Bruce L. Gary, Hereford Arizona Observatory; 2007.04.17

At my southern observing site the star that Pluto occulted exhibited a 23 ± 4 % fade during the March 18, 2007 occultation. This star flux loss amount is based on measurements of Pluto and the occulted star made one Pluto rotation after the occultation, showing that the star's brightness was ~33% of the total flux (Pluto plus star). The measured occultation duration was 5.3 ± 0.7 minutes . If the center of Pluto's disk had occulted the star the mid-occultation star flux would have dropped 100 % and the total duration would have been 6.7 minutes. The 23 % loss and 5.3-minute duration lead me to conclude that the light curve measured at my site corresponds to an "atmospheric occultation." Aside from any "science" that might come from this observation, related to Pluto's atmosphere, it at least supports the notion that amateurs with "small" telescopes can be counted on to produce useful observations of future Pluto occultations.

Links internal to this web page
    Occultation observations
    Observing site & hardware
    Data analysis
    Measurement of star to Pluto flux ratio
    Converting magnitudes to star flux ratio
    All-sky photometry

Occultation Observations

On March 18, 2007 Pluto was predicted to occult a 15.7 V-magnitude star for a path extending from Southern.California to Texas and including areas as far north as Colorado and Washington state. My observatory in Southern Arizona was close to one of the predicted centerlines, but apparently the actual centerline was far north of me. Pluto was brighter than the star at all bands (BVRI), based on measurements made one Pluto rotation after the occultation date. Since I observed unfiltered my effective band was somewhere between V and R. Pluto has an unfiltered brightness converted to R-band, CR, of 13.75, while the star has CR = 14.60. If an R-band filter had been used a complete occultation of the star should have produced a drop in brightness of 0.40 magnitude, from a "Pluto plus star" CR = 13.35 to "Pluto only" CR = 13.75. A centerline duration would have lasted 6.7 minutes. I was skeptical that a telescope as small as my 14-inch Meade could observe such a small change with temporal resolution of 6 seconds, which corresponds to what is needed for scientific studies of the atmosphere (the time it takes to pass through a scale height of Pluto's atmosphere for a centerline occultation). My exposures were 3-seconds and due to overhead for readout, downloading and recording the image spacing was 4.8 seconds. Here's my light curve (LC):


Figure 1. Light curve for a 1-hour observing session centered on the predicted occultation. According to this presentation of the data the occultation fade has a depth of 85 mmag, a total length of 5.7 ± 0.8 minutes (see revision below) and a mid-occultation time of 10:53:38 UT. The dashed blue trace is what was predicted for centerline occultation (using a revised depth, based on all-sky measurements of R-magnitudes). Unfiltered, 3-second exposures were made with a Meade LX200GPS 14-inch telescope and SBIG ST-8XE CCD. There was no autoguiding except for an occasional manual nudge.

The maximum depth is 85 ± 10 milli-magnitude instead of the 400 milli-magnitude expected for a complete occultation of the star. The fade event is centered on 10:53:38 UT, or ~6.6 minutes later than predicted. Based on the small depth of the brightness change it is tempting to suggest that only Pluto's atmosphere occulted the star. Observations by other observers are fit by a model in which the centerline was far north of my site ("off the edge of the Earth").

There are various ways of creating a LC for the same set of measurements. The following graph is a "folded" version that is motivated by the expectation of symmetry about the time of mid-occultation (suggested by Tom Kaye):

Folded LC

Figure 2. Zoom of the light curve's fade event. Two averaging choices are shown (27-sec and 33-sec). The 33-sec average data are folded about the time of minimum brightness. Depth at mid-occultation is 96 mmag and the length (contact 1 to 4) is 6.3 minutes.

This figure may be an excessive attempt to extract information from a noisy light curve, but for what's it worth I include it here. I've folded the 33-sec averaged data about the time of minimum brightness in order to better fit a symmetrical model for the fade event. A slight offset was adopted for the 11-point averaging groups that produces points at the time of mid-occultation (which might unfairly enhance the sharpness of this LC's minimum feature). This LC's shape is better fit by a V-shaped model. It is interesting to note that this shape argues against a disk occultion. I have no idea what the V-shape means. The data might just be too noisy to attribute anything significant to the shape. With better SNR the shape might have been seen to be flat-bottomed. Data from other observers will be useful in sorting this out.

Another way to present same observations is to convert magnitudes to "occulted star flux fraction" versus time. To do this it is necessary to adopt a value for the ratio of the star's flux to Pluto's flux using my telescope system (unfiltered). The required flux ratio is Sstar/Spluto = 0.495, as determined on March 25 (described in a section below this one).

Revised LC

Figure 3. Star flux fraction light curve with a fit having a mid-occultation fraction = 0.79 and duration of 5.0 minutes.

This LC differs slightly from the previous magnitude LCs, again due to a slightly different 11-point averaging group starting choice.

The three ways of treating the measurements produce the following mid-occultation star flux losses:
    Fig. 1:  23 % (based on 85 mmag and Sstar/Spluto = 0.495)
    Fig. 2:  26 % (based on 96 mmag V-shaped LC and Sstar/Spluto = 0.495)
    Fig. 3:  21 % (based on fit of LC plot of calculated star flux fraction)
I will claim that my measurements have the following solution:

    Mid-occultation star flux loss = 23 ± 4 %
    Total duration = 5.3 ± 0.7 minutes

The following sections present supporting observation and analyses.

Observing Site & Hardware

My Hereford Arizona Observatory (G95) is located at Lat = +31.4522, Lon = -110.2377 at an altitude of 4660 feet. The telescope is a 14-inch Meade LX200GPS. My Cassegrain optics consists of a SBIG AO-7 image stabilizer, focal reducer, CFW and SBIG ST-8XE CCD (1530x1020 pixels, each 9 nm square). The plate scale for this configuration is 0.67 "arc/pixel. For the Pluto occultation observations I did not use the AO-7 image stabilizer. To decrease the spacing between images I defined a subframe of 85x62 pixels near the center of the CCD. I binned 3x3 and recorded compressed images. The readout, downloading and recording consumed 1.8 seconds per image, so the image spacing was 4.8 seconds. I observed unfiltered. The CCD cooler was set to -25 C. MaxIm DL v4.58 was used to control the telescope and CCD.

At 10.45 UT I noticed the need for a focus adjustment, so I stopped observations and used a wireless focuser to achieve ~4.5 "arc FWHM PSF quality, and resumed observations at 10.58 UT. My polar axis is aligned to an accuracy of about 3'arc, so there was minimal drift or image rotation of the star field during the observations. However, on about 5 occasions I did manually nudge the telescope motors to keep the stars as closly fixed to the pixel field as possible. The image FOV is 2.8 x 2.1 'arc, as shown in the next figure.


Figure 4. Finder image showing the reference star used to monitor Pluto's brightness. The reference star is 49 "arc west of Pluto and it is 1.9 mag brighter than "Pluto plus occulted star." The star labeled "Pluto" is actually Pluto plus the 14.5 mag star (so close they are on the same pixel, since this image was made during the occultation).  FOV = 2.8x2.1 'arc.

Image Processing and Data Analysis

A set of 30 dark frames were taken at the end of the observing session, with the CCD at the same temperature as during the occultation observations. An earlier set of darks is also available but since the TEC cooler couldn't keep up with an ambient warming I used only the post-occultation set of darks since they were at a more representative temperature. The darks were taken with the same3x3 binned  85x62 subframe that was used for the occultation observations. All raw images were calibrated using the post-occultation master dark. No flat field correction was made. This is something I neglected to deal with at the time, and will assess the need for making such a flat field later.

A total of 689 images were recorded during the 1-hour occultation session. Groups of 100 images were calibrated using the master dark, then were offset aligned using the bright star 49 "arc to the west. The images were doubled in size in order to accomodate an artificial star that was added to each image (in the upper-left corner). The artificial star has the same flux in all images, and serves to determine extinction for the observing session. MaxIm DL's photometry tool was used to measure fluxes for Pluto, the reference star and the artificial star. The fluxes for these three stars from the group of 100 images was recorded as a CSV-file.

A program read all CSV-files and calculated air mass for each image, then recorded a CSV-file with UT, air mass and the magnitude differences between Pluto/star and the artificial star (used as an intermediate reference), and the magnitude difference between the bright star to the west (labeled "REF" in Fig. 2) and the artificial star, for the entire 689 image set. This file was imported to an Excel spreadsheet. The star labeled "REF" was used to create an extinction plot (flux versus air mass), the slope of which is identified as zenith extinction for the observing session. For this date's observations zenith extinction agreed with my site's typical value of 0.14 magnitude/airmass. I adopted this zenith extinction coefficient and spreadsheet cells calculated an extinction corrected magnitude difference for Pluto/star and REF star. The extinction-corrected Pluto/star magnitude was compared with the extinction-corrected REF star magnitude to produce an offset for each image. In this way the REF star then became the final "reference star" for the Pluto/star measurements.Outliers were identified using neighbor differences, and a few data were rejected (usually just the images affected by the times I nudged the telescope to keep the star field fixed to the pixel field). An arbitrary magnitude offset was applied to all Pluto/star magnitudes to achieve an average magnitude of 14.6. Eventually I'll measure the reference star's unfiltered CV magnitude and not use the arbitrary offset.

The "model" trace in Fig. 1 is based on an exoplanet model that has free parameters for time of ingress and egress, depth at mid-transit, time between contact 1 and contact 2, temporal slope and an air mass correction model (for the use of reference stars that differ in color from the target star). For the Pluto occultation I didn't need to use the air mass model but all other free parameters were set by hand to produce a "pleasing fit" to the data.

Measurement of Star to Pluto Flux Ratio

The modelers need to know what fraction of the star's light was lost during the occultation. When an asteroid occults a star the required information is obtained by waiting an hour and imaging the same star field. In that time the asteroid and star are far enough apart to be measured individually. Pluto moves much slower, so waiting a day ot more is required for that comparison image.

The professional modelers will want to know the magnitude difference between the occulted star and Pluto, using the same telescope and filter, and observing at the same approximate air mass. This will enable them to convert magnitudes to star flux components, which is needed to calculate the star's flux ratio, which I'll define as R = Smid / So, where Smid = star flux at mid-occultation and So = star flux out of occltation.

In case someone wants guidance converting their magnitude change to R, the remainder of this section illustrates what's involved using my observation as an example.

On 2007.03.25 I observed the Pluto star field with the same unfiltered configuration used on the occultation night. The next figure is a plot of the ratio of the occulted star's flux to Pluto's flux.

Figure 5. Ratio of occulted star flux to Pluto's flux versus air mass, observed on 2007.03.25 when Pluto and the occulted star were far apart. The vertical dashed line at air mass = 2.09 corresponds to the observing situation at the time of the occultation on 2007.03.18.

The ratio of fluxes (occulted star to Pluto) is R = 0.495 ± 0.015 when air mass is the same as during the occultation, m = 2.09.

This information allows us to calculate the depth of the occultation fade in terms of only the star's flux. The star's flux component at mid-occultation (Smid) normalized to the star's out-of-occultation flux level (Sooo), is given by the following equation:

    Smid / Sooo = ((1+R) × 2.512-dM-1)/R                                                                                                                                                                                                          Eqn 1
          where R = ratio of star flux to Pluto flux (out-of-occultation),
          dM = change in magnitude during occultation

For R = 0.495 ± 0.015 and dM = 0.085 ± 0.010 magnitude,

     Smid / Sooo = 0.773 ± 0.027

This depth is clearly not close to zero, which suggests that the occultation at my site was a Pluto atmospheric occultation. Based on deeper depths at site north of mine I conclude that my light curve is a probe of Pluto's southern polar atmosphere.

Calculating Fluxes From Magnitudes

What if an observer hasn't been able to produce a plot like Fig. 4, but they want to make use of known magnitudes for Pluto and the occulted star to derive a S*mid / S*o ratio?

This can be done with good accuracy provided the telescope's "photometry coefficients" are known. These coefficients can be derived by observing a Landolt star field and solving for the constants. For example, my system has the following flux to Rc magnitude conversion equation:

    Rc = 19.92 - 2.5 × LOG (S / g) - 0.13 × m - 0.10 × C                                                                                                                                                                          Eqn 2

          where S is measured star flux (using a large photometry signal aperture),
          h = exposure time [seconds],
          m = air mass, and
          C' = C + 1.3 × C2, and C = V - R - 0.31 (note that C' is a linearized star color).

The constants and coefficients (19.92, 0.13 and -0.10) were determined by observing many Landolt stars at several air masses.

Equation 2 can be re-written:

       S = g × 10 (( 19.92 - R - 0.13 × m - 0.10 × C' ) / 2.5)                                                                                                                                                                                     Eqn 3

Each observer will have to substitute values for their telescope system. For the purpose of this occultation task it is not necessary to use a correct zero-shift constant (19.83 for my system), but it will be important to know zenith extinction for your site and date, if it changes much (0.13 mag/airmass for my site), and the star color sensitivity coefficient is moderately important (-0.10 for my telescope system). If BVRcIc filters are used, and if your CCD has a QE(wavelength) function similar to mine (ST-8E with a KAF1602E chip), then you can probably adopt my star color sensitivity coefficients:

    B  = +0.38 ± 0.05
    V  = -0.05 ± 0.03
    R  = -0.10 ± 0.03
    I  = +0.02 ± 0.03
    CR = -0.20 ± 0.10

If you don't know your site's zenith extinction coefficients, then maybe the following graph can be a guide.

Figure 6. Extinction components (Rayleigh scattering and dust Mie scattering) versus wavelength for 3 site altitudes.

This graph can be used to estimate a typical (yearly average) zenith extinction for any filter based on the observing site's altitude. This is done by reading the dust component and Rayleigh scatter copmponent, and adding them. The solid circles are the addition of these two components for my site's altitude (4660 feet), and the agreement is good. Of course there's an annual variation, plus day-to-day variations, but in the absence of having an actual measured senith extinction this graph is one way to estimate zenith extinction.

Before we can substitute values in Eqn. 3 we need to know the R-magnitudes and V-R colors for Pluto and the occulted star. Let's assume the following (based on measurements made one Pluto rotation after occultation date and presented in the All-Sky section, following this one):

        Pluto R-mag = 13.75, V-R = 0.58
        Star R-mag  = 14.60, V-R = 1.13

Substituting the Pluto and occulted star R-magnitudes in Eqn. 3, and using a zenith extinction of 0.13 and star color sensitivity of -0.10, we calculate the following fluxes for Pluto and the star:

       Spluto = 753 counts
       Sstar   = 304    "

This would mean that just prior or after the occultation the occulted star contributed 29 % of the total flux (measured by a photometry aperture that contained both of them). The parameter we need for present purposes, however, is R = Flux Star / Flux Pluto = 0.40. This value for R is based on all-sky photometry solutions for the star field observations of March 25, 2007. It is not as direct as the plot in Fig. 5, where the flux ratios were plotted for many images as the star field passed through the desired elevation. The two values for R, 40% and 49%, serve as an internal consistency check. I have adopted R = 0.495 for the Eqn.1 calculation above.<>

All-Sky Photometry

The following false color image shows Pluto and the star it occulted.

Figure 6. False color image of the Pluto occultation region on 2007.03.25 UT. In place of LRGB I used CIRV. FOV = 11.9 x 8.3 'arc (cropped of original 17 x 1 'arc image). P445.3 is the star Pluto occulted, and the star labeled "REF" is the one I used for my light curve. FWHM = 3.2 "arc. [Total exposures for C, I, R and V = 40 sec, 290 sec, 290 sec, 60 sec.]

Notice how red  most stars are! This may be due to interstellar dust reddening. After all, the galactic latitude and longitude are 3.8 and 11.6 degrees, respectively.

Figure 8. All-sky photometry measurements for V and Rc magnitudes for Pluto and other stars. Since Pluto brightened 0.01 magnitude between the occultation and the time of these all-sky calibrations, to obtain BVRcIc magnitudes for Pluto at the time ofoccultation it is necessary to add 0.01 magnitude to the entries in this figure. The reddest stars were too faint in B-band for useful measurements to be obtained, and this includes the star that Pluto occulted.

The estimated SE for V, Rc and Ic are 0.03 magnitude. This is based on the scatter of Landolt star magnitudes about a telescope system coefficients solution: RMS = 0.027 mag for V (N=21), RMS = 0.017 mag for Rc (N = 29) and RMS = 0.026 mag for Ic (N=19). B magnitudes could not be measured for 6 stars (the reddest stars). For those with magnitude entries in the above figure the stochastic SE ranges from SE = 0.06 for B = 16.5 to SE = 0.03 for B = 15.5, and is better for brighter stars. The air mass range is 1.2 to 2.1.

Because the star that Pluto occulted is so red (due in part to interstellar dust reddening) the ratio of fluxes changes a lot versus wavelength, as the next figure shows.

Figure 9. Fluxes for Pluto and the star it occulted (relative sccale) and flux ratio (star to Pluto), versus wavelength. (Assumes star color sensitivity same as my telescope system.)

The observer who doesn't know his telescope system's photometry constants, who is willing to adopt those of a typical amateur system (mine), this figure can be used instead of Eqn 3 above to estimate a flux ratio for the filter used.

Related links:
    Bruno Sicardy (really neat)
    Chris Peterson 
    Brian Warner
    Tony George
    Daniel Caton
    Peterson, Herrero & Schlottman
    Bruce's Astrophotos

Note: Lots of professionals have data but I can't find any web sites that are in the public domain.


This site opened:  March 20, 2007 Last Update:  April 17, 2007