Amateur Observations by Co-Author Bruce L. Gary
Hereford Arizona Observatory (G95)
This web page describes contributions to the study of the XO-1 exoplanet system using observations with the Hereford Arizona Observatory 14-inch amateur telescope during the past year (i.e., most of which precede the Space Telescope Science Institute press release on May 18, 2006). This web page has a Highlights section that summarizes "observational results" for those not necessarily interested in the techniques used to achieve them. Following that is a Detailed Descriptions appendix meant for amateurs interested in my observing and data analysis techniques. In the appendix I use the 2006.03.14 transit for a "how to" case study tutorial, illustrating my belief that the two most important considerations for achieving good exoplanet transit data are: 1) keep the star field fixed to the same location on the CCD chip for the entire observing session, and 2) use an R-filter. Since I occasionally join with my neighbor (Dave Healy) in the use of his 32-inch RC I will also include those results on this web page. The most recent update will always be at the top (the item and figure numbering are therefore in reverse order) .

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

Combined R-band LC

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.

Item 5) R-band Transit of June 1, 2006

XO! R-band LC 2006 Jun 1

Figure 5. This R-band "light curve" is for the June 1, 2006 exoplanet transit of the 10.8 R-magnitude star XO-1 by the Jupiter-sized planet XO-1b. The solid red circles are non-overlapping 5-point averages (spaced 6.9 minutes apart) of magnitudes from images with a 1-minute exposure time. An air mass trend correction of -0.004 magnitude per air mass has been applied (maximum correction = 1.6 mmag), due possibly to color differences of the reference stars and XO-1. The red trace is a model fit (described in the text) shifted 1.6 minutes earlier than the predicted transit time. Mid-transit is at 5.829 ± 0.020 UT. The mid-transit depth is ~23.6 ± 1.0 mmag. (Measurements precision suffered during this observing session due to several episodes of downslope winds that caused star field movements that were faster than my image stabilizer was able to follow.) [Meade RCX 14-inch telescope, SBIG AO-7 tip/tilt image stabilizer, SBIG ST-8XE CCD; MaxIm DL for telescope/CCD/AO-7 control and image analysis; Hereford Arizona Observatory]

Mid-transit occurred 1.6 ± 1.2 minutes earlier than predicted (using Table 3 in the ApJ publication). This is consistent with the previous transit (4 days earlier) occurring 1.1 ± 0.5 minutes early. All mid-transit calculations are performed using HJD, which are then converted to JD and UT. The timing of XO-1b transits can be affected by another planet, especially if it is a resonant orbit. Additional timings are needed to establish evidence for such a planet based on timing departures.

Transit durations are worth monitoring in case there's any variation of planet's orbit inclination or orbital velocity at the time of transit. Instead of ingress to egress duration I choose to use something I'll refer to as "1/3 depth duration" - the time between 1/3 of maximum depth times. The 1/3 depth corresponds closely to the planet center coinciding with the star's edge (for transit paths that come close to the star's center (i.e., closer than ~3/4 of the star's radius; for XO-1 the path comes as close as ~1/2 the star's radius). This "1/3 depth duration" geometry is convenient for calculating the transit chord length and therefore orbit inclination. The three dates have the following 1/3 depth durations: 2006.03.14 = 2.53 ± 0.03 hours, 2006.05.24 = 2.56 ± 0.03 hours, 2006.06.01 = 2.56 ± 0.03 hours. So far there's no statistically significant change in this measure of transit duration.

Transit depths at R-band are the same for the March 14 and June 1 transits, being 23.8 ± 0.5 and 23.6 ± 0.5 mmag, both of which are less than the depth for B-band (next item)..  

Item 4) B-band Transit of May 24, 2006

B-band LC

Figure 4. This B-band "light curve" is for the May 24, 2006 exoplanet transit of the 11.8 B-magnitude star XO-1 by the Jupiter-sized planet XO-1b. Measurements of individual images (1-minute exposures) are shown by small dots, and they exhibit a 1.96 mmag RMS scatter (>6.2 UT). The solid blue circles are non-overlapping 5-point averages (spaced 6.9 minutes apart). The 5-point averages exhibit an RMS scatter of 1.17 mmag (non-transit portions >6.2 UT). An air mass trend correction of +0.006 magnitude per air mass has been applied (maximum correction = 2.4 mmag), due possibly to color differences of the reference stars and XO-1. The blue trace is a model fit, using a simple limb-darkening model, shifted 1.1 early with respect to the predicted transit time. Mid-transit is measured to be 8.640 ± 0.008 UT. The dashed red trace is from an R-band transit observation (next item) made 2006 March 14 (with a 14-inch Celestron). The B-band mid-transit depth is ~24.8 ± 0.5 mmag (i.e., 2.31%), which is slightly larger than the R-band depth (23.8 ± 0.5 mmag) due to a steeper B-band limb darkening for the star XO-1. (Data past 10.8 UT suffer from clouds.) [OGS Ritchey-Chritien 32-inch telescope, David Healy (Director), MPC code 701, SBIG STL-6303E CCD camera, MaxIm DL for CCD control and image analysis; Junk Bond Observatory, Sierra Vista, Arizona]

Limb darkening models for a sun-like star predict deeper transit depths at B-band than R-band. This was shown by observations with the Lowell Observatory Perkins 72-inch telescope (made by the Boston University group led by Prof. Ken Janes, and reported in the ApJ article). The present result is a confirmation of this color dependence, based on observations made with two different (amateur) telescopes and a model fit using Rp/Rs = 0.144 and simple linear limb darkening model with a "1-cos(theta)" coefficient of 0.60. The May 24 transit occurred 1.1 ± 0.5 minutes earlier than predicted. A WWV radio check was made of the computer clock which was the source for FITS header time tags, and the computer clock was accurate to ~1 second.

Item 3) R-band Transit of March 14, 2006

 Light curve of 2006.03.14 transit

Figure 3. This "light curve" is for the March 14, 2006 exoplanet transit of the 10.8 R-magnitude star XO-1 by the Jupiter-sized planet XO-1b. Measurements of individual images (1-minute exposures) are shown by dots, and they exhibit a 2.6 mmag RMS scatter (for air mass < 1.5). The red circles are non-overlapping 5-point averages (spaced 6.5 minutes apart). The 6.5-minute averages exhibit an RMS scatter of 1.2 mmag (air mass < 1.5). A trend correction of +0.0004 magnitude per hour has been applied, due possibly to color differences of the reference stars and XO-1. The dashed blue trace is an empirical fit, forced to be symmetric about mid-transit (9.96 UT). The open circle is suspect data when a hair dryer was used to evaporate frost from the telescope's corrector plate. The mid-transit depth is ~23.8 mmag (i.e., 2.2%). [Celestron 14-inch telescope, SBIG AO-7 tip/tilt image stabilizer, SBIG ST-8XE CCD; MaxIm DL for telescope/CCD/AO-7 control and image analysis; Hereford Arizona Observatory]

This light curve was made during an exceptionally calm and clear night with better than usual "atmospheric seeing." The SBIG AO-7 tip/tilt image stabilizer kept the star field fixed with respect to the CCD pixel field (RMS ~1 pixel) which minimized degrading effects related to an imperfect "flat field" (a calibration to correct for "vignetting"). Although slightly better quality observations of this star have been obtained in April, at times when no transits were scheduled to occur (with a Meade RCX-400 14-inch telescope), this is my most successful observation of an exoplanet transit to date. Following this "Highlights" section I present a tutorial illustrating observing and analysis procedures that I recommend for exoplanet transits. Dr. Peter McCullough used this transit, plus observations of several others by myself and other team members beginning in June, 2005, to establish an orbital period for XO-1b of 3.941534 +/- 0.000027 day.

Item 2) Search for Additional Planets

During April and early May there were no transits of XO-1b that could be observed from my longitude. I used this non-transiting interval to search for transits by other planets in the XO-1 system and to determine if the star XO-1 exhibited brightness variations when no transit was in progress. A total of 37.5 hours on 20 nights have been used in this search. The two transit features that would be produced by another planet, and which could be detected using my amateur equipment for a planet as small as 1/3rd the diameter of XO-1b (1/9th the transit depth, or 2.6 mmag) are: 1) ingress or egress changes in brightness during the observing session, and 2) night-to-night differences in brightness caused by an observing session being brief and confined to between ingress and egress.

A search of each night's observing session showed no ingress or egress features. Also, the night-to-night average brightness did not change in a way that could be interpreted as produced by a transit exceeding 5 mmag, which represents this study's null result for additional planet transits. The constancy of XO-1 appears to be better than 5 mmag during the 4-week observing period. The following graph shows nightly R-magnitude averages for XO-1 and a nearby faint check star. 

Nightly variations

Figure 2. Nightly brightness of XO-1 (when XO-1b is not transiting) and a nearby check star (1/4th as bright as XO-1). Observing sessions were typically 2 hours long. A correction has been applied for small variations of reference star brightness. Error bars are stochastic SE and do not include unknown systematic effects that apparently exist at the 3 mmag level. The sinusoidal "fit" to the XO-1 data (repeated in the check star plot) has an amplitude of 1 mmag and a period of 38 days, but data uncertainties are insufficient to claim that the variation is real. [Meade RCX400 14-inch telescope; Hereford Arizona Observatory]

XO-1's brightness appears to have been stable during the 4-week observing period. This result is somewhat dependent upon my analysis of reference star variations and the removal of their effect upon XO-1 brightness. A detailed description of this analysis is given at ReferenceStarVariability.

I want to mention that this is my first observing project with a newly-purchased Meade RCX400 14-inch telescope. This telescope, mounted on an equatorial wedge, is ideal for exoplanet monitoring for the following reasons: 1) it's a fork mount (no meridian flips to interrupt observing), 2) the tube is made from low thermal expansion material (no focusing changes that would interrupt observing), 3) collimation is easy (no excuses for coma effects on photometry), 4) sturdy mount and OTA (same polar alignment every night, less shaking due to wind), 5) good tracking (easier to keep the star field fixed with respect to the CCD pixels), and 6) the RCX optics produce good image quality for a larger FOV, which means a larger CCD chip can be used, which means there's a greater likelihood of including bright reference stars in the FOV, and this translates to smaller Poisson and scintillation components of uncertainty for the exoplanet's ensemble photometric brightness measurement.

If the Jupiter-sized planet XO-1b has a moon the planet and moon will orbit around their center of mass (i.e., their "barycenter"). It takes 23 minutes for XO-1b to cross the star's edge (contact 1 to contact 2). If, for examle, XO-1b has a moon with mass 1/10 that of XO-1b in an orbit that's just as large as Io's orbit around Jupiter (scaled up by 1.3 so it has the same ratio to its planet's radius as Io's orbit has to Jupiter's radius), then every 2.7 days XO-1b would orbit around the barycenter with a total movement of ~60% of its diameter. This would produce transit timing shifts with an amplitude of ~7 minutes (~14 minutes peak-to-peak). Given that transit timings are the same as predicted to within ~2 minutes, such a large moon can be ruled out. However, we cannot yet rule out a moon in the same orbit with a mass 1/70th that of XO-1b. Amateurs should be able to achieve timing accuracies of ~1/2 minute per transit. This means there's an opportunity for asmateurs to constrain the mass of any hypothetical XO-1b moon to the level ~1/300 the mass of XO-1b (or some combination of orbital distance and mass). Since the Hubble Space Telescope has apparently eliminated the possibility of a moon for exoplanet HD209458b (from the shape of the transit) it is a "long-shot" project to be looking for effects of a moon orbiting XO-1b.

Item 1) Creation of Photometric Sequence

There are two reasons to establish a photometric sequence of the XO-1 star field. First, the brightness of star XO-1 is used to derive a distance, which in turn is used to determine a most probable stellar mass and radius, and at a later stage this is needed to solve for the planet's mass and radius (and density). Second, in order for different observers to compare observations made at different times it is useful to adopt magnitudes for nearby stars so that they may serve as a common "reference."

I observed standard star fields established by Landolt (1992) on two dates (2006.02.25 and 2006.03.14) for the purpose of establishing a B, V, Rc and Ic photometric sequence for stars near XO-1. The Landolt regions were near the celestial equator at RA 04:52 and 12:42, and  there were 28 stars bright enough for the establishment of constants for my telescope's "zero shift" and "star color sensitivity." The observations were timed so that air masses were the same for the Landolt stars and XO-1, and they were taken close in time in order to reduce any effects of temporal extinction changes. Additional information about these all-sky observations can be found at AllSkyXO1.

Eight potential reference stars were chosen for this analysis. The two sets of Rc magnitudes were in good agreement (average difference = 0.005 magnitude). Here's a finder chart for the 8 stars.


Figures 1a. Eight stars for which all-sky BVRcIc magnitudes have been performed. An "X" is next to XO-1. FOV = 16 x 21 'arc. Figure 1b. Table of all-sky magnitude determinations.

The estimated SE accuracy for these stars is:

    B  SE = 0.04 magnitude
    V  SE = 0.03     "
    Rc SE = 0.020    "
    Ic SE = 0.03     "

_______________________________   This is the end of the HIGHLIGHTS section   ______________________

Links Internal to this Web Page
    Site and Hardware
    Software for Telescope Control and Analysis
    Planning a Typical Night's Observations
    Exposure Times
    Observing and Reduction Logs
    Flat Frames
    Dark Frames
    Automating Observing Sequence
    Image Stabilization and Tracking
    Maintaining an Observing Log
    Image and Data Analysis
    Spreadsheet Analysis
    Updated Finder Chart
    Final Photometric Sequence
    Searching for Other Planets in the XO-1 System
    Poisson NoiseScintillation Noise (compared with observed precision)
    Transit Ingress & Egress Schedule for May and June, 2006
    Related Links (other XO-1 transit observations, transits of other exoplanet systems, etc.)


The star XO-1 is located in the constellation Corona Borealis, at RA = 16:02:11.6, Dec = +28:10:11 (see CB for a zoom sequence showing XO-1's location). I have measured its brightness (all-sky photometry) to be B = 11.85, V = 11.19, Rc = 11.806 and Ic = 10.43. The exoplanet XO-1b has an orbit that causes it to transit in front of the star every 3.941534 days (McCullough et al, in press). The star is very similar to our sun in size, mass and surface temperature. This new solar system is ~200 parsecs away (650 light yeaers). The planet has a mass ~0.9 times that of Jupiter, and its spherical-equivalent size is ~1.3 times that of Jupiter (McCullough et al, in press). The planet's density is ~0.57 times that of water, which is slightly less than the density of Saturn (0.69 times water) and much less than the density of Jupiter (1.33 times water). As described in the article by McCullough et al, the exoplanet system was discovered in early 2005 by a wide-field survey (McCullough et al, 2005). Four amateur observers contributed to the confirmation of the transit light curve shape being planet-like starting in mid-2005: Tony Vanmunster, Ron Bissinger, Paul J. Howell and Bruce L. Gary. Dr. Peter McCullough confirmed the planet identification using Doppler velosity observations in early 2006. So far no transits have been found beside those produced by XO-1b.

This rest of this web page emphasizes one night's observations with a 14-inch telescope. Links are included that treat related issues, such as subsequent searches for additional planets in the XO-1 system, other transit observations by this observer (in 2005 and 2006), other people's web sites, and my all-sky observations used to derive a BVRcIc photometric sequence for stars near XO-1. Much of the following material is "tutorial" in nature, as it is meant to illustrate the way this amateur conducts exoplanet observations.

Site and Hardware

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."

 Hereford Arizona Observatory

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.

 SRO roof open

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.

RCX400 & author

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%.


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.

Automated Exposure Sequence

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.

Updated Finder Chart

Observations of two Landolt star fields at three times of this night's observing session have led to a new all-sky photometry sequence for the XO-1 region.

Figure A6. Finder chart showing 4 reference stars. New R-magnitudes for them are listed in the text. FOV = 14 x 19 'arc.

Differential photometry does not easily lend itself for establishing photometrically correct target star magnitudes. This is because differential photometry does not implement CCD transformation equations (or their countpart, Simple Magnitude Equations). Whereas the 4 stars that I use for "reference" have Rc-magnitudes of 11.046, 9.261, 10.680 and 10.330, I must use 11.09, 9.30, 10.77 and 10.42 in order to produce the correct XO-1 Rc-magnitude of 10.806.  These small differences will be different for every observer, since every telescope system has a unique response to star color. Every observer will have to establish their own set of reference star empirical magnitudes that achieve the correct target star magnitude.

Searching for Other Planets in the XO-1 System

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.

Poisson Noise

"Poisson noise" is related to the fact that a finite number of stochastic events lead to a "counts" reading from each pixel. Consider the process of a photon dislodging an electron from a silicon crystal in the CCD (somewhat related to the "photoelectric effect"). This one event yields one electron for detection after the exposure is complete. When a pixel is "read" by electronic circuitry this one electron will contribute to that pixels count value by an amount that depends on the CCD gain. For a SBIG ST-8E CCD, the gain is 2.3 electrons per count (where each "count" is also called an ADU, or analog data unit). Therefore, the number of photon-dislodged electrons needed to produce a count of C is n = 2.3×C (for this CCD). Stochastic events have the property that the SE uncertainty of the total number of events is the square-root of the number of such events. Thus, when we measure n stochastic events we must state that we have really just measured a value n ± sqrt(n) events. Since the measurement C is based on 2.3×C events (for this particular CCD) we must state that we have measured: 2.3×C ± sqrt (2.3×C) "events." Stated in terms of counts, we measure C ± sqrt (C/2.3). This fundmental uncertainty is referred to as Poisson noise. To summarise this, Poisson noise from a bright star is:

    Np = sqrt (C / gain)
    Np = sqrt (C / 2.3) for SBIG ST-8E.

So far this treatment assumes that there is no noise contribution from the process of "reading" the CCD ("CCD read noise"), or noise produced by thermal agitation of the crystal's atoms ("CCD dark current noise"), or from noise produced by a sky that is not totally dark ("sky backgound noise"). These are three additional sources of noise in each CCD reading, and the last two are Poisson themselves since they are based on discrete stochastic events. These three noise sources are small when the star in the photometry aperture is bright and the CCD is very cold (to reduce dark current noise). For this situation we can state that the star's measured flux (total counts within the aperture minus a background level of expected counts) will be uncertain by an amount given in the previous paragraph. If, however, the CCD is not very cold, which is going to be the case for amateurs without LN2 cooling, the noise will be greater. If there is no star within the signal aperture then we can calculate that the noise produced by reliance upon the number s pixels within the photometry signal aperture will be:

    Ns = sqrt (s) * Ni

where s is the number of pixels within the signal aperture of the photometry circles, and Ni is the noise of each pixel. Ni is calculated as the RMS difference of the counts for the r pixels within the sky background annulus. If a star is present the total noise from the signal aperture's count reading is the orthogonal sum of the star's Poisson noise, Np, and Ns.

Finally, the sky background level cannot be determined with perfect accuracy. The average level of counts from the r pixels contained within the "sky reference annulus" is:

     Nr = sqrt (r) * Ni

Since Ni and r have non-zero values, Nr will have a non-zero value. In practice, however, r is so large that Nr is small enough that it can be ignored.

The total noise for a photometry reading (using a SBIG ST-8E) is therefore given by the equation:

    N2 = Np2 + Ns2 + Nr2

    N2 = C / 2.3 + s × Ni2 + r × Ni2 

The signal-to-noise ratio, SNR = C / N. Given that magnitude uncertainty is 1.085 / SNR, we can state that millimagnitude precision is:

     SE [mmag] = 1085 × sqrt ( C / 2.3 + s × Ni2 + r × Ni2 ) / C

where it is easy to identify the three contributions to uncertainty associated with the bright star's Poisson noise, the signal circle's (CCD read, dark current, sky background) noise, and the sky background reference annulus' (CCD read, dark current, sky background) noise.

Let's insert some typical values into this equation, then calculate SNR - which is easily converted to "millimagnitude precision."

I'll adopt the following: telescope with 14-inch aperture telescope, seeing ~4 "arc (FWHM), R-filter, air mass = 1.1, a SBIG ST-8E CCD cooled to -25 C, plate scale ~1.0 "arc per pixel. The longest exposure that avoids saturation for XO-1 is ~4 minutes. This is long compared with the temporal resolution that's desired for exoplanet transists, so let's calculate noise for 1-minute exposures. A 1-minute exposure produces C = 225,000 counts. The background noise for each pixel ~11 counts. Good performance is achieved using photometry aperture circles with radii of 12, 3 and 12 pixels (radius of signal aperture circle, gap width, sky background annulus width). The number of pixels in the signal aperture circle is 452 and the number in the sky background annulus is 1583. The three sources contribute the following noise to SE [mmag] for 60-second exposures:

    1.51 mmag    Bright Star Poisson noise
    1.10 mmag    Signal aperture (CCD read, dark current, sky background) noise
    0.03 mmag    Sky background annulus (CCD read, dark current, sky background) noise

    2.01 mmag   Total noise (orthogonal sum)

I measured an empirical noise of 2.23 mmag, so there might be another component of 0.20 mmag. As described in the next section, scintillation is a likley candidate.

Since the signal aperture contributes a significant amount to the total noise, I thought there might be merit in reducing the signal aperture, thus reducing s × Ni2. However, when I re-reduced the 2006.03.14 XO-1 transit images using signal aperture radii of 8, 10 and 12 pixels, the best performance was with the 12 pixel radius.

Scintillation Noise

At tropopause altitudes clear air turbulence is common, and it causes stars to "twinkle." (Atmosphereic seeing is degraded mostly by turbulence near the ground.) Everyone knows that stars twinkle different amounts on different nights. Twinkling also is greater near the horizon. Faint stars twinkle as much as bright stars. Planets don't twinkle as much as stars.

These common facts are helpful in understanding what to expect for attempts to monitor the brightness of a star that is undergoing an exoplanet transit. For example, the fact that planets don't twinkle means that a reference star's scintillation (another word for twinkling) will be uncorrelated with the target star's scintillation. This is unfortunate, for it means that a differential photometry analysis that uses one reference star will increase the target star's brightness variations due to scintillation by ~41% (i.e., root-2 more variation). Using many reference stars reduces the effect of uncorrelated reference star scintillation back to where it is dominated by just the target star's scintillation. It also can be stated that there's no need to chose reference stars that are near the target star to reduce scintillation, since essentially all correlation is lost with angular distances of 10 "arc (a typical planet angular diameter).

Andy Young conducted a classic study of scintillation in the 1960s (Young, 1967, 1974). He studied it's dependence upon telescope aperture, air mass, observatory altitude and exposure time. His equation relating all these parameters is:


where sigma = fractional intensity RMS fluctuation (scintillation), D = telescope diameter [cm], sec(Z) = air mass, h = observatory site altitude above sea level [m], h0 = 8000 [m], and T = exposure time [sec].
For my site, and specifically for the 2006.03.14 observations of XO-1, for which I have measurements to compare with theory, I calculate expected typical scintillation using the following input:

    D = 35.6 cm
    air mass = 1.1
    h = 1420 meters,
    T = 60 seconds,

The predicted scintillation using this input is 0.82 mmag.

As stated in the previous section Poisson and other CCD-related noise accounted for only 2.01 mmag of an empirically measured 2.23 mmag noise for XO-1 on the night of 2006.03.14 (near zenith). The missing 0.20 mmag is likely to be due to scintillation. Why, you mihgt ask, was the missing noise source as small as 0.23 mmag when the scintillation equation predicts 0.82 mmag. Recall, scintillation varies from night to night, and the equation is for "typical" scintillation fluctuations. On the night in question a high pressure was overhead, and the winds at ground level were uncommonly low (being zero mph for hours at a time). I conclude that I was lucky with good weather for the 2006.03.14 observations and my scintillation noise was ~0.23 mmag.

To summarize, the measured precision of 2.23 mmag per 60-second image is close to the theoretical limit of 2.17 mmag. The noise sources for a 60-second image using my telescope system are summarized in the following table:

                                 NOISE BUDGET FOR 14-INCH TELESCOPE
  (Assuming Target Star is at 12% of Full-Scale and Ensemble Photometry Using Many Bright Stars)

Noise Value
 Noise Source
1.51 mmag
 Bright star Poisson noise (12% of full scale, flux ~225,000 counts)
1.10 mmag
 Signal aperture (CCD read-out, dark current, sky background) noise
0.82 mmag
 Scintillation (typical)
0.03 mmag
 Sky background annulus noise (dark current, sky background, CCD read-out)
2.17 mmag
 Total SE for 1-minute exposure

In conclusion, to achieve that "gold standard" 1.0 mmag SE for XO-1, using a 14-inch telescope and ensemble photometry that includes a reference star 1.53 magnitudes brighter than XO-1, it will be necessary to average the results from at least four 1-minute exposure images.

Larger apertures should be able to achieve millimagnitude results more easily, although their exposure times will have to be shortened to avoid saturation. It should be each observer's responsibility to use the concepts described here to calculate their own optimum observing strategy.

Transit Schedule for the Remainder of 2006

Transit schedule for July - Oct, 2006

Figure A8. Predicted mid-transit times for the remainder of 2006.  For ingress  (contact 1) subtract 1.5 hour, for egress (contact 4) add 1.5 hour. Blue-shaded dates are ideal  for Western USA. Later dates are observable from longitudes eastward of Western USA. Assumed period is3.941534 days (as given in the ApJ article); actual times may be a few minutes earlier.

After the Oct 25 transit XO-1 is too close to the sun for favorable viewing for the remainder of 2006. For the Western USA there are only 3 dates when a complete transit can be observed (Aug 3, 7 and 11).

Related Links
    Astrophysical Journal article:
          http://xxx.lanl.gov/abs/astro-ph/0605414 (Abstract)

    Co-author sites:
          http://hubblesite.org/news/2006/22  (Peter McCullough, STScI)
          http://www.media.rice.edu/media/NewsBot.asp?MODE=VIEW&ID=8563&SnID=692431138 (Johns-Krull, Rice University)
          http://www.bu.edu/phpbin/news/releases/display.php?id=1136 (Kenneth Janes, April Pinnick & Paul Howell, Boston University)
                    (Peter McCullough & James Heasley, STScI; Bill Giebink, Les Hieda, Jake Kamibayashi, Daniel O’Gara, and Joey Perreira, Univ. Hawaii staff)
          http://www.cbabelgium.com/ (Tonny Vanmunster)
          http://ronbissinger.home.comcast.net/favorite.htm (Ron Bissinger)
          http://www.howell-ltd.com/Astronomy/html/exoplanet.html (Paul Howell)

    My other exoplanet related web sites:
          Observations of other XO-1 transits
          Modeling Size of Planet - General Case (an amateur's version)
          Modeling Size of Planet XO-1 (an amateur's version)
          Estimating planet size from only transit shape and star color
          Exoplanet transit observations of TrES-1
          Exoplanet Transit Observations of HD209458
          HD37605 exoplanet (possible transit system)
          HD74156 exoplanet (possible transit system)
          IL Aqr exoplanet reference stars

   Mscellaneous Related Web Sites
         Arto Oksanen's first-ever amateur exoplanet light curve
         Sky & Telescope article on XO-1
         Artifical Star Photometry
         All-sky photometry using Simplified Magnitude Equations
         Bruce's Astrophotos (with many other links)

    My email address: b r u c e g a r y 1 @ c i s - b r o a d b a n d . c o m


Landolt, A. U., 1992, AJ, 104, 340

McCullough, P.R., Stys, J. E., Valenti, J. A., Fleming, S. W., Janes, K. A. and Heasley, J. N., 2005, PASP, 117, 783.

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