## Computer Programs for Data Analysis

Available today are computer programs that will assist you in performing sophisticated mathematical analysis of your data such as searching for and fitting sinusoidal patterns within time series data, Discrete Fourier analysis, and phase dispersion minimization (PDM). Without possessing an advanced degree in mathematics, you will be able to use these powerful mathematical tools to aid you in understanding variable stars. Of course, an understanding of mathematical methods that goes beyond the elementary level will enhance your understanding and appreciation of your analysis. This deeper understanding of the necessary math will come with a little effort once you start using these various methods and after you feel a need to really understand what your data is saying to you. Don't let the math intimidate you.

In all likelihood, one of your first needs for sophisticated computer analysis will be to determine the period of a variable star. There are several things to remember regarding the search for a variable star's period: not all variable stars are strictly periodic (in other words, there may not be a detectable period),

Figure 13.3. R Leo data organized for TS application. Notice one space between the JD and magnitude estimate. Data provided by VSNET.

Figure 13.3. R Leo data organized for TS application. Notice one space between the JD and magnitude estimate. Data provided by VSNET.

many variable stars have more than one period, and there are going to be gaps in your data.

A fast and simple program for detecting a variable star's period that is available from the AAVSO is TS11 (TS). This program is available at their Web site (www. aavso.org) and is free. There are other programs available, some more complex than TS11, but we'll use the AAVSO program here. When you feel the need for more advanced programs, move on. It's not unusual to use more than one or two programs to conduct period analysis.

TS needs two pieces of information: time and magnitude. The program expects your data file to be a text file (name.txt) or data file (name.dat) and to consist of columns with one blank space separating the columns. For example, the data from Figure 13.1 was stored as "RLEO.txt" and consisted of the two columns shown (Figure 13.3). The maximum number of data points that can be loaded at one time is 4000. If you wish to analyze more than 4000 data points you must do so using additional runs.

During the analysis run, TS stores the processed data in a second file (name.ts) that you can further analyze using a spreadsheet. We'll use Microsoft Excel in this

Figure 13.4. Power spectrum produced using TS-11 using R leo dato. Data provided by

VSNET.

book but any spreadsheet will provide the basic tools necessary for fundamental analysis.

TS gives you the ability to perform the following mathematical operations: average your data, fit a polynomial (using the method of least squares), compute residuals, discrete Fourier analysis (for period and frequency), and model your data. The instructions for TS are included in the files that you download from AAVSO. Plan on spending an hour learning how to use this program.

Figure 13.4 shows the power spectrum, illustrated as a two-dimensional graph, that displays the Fourier analysis of the data from Figure 13.3.

This chart was made using the file RLEO.ts produced by the program (Figure 13.5).

Frequencies (displayed along the X-axis) indicated by the highest power levels (displayed along the Y-axis) are the most likely candidates for the actual frequency of a periodic fluctuation in your data. A critical examination of the tabular data stored in the file (narne.ts) produced by TS allows you to precisely select the best candidate frequency. The chart is an imprecise tool that allows you to visualize your analysis so you must carefully analyze the name.ts file. Nothing will replace hands-on experience for becoming familiar with this program.

You can see that the frequency of 0.003209166 (the period equals 24 divided by the frequency and then divided again by 24, in this case, 311 days) corresponds

Figure 13.4. Power spectrum produced using TS-11 using R leo dato. Data provided by

VSNET.

 rfiaijiiaj^J-ilí m Toot, tfntftr* (je» -IJIxl El Al il|ii|l&|»|4l||HX» ~3SM ~trr--Jl10 -d "I'l n|«l«NSl »KI.lMl.-3l -H

Figure 13.5. Time series data file produced from analyzing R Leo dola.

to the highest power rating (amplitude) of 399.8695. This power rating is a numerical discriminator. Of course, to be absolutely sure, further analysis will be necessary before you can safely conclude that the highest power rating relates to an accurate period or frequency. Occasionally, the highest power rating does not propose the correct period or frequency. Check your work. Then check it again.

This data was checked for a period every 12 hours. If this particular star, as a result of its intrinsic behavior, possessed a period of less than 12 hours, we would miss it using this resolution (for example, a 8 Scuti type variable). On the other hand, searching with a resolution of 0.0001 day over a period of 300 days will take a significant amount of computer time that could be better spent. This is where your understanding of stellar evolution and variable stars becomes important. You should have, at least, an educated suspicion regarding the variability of the star or stars that you will study. Occasionally, you will have no idea but these types of situations should be relatively rare. Good preliminary work on your part should reduce wasted time and improve your ability to conduct good analysis. Check the literature and look at other observation reports.

Figure 13.5. Time series data file produced from analyzing R Leo dola.

Observing Variable Stqrj

Examples of the questions that you will be asking yourself may approximate the following:

• What resolution is best based upon the stellar spectral type?

• Is there a possibility of multiple periods? Is there a possibility that the star in not strictly periodic?

• Is my data baseline too short to detect long periods?

The Fourier analysis just discussed is a good tool for detecting and quantifying periodic fluctuations in times series if by periodic we mean of truly constant period, amplitude, and phase. Real astrophysical systems rarely exhibit such consistency of fluctuation. Often periodic fluctuations arise intermittently as transient phenomena. Even for a time series with consistent periodicity you will usually see time evolution of the parameters of the fluctuation. Discrete Fourier analysis can detect, and to some degree quantify, such behavior, but it is far from ideal for such purposes. So, "What is Fourier analysis?" Jean Baptiste Joseph, Baron de Fourier was born on March 21, 1768. A physicist, Fourier was studying how heat flows through an object when it is heated. He was able to determine that the movement of heat also behaves like a wave. After careful study, Fourier discovered that, although in a very complicated way, heat waves are periodic waves. Periodic waves consist of the same pattern or waveform repeated over and over and Fourier discovered that no matter how complicated, a wave that is periodic with a pattern that repeats itself, consists of the sum of many simple waves. His method is known as Fourier analysis.

Fourier analysis is a powerful tool used by variable-star observers to determine the period exhibited by some variable stars. Of course, the important consideration is periodic behavior. The variable star to be analyzed must be periodic or at least approximately periodic. As you know by now, not all variable stars are

Figure 13.6. light curve of AM Her showing the nonperiodic nature of the outbursts. The Julian date is indicated along the horizontal axis.

2443000 2444500 2446000 2447500 2449000 2450500 2452000

periodic. For example, cataclysmic variable stars such as dwarf novae are not periodic. Their period, the time between outbursts, is an approximate average. For example, a light curve of the cataclysmic variable AM Her is shown in Figure 13.6.

Chapter 14

Variable Star Reporting and Recording Organizations

It is therefore necessary that memorable things should be committed to writing ...

Sir Edward Coke

"Each observation is unique and can never be repeated."

This statement expresses the underlying significance of each observation that you make. However, it is not only the actual observation that is unique but also your personal experience each night. Every night of observing will be a memorable affair. You may be with friends or a family member, you may be observing at a new location, you may witness in solitude, a meteor's fall from the heavens or an aurora resulting from solar activity two days earlier. Each of these different situations, and myriad others, will define many nights of observing that you will want to remember. Don't lose something important because you didn't record its happening. Make it a habit to write down in you log or record book everything that is not mundane. You won't regret it.

By using the Internet, it is possible to immediately communicate with, and report your variable-star observations to individuals, groups and organizations from around the world. One of the most valuable benefits of using the Internet will be your ability to compare your observations with others to see how well you are doing when estimating brightness or to look at estimates made during times that you are unable to observe.

Included here are a few organizations that provide assistance, guidance, publications and support to amateur variable-star observers. Certainly there are more organizations than can be listed in this chapter and I have not omitted any organization intentionally. One of the joys of amateur astronomy is discovering the treasures hidden within the Universe, including the Internet.

Contact one or more of these organizations once you feel comfortable with observing variables stars; perhaps after a week or so. At least, become familiar with some of the reporting procedures. You need not wait until you feel completely competent but understanding the basic methods, nomenclature and various other aspects of the hobby will make communicating a bit easier. You'll feel less intimidated too.

I can't recommend one organization over another; they're all good and all will welcome you as a participant or as a member. Don't worry about the number of observations you've made (or haven't made), the equipment you have (or don't have), or the length of time you've been observing variable stars. Within each organization you'll find many observers, new and old, who will have questions and concerns similar to yours. Check them out. They not only want your data, their membership is composed of hundreds of other variable-star observers. Each began their study of variable stars much as you have started yours. You will find most members more than willing to help you, answer your questions, share their ideas and assist you in many ways.

British Astronomical Association, Variable Star Section (BAA VSS), Burlington House, Piccadilly, London, W1V 9AG (http://www.telf-ast.demon.co.uk/) The British Astronomical Association (BAA) was formed in 1890 and the Variable Star Section (VSS) was created the following year with the goal of collecting and analyzing variable-star observations.

Observations are reported through The Astronomer, a monthly magazine publishing new observations in all fields of astronomy. As well as assisting amateur astronomers monitor the activity of hundreds of variables and develop light curves, their database enables the section to supply records to professional and amateur astronomers for analysis. An excellent organization composed of very serious amateur astronomers.

The Variable Star Network, Kyoto University (VSNET), Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan (http://www.kusastro.kyoto-u.ac.jp/vsnet/) The Variable Star Network (VSNET) should be recognized as one of the best resources for amateur astronomers when it comes to the study of variable stars simply because of volume. This group of professional astronomers produce nightly lists of variable-star observation reports, monthly activity reports, alerts, and calls for collaboration as well as answering question asked by the amateur astronomy community. The VSNET is found within the Department of Astronomy, Kyoto University, and consists of many, many mailing lists that are used to distribute various messages pertaining to variable stars, especially cataclysmic variables (CVs) and related objects. VSNET distributes observational data regarding the discovery of supernovae, novae, rare outbursts, discovery of new variable stars, and dramatic changes of known variable stars, including compiled data and preprints. VSNET also provides discussions more diversely related to variable stars and variable star observing as well as providing finding charts. They also offer Mira and eclipsing binary data exchange and discussions, newly discovered variable stars and VSNET circulars for CVs and long-period variables. Another excellent organization.

The Astronomical Society of South Australia (ASSA), Honorary Secretary, Astronomical Society of South Australia Inc, GPO Box 199, Adelaide, SA 5001, Australia (http://www.assa.org.au/info/) The Astronomical Society of South Australia was founded in 1892 and is the oldest society of its kind in Australia. It is the only representative body for amateur astronomy in the state of South Australia. Membership is open to people of all ages and professions - the only prerequisite is an interest in astronomy. The objectives of the Society are to promote the science of astronomy and all its branches. You will find charts and information regarding many southern hemisphere stars here. Very serious amateur astronomers with excellent information.

The American Association of Variable Star Observers

(AAVSO), 25 Birch Street, Cambridge, MA 02138 USA (http://www.aavso.org/) The AAVSO coordinates and collects the observations of approximately 600 observers from around the world through a variety of observing programs. Since the founding of the AAVSO

in 1922, about 10 million observations of variable stars have been contributed to the AAVSO International Database by about 6000 observers. Variable star observations are collected, formatted, and submitted each month. There is a very specific format for reporting your observations and there are several ways to submit your reports to AAVSO Headquarters and several observation programs that encourage amateur participation are being conducted under the auspices of the AAVSO. The photoelectric monitoring of bright B[e) stars, the observation of small-amplitude red variables (SARVs), and PEP observation of RR Lyrae stars are just a few of the programs. Another great resource for amateurs since several professional astronomers are associated with AAVSO and are willing to assist those amateurs needing help.

Bundesdeutsche Arbeitsgemeinshaft fur Veranderlicht Sterne (BAV), Munsterdamm 90, 12169 Berlin, Germany (http://thola.de/bav.html) Founded in March 1950 by amateur astronomers in Berlin with the goal to collect, evaluate and record observations in Germany, BAV also produces ephemerides, charts, and publications. The BAV is organized into the following sections: 1) Evaluation and Publication, 2) Eclipsing binaries, 3) Short period stars, 4) Mira stars, 5) Pulsating stars, 6) Cataclysmic and eruptive stars, 7) Photoelectric and CCD-observation, and 8) Charts. Much of this Web site is in English but even if it wasn't, it's another great resource well worth your time.

Association Française des Observateurs d'Etoiles Variables (AFOEV), Observatoire Astronomique de Strasbourg, 11 rue de l'Université, 67000 Strasbourg (http://cdsweb.u-strasbg.fr/afoev/) The French Association of Variable Star Observers was founded in 1921 and the association headquarters is located at the Strasbourg Observatory. Currently, the association has about a hundred observers from 15 countries around the world. The observations made or received by the association has been published in their entirety in Bulletin de l'AFOEV - 2nd series (BAFOEV). They have been stored in the computer of the Centre de Données astronomiques at the Strasbourg Observatory. These observations now number more than 1,500,000 with the first recorded observation dating back to 1896. This database also includes observations made by other associations, including BAV (Germany), HAA (Hun gary), NHK (Japan), NVVW (The Netherlands), Belgian, Norwegian, Swedish, Ukrainian and several astronomical groups in Spain. The observations are supplied free of charge. As with BAV, much of this Web site is in English and it will be worth your time to visit the AFOEV.

The Variable Star Section of the Royal Astronomical Society of New Zealand (RASNZ), PO Box 3181, Wellington, New Zealand (http://www.rasnz.org.nzf) The Royal Astronomical Society of New Zealand collates and coordinates southern hemisphere observations. By a long-standing reciprocal agreement, the RASNZ and BAAVSS exchange observational data on selected northern/southern hemisphere variables. The aim of the Society is the promotion and extension of knowledge regarding astronomy and other related branches of science. The RASNZ encourages an interest in astronomy, and as such is an association of observers and others providing mutual help and advancement of science. It was founded in 1920 as the New Zealand Astronomical Society and assumed its present title on receiving the Royal Charter in 1946. In 1967 it became a Member Body of the Royal Society of New Zealand. A great source of charts, data and other information for southern hemisphere stars. An excellent site and one you should visit.

BBSAG, M. Kohl, Im Brand 8, CH-8637 Laupen ZH ([email protected]) The group of eclipsing binary observers of the Swiss Astronomical Society (BBSAG) acquires data of minima-times of eclipsing binary systems. Estimation of the magnitude itself is usually not required. The aim is to try to determine most exactly the time of maximum eclipse i.e. the time of minimum brightness. Long-term observations allow researchers to make statements on the evolution of such a system. Observations take several hours a night to cover an entire eclipse. A really excellent resource for eclipsing binaries.

The International Supernova Network (ISN) (http://www.supernovae.net/isn.htm) The ISN is strictly an Internet Web site. Its purpose is to share information among supernovae enthusiasts, both amateurs and professionals worldwide. The mailing list is used by members of the ISN to inform of newly discovered supernovae, to share observations, and to discuss topics concerning the search and observation of supernovae. The mailing list produces only a few messages per week but then supernovae are rare. You'll find everything that you need to hunt for supernovae at this Web site.

IAU: Central Bureau for Astronomical Telegrams (http://cfa-www.harvard.edu/cfa/ps/cbat.html) The Central Bureau for Astronomical Telegrams (CBAT) operates at the Smithsonian Astrophysical Observatory, under the auspices of Commission 6 of the International Astronomical Union (IAU) and is a nonprofit organization. The CBAT is responsible for the dissemination of information on transient astronomical events, via the IAU Circulars (IAUCs), a series of postcard-sized announcements issued at irregular intervals as necessary in both printed and electronic form. This Web site can be overwhelming when you first visit. Take your time, visit it several times. There is much of great value to be found here.

The Astronomer's Telegram (http://atel.caltech.edu/) The Astronomer's Telegram (ATEl) is for reporting and commenting upon new astronomical observations of transient sources. Content is limited to 4000 characters.

Chapter 15

i Variable Star I Observing and Amateur Astronomers

It is not the critic who counts; not the man who points out how the strong man stumbles, or where the doer of deeds could have done them better. The credit belongs to the man who is actually in the arena, whose face is marred by dust and sweat and blood; who strives valiantly; who errs, and comes short again and again, because there is no effort without error and shortcoming; but who does actually strive to do the deeds; who knows the great enthusiasms, the great devotions; who spends himself in a worthy cause; who at the best knows in the end the triumph of high achievement, and who at the worst, if he fails, as least fails while daring greatly, so that his place shall never be with those cold and timid souls who know neither victory nor defeat.

### Theodore Roosevelt

Doubt has always existed among amateur astronomers regarding their contributions to the science of astronomy. Naturally, your equipment cannot compare with the professional's; you're unable to build a large telescope on some lofty mountain top and, if you're like the great majority of amateur astronomers, you lack the specialized training and experience of the professional astronomer; so the question of quality is posed. Occasionally, you may wonder, "Are my contributions even needed today?" when orbiting telescopes and 10-meter mirrors are being used by professional astronomers. The superiority of the professional and their equipment appears to leave not the slightest niche for you and me.

In reality, we have many advantages over our professional counterparts. We have access to a telescope whenever we wish, with due consideration for weather, family and social commitments. We have at our finger tips sophisticated equipment that until recently was only available to professional astronomers. As a result, we can produce quality data with very little notice and so we are able to make serious contributions to the science. Like the professional astronomer, we can possess indefatigable resolve, determination and love for the science of astronomy. However, the original question posed, the overall concern regarding valuable contributions, is a valid one.

In reality, the opportunities for us are growing, especially when the interest is variable stars. So as to assuage your concern, I am not attempting to compel you to make contributions to the science of astronomy. Your desire to do so will come naturally or it won't. My belief is that your desire to do so will evolve swiftly as your mind is drawn to the ever increasing wonder and awe that you will most assuredly experience and as the desire to share this new-found experience grows within you.

Without a doubt, the road on which you are about to travel will expose you to amazing sights but it can be rough and difficult; at times it may even appear to be impassable. However, variable-star observers are a tenacious, rugged lot. As a tribute to the amateur astronomer, in 1916, George Ellery Hale wrote:

Hampered, it may be, by lack of equipment, situated where the conditions for research are not of the best, and often compelled to devote <their> best hours to other pursuits, the amateur, rising above all discouragement has continued to pour a flood of new ideas and significant observations into the ever-widening sea of scientific knowledge.

A more stirring testimony to the devotion, determination and passion of the amateur astronomer will be difficult to find.

The history of amateur astronomy, especially variable-star observing, proclaims a strong tradition of contributions. The word "amateur" has its root in the Latin word "amator," or lover. The contemporary definition in vogue is "one who cultivates any art or pursuit for the love or enjoyment of it, instead of professionally or for gain." This definition, with emphasis on "pursuit for the love or enjoyment of it," certainly applies to variable-star observers. You're not going to make any money observing variable stars so if you do it, it must be for love.

The title of this chapter, in essence, refers to you and me. After reading the chapter title, you probably have formed within your mind's eye lists of variable stars, tables of data, detailed observing programs, and all sorts of complex and convoluted exercises developed to keep you occupied and interested. I leave all of that for you to develop. Really, much of the fun you're going to experience is in putting all of that together for yourself. You don't need me, or anyone else, forcing their own agenda down your throat. Refer back to Chapters 10 and 11 for guidance. I've provided you with just enough information so that you can develop your own observing programs or, if you desire, so that you may contact one of the variable-star organizations and request assistance. Chapter 12 provides sufficient guidance for you to begin observing variable stars. Nothing will be gained if I continue to tell you what to observe, when to observe it, or how to operate your equipment. All that you need now is to get out, under the stars, and begin. Start slow, eventually reach beyond your grasp, falter, strive, recover and move forward a little bit at a time. There really is no destination; it's all a journey.

So, in this regard I propose a handful of suggestions to help you during your investigations; some tools that will make you a better variable-star observer, a better amateur astronomer and a better scientist. Are you smiling? I do not use the word "scientist" loosely.

The definition to which I refer, "a scientific investigator," lays a heavy burden upon you. You must decide whether you will remain simply an observer, a humble spectator, one who watches from the side lines, in a sense just counting beans, occasionally excited by others to brief moments of enthusiasm but having no real impact on the overall adventure. Or perhaps, to decide to become a player, one of the team members on the field of play with a chance to make a real difference or at least to enjoy yourself by attempting difficult things. In any case, if you're serious, you're going to be investigating along scientific lines. You will, in fact, be a scientist. As such, while enjoying yourself, be serious about what you are doing. It's important.

Develop your target lists and tables of data, and prepare detailed observing programs. Read the current literature and make bold plans. And while doing so, especially during your serious study of variable stars, make an effort to consider the following suggestions:

Faithfully record important data and take meticulous notes. Both of these activities are acquired skills and both are different. Learn what is important and record it. You'll improve your skills by doing both and you'll get better as time passes. The difference between meticulous and verbose will become clear with time. Important information will soon become evident. And don't forget, not all of the important things will be seen through your eyepiece.

Follow the scientific method. If you're serious, then take yourself seriously so that others will also. Amateur sky divers are serious and take themselves seriously as do amateur cyclists, amateur scuba divers, amateur bird watchers, amateur gardeners and amateur cooks. As an amateur astronomer, you have an obligation to be serious about your work. The scientific method isn't perfect but it has worked well for those who have used it. Learn what it is, how it works and doesn't work, and apply it. You'll be surprised with your results. Believe that what you are doing is going to make a difference.

Do not jump to conclusions. Apply insight, logic and the scientific principle to describe your observations and subsequent analysis. Do not substitute the "law of parsimony" to make or defend a conclusion. Logical consistency and empirical evidence are absolute. Look for the simple answer. Simple revelations can be found within complicated and complex circumstances. Using a principle known as Occam's Razor, scientists realize that all things being equal, the simplest explanation is usually the correct one. The principle states that entities should not be multiplied unnecessarily. Albert Einstein plainly stated, "Everything should be made as simple as possible, but not simpler."

Submit proposals and results to peer review. You must learn to seek and accept "peer" review and criticism from other amateurs and from professionals of your observation programs, methods, and your results. This will be an important step in your continuous struggle to produce the highest quality results in all aspects of your activities. Peer review ensures that your science is sound, is consistent with prior knowledge found within the literature, and that your methodology and your results are repeatable by other competent individuals. Quite frankly, few amateur astronomers are willing to do this without arguing.

On the other hand, few professional astronomers are willing to take amateurs seriously enough to provide the needed attention and guidance with good explanations and gentle patience.

Fortunately, there are some within the professional astronomical community that selflessly help structure and guide amateur efforts: Dr. Arne Henden at the US Naval Observatory in Flagstaff, Arizona; Dr. Joe Patterson, Columbia University; Dr. John Percy, University of Toronto; Dr. Douglas Hall, Dyer Observatory and Dr. Taichi Kato, Kyoto University, come to mind. A handful of others exist too, but you must seek them out with due courtesy and respect.

Organizations and groups of variable-star observers will help you too. Organizations such as the Variable Star Network (VSNET); the British Variable Star Section (BAA VSS); the American Association of Variable Star Observers (AAVSO), the International Amateur-Professional Photoelectric Photometry (IAPPP); and the Center for Backyard Astrophysics (CBA) all exist to foster amateur-professional relationships. Look to them for assistance and guidance.

However, the greatest initiative must come from you. You have the most at stake because you are the one who may invest thousands of dollars on equipment, observing aids, and books with the expectation of serving science, and you will probably spend hundreds of hours observing each year in the hope that your results will make a real contribution to astronomy. For all of this to be productive, you, the amateur astronomer must strive for a new and stronger relationship with the professional community.