Photometry


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PHOTOMETRY TECHNIQUES

When you observe stars with your eyes, or with a telescope, you are receiving starlight that has traveled vast distances. Amazingly, the light remains virtually unaffected by the first 99.999999999999% or so of its journey. However, in the trip through the Earth’s atmosphere, and even through the optics of the telescope, the light may finally be affected causing the brightness of the star to differ from one observation to the next.

Photometry is the process of measuring the amount of light received from an object. When you display an image using HOU, you can use the cursor to see the amount of light registered by each pixel in the image. This value is given in Counts. The Auto Aperture and Aperture, routines add up all the Counts within a specific range of pixels to give the total Counts for a star. These routines are designed to subtract background light caused by other objects and give only the Counts created by the star itself. The brightness of the stars in an image also depends on the exposure time for the observation. If the telescope observes the star for a longer period of time, it will gather more light so the star will appear brighter. In most cases, if the exposure time is doubled the amount of light the telescope receives is doubled.

One way astronomers use photometry is to measure the brightness variation of an object such as a variable star or a supernova. To measure variation, images are taken on several successive nights of the same star and its Counts are compared with those of a steady star in the image. Another reason for using photometry is to measure the apparent brightness of a star in order to calculate its distance. This method involves calibration using a standard star. The Photometry Techniques Unit explains each of these processes. Photometry words used in the unit are defined as follows:

Counts - The measure of light that each pixel of the CCD receives from the star. This measurement is particular to the equipment used and to the atmospheric conditions during the observation. When we display an image, the grayness or color at each pixel is based on the Counts for that pixel.

Apparent Brightness - The amount of light reaching Earth per second from a star under ideal conditions (as if there were no atmosphere). This is a standard value that anyone could obtain from their measurements after correcting for observing conditions. The units for apparent brightness are Watts/meter2.

Luminosity - The amount of light emitted per second by a star. It is an inherent property of the star, unlike Apparent Brightness, and is independent of where the observations were made or what telescope is used. Generally the luminosity of a star cannot be measured directly but must be inferred from other characteristics of the star. The units for luminosity are Watts.

Reference Star - A star whose apparent brightness and luminosity does not change from one night to the next. The apparent brightness value of the star, however, is typically not known.

Standard Star - A steady star is like a reference star but with a known, agreed upon value of apparent brightness.

Apparent Magnitude - A measure of apparent brightness commonly used by astronomers. The magnitude scale is inverse, meaning brighter stars have lower magnitudes.

Absolute Magnitude - This quantity is analogous to the luminosity but is expressed on the magnitude scale.


Measuring Brightness Variations

Suppose you have images of the same region of the sky taken on two different nights. The region contains two stars. One is your target star, the star you have chosen to study. It may be a Cepheid variable star or a star that has just gone supernova or any other star for which you wish to measure brightness variation. The other star is known to have constant luminosity, meaning the brightness of the star itself does not change from one night to the next. This star is called the reference star. You do not need to know the exact brightness of the reference star, just that it remains constant. For images of objects beyond our own galaxy, foreground stars are typically chosen. These are stars within our galaxy that are in the same line of sight to the further away object. If the observing conditions did not change from one night to the next, the reference star would have the same brightness in both images. If the second night was clearer than the first, the reference star will be brighter in the second image than in the first. The target star may appear brighter or dimmer in either image, but until changing observing conditions are accounted for, it can be unclear whether the change in brightness in the target star is caused by changing observing conditions or by changes in the star itself.

One way to find the brightness variation of the target star over time is to use the ratio of the Counts measured for the target star to the Counts measured for the reference star in each image. Variations in this ratio are comparable to variations in brightness of the target star.

Counts ratio = Ct /Cr

where Ct = Counts measured for the target star

Cr = Counts measured for the reference star

Calibration To Find Apparent Brightness

The Counts ratio gives a way of finding variation in brightness of a star but not the Apparent Brightness value itself. You need a further procedure for finding the brightness of a star that is independent of observing conditions so that anyone, anywhere on Earth, under any observing conditions, will get the same brightness. In addition, each CCD reacts differently to light and yields a different number of Counts for a given brightness. In order to use your data in the context of other observations and reference tables, you need to get the brightness of the star in units that are independent of a particular CCD.

Calibration allows you to deal with both changing observing conditions and different CCDs simultaneously. The process of calibration involves an image of a star whose brightness you want to measure (the target star) and another image of a standard star. The standard star should be in the same region of the sky as the target star so it will experience the same observing conditions as the target star at any given time. It also helps to have a star within the optimal brightness range for the telescope (not too bright and not too dim) to assure a good image. Most importantly, the standard star is a star with known apparent brightness an agreed upon standard value.

With identical observing conditions for the target and standard stars, the ratio of their Counts is equal to the ratio of their apparent brightness. This means that on the basis of one pair of images, not the series of images over time necessary for measuring variation, the value for the target star's apparent brightness can be calculated.

Let Ct = Counts measured for the target star

Cs = Counts measured for the standard star

Bt = apparent brightness of target star

Bs = apparent brightness of standard star

Then Ct /Cs = Bt /Bs or equivalently Ct /Bt = Cs /Bs

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