A search for pulsating B-type variable
stars in the southern open clusters
NGC 6204 and Hogg 22
Jaco Mentz, B.Sc. Hons.
A dissertation submitted in partial fulfillment of the requirements for the degree Magister Scientiae at the Potchefstroom Campus of the North-West
University
Supervisor : Prof. D.J. van der Walt Assistant supervisor : Prof. A Pigulski
Abstract
The theory of stellar evolution and stellar structure relies on the observation of stars in different phases of their evolutionary cycle. The relation between observations and theory can be strengthened by obtaining observational data of a large sample of stars in a particular evolutionary phase. The search for β Cephei stars, as conducted in this study, can contribute to the sample of known β Cephei stars, where these interesting stars are massive non-supergiant early B-type stars, displaying pulsating behaviour which is not well understood.
Stars tend to form in clusters where it can therefore be expected that young massive stars can be found in open clusters. For this reason two young southern open clusters were observed in order to search for B-type pulsating stars. The region of NGC 6204 and Hogg 22 was observed over a period of thirteen nights in Johnson B, V and I bands. NGC 6204 is believed to be the oldest cluster of the two at a distance of 0.8 kpc while the much younger Hogg 22 is more distant at 2.8 kpc. These two open clusters are located 6 arcminutes apart which made it possible to observe them simultaneously with a 12.8 × 12.8 arcminute field of view. The observations were done with the newly installed 1600
telescope of the North-West University, South Africa.
In order to do a variability search, periodic stars need to be identified from the cluster data, where a typical data set may contain thousands of scientific images. In addition to the main motivation for this study, a pipeline was created in order to automate the photometry and data reduction processes. A Lomb-Scargle transform was applied to the stellar light curves in order to identify periodic sources. 354 significantly periodic stars were identified from the 3182 observed stars. Amongst them, two new possible β Cephei stars were found together with a possible slowly pulsating B star (SPB), and numerous eclipsing binary systems.
By using photometry of this region obtained by Forbes & Short (1996), instrumental magnitudes were transformed to a standard system in order to compare photometry results. From the constructed colour magnitude diagram of the two clusters, it could be seen that some stars, indicated by Forbes & Short (1996) to be cluster members, were in fact field stars belonging to neither cluster.
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The reduction and photometry pipeline was implemented successfully on the data set, which also highlighted the importance of instrumentation and correct data analysis procedures. Possible improvements were identified in order to overcome difficulties ex-perienced during this study.
Keywords: stellar evolution, stellar structure, evolutionary cycle, β Cephei stars, pul-sating stars, open star clusters, photometry, Lomb-Scargle transform, light curves, slowly pulsating B stars, eclipsing binary systems, colour magnitude diagram, field stars.
Opsomming
Die teorie¨e rakende die struktuur en evolusie van sterre is afhanklik van genoegsame observasie van sterre in verskillende fases van hulle evolusionˆere siklus. Die verband tussen observasie en teorie kan versterk word deur die waarneming van ‘n groot aantal sterre in ‘n spesifieke evolusionˆere fase. Die soektog na β Cephei veranderlike sterre, soos gedoen in die huidige studie, kan bydra tot die totale aantal bekende sterre van die bepaalde klas. Hierdie interessante pulserende sterre is massiewe nie-superreus sterre met spektraaltipe B wat pulserende gedrag toon waaroor daar nog heelwat onsekerheid bestaan.
Sterre word in sterswerms gevorm en daarom kan verwag word dat jong massiewe sterre in oop sterswerms gevind kan word. Om hierdie rede is twee jong suidelike sterswerms waargeneem met die doel om vir B-tipe pulserende sterre te soek. Die gebied van NGC 6204 and Hogg 22 was waargeneem oor ‘n tydperk van dertien nagte in Johnson B, V en I filters. NGC 6204 is vermoedelik die oudste en gele¨e op ‘n afstand van 0.8 kpc terwyl Hogg 22 heelwat jonger is maar verder gele¨e is op ‘n afstand van 2.8 kpc. Hierdie twee oop sterswerms is 6 boogminute van mekaar gele¨e wat gelyktydige waarnemings van die twee sterswerms moontlik gemaak het deur ‘n sigveld van 12.8 × 12.8 boogminute. Die waarnemings is gedoen deur gebruik te maak van die nuwe 1600 teleskoop van die Noordwes-Universiteit, Suid-Afrika.
Die hoofsaak van ‘n veranderlikheidstudie is die identifisering van periodiese sterre vanuit ‘n datastel wat duisende beelde kan bevat. ‘n Pyplyn was ontwikkel bykomend tot die hoof motivering van die huidige studie om die prosesse van data verwerking en fotometrie te outomatiseer. ‘n Lomb-Scargle transform was op die ligkrommes van sterre toegepas om sodoende periodiese bronne uit die data te identifiseer. 354 periodiese sterre is ge¨ıdentifiseer uit ‘n moontlike 3128 sterre wat waargeneem is. Daaronder was twee nuwe moontlike β Cephei sterre gevind. ‘n Moontlike stadig pulserende B-tipe ster is gevind asook ‘n aantal verduisterende dubbelsterre.
Die instrumentele magnitudes vanuit die huidige studie is getransformeer na ‘n standaard sisteem, deur gebruik te maak van fotometrie verkry deur Forbes & Short (1996), wat noodsaaklik is voordat fotometrie van verskeie studies vergelyk kan word. Vanaf die saamgestelde kleur-magnitude diagram van die twee sterswerms kan daar gesien word dat sommige sterre wat deur Forbes & Short (1996) aangedui is as lede van die sterswerm, as veldsterre gereken moet word wat nie aan een van die swerms behoort nie.
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Die pyplyn wat saamgestel is vir die dataverwerking en fotometrie was suksesvol ge¨ımple-menteer, waardeur die belangrikheid van instrumentasie en korrekte dataverwerking weereens beklemtoon is. Moontlike verbeterings op die bestaande verwerkingsmetodes is ge¨ıdentifiseer om sommige probleme wat ondervind is tydens die studie op te los. Sleutelwoorde: ster evolusie, ster struktuur, evolusionˆere siklus, β Cephei sterre, pulserende sterre, oop sterswerm, fotometrie, Lomb-Scargle transform, ligkrommes, stadig pulserende B-tipe sterre, verduisterende dubbelsterre, kleur-magnitude diagram, veld-sterre.
Acknowledgements
I hereby wish to express my sincere gratitude and appreciation to those who made this study possible and assisted in its completion.
• My supervisor Prof Johan van der Walt for his support and guidance throughout my undergraduate and postgraduate studies.
• Prof Andrzej Pigulski, my assistant supervisor, for his expert advice, encourage-ment and for all the valuable skills learned during this study regarding observations and data analysis.
• Mrs. M.P. Sieberhagen, Mrs. E van Rooyen, and Mrs. L. van Wyk for their assistance in administrative matters.
• The National Research Foundation and the Center for Space Research at the North-West University for financial support throughout my studies.
• My parents for their interest and the way in which they supported and encouraged me.
• My father for his assistance in the technical editing.
• My wife Annariet for her love, support and encouragement throughout my studies. To God be the glory.
Contents
Abstract i Opsomming iii Acknowledgements v List of Figures ix List of Tables xi 1 Introduction 1 1.1 General introduction . . . 11.2 Motivation and problem statement . . . 2
1.3 Region of study . . . 3
1.4 Chapters to follow . . . 5
2 Theoretical background 6 2.1 Introduction . . . 6
2.2 Star formation . . . 6
2.2.1 Giant molecular clouds (GMCs) . . . 6
2.2.2 The Initial mass function (IMF) . . . 9
2.3 Stellar evolution . . . 10
2.4 Stellar structure . . . 11
2.4.1 Hydrostatic equilibrium . . . 11
2.4.2 Chemical composition . . . 13
2.4.3 Opacity . . . 13
2.5 Open galactic clusters . . . 15
2.5.1 Interstellar extinction and reddening . . . 17
2.6 Classification of variable sources . . . 19
2.6.1 Classification and properties of B-type pulsating stars . . . 20
2.6.1.1 β Cephei stars . . . 20
2.6.1.2 Slowly pulsating B-type stars . . . 23
3 Data acquisition, reduction and photometry 24 3.1 Introduction . . . 24
Contents vii
3.2 Data acquisition . . . 25
3.2.1 Setup and instrumentation . . . 25
3.2.2 Observational strategy . . . 26 3.3 Data reduction . . . 27 3.3.1 Debiasing . . . 29 3.3.2 Dark frames . . . 29 3.3.3 Flat fielding . . . 30 3.4 Photometry . . . 31
3.4.1 Preparation for automated photometry . . . 32
3.4.2 PSF photometry . . . 34
3.4.3 Aperture photometry . . . 37
3.5 Differential photometry . . . 37
3.5.1 Cleaning of time series data . . . 38
3.6 Timing . . . 39
4 Results and discussion 41 4.1 Introduction . . . 41
4.2 Photometry pipeline . . . 42
4.3 Periodicity extraction . . . 43
4.3.1 Lomb Scargle periodogram . . . 43
4.3.2 Significance level . . . 44
4.3.3 Inspection of extracted frequencies . . . 49
4.4 Classification of variable sources . . . 50
4.4.1 Frequency identification . . . 51
4.4.2 Identification of high amplitude variable sources . . . 53
4.5 Calibration of instrumental magnitudes . . . 57
5 Summary, conclusions and future prospects 61 5.1 Introduction . . . 61
5.2 Summary . . . 62
5.2.1 Observations . . . 62
5.2.2 Data reduction and photometry . . . 62
5.2.3 Periodic analysis . . . 63
5.2.4 Calibration of magnitudes . . . 63
5.3 Conclusions and future prospects . . . 64
5.3.1 Telescope and instrumentation . . . 64
5.3.2 Reduction and photometry pipeline . . . 65
5.3.3 Periodic analysis . . . 65
5.3.4 Identification and classification of periodic sources . . . 66
A Extinction and reddening 67 A.1 Extinction and reddening for NGC 6204 and Hogg 22 . . . 67
Contents viii
List of Figures
1.1 DSS image showing the region of study: NCG 6204 and Hogg 22 . . . 3 2.1 Mass-luminosity relation of 400 galactic open clusters as given by
Bat-tinelli et al. (1994) . . . 16 2.2 The simultaneous correction of the distance and reddening to the Padova
stellar evolutionary track shows a diagonal movement to the lower right side of the diagram. The uncorrected red evolutionary track is corrected for distance, resulting in the green track, where the green track is cor-rected for reddening, which gives the blue track. . . 19 2.3 Provisional radial velocity curve presented by Frost (1906) . . . 20 2.4 Hertzsprung-Russell Diagram reproduced from Pamyatnykh (1999),
show-ing instability regions in the upper main sequence . . . 21 3.1 The new 16 inch telescope setup on the small observatory, Nooitgedacht,
of the North-West University, where the more recently installed autogu-iding system can also be seen. . . 26 3.2 Schematic diagram of reduction process followed in this study . . . 28 3.3 Left: Averaged bias frame. Right: Histogram of the average combined
bias frame showing the number of pixels as a function of the ADU value of each pixel. The mean bias level is around 208 ADU. . . 30 3.4 Construction of the master list of stars by using the most shifted images
together with the master image(blue). . . 33 3.5 Field of NGC 6204 and Hogg 22 shown before (left) and after (right)
subtracting the PSF function. . . 35 3.6 Light curves of the stars selected to be used as constant stars in the
differential photometry process. Note that the differential V magnitude is indicated on different scales. . . 38 3.7 The light curve of the known Beta Cephei star from Hogg 22, shown
under a four sigma clipping. One outlier can be seen in the figure from the second night of observation. The green line shows the four sigma level above the average of the light curve and the blue line indicates the four sigma level below the average. . . 39 4.1 Periodogram of a random noise time series with the same times as the
observational times. . . 45 4.2 Spectral power distribution with normalized distribution (red) of random
noise time series representing the null hypothesis of the Lomb-Scargle periodogram . . . 45
List of Figures x
4.3 The normalized spectral power of a frequency obtained from a sine wave within a variable noise level. The SNR is defined to be the ratio between the amplitude of the input sine function and the standard deviation of the Gaussian noise. . . 46 4.4 The retrieval accuracy presented as the relative deviation from the input
signal as a function of SNR (as defined above), when applying a Lomb-Scalgle transform on a sine wave in a variable noise level. . . 47 4.5 The distribution of variable sources found above the indicated normalized
spectral power value. . . 48 4.6 Differential magnitudes shown for the two β Cephei candidate stars. . . . 50 4.7 A set of periodograms from the data of id11 (β Cephei star), showing
the periodogram after the subtraction of a sine wave with frequency as indicated. This method was used to identify the true frequency, shown by 4.45 d−1, resulting in a periodogram without the alias frequency pattern observed in the initial periodogram. . . 52 4.8 Light curves and corresponding periodograms of the β Cephei star id11
with period of 0.22426 days and eclipsing binary id16 with an orbital period of 1.187 days. . . 54 4.9 Light curve and periodogram of id726. A one day alias of double the
frequency was observed in the periodogram leading to a period of 0.7304 days. The light curve of id83 showing only one eclipse during the 13 days of observation, therefore with no period associated with a recurrence . . . 54 4.10 A one day alias of double the eclipsing frequency was observed in the
periodogram of id1081 showing a period of 0.40172 days. For the possible EA-type eclipsing variable, id1516, double of the eclipsing frequency was observed which gives a frequency of 1.189 d−1 or a period of 0.8409 days. 55 4.11 The possible Bp-type id35 showed a increase in magnitude on three
dif-ferent nights with a possible period of 2.4547 days. The period observed for id1415 was a daily alias of double the true frequency, resulting in a period of 0.34944 days . . . 56 4.12 The relation between the (B-V) and (V-v) colors to (b-v), showing the
color transformation by using B and V magnitudes obtained from Forbes & Short (1996). . . 58 4.13 Color magnitude diagram of all stars from the photometry master list
(red) together with identified cluster members from Forbes & Short (1996) (NGC 6204: blue; Hogg 22: green). . . 58 4.14 Possible field stars identified on the cluster diagram from Forbes & Short
(1996) . . . 59 4.15 Colour magnitude diagram showing cluster members from Forbes & Short
(1996), all stars from this study (red), and isochrones overplotted to each cluster as described in the text (NGC 6204: blue; Hogg 22: green). . . 60 4.16 Two possible β Cephei stars together with one known β Cephei star in
Hogg 22, indicated on the two colour diagram from Forbes & Short (1996). The reddening arrow is indicated on the diagram, showing that these three stars have the same spectral type. . . 60
List of Tables
4.1 Distribution of the VGUIDE variable stars used as guide stars by the Chandra X-ray telescope. Data obtained from Nichols et al. (2010) . . . . 49
