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# 3D

## Part 3D: Standard Stars

Once astronomers defined the precise mathematics of the magnitude scale, they needed to develop a procedure that allowed them to take accurate measurements of objects with unknown brightness (brightness is the same as magnitude, just a different unit) no matter how clear or dark the skies are. This can be done by comparing a well-known stable star to the object you are investigating. We know that some stars and most asteroids change brightness over time. Stars that do not change brightness over time are called standard stars.

Let’s hear what Chris has to say about standard stars in this 3:35 video:

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### STANDARD STARS: How do we use them?

1. We can compare other stars or asteroids to standard stars to determine the difference in apparent magnitude (or brightness).

We will use a mathematical ratio. Ratios are great for comparing one thing to another.

In this case, we will use a ratio of the counts collected by a CCD camera for both a standard star and the object we are interested in.

2. For example, start with a single image which contains two stars, Star A and Star B, neither of which changes brightness over time.

Now imagine you have a second image, which also contains both Star A and Star B. The first image was taken on a clear, moonless night and the second image on a night with a quarter moon nearby.

Even though the number of counts you measure for each star will be different in these two images because they were taken on different nights with different conditions, the ratio of the counts for Star A to Star B should remain constant.

In other words, in any image that contains both Star A and Star B, if you divide the counts from Star A by the counts from Star B, you will always have the same result.

This is why we call them Standard Stars.

#### JOURNAL QUESTIONS

1. Imagine two objects that are close together. One object is a standard star.

• What would we need to do if we want to determine if the second, unknown object, varies in brightness?

2. Why do we need a standard star in the image when we are creating a light curve for an asteroid?

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Recall that the light curve of an asteroid is a plot of the magnitude of the asteroid versus the time of that observation.

We know the asteroid’s apparent magnitude will change with time because it is rotating.

Its magnitude in the image is unknown. We must calculate that magnitude using what we know and what we can measure.

Here is a list:

• 1) We know a standard star’s apparent magnitude does not change – it is stable.
• 2) We can measure the counts of the standard star in an image using an image processing program (in our case, Afterglow Access).
• 3) We can measure the counts of the asteroid in the same image.
• 4) We can calculate a ratio of counts for the standard star to the counts for the asteroid
• 5) We can relate this ratio to the difference in magnitude between the standard star and asteroid.

Let’s look a little closer at the relationship between the ratio of counts and the difference in magnitude:

Recall: in Part 3C you did a Quorum exercise about the multiplicative scale of the magnitude system.

Let’s relate that Quorum exercise to what we are talking about here: the difference in magnitudes and the counts ratio:

• The step height NUMBER represents the magnitude difference.
• The HEIGHT calculated represents the counts ratio.

For example, if the step height is two, that means the objects differ by 2 magnitudes and will have a count ratio of about 6.3 (found by taking 2.512, our multiplicative factor, and raising it to the magnitude difference, which was 2 in this case).

That ratio, 6.3, was the calculated step height for 2. If the step height is 3, that means the objects differ by 3 magnitudes and will have a count ratio of about 16 (2.512^3), which was the calculated step height for 3.

#### Try the following examples. Record your answers in your JOURNAL.

3. If Star A and Star B have a magnitude difference of 7, what is the count or brightness ratio? What does this mean about Star B if we know Star A is brighter?

4. What is the magnitude difference between two objects if the intensity (count) ratio is about 40? Refer back to the scale you made using Quorum in Part C.

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Magnitude differences are not always a whole number. A more precise method would be to use an equation.

If you would like to learn how to use Quorum to solve these equations, you may do the next part which contains two optional exercises. These will take you through two equations for calculating the apparent magnitude. It is a glimpse into what is happening behind the scenes when you use the photometry tools in Afterglow Access.