Errors in Quadrature

In the CMD activity, values are calculated for B and V magnitudes, along with their associated uncertainties. It is then possible to calculate a B-V value which represents the star's colour and use this on the x-axis of the CMD.

While the B-V value itself is a simple subtraction, its associated uncertainty is not quite so straightforward and is calculated in the following way, known as quadrature.

Uncertainty in B-V = square root ((uncertainty in B)2 + (uncertainty in V)2)

In other words, we square both uncertainties, add them and take the square root of this value. For example:

Uncertainty in B = 0.03, uncertainty in V = 0.01

Uncertainty in B-V = square root (0.032 + 0.012) = 0.032

So the final uncertainty is greater than either individual uncertainty but not as large as if we simply added them together. In this example, the uncertainty in the B value accounts for the majority of the final value and is said to be the dominant error.

Note: calculating uncertainties based on magnitudes (which are logarithmic) should actually be done in a more complicated way than shown above; for the purposes of this activity, however, the method shown above will give a value that is very similar to the more thorough treatment that we should apply.

Read about uncertainties.