Variable Stars

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Introduction

A star is classified as variable if its apparent brightness (i.e. that seen from Earth) changes over time.

The variation in brightness can result from:

(i) internal changes to the amount of energy being emitted by the star, or

(ii) an external process, such as, some of the light from the star being blocked by an orbiting companion star or planet.

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Brief History

Although ancient civilisations had recorded the appearance of new stars (or nova), it was not until 17th century that variable stars were discovered.

In 1638, Johannes Holwarda noticed that the bright star Mira pulsated in a cycle that took around 11 months;

By 1786, astronomers knew of 10 variable stars, and were just beginning to understand some of the processes involved.

Today we know of more than 65,000 variable stars.

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Types of Variable Stars

There are many different kinds of variable stars, however, due to time constraints we will only discuss four of the most common. Namely:

Cepheid Variables

RR Lyrae Variables

Mira Variables

Eclipsing Binary Stars

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Cepheid Variables

Cepheid variables are yellow giant stars that pulsate on a very regular basis.

They have relatively short periods, lasting from days to weeks.

The period of the pulsation is directly related to their “intrinsic” brightness.

This allows astronomers to calculate their distance.

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When you plot a graph of the brightness of a star against time, it is known as a light-curve.

Cepheid Variable Mechanism

Variations caused by variable opacity layer of helium. In other words, one that becomes more and less “see-through”.

In non-ionised state, internal energy can escape and star contracts.

However, the in-falling outer layers heat up helium layer. Helium becomes ionised and the opacity of the layer increases.

Internal temperature and pressure now increases and the star starts to expand.

Cycle repeats.

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RR Lyrae Variables

They are similar to cepheid variables, but are intrinsically dimmer.

Brightness varies from as little as 20% for some stars, up to 500% for others.

Again, their periods are directly related to their “actual” brightness.

Rate of brightness increase is much sharper than for cepheids.

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Mira Variables

Very cool supergiant stars undergoing extremely large pulsations.

They can vary anything between 5 and 30,000 times their minimum brightness over the period of many months.

Variations are more symmetrical than previous cases - almost sinusoidal.

Caused by a variable opacity layer of molecular hydrogen acting like a release valve mechanism.

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Eclipsing Binary Stars

The most common form of variation caused by an external mechanism.

Occurs when the orbital plane of a binary star system lies in our line of sight.

We see periodic “dimmings” in the light-curve due to two eclipses during the orbit.

Eclipsing binary stars allow (with spectroscopy) astronomers to calculate the size, mass and density of both components in the system.

EBs are the key to all modern understanding of the structure of different star types.

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Observing Variable Stars

In this workshop, we will be creating a light-curve for a variable star, using data from the robotic Liverpool telescope.

The data was secured during July 2010

The star is a known variable, of a type described in the previous slides.

Your task is to try and identify what type of variable star we have observed.

Before we create the light-curve, we need to learn how to measure the brightness of a star.

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The Liverpool TelescopeSited on the Island of La

Palma

To begin with, you need to ensure that you have installed the NSO’s image processing software on your system. LTImage is freely available on the NSO website at the following link:

http://www.schoolsobservatory.org.uk/astro/tels/ltimage

Once you have installed LTImage on your system, start it up and a window similar to the background of this slide should

appear on your computer screen.

You also need to have access to the Liverpool telescope images that are included with this workshop.

Variable Stars

When you first open LTimage the viewing area (where this text is) appears blank. This just mean there is no data

loaded into the buffers.

The lower right portion of the LTImage window confirms that all four image stores are empty since no preview images are shown in the small boxes above the numbered image stores.

Check that the first image store is selected, such that a dot appears in the little circle next to the number 1, as below.

Open the LTImage software

It’s now time to load in some data. Select the File menu and then the Open Data Image option. Navigate to the unzipped

directory containing the Liverpool telescope images, and select the first data file. Click on the Open button.

Loading in an Image

Don't worry about the darkness of the image, this is quite normal. The telescope detector was designed to count the

number of photons (packets of light) it receives, rather than to take pretty pictures. When an image appears dark, it just means that we didn’t get many photons from objects in the image. To reveal more detail from dimmer objects in

the frame, we need to adjust the scaling.

To scale the image, select the Display menu and then the Scaling option. Now use the mouse to click, hold and drag the right-hand slider bar down until more detail is reveled.

When you are happy with what appears in the preview window above the sliders, release the mouse button.

Finally, click on the Use new Values button and the image will be scaled accordingly.

Scaling the Image

The next step is to use this slide to identify your target

variable star and two comparison stars.

Use the Finding Chart

Relative Brightness Analysis

We need two comparison stars because we will be using the Relative Brightness method of analysis.

Rather than record a brightness that is related to the number of photons received (referred to as counts), we give the brightness of the target star (TS) relative to a nearby comparison star (CS1).

This means that our analysis is not affected by variable observing conditions, such as thin cloud passing in front of the target star and thereby reducing the number of photons that arrive.

The relative brightness method involves dividing the number of counts for the target star (TS) by the number of counts for the first comparison star (CS1). i.e. TS/CS1.

We use a second comparison star (CS2) to ensure that the first comparison star (CS1) is not itself a variable star, thereby rendering our results useless. This is achieved by making sure that CS1/CS2 remains steady throughout the observations.

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Finding Chart

We can now measure the brightness.

To do this, select the Brightness Measurement option from the Astro menu. Now move the mouse to the centre of the star to be measured. Click and hold the left mouse button

and slowly drag the mouse outwards to reveal a circle.

When the circle fully contains the star, release the mouse button and a set of rings will appear around it. The region between the outer green circles is used to calculate the

average brightness of the night sky.

This value is subtracted from the number of counts (or photons) within the central circle to give a result for the

amount of light coming from the target alone.

Now click Calculate button to the right.

The computer will work out how many counts (or photons) can be attributed to the stars being measured.

Record that value on a spreadsheet.

Now do the same for the two comparison stars. Ensure that the central circle is about the same radius i.e. ~25 pixels. Also, make sure you use this size with the other images.

The final thing you need to record for each image is the time of the observation. This will allow us to create a plot of

relative brightness against time.

You can find the time of observation by selecting the Image Properties option in the main Astro menu.

Then select The Observation option on the right.

The time is shown above right. Record this on your spreadsheet, alongside your brightness measurements for the target star (TS) and two comparison stars (CS1,CS2).

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Recording your Measurements

When you write down your results, try to record them on a spreadsheet in a similar format to the following:

Because we are using the relative brightness method, remember to include two columns for TS ÷ CS1 and CS1 ÷ CS2, and check that the calculation is being done correctly by the spreadsheet.

Now go through all the observations that were provided and record the same information. This task can be split up between individual students, with the results being recorded on a central spreadsheet.

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Observation Time TS(Counts)

CS1(Counts)

Cs2(Counts)

TS/CS1 CS1/CS2

c_e_20100726_34_1_1_1

22:33:51

393510 328109 292341 1.20 1.11

Plotting your Measurements

Once you have all your measurements recorded, use it to plot two graphs; one of column TS/CS1 against the time column, and one of CS1/CS2 against time.

This brief example shows what you might expect, although there will be many more columns for your analysis. By the way, the above are not genuine results.

Note that the value for TS/CS1 should change, as we might expect from a variable star, however the value of CS1/CS2 remains steady. This confirms that CS1 is not a variable star and thus our results for TS/CS1 are valid.

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Observation Time TS(Counts)

CS1(Counts)

Cs2(Counts)

TS/CS1 CS1/CS2

c_e_20100726_34_1_1_1

22:33:51

393510 328109 292341 1.20 1.11

c_e_20100726_36_1_1_1

23:29:05

420606 311560 280684 1.35 1.11

c_e_20100726_51_1_1_1

00:45:38

473116 315411 284154 1.50 1.11

Creating the Light-Curve

The best type of light-curve to create is a scatter graph of your points. If you are not sure how to create these using a spreadsheet, such as Microsoft Excel, then please ask your teacher or an IT advisor to show you how.

You should be able to reproduce something similar to the following:

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Graph of TS/CS1 vs Time Graph of CS1/CS2 vs Time

Final Result

Your light-curves will, of course, differ to those shown on the previous slide. For one, you will have more points; plus there should be an obvious and identifiable shape to the light-curve.

All being well, there will be variation in TS/CS1, but not in CS1/CS2. If the latter did vary, then you would need to choose different comparison stars.

Compare your light-curve of TS/CS1 to the variable star light-curves shown earlier in this presentation. In particular, look at the shape of the light-curve, the time-frame involved and the amount of change that is occurring.

• Which type of variable star do you think we were observing?

• Why do you think that?

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So, what’s the Answer

Hopefully, you will have come to the conclusion that the target we are looking at, namely a star called 2MASSJ18515077+2422352, is an:

Eclipsing Variable Star

for the following reasons:

(1)The shape suggests it could be an eclipsing binary or Mira variable.(2)However, we do not see a 5-fold or more variation in the brightness, which leads us to think that it may be an eclipsing binary star.(3)Also, this takes less than a day, not the months required for Mira variables.

Anyway, that is the end of the workshop. Well done on getting this far

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