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 lightcurve 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 Telescope
Sited on the Island of La Palma
Variable Stars
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.
Open the LTImage software
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.
Loading in an Image
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.
Scaling the 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.
Use the Finding Chart
The next step is to use this
slide to identify your target
variable star and two
comparison stars.
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).
.
Recording your Measurements
When you write down your results, try to record them on a spreadsheet in a
similar format to the following:
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
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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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.
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
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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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:
Graph of TS/CS1 vs Time
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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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