The Palomar Transient Factory Photometric Calibration

The Palomar Transient Factory¹⁴ (PTF; Law et al. 2009; Rau et al. 2009) is a synoptic survey designed to explore the transient sky. The project utilizes the 48'' Samuel Oschin Schmidt Telescope on Mount Palomar. The telescope has a digital camera equipped with 11 active CCDs, each 2K × 4K pixels (Rahmer et al. 2008). Each PTF image covers 7.26 deg² with a pixel scale of 1.01'' pixel^-1. From the beginning of the PTF survey in 2009 March until 2011 January, most of the images were taken with the Mould R filter. Starting 2011 January, we performed the PTF main survey in the g band during dark time and in the R band during bright time. In addition, a few nights around times of full Moon are used for taking images with narrowband Hα filters. A PTF system overview and review of the first year's performance are given in Law et al. (2010).

Accurate photometric calibration is a nontrivial task, since one must know both the atmospheric transmission (e.g., Padmanabhan et al. 2008; Burke et al. 2010) and the optical/detector system response as a function of wavelength, time, and sky position. Moreover, observations of flux standards are required, and the true spectral energy distribution of these standards needs to be known. In practice, simplifying assumptions are made in order to achieve solutions that are good to the few-percent level. For example, in many cases, it is customary to use the calibrated magnitudes of the standard stars instead of their spectral energy distribution and to assume that the atmospheric transmission is a smooth function of air mass. We note that relative-photometry approaches (e.g., Gilliland & Brown 1988; Gilliland et al. 1991; Honeycutt 1992; Everett & Howell 2001; Ofek et al. 2011) can achieve better accuracy from the ground, but are limited by scintillation noise (e.g., Young 1967; Gilliland & Brown 1988), Poisson noise, and flat-fielding errors.

There are several approaches to photometric calibration. For example, the Sloan Digital Sky Survey (SDSS; York et al. 2000) images are calibrated using an auxiliary 20 inch telescope, which determines the photometric condition on a nightly basis (Hogg et al. 2001). This telescope measures the extinction and photometric zero point using a network of standard stars (Smith et al. 2002), which, in turn, are tied to the standard star BD + 17:4708. Furthermore, the photometric uniformity in the SDSS is achieved by the algorithm described in Padmanabhan et al. (2008). The SDSS photometry is uniform to better than 2% in all bands (Adelman-McCarthy et al. 2008).

Ofek (2008; see also Pickles & Depagne 2010) has suggested using Tycho-2 (Hog et al. 2000) stars to photometrically calibrate astronomical images. The SDSS griz magnitudes of such stars are based on synthetic magnitudes of stellar spectral templates fitted with the Hipparcos B_T and V_T magnitudes and the 2MASS (Skrutskie et al. 2006) JHK magnitudes. However, this strategy requires images containing unsaturated Tycho calibration stars, which lie in the range. The saturation limit for the PTF g- and R-band survey is typically¹⁵ around 14 mag.

Herein, we describe the method we have developed for the photometric calibration of PTF data taken in the g and R bands. The photometric calibration of the PTF Hα survey will be described elsewhere. We note that the relative photometric calibration of PTF currently¹⁶ achieves precision as good as 3 mmag, in given fields, at magnitude 15 (e.g., van Eyken et al. 2011; Agüeros et al. 2011; Law et al. 2011; Levitan et al. 2011; Polishook et al. 2011). The PTF relative-photometry pipeline will be described in Levitan et al. (2012, in preparation).

Our method of photometric calibration for PTF data is similar to the "classical" method of observing a small number of calibration stars (e.g., Landolt 1992) through various air masses and assuming photometric conditions—i.e., the atmosphere transmission properties are constant in time and are a continuous function of air mass. The main difference is that we are using SDSS stars as standard standards and we typically observe ∼10⁵ SDSS stars with high signal-to-noise ratio in each CCD per night. Another important difference is that PTF observations are done in a single filter each night. Therefore, in order to relate the PTF calibrated magnitudes to one of the common absolute systems, one need to apply color terms. The article is organized as follows. In § 2, we describe the PTF photometric-calibration method. In § 3, we discuss the illumination correction, while § 4 describes a related problem that plagues early PTF data. In § 5 we describe the data products and what calibration information is stored with the image-product data. The performance of the PTF magnitude calibration is given in § 6, and the derived photometric parameter statistics are discussed in § 7. We provide the color transformation between the PTF magnitude system and other systems in § 8. Finally, we conclude the article in § 9. Unless specified otherwise, the statistics given here are based on all PTF data obtained from 2009 March to 2011 July.

PTF has two main data-reduction pipelines. The first is for real-time (≈30 min; e.g., Gal-Yam et al. 2011) image subtraction and transient detection, hosted by the Lawrence Berkeley National Laboratory (Nugent et al. 2012, in preparation). This article will make no further mention of this pipeline, as only the second pipeline is relevant here, as discussed subsequently.

The photometric calibration described in this article is implemented in the second pipeline. This pipeline, hosted by the Infrared Processing and Analysis Center (IPAC), performs final image reduction and extracts the source catalogs. The processing includes splitting the multiextension FITS images, debiasing, flat-fielding, astrometric calibration, generation of mask images, source extraction, and photometric calibration (the subject of this article). This pipeline is described in Grillmair et al. (2010) and Laher et al. (2012, in preparation).

Our photometric-calibration process runs on PTF data separately for each night, filter, and CCD. It first attempts to match the sources extracted from the PTF images taken during a given night with SDSS-DR7 PhotoPrimary¹⁷ point sources (i.e., SDSS type = 6). In order to ensure good photometric quality, only SDSS stellar objects with photometric errors smaller than 0.05 mag in r and i bands and that are fainter than 15 mag (to avoid saturated stars) in the g, r and i bands are used. The photometric solutions are calculated only if more than 30 science images were taken during the night and only if we were able to select more than 1000 SDSS stars in all the images taken with a given CCD and filter during the entire night.

We use the SDSS-matched stars as a set of standard stars and solve for the photometric zero points, air-mass terms, and color terms in a given night. The fitting process is done separately for each one of the 11 active CCDs and the g- and R-band filters. This is required, since the CCDs are not identical and some of them have a different spectral response (see Law et al. 2009 for details). For observations taken using the R-band¹⁸ filter, we fit the following model:

while for g-band observations we fit

Here, is the PTF instrumental magnitudes in band f (either R or g); f_SDSS is the SDSS magnitude in band f (either g, r, or i); ZP_f is the photometric zero point for filter f; α_c,f is the color term for filter f; α_a,f is the extinction coefficient (air-mass term) for filter f; α_ac,f is the air-mass/color term for filter f; AM is the air mass; α_t,f and α_t2,f are the polynomial coefficients for the change in the zero point of filter f as a function of time, t, in days, during the night, where t_m in days is the middle of the night; and δt is the exposure time in seconds.

The instrumental magnitudes used in the photometric-calibration process are based on the SExtractor (Bertin & Arnouts 1996) MAG_AUTO magnitude¹⁹ (see also § 6.1), with an internal SExtractor zero point of 0. The preceding set of equations is solved using linear least-squares fitting. The errors in are taken as , where Δr_SDSS is the SDSS magnitude error, is the PTF magnitude errors, and 0.015 is the assumed internal accuracy of the SDSS photometric calibration (Adelman-McCarthy et al. 2008). The fit is performed iteratively, up to 3 times, with sigma clipping of 3σ. The sigma clipping ensures removal of stars with bad photometry (e.g., influenced by cosmic rays; saturated pixels).

Next, in order to be able to correct for zero-point variations across a given CCD (see § 3), the residuals from the best fit of equations (1) or (2) are binned in cells of 256 × 256 pixel² along the X and Y dimensions of each CCD. In each cell, we take the mean of the residuals and subtract from it the mean of the residuals in the center-of-image cell,²⁰ in order to render the residuals relative to the residual at the image center. The resulting coarse image of the mean of the residuals is linearly interpolated to generate an image at the resolution of PTF images of pixel-to-pixel zero-point variations. This image product is equivalent to an illumination correction and herein is also called the zero-point variation map (ZPVM; see § 3). The uncertainty in the ZPVM is estimated by calculating the standard deviation (StD) of the residuals in each cell.²¹

We note that the PTF illumination-correction images are usually smooth on large scales (comparable with the CCD image size). Therefore, in most cases the ZPVM can be represented by low-order polynomials. In order to provide users with a simpler version of the illumination correction, we also fit versions of equations (1) and (2) that consist of a low-order-polynomial representation of the ZPVM, e.g., for the R band:

where X and Y are the positions on the CCD; X_size is the size of the CCD, in pixels, in the X dimension (2048 pixels); and Y_size corresponds to the Y dimension (4096 pixels). A similar equation is fitted for the g-band observations (see eq. [2] for an analogy). Here, the illumination correction is represented by polynomials with coefficients α_x1,f, α_y1,f, α_y2,f, α_y3,f, and α_xy,f. This representation usually provides a good estimate of the illumination correction over the image. We note that for each solution we store a variety of information regarding the quality of the fit (see § 5).

The ZPVM and its polynomial representation amount to an illumination correction that describes the variations in the photometric zero point spatially across the image (e.g., Regnault et al. 2009). Naively, such zero-point variations should be removed by the flat-fielding process. However, for example, if the fraction of flux in the stars' point-spread function (PSF) wings, relative to the flux integrated to infinity in the PSF, is variable as a function of position on the CCD, then this may induce variations that are not removed by the flat-fielding process. Such CCD position-dependent variations are indeed detected in PTF images (e.g., § 4). Figure 1 presents two examples of illumination-correction images. The left panel shows a typical case, in which the illumination corrections have a low range of variations. The right panel shows one of the worst cases we encountered thus far, with larger amplitude variations (see § 4). We note that the median peak-to-peak variations in the zero point across the image over all photometric nights, filters, and CCDs is about 0.06 mag.

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In the first year of the PTF project following first light, we detected a problem with the PTF image quality. This issue is referred to as the fogging problem, and it manifested itself as a diffuse halo around bright stars and a prominent large-scale nonuniformity in the illumination corrections. The fogging problem and our testing and subsequent apparatus modifications for ameliorating its effects are described in § 4.

The PTF camera window, which also acts as a field flattener, is fairly large (≈320 cm²). The window surface temperature is ≈16°C below the ambient temperature. To prevent condensation from forming on the window, a constant stream of dry air or nitrogen is blown across the window's outer surface. In the original installation of the camera, new nylon tubing was used to convey the gas to the window. This tubing was selected for its reported high durability, flexibility, and low outgassing properties. Once the window fogging problem was discovered, a test chamber was assembled, which simulated the cold window environment in which dry nitrogen could be conveyed across a cold test surface.

The outgassing properties of various tubing materials were evaluated in the test chamber. The nylon tubing used in the original camera installation was found to have a moderate amount of outgassing, which produced volatiles that would condense on the cold test surface. Tubing made from Teflon FEP (fluorinated ethylene propylene) was found to have low outgassing with no detectable volatile condensation on the cold test surface. The camera window was cleaned, and all tubing between the dry nitrogen supply and the camera window was replaced with this material on 2010 September 2. No window fogging issues have been observed since the tubing material was replaced.

We note that the camera window was cleaned several times during PTF operations, and after each cleaning an immediate reduction in ZPVM deviations from zero is expected. The cleaning dates are listed in Table 1.

Fortunately, the method described in § 2 provides an estimate of the zero-point variations across the CCD image. Therefore, the illumination correction is used to correct our photometry and to monitor the PTF image quality.

The parameters required for calibrating the instrumental magnitudes are stored in the PTF database, as well as in the image and catalog FITS file headers (§ 5.1). In addition, a full version of each illumination-correction image is stored as ancillary calibration data in a FITS file, and associated metadata are stored in the PTF database (§ 5.2). The use of these data products is discussed in § 5.3.

5.1. FITS Headers

The parameters based on the solution of equation (3) are stored in the image headers. Moreover, generated from each image is a FITS binary table containing all the sources extracted from that image using SExtractor. The FITS binary table catalogs contain three header and data units (HDUs) and two FITS extensions. The first HDU (i.e., the primary HDU) contains a header with metadata from SExtractor and no data. The second HDU, or first FITS extension, is a binary table containing the properties of the sources extracted from the processed image, with its header giving information about the table columns. The source properties in the binary table include aperture-photometry instrumental magnitudes and other SExtractor outputs. The binary table has also been augmented with an additional column called ZEROPOINT, which stores the source-dependent zero points computed from our photometric-calibration parameters; these zero points already include the 2.5 log(δt) contribution for normalizing the image data by the exposures time, δt, in seconds, and so straightforwardly adding the instrumental magnitudes to their respective zero points will result in calibrated magnitudes. The third HDU, or second FITS extension, contains an empty image whose header is a copy of the processed-image header, which includes information about the photometric calibration, as previously mentioned. The header keywords related to the photometric solutions are summarized in Table 2.

The FITS headers contain additional parameters related to photometric calibration. However, these parameters are based on different routines that are no longer supported. For completeness, these parameters are listed in Table 2 under the obsolete parameters heading. These keywords are products of our first attempt at photometric calibration of PTF images, which is less sophisticated than the method presented here. Both methods are still being run in the pipeline, and the results from both methods are still being written to the FITS headers of the processed images. A detailed description of the first version of photometric calibration is beyond the scope of the current article, but will be available from online documentation.

5.2. The Illuminatin-Correction FITS Image

5.3. Use of Data Products

Each processed PTF image is accompanied by an associated FITS binary table containing a catalog of objects extracted from the processed image by SExtractor. The catalog source magnitudes are instrumental magnitudes, and users of this product can convert instrumental magnitudes into calibrated magnitudes using the provided PTF photometric parameters and the following procedure. In order to convert the MAG_AUTO²² instrumental magnitudes to calibrated magnitudes, one needs to apply equations (1) or (2) and add the value of the ZPVM image at the location of the object. Alternatively, it is possible to directly use equation (3).

Applying equations (1), (2), or (3) requires the colors of individual sources in the SDSS system. If the color of a source is known, from PTF observations or other surveys (e.g., SDSS), then it is possible to use these equations to get the magnitude of that source in the SDSS system. However, not all PTF fields were observed in both the g and R filters or are within the SDSS footprint. In these cases, setting the color terms α_c,f and α_ac,f to zero will return the object's magnitude in the non-color-corrected PTF magnitude system (i.e., the natural PTF magnitude system). We denote magnitudes in this system by f_PTF, where f is the filter moniker. PTF magnitudes that are color-corrected (i.e., the source color is known and applied to eqs. [1], [2], or [3]) are denoted by f_PTF/SDSS. We note that applying equations (1), (2), or (3) is done by isolating f_SDSS and replacing it with f_PTF/SDSS in cases where the color is known or with f_PTF if the colors are set to zero. We note that the calibrated f_PTF magnitudes of all sources detected in PTF images are available from the PTF database.

As in the case of any other magnitude system, in order to convert the PTF non-color-corrected magnitudes to other systems, one needs to know the color index of the source. In some cases, it is possible to use some prior knowledge about the mean color index of a class of objects (e.g., RR Lyr stars; asteroids), in order to convert their PTF magnitudes (in a single band) into SDSS magnitudes. For example, 68% of main-belt asteroids have an r - i color index in a narrow range of about 0.2 mag (e.g., Ivezić et al. 2001). Therefore, given the PTF R-band color coefficients, α_c,R ≈ 0.2, the scatter in the mean color correction for asteroids is about 0.04 mag. Neglecting the air-mass/color terms (which are typically small; see Table 3), the relations between the PTF and the SDSS magnitude systems, for objects with stellarlike spectra, are given by

and

where the values of the color terms are listed in Table 3.

In order to apply the illumination correction to individual images, we need to multiply, pixel by pixel, the processed image by 10^-0.4×ZPVM, where ZPVM is the illumination-correction image. Alternatively, one can use the less accurate polynomial representation of the ZPVM image.

The accuracy of our calibration process, relative to SDSS, is discussed in § 6.1, while in § 6.2, we discuss the repeatability of our photometric calibration.

6.1. Accuracy

As described in § 5.3, the PTF calibrated magnitudes can be given in two systems. One is a color-corrected magnitude system, denoted by R_PTF/SDSS or g_PTF/SDSS, in which the known color of the object is applied to equations (1), (2), or (3). By construction, this magnitude system is similar to the SDSS system. The other possibility is a "natural system" in which all the color terms involving α_c,f and α_ac,f are set to zero (i.e., the color indices of the objects are ignored). These magnitudes are denoted by R_PTF or g_PTF.

To demonstrate the current accuracy of the PTF photometric calibration, we show in Figure 2 the differences between SDSS magnitudes and color-corrected PTF R-band magnitudes (R_PTF/SDSS), as a function of SDSS magnitude.

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In this particular example, the StD in the r_SDSS - R_PTF/SDSS for bright stars is smaller than ≈25 mmag. Figure 3 shows the same, but for PTF magnitudes not corrected for the color term (R_PTF). The scatter in the uncorrected color plot is larger, as expected. The larger scatter in Figure 3 is due to the fact that different stars in the field of view have different colors. The 95th percentile range of r - i color of SDSS stars in the r-band magnitude range of 16 to 17 is between -0.2 and 1.2 mag (see Fig. 4). Given that the PTF mean r - i color term is about 0.2 mag, this corresponds to a color correction between -0.04 and 0.24 mag.

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We note that in Figures 2 and 3, the magnitude difference is systematically tending toward larger negative values, starting around magnitude 19.5. This is due to the use of MAG_AUTO. Indeed, using aperture magnitude (i.e., MAG_APER), we do not see any evidence for this bias. This is because MAG_AUTO adjusts the aperture used to extract the source magnitude for each object. Therefore, if MAG_AUTO is used for sources near the survey detection limit, it is recommended to estimate the aperture correction for these sources in order to obtain their unbiased magnitudes. We note that the MAG_AUTO is different from aperture or PSF magnitudes. In order to convert between MAG_AUTO and other kinds of magnitude estimators, one needs to find the aperture correction between these magnitudes. Both MAG_AUTO and aperture magnitudes in five predefined apertures are available in the FITS binary source catalog associated with each image. Future versions of the PTF photometric pipeline will use aperture or PSF magnitudes.

6.2. Repeatability

The stability over time of the PTF R-band photometric solutions is demonstrated in Figure 5. This figure shows the scatter in the calibrated magnitude of each star, over multiple epochs, as a function of magnitude. The scatter is calculated using the 68th percentile range divided by two (i.e., equivalent to StD in case of a Gaussian distribution). This is based on 27 images of PTF field ²³ 100037 CCDID = 0 ²⁴ taken between 2010 March and October, which have photometric-calibration bright-star root-mean-square (rms) values (parameter APBSRMS in Table 2) of less than 0.04 mag.

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We choose to use the 68th percentile range instead of StD, since it is more robust to outliers. For example, if a night was "photometric" for 90% of the time (e.g., clouds entered only toward the end of the night), then our pipeline might claim that the night was photometric, but the calibration of some of the data will be poor. Therefore, in order to get the calibrated source magnitudes, it is important to average the data taken over several photometric nights. We note that we are using this approach for the compilation of the PTF photometric catalog (Ofek et al. 2012, in preparation). In turn, this catalog will be used in later phases to calibrate the entire PTF data.

Figure 5 suggests that, at the bright end, the repeatability of PTF calibrated magnitudes is good to a level of 0.02 mag. Figure 6 shows the same, but for stars in 100 representative PTF fields and all CCDs. The typical repeatability of PTF magnitudes is field-dependent. The median repeatability over all these 100 fields, for all CCDs, for stars between 15 to 15.5 mag, is about 11 mmag, and the 95th percentile range is between 2 mmag to 44 mmag. We note that PTF g-band observations achieve similar repeatability.

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The term "photometric night" is not well defined and depends on the required accuracy. Figure 7 shows the cumulative histogram of the rms of the best-fit residuals of bright stars (parameter APBSRMS in Table 2) in all the images taken by PTF.

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This figure suggests that about 62% (50%) of the R-band (g-band) images taken by PTF have photometric calibration with bright-star rms values smaller than about 0.04 mag. Figure 8 shows the R-band air-mass term (α_a,R) versus the color term (α_c,R), while Figure 9 shows the same for the g band.

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These figures suggest that some nights that have small bright-star rms values (i.e., smaller than 0.04 mag) have anomalous air-mass or/and color coefficients. Therefore, it is better to select data taken in nights for which the air-mass and color terms are close to their average values (e.g., see Table 3). Here, we define photometric nights as nights with bright-star rms values smaller than 0.04 mag and α_c,f within the range of 〈α_c,f〉 ± 3Δ[α_c,f] and α_a,R within the range of 〈α_a,f〉 ± 3Δ[α_a,f]. Here, 〈α_c,f〉, Δ[α_c,f], 〈α_a,f〉, and Δ[α_a,f] are the median and 1-σ width of the color and extinction coefficients for each CCD, as listed in Table 3. We find that 59% (47%) of the R-band (g-band) PTF data were taken on such photometric nights.

The atmospheric extinction coefficients depend on the atmospheric conditions. Therefore, they may vary with season. Figure 10 shows the median R-band air-mass coefficient (α_a,R) and the color term (α_c,R) as a function of month in the year. The error bars are given by the StD within each month divided by the square root of the number of photometric nights in each month. This figure indicates that there are small, but significant, seasonal variations in both the R-band extinction and color terms.

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Table 3 presents the median and 68th percentile range divided by 2, of the color-term, extinction-coefficient, and air-mass/color terms for each CCD and filter. These are calculated based on data from all nights in which the rms of the best-fit residuals of bright stars is smaller than 0.04 mag and the limiting magnitude²⁵ is fainter than 20.5. We note that the R-band color terms are roughly the same for all CCDs, while the g-band color terms have a wider range.

Approximate relations between the non-color-corrected PTF magnitude system and the SDSS magnitude system are given in equations (4) and (5). The exact relations between the two systems depend on the details of the object's spectral energy distribution and the atmospheric conditions at the time of the observations.

Using equation (4) and the color transformations between the Johnson-Cousins (UBVR_c I_c) system and the SDSS system,²⁶ we find an approximate transformation between PTF R-band magnitude and the Johnson-Cousins system:

Similarly, using equation (5) for the PTF g band, we get

Here, T_1,f and T_2,f are the color-transformation coefficients for filter f. These parameters are listed in Table 3.

Assuming²⁷ V = +0.03 and V - R_c = R_c - I_c = 0, for the A0V star Vega we find

and

For the absolute magnitude of the Sun, assuming V = +4.82, V - R_c = +0.36, and R_c - I_c = +0.32 and using SDSS color transformations, we find

and

A wide variety of scientific applications require photometric calibration of astronomical images. In this article, we provide a description of the current PTF photometric-calibration process and products. We show that roughly half of the PTF data were taken under conditions that allow calibration of the images to an accuracy of 0.02–0.04 mag relative to SDSS. Most importantly, the rest of the data, taken under nonphotometric conditions, can be calibrated using data taken in photometric conditions. At the bright end (≈15 mag), the PTF photometric calibration is stable to a level of ≈0.02 mag. Future improvements to the PTF photometric-calibration process that are important for the PTF Type Ia and Type IIp supernovae cosmology projects will be described elsewhere.

The PTF photometric calibration allows us to measure the calibrated magnitude of transients outside the SDSS footprint. We have used the PTF data set to compile a photometric catalog. The first version of this catalog is described in Ofek et al. (2012, in preparation). We note that our tests show that PTF data can deliver relative photometry, in single images, with precision as good as 3 mmag (e.g., van Eyken et al. 2011; Agüeros et al. 2011). This capability is being built into the PTF relative-photometry pipeline and will be described in Levitan et al. (2012, in preparation).

We thank Andrew Pickles and an anonymous referee for useful comments on the article. This article is based on observations obtained with the Samuel Oschin Telescope as part of the Palomar Transient Factory project, a scientific collaboration between the California Institute of Technology, Columbia University, Las Cumbres Observatory, the Lawrence Berkeley National Laboratory, the National Energy Research Scientific Computing Center, the University of Oxford, and the Weizmann Institute of Science. E. O. O. is supported by an Einstein fellowship and NASA grants. S. R. K. and his group are partially supported by the NSF grant AST-0507734. S. B. C. acknowledges generous financial assistance from Gary and Cynthia Bengier, the Richard and Rhoda Goldman Fund, NASA/Swift grants NNX10AI21G and GO-7100028, the TABASGO Foundation, and NSF grant AST-0908886.