1. Alexander Millington, 1300 9253 – Keele University
4-26-2016
Individual Report – Classifying
RR Lyrae Variable Stars using
WASP-South 85mm data.

2. Alexander Millington
Page | 1
Abstract
The SuperWASP-South telescope is one of two telescopes used in the wide angle search for
planets (WASP) project. One telescope, SuperWASP-North, is located on the island of La Palma and
the other, used in this study, is on the site of the south African astronomical observatory (SAAO)
(Pollacco, 2006). I aim to classify a set of stars using data provided by the SuperWASP-South
telescope. My objectives are to determine a pulsation frequency for each star and then from this be
able to create a phased light curves. From these I will be able to determine with certainty what
classifications to give each star. Initially, I took the raw data from the SuperWASP-South telescope
and cleaned it. Next by using the program Period04, I identified the pulsation frequencies of the four
stars. Once these were established I could move onto creating the phased light curves for each star
which would in turn, along with the data, help me to come to a sure conclusion on what
classification I could give to each star. Finally, after managing to successfully classify the stars, I
wanted to determine what percentage of flux was contributed by a target stars’ neighbour. The
values of these percentages directly correlate with the quality of the results.
Table 1 - Calculated periods[days] and amplitudes[mag] for the four stars studied.
The period of 0.62434 days in Table 1 of star VSX091251 corresponds to a sub-harmonic
frequency. Out of the four stars studied, I identified three (013997, 017283 and 026353) as being of
the RRab subtype of the RR Lyrae stars and one (091251) as being a rotating ellipsoidal variable (ELL)
star. I decided these classifications for the stars by taking each phased light curve generated and
their amplitudes and periods and comparing them to the typical criterion for the classifications. I
found that for the stars VSX:013997, 017283, 026353 and 091251; 40%, 23%, 19.1% and 9.1% of the
flux was contributed by a neighbouring celestial body to the data of each star respectively. The
calculated period of star VSX013997 agrees with the GCVS1
to 2 decimal places. For stars VSX:017283
and 026353 the study agrees with the GCVS to 4 decimal places. Both VSX013997 and VSX017283
are classified as RRab’s in the GCVS. This agrees with the analysis performed here but for star
1
General catalogue of variable stars.

3. Alexander Millington
Page | 2
VSX026353, the classification is simply RR in the GCVS; whereas I have classified it as RRab. Finally,
for star VSX091251 I could not find another source which defined its classification for this star.
Introduction
The term ‘RR Lyrae’ refers to the name given to a particular variable2
star which was
discovered by Wilhelmina Fleming on July 13, 1899 (Templeton, 2010). The star can be found in the
Lyra constellation, roughly 860 light-years away. The name given to the star refers to the
constellation in which it lied and the ‘RR’ to the order in which discoveries are made; in this case RR
Lyrae being the 10th
variable star found in the constellation.
The RR Lyrae variable stars, as well as the Cepheid variable stars, are classed as ‘’standard
candles’’ for determining distances to the globular clusters. If the absolute (M) and apparent (m)
magnitudes of the star are known, the distance (r) in parsecs to them can then be calculated by
equation 1 below:
𝑚 − 𝑀 = 5 log (
𝑟
10
)
Equation 1 – Distance modulus equation (Technology, n.d.)
They typically have periods ranging from 0.1-1 days and amplitudes up to 1.5 magnitudes in
V3
(Simonsen, 2012). RR Lyrae stars are also part of a very specific group of pulsating variables. This
specific group is located in a thin nearly vertical area of the Hertzsprung-Russell diagram which is
referred to as the ‘instability strip’, the stars in this particular region all pulsate due to the same
cause. Such pulsations are induced by the limited escape of radiation from the star (Templeton,
2010).
RR Lyrae variable stars are important celestial bodies since as stated previously, they are
classed as ‘’standard candles’’ which are extremely helpful for distance calculations. Such stars also
harbour detailed information regarding the chemical ‘make-up’ in the halo and old disk population
of our galaxy. Finally, they are largely studied due to research in stellar structure, stellar evolution
and hydrodynamics4
(Lub, 1978).
2
A variable star is one whose brightness changes periodically.
3
This is the apparent magnitude which is effectively the brightness of a star.
4
Science which studies dynamics of fluids, primarily those which are incompressible.

4. Alexander Millington
Page | 3
When classifying a RR Lyrae variable star there are two subtypes which are most abundant,
these being the RRab and RRc types. When deciding which classification to give a star in question,
the following constraints can be applied. Stars which fall into the RRab category typically have
periods from 0.3-1.2 days and amplitudes from 0.5-2 in V. The RRc subtype stars typically have
periods from 0.2-0.5 days and amplitudes of 0.8 or less in V (Good, 2003). Further than this, both
subtypes have drastically different looking ‘phased light curves'5
. In most cases where the star is
non-variable a simpler light curve is used where it’s plotted against time. These phased light curves
show in what way the brightness of a star changes as a function of phase. It can be seen in figure 1
below, that the Phased light curve of the RRab type RR Lyrae variable star shows a sharp peak;
whereas that of the RRc subtype shows a subtler jump in magnitude. Examples of typical shapes of
these light curves are shown below:
Figure 1 - On the left, the typical shape of the phased light curve for an RRab subtype and
on the right, that of an RRc subtype (Clement & Shelton, 1997).
The SuperWASP project is the UK’s cutting edge ‘extra-solar planet detection programme’
and consists of two telescopes, SuperWASP-North which can be found on the island of La Palma and
SuperWASP-South, which is located on the site of the south African astronomical observatory
(SAAO) (Pollacco, 2006). WASP stands for wide angle search for planets and the project’s aim is to
search for exoplanets and their parent stars.
The SuperWASP south telescope which provides the necessary data for this study features
new 85mm, f/1.2 lenses. They have a much larger field of view than their 200mm predecessor and
due to the aperture value, can see fainter objects causing the magnitude limit to change from 9.5 to
7 in V (Smith & , 2014). Also due to the new lens type, the exposure time has been shortened to 20
seconds, rather than the original 30 seconds with the 200mm lens type. The effect of this shortened
exposure time means that more images can be taken on a given night. The filter on the lens is the
5
A phased light curve is a graph of V against phase.

5. Alexander Millington
Page | 4
SSDS6
r’ type, where the lens has a magnitude range of 6 ≤ 𝑉𝑚𝑎𝑔 ≤ 11 (Turner et al., 2015).
Typically, the both the SuperWASP-South and North will analyse somewhere around 12 areas of sky
per night. The telescopes will then continuously analyse the same set of areas in the sky for about 5
months in order to obtain a through data set (Smith & , 2014).
All the data used in this study was taken from the ‘International variable star index’
otherwise known as the VSX catalogue (Watson et al., 2015). This catalogue was used to produce a
group of RR Lyrae variable stars which was then compared to the WASP data of stars who had
accumulated at least 1000 observations each. The resulting set of stars were then taken and
analysed.
The objectives to be achieved are, firstly taking the raw data of each star, cleaning it, i.e.
removing any anomalies and outliers from the data, such as birds, planes, clouds etc using Inspect
(Maxted, 2015). Then secondly finding the frequencies using Period04 (Lenz & Breger, 2005) and
hence the periods of each of the stars and then plotting the phased light curves of each using Topcat
(Taylor, 2005). With the data gathered from these processes, it will then be possible for me to
classify the set of stars. The aim of the study is to classify a small set of stars, these being
VSX:013997, 017283, 026353 and 091251, using the data provided by the SuperWASP-South
telescope.
Experimental
Initially I took the raw uncleaned data for each star and entered it into the Inspect cleaning
program. I carefully analysed every night of data consecutively and deleted those points with large
error bars and any outliers in the data which did not follow a trend in magnitude. Sometimes if one
nights’ data were bad enough, that nights’ data would need to be discarded. On average, each data
file examined contained around 150 to 210 nights of data, although some stretched up to around
270 nights. By following this cleaning process thoroughly, I was able to reduce the data to nights that
only displayed ‘clean’ light curves with no anomalies. This cleaning amounted to removing around 5-
10% of the entire data for one stars’ observations.
Secondly, I took the cleaned data for each of these stars and consecutively entered them
into the Period04 program. Using this program, I used a Fourier analysis algorithm to fit a function to
6
Sloan digital sky survey.

6. Alexander Millington
Page | 5
the displayed behaviour of the stars observed. The result of this was having a ‘best fit line’ that
closely approximated the fluctuations of the brightness of the star to a good degree of accuracy. This
is done by first allowing the program to find the frequency with the highest amplitude present in the
data; if this frequencies’ amplitude was considerably higher than others present, say by one or two
orders of magnitude, it could be said that this was the stars’ ‘fundamental’ pulsation frequency.
Once this frequency was identified, then by taking the main, ‘fundamental frequency’, harmonics
(multiples) of this frequency could be fitted which would allow the Fourier analysis algorithm to
accurately model the given data set. As can be seen below in figure 2, the black line displays the
‘best fit line’ of the red data points from the stars.
Figure 2 - Fourier fits of stars VSX:013997, 017283, 026353, 091251, respectively.

7. Alexander Millington
Page | 6
As can be seen from figure 2, Period04 managed to model the behaviour of the first three
star’s data to a good degree of accuracy. Conversely, it can be seen that the algorithm did not
manage to model the data as accurately for star VSX091251. Nevertheless, the fit was still of
reasonably good quality. The quality and accuracy to which the data are modelled determines the
quality and reliability of the final results and will definitely affect the classifications.
Next after modelling the behaviour of the data points to the highest accuracy possible, I
then consecutively exported three individual sets of data from Period04 into the TOPCAT program,
these being ‘Time, Observed and Calculated’, from the main data set; along with the ‘’WASP 85-mm
data for RR Lyr stars’’ file. This 85mm file contains data from the VSX catalogue for all the stars in
this study, including their suspected classifications, frequencies, periods etc. This file then acts as a
reference point since if a frequency is obtained which is far off the VSX value, then it may be
incorrect.
Once these two data sets were inside the program, I created a new column called ‘Phase’
within the exported data set. After this using the observed, calculated and phase columns I then
plotted a phased light curve over two cycles using a ‘phase + 1’ argument. The phase against
calculated data plot essentially worked as a best fit line in the phased light curves. The phase against
calculated data curve, as well as the phase + 1 argument helped to see whether there were any
discrepancies with the period used in the phase calculation.
In order to calculate the amplitudes of each of these light curves, I looked at the
phase/calculated black line which ran through the centre of each of light curve; taking time to
accurately work out the difference between the maximum and minimum magnitude values. After
completing the construction of the phased light curves and gathering all the data I could, I could now
get to work on comparing them to predefined parameters for classification of these stars.
I next wanted to check whether any nearby stars could be contaminating the photometry of
a star being investigated. Initially I imported the 85mm data into TOPCAT and then put the data
points onto a sky plot. This plot places stars at positions on a sphere according to their longitude and
latitude values in degrees. I then colour coded the stars in accordance with their periods using the
‘Aux axis’ function. Next I configured the ‘Activation action’ button in order to display a 5x5
arcminute image from the ‘SuperCOSMOS All-Sky Red’7
survey which was centred on the star’s
7
SuperCOSMOS – An advanced photographic plate digitising machine (WFAU, 2008)

8. Alexander Millington
Page | 7
position. A SuperCOSMOS sky survey is used since the pixel size is just 10 microns, compared to
other much larger alternatives (WFAU, 2008). The number of pixels associated with 5 arcminutes
was approximately 448 pixels.
Results
Results from the analysis of stars are shown below, including the initial number of data
points and the quantity remaining after cleaning as well as the quality of the data and calculated
period:
Table 2 - Data gathered for the four stars.
The system I put in place for choosing the number of harmonics fitted for each star, was
once the value of the residuals stops decreasing significantly I chose this number of harmonics. As
can be seen from Table 2, the amount of data conserved was kept to a high percentage; this reflects
positively on the quality of data for each of these stars showing that there were few anomalies or
aberrations in the data. Also on the topic of quality, the difference in period between the published
period and calculated period is very small, this also reflects on the quality of the data. For star
VSX091251 in Table 2, it can be seen that there are two frequencies listed. The first, 0.31217 days
corresponds to the initial frequency of approximately 3.20 1/days which Period04’s frequency search
produced. It turns out that this frequency is not actually the correct pulsation frequency for this star
and that it does in fact represent 2𝑓0. And so the period of 0.62434 days corresponds to the sub-
harmonic frequency of about 1.60 1/days. This means that the actual frequency for star VSX091251
is 𝑓0 = 1.60170025.
From the data gathered, the phased light curves can now be plotted, they are shown below
for the four stars:

9. Alexander Millington
Page | 8
Figure 3 – Phased light curves of the four stars, with amplitudes no larger than 1.13 mag in V.
As can be seen from Figure 3, the first three phased light curves of the stars VSX [013997,
017283 and 026353] all show the shape of a typical RRab type RR Lyrae variable star. Star
VSX091251 is quite different however and can be classed as a non-RR Lyrae variable star, the
secondary minima of the star have a smaller amplitude than the primary maxima. This type of
behaviour is typical of a rotating ellipsoidal variable star (ELL) (Simonsen, 2012). This is a binary star
that varies with a period equal to that of its orbital motion. Since in an ELL binary system the two
stars are so close to each other, there is a very large gravitational force of attraction between them.
So strong that both components of the system are warped out of shape. The results for all four stars
are shown below in Table 3:
Table 3 - Data gathered from phase light curves and their classifications. With the period of 0.62434
corresponding to the sub-harmonic frequency.

10. Alexander Millington
Page | 9
Finally, after completing production of the phased light curves for the stars I went on to
check whether the photometry8
of each star in question, was being adversely effected by any nearby
celestial bodies. The sky images for each star are shown below respectively in Figure 4:
Figure 4 - Sky images of analysed stars.
The data gathered from this photometry analysis is shown below:
Table 4 – Results of determining the flux contributed to the data by the target stars’ neighbour.
As can be seen above in Table 4, the flux contributed by the neighbour star can be seen to
be significant for the VSX13997 star, but not so much for the other three stars. Although it’s
important to bear in mind that for VSX91251; the other star cannot be found since it may well be
behind the target star itself since they are in a binary system. Particularly since VSX091251 is
8
The measurement of light.

11. Alexander Millington
Page | 10
possibly a rotating ellipsoidal variable star (ELL), a property of such stars is that the components of
the binary system are orbiting each other very closely and a consequence of this would mean that
seeing the second component would be more difficult here. The percentage flux is calculated using
the ‘Apparent-magnitude’ equation, rearranged to give the ratio of the fluxes of the target star and
its neighbour:
Equation 2 - Apparent magnitude equation (Michigan, n.d.).
In equation 2 above, the B values correspond to the stars’ flux and the m values to the ‘r_mag’ of the
stars.
Research on ‘Double-mode’ pulsators
A name given to the class of star which pulsates with two frequencies is called a ‘double-
mode’ star. The first star to be categorised as being a double-mode RR Lyrae variable star or RRd for
short, was called AQ Leo. It was initially classified as an RW Aurigae type variable star in 1944 by
Hoffmeister at the Sonneberg Observatory (Michael Gruberbauer et al., 2007).
An RRd type star is the third and considerably less common subtype of the RR Lyrae variable
stars. Out of a given set of RR Lyrae variable stars, approximately 4% of those would be the RRd
subtype according to (D-W & Coryn, 2015). It’s a type of star which pulsates in both the fundamental
mode and first overtone. Normally the first overtone frequency has a greater amplitude than the
fundamental, but it’s not always the case (Wils, 2010). A typical value for a RRd type stars’
fundamental period is around 0.5 days. Another way of recognising if it’s an RRd type is that it has a
period ratio 𝑃1/𝑃0 which is equal to around 0.74, associated with the fundamental mode and first
overtone. Alternatively, it could also pulsate in the first and second overtones, with a period ratio of
approximately 0.80 (Index, 2005-2013).
Due to the RRd type variable stars being a double-mode type, they have a very special
property which grants the opportunity for their masses to be calculated based on their period ratio.
A great outcome of this is that the mass for a double-mode star can be calculated much more

12. Alexander Millington
Page | 11
accurately of that of a single-mode RR Lyrae variable star (Michael Gruberbauer et al., 2007).
Although contrary to this, it has been stated by (Kovacs et al., 1991;1992) that in order to precisely
calculate the mass of an RRd type variable star, one must know the stars’ quantity of metal present.
Furthermore, that that perturbations from the ratio of solar elemental quantities will most probably
affect the calculated mass of a given star.
After analysing all the stars for signs of an overtone frequency present, I can conclude that I
did not find evidence of any. Below is the table of all the frequencies and periods, fundamental, first
and second potential overtones. By first finding the fundamental frequency and then fitting its
harmonics, then taking residuals of these, I looked for an overtone frequency present. The results of
this analysis are shown below:
Table 5 – Data for fundamental, first and second overtone frequencies.

13. Alexander Millington
Page | 12
Conclusion
The three stars which I classified as RRab types satisfy the restrictions imposed on the period
and amplitude for this subtype, described in the introduction. The conditions for being an ellipsoidal
variable star are such that the amplitude does not typically exceed 0.1 mag in V (Index, 2005-2013),
although star VSX091251 does, it’s not by much and could be down to data inaccuracies. The period
of star VSX013997 calculated by the study here agrees with the GCVS to 2 decimal places. For star
VSX017283, the study agrees with the value in the GCVS to 4 decimal places. For star VSX026353,
again the study agrees with the GCVS to 4 decimal places. Both VSX013997 and VSX017283 are
classified as RRab’s in the GCVS, agreeing with the analysis performed here. But for star VSX026353,
the classification has been left as RR in the GCVS; whereas I have classified it as RRab. As for the
variable star I classified as being ELL, I could not find any source which defined a classification of this
star. So at this point, this is the only classification of this star and is subject to questioning.
According to Table 4, the percentage by which the flux is contributed by the neighbouring
star is at a high 40% for star VSX013997. This could directly correlate with the low accuracy of 2
decimal places for the period, when comparing the calculated value with the value listed in the
GCVS. To further support this statement, since the values for the periods of stars VSX:017283 and
026353 agree with those in the GCVS correct to 4 decimal places; and the percentage flux
contributed by the neighbouring star for both is approximately 20%. It again can be said that the
larger the flux contributed by a neighbouring star, the greater the inaccuracy in the calculated period
of the target star.
From Table 5, it can be concluded that out of all the stars studied, including the four in this
study, there are no double-mode pulsators present which pulsate in the fundamental and first
overtone frequency at least. Since as stated previously that 4% of a given data set of RR Lyrae stars
should contain an RRd, increasing the data set in this case would help to reproduce that result.
There are some limitations to the data obtained for this study, to speak of a few, due to the
lens’s specifications only stars with a 𝑉𝑚𝑎𝑔 between 6 and 11 are contained in this experiment. This
straight away puts a cap on the range of stars available to analysis. It can also be said that due to this
limitation, we are performing an analysis of an incomplete data set and in order for results to be
more accurate, a larger 𝑉𝑚𝑎𝑔 range is needed. Carrying on with the topic of a limited data set, not
100% of the sky has yet been mapped by the WASP project as can be seen below:

14. Alexander Millington
Page | 13
Figure 5 - The WASP coverage map, as of September 2013 (Smith &, 2014). Where the red colour denotes a higher number
of data points and the blue colour a reduced number of data points per star.
As stated previously, increasing the amount of sky area covered would increase the quality
of data. Also with reference to the above Figure 8, since the blue areas mark the stars with the least
amount of data points on average, it would drastically increase the data quality and reliability of
those stars if more observations were made in those areas.
For future research, the data sets of the stars classified as RRab’s could be improved on by
more observation time with reference to the large degree of flux contributed by their neighbouring
star. This improvement could lead to a more accurate value for the period for these stars, which is
critical since for star VSX013997 since it’s only accurate to 2 decimal places when compared to the
values in the GCVS. A similar argument can be said for the remaining three stars which could lead to
even more accurate periods. Also, on the side of research for double-mode pulsators in this set of
stars, since there are none which pulsate in the fundamental and first overtone frequencies. Looking
into whether they pulsate in the first and second overtone could harbour interesting results.
References
B. e. a., 2014. RR Lyrae Stars in the GCVS Observed by the Qatar Exoplanet Survey. Konkoly
Observatory.
Clement, C. M. & Shelton, I., 1997. The Structure of the Light Curves of the RR Lyrae Variables in the
Oosterhoff Type I Cluster NGC 6171. Astronomical Journal , Volume 113, pp. 1711-1722.

15. Alexander Millington
Page | 14
D-W, K. & Coryn, A. L. B.-J., 2015. A package for the automated classification of periodic variable
stars. Astronomy & Astrophysics.
Good, G. A., 2003. RR (RR Lyrae stars). In: Observing Variable Stars. s.l.:Springer-Verlag London
Limited, p. 86.
Horace, A. S., n.d. [Online]
Available at:
https://books.google.de/books?id=dMv_r82moCQC&printsec=frontcover&dq=rr+lyrae+stars&hl=de
#v=onepage&q&f=false
[Accessed 2016].
Index, T. I. V. S., 2005-2013. Variable Star Type Designations in VSX. [Online]
Available at: https://www.aavso.org/vsx/help/VariableStarTypeDesignationsInVSX.pdf
[Accessed 19 04 2016].
K. e. a., 1991;1992. RR Lyrae pulsations revisited;Chemical composition effects and double-mode RR
Lyrae masses. Astronomy and Astrophysics, pp. 27-30;46-48.
Kolenburg, K., 2012. RR Lyrae Stars: Cosmic Lighthouses With a Twist. JAAVSO Vol. 40.
Lenz, P. & Breger, M., 2005. Communications in Asteroseismology.
Lub, J., 1978. RR Lyrae Stars. Issue https://www.eso.org/sci/publications/messenger/archive/no.13-
jun78/messenger-no13-15-17.pdf, p. 15.
Maxted, P., 2015. Inspect User Manual. Keele University.
M. G. e. a., 2007. MOST* photometry of the RRd Lyrae variable AQ Leo: Two radial modes, 32
combination frequncies, and beyond.
Michigan, U. o., n.d. Birthness and Surface Brightness. [Online]
Available at: https://dept.astro.lsa.umich.edu/ugactivities/Labs/brightness/
[Accessed 19 4 2016].
P. e. a., 2006. The WASP Project and SuperWASP Camera. Astronomical Society of the Pacific,
Volume 1407-1418.
Samus, N. N. & Durlevich, O. V., 2009. GCVS Variability Types. Moscow Institute of Astronomy.
S. e. a., 2011. The Optical Gravitational Lensing Experiment. The OGLE-III Catalog of Variable Stars.
XI. RR Lyrae Stars in the Galactic Bulge. Acta Astronomica.
Simonsen, M., 2012. Variable Star Classification and Light Curves. p. 32.
Smith, A. M. & T. W. c., 2014. The SuperWASP exoplanet transit survey. pp. 5005-512.
Taylor, M. B., 2005. TOPCAT % STIL: Starlink Table/VOTable Processing Software.
T. e. a., 2015. Planets Transiting Bright Stars with WASP-South. Twenty years of giant exoplanets, pp.
147-152.
Technology, S. U. o., n.d. Distance modulus. [Online]
Available at: http://astronomy.swin.edu.au/cosmos/D/Distance+Modulus
[Accessed 16 4 2015].
Templeton, M., 2010. RR Lyrae. [Online]
Available at: https://www.aavso.org/vsots_rrlyr
[Accessed 16 April 2016].

16. Alexander Millington
Page | 15
W., 2008. Introduction. [Online]
Available at: http://www-wfau.roe.ac.uk/sss/intro.html
[Accessed 18 4 2016].
W. e. a., 2015. AAVSO International Variable Star Index VSX. CDS/ADC Collection of Electronic
Catalogues, 1, 2027.
Wilson, D., 2014. Welcome to the WASP website. [Online]
Available at: http://www.superwasp.org/
[Accessed 17 4 2016].
Wils, P., 2010. New Double-Mode and Other RR Lyrae Stars From WASP Data.