CALIBRATION OF VESTA & CERES OBSERVATIONS AT HEREFORD ARIZONA OBSERVATORY IN 2014
Webmaster: Bruce L. Gary, Hereford, AZ; USA; Last Update: 2015 Feb 22

This web page describes the calibration of observations of Vesta and Ceres at the Hereford Arizona Observatory (HAO) during their 2014 opposition. Dawn spacecraft Framing Camera (FC) filters were used, so no stars were available that had been calibrated for these bands. Therefore, Phase 1 for this project entailed calibrating stars near the Vesta and Ceres locations using Vega as a primary standard. This, in essence, amounted to the creation of a new 7-band magnitude system. For each FC filter the flux of Vega was transferred to several stars using all-sky calibration techniques. Phase 2 consisted of observations of Vesta and Ceres, and these also required the use of all-sky techniques since none of the secondary calibration stars were within the field-of-view of Vesta or Ceres images. I estimate that for all FC bands an accuracy of ~ 3.3 % was achieved.

Links
    Phase 1, Transferring Vega Fluxes to Secondary Stars  
    Phase 2, Using Secondary Standard Stars to Calibrate Vesta and Ceres Observations 

    Supporting Material for Creating a New Magnitude System (another web page)

Introduction

The goal of this observational project is to measure the geometric albedo of Vesta and Ceres. This requires a method for measuring the flux reflected by the asteroid and comparing it with what it intercepts from the sun. The flux within a specified range of wavelengths is related to magnitude by a simple equation, such that knowing one means you also know the other (see SED for a fuller description). The approach to measuring an asteroid's albedo involves comparing its flux at a specific wavelength interval with the flux from a star whose flux within that same wavelength range is known. That is equivalent to stating that an asteroid's albedo involves measuring its magnitude by calibrating it with a star whose magnitude is known.

Calibrations with a CCD camera are usually performed using background stars that have calibrated magnitudes listed in a catalog, such as the UCAC4 catalog that includes APASS BVg'r'i' magnitudes. If a V-band filter is used, then stars in the same image as the asteroid that have APASS V-magnitudes are used for calibration. Since there are always small differences between the telescope system spectral response function (above the atmosphere) and the response function used to define a magnitude system, "CCD transformation equations" are used by the conscientious observer to provide more accurate calibration of the asteroid magnitude.

When spreadsheets came into common use a simpler alternative to CCD transformation equations became an option. This involves constructing a plot of "instrument magnitude minus APASS calibrated magnitude versus star color of the calibrated star (such as B-V, or g'-i')." With such a plot, fitted by a magnitude offset and slope, it is possible to convert the instrumental magnitude of any target of interest to a calibrated magnitude - provided the target of interest has a known color (B-V, etc). Since most asteroids do not have a known color it is commonly assumed that they are slightly redder than the sun (B-V = 0.64), which is OK for assigning a provisional magnitude to the asteroid until its color can be measured. Measuring the color of an asteroid involves an iterative procedure, which is straightforward and has fast convergence. Few observers go to the trouble of making the necessary observations for achieving accurate asteroid magnitudes, regardless of which band they use. Phase function plots can be subject to systematic errors produced by this neglect, and this should be "kept in mind" by anyone using phase effect data for scientific analysis for deriving regolith properties.

When using filters that have no analogue in a catalog of calibrated star magnitudes, such as the Dawn FC filters, these issues are especially important. Usually it is possible to construct a phase effect plot without careful attention to CCD transformations (or their equivalent), since most asteroids have the same color for all observing sessions used to establish the phase effect relation. However, such data can be expected to produce an unreliable zero phase magnitude (H) since all data will share an unknown calibration offset error. The situation can be even worse for an asteroid that exhibits changes in color as it rotates, such as Vesta; unless careful calibration is performed such an observed phase effect will exhibit subtle systematic errors affecting phase effect shape as well as the H value.

For these reasons there is merit in creating a magnitude system designed for use with only the the FC filters for characterizing the phase effect relations for
Vesta and Ceres.


Figure 1. The FC filters in a 10-slot color filter wheel.
 

Figure 2. FC passbands compared with SDSS passbands (g'r'i'z'), multiplied by a typical CCD QE function and atmospheric transmission function, showing the difficulty in finding an equivalence between FC filters and SDSS filter for calibration purposes.(The situation is even worse comparing FC filters with the Johnson-Cousins BVRcIc filters).

Phase 1: Transferring Vega Fluxes to Secondary Standard Stars

This may be hard to believe, but the following Phase 1 material is the "short version" describing how I created a new magnitude system for the FC filters. If anything on this web page isn't explained in sufficient detail then consider viewing the web page linked to above under "Supporting Material...", where I treat some basic concepts for anyone creating a magnitude system.

A new magnitude system was created for each of the 7 FC filters using Vega as a primary standard for establishing zero magnitudes (above the atmosphere). Secondary standard stars were calibrated using Vega; two A0V stars (same as Vega) and several sun-like stars were included as secondary standards. These secondary stars were located close to the position of Vesta and Ceres for the 2014 opposition (March through June, 2014). Once calibrated, any of the secondary standard stars could be used to calibrate observations Vesta and Ceres since they were all at the same air mass and observable at the same time. This web page describes how the task of "deriving a magnitude system" was accomplished and how the same all-sky calibration techniques were used for calibrating the Vesta and Ceres observations.

Phase 1 measurements were made March 16 to 25, 2014 using a Celestron 11-inch (CPC1100) Schmidt-Cassegrain telescope, with a 10-position CFW and SBIG ST-10XME CCD. The telescope was inside a dome in my backyard, and all equipment was controlled from inside my house using MaxIm DL (v5.3) through 100-foot buried cables to the dome observatory. Phase 2 observations were conducted with the same Celestron 11-inch telescope system (March 20 to May 01) and with a Meade 14-inch Schmidt-Cassegrain telescope (May 5 to June 20) located in a different dome but using the same filter wheel and CCD. Additional description of these two observatories can be found at http://www.brucegary.net/HAO/.

Vega is probably the most-studied star in terms of flux spectrum, Fλ [Watts/m2/micron]. The low-resolution spectrum used for this analysis is shown in Figure 3, and is based on the tabulation by Kurucz (2003).


Figure 3. Vega flux spectrum, a primary standard used to establish flux spectra for a set of secondary standard stars near the Vesta and Ceres sky location. The V-band filter bandpass is shown.


Figure 4. Solar flux spectrum, based on the ASTM E-490 model. The V filter response function is also shown.

The solar spectrum, shown as Fig. 4, is also well-established. I use the "2000 ASTM Standard Extraterrestrial Spectrum Reference E-490-00" for this analysis. Here's a link to a tabulation of the Vega flux and solar flux that I use, plus typical atmospheric transmission, with a 1 nm resolution: link. The Vega and solar flux spectra are probably more accurate than 1% within the wavelength region spanned by the FC filters (0.4 to 1.02 micron).

The concept of transferring flux information from a primary standard star to another one, to be used as a secondary standard, is straightforward to understand but difficult to implement. Let's begin with the simple case of the two stars being next to each other, within a CCD image FOV. The transfer could be accomplished by measuring the total ADU counts within a large photometry aperture for each star and taking their ratio. Some subtleties exist even for this simple case: a good quality flat field would be required, many such images would have to be made in order to reduce scintillation and Poisson noise, and a large number of images would be needed that sample a range elevation angles in order to remove the effect of atmospheric extinction producing ratios that vary with air mass due to the two stars' different spectral slope across the filter passband. This last effect is important because star magnitudes are defined in terms of what would be observed from above the atmosphere.

Imagine, now, the additional observing requirements when the two stars are in quite different parts of the sky. For example, when I performed the calibration transfer from Vega to a set of secondary standard stars near Vesta and Ceres, during March, Vega would rise through 25 degrees elevation at 1:30 am when Vesta and Ceres were at ~ 60 degrees elevation. Overcoming this problem is what "all-sky photometry" is all about. The usual all-sky solution is to observe when both stars are at about the same elevation at the same time, and go back and forth observing them in alternation. (For Vega and the Vesta/Ceres part of the sky, this occurred a couple hours before sunrise.)

One has to assume that atmospheric extinction is the same in both parts of the sky, such that extinction at a given air mass is the same. Since this may be true for some wavelength regions it is not necessarily true for other wavelength regions. This is due to atmospheric extinction consisting of four different sources: Rayleigh scattering, aerosols, stratospheric ozone and tropospheric water vapor. Rayleigh scattering is proportional to surface air pressure, aerosol scattering (and absorption) vary with the burden of dust in the lower troposphere, ozone absorption varies with the circulation of stratospheric ozone from the tropics to mid-latitudes and water vapor varies with the synoptic and mesoscale circulation of lower tropospheric air masses. The greatest horizontal gradients of atmospheric extinction are due to water vapor and aerosols. The best way to overcome horizontal gradient problems is to repeat observing sessions on several dates, when presumably the horizontal gradients will "average out." I observed Vega and the secondary standard stars on three dates, and achieved similar results - indicating that horizontal gradients were not a significant problem during these observing sessions.


Figure 5. Atmospheric extinction at my observing site (4670 feet ASL) on one winter date, showing the four components contributing to extinction.

Another problem associated with transferring calibration from a bright star to fainter ones is that all exposures must assure that the bright star is not "saturated" (i.e., with maximum ADU counts < ~ 50,000) and that the fainter stars have sufficient SNR to be measured with good precision. Vega was ~ 100 times brighter than the secondary stars, and I couldn't expose for a short enough time to prevent saturation (for even a good CCD camera exposures should exceed ~ 1 second to maintain accuracy). My solution to this was to use an aperture mask with a 1-inch hole for Vega observations, and observe the secondary standard stars without the mask; this allowed similar exposure times to be used for both. The 1-inch hole had to be calibrated, and this was done using one of the secondary stars. By alternating observations of a star with and without the aperture mask, on two dates, it was determined that the ratio of "collecting area," unmasked to masked, was 98.63 1.28, or 4.985
0.014 magnitudes. This component of uncertainty is less important than the transfer of fluxes from Vega to the secondary standards. Below is a list of stars considered for use as secondary standards.


Figure 6. List of stars considered for use during the calibration transfer phase of observing. A stars and S stars refer to spectral type A and solar spectral type.

Star #6, in the above list, became the most relied upon secondary standard star. It is also called 59 Vir (in Virgo). It has a B-V essentially the same as the sun. This was an important consideration in placing greater reliance upon it for the asteroid observations. To the extent that Ceres, for example, has the same spectrum as the sun there should be minimal variation in the ratio of Ceres to 59 Vir as atmospheric extinction changes (due to air mass changes, or any other atmospheric changes). Another advantage in choosing 59 Vir for the most used secondary standard star is that it allowed me to switch telescopes, from the Celestron 11-inch to a Meade 14-inch, in the middle of the project. Any differences in corrector plate transmission function would have minimal effect on the ratio of Ceres to 59 Vir. Even that concern is small considering that the only difference in corrector plate transmission that matters would be across the wavelength range of any given FC filter, and all FC filters were quite narrow (~ 100 nm).


Figure 7. Magnitudes of 3 secondary standard stars compared with Vega, assumed to be zero for all bands. Entries are described in the text (next paragraph).

Figure 7 summarizes results of the Vega calibration transfer observations to three secondary standard stars. The FC# notations are those defined by the Dawn Framing Camera experiment team. I have assigned CFW# labels, corresponding to their sequence in the color filter wheel - which was also their wavelength sequence. One exception is the r'-band filter, which I originally intended to use as a "reality check" but later dropped when I felt that there were no problems requiring a reality check.

This table shows magnitudes in the invented magnitude system for each FC filter band. The way to convert a magnitude to flux is to use the equation at the bottom of the figure. For example, using the 548 nm filter the flux for 59 Vir is 3.584e-8 2.5119^(-5.135 0.028), which is (3.166 0.081)
1e-10 [watts/m2/micron].


Figure 8. FC magnitudes for secondary calibration stars from 3 dates, plus the sun's spectrum re-scaled to appear on the graph. Vega, by definition, has FC magnitudes that are all zero.

This plot shows that star A2, spectral type A, has magnitudes versus wavelength, relative to Vega, that are "flat," meaning that it has the same spectral shape as Vega.
This is to be expected. Star S1, spectral type G0V, is quite different and resembles the sun's spectral shape. Again, this is to be expected since its spectral type is similar to the sun's (G2V). Star S2 (59 Vir) has FC magnitudes versus wavelength that also resemble the sun's in shape, as expected since Vir 59 has a spectral type of G0V. The differences in S2 (59 Vir) magnitudes are used to estimate the uncertainty of the average (plotted as a solid black trace and listed in Fig. 7). The star S2 (59 Vir) has a flux with an uncertainty of ~ 2.8 %. This is the largest uncertainty in the chain of calibration steps leading to geometric albedos for Vesta and Ceres. Recall that there is a 1.8 % SE associated with the ratio of collecting area of the 1-inch mask hole to the unmasked aperture. Combining this with the 2.8 % SE yields a total SE of 3.3 %. Given that Ceres has a geometric albedo of ~ 9.6 %, calibration uncertainties will account for a geometric albedo uncertainty of ~ 0.32 % (e.g., Ag = 9.60 0.32 %).

By observing either Vesta or Ceres in alternation with 59 Vir, for example, using techniques described in the next section, it is possible to determine a ratio for the flux of the asteroid to 59 Vir, which a simple multiplication by the flux of 59 Vir yields the flux for the asteroid.

A few subtleties should be addressed now.

Notice that in Fig. 7 the wavelength (WL) rows have slightly different values for Vega and "solar." This is because the slopes of the Vega and solar spectra differ, and the spectrum-weighted average wavelength is therefore slightly different for each source.

In deriving fluxes for the secondary calibration stars the ratio of brightnesses, star/Vega, is multiplied by the effective flux of Vega. This latter is the filter passband weighted flux of Vega, where the passband is shown in Fig. 2 and the Vega flux spectrum is shown in Fig. 3. What if the real filter response function is flawed by a "light leak." For example, suppose the shortest wavelength FC filter leaks some light at the longer wavelengths (leaks at shorter wavelengths won't matter since flux decreases fast on the short wavelength side). Light leaks are common at levels below ~ 1% for filters used by amateurs; this engineering problem is difficult to solve when the wavelength of interest is at one end of the spectral energy of the target star (and instrument response function). Therefore, the 428 and 966 nm FC bands are at the greatest risk of having light leaks. Because of the very different spectral energy distributions of Vega and the sun the effective wavelength of either of these filters could be significantly different for the two sources than was calculated for the assumption of no light leaks. A light leak for the 428 nm band, for example, would be influenced more by solar type stars than Vega, and this would produce an positive error in the 59 Vir flux (c.f., Fig. 9). This, in turn, would cause asteroid fluxes to appear greater than they actually are, which would be interpreted as a higher geometric albedo than is actually the case. This is something we should be on the lookout for in the Vesta and Ceres geometric albedo results.



Figure 9. Comparing flux spectra of two sun-like secondary stars to the sun's spectrum (re-scaled).


Figure 10.  Comparing shapes of FC spectra for two solar like stars (G0V) with the sun's FC spectrum (spectral type G2V),
showing a suspicious "too high" flux for the 429 nm FC band (consistent with a "light leak" for that FC filter).

Another subtly is the matter of stellar variability of the secondary standard stars. "All stars are variables" at some level, but could 59 Vir, for example, be variable at a level that would matter for the goal of measuring and monitoring geometric albedo? In every observing session where 59 Vir and the other secondary calibration stars were measured on the same observing session there was no evidence for changes. 59 Vir has a spectral type of G0, so it is unlikely to be variable. 

Phase 2: Transferring Secondary Standard Stars to Vesta and Ceres

The same all-sky procedures used for transferring Vega fluxes to secondary standard stars, described in the previous section, were used to transfer fluxes from the secondary standard stars to Vesta and Ceres. Since Vesta and Ceres were closer in the sky to the secondary standard stars this transfer process is expected to have been achieved with much better accuracy.

In the interest of brevity I'll refer to just one secondary standard star, S2 (i.e., 59 Vir), even though others were sometimes also observed, and I'll refer to observing Ceres even though I often observed Ceres and Vesta during the same observing session. Since Ceres and S2 were in the same part of the sky they rose and set together, and had a similar air mass versus UT in between. This meant that it was possible to alternate observations of them in a way that assured similar air mass values, and it also assured that temporal variations of atmospheric extinction would have negligible effect upon their flux ratio comparisons. In almost every case I used the odd/even rule for observing target and reference. For example: tgt/ref/tgt has an odd number of target observations and an even number of reference observations, and the average time of their observations is close to the same and therefore unaffected by linear trends (of atmospheric extinction, for example). A range of high air mass to low air mass observing was also planned, which would allow a more accurate measurement of that observing session's atmospheric extinction.

The Ceres image set  for one FC band (all images for the night) would be loaded into MaxIm DL for processing. After calibration (bias, dark and flat) all images would be aligned so that Ceres was at the same pixel location. An artificial star would then be inserted in a corner of each image (64x64 image with Gaussian function having FWHM = 3.77 pixels and peak DN = 65,535 on a field of zeros). A photometry aperture was selected that assured >99% capture for all (accepted) images. The photometry tool was used to produce a CSV-file with 3 columns:  JD, target magnitude and reference (artificial star) magnitude (allowed to default to zero for all images). The same procedure was used to process each secondary calibration star's image set. All CSV-files were imported to a spreadsheet  template that was designed for this project. By entering Ceres target RA/DE coordinates, and selecting RA/DE from a table for the secondary standard stars, the JD values could be converted to air mass values for each image. The spreadsheet was used to derive an atmospheric extinction vs. UT function (details too tedious to describe). I'll just state here that the Ceres instrumental magnitudes couldn't be used for deriving extinction because the asteroid changed brightness during the night; thus, all atmospheric extinction solutions were performed on the secondary star measurements. Figure 10 illustrates how an extinction model was adjusted (Rayleigh, aerosols, ozone and water vapor) to match measured average extinction for an observing session. The theoretical atmospheric model "guided" a choice for the model of extinction vs. UT for the observing session.


Figure 11. Atmospheric extinction for 7 FC bands for Vega and S1 on one date, compared with an extinction model.

After settling on a model for extinction vs. UT for a FC band, Ceres magnitudes were determined by comparing Ceres instrumental magnitudes with the secondary star instrumental magnitudes (where each secondary star had a magnitude assigned to it by the "Vega to secondary star calibration procedure," described in the previous section).

The procedure just described was performed for each of the FC bands, and an archive of Ceres calibrated magnitudes was created for each observing date in this manner.  After each observing session had been processed to the stage of having calibrated magnitudes for each FC band an optional next level of processing was usually performed. This consisted of converting magnitudes to standard values (the 1,1, or 1 au and 1 au versions), and fitting them with a HG and rotation model. The rotation model used phase-folding for an adopted rotation period, with a small phase shift associated with the Ceres sky location. On occasions (weeks apart, usually) the standard magnitudes for all dates (for one FC band) would be copied and sorted, and a running median was used to establish a new rotation variation model (for the FC band). This was used to identify outliers in all previous data, and the non-outlier data was used to refine the HG model fit. These data were converted to geometric albedo and plotted as a way of monitoring adequacy of the accumulated observations. Figure 11 is an example of this for one FC band.


 
Figure 12.
Rotation variation of geometric albedo for the FC 548 nm band, using a HG model that minimized residuals. Different symbols are used for different observing session dates.

At the completion of the Ceres opposition observing season the magnitudes for all FC bands was converted to fluxes and shared with team members for additional modeling analysis.


Plots of geometric albedo versus wavelength for a selection of rotation phases, showing a slight "blueness" color for at all times. The absorption feature at 920 nm is evident, and appears to have a different depth with rotation.  


Depth of the absorption feature at 920 nm, Band I, is deepest at a rotation phase corresponding to sub-Earth longitude of ~ 90 deg, which is also the rotation phase time when geometric albedo is maximum.

This last graph can be used to estimate "relative calibration" uncertainty, or band-to-band calibration SE. I have estimated that the "absolute calibration" SE is 3.3% for all bands except the shortest wavelength band (438 nm), where absolute calibration SE is probably 5%. Some of the uncertainty components are shared by all bands, such as the 1.8% SE associated with the aperture mask used to observe Vega for transfer of its fluxes to the fainter secondary calibration stars. Therefore, the band-to-band calibration SE is smaller than the 3.3% and 5% values. It is sometimes difficult to estimate "relative SE" but we can infer an approximate estimate "after the fact" by comparing how results are related to each other with guidance from an understanding of how they "should" be related to each other if calibration uncertainties didn't exist. Consider the above graph. If the positive correlation between geometric albedo and Band I were perfect, for example, then the small departures from such a correlation would require errors in geometric albedo on the order of 0.1% (i.e., geometric albedo for each measurement ~ 9.5 0.1%). If, on the other hand, the geometric albedos were subject to random errors greater than 0.1%, how could the correlation pattern in the above graph exist? If the position is taken that there is no relationship between Band I depth and geometric albedo then the scatter of Band I depth values about an average implies that individual albedo determinations have srrors of ~ 0.03% (i.e., geometric albedo ~ 9.5
0.3%). This would be the most conservative interpretation of the above graph, so I conclude by suggesting that whereas the absolute calibration SE for geometric albedos for wavelengths longer than 500 nm is 3.3%, their band-to-band relative SE is ~ 0.3%. Stochastic SE for other graphs of geometric albedo will of course be an orthogonal sum of the 0.3% band-to-band albedo SE with the appropriate stochastic albedo component.

A summary of results of my analysis of these data can be found at: http://brucegary.net/Dawn/Ceres.html 

Lessons Learned

The most important uncertainty in the calibration process came from the transfer of Vega fluxes to a secondary standard star. This 2.8% uncertainty is greater than the 1.8% uncertainty associated with measuring the ratio of collecting area for the 1-inch hole mask and the unmasked aperture.
If I were to do this project over I'd devote more observing sessions to the task of transferring Vega flux to a secondary standard star.

The APASS BVg'r'i' magnitudes exhibit an internal consistency of ~ 10 mmag for most star fields. It is estimated that the accuracy of the g'r'i' magnitudes is somewhere in the 1 to 2 % region (reference needed; ask Arne). If it's 1.5 % then this is twice as good as what I achieved. This means that a more accurate determination of the Ceres geometric albedo spectrum could be achieved by observing with SDSS filters. Since the FC filters response functions are narrower than those for the SDSS filters there would be a loss of spectral resolution, but this would only be important where spectral structure exists - such as Vesta's Band I region. There appears to be almost no structure in the Ceres spectrum, so SDSS filters should be free of any spectral resolution loss. I therefore recommend that any future attempt to improve the FC calibration be performed using SDSS filters.
 
Data File

Ceres data file of fluxes: link

References
Kurucz, R. L., 2003, Index of Stars: Vega, http://kurucz.harvard.edu/stars/vega 
2000 ASTM Standard Extraterrestrial Spectrum Reference E-490-00: http://rredc.nrel.gov/solar/spectra/am0/ASTM2000.html 

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This site opened:  2015.01.12 by Bruce L. Gary (B L G A R Y at u m i c h dot e d u).