Photometric Observing

This section sketches the practical side of the three basic types of CCD photometry: all-sky, "do-what-you-can," and differential. Use the method that is most appropriate for your circumstances.

The goal of differential photometry is to produce accurate magnitude differences between (supposedly) steady comparison stars and program stars. Differential photometry asks, "How has this star changed?" Not surprisingly, this technique is much easier than all-sky photometry because, to a first approximation, extinction coefficients don't matter (both stars suffer the same extinction); and so long as the comparison star has a similar color to the variable, transformation to the standard system is not necessary (because you are interested only in how much the star has changed).

The goal of all-sky photometry is to be able to point your telescope at any sky location, shoot images, and produce magnitudes in the standard system. In a session of all-sky work, you must determine extinction coefficients so that you can correct raw magnitudes for that factor; and you must determine transform coefficients in order to convert instrumental magnitudes into the standard system— which imposes a burden on the observer to record extinction stars and standard stars as well as the program stars that are the point of the observing program. All-sky photometry seeks an exact answer to the question, "How bright is that star?"

"Do-what-you-can" photometry is a simplified method of all-sky photometry advocated by photometrist Brian Skiff of the Lowell Observatory. It is designed to allow amateurs to make meaningful measurements with short observing sessions under poor skies. Briefly, you determine the instrumental transforms and measure extinction values carefully just once, and thereafter sandwich photometric images of variables between images of standard fields. Reducing the data is equally simplified by adjusting the "fit" of the standards and then assuming that variables can be adjusted the same way. "Do-what-you-can" is a practical way for amateurs to produce good results.

10.4.1 Preparing to Observe

Photometry demands forethought, careful record keeping, and meticulous procedures in extracting the data contained in the images. Although an observatory is not absolutely necessary, nothing makes for better observations than a controlled environment with everything at hand and ready to go.

An observing session begins well ahead of time, with the preparation of a list of targets. Some observers track several dozen stars on a nightly, weekly, or monthly basis; while others observe eclipsing binaries drawn from an ever-changing list of stars that need "work." Some observers run intensive programs on targets of opportunity such as newly-discovered variables, novae, or supernovae; while others work closely with professionals to monitor objects like X-ray binaries for sudden (and unpredictable) activity—which, if detected, makes it the target of an orbiting X-ray observatory. Whatever your objective, you must organize and have at hand the necessary finding charts for program, extinction, and standard stars. With your observing plan in hand, you are ready to begin.

• Turn on the CCD camera early. Allow it an hour to reach thermal equilibrium before you start observing. Open the telescope so that it too reaches air temperature.

• Set the clock in your image-logging computer. The best way is to log onto a time service web site that will synchronize the clock in your computer to the correct time. Although computer clocks are not terribly accurate, most maintain time well enough for a night's observations. Another solution is to install a GPS card in your PC, and you'll have precise time all the time.

• Before you begin work, start a new page in your observing notebook. Note the date in civil time (i.e., November 5/6, 2007) as well as the Julian date. Write down the equipment in use (it's amazing how quickly you can forget important details if you don't record them), your planned observing program, and notes on the sky condition.

Throughout the evening, continue making notes. Many high-tech astronomers have discovered the hard way that notes written on paper are easier to access and last longer than text files on a hard disk. Without supporting documentation your data can lose their value.

The following sections present brief scenarios that illustrate strategies and methods typical of all-sky, do-what-you-can, and differential photometry.

10.4.2 Differential Photometry

In CCD photometry, all of the stars in an image have been observed at the same time and through very nearly the same atmospheric path. As a result, atmospheric extinction is the same for all of them, and variations in atmospheric transmission due to haze or light clouds very nearly cancel out. These simplifications are the basis for differential photometry.

Differential photometry varies considerably depending on the observing program, but the underlying principles remain constant: obtaining a series of images showing an object of interest (referred to as "V"), a comparison star (a normal star that hopefully does not vary, called "CI"), and a second comparison star

Differential Photometry Astronomy

Figure 10.7 Phil Kuebler obtained differential photometry on BR Cygni with 40 images taken at two-minute intervals with a Cookbook camera, a 10-inch SCT, and 60-second integrations with a V filter. Despite soft images and poor tracking, he got excellent photometric results. The light curve appears in Figure 10.8.

Figure 10.7 Phil Kuebler obtained differential photometry on BR Cygni with 40 images taken at two-minute intervals with a Cookbook camera, a 10-inch SCT, and 60-second integrations with a V filter. Despite soft images and poor tracking, he got excellent photometric results. The light curve appears in Figure 10.8.

called "C2," or the "check" star. The purpose of the check star is to verify that the CI comparison star does not vary. A time series of images can run for many hours and contain hundreds of images.

When reduced, the observation is the magnitude difference between the variable and comparison star, usually written as V - CI (variable minus comparison). To monitor that nothing has gone awry, the difference between C1 (the comparison star) and C2 (the check star) is also extracted as C2 - CI2.

For greater precision, observers sometime employ more than two comparison stars. By summing multiple comparison stars, they create an aggregate comparison star with a large photon count and reduced statistical error.

Below are profiles of a few typical observing programs.

Eclipsing Binary Stars. When the angle between the orbital plane of a binary star and our line of sight is small, we observe eclipses with each orbital revolution. Periods of close binaries range from a few hours to several days. If the period is constant, we can predict the time of eclipse years in advance; but if the stars are interacting and gas flows from one to the other, the period can change. Measuring the time of mid-eclipse provides a very sensitive tool for probing the physical nature of the stars; hence, professional astronomers have a continuing need for measured times of mid-eclipse. Requests for observations of particular

BR Cygni

Phil Kuebler

Scorpius Constellation Number

0.625 0.650 0.675 0.700 0.725 0.750 Julian Date 2,450,996+

Figure 10.8 This light curve shows the eclipsing binary BR Cygni at mid-eclipse, as measured from 40 images like the one in Figure 10.7. Filled circles are V -C1 and open circles are C1 - C2. Phil measured the time of minimum as JD 2,450,996.6709 ± 0.0003. Image and data courtesy of Phil Kuebler.

stars are most often channeled through organizations such as the AAVSO and the Center for Backyard Astrophysics.

The observing protocol is simple: as a clear evening comes up, the observer scans a list of program stars and computes their expected times of minimum. If a program star is expected to eclipse that night, the observing run is scheduled to begin an hour or two before the anticipated time of minimum. Before and after the observing run itself, the observer allows time to make dark frames and flat fields.

The observing run consists of making images at regular intervals (usually one or two minutes) through the time of eclipse and for an hour or two afterward. If the camera software has an "autograb" or "multiple image" feature and the telescope tracks well, the observer has little to do but oversee that everything moves along smoothly. A second set of dark frames and flat fields is then taken as a hedge against changes in the camera or telescope.

To reduce the data, the images are calibrated and the V, CI, and C2 stars are measured on each one. If the time-of-minimum prediction was good, the eclipse is obvious in the plot of V - CI against time. If the equipment functioned properly, the corresponding plot of C2 - C1 is flat and straight. To extract as much information as possible from the light curve, the data can be analyzed statistically to obtain the best-fit time of minimum, often within less than one minute. See Figure 10.8.

The observed time of minimum is then reported to the AAVSO or to the astronomer who requested observations of the star.

Exoplanet Transits. Planets orbiting stars other than the Sun can be discovered and their properties determined by observing the decrease in the star's light when the planet transits its disk. Although a signal-to-noise ratio of 100 or better is required, this is well within the ability of many CCD observers.

Preparation for an exoplanet transit observation is much like that for an eclipsing variable star. Check the ephemeris for future transits, and begin a time series several hours in advance. Continue observing through the predicted transit time, and continue as long as practical after the transit. The "baseline" magnitude established before and after the transit enables you to distinguish the slight decrease in magnitude from variations caused by statistical uncertainty and other sources of noise.

If you are serious about exoplanet work, join a group that regularly observes and reports on newly discovered planets. Amateur observations help to establish the reality of the transit, aid in pinning down its period and amplitude, and ultimately, in documenting the characteristics of the planet.

Other Variable Stars. To obtain good light curves for variables with periods of a few days to a year or more, regular observations are needed. These may be Cepheid variables (which sometimes do strange things—like Polaris, a Ceph-eid that nearly quit varying), RR Lyrae stars, RS Canum Venaticorum stars (which vary because of enormous starspots on their surfaces), or many other types. The AAVSO maintains lists of interesting variables that need to be observed.

With a clear evening in the offing, the observer makes up a list of program stars. For extremely slow variables, only one observation per month may be needed, but for more rapid ones, an hourly check may be called for. The run itself depends on what's on the schedule. For slowly-changing stars, an observation might consist of three 60-second integration images through each of three filters (such as B, V, and I) and take a total of 15 minutes. If the program consists of a dozen such stars, the observer could begin at dusk and complete precise three-color differential photometry on 12 objects by midnight.

When time permits, the images are calibrated and V - CI and C2 - CI are measured on each one. Since everyone working on this particular variable uses the same comparison star, the V - C1 measures from different observers mean the same thing. Of course, you check the C2 - CI values for consistency from one observing session to the next.

At the end of the month, observer sends a report to AAVSO headquarters listing high-quality three-color differential measurements on 16 stars made during five observing runs.

10.4.3 All-Sky Photometry

A night of all-sky photometry requires orchestrating three simultaneous observing programs: finding extinction coefficients, finding transformation coefficients, and observing program stars. This makes it challenging, to say the least, but also an skill well worth pursuing.

To illustrate what's involved in this method, suppose you have been asked to assist with two new comparison-star charts for use by the observers who contribute visual estimates to a well-known variable-star organization. Each chart is 15 minutes of arc square and centered on a variable. Suitable comparison stars are marked with their visual magnitudes. Observers estimate the magnitude of the variable by comparing its brightness with the comparison stars. If the magnitudes of the comparison stars are not accurate, the estimates will not be correct. Your photometry must be as accurate as possible.

To make sure that the comparison stars will serve their purpose, you need to observe each candidate in B, Y, and I to insure that no red stars (which tend not only to be variable, but also to fool the eyes of visual observers) are included among them.

You begin planning for the observation by figuring out when the chart fields will be highest in the sky, and you identify two Landolt Selected Areas—one that will cross the meridian an hour before and the other an hour after the chart fields. Fortunately, you have three hours of darkness before the chart fields transit, so there is ample time to obtain extinction and standard-star images. This adds to your program a third Landolt field that will transit shortly after full darkness falls.

After rejecting several nights for streaks of high cirrus after sunset, you rejoice when a big front clears the dust and haze from the lower air and leaves the whole sky crystal clear. At last you have your "photometric" night! An hour before darkness, you have set the computer's clock, fired up the CCD, and opened the telescope to cool.

During twilight, shoot your bias, dark, and flat-field frames. Then, as twilight ends, you'll be ready to identify two Landolt areas that are rising. Make two 120-second integrations of each field through each of the three filters. Between each exposure move the telescope slightly so the star field falls on slightly different groups of pixels. As the evening progresses, you must come back to observe these fields as they rise and are viewed through progressively less air mass. Also, shoot some Landolt areas close to the meridian. In this way you can piggyback the exposures needed for extinction data while simultaneously making standard star fields.

With the high-air-mass exposures taken, you locate the Landolt area that is flear the meridian, carefully focus, and repeat the exposure sequence. As the night progresses, you will make more images of this region as it sets into progressively greater air mass. It doesn't hurt to check that extinction coefficients for the eastern and western sky are the same.

At this point, you cap the telescope and take 16 bias frames and 16 dark frames; then rig the light box on the telescope and take 16 flats through each of the three filters, and take 16 flat darks. Good calibration is vital to accurate photometry, but it certainly helps to fill up the hard disk on the computer! The bias and flat-frame exposures are short, but a set of dark frames can take half an hour.

If your telescope is light-tight, make dark frames during twilight.

With calibration behind you, you concentrate on imaging the two rising Landolt fields through the three filters. You want plenty of data points to extract extinction coefficients and transform the magnitudes to the standard system.

As the chart fields approach the meridian, and you locate and make three exposures with each filter for each chart field, shoot the Landolt areas, and then shoot the chart fields again. Finally, shoot another set of images of the third Landolt field, which has sunk low in the western sky.

In theory, you now have all the data that you need—but as a conscientious observer, you image the two Landolt fields again and make a backup set of calibration images. By the time you close up for the night, you have gathered a very complete set of data. Of course, if you have time, you'll make another set of observations on another night as proof against zero-point errors, and as a check that none of the new standards is itself a variable!

Extracting magnitudes is a time-consuming but satisfying activity. You begin by computing the air mass for every exposure made during the night. Next, to be sure that you can identify the correct stars in each of the Landolt fields, print a negative hard-copy of each field and verify the identification of each standard star astrometrically. You have selected eight stars in each Landolt field as your standards, but it only takes a few extra minutes to make sure that no errors will creep into your work.

Now examine each image and perform aperture photometry on each standard star. As you measure, transfer the data—the raw instrumental magnitude, the air mass, and Landolt's standard magnitude—to a spreadsheet program. Since you obtained five images in each of three colors for the rising Landolt fields, and four images in each of three colors for the setting Landolt field, you have 42 images to measure. When you are done, the spreadsheet solves for extinction coefficients in each color and produces transform coefficients that convert your raw instrumental magnitudes and air masses into standard B, V, and / magnitudes. Be glad you don't have to compute these values by hand!

Now comes the fun part: examine the images of the chart fields, two sets of three exposures in three colors for each of the charts—18 images in all. Again, measure raw instrumental magnitudes for each star; then enter those and the air mass for the image into spreadsheet software. This time, the output is a standard B, V, and I magnitude for each star in the chart field. To your pleasure, the results from the separate images agree to better than 0.02 magnitude in every case. The result of your work is standard B, V, and I magnitudes for 46 candidate comparison stars in the two charts. As you submit your report, you know you have done a good job.

10.4.4 "Do-What-You-Can" Photometry

Most amateur astronomers live and observe at humid, low altitude sites. They can rarely observe more than a few hours simply because it usually doesn't stay clear any longer than that, or because they have to go to work the next morning. Con ventional all-sky photometry appears too daunting, quite apart from the complexity of performing data reduction, so no photometry gets done.

A realistic solution to this dilemma is to adopt a mode of observing that makes some approximations; that is, observing in "do-what-you-can" or "what-you-can-get-away-with" mode. As long as you don't feel compelled to press for high accuracy, you can rest assured that your results are pretty good. Very importantly, observations can be made quickly in this mode, so you will make the observations.

To begin with, you need only two filters: Vand I. This allows you to measure and correct for the color terms. The V filter ties into the V and visual magnitudes. Also, the V-1 color is an excellent temperature indicator for all stars, and it even works for the reddest stars. This field is challenging enough in its own right that trying to do photometry in four colors is bound to be discouraging. Instead, do what you can do, which is accurate two-color photometry.

At some point early on in the process of getting data from a CCD, would-be photometrists should spend several stable photometric nights—the kind of nights that occur only once or twice a month—observing nothing but bona-fide standard stars. The idea is to establish a good set of instrumental transformations and to get a feeling for the extinction values at your locale. Once you have established the transformations, check them once or twice a year to detect changes or problems.

In an ideal world, every observer would measure the extinction coefficients every night. However, if you observe from a site below 1,500 feet elevation, you can simply assume a V coefficient of 0.35, except on winter nights when the air is particularly dry and clear (when you can assume a V coefficient of 0.25). Extinctions for colors other than V are offsets; for B, the extinction coefficient is 0.13 higher than V; for R, it is 0.04 lower than V, and for /, it is 0.08 lower than V.

With the instrumental transformations established, the main thing needed for new observations is the zero point. This varies mainly because of night-to-night changes in extinction and, to a lesser degree, instrumental variations. A simple procedure to set the zero point is to shoot one or two standard fields, then shoot the target, and reshoot the standard field. That's it! Your standard field can contain a single star if need be, but it is usually not hard to find a good sequence near the target.

To reduce your observations, apply the mean extinction value and the previously determined color terms to the data. This will produce nearly-correct standard magnitudes for the reference stars. Then compare these magnitudes with "real" magnitudes of the standards, and apply any difference to the magnitude and color of the target. As long as you do not observe targets at high air mass, using approximate extinction coefficients will not compromise your data, because the standard stars are close to the target, and errors in extinction show up only when there is a difference in air mass between the standard fields and your targets.

"Do-what-you-can" photometry has the merit of being quick, which is a big advantage at a poor site. A set of observations in two colors shouldn't take more than 10 to 20 minutes, depending on how faint the target is and how well the tele scope points. The speed of working minimizes transparency variations, and the method does away with making tedious extinction observations.

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