number by taking the ratio of brightnesses at two different wavelengths. Because the magnitude scale is logarithmic this is equivalent to taking the difference of two magnitudes. Astronomers refer to this difference as the colour index defined by, for example,

Colour index, B-V = mB- mV

Note that cooler (and therefore redder) stars emit more light at longer wavelengths and will therefore have larger values of B-V (see Figure 2). From Figure 2, we can see that the B-V colour index is related to the star's temperature as calculated using Wien's Law.