FAINT NEAR-ULTRAVIOLET/FAR-ULTRAVIOLET STANDARDS FROM SWIFT/UVOT, GALEX, AND SDSS PHOTOMETRY

The last three decades have witnessed the advent of numerous space-based ultraviolet-sensitive instruments. Programs such as the Hubble Space Telescope (HST) Faint Object Spectrograph, Space Telescope Imaging Spectrograph (STIS), and Advanced Camera for Surveys, International Ultraviolet Explorer, Far-ultraviolet Spectroscopic Explorer, Galaxy Evolution Explorer (GALEX), and Hopkins Ultraviolet Telescope have created an infusion of scientific discovery, particularly in hot or high-energy environments.

The expansion of ultraviolet astronomy, however, has run into a problem of calibration. The primary set of UV calibration standards for the above missions consists of four hot white dwarf stars—G 191-B2B, GD 153, GD 71, and HZ 43 (Bohlin 1996, 2000, 2007; Bohlin et al. 2001; Bohlin & Gilliland 2004; Nichols & Linsky 1996; Kruk et al. 1999). All four, however, are brighter than m_V = 13.4 (Holberg & Bergeron 2006). While such bright standards were excellent for previous generations of instruments, they are too bright for the latest generation of telescopes. The Bohlin standards would quickly saturate CCD cameras on large telescopes (or, in the case of the Cosmic Origins Spectrograph, potentially damage the detector) and short exposure times bring shutter resolution into play. Observations with photon-counting instruments—such as the Swift Ultraviolet Optical Telescope (UVOT), ASTROSAT's Ultraviolet Imaging Telescope or the Tel Aviv University UV Explorer—are compromised by coincidence loss. Coincidence loss occurs when two or more photons from an astronomical source arrive within a single detector read time and are therefore read as a single photon (Fordham et al. 2000). The brighter the source, the greater the coincidence loss. Coincidence loss cannot be ameliorated by shorter exposure times. Beyond a certain range (with UVOT, about 100 photon s⁻¹) coincidence loss becomes so great as to make measured brightnesses unreliable (see Poole et al. 2008, hereafter P08, their Figure 6).

Recent calibration efforts using faint UV standards have been made by the Swift/UVOT team (P08). However, even UVOT is only calibrated to three objects—WD 1657+343, WD 1121+145, and WD 1026+453—in the UV passbands. These hot white dwarfs have U magnitudes of 14.8–15.4 and were observed as part of an HST faint extension calibration program (10094). However, the HST program was unable to proceed after 2003 owing to the failure of STIS and a fourth faint standard (WD 0947+857) was suspected to have a composite UV–optical spectrum (Lajoie & Bergeron 2007). The need for a larger number of faint UV standards remains critical.

A recent study by Allende Prieto et al. (2009, hereafter AP09) has taken the first step in this direction. Using data from the Sloan Digital Sky Survey (SDSS), they identify nine hot faint DA white dwarfs as potential spectrophotometric standards. Hot DA white dwarfs are suitable as UV standard candles because of their high UV luminosities, blue colors, and the paucity of spectral lines that makes them easy to model. In turn, because the UV passbands are sensitive to the properties of white dwarfs (see Figure 1), studying white dwarf standards can provide a reciprocal test on the white dwarf models themselves and provide additional constraints on the properties of white dwarfs.

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Our study complements the AP09 study by using Swift/UVOT to observe 11 faint hot DA white dwarfs selected not only from the SDSS but also from the GALEX catalog. We use the combined data, covering the spectral range from the near-IR (NIR) to the far-UV (FUV), to provide tight constraints on the temperatures of the white dwarf stars. Moreover, we test the ability of pure hydrogen models of white dwarfs to reproduce the measured photometry. The result is a group of stars with calibrated observations in 11 passbands, published SDSS spectra, and well-constrained model spectra that can be used to calibrate existing or future instruments that may use different filters.

2.1. Sample Selection

2.2. Photometry

2.3. Photometric Stability

The photometric uncertainty of any particular standard star's photometric measures is the combination of the Poisson noise of the observation,¹⁰ the uncertainty in the photometric zero points and, in the case of aperture photometry, any variation in the PSF. As a photon-counting instrument, UVOT's read noise is irrelevant to the error budget. In the case of UVOT, the first two sources of uncertainty are quantified by our photometry pipeline and P08, respectively, and included in Table 3. The third—variation of the PSF—has been quantified by B10, along with other small instrumental effects. However, it can be independently checked from our standard star data.

The observations of our standard stars consist of 1–3 epochs of UVOT data. Each of these epochs is, in turn, comprised of many (mean of 30) independent UVOT exposures taken over multiple orbits of the Swift satellite. The photometric measures in Table 3 are taken from deep images produced by combining all the extant data. However, the 10–45 independent UVOT exposures that comprise each stacked image allow us to check for any photometric zero-point residuals in the data. More importantly, the independent images allow a check on the photometric stability of the standard stars themselves.

We photometered the individual UVOT exposures using the APPHOT package in IRAF, with apertures set to the 50 optimal apertures specified in P08. The raw photometry was corrected for coincidence loss using the formulation of P08 and calibrated using the transformations of P08 and iterative matrix inversion techniques described in Siegel et al. (2002). The iteration process derives and corrects for exposure-to-exposure zero-point residuals within each photometric passband, with residuals measured from the mean zero point.

Figure 2 shows a typical result of our investigation—the distribution of exposure-to-exposure photometric zero-point residuals for SDSS J002806.49+010112.2. The distribution is roughly Gaussian with a typical zero-point dispersion of 0.02–0.04 mag. This dispersion is comparable to the scale of the instrumental effects quantified in B10.

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The individual UVOT exposures, however, are shallow and have few stars with which to make comparisons (2–60, with a median of 7). With such small numbers of comparison stars, a single bad measure could dramatically alter the measured residuals. To improve the statistics, we combined the UVOT images from each epoch separately and photometered them using the techniques described above. In this case, exposure time was no longer constant across the stacked image owing to the roll and pointing uncertainty of the spacecraft, but was easily corrected from the exposure maps produced by the UVOT reduction pipeline. The dispersion of these epoch-to-epoch photometric residuals was calculated from a much deeper sample of 10–163 (median 30) common stars and shows a much clearer Gaussian pattern with a dispersion of 0.01–0.02 mag (Figure 3). The reduction in the residual dispersion is consistent with having averaged out by subsampling some of the PSF variability in the combination. We expect that further improvement of the UVOT pipeline or attention to the systematics quantified by B10 will further reduce or eliminate these residual effects.

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Removing these small zero-point residuals using the aforementioned iterative calibration allows a more precise check on the variability of our new UV standards. Figure 4 shows the ratio of measured photometric scatter to measurement uncertainty as a function of magnitude, after the correction for the zero-point residuals. This measure is, essentially, the χ² of a constant magnitude fit to the data. While a few stars have high variability measures, the majority are clumped at low values, with a mean variability index of 1.41 and a 90% interval between 0.4 and 3.1. This would be consistent with some residual zero-point systematic error in the photometric measures inflating the ratio over its expected value of 1.0. The white dwarf stars have a mean variability index of 1.55 with a maximum of 2.87, well within the bulk of field star distribution. The variability indices are listed in the final column of Table 3.

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Within the limits measured by our UVOT program, our standard stars appear to be photometrically stable. Further monitoring, to measure any potential variation over year-long timescales, is recommended.

As a further check on the photometric stability of the stars, we have examined the SDSS photometry of two stars which fall within the SDSS Southern Stripe (Stripe 82), a section of the DR4 which has been repeatedly observed, yielding data of 1% precision, half the more typical 2% precision of SDSS data (Ivezić et al. 2007). We confined our analysis to data taken before MJD 53,400 (12:00 pm 2005 January 29 UT). Beyond that date, the photometric measures are more dense but include many data taken under non-photometric conditions.

Figure 5 shows the measured photometry and no variability is seen. The variability indices are all significantly less than 1.0, indicating excellent photometric stability over the 5–6 year time scale of the observational set. We note that SDSS J231731.36−001604.9, which has a variability index in the Swift data of 2.35, shows minuscule variability in the more extensive Sloan data.

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As a final check, we took advantage of the simultaneous X-ray observations of our targets produced by the XRT. While our white dwarf stars are too faint and cold to produce noticeable X-ray flux, an X-ray signal could be produced in the (unlikely) event that one were an accreting X-ray binary. After running the automated analysis of Evans et al. (2009), however, we find no X-ray source at the position of any of our standard stars.

With the suitability and photometric stability of our standards assured, we can now constrain the underlying white dwarf spectral model and test the ability of the models to reproduce the observed photometry. A reliable model spectrum could be used for calibrating other UV telescopes regardless of whether their filter response curves resemble those of UVOT or GALEX. While Eisenstein et al. and AP09 have fitted SDSS white dwarf parameters from optical and near-infrared spectra, our UV photometry provides additional leverage on the effective temperatures of the white dwarfs because the UV samples a much more sensitive portion of the white dwarf spectrum.

The complexity of modeling the photometry is greatly reduced by our limiting of the candidate list to DA stars without evidence of magnetic fields, metal lines, or companions. The key parameters of the models are T_eff, log g, and A_V, the V-band foreground extinction.

As a preliminary step, we re-fitted the continuum-corrected SDSS spectra using the methods outlined in AP09. This was done primarily to better constrain log g, which our photometry proved to be relatively insensitive to. The parameters of the purely spectral fits are given in Table 5 and the continuum-corrected fits are shown in Figure 6. They are similar to those of Eisenstein et al. with the notable exception of SDSS J092404.84+593128.8, for which we find a lower gravity. In all cases, the χ² of the fit is less than 1.0.

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Before fitting the photometry, we corrected the models for extinction by simply taking the V-band extinction values (A_V) from the reddening maps of Schlegel et al. (1998) listed in Table 1 and applying the extinction curve given in Pei (1992) to the model spectra. This technique is essentially an inversion of the "extinction without standards" method outlined in Fitzpatrick & Massa (2005), which combines photometry with spectral models to derive a UV extinction curve. In this case, we used photometry and an assumed extinction curve to constrain the spectral models.

Attempts were made to fit A_V directly from the photometric measures by producing multiple families of models with different foreground extinction values and UV extinction laws. However, we found the fitted A_V values to be both imprecise (typical fitting uncertainty was 0.1 mag—an uncertainty larger than the total Schlegel et al. 1998 measures) and co-variant with the fitted T_eff.

It is possible that using the full Schlegel et al. (1998) values over-corrects the models for extinction. The Schlegel et al. values are for the full dust column and have been shown to be possibly over-estimated (see, e.g., Cambresy et al. 2005). However, our white dwarfs are typically at distances of 150–250 pc. Given an exponential dust scale height of 134 pc (Marshall et al. 2006), it is likely that we are viewing the white dwarfs through 70%–85% of the total dust along the line of sight. The difference between this and the full Schlegel et al. values is less than 0.01 mag.

The significance of a 0.01 mag uncertainty in the foreground extinction is small. Analysis of our models indicates that changing the assumed reddening by 0.02 mag would alter the derived temperatures by, on average, 100°, with overestimates of reddening producing overestimates of temperature and underestimates being similarly covariant. Thus, the effect of reddening uncertainty on our model fitting is expected to be less than that of the photometric uncertainties.

With revised log g values and A_V values, we turned to constraining the white dwarf temperatures based purely on the photometry. We calculated a grid of pure hydrogen non-LTE models using Version 204 of TLUSTY (Lanz & Hubeny 1995), including the quasi-molecular satellites of Lyα and Lyβ. These models do not include the new Stark broadening calculations of Tremblay & Bergeron (2009), which could shift the derived T_eff by as much as +1500 K.

A grid of model spectra was calculated for T_eff = 20, 000, 22,500, 25,000, 27,500, 30,000, 32,500 and 35,000 K and log g = 7.0, 7.5, 8.0, 8.5, and 9.0. We linearly interpolated these spectra to a resolution of 100 K and 0.05 in log g. We then reddened the models based on the foreground reddening and Pei dust curve. At each temperature and gravity combination, synthetic magnitudes were then calculated by convolving the synthetic spectrum with the most recent filter response curves for UVOT, GALEX, and SDSS using the formulation:

$$\begin{equation} m = -2.5 \log \left(\frac{\int\! d(\log \lambda) \lambda ^2 f_{\lambda } S_{\lambda }}{\int\! d(\log \lambda) S_{\lambda }} \right) + C, \end{equation} \tag{ 1 }$$

where f_λ is the model spectrum flux and S_λ is the system throughput per unit wavelength. C is the zero-point magnitude.

Observed magnitudes were compared to model magnitudes using

$$\begin{equation} \chi ^2 = \displaystyle \sum _i \frac{(m_i - m_{{\rm model},i} + c)^2}{\sigma _i^2} \end{equation} \tag{ 2 }$$

where m_i is the observed magnitude, m_model,i is the model magnitude, and σ_i is the photometric error for in the ith filter. The summation is over all 11 filters shown in Tables 2 and 3 and described in Section 2.2.

The value c is a normalization constant which matches the observed and model spectra to the same level. The optimal value of c can be analytically determined by setting ∂χ²/∂c = 0. Solving for c yields

$$\begin{equation} c = \frac{\big(\sum _i \frac{m_{{\rm model},i}}{\sigma _i^2}- \sum _i \frac{m_i}{\sigma _i^2}\big)}{ \sum _i 1/\sigma _i^2}. \end{equation} \tag{ 3 }$$

The value of c was calculated independently for each combination of observed and model magnitudes and use to calculate and minimize χ².

To quantify the nonlinear effect of photometric uncertainty upon our model fits, we performed a Monte Carlo simulation on the data. The photometric measures were perturbed by the photometric errors and T_eff was refit using Equation (2). A general description of the Monte Carlo technique can be found in Press et al. (1992). Given the relative brightness of our candidate stars, the photometric errors were dominated by systematic zero-point errors and not the random Poisson errors for all stars in all bands. Zero-point errors were modeled as uniformly distributed with end points set the photometric uncertainties. For each star, this process was repeated for 10,000 Monte Carlo realizations. The resulting distributions of T_eff were used to determine the best values from the median and 90% error bars.

The best-fit model parameters are given in Table 6. The model fits and Monte Carlo error simulations are shown in Figures 7–10. For all of our dwarf stars, we find a favored T_eff that accurately reproduces the observed photometric measures across all 11 passbands. No star has a reduced χ² greater than 1.51 and the mean χ² is 0.92, indicating that the residuals are within the photometric uncertainties.

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Figures 11 and 12 show the photometric residuals (Δ_m = m_model − m_data) for all of our stars in each filter while Table 7 lists the mean, median, and dispersion of the residuals in comparison to the systematic uncertainties in the photometric zero points (σ_sys) for each filter. In almost all cases, the mean and median Δ_m are within one or two σ_sys of zero, indicating that our models agree with the measured photometry within the zero-point uncertainties compiled in Tables 2 and 3. The mean $\frac{|\langle \Delta _m\rangle |}{\sigma _{\rm sys}}$ is 0.99, indicating excellent agreement between the models and data. This confirms that the spectra can be used by future investigations to extrapolate predicted magnitudes in other passbands. It also confirms the quality and consistency of the most recent UVOT calibration.

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Table 7. Residuals of Fits to Photometry

Filter	〈Δm〉	Median (Δm)	$\sigma _{\Delta _m}$	σsys
FUV	−0.054	−0.055	0.047	0.05
NUV	0.044	0.047	0.013	0.03
uvw2	−0.014	−0.011	0.011	0.03
uvm2	0.010	0.014	0.026	0.03
uvw1	−0.038	−0.034	0.022	0.03
u (UVOT)	0.029	0.031	0.019	0.02
u (SDSS)	−0.032	−0.026	0.029	0.03
g	−0.008	−0.016	0.025	0.01
r	−0.013	−0.015	0.015	0.01
i	0.002	−0.001	0.014	0.01
z	0.029	0.023	0.047	0.02

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Figure 13 compares the Eisenstein et al. (2006) effective temperatures against those derived in our model fitting. While the values roughly track each other, we find that our temperatures average slightly lower than those given in Eisenstein et al. A similar result was found in AP09, who found the Eisenstein et al. temperatures to be a few percent lower than theirs up to 30,000° and slightly warmer at higher temperatures.

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The fitted spectral models are included in the online version of the journal (Table 8). These can be compared to measured spectra or convolved with filter functions using the procedure outlined above to predict standard stellar magnitudes in non-UVOT passbands. However, given uncertainties in any model fitting and the likelihood of future updates to the TLUSTY code, it may be advisable for future calibrations to use our published photometry and fit parameters as a starting point for a refined exploration of these new standard stars.

We have created a catalog of 11 faint DA white dwarf ultraviolet standards for use with space-based UV detectors. Our stars have been carefully chosen for simple modeling, low extinction, a lack of nearby stellar companions, even distribution across the sky and faintness that will avert problems of saturation or coincidence loss. In combination with SDSS and GALEX, we provide precise photometry for these stars from the NIR to the FUV. Checks from both UVOT and SDSS data show that our white dwarf stars are photometrically stable. When combined with the recent sample of spectrophotometric standards recommended by AP09, up to 20 new UV standard stars are now potentially available to the community, all of which have published SDSS photometry and 11 of which now have published NUV and FUV photometry.

We have fitted both the SDSS spectra and measured photometry of our standard stars with relatively simple white dwarf stellar atmospheric models. We find that these models provide strong and consistent constraints on the properties of the white dwarf stars, reproducing the photometric measures to within the 1%–5% uncertainty of their photometric zero points. This indicates outstanding suitably of our standard stars for calibration of future missions that may not share the filter set of UVOT and GALEX through the use of simple white dwarf atmospheric models.

Of our 11 stars, we do not find any that are of poor or limited quality. The mean reduced χ² of the model fits to spectra and photometry is 0.64 and 0.92, respectively, indicating excellent agreement between models and data. Measurement of stellar variability shows some stars to have moderately elevated photometric scatter. However, this scatter is within the distribution of stable field stars and does not appear in the more extensive SDSS Stripe 82 data. We do, however, recommend further monitoring to ensure that the stars are photometrically stable.

The two most significant uncertainties in our standard stars are (1) the systematic uncertainty in the photometric zero points of GALEX and UVOT, which limit the models to reproducing the photometry within the 1%–5% uncertainty of the zero points and (2) the previously known uncertainty in the UV extinction law. These systematic uncertainties dominate over our random errors. We are engaged in an effort to better understand the UV extinction curve in Galactic dust. We also recommend further investigation to improve the calibration of both GALEX and UVOT. In combination, these two endeavors—dust properties and calibration—would enhance the precision of our faint UV standard to better than 1%, which would both improve the capabilities of UVOT and help other missions to explore the ultraviolet range of the spectrum.

The good agreement between model, spectra, and photometry is indicative of the outstanding suitability of DA white dwarfs as UV standard stars. As the models and especially our understanding of the UV properties of the dust improve, our ability to characterize the white dwarf properties will also improve. This will allow further investigation into more distant and/or more reddened white dwarfs to improve our understanding of these stellar relics.

The authors acknowledge support in the form of GALEX grant NNX08AK62G and sponsorship at PSU by NASA contract NAS5-00136. We thank I. Hubeny for assistance with the TLUSTY software and the anonymous referee for useful comments.