Citizen Science with variable stars Brought to you by the AAVSO, the Na3onal Science Founda3on and Your Universe Help Astronomers Make Discoveries! Variable stars are stars that change in brightness over 1me. There are too many for professional astronomers to monitor alone. So, thousands of amateur astronomers help out by watching these stars over days, months and years. Amateurs are also helping with the analyza1on of that variable star data. This guide will introduce the basics in variable star data analysis. Eventually, we hope you can write scien1fic research papers to be submiaed to professional research journals. This tutorial is the first step on that path Ci#zenSky is a collabora*on of the American Associa*on of Variable Star Observers (AAVSO), the University of Denver, the Adler Planetarium, the Johns Hopkins University and the California Academies of Science with support from the Na*onal Science Founda*on. Par1cipate in one of the oldest ci1zen science projects in history! Thousands of people just like you will also be helping out. Astronomers need large numbers of people to get the amount of precision they need to do their research. You are the key. This is a companion to our 10 Star Tutorial which teaches you how to observe variable stars. Visit CitizenSky.org to download that tutorial. Header artwork is reproduced with permission from Sky & Telescope magazine (www.skyandtelescope.com)
What is epsilon Aurigae? Epsilon Aurigae is an enigma. It looks like a single, bright star from Earth. However, it consists of at least two stars (and possibly more) in the same solar system. Unlike our rela*vely stable and clean solar system, this one is very complex and dusty. Every 27 years, epsilon Aurigae is eclipsed by a very large object. Astronomers don't know what the star's colossal partner is, but one leading theory suggests it's a gas cloud more than a thousand *mes as wide as the sun that harbors one or two small stars at its core. Alterna*vely, the object at the center of the cloud may be a black hole or a single larger star that has somehow siphoned gas from epsilon Aurigae to create an enveloping cloak of darkness. Each eclipse lasts nearly two years, by far the longest in any known binary star system. The most recent eclipse began in August, 2009 and is expected to last un*l May, 2011. Amateurs (and a few pros) are observing this star as part of an interna*onal campaign run through the Ci*zen Sky web site. Most use their regular eyes to make a visual es*mate. But a few use DSLR cameras, web cams or PEP detectors to make a photometric es*mate. These es*mates of epsilon Aurigae s brightness act as data for researchers - both amateur and professional. This 5- Star Analysis Tutorial is meant to introduce you to basic ways of data processing and inspec*on. It does not assume a background in astrophysics, sta*s*cs or anything similar. However, all good researchers need to understand what their data actually mean. So if you have never made a variable star es*mate before, we strongly recommend reading our 10- Star Observing Tutorial. That will give you an idea of where these data come from and what it means to actually observe a variable star. The tutorial is at this URL: h]p://www.ci*zensky.org/content/10- star- training. As always, visit the Ci*zen Sky web site for much more informa*on on epsilon Aurigae, variable stars, data analysis, latest news and more. Also, visit our online forums for help and ideas! www.ci1zensky.org
Looking at a Light Curve Change over <me What is a light curve? Sadly, they are not cool weapons from Star Wars (although Jedi may find such items useful for figh3ng around corners). Light curves are a fundamental tool for variable star astronomy. They are rela3vely simple and easy to grasp. They are simply a graph of brightness (Y axis) vs. 3me (X axis). Brightness increases as you go up the graph and 3me advances as you move to the right. Here is a light curve of epsilon Aurigae from its last eclipse: Each of these data points is a single brightness es*mate of the star made by an amateur astronomer This light curve shows that the star began at a brightness of magnitude 3 in 1982. Around mid- year it began to rapidly dim un3l it reached brightness of magnitude 3.8 by the end of the year. It remained there un3l the beginning of 1984 when it began a slower climb back to normal brightness. By the middle of 1984, it was almost back to normal brightness.
That previous light curve was idealized, in that it was processed to only include the best observa3ons to make it clear. Now let's look a more complicated, real- world light curve. Here is a recent light curve of the bright star Betelgeuse (a.k.a Alpha Ori to astronomers) in the constella3on Orion: Each dot in this light curve is a visual observa3on of the star submized to the AAVSO Interna3onal Database. The numbers on the X- axis are Julian Dates. That's a standard format that astronomers, especially variable star astronomers, use to record dates. This light curve covers observa3ons made from mid 2007 to mid 2009. No3ce that there are many observa3ons made on the same dates. But some3mes they don't agree! That's because we're all human (poli3cians excepted) and so will make different es3mates of a star's brightness. We chose this star as an example because it is very bright and very red. This makes it extra hard for humans to make consistent observa3ons. We call this varia3on in brightness es3mates sca/er.
Mean Curves They are actually quite nice Here is the same light curve, but with a mean curve drawn through it. The red line reflects the average observa3on made at that 3me. More precisely, we calculated an average brightness of the star in 30- day increments then drew a line between the average points. The ver3cal red bars you see along the line is an error es3mate. It's a sta3s3cal value that provides an idea of how much you can trust the red line. (There is a 95% chance that the real data falls within that horizontal error - a common benchmark scien3sts use.) A good rule of thumb is to try to draw a straight, horizontal line between the error bars. If you cannot draw such a line, then you can be confident the varia3on is real. If you can, it means there is no clear varia3on in the data. There may s3ll be real varia3on, but you ll need more analysis to prove it. No3ce in the first set of data in the light curve that you cannot draw such a line. But you can through most of the data in the second set. The second set is noisier (i.e. has more scazer) and we re less confident that is shows varia3on.
Make Your Own Light Curves - Web Ci3zen Sky has two free variable star light curve generators you can use. One is on the web site and the other is a downloadable Java applica3on. The online light curve generator is available at Ci3zenSky.org by clicking on the Data- >Submit- >Create a Light Curve tab at the top of the home page. To plot a light curve, just choose a star from the list*, enter a date range and then click Plot Data. It s that simple! The rest of the options are just that - optional! If you have submitted observations of any of these stars, type in your observer code here and your observation will be highlighted, allowing you to compare your observation(s) with others. *For simplicity reasons, this interface is limited to just the 10 stars in our 10-Star Observing Tutorial. However, you can use the AAVSO Light Curve Generator to plot a light curve of any variable star in the database (tens of thousands!). It is at: http://www.aavso.org/data/lcg/
Make Your Own Light Curves - Java One of the Citizen Sky participant teams has been working since June 2009 on a variable star analysis software package called VStar. It can be downloaded from the following URL: hzp://www.ci3zensky.org/content/vstar Simply click on the Download Vstar Now BuZon. The soiware requires Java and has been tested on Windows, OS X, Linux and other plakorms. The program should launch directly from your web browser. No need to formally install it. The first 3me you run it, you ll see something like this: Click on this button to load data. You ll be prompted for the star name and a date range of data you d like to see. VStar currently requires this date range to be in Julian Date format, but a future version will accept standard calendar dates. Until then, you can convert calendar dates to JD at this URL: hzp://www.aavso.org/jd- calculator
Make Your Own Mean Curves - Java Look familiar? The light curve looks a lot like the one on page 4 of this tutorial. Except we now have some green colored dots. Those are photometric observa3ons made by digital detectors instead of eyeballs. You can add/remove them by clicking Change Series ( series meaning a collec3on of related data). You can zoom in on a group of data by just drawing a box around it. Zoom out by lei- clicking anywhere on the graph. You can plot a mean curve by selec3ng Plot Observa=ons and Means. Type in different values in the Days per Mean box to see how it affects the mean curve. This is a tricky part of analysis. How much do you manipulate the parameters before you are stretching your results?
Modeling Data Test your ideas We have also created an online tool to to see how well various parameters recreate the photometric light curve observed during the past and current eclipses. This is also a Java tool so it also requires Java to be installed on your computer. However, this tool is run within a web browser window. Load it at the following URL: hzp://www.ci3zensky.org/content/epsilon- aurigae- simulator The program lets you change various physical parameters of the epsilon Aurigae system and see what the resul3ng light curve would look like. Use this tool to compare the light curves of epsilon Aurigae with your ideas of the system. What does it say about the shape of light curves in general?
Phase Diagrams The shape of things When the same cycle repeats over and over as regularly as clockwork, we refer to this as periodic behavior. If a star (or any other phenomenon) is perfectly periodic, then its variation depends only on where it is in its cycle, a quantity called the phase. For example, a 24-hour clock repeats the same behavior - with a period of 1 day. Each day the clock goes through one cycle, and each cycle is just like every other cycle. If we want to know what the clock reads, we do not need to know which day (cycle) it is, we just need to know the time of day (how far we are into the cycle). Ex: 2:15 a.m. is 2 hours, 15 minutes into the cycle of the day. A phase diagram will fold a light curve on a certain period. This allows us to see the shape of the light curve as if all the data occurred in the same cycle. For example, the light curve of delta Cephei to the right shows many cycles so it s difficult to see its shape. But with a phase diagram (right), we put all the data on one (fictional) cycle and can see the shape of the light curve quite well. In this example, we can see that delta Cephei rises in magnitude very quickly, but takes much longer to drop in magnitude. Much more info on phase diagrams is available in Chapter 12 of our online curriculum Variable Star Astronomy, available at the following URL: h?p://www.aavso.org/educabon/vsa/
Period Analysis The length of things One of the most important proper3es of a variable star is its period. Astronomers have lots of tools at their disposal to look for periods in variable star data. One of the most basic tools is the previously men3oned phase diagram. A more advanced tool is Fourier Analysis*. VStar has a basic Fourier analysis rou3ne under the Analysis menu. Below is the result of running the period search on delta Cephei. Amplitude is a measure of the change in brightness detected. The Frequency is the period in cycles per day. The peak at 0.2 means that delta Cephei completes a cycle every 5 days or so (1/0.2=5). In general, you want to look for peaks that stand out above all their neighbors, as this one does. * A full discussion of Fourier Analysis is beyond the scope of this tutorial. But a good start is an online Bme series analysis tutorial wri?en by Dr. Ma?hew Templeton and available at: h?p://www.aavso.org/bme- series- tutorial
What s Next? On the following pages are tutorials based on five different variable stars. The goal is to become comfortable with using VStar (or other light curve generating software) to view and manipulate variable star data. This tutorial is a very elementary look into variable star data analysis. Consider this just a first step. Citizen Sky will continue to post more advanced tutorials on the web site over the coming years. We also have an online discussion forum dedicated to data analysis. Post your ideas and questions there! California Academies of Science The 2nd Citizen Sky workshop was held at the California Academies of Science on San Francisco Sept. 3-5, 2010. The focus of this workshop was on data analysis and scientific paper writing. Video for the workshops has been placed online for those who cannot attend at the following URL: http://www.citizensky.org/content/talks-second-citizen-sky-workshop Got a research question? You don t have to do it all yourself. Setup a Citizen Sky team! We will assign an astronomer to act as an advisor to your project. Work with others to find a good research question, analyze data, prepare results, etc. We can also help you come up with project ideas.
Mira (omicron Ce3) Mira is one of the most popular and well studied variable stars. It is a pulsating red giant with a companion that is likely a white dwarf. You can see these pulsations in its light curve. At its maximum (peak), it can easily be seen with the naked eye. At its minimum (nadir), it requires good binoculars or even a telescope to see it. Your Mission to inves1gate a light curve. Use VStar and load data for Mira from 2000-2010 (JD 2451544.5-2455197.5). NoBce the magnitude range between the maxima and the minima, will it ever be brighter than epsilon Aurigae? Zoom in on the latest cycle. How bright do you think it will be tonight? What about a month or even a year from now? NoBce there are gaps in the data. What do you think causes them? X- ray image of Mira showing both stars and a tail of material between them. Image by NASA/CXC/ SAO/M. Karovska et al. Zoom out (right click then choose Auto Range) to load the enbre light curve on the screen. Click Change Series and then click the boxes next to the Johnson B, R, and Cousins I bands. This will load photometry in the blue, red, and far- red/infrared bands. Which band of data is the brightest? Can you explain why? Click Change Series again and check the box next to Fainter Than. This will load reports where the observer said I can t see it, but the faintest comparison star I can see is X and X is the brightness of that comparison star. Basically, this is saying that Mira is fainter than the reported magnitude, but the observer didn t know exactly how much fainter. NoBce any trends in the fainter- than data? Lastly, select Preferences in the File menu. You can change all the colors of the data there. Feel free to set it to colors that are easy on your eyes!
Betelgeuse (alpha Orionis) Alpha Orionis is a famous star. It s the bright red supergiant in the armpit of Orion the hunter. It is so large that it is likely to become a supernova at the end of its life (perhaps in a few thousand years). Because it is so bright and so red, it is difficult to observe visually. When humans look at a red star over a long period of Bme, it appears to get brighter. This is a result of the Purkinje effect and it creates lots of sca?er in light curves. Unlike Mira, Alpha Ori s atmosphere is not stable, so it pulsates semi- regularly with no dominant long term period. Together, that makes for an interesbng light curve to untangle! Your Mission to make some mean plots. Use VStar and load data for alpha Orionis. Select All Data. When you have noisy data, somebmes a mean curve can be more informabve. Click Plot ObservaBons and Means. Then zoom in on the last 5-10 years of data. Change the bin size of the means. Experiment with values between 7 and 100 days. Watch the error bars. Near- infrared image of Betelgeuse from ESO s Very Large Telescope. Which values give you mean curves that best represent the acbvity of the star? How did you make that decision? Select Change Series and uncheck the visual and Johnson V data. This will remove the clu?er, allowing you to focus on the mean curve. Can you esbmate what the brightness of alpha Orionis will be tonight, next week or a year from now? What are the major differences you see between this light curve and the one you saw from Mira? Discrepant Data: This is data that AAVSO staff has flagged as being of quesbonable accuracy for a variety of reasons (typo, misidenbficabon of star, etc.). Usually you ll want to ignore discrepant data. But somebmes it is interesbng to look at it. In this case, click Change Series and check the discrepant data. NoBce how the light curve changes when discrepant data is displayed!
X Cyg X Cyg is a variable star discovered by a Boston- area amateur astronomer in 1886. It is a cepheid variable star. Cepheids are among the brightest variable stars being about 1,000 to 100,000 Bmes brighter than the Sun and 3-30 Bmes as massive. They usually have a very reliable period and shape, which allows them to be used as standard candles for esbmabng the distances to nearby galaxies. The disbncbve shark fin- like pa?ern in the shape of the light curve is the trademark of a Cepheid, in that the rise to maximum is usually much faster and smoother than that of the rate of decline. Your Mission to make phase plots Use VStar and load data for X Cyg. Select data for JD 2447000-2448000 (roughly 1987-1990). NoBce that when you zoom in on the data, you can see that the star s brightness changes but you can t see the shape of the cycle. Under the Analysis menu, select Phase plot. The period that shows up in default (16.386332 days) is taken from the AAVSO database and was determined by other researchers. SomeBmes it is accurate, somebmes it is not. To test it, just click OK. Ah, now you can see a shape. VStar always show you two cycles (nobce the X- axis units). ` Click New Phase Plot and change the period to 16.0 days. NoBce how large of a difference such a small change makes! Click New Phase Plot and change the period to 32.8 days, which is double what the default period was. How can you explain the new shape of the phase plot? Note: Phase plots only work on stars that have stable periods. So some stars will never have nice phase plots. The Cepheid variable X Cygni and its discoverer, Seth C. Chandler, Jr. (1846-1913).
Delta Cephei Like X Cyg, Delta Cephei is also a cepheid variable star. In fact, delta Cephei is the prototype star, meaning it was the first of the type (and got the honors of naming the classificabon). It is a bright visual variable star with a magnitude range of around 3.6-4.6 and a period of only 5.6 days, making it an easy- to- observe star for beginning variable star observers. Your Mission to search for periods. Use VStar and load data for delta Cephei. Select data for JD 2440587-2444239 (1970-1980). Under the Analysis menu, select Period Search. Arer a few seconds, a dialog box will appear with the results. Any periods detected appear as peaks in the plot. The cleanest periods are ones with sharp peaks that are high above any neighboring peaks. You can zoom in on a period by drawing a box around it. Remember that cepheids have nearly perfect periods. What is the length of the period you see? (Convert frequency from cycles/day or click the Amplitude vs. Period plot.) Close the dialog box, then plot a phase diagram with the new period you detected. How does it look? (Remember to plot mean curves if there is sca?er in the data.) AAVSO/CiBzen Sky observing chart for delta Cephei. A larger version of the chart is available in our 10 Star Tutorial for visual observing of variable stars.
LX Cyg LX Cyg is a red giant star, similar to Mira. However, monitoring over the past century has revealed some interesbng behavior. It may be going through a phase called a thermal pulse, an burning of the helium shell surrounding the degenerate carbon- oxygen core of the star. Your Mission to search for more periods. Run VStar and load all data for the star LX Cyg. Do a period search. NoBce the period is noisy in that there are lots of periods bunched around each other. That means there is no clearly dominant period in this analysis. Load the data for just 2439800-2447500 and do a new period search. NoBce it is a li?le cleaner in that the periods are sharper. Click the Data tab to see the raw data. The power column tells you the stabsbcal significance of the frequency. The greater the power, the greater the significance. NoBce a bunch of strong signals near the top of the table near frequency 0. This is called red noise and can be ignored for this analysis. Look for the frequency range that corresponds with the peak in the analysis plot. Which frequency has the highest power? That is the period found in your analysis. (Hint: You can click Top Hits to skip to the periods with the highest power) Now do the same for the data from 2447500 to 2455000. Compare the periods from the two data sets. What could that mean? The period column is just the frequency translated into days (p=1/f) Note: If this star interests you, also check out the data for S Ori!
Publica1on Hypothesizing, collecbng data and analysis are major parts of the scienbfic method. However, they are not worth much if they are not ulbmately shared with the greater community. It is only through this sharing that research can be independently verified and expanded. Since 1975 the AAVSO has published a journal of research papers by amateur and professional astronomers. The Journal of the AAVSO (JAAVSO) is peer- reviewed by professional astronomers. It is also indexed in NASA s Astrophysical Data Service (ADS), which is the main index of astronomical research publicabons and the first place any astronomical researcher goes when searching literature. As a result, any paper published in the JAAVSO will appear in ADS search results and can be cited by other authors. The JAAVSO is available free to the public at: h?p://www.aavso.org/publicabons/ejaavso/ A special edibon of the JAAVSO will be dedicated to papers wri?en by parbcipants in the CiBzen Sky project. These papers can range from rigorous research arbcles to review arbcles to le?ers- to- the- editor. A call for submissions will be posted in 2011 with a 2012 deadline. If you are interested in submitng a manuscript please stay tuned to the CiBzen Sky web site. Details will be announced there around the Bme of the 2nd CiBzen Sky workshop in September 2010. Teams will be established for people who do not feel up to the task of wribng a paper on their own. But the first step is to become familiar with this tutorial, then start thinking of your own quesbons about variable stars.