Astronomy 142 — Project Manual

Spring 2019

1 RR Lyrae stars and the distance to globular cluster M3

1.1 Introduction

In the following, we repeat a classic experiment: detect the periodically-varying stars in a globularcluster and thereby measure its distance, by considering the stars to be standard candles. Specifi-cally, we will measure the time-average luminosity of the nearby star RR Lyrae and the time-averageflux of stars in M3 that vary with the same period as RR Lyr, combining these measurements todetermine M3’s distance.

This observing project will involve frequent visits to the telescope over the course of1–2 weeks, hopefully including a few nights in a row. Everyone who opts for this projectwill share their data and receive everyone else’s in return. Each student will performhis or her own analysis and write an independent report on the results.

Stars in the instability strip of the HR diagram have been fundamental in the determination ofthe distance scale of the Universe. These stars radially pulsate, often in their fundamental acousticmode. As we have seen in class, their pulsation periods Π vary inversely with the mass density ρ ofthe star:

Π = 4

∫ R

0

dr

vs∼=√

6π

γGρ(uniform density star) (1)

Lower average density leads not only to longer periods, but also to larger luminosities L, in partbecause lower-density stars are much larger than higher-density stars of the same mass. Thus, agiven type of pulsating star exhibits a strict relation, often linear, between Π and L. Such relationscan be determined by observation of the periods and fluxes for stars whose distances are accuratelyknown, for example, by trig. parallax. Once the Π–L relation is determined, it can be used as astandard candle to measure much greater distances to faint stars of the same type and period. Themeasured period Π tells us what the star’s luminosity is, and the measurement of the star’s flux fyields the distance r,

r =

√L

4πf(2)

Henrietta Leavitt invented standard candles in the course of her observations, during 1908–12,of thousands of periodic variables in the Magellanic Clouds. Her variables are classical Cepheids,the highest-luminosity Population I inhabitants of the instability strip; the Π-L relation for classicalCepheids is called Leavitt’s Law in her honor.

The instability-strip variables in globular clusters include supergiants, giants, and stars close tothe Main Sequence: W Vir stars, RR Lyr stars, and SX Phe stars, respectively. RR Lyr stars areby far the most numerous. Few of these stars lie in the solar neighborhood; it has been possibleto measure trig parallax for only a handful of RR Lyr stars.1 One of these is RR Lyrae itself, forwhich such variability was discovered by Williamina Flemming in 1901. Taking RR Lyrae to be astandard candle, we can measure accurate distances to globular clusters, the distribution of whichis a good tracer of the global structure of the Milky Way.

1The ESA Gaia mission will provide parallaxes for many more field RR Lyr stars. It will not, however, be able tomeasure parallax for stars in many globular clusters; the RR Lyr standard-candle technique used in this project willremain the best way to measure globular-cluster distances for a long time.

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1.2 Experimental procedure

1.2.1 Planning

1. Form, or join, a team of two or three. Members of each team must have compatible schedules;make sure each of you can generally go observing on the same set of nights of the week.

2. As a stretch of clear weather approaches, choose your observing night in coordination withother teams. Look up or calculate the times of sunset and sunrise, and the length of the night.Also look up or calculate the times during which M3 and RR Lyrae will be high enough in thesky to observe (> 20◦ elevation), and the times at which each object transits.

3. If other groups are also interested in this experiment, agree with them on the details of theobservations: basically, adherence to the procedure described below, and on how you will namedata files. There are virtues in compiling data from multiple nights.

4. Unlike the observing project in AST 111, this one takes all night. Therefore, you will berequired to sleep at the Gannett House after your observations are complete and before re-turning to campus. Plan accordingly by packing for an overnight stay and discussing withyour team and the instructors the all-important requirement of packing sufficient food. (Un-fortunately, Mees is beyond the range of pizza delivery.) Familiarize yourself with the rules ofthe observatory sleeping quarters at the Gannett House.

5. Bring your notebooks, and bring a USB drive with at least a few GB of free space. You woulddo well to also bring your personal laptop or tablet computer. Paper copies of the experimentprocedure (i.e. this document), telescope checklist, and CCD-camera observing guide will alsoprove useful, though these will also be accessible to you online at Mees.

6. Arrive well before sunset. You have one important task to carry out before the sky getsdark: the acquisition of flat-field data. The telescope and camera must be ready to observe,and your team must be ready to work, no later than sunset.

1.2.2 At the telescope

Two team members should be stationed at one of the following two jobs: telescope operator andCCD camera operator. The third member (if there is one) should help with reading the instructionsand assisting the other two members at their tasks. Rotate the team members among the jobsfrequently enough so that no one gets bored.

1. Start the telescope and initialize its pointing by following the steps in Section I of the MeesObservatory telescope checklist. This leaves you with DFMTCS, FrameGrab, and TheSkyrunning on the TCS computer.

2. Start the CCD camera, its computer, and CCDSoft, and focus the telescope by following thesteps in Section I of the Mees Observatory CCD camera checklist. This includes taking flat-field data, following the steps listed in Section V of the camera checklist. You should nowhave CCDSoft running on the CCD camera computer, and both the camera and telescope areready to observe.

3. On TheSky, search for M3 (Cntl-F for the search window), click on it to bring up its informa-tion window, and check to see if it is above the telescope’s artificial horizon (elevation > 20◦).If so, you are ready to start observing! (If not, point at something that is above the horizonand take a look at it through the eyepiece. You should not have to wait too long before M3rises.)

Go up to the telescope and look at M3 through the eyepeice. Make sure everyone has a chanceto do so before continuing!

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4. As a guide star, we recommend a 12.5 magnitude star which is known to TheSky as GSC2004:639. Find it by bringing up the search window (Cntl-F) in TheSky and entering itsname. Follow the steps in Section II of the camera checklist to commence autoguiding.

5. As in Section III, Step 3 of the camera checklist: set up for R, G, and B observations of M3:5-minute exposures, 1x1 binning, set Take to 1 for R and G, and 2 for B. Active status shouldbe checked for R, G, and B, and unchecked for L. This four-image, approximately 20-minutesequence will be repeated over and over throughout the experiment.

6. Observe M3 continuously until RR Lyrae rises into view (around 2:45am). On Camera Control

> Color, set Series Of: accordingly (e.g. a series of 6 for two hours). Then push the Take

Color button.

7. Relax for awhile. Watch the imaging results attentively for the first cycle to make sure theautoguiding remains stable through the filter changes. After that, check every several minutesto make sure that the guide star is staying in the middle of the box. And check on TheSkynow and then toward the end of this segment, to see when RR Lyrae will become available.RR Lyrae is known to TheSky as SAO 48421.

While relaxing: please do not stream movies at the observatory unless it is after midnight. Weget unlimited bandwidth between midnight and 6am, but we are restricted at other hours andpay extra for exceeding our limit.

8. As soon as RR Lyrae is viewable, let the current M3 RGB cycle finish — pushing Abort afterthe second B if necessary. Back on Camera Control > Autoguide, push Abort to turn offthe autoguider. Then point the telescope at RR Lyrae = SAO 48421. On Camera Control

> AutoSave, change to the appropriate file name prefix. (Do not reset the starting num-ber. CCDSoft does not ask permission before overwriting files!) On Camera Control > Take

Image, take a 2-second image with the L-filter to make sure that the star is reasonably closeto the center of the CCD; move it and take another image if necessary.

9. Observe RR Lyrae. The parameters in Camera Control > Color should be the same as beforeexcept for exposure time: 2 seconds in each image for RR Lyrae. Set Series of: to 8 andpush the Take Color button. This will be done in a few seconds; there is no need to autoguide.

10. From now until dawn, alternate between four-frame, 20-minute M3 sequences as in Step 5 andbursts of short images of RR Lyrae as in Step 9. Do not forget to keep changing the file nameprefix as you do!

11. When the Sun comes up, copy the working directory to your USB drive(s).

12. Exit CCDSoft, and shut down the CCD camera computer. Disconnect the power supply andcables from the camera, coil them, and return them to the black nylon briefcase.

13. Shut down the telescope by following the steps in the Telescope Shutdown section of thetelescope checklist.

14. Go to the Gannett House and get some sleep. You may not return to campus until at leastthe driver(s) sleeping for at least four (4) hours. This safety rule will be strictly enforced.

1.3 Data reduction

Each team will carry out the first stages of processing on their data before we merge data from allthe teams. These stages will include construction of your master flat-field images and calibration ofyour M3 and RR Lyrae data: bias and dark subtraction, flat fielding, and bad-pixel correction. Thiswork breaks into three roughly equal size parts, one for each filter. Make sure your team divides thedata reduction workload equally among the members.

Set aside a few hours for your team to meet in the POA Library in the company of the USBdrive carrying your data and one of the astronomy-lab computers on which the programs CCDStack

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and IDL reside. Find the directory on this computer’s desktop in which the Master Dark and Biasframes are kept. Then:

1. Copy your working directory from the USB drive to the desktop of the lab computer.

2. Start CCDStack, using the icon in the Windows taskbar.

3. If you have not done so already, follow the procedure in the camera checklist, Section V, tocreate master flat fields from your flat-field observations. Use the master flats you create whencalibrating the M3 and RR Lyr data.

4. Open all of the R images of M3, using File > Open and navigating to your working directory.This will present you with the full stack of these images, which you can page through andexamine with the tools on the left side of the window.

5. Calibrate these images. Choosing Process > Calibrate evokes the Calibration Manager

dialog. Using the two tabs and three buttons, specify the master dark frame, bias frame, andflat field frame appropriate to CCD temperature (-20◦C), binning (1×1) and, for the flat, filter(R). Then click Apply to All.

6. Next, remove hot pixels: those with (permanently) high and variable dark current that doesnot subtract out in calibration. Choose Process > Data Reject > Procedures. In the re-sulting dialog choose reject hot pixels from the dropdown menu, specify a strength of 50,check clear before apply, then click Apply to All. Then choose interpolate rejected

pixels from the dropdown menu, and again click Apply to All.

7. Then cold pixels: also with permanent dark-current problems, if not completely dead. RepeatStep 6, substituting cold for hot in the first dialog.

8. Align all of these images so the stars are in precisely the same places. First, page throughthe images until the one taken when M3 was closest to transit is on top. Choose Stack >

Register, which brings up the Registration dialog.

9. On the Star Snap tab, click remove all reference stars, then select/remove reference

stars. Double-click to select 6–8 stars which do not have any particularly close neighbors,are not close to the edge of the image, do not include extremely bright looking stars, and arespread uniformly around the cluster. Page through the stack of images to see how close tobeing in alignment they already are. Drag any misaligned ones into closer alignment. Thenclick align all to shift the frames into rough alignment.

10. Switch to the Apply tab, choose Bicubic B-Spline from the dropdown box, and click Apply

to All to shift the frames very accurately into alignment. Page through the images to makesure it worked. It should now be difficult to tell when you page from one image to the next.

11. Adjust all the images to remove atmospheric extinction. Again, page through the imagesuntil the one taken when M3 was closest to transit is on top. Choose Stack > Normalize

> Control > Both. In response to the subsequent instructions, drag a rectangle well off thecluster’s center to represent background, and click OK. Then drag a rectangle encompassingthe densest part of the cluster to represent the highlights, again clicking OK.

12. Now that the stack of images is registered and normalized, it can be corrected for cosmic-ray hits and satellite trails. Choose Stack > Data Reject > Procedures. In the resultingdialog pick STD sigma reject from the dropdown box, specify a factor of 2.2 (sigma) and aniteration limit of 8, and click Apply to All. Then select interpolate rejected pixels

from the dropdown menu, and again click Apply to All.

13. Choose File > Save > All. In the File name box of the resulting dialog, enter a suffixindicating the degree of processing the images have had, e.g. CalRegNormFix. Set the fileformat to FITS. Then click Save.

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14. The Red images are now tidied up; choose File > Remove all images - Clear.

15. Repeat Steps 4–14 for the G images of M3. Then repeat them for the B images, except: donot clear the stack at the end of the B image reduction.

16. Only if you are the first group analyzing the data, use the stack of B images in a quicksearch for variable stars. Page to the first M3 image of the night, then use the Navigate

Back and Navigate Forward buttons to toggle between the first and last blue images. Howmany stars can you find that substantially changed brightness between the beginning and endof the night? Keep a list of their pixel coordinates, noting that what is under the cursor isdisplayed at bottom right of the CCDStack window. Repeat this with image pairs separatedby different time intervals, such as beginning/halfway and halfway/end. Note that the Blink

button results in continuously and automatically paging through the contents of the stack withapproximately half-second intervals between images.

17. Now clear the stack and repeat this procedure on the RR Lyrae images, with two differences:

(a) Do not normalize the images to correct for atmospheric extinction (Step 11), and do notfix cosmic ray hits (Step 12) just yet.

(b) Instead, save the stack after registration, with file name suffix CalReg, and clear the stack.Then open, one at a time, each series of eight consecutive two-second exposures. As inStep 12, choose Stack > Data Reject > Procedures, pick STD sigma reject with afactor of 2.2 (sigma) and an iteration limit of 8, and click Apply to All. Then selectinterpolate rejected pixels from the dropdown menu, and again click Apply to

All. Save the series with the suffix Fix. Choose Stack > Combine > Mean to producean average of the series. Save this new image as a FITS file, accepting CCDStack’ssuggested prefix of Mean. Then clear the stack and proceed to the next series.

(c) After processing all the individual series, clear the stack and load all of the blue RR LyraeMean images. Put them on Blink, and note that the brightness of RR Lyrae changes byquite a bit from the beginning to the end, while the rest of the stars in the field change bymuch less. Thus, RR Lyrae varies like many of the variables in M3. The small changesin the rest of the stars turn out to be the systematic effect of atmospheric transmission;this was taken out of the M3 data in the Normalize step, but in the case of RR Lyrae,which is the brightest object in a frame with few stars, normalization has to be done morecarefully, in the next set of tasks.

1.4 Analysis

Next you will measure the fluxes of the M3 variable stars and of RR Lyrae as functions of timethrough your observing night. Using these data, you will measure the distance to M3.

1. In CCDStack, open the blue M3 frames again (File > Open Selected...), with File Strings

blue and CalRegNormFix, and by blinking frames taken at least a few hours apart, identify atleast 16 variable stars that are not in particularly crowded neighborhoods and have no closecompanions.

(a) Make a list of the variable stars’ pixel coordinates.

(b) Only if you are the first group analyzing the data, open one of the blue M3 framesin SAOImageDS9. Find the best scaling for the image by adjusting the settings in theScale drop-down menu (ASINH at 99.5% is a good place to start). Select Region from theEdit menu and click on the image to draw a circle region around each of your identifiedvariable stars. To change the location and size of the drawn region, double-click on theregion. In the resulting pop-up window, specify the center position and radius of theregion, and label the star with a number in the Text block. Save this annotated imageas a EPS file (File > Save Image > EPS) and send it to Prof. Douglass so that it canbe uploaded to the class website for reference.

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2. Run IDL using the icon in the Windows taskbar. Then type ATV <Enter> at IDL’s commandprompt at the bottom of the window. The ATV window will appear. On its Mouse Mode

dropdown menu, choose ImExam.

3. It is easier to spot the variable stars in B images, but to compare stellar fluxes to other people’smeasurements, it is better to measure them in G images, as G is essentially the same as theJohnson V band. So, open the first of your G images of M3 in ATV, using File > ReadFITS.

4. Unlike CCDSoft and CCDStack, IDL displays images with the pixel coordinates at lower leftinstead of upper left, so your images will look inverted top to bottom. (The coordinates of agiven star are always the same, though.) If this will be too confusing, choose Rotate/Zoom >

Invert Y to set it right.

5. Click on any star to bring up ATV’s aperture photometry window. In this window, click theShow Radial Profile button, which displays the flux per pixel of your star as a function ofdistance away from its centroid. This window tells you the centroid position and the flux ofthe star, given by the total flux within the aperture radius minus the flux in the sky annulusbetween the inner and outer radii. By entering new values in the boxes provided, adjustthese parameters so that the star’s flux is essentially completely contained in the aperture.Aperture/Inner/Outer = 8, 10, 16 usually works in the less-crowded regions.

6. In ImageInfo, display the current image’s ImageHeader and copy the UT date and time theimage was taken, recorded in the header as DATE-OBS.

7. In the aperture photometry window, click Write results to file... and enter a file namein which to store star fluxes. It will be useful to have the observation date and time as all orpart of the file name. While this file is open, a click on a star will write its centroid position,flux (as “counts”), and FWHM diameter in pixels.

8. Click on each of the variable stars in this image. Note any cases in which the radial profileindicates that nearby stars are influencing the measurement of the variable. Throw the staroff the list and choose a different one if there is not a good way to exclude too-bright starsfrom the sky annulus. When you are finished, click Close photometry file.

9. Repeat Steps 3-8 for each of the G images of M3 you acquired.

10. Repeat Steps 3-8 for each of the Mean G images of RR Lyrae you acquired. In this case there isonly one variable star, RR Lyrae itself, but click the next four brightest stars as well to enablethe correction for atmospheric extinction that we postponed from Data Reduction, Step 17.

11. From the information in your photometry files, make a spreadsheet which lists the flux, inCounts, as a function of time for each of the M3 variables. Use this to calculate the averageand standard deviation for the flux of each variable star, and to plot the flux vs time — i.e.the light curve — for each of the variables. Traditionally, these plots use the Day as the unitof time. Have these plots and the table of averages available for use in your lab report.

12. Repeat Step 11 for your RR Lyrae data, with one difference. For each image, calculate theratio of fluxes for the non-RR Lyrae stars to the fluxes these stars have in the image takenclosest to transit. Average these ratios for each image. Then create new columns containingstellar fluxes divided by the average ratio for their images. Use these new columns to calculateRR Lyrae’s average flux and standard deviation, and plot the light curve for RR Lyrae. Again,have these data available for use in your lab report.

13. Discuss the light curves for M3’s variables and RR Lyrae. Which M3 light curves resembleRR Lyrae’s most closely? Are there light curves in which you see clear minima and maxima?Are there light curves in which you see two maxima or minima, and can thereby measure thepulsation period?

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14. Assume that RR Lyrae and the M3 variables with similar light curves all have the sameluminosity. The distance to RR Lyrae has been measured by trig parallax; it is r = 260±10 pc(Catelan & Cortes 2008). So what is the distance to M3, and what is the uncertainty inthis distance? Use the average fluxes and uncertainties obtained in Steps 11 and 12 in thisdetermination.

15. Before Gaia, the largest stellar distance we knew from trig parallax was about 500 pc. Bywhat factor is the distance to M3 larger than this?

16. (Optional) From your M3 data, you could make a color image of the cluster and thus a superbornament for your website or Facebook page. Here is how to make it, back in CCDStack:

(a) For each filter, open all of the CalRegNormFix files, as in Step 1, and create an average ofthem, with Stack > Combine > Mean. Save the Mean image and clear the stack beforeproceeding to the next filter’s CalRegNormFix files.

(b) Clear the stack if it is not already; then open the three Mean images you just created.Choose Color > Create. CCDStack will magically identify your R, G and B images andoffer the filter scaling factors for adjustment. Enter Filter Factors of 1.00, 1.16, and1.58 for R, G, and B, respectively, which will scale the colors so that an A0V star lookswhite. Then click Create. You will be prompted to drag a rectangle on the image toidentify a background area well away from the cluster center; do so, check Desaturate

background, and click OK. Then click Yes on the next dialog, and Apply to this in theone after that. Save this image under some suitable name, e.g. M3 RGB.FITS.

(c) Use Adjust Display to tweak the image for display of the faintest stars while keepingfrom “overexposing” the brightest stars and the cluster center. When you are satisfied,choose File > Save Scaled Bitmap to make a JPEG image, or Save Scaled Data tomake a TIFF image, the better to be imported into Photoshop.

17. If other teams have M3 observations, ask for their light curve data in return for yours. Foreach of the variable stars in common, plot flux as a function of time since the earliest of allthe observations. For how many stars can you see complete pulsation cycles?

1.5 Lab reports

Each student must write their own report, in which they explain the purpose, methods, and outcomesof the observations, and answer all of the questions raised in the sections above. We offer a samplelab report on the AST 142 course website, to give an idea of the length and level of detail expected.

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2 The Messier Marathon

2.1 Introduction

The first interesting catalog of non-stellar objects that do not belong to the Solar system was thatcompiled by Charles Messier in the late eighteenth century. In the era of Messier’s activity, solar-system astronomy seemed the most exciting frontier, exemplified by Herschel’s (1781) discovery ofUranus and the realization that the orbital anomalies of the new planet could be explained mosteasily by another planet, or planets, further away. Within this rubric was the study of minor solarsystem bodies, which in those days meant comets, as asteroids were not discovered until 1801.Messier was a hunter of comets. In his hunt, he and his assistant Pierre Mechain also discoveredmany fuzzy, extended objects that could be mistaken for comets at a glance, but which seemed not tomove with respect to the fixed stars. Messier published this list (1781) as a warning to fellow comet-hunters. Originally containing 103 objects2, the catalog expanded slightly during the 20th centuryas astronomers, notably Camille Flammarion and Helen Sawyer Hogg, re-read additional notes anddescriptions of observations kept by Messier and Mechain. There are now officially 110 Messierobjects. The catalog includes most of the brightest examples of stellar clusters, gaseous nebulae,and galaxies visible from the northern hemisphere. Very influential in its day, the M catalog spawnedmany more collections of extended celestial objects, starting with the General Catalogue of Nebulaeand Clusters of Stars (GC; 1864), the New General Catalogue (NGC; 1888), and its appendices theIndex Catalogues (IC; 1896, 1905), compiled by John Herschel and John Dreyer, from observations byWilliam, Caroline and John Herschel. Professional and amateur astronomers alike remain fascinatedby the wide variety of astrophysical processes which can be studied in detail in the Messier objects.

The Messier catalog has two features that many find particularly interesting. First, there are twobrief intervals each year in which every object in the catalog could in principle be observed betweensunset and sunrise. Second, the number of objects is sufficiently small that a good observer can pointa telescope at each object during the course of one clear dark night, but sufficiently large to make ita challenge. This observing program — all, or at least nearly all, the M objects in a single night —is called the Messier Marathon. The Marathon is very popular among amateur astronomers. Thelonger of the two Messier-catalog visibility windows lies in the last couple of weeks of March andthe first couple of weeks of April, and thus falls within the prime AST 142 observing season. In thisexperiment, we will run the Messier Marathon, recording CCD images of the M objects, or at leasttheir centers.3

2.2 Experimental procedure

2.2.1 Planning your Messier Marathon

There are 110 objects in the catalog and less than 12 hours of darkness in which to observe them,so each object needs to be acquired and imaged in less than six and a half minutes. Thus no onesucceeds at the Messier Marathon without carefully planning the sequence of observations. It is notpossible to simply go through the list in right-ascension or catalog-number order. Instead, you needto take account of the times at which objects set and rise, noting the constraints imposed by the

2Some of the objects were known to be non-stellar and non-planetary for a long time before Messier. For example,of the first 45 catalog objects he published, the last four are naked-eye nebulosities known to the ancients, whichMessier added for completeness: the middle “star” of Orion’s sword (M42 and M43), the Beehive Cluster in Cancer(M44) and the Pleiades in Taurus (M45). The Andromeda Nebula (M31), also visible to the naked eye, was knownat least 800 years before Messier’s time. Several other M objects were discovered within the generation or two beforeMessier: for instance, the Great Hercules Cluster (M13), which is barely visible to the naked eye under perfectconditions, was described by Halley, and the Crab Nebula (M1) by Bevis, early in the 1700s. But Messier was thefirst to collect these scattered observations, add many other examples systematically, and publish the results, so hiswork had more impact than that of his predecessors.

3Serious amateur astronomers usually consider the use of computer-controlled telescopes to be against the rules ofthe Messier Marathon. Beware of thinking that completion of this project entitles you to stand in the august companyof those who have done it with Dobsonians pointed by hand; they will consider you a cheater. On the other hand,most of them do not record images of the targets while they are running the Marathon, and you will.

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southernmost objects that are not above the horizon for very long, and use the flexibility of the longobserving windows for the northernmost objects.

During the past few weeks of Learn Your Way Around The Sky lessons in recitation, you havelearned everything you need to know to calculate the rising and setting times of each object and theSun, to the required, better-than-a-few-minutes accuracy. First, there is the relation between zenithangle ZA and hour angle HA, in terms of an object’s declination δ and the observer’s latitude λ:

ZA = cos−1 (cosHA cos δ cosλ+ sin δ sinλ) (3)

which you derived in Recitation 5. Then there is local sidereal time, ST , which depends upon theobserver’s longitude L, time t (in UT) since the Vernal equinox (at t1), longitude L1 at which it wasnoon at the Vernal equinox, and Earth’s orbital parameters, including the sidereal rotation periodP⊕, the length of the day, the semimajor axis length a, eccentricity ε, and ecliptic obliquity Ψ. InRecitations 4, 6, and 8, you derived the components of sidereal time, which expressed in siderealdays is

ST = (t− t1)

(1

P⊕− 1

day

)+

1

2π[L− L1 + ∆θε(t) + ∆θ0(t)] + mod

(t− t1day

, 1

)(4)

where by mod(x, 1) we mean the part of x in excess of the largest integer smaller than x, or in thiscase time of day on a 24-hour clock, with the integer number of previous days subtracted off, andwhere

∆θε(t) =∆ω0

ωsinω(t− t0) ∆θ0(t) =

1 − cosψ

2sin 2ω(t− t1) (5)

Here ω is the angular frequency of the mean Sun, ∆ω0 is the difference in Solar angular frequencybetween perihelion and aphelion, t0 is the time of perihelion, and ψ is the obliquity of the ecliptic.Finally, there is the celestial position of the Sun, for which you obtained the declination in Recitation9, and for which the right ascension is only slightly different from sidereal time:

α� = mod

(2π(t− t1)

(1

P⊕− 1

day

)+ ∆θε(t) + ∆θ0(t), 2π

)δ� = −ψ cos [ω(t− t2) − ∆θε(t) − ∆θ0(t)]

Here the results would be in radians, t2 is the time of the last winter equinox, and (mod x, 2π)again means that the largest integer multiple of 2π is subtracted off, that can still leave a positiveresult.

“All” that needed to be done, then, to obtain the rising and setting times of each Messier objectand the Sun for any arbitrary night of the year, is to solve for the times t on that night which satisfy

cosZAmax = cos (ST (t, L) − α) cos δ cosλ+ sin δ sinλ (6)

for each target’s α and δ. Then take the rising and setting times and arrange the order of obser-vation, such that the average pace of the observations — say, one every five or six minutes — canaccommodate observation of each object after it rises and before it sets. In Figure 1, the results ofsuch a calculation are rearranged into one practical realization of the Messier Marathon.

Fortunately, you will not have to go to this much trouble. The popularity of Messier Marathonsamong amateur astronomers has led to the presence on the Web of several Messier Marathon plannerswhich can be customized for any observing date: just google “Messier Marathon planner.” But youdo know how to do the calculations which these planners do, and you could do them if you wantedto. We will not ask for them in this project, because they involve the use of numerical root-findingroutines which are not easily implemented.

With all this in mind, here is the pre-observing procedure to be followed:

1. Form or join a team. As you will see, there is very little down time for anyone on the ob-serving team during the course of this project. There are three tasks that must be performedconstantly through the night, and we presume that team members will rotate periodically sothat everybody gets to enjoy each different task.

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Figure 1: Rising and setting times for the Messier objects, organized in a sequence to aid in deter-mining the order of observations during the Messier Marathon.

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2. Download the Messier catalog, available as an Excel spreadsheet on the AST 142 Projectspage.

3. Calculate the amount of time each object is over the effective horizon, 2HA(ZAmax). Identifythe objects which never get above the horizon and should therefore be left out of the observinglist. Identify circumpolar objects and prepare to keep them handy: you must always beobserving something, and these may serve if you would otherwise have to wait for an objectto rise.

4. Choose the observing night. Look up or calculate the times of sunset and sunrise, and thelength of the night.

5. Refine your observing list by identifying the objects which rise too late or set too soon. De-termine your time budget: the number of seconds available for each object on the average. Byconsulting online Messier Marathon plans and Figure 1, determine the order in which the listshould be observed. Make a spreadsheet list of targets and times at which you should beginobserving each target.

Hint: Note the position of M68 in Figure 1. Consider how this, and other objects with verynarrow windows of observability, constrain the schedule.

6. Plan to take at least 2 minutes of imaging data per object with the L filter. The imagingshould be in the form of a short exposure (20–30 sec) followed by centering if necessary, andeither a longer exposure or a series of short ones. For faint objects (e.g. most galaxies) in adark sky, it would be best to take one long exposure; for bright objects (e.g. M42) or brightsky conditions (twilight or moonlight) it works better to take a stack of short exposures andaverage them afterwards.

7. Learn enough about the Messier objects to know which are unlikely to have their interestingparts fit in the 15.4 arcminute wide camera field. Flag these objects on your observing planspreadsheet. For these targets, you will record images of the center with the camera but willsupplement these images with descriptions of the view through the finder telescope or theimage-stabilized binoculars.

8. Present your list, with calculations and order appropriate for the observing night, to theinstructors for review. No group gets to go to the telescope without presenting a blow-by-blowplan in advance.

9. Unlike the observing projects in AST 111, this one takes all night. Therefore, you will berequired to sleep at the Gannett House after your observations are done and before returning tocampus. Plan accordingly by packing for an overnight stay, and discussing with your team andthe instructors the all-important requirement of packing sufficient food. (Unfortunately, Meesis beyond the range of pizza delivery; the nearest restaurants and grocery stores in Naples, andthe nearest restaurants on your way home that are likely to be open are in Victor.) Familiarizeyourself with the rules of the observatory sleeping quarters at the Gannett House.

10. Bring your notebooks, and bring a USB drive with at least a few GB of free space. You woulddo well to also bring your personal laptop or tablet computer. Paper copies of the experimentprocedure (i.e. this document), telescope checklist, and CCD-camera observing guide will alsoprove useful, though these will also be accessible to you online at Mees.

11. Arrive at least 45 minutes before sunset. The telescope and camera must be ready to go,and all team members must be at their stations, before the sun goes down.

2.2.2 Observations

Three team members should be stationed at three specific jobs: telescope operator, CCD cameraoperator, and scribe:

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• The Scribe orders the observations, enforces the schedule, and maintains a spreadsheet inwhich they record the correspondence between file name and object being observed, exposuretimes, etc.

• The camera operator takes the data and is in charge of quality control: making sure imagesare not saturated, making sure the target is centered properly, etc.

• The telescope operator moves the telescope to acquire the targets; offsets the telescope at therequest of the camera operator, in the process of centering targets, using DFMTCS Telescope

> Movement; and looks for opportunities to sync the telescope coordinates whenever a starhappens to be centered in the camera, thus to keep the pointing sharp.

Rotate the team members among the jobs at least once an hour. Here is the recipe that should befollowed:

1. Start the telescope and initialize its pointing by following the steps in Section I of the MeesObservatory telescope checklist. This leaves you with DFMTCS, FrameGrab, and TheSky runningon the TCS computer.

2. Start the CCD camera, its computer, and CCDSoft, and focus the telescope by following thesteps in Section I of the Mees Observatory CCD camera checklist. Notable differences fromordinary observations:

(a) You should take flat-field data at sunset, but only for the L filter and unusually with 2×2binning, following the steps listed in Section V of the camera checklist. Do not stop tocreate the Master flat; just take the data and get on to the M objects.

(b) Note that you can find stars near the zenith, and sometimes even focus the telescopeadequately, before sunset. Give it a try.

(c) You will not have time to change the file name prefix for every object. Rely on a genericprefix and the serial numbers, and the spreadsheet maintained by the scribe, to keep yourtargets and data sorted.

(d) No time, or need, to autoguide.

(e) Because you will be using only one filter, but changing targets and exposure times sofrequently, it will be more convenient to take data with CCDSoft’s Camera Control >

Take Image tools instead of the usual Camera Control > Color.

You now have CCDSoft running on the CCD camera computer, and both the camera andtelescope ready to observe and autosave the data.

3. Begin the Marathon. The scribe is in command, enforces the following of the plan, andmaintains the spreadsheet of file names and targets. Illustrations of the routine:

Scribe Move to Mxx.

Telescope We’re there.

Camera Looks like a galaxy nucleus in the 20 second image, please move us 5 minutes westand 3 minutes north.

Telescope Done.

Camera Two-minute exposure in progress. By the way, the 20 second image was number 147and the current one is 148.

Scribe Duly noted. Get ready for Myy next.

Telescope Ready.

Camera Image 148 done and ready for next.

4. Occasionally:

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Camera 20-second image number 230 already beautiful, brightest stars barely on scale. Canwe do 16 20-second images?

Scribe No time for that; make it 9 20-second images.

Camera Oh, all right. 230 through 239 in progress.

5. When necessary:

Camera Not much in Image 86; what does it look like in the finder?

Off-duty observer (after running up the stairs and peeking through the 6” finder telescope)Open cluster, big on the scale of the finder’s field, no nebulosity. No wonder you are notseeing much.

Scribe Duly noted.

6. The non-routine: Whenever an object is not clearly seen in the camera or finder, quickly pointto a nearby bright star, center it in the camera, and update the TCS telescope position, thenpoint back to the target. You will have to learn how to do this in no more than a couple ofminutes.

7. When all this is done, or when the Sun comes up — whichever comes first — copy theworking directory to your USB drive(s).

8. Exit CCDSoft, and shut down the CCD camera computer. Disconnect the power supply andcables from the camera, coil them, and return them to the black nylon briefcase.

9. Shut down the telescope by following the steps in the Telescope Shutdown section of thetelescope checklist.

10. Go to the Gannett House and get some sleep. You may not return to campus until at leastthe driver(s) sleeping for at least four (4) hours. This safety rule will be strictly enforced.

2.3 Data reduction

Now we calibrate your Messier Marathon images. Since the images differ only in target and inte-gration time, this task benefits greatly from CCDStack’s automation. Make sure your team dividesthe data-reduction workload equitably among the members.

Set aside a few hours for your team to meet in the POA Library, with the USB drive carryingyour data and one of the astronomy-lab computers on which the programs CCDStack and IDLreside. Find the directory on this computer’s desktop in which the Master Dark and Bias framesare kept. Then:

1. Copy your working directory from the USB drive to the desktop of the lab computer.

2. Start CCDStack, using the icon in the Windows taskbar.

3. If you have not done so already, follow the procedure in the camera checklist, Section V, tocreate master flat fields from your flat-field observations. Use the master flats you create whencalibrating your images.

4. Open all your Messier Marathon images using either File > Open... or File > Open Selected...

and navigating to your working directory. This will present you with the full stack of theseimages, which you can page through and examine with the tools on the left side of the window.

5. Calibrate the images en masse. Choosing Process > Calibrate evokes the Calibration

Manager dialog. Using the two tabs and three buttons, specify the master dark frame, biasframe, and flat field frame appropriate to CCD temperature (-20◦C), binning (1×1) and, forthe flat, filter (L). Then click Apply to All.

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6. Next, remove hot pixels: those with (permanently) high and variable dark current that doesnot subtract out in calibration. Choose Process > Data Reject > Procedures. In the re-sulting dialog choose reject hot pixels from the dropdown menu, specify a strength of 50,check clear before apply, then click Apply to All. Then choose interpolate rejected

pixels from the dropdown menu, and again click Apply to All.

7. Then cold pixels: also with permanent dark-current problems, if not completely dead. RepeatStep 6, substituting cold for hot in the first dialog.

8. Choose File > Save > All. In the File Name box of the resulting dialog, enter a suffixindicating the degree of processing the images have had, e.g. Cal. Then click Save.

9. You are now done with the entire stack; choose File > Remove all images - Clear.

10. Now, using the scribe’s spreadsheet of observations, identify all multiple images of given ob-jects, such as those described in step 4 of Section 2.2.2.

(a) Use File > Open... to open the first set.

(b) Align all of these images so that the stars are in precisely the same places. Choose Stack

> Register, which brings up the Registration dialog.

(c) On the Star Snap tab, click remove all reference stars, then select/remove reference

stars. Double-click to select 6–8 stars which do not have any particularly close neigh-bors, are not close to the edge of the image, do not include extremely bright looking stars,and are spread uniformly around the cluster. Page through the stack of images to seehow close to being in alignment they already are. Drag any misaligned ones into closeralignment. Then click Align All to shift the frames into rough alignment.

(d) Switch to the Apply tab, choose Bicubic B-Spline from the dropdown box, and clickApply to All to shift the frames very accurately into alignment. Page through theimages to make sure it worked. It should now be difficult to tell when you page from oneimage to the next.

(e) Choose Stack > Normalize > Control > Both. In response to the subsequent instruc-tions, drag a rectangle well off of the cluster’s center to represent background, and clickOK. Then drag a rectangle encompassing the densest part of the cluster to represent thehighlights, again clicking OK.

(f) This registered, normalized stack of images can be corrected for cosmic-ray hits andsatellite trails. Choose Stack > Data Reject > Procedures. In the resulting dialogpick STD sigma reject from the dropdown box, specify a factor of 2.2 (sigma) andan iteration limit of 8, and click Apply to All. Then select interpolate rejected

pixels from the dropdown menu, and again click Apply to All.

(g) Choose File > Save > All. In the File name box of the resulting dialog, enter a suffixindicating the degree of processing the images have had, e.g. RegNormFix. Then clickSave.

(h) Average the stack of images using Stack > Combine > Mean. Save this image as well(File > Save > This), using the first file name in the stack as a suffix, and Mean as aprefix.

(i) Choose File > Remove all images { Clear.

(j) Repeat steps a–i for each multiple observation.

11. Using File > Open Selected..., open all of the calibrated images (Cal suffix).

12. Page through the images and remove from the stack (Ctrl-R) all of the images which wentinto an average: those with suffix CalRegNormFix.

13. Using File > Open Selected... again, open all of the averages of the multiple images (Meanprefix.

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14. Now comes the time consuming part. You now have as many as 110 images in the stack: yourbest try on each of the Messier objects you observed. Go through them one by one, and makeeach look as good as possible by use of the Adjust Display tools. By “good,” we should meanthat the image stretch (Gamma and DDP parameters) is adjusted to show all details of the objectfrom brightest to dimmest, that Maximum is chosen not to saturate too much of an image’sbrightest parts, and that Background is chosen so that the image is black at levels below thedimmest detected part of the object: thus blotting out any sky background, but none of thestars brighter than that.

15. When you are done beautifying the images, save them all in scaled form: File > Save >

All, with JPEG as the Save as Type. Leave copies of all images in the working directory youcreated on the lab computer.

2.4 Analysis

As your main result, you have digital images and sometimes eyepiece descriptions of the vast majorityof the Messier objects.

1. Make a master table of final images and object descriptions, with the objects listed in the orderyou actually observed them. Include in the descriptions all comments collected while lookingthrough the eyepiece or binoculars, and a classification of each object made in accordance withits appearance. For each galaxy, this should include your estimate of the Hubble type as isconsistent with the image you took.

2. Make an additional cross-reference table in which the objects are sorted according to theirclassification: open cluster, globular cluster, planetary nebula, Hii region/reflection nebula,supernova remnant, elliptical galaxy, spiral galaxy. Comment on the ranges of brightness andangular size observed under each of these classes.

3. Pay particular attention to the identification and classification of three objects: M40, M73,and M102.

2.5 Lab reports

Each student must write their own report, in which they explain the purpose, methods, and outcomesof the observations, and your complete set of images, object descriptions, and cross references. Weoffer a sample lab report on the AST 142 course website, to give an idea of the length and level ofdetail expected.

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