HIGHLIGHTS

This section describes highlights based on observations made at two observatories in Southern Arizona (Hereford Arizona Observatory and Junk Bond Observatory). Items 1 and 3 were used in the article accepted for publication by the Astrophysical Journal ("A Transiting Planet of a Sun-like Star" by McCullough et al, complete reference at bottom of this web page). Items 2, 4, 5 and 6 became available after the manuscript was submitted to the ApJ and are only available on this web page. Please understand that the contents of this web page may be revised as I continue to figure out how to process transit data. I'm just an amateur without the benefit of internal review by colleagues. I welcome suggestions for improvement and suspected errors.

Item 6) Combined R-Band Transit Observations



Figure 6. Combined 2006.03.14 and 2006.06.01 R-band light curve. The pink dots are measurements of 1-minute exposures and the filled red circles are 9-point averages (non-overlapping). The mid-transit depth is 23.4 mmag and the duration is 2.8 hours (contact 1 to contact 4).  The black trace is a fit using a very simple transit model.The 9-point averages exhibit an RMS scatter with respect to the model of ~1 mmag. [Hereford Arizona Observatory, 14-inch telescopes (Celestron CGE-1400 for 2006.03.14 and Meade RCX-400 for 2006.06.01), Hereford, AZ]

This figure is an average of two R-band transits (items 3 and 5, below) using two different 14-inch telescopes at the Hereford Arizona Observatory (MPC code G95). The data appear to "fit" a very simple model, described at model, which uses Rp/Rs = 0.144 (ratio of planet radius to star radius, both circular) and a linear limb darkening modeled using a "1-cos(theta)" coefficient of 0.60.

The "Hereford Arizona Observatory" (HAO) is used for observing gamma-ray bursts, supernovae light curves, cataclysmic varible super-hump monitoring, and faint asteroid rotation light curves. The observatory has a Minor Planet Center designation of G95. HAO is located in the rural community of Hereford, in Southern Arizona, 90 miles southeast of Tuscon, 7 miles from the border with Mexico. The altitude and coordinates are 4660 feet, -110.2377, +31.4522. A mountain range is located 5 miles west of the site, reaching an altitude of 9400 feet, which too frequently produces downslope winds that degrade "atmospheric seeing."

Figure A1. View of HAO, looking southwest. The two mountain peaks are at 9400 feet, or 4700 feet higher than the HAO. Downslope winds occur almost every night (at ~1-hour intervals), and they may originate in the canyon between the two peaks (as radiatively cooled air becomes dense and starts falling through ambient air and spreads out over the valley).

The telescope used for the 2006.03.14 transit observation is a 14-inch aperture Celestron Schmidt-Cassegrain, model CGE-1400. The GE means "German Eqauatorial," which means trouble! Every meridian crossing requires a manual "meridian flip," plus associated changes to software settings for image orientation and tracking directions. (I'll never buy a GE again! I'm so happy to be rid of the meridian flips.) The telescope is located in a "sliding roof observatory" 70 feet from my house office "control room." Cables are buried in conduit for control of the telescope. The Celstron used a MicroTouch/Feathertouch focuser (made by Starizona); it's a wireless focuser that adjusts the primary mirror. The Meade RCX is focused using an ASCOM telescope driver (written by Ajai Sehgal). A wireless video camera and microphone are used to monitor observatory conditions from the remote office control room.

Figure A2. The canvas-covered roof is open showing the Celestron 14-inch telescope. Note the two buried conduits entering the building; one is for AC and the other is for several control cables.

Figure A3. My new Meade RCX400 14-inch telescope. (This is a great telescope for exoplanet observing, as I describe at paean.) 

The CCD is a SBIG ST-8XE, with 9-micron pixels, 1530x1020, and a "237" autoguider chip next to the main chip. The filter wheel is a SBIG 5-position CFW-8. The CCD and CFW are mounted at the Cassegrain location behind a focal reducer lens and image stabilizer. The image stabilizer is a SBIG AO-7, which works with the autoguider chip's image to produce tip/tilt adjustments at ~3 Hz. The focal reducer is located ~4 inches from the CCD chip, which quadruples the FOV solid angle and affords smooth flat fields. (If the focal reducer lens is too close the flat fields have too much structure that's different for each filter.) The image scale for this configuration is 0.97 "arc/pixel. The FOV is 24.7 x 16.5 'arc. For this particular exoplanet transit project the CCD assembly is rotated so that the longer FOV dimension is north-south, with a bright star in the autoguider's FOV.

My computer clock uses AtomicTime, a utility that updates the computer clock every 3 hours. I verified that it was correct by noting that it agreed with a wireless (WWV signal) clock to within 1 second.

I have a Davis "wireless" weather station near the observatory with sensors at 11 feet AGL. It transmits signals to a receiver in my office where a data logger records many weather parameters; these data are available for download to a dedicated weather computer. The weather computer produces a graphical display of wind speed and direction, temperature, dew point and RH, and barometric pressure. The wind and temperature traces can be used to predict "atmospheric seeing" degradations (~5 minutes ahead of time) since the downslope winds begin with a slow rise of wind followed 5 minutes later by a rise of temperature (due to adiabatic heating as the air that is sinking out of a nearby canyon).

Software for Telescope/CCD/focuser Control and Analysis

I use MaxIm DL (MDL) for control of telescope pointing, CCD camera and AO-7 image stabilizer. MDL uses MaxPoint, also from Diffraction Limited, to correct for polar alignment errors and mount flexure; this assures accurate pointing (but does not improve tracking). MDL has two ways to accomplish aperture photometry. The on-the-fly display of star flux at the cursor location is a crude tool since it does not reject comic ray defects or interfering stars in the sky background annulus. If used with care it is a very useful tool however (I use it for all my all-sky photometric sequence analyses). The second way to perform aperture photometry is with MDL's Photometry Tool (Analyze/Photometry). A set of images (~30) can be processed using ensemble differential photometry, and this is what I use for analyzing exoplanet transits. The photometry tool creates CSV-files that can be imported into a spreadsheet. More on this later.

TheSky 6 is a "planetarium" program that shows the sky's star field. It is an indispensable tool for planning an observing session and in reducing data. In the afternoon before a night's observing I use TheSky to schedule what to observe and when. For all-sky photometric sequence observing it is important to schedule observations of Landolt star fields at the same air mass as the region of interest (ROI). TheSky shows when the ROI transits, which requires a 10-minute break in observing to accomodate a manual meridian flip and software settings changes. For data reduction it is convenient to use TheSky to determine air mass for image groups.

Finally, I like spreadsheets. I now use Excel, inspite of it's orientation to business users. I have template spreadsheets that facilitate the kind of analyses that I frequently perform.

Planning 2006.03.14 Observations

For the night of March 13 (2006.03.14 UT) I used TheSky to schedule all-sky observations of two Landolt star fields before XO-1 transit. I did this partly to verify that the candidate reference stars near XO-1 had not varied from the date that I first established their brightnesses (2006.02.25). TheSky showed that XO-1 transited at 11:59 UT (4:59 AM). This was ~45 minutes past egress, and also just before dawn, so I decided to terminate observations at transit. The scheduled ingress, at 08:47 UT (01:47 AM), occurred while XO-1 was rising through an elevation angle (EL) of 49 degrees. XO-1 was scheduled to rise through EL = 15 degrees at 11:00 AM, so I scheduled observations 15 minutes earlier of the Landolt star field LA1242 (located at RA = 12:42 near Dec = 0). XO-1 would be at LA1242's elevation (~40 degrees) 2 hours later. Shortly after sunset on this night I scheduled observations of LA0452 using V and R filters (for another project). The two R-band observations of Landolt stars would provide a check that extinction was not changing.

I prefer R-band for exoplanet work for several reasons: Extinction is low for R-band (typically 0.11 mag/air mass at my site), the CCD's QE is high and the observed flux for a typical star is greatest for R-band (being 36% of clear), and scintillation is lower than for B or V due to R-band's longer wavelength. Unfiltered observing is unwise because reference stars with different colors fade differently with air mass (due to extinction); this could cause an exoplanet to have trends that are difficult to remove (especially when pre-ingress and post-egress times are not observed).

Exposure Times

Exposures must be kept short enough that the brightest reference star is not saturated. For this star field the brightest star has R-mag = 9.28 which requires that my exposures be no longer than 60 seconds. If "atmospheric seeing" gets too good the telescope has to be purposely de-focused in order to assure that no pixels are saturating.

As an aside, for large apertures very short exposure times are required. This has two penalties: 1) image download times can be comparable with exposure times (leading to low duty cycles), and 2) scintillation increses as exposure times are shortened. For example, a 32-inch telescope would require 11 second exposures instead of a 14-inch telescope's 60 seconds (assuming both CCDs used 16-bit A/D converters). If the download time per image is 8 seconds the duty cycle for the two telescopes would be 88% and 58%. Poisson noise per image will be the same, since for each telescope the maximum counts for the brightest star will be ~30,000 counts, but the larger telescope acquires more images per unit of observing time (3.1 images per minute for the 32-inch versus 0.9 images per minute for the 14-inch). Scintillation depends on both aperture and exposure time, and smaller apertures are net winners on this consideration (see the section on scintillation, below). The large aperture penalty for this example is 32%, but the 3.5-fold greater number of images per observing minute is more important. The point of this aside is to show that although larger apertures are better for exoplanet observing their advantages are not as dramatic as for faint object observing.

Another consideration is when to start observing the exoplanet. I decided to start when it was low in the sky in order to have sufficient air mass range to search for air mass related systematic errors. My range extends from air mass, m = 3.5 to 1.00. Experience shows that good data is usually not possible until air mass is less than 1.5 or 2.0.

Observing and Reduction Logs

I'm a firm believer in maintaining logs for all observing sessions. At the top I record my goals and plans for the night, as well as sky conditions (cloud cover and type, plus wind). The plan includes what to do and at what times. For decades I would use only ink for the observing log, and pencil for the reduction log, but since retirement I've relaxed that "rule" and I now use pencil for both with a rigorous rule of not altering my observing log (except as carefully noted). For me, an observing log is more sacred than the bible!

I noted in the March 14 observing log that the weather was excellent. The sky was cloudless and the wind was calm, conditions that I categorize as "photometric."

Flat Frames

After opening the observatory I turned everything on, placed a T-shirt over the telescope aperture (secured by a bungee cord), and manually pointed to zenith. I set the CCD cooler to 0 C (a modest cooling seems to improve my flats; after the flats I specify a colder setting for use with the ROI). Flat frames were taken for each filter to be used that night (plus Clear, in case an interesting GRB was announced while observing). Exposure times ranged from 1 to 20 seconds. Shorter than 1 second might produce an artificial vignetting from the way the CCD shutter operates. Exposure times were carefully changed to assure that the maximum count was in the range 28,000 to 34,000. This is about half the maximum for a 16-bit A/D converter, and for my CCD model this assures that saturation effects are minimal. I specified that dark frames be taken with the flats as a precaution for hot and dead pixels.

I took 11 flats with the R-filter (plus others with the V- and C-filters). I used to "median combine" the flats for each filter, using "normalize," but I've discovered that the normalize feature does funny things to image intensity scaling that produces subtle defects in the final flat frame. Image averaging is a safer procedure, provided each individual image to be averaged is first visually inspected for cosmic ray defects. I averaged the R-band flats in 3 groups and compared, noting that slight changes had occurred as the exposure times increased. I weight-averaged the flats to produce a master flat for the night, giving preference to the longest exposure set. The R-band master flat had a vignetting pattern that was smooth except for one persistent dust donut, and at the corners the response was ~65%. I try to not use reference stars in the corners even though I believe that the flat frames correct vignetting to the 1% level.

Dark Frames

I believe in establishing a master dark frame for each temperature and exposure time setting to be used for the ROI. The first half of the night's observing session was with a CCD cooler temperature of -15 C, while the XO-1 observations were at -25 C. I took a set of 40 dark frames at -15 C (60-second exposures) during a dinner break, and later a set of 16 dark frames at -25 C (before the XO-1 observations). I don't deal with bias frames since I always use dark frame exposure times that are the same as my ROI exposures. (I don't like the variable results of correcting for CCD temperature and exposure when calibrating with dark frames made under different conditions). By creating a master dark frame from 16 individual dark frames, median combined, the master dark frame has a pixel noise that is about 1/3 of the individual ROI pixel noise. After subtracting such a master dark frame from a ROI light frame the pixel noise increases by only 11%.

Focusing

My Celestron tube shrinks with cooling temperature, so focusing has to be monitored. I always focus unfiltered, and add previously established offsets for each filter. Past midnight the focus doesn't change much, so I usually monitor it by noting star "shapes." My collimation is such that a defocused star changes shape to an oval with an orientation that I can "read" for the direction of needed focus change. Between exposures I change the focus by a small amount and note the effect on star shape. This procedure allows me to continue observing without an interruption of the automatic expsoure schedule. At the beginning of the observing session my best focus gave FWHM = 4.2 "arc. This was established from a plot of the best of several FWHM at a sequence of focus settings. Not great seeing, but acceptable for photometry. I made several adjustments (as described above) throughout the night, and 60-second exposures had typical FHWM that ranged from 3.5 to 4.4 "arc.

There may be occasions when it will be desireable to intentionally maintain a defocused condition. For example, saturation of the brightest pixel must be avoided, so in order to accommodate a very bright star for use as a reference star a defocused image can be used to lower the brightest pixel value to below saturation (~50% of full-scale for non-ABG CCDs). The star's total flux will be unaffected, and the star's Poisson noise won't be affected. The only penalties are 1) signal aperture noise will be higher (due to having to use a larger radius), and 2) interfereing stars may be present in the sky background reference annulus (due to having to use a larger reference annulus). The appendix provides conceptual tools for assessing the penalty for using a larger signal aperture.

MaxIm DL (MDL) has an automated exposure sequence feature that allows the user to specify a filter, exposure time, binning, delay time after each exposure, repeat count for the sequence, file name for each exposure and destination directory for recording images. I chose R-filter, 60 seconds for each exposure, binning of 1x1, and a 10-second delay after each exposure (as explained in the next section). Each sequence consisted of 10 exposures, numbered 0 thorugh 9, and I set the sequence repeat count to 99.

Image Stabilization and Tracking

In the abstract I stated that it's important to keep the star field fixed to the same location on the chip for the entire observing session. Doing this reduces the effect of flat field imperfections. In fact, if you are successful in keeping the star field fixed it should not be necessary to even employ flat field corrections (provided FWHM >> 1 pixel). On this date I succeeded in keeping the stars fixed to within a few pixels for the entire 5-hour main exoplanet observing session. Here's how I accomplished it.

My AO-7 image stabilizer adjusts the tip/tilt mirror at ~3 Hz to keep the guide star's image fixed, thus keeping the star field on the main chip fixed. However, my polar axis was ~0.2 degrees off, so there was a drift that typically caused the AO-7 to reach it's tracking limit in ~4 minutes. MaxIm DL (MDL) is supposed to "nudge" the telescope drive in the required direction whenever the AO-7 exceeds a user-specified correction threshold. However, since a lightning strike near my site last summer I have been unable to use that feature. So, when I used the Celestron CGE-1400 I intentionally specified a 10-second delay after each exposure for manually nudging the telescope in a way that should be done automatically. (Hey, I knew I was getting a new scope a month later, so it wasn't worth fixing!) This made for a lot of extra work! It meant that I had to stay close to the control computer to perform the nudges, which I usually perform after each exposure. Since my exposure time was 60 seconds I had to "attend" to nudging every minute - which I did for the entire 6-hour XO-1 observing session described below! I now have a Meade RCX400 14-inch, and it nudges "like a charm" - keeping the star field within the AO-7's range and assuring that the stars on the main CCD are fixed to within a few pixels for hours at a time, without supervision.

If the polar axis is adjusted to be close to perfect, it's true that fewer manual nudgings would be required but another problem would exist. Whenever a Declination nudge in the opposite direction is needed there would be a backlash issue. For the Celestron telescope the backlash was ~15 seconds of nudge, and this would make Dec reversing difficult. (Yes, I could tighten the Dec backlash gear again, but that would mean another polar alignment session, MaxPoint calibration - and hey, I knew I was getting a Meade in a amonth!)

Maintaining the Observing Log

I'm wary of the degrading effects of cirrus clouds, dew or frost accumulation on the telescope corrector plate, the need for focusing changes, wind-driven smearing, waves in the atmosphere that cause smearing along one direction and other unforseen problems, so I perform a minimal processing of each raw image as it is downloaded.

Here's a sample of my observing log for 2006.03.14.

 

Figure A4. Sample observing log (page 3 of 4). Left columns is UT start time for a sequence. Next number for each group is the observing sequence number, then elevation. Then there are 10 coded number groups, one for each image, describing FWHM and 3 digits for the kilo-counts flux of Reference Star #5 (Fig. 5a). Focus adjustments are also noted.

At the bottom of this observing log page, at the end of the observing sequence #33, that started at UT 10:46, there's a notation "Must be frost." The next observing sequence has the notation "Finished hair dryer." At that time the outside air temperature (at roof level) was 28 F, the dew point was 19 F (RH = 70%), and I was concerned about frost forming on the corrector plate. What aroused my concern? Let's take a moment to describe what I record for each opbserving sequence.

Look at the sequence that starts at 10:46 UT (sequence #33). It starts out with "..." that refers to the info at the top of the page: object is X634 (part of an earlier name for XO-1), RED filter, and AO-7 set to 0.4 second exposure times. Then it states that elevation angle was 74.8 degrees (at the start of the sequence - serving as a reality check when using TheSky later to derive air mass). Then there's a set of coded numbers, one for each image. The first one is for image 330. The notation is "330_42.199." This means that X634 had a FWHM of 4.2 "arc (actually smaller since my aperture was set to maximum radius), and the star's flux started out 199 (actually it was 199,033). I keep track of the need for focusing with the FWHM entry, and the possibility of cirrus clouds and dew or frost with the star flux. The set of star fluxes for this sequence is: 199, 200, 200, 200, 200, 198, 197, 198, 196, and 194. The downward trend at the end alerted me to the need to check the sky or frost on the corrector plate. So I went outside, the sky looked clear (thanks to a full moon for showing cirrus), so I concluded there was frost on the corrector plate. I checked it with a flashlight, and used a hair dryer to blow warm air on some frost that had formed on the corrector plate (while pointed at zenith and taking data for Sequence #34). As noted for the last sequence on this page I finished the hair dryer treatment at ~11:05:40 UT, with the possibility of ruining images 341 - 344 (with a hair dryer obstructing some of the aperture and a flashlight checking for frost). The post-hair dryer star fluxes did indeed rise, ~4%, showing that the frost had indeed been accumulating since maybe 10:36 UT (using the other star flux notations to establish the beginning of the downward trend).

Did the hair dryer episode affect exoplanet observations? If we're trying for 1 or 2 mmag precision then surely placing a hair dryer over the aperture and shining a flashlight should have had some effect! OK, yes, it dropped the exoplnet observed brightness by 4mmag! This can be seen in Fig. 1, where there's a low point at 11.07 UT.

This example of frost effects illustrates the value of paying attention in real-time to downloaded images and quality checking to avoid unrecoverable problems. If I hadn't noticed the decrease in star flux due to frost I might have lost the entire egress.

Image and Data Analysis

After a nap and breakfast, there remains a short session of dealing with images and a longer session of spreadsheet analysis.

I used to produce exoplanet magnitudes like everyone else, using a procedure called "Differential Photometry." The simplest form of differential photometry assigns a magnitude to a reference star and a photometry tool measures the flux of that star and the star of interest. The ratio of fluxes is converted to a magnitude difference, and this is added to the reference star's magnitude. A variant of this procedure is to assign several stars to reference status, and use the average of their solutions for the star of interest as the final result for that image. This is called "Ensemble Differential Photometry."

A few months ago I abandoned both forms of differential photometry in favor of a procedure I call "Artificial Star Photometry." This procedure allows for the identification of images affected by clouds, or poor seeing, or poor tracking, and permits the user to specify objective criteria for data rejection. It also provides the user with a wealth of information about the brightness behavior of other stars, including reference stars. If, for example, a reference star is too close to the edge of images and an imperfect flat field causes that star's flux to vary in a way that it wouldn't vary if it were at the image center, the user can readily see that this is occuring and reject using that star for reference purposes. The standard differential photometry procedures don't allow this insight; the user is therefore blind to this and similar defects in the images. My Artifical Star Photometry procedure is labor intensive, and since it also makes extensive use of spreadsheets (which not everyone likes), I will describe it in another web page: Artificial Star Photometry  The next two sections of this web page describe use of the Ensemble Differential Photometry procedure for exoplanet monitoring, which most amateur photometrists would consider adequate.
 
A group of ~30 images are loaded into MaxIm DL (MDL). They are subjected to a "Calibrate All" command which applies a dark frame subtraction and flat frame division. Next I use the MDL Photometry Tool to batch process the group of 30 images using ensemble differential photometry. For XO-1 I used 5 reference stars that surrounded XO-1 (I now use only 4 reference stars; the 12.30 star is too faint, and adds noise to the XO-1 result).

  

Figure A5. Finder chart showing my 5 reference stars (ensemble photometry) and a set of R-magnitudes. These aren't the actual R-mags but they're close to the apparent R-mags I get using my telescope without correcting for star color. FOV = 16.4 x 20.6 'arc (cropped version of an original). [Note: starting in April I have omitted use of the star labelled 12.30 since it added noise to the XO-1 observations.]
 
The reference star south of XO-1 is fainter than XO-1 by a factor of 4 (R-mag = 12.3 vs 10.8) but I used it as a reference star (mistakenly, I now believe) because of its close proximity to XO-1. Three stars are brighter, and with ensemble the average magnitude for all of them is used to establish the target's magnitude. That 12.3 magnitude star has a SNR ~250 for my 60-second exposures, so it's magnitude is uncertain by ~4 mmag based on CCD noise stochastic arguments. Scintillation is probably comparable, and is experienced by all stars in the FOV. The ensemble differential photometry result for XO-1 is uncertain by 2.6 mmag per 60-second image (based on a spreadsheet analysis of this transit). Averaging the results from 5 images leads to a stochastic uncertainty for the exoplanet of 1.2 mmag per 6.5-minute group of 5 average, plotted as red circles in Fig. 1.

Before performing the ensemble differential photometry it's important to select a signal aperture radius that includes most of the flux from stars for the range of seeing conditions of the observing session. In changing signal aperture radius there's a trade-off of SNR and "flux recovery ratio," which I'll call Fr (where Fr is the ratio of flux for a given aperture radius, r, to that for a large radius). Theoretically, going from very small radii to large, SNR increases, reaching a maximum at r = 0.75 * FWHM (assuming a Gaussian PSF), then begins to decrease to low values for large radii. At the same time the plot of Fr grows monotonically from zero to one. The "sweet spot" is a radius such that Fr ~99% (which is my subjective estimate). As seeing varies Fr will vary, but it should vary the same for all stars in a specific image (assuming minimal coma), so the fact that Fr is as low as 99% does not imply that there will be 1% uncertainties in the resultant magnitude estimate (this would be true for all-sky analyses, however). The relevant parameter is the change of Fr with location on the image, and my crude estimate of this (for my present collimation setting) is that setting r = 12 pixels when FWHM = 4 pixels, leads to Fr values that are the same (~0.99) for all reference star locations, with a max-to-min variation of 0.0018 (RMS = 0.0007). Therefore, errors from this source are likely to be 0.7 mmag for typical images.

MDL's Photometry Tool "asks for" reference star magnitudes, and it is not important to use accurate values. Even if one of the reference stars is a long period variable and has a brightness different from the assumed one by possibly a magnitude, little harm is done to the ensemble photomtry result for the target. For example, according to my spreadsheet analysis the above 5 reference stars differed from their assumed magnitudes (based on observations of 2006.03.06) with an RMS = 0.035 mag. Their average difference was 0.00 mag. I conclude that none of the 5 reference stars are variable on timescales of a few days. The persistent differences for the 5 reference stars (of one night with respect to another) is probably related to differences in the flat field used for the two observing dates. But it really doesn't matter that each refernce star could be wrong by as much as 0.038 mag since the star field on the CCD chip did not move more than a few pixels for the entire observing session.

After MDL performs its ensemble differential photometry, assigns the unknown target star a magnitude, and calculates the image's mid-exposure time in JD units, the user may then record the results as a CSV-file (comma separated values). These CSV files can then be imported to a spreadsheet.

Spreadsheet Analysis

Each CSV-file import has a title header line that can be removed by deleting its row. Thus, after all CSV-files have been imported there are no row gaps between data. The data should be uniformly spaced in time since an observing sequence with a large repeat count there were no pauses between sequences. For my observations all image mid-exposure times in the spreadsheet are 78 seconds apart.

Occasionally a cosmic ray artifact will be present near the center of a star image. If this occurs for a reference star (or the target star) the ensemble photometry result will be affected. Therefore, outlier target star data must be identified and rejected. My favorite routine for this is to calculate in a spreadsheet column the difference between a target magnitude and the average of the 4 nearest neighbors. Visual inspection of this column readily shows where bad data exist. I found only one such outlier among the total image count of 224 images (excluding the first 0.6 hour, which corresponds to air mass greater than 2.5).

Once outliers have been deleted I calculate group-of-5 averages. Each group is for different data compared to the neighboring group average (i.e., it's not a sliding boxcar, which can be misleading). The group-of-5 data should have less than half the scatter of the individual values. For the data with air mass < 2.5 the group-of-5 data exhibit an RMS scatter of 1.17 mmag. The way this is calculated renders it insensitive to slow changes in the true target brightness. Any abrupt structure near ingress and egress will add a negligible amount to this SE estimate.

For my longitude (110 W) there are two transit "windows" for 2006: March 6 to April 3, and May 16 to June 9. I've used the interval between these windows to monitor XO-1's brightness stability in order to check the possibility that other planets are in the same orbital plane as XO-1b and have orbits small enough to transit XO-1. To date, no convincing candidate fades have been observed.

On April 3 I sold the Celestron that had been used for the previous year to observe XO-1 transits, and took delivery of a Meade RCX400 14-inch telescope. On April 16 I began observing XO-1 every clear night for ~2 hours each night. My goal was to either capture an ingress/egress feature, or produce an average magnitude for the observing session that was significantly fainter than the average for other nights. This latter approach to detecting a planet assumes that the observing session was fortuitously confined to a transit event, which is possible when observing sessions are shorter than 2.7 hours (derived in the next paragraph). The observations of nightly-average magnitude versus date are shown in the next figure (repeated from Fig. 2).



Figure A7 (Expanded version of Fig. 2, left panel). Nightly brightness of XO-1 when XO-1b is not transiting for observing sessions typically 2 hours long. [Meade RCX400 14-inch telescope]

If an additional planet exists that transits the star as seen from earth, it will necessarily be in an orbit in close proximity to the Jupiter-mass planet XO-1b. For it's orbit to be stable it will be in a resonant orbit. The two most likely possibilities are a 2:3 resonance inner orbit and a 3:2 resonance outer orbit. The inner orbit will be subject to greater gravitationally destabilizing forces, so the most likely orbit is a 3:2 resonance outer orbit. The period for the outer orbit would be 5.91 days (141.9 hours) and the orbit radius would be 1.31 times larger than that of XO-1b. Assuming a tilt of the orbit plane 2.3 degrees (i.e., inclination 97.7 degrees), the planet would still transit in front of the star's disk. It's chord length would be 83% of the star's diameter (versus 91% for XO-1b). The transit duration would be about the same as for XO-1b, 2.74 hours instead of 2.60 hours. The transit "duty cycle" (fraction of time spent transiting the star) would be 1.93 %.

What is the feasibility of detecting such a 3:2 resonance planet? Let's assume that we can detect it if it produces a mid-transit fading depth of 3 mmag. This corresponds to a solid angle ratio of 14% that of XO-1b, which corresponds to a diameter ratio of 37%. If XO-1 could be observed for a continuous 142 hours, and no additional transit was found, such a planet could be ruled-out. If half that observing time were accumulated, and assuming there was no phase overlap, then a non-detection would constitute a 50% ruling-out of such a planet.

So far I've observed XO-1 out-of-transit on 20 dates for a total of 37.5 hours. Assuming these 37.5 hours are not overlapping in phase (for a 142-hour period) this corresponds to ~26% coverage of a hypothesized 3:2 outer orbit resonance planet. In other words, I can't rule-out such a planet, but the chances of it existing are reduced with every additional increment of observing time that does not show the star to be >3 mmag fainter than usual.

There are two candidate fade dates in Fig. 7, DOY = 121 and 134. Both are of the order 3 mmag, yet I do not beleive either are real and credible candidates for an actual additional exoplanet transit. I have three reasons for taking this position: 1) there's a positive feature of similar magnitude (DOY = 130) whcih cannot be explained, 2) the DOY 121 observing session was 3.1 hours long and the longest transit duration is 2.74 hours for a 3:2 resonance orbit, and 3) many dates exhibit 2 to 3 mmag differences from the average that are also much larger than their stochastic SE.

This last point is the most significant one, since it highlights the fact that there are unexplained systematic errors that are larger than the stochastic kind. A larger aperture telescope is not necessarily going to overcome these systemtic errors. Rather, better observing procedures or image analysis procedures are to be investigated.

There appears to be an auto-correlated variation of XO-1 R-magnitude, somewhat resembling a monotonic rise in brightness during the 4-week observing interval. The XO-1 brightness is based on "ensemble photometry" using four reference stars. At least two of these reference stars is variable at the 5 to 10 mmag level, and I have modeled the variability of all four. Their different periods will produce apparent XO-1 variations with similar periods, and I believe that this will eventually explain the systematic deviations from an average brightness exhibited by XO-1 in Fig. 7. Additional observations are needed to be sure of this explanation, and to possibly remove their effect on XO-1 when the variable reference stars are characterized. More information on this project can be found at VariableReferenceStars.

This site opened:  May 11, 2006.  Last Update:  October 06, 2006