# A Guide to Photometry

### Photometry

When you look up at the night sky on a clear night, each star looks like a distinct point of light. Using a telescope shows us that the Earth’s atmosphere smears this point into a disc and that the worse the atmospheric conditions are, the bigger this disc becomes. This can be seen in the images in Figure 1, which are of the same star field using the same telescope and exposure time. It is possible, even by eye, to see that the image on the right features stars that cover more pixels and are less 'point-source-like'. We can actually quantify this as a value known as seeing. If we want to measure the total amount of light coming from the star, we will need to account for this to ensure that we add up all of the light.

The most basic information that we can derive from point sources such as stars is their flux – that is, the amount of light (or electromagnetic radiation) that we receive from them. The science of measuring this flux is known as photometry, and this can be used to calculate the distance to an object. The word comes from the Greek 'photo' meaning light and 'metron' to measure and so is the science (or perhaps the art!) of measuring this incoming light.

Measuring the amount of light an object emits at various wavelengths can also help in us understanding other parameters such as its temperature, size, mass, luminosity (the amount of light a particular object is emitting), chemical composition and an understanding of the physical processes at work where the light is being emitted.

Other techniques used in astronomy include spectroscopy, astrometry and polarimetry.

Photometry is often used in conjunction with spectroscopy, which concerns us more with the spectrum of light that an object emits and can be considered as a graphical representation of an object’s brightness against photon energy (usually represented as wavelength or frequency).

### So what can we use photometry for?

We can observe variable stars such as Cepheid variables (see Figure 2) or eclipsing binaries. From this, we can produce a lightcurve which is a plot of an object’s brightness against time. Some types of objects, such as binaries will demonstrate a repeat pattern in these measurements indicative of two objects orbiting a common centre of mass. Lightcurves can also allow us to examine the behaviour of supernovae (Figure 3) and asteroids (Figure 4).

Figure 2 shows a lightcurve for a Cepheid variable star, which brightens and fades regularly (by around 1 magnitude) over a period of around 6 days. This type of star behaves in a regular and predictable way, allowing us to make measurements based on this period to determine its luminosity and hence its distance.

Figure 3 shows a plot of the rapid rise and slow fade (known as the decay) of the supernova, SN1987a. This object increases by around 2 magnitudes over a few weeks, before fading by around 10 magnitudes over the following months. This corresponds to a decrease in brightness of a factor of 10,000. SN1987a was associated with the death of a 12th magnitude blue supergiant star known as Sanduleak -69 202a.

Another example of the use of photometry is given in Figure 4. By plotting the lightcurve for an asteroid, it is sometimes possible to determine the rate at which they are spinning. This is achieved by looking at the repeated variability in their intensity as they tumble around their orbits. Repeated patterns such as these usually denote objects that are rotating. We see a pattern in the light curve which relates to the changing brightness in the surface of the object as sunlight reflects off different materials on the surface, as well as the change-sectional areas as viewed from Earth (since very few asteroids are spherical).

Photometry also allows us to discover or confirm the existence of extrasolar planets (or exoplanets), planets around other stars.

### Counting Photons

If we look at an image of a star cluster, we see several dots or small circles representing the individual stars in the cluster. The circle's size is partly determined by the brightness of that particular star (other factors are due to the atmosphere and the optics of the telescope used). The areas of bright starlight on the dark background (astronomers often invert the image as 'black' stars on a light background are easier to look at) are determined by the number of photons which hit the camera's detector during the exposure (along with the efficiency of the detecting system itself). We are able to use a photometry package to 'count' these photons to give us information about the brightness of the objects in the image e.g. twice as many photons from star A as opposed to star B suggest that star A might be twice as bright as star B (but see the 'Measuring Magnitudes' section).

If we were interested in how the brightness of one particular object changes with time, we might compare how the number of photons received from it in a given time period changes over a set of images. We could then plot this difference against time to produce a lightcurve as in Figures 2, 3 and 4.

### Performing Photometry

Since the effects of the atmosphere and the size of our telescope determine the size that each star appears on our image, we need to take account of this before we can measure the stars properly. We place a circle (or aperture) over the star in question and measure its intensity. We can consider this to be the number of photons collected by the telescope during the exposure, although more accurately, it represents the number of electrons dislodged by the incoming photons as measured by the CCD itself. The value we measure is known as the 'counts'.

To do this, we must calculate a value for the radius (in pixels) over which we wish to measure our circular star. There is a guide as to how best to do this, however experience suggests that values between 8 and 12 are usually okay. Once a radius value is chosen, it is important to stick to the same radius for all images for a particular dataset. For example, if you are performing photometry on the same star cluster in two different filters (e.g. B and V), then you should use the same radius for both images to ensure that you are comparing 'like with like'. Equally, this should be the case if you intend performing photometry of a single object to create a lightcurve over time.

### So what do I need?

There are several software packages that are useful for photometry, however we need to find a reliable package that produces meaningful results, while being Windows friendly, easy to install and free-of charge. One such package is Makali'i (the word is Hawaiian for the Pleiades). You may also want to use a spreadsheet package to create a graph of your results.

Once you have downloaded Makali'i, the next step is to find some data to analyse.

Find out more about the associated techniques of spectroscopy, astrometry and polarimetry.