TIMING OF ASTEROID OCCULTATIONS
John Broughton (Updated 2010-07-20)
Occultations present the opportunity to remotely investigate shape and dimensions of planetary objects with orders of magnitude gain in resolution over direct imaging. I have in the past observed visually a spectacular Jupiter occultation of 2.6-magnitude Beta SCO and measured brief disappearances of a fifth magnitude star by ringlets of Saturn but until 2003 I had never observed the more common variety of occultation by an asteroid. Following on from the development of Dave Herald’s Occult software, the turning point came with the advent of Steve Preston’s updated predictions, the accuracy of which made viable a CCD imaging and timing technique I had under consideration many years earlier. The original inspiration was a trailed photograph of a Metis occultation taken by Paul Maley in 1979.
Due to their slow image transfer rate, most astronomical CCD cameras cannot record short-term variability on consecutive frames without missing out on most of the action; hence an occultation is best recorded on a single frame. One technique that has been particularly useful in recording rapid changes during lunar occultations is called TDI (time delay integration) where the CCD array is read out line by line to produce a trailed image. Not many cameras including my own have operating software supporting this electronic option but any integrating camera attached to a stationary telescope can take trailed images as a consequence of Earth’s extremely regular rotation, which just happens to provide a rate of motion well suited to recording asteroid occultations.
With the advantage of noise reduction, a cooled CCD camera provides a substantial magnitude gain over non-integrating video cameras. From a moderately light-polluted location under otherwise favourable circumstances, sidereal-rate star trails as faint as magnitude 14 can be acquired with a telescope of 25cm aperture. A single image provides a convenient record for analysis, producing in most cases an unambiguously positive or negative result. Although cloud induced disappearances can mar an observation, they equally affect all nearby trails, making them easy to differentiate from the real thing.
Rigorous timing methods were devised and first employed for the Lutetia occultation of August 24, 2003. An accuracy of around .05 second can be expected for well-recorded events, leading to kilometre resolution in chord length and potentially an extremely precise celestial position for the asteroid. Lutetia incidentally has since been announced by ESA as the major asteroid flyby target of its currently enroute Rosetta comet rendezvous mission. Events previously considered unobservable may be within reach of observation; at right are the first 11 positive occultations recorded from my Reedy Creek, Gold Coast observatory in eastern Australia. The Euterpe event had a 0.3-magnitude drop, Echo occulted a star of magnitude 11.9 only 15 degrees from a full moon and the Rockefellia occultation was observed through cloud! Over a six-year period, 45 positive asteroid and dwarf-planet occultations have been recorded from the one location, all but four being drift-scan observations. Drift-scan reports appear from time to time on RASNZ’s Occultation Section results pages and also on the site are commented predictions for Australasia.
COORDINATING CCD AND
VIDEO DRIFT-THROUGH OBSERVATIONS
The telescope is pre-pointed to a fixed position in the sky where by virtue of Earth’s rotation; the target will drift through the centre of field at the time of occultation. Because the trail ends of drift scans are used in the timing calculations, the exposure must begin and end while the star is within the frame boundary, therefore it is important to employ accurate and fail-safe methods of coordinating both telescope and camera, especially when the field of view is small. Originally developed in 2004, ScanTracker now includes three pre-pointing modes and a printable chart of alignment stars, making it easy to point all kinds of telescopes whether used for drift scan, video or visual drift-through observations. The new modes enable an alignment on a naked-eye star followed by a single-axis offset and no faint-star hopping is required. Altazimuth mode is especially useful for rapid set up of portable telescopes. Recent developments include an extension of the charted limiting magnitude from 6 to 12; dispensing with the need to rely on other planetarium software for alignments in any mode. Version 4 released in July, 2010 is freely available here. View the readme file for instructions.
The camera is preferably oriented north up to produce left to right drift along rows of the CCD array; quite straight forward on a polar-aligned equatorial. For an altazimuth SCT, the east-west line of occultation displayed in ScanTracker will give an idea of the orientation. Final adjustments can be made with the aid of trial and error imaging of star trails.
In the drift-scan exposure section, its length is adjustable from 10 seconds up to a maximum dependant on field width and declination. An exposure 20 times longer than duration of the occultation is necessary if you want to cover the region in which an asteroid satellite could reside. Exceeding this can be disadvantageous since there is loss of limiting magnitude by sky glow the longer the exposure lasts. A 200 second exposure for instance may lose 2 magnitudes over one of 20 seconds at a moderately light-polluted site. For this reason it is good practise to shorten the exposure if circumstances are unfavourable for obtaining a well recorded image such as might be caused by bright moonlight or twilight, poor seeing, small magnitude drop, low elevation or combinations thereof. A minimal exposure should always be employed when there is threat of obscuration by cloud. With reference to an updated prediction, a rule of thumb I use to find minimum exposure is to add the maximum duration of the occultation to the time uncertainty plus 15 seconds for some margin of safety. Another reason to use an exposure shorter than the maximum allowed for your field-width is to avoid an overlap by a trail of equivalent or brighter magnitude. Such overlaps contain their own contrast-reducing seeing variations. GUIDE 8 with UCAC stars enabled is my preferred planetarium software when checking a target’s surroundings for interfering stars lying within 8 arc seconds of the same declination and within the intended exposure length in seconds of RA. In general, a drift scan of an occultation fainter than Magnitude 13.5 in a crowded field is not likely to produce measurable results.
The simulated drift scan at the bottom of ScanTracker displays the field of view and estimated limiting magnitude relevant to the selected telescope-camera combination. The magnitude represents the faintest star whose occultation is potentially detectable under favourable moonless conditions. A 2-magnitude loss from the listed limit can be expected when a full moon is present.
MANUAL TIMING OF THE
In the Windows operating system, the time listed in image file headers can easily be off by a second, even shortly after setting the clock and as in my case the exposure length may not be exactly as commanded, so for timing occultations I disregard this information. Because computer equipment floods short-wave with static, a digital timer previously synchronised to WWVH can be visually monitored during the beginning and end of exposure. If the camera lacks an audible shutter, a cardboard disk taped to a tennis racket can be used to unblock and block the telescope aperture (without actually touching the telescope) at the intended times within an electronic exposure a few seconds longer in duration. If as is preferable the camera has a mechanical shutter, the times when the shutter is heard to open and close are written down with the fractional second part estimated. Either method may be as accurate as 0.2-second, depending on the individual.
OF THE MECHANICAL SHUTTER
A $10 quartz analogue clock provides a low-cost means to derive accurate timing of the sub-second part, using the ticking sound. The small unit containing the workings can be removed from the clock and placed in contact with a microphone. Audio tests on mine revealed an hourly drift rate of only .008 second! The battery can be inserted by trial and error until the ticking is heard synchronized with short-wave UTC. This is then recorded on one channel of a stereo tape recorder while UTC is simultaneously recorded on the other through a second microphone or line-in. This recording is done prior to, or after the event when computer and camera equipment are not operating and causing radio interference to the short-wave signal. The microphone that recorded from the radio is then fastened in contact with the CCD camera to record its shutter clicks during the occultation. As in the first recording, the clock ticks are recorded on the other channel, guaranteeing a clear time signal at the critical time. It’s possible to make the drift-scan observation autonomous in order to observe the same event from another site. Both ScanTracker and MaxIm DL support delayed exposures of up to 32768 seconds (9.1 hours). The tape recorder could be on a power-point timer and an alarm set up to go off at the beginning of a specific minute and be audible on the clock-tick channel.
Audio software such as GoldWave is later used to analyse both stereo recordings in deducing the times the shutter opened and closed relative to UTC, as is shown in the diagram of a 1-second interval between clock ticks. Such timing measurements done within second intervals are not prone to errors caused by tape stretch. If the short-wave signal is faint and immersed in static, the clearest part of the recording can be selected, the volume maximised and noise reduction button pressed a few times until the UTC second marker stands out more clearly. The spike in the audio plot repeats every second in the same place relative to the clock tick. In my experience if the signal can be heard, then its position can be measured. To correct for propagation, 0.01-second for every 3000 km from the short-wave transmitter should then be added to the shutter timings.
More conveniently, the short-wave time signal and clock can be replaced by a GPS-based timer for simultaneous recording with the shutter clicks, in which case only a single stereo recording is necessary and propagation does not apply. Suitable devices are the KIWI beeper system, the GPS Clock and the VNG-uc GPS Time Signal Generator. This last one is the only fully self-contained GPS timing device capable of recreating short-wave UTC signals but hasn't been put into production.
Cameras lacking mechanical shutters give no audible cue we can use to time the exposure, so a different approach is required. A tie-clip mike can be attached to the RA drive motor instead of the camera. If sidereal tracking is turned on for just a second or two near each end of the exposure, a star image will show up near each end of the trail to become measurement points instead of the trail ends themselves. From the audio recording of the time signal and drive motor noise, it is the time of the end of the first short tracking period and beginning of the second that represent the star image centres on the trail. The tracking periods are kept short to minimise any degradation of timing accuracy by periodic error. I’ll later refer to trails of this type as having star-bump profiles to distinguish them from normal ones.
As with any CCD image, the drift scan should be calibrated with bias, dark and flat field frames to achieve the highest signal to noise ratio. Contrary to popular belief, timing resolution of an occultation using a CCD drift image is not limited by pixel size, except in unlikely events of very short duration. Trail ends can be measured at the sub-pixel scale by interpolation of the values contained in adjacent pixels; in effect joining the dots to find the point where the profile crosses a certain brightness level. For best results, the whole width of the trail needs to be taken into account by averaging X values over several rows on the Y-axis. In MaxIm DL this can be achieved automatically using a horizontal box aperture. First though it may be necessary to precisely level the trail using the edit menu rotate function with the bicubic resample box ticked. Next hold down the left mouse button to drag a long narrow aperture around the trail starting at the left edge of the frame, excluding any adjacent trails and as much background as possible. Then use the view menu line profile function, select horizontal box and the mean sample option and press the export button to save it to disk in the form of a comma-separated-values file.
A normal profile is a stretched version of a fixed
star’s bell-shaped curve and being a time variable image, it is
modified by atmospheric turbulence. Calculations I did in 2004
showed the end of trail profile to be stretched 200% compared to that
of a fixed-star radius, and the point of origin to be located exactly
midway in height between the trail and background levels.
Measurement levels derived from the lengths of many rigorously timed
trails in 2003 averaged within 1% of the 50% level. Even under the
influence of diffraction, the measurement level of the occulted part
was calculated to be at or very close this level so I believe
diffraction to be self-cancelling in the case of sidereal-rate drift
scans. This is different from the measurement level of
high-frame-rate video recordings where diffraction theory indicates
should be made at the 25% level.
This trail measuring application includes dynamic vertical scaling, smoothing of scintillation and signal noise, cancellation of optical distortion effects and calculation of overall timing accuracy. The LOAD button facilitates loading a profile such as included example file 050521 Bilkis.csv. The four measurements on the profile are always made in left to right order. Clicking the plot produces an expanded view whose width in pixels can be zoomed in as far as 32 or all the way out using those arrows that appear either side of the SMOOTH button. Clicking in this expanded view where the levels change brings about a sub-pixel X measurement displayed in green. A right click returns the full profile where the next position can be selected. Once the fourth measurement is made, times for the occultation based on the 50% level are computed and displayed. Measurements can be re-done by use of the BACK button. Scanalyzer recognises and can measure star-bump profiles, in which case ‘Star Bump’ replaces the terms ‘Trail Start’ and ‘Trail End’ after the first position is measured.
Since in practice the moving star is a distribution of light on the CCD two or more pixels wide, sudden changes caused by an occultation always have a slope and are less abrupt than the rapid variations due to scintillation and signal noise. The SMOOTH button applies a gaussian filter to suppress this high-frequency interference and improve accuracy without biasing the measurements. Smoothing should be applied at least once and can be done twice in the case of poor seeing conditions. On the third press, the original raw state is restored. Lights below the button indicate the level of smoothing and timing results are updated automatically.
When loading a CSV profile file, Scanalyzer also loads a TXT file of the same name if present in the same directory. Previously edited in Notepad by the user, this file holds two lines for trail-end shutter timing followed by one line for accuracy, followed by four lines of astrometric data used in averting a distortion-induced warp in timing. If this file is absent, timings can be manually entered into the white boxes or alternately the file can be present but omitting the four lines of astrometry. Lacking astrometry, computations are based on a simple extrapolation of image coordinates to time, which scarcely matters in the case of telescopes with negligible distortion such as unmodified SCTs. On the other hand a focal reduced SCT will have a little distortion while Newtonians and Cassegrains suffer considerably more. The astrometric data can be measured from any image taken with the same optical configuration. After calibration to celestial coordinates using Astrometrica, four positions are measured near the X and Y image coordinates equivalent to trail start (alternately star-bump), disappearance, reappearance and trail end (alternately star-bump). A Ctrl-click operation enables measurement within a pixel or two of where intended and the X parameter is displayed to two decimal places in the PSF-Fit box. This figure is to be manually incorporated into a contiguous object name of the form X468.55 when saving a position. X can be followed by anything up to 4096 but there must be no spaces. The four lines of data are then copied from Astrometrica’s MPCReport.txt and added to the timings as in the example file 050521 Bilkis.txt. These positions show up as red dots in the Scanalyzer profile plot to indicate astrometric data is loaded and verify their locations align approximately with the four measurement positions. Relative scales between these astrometric positions are derived and applied as corrections to the timings.
Faintly recorded occultations having depth comparable to the amplitude of seeing irregularities and random noise might produce what is obviously a bad measurement. A hump or hollow may interfere where a level is being averaged or could cause the profile slope to level out temporarily just where X is being interpolated. In such cases the keyboard Ctrl-up and Ctrl-down arrow keys enable modification of the profile at the position of the cursor. This is best done after returning the profile to an unfiltered and unmeasured state via the SMOOTH and BACK buttons. After adjustments to the problem area, the profile is resmoothed and remeasured. Keep in mind that such modifications disappear if the profile is again restored to its original state.
Timing accuracy is derived from the sum of the audio recording measurement uncertainty and profile measurement uncertainties for both occultation and trail end. The latter calculations involve a simulated drop in light in an unocculted part of the profile made at a string of consecutive pixel locations before being averaged. A magenta coloured line represents that region. The Bilkis drift-scan observation made with a 0.5-m telescope seems to indicate that for larger apertures, the best events measured in Scanalyzer will approach 0.01-second accuracy once the audio measurement uncertainty is effectively zeroed with the aid of direct GPS-based timings. Scanalyzer is free to download here.
ACKNOWLEDGEMENTS The camera used by the author was acquired following a Planetary Society Gene Shoemaker NEO research grant. Keith Gelling made diffraction calculations on an example asteroid occultation. I thank the principal members of IOTA and the RASNZ Occultation Section for recognizing the value of this work.
LINKS IOTA Euraster RASNZ Occult Updated Predictions Guide 8 MaxIm DL Astrometrica GoldWave ScanTracker Scanalyzer