HUBBLE SPACE TELESCOPE CALSPEC FLUX STANDARDS: SIRIUS (AND VEGA)

The STIS absolute flux calibration is based on model atmosphere SEDs for the three primary WDs G191B2B, GD153, and GD71. Gianninas et al. (2011, G11) fit new Balmer line observations of these WDs with updated NLTE, pure-hydrogen models that include improved theoretical calculations of the Balmer lines (Tremblay & Bergeron 2009). G11 found T_eff and log g of 60,920 K and 7.55 cm s⁻² for G191B2B, 40,320 K and 7.93 cm s⁻² for GD153, and 33590 K and 7.93 cm s⁻² for GD71. For G191B2B, RWBK computed line-blanketed NLTE models and reported a best fit to the absorption lines in STIS and FUSE high dispersion spectra of T_eff = 60, 000 ± 2000 K and log g = 7.60. However, a T_eff = 59, 000 K model is within the uncertainty and is more consistent with the STIS relative UV flux among the three stars. In addition, RWBK found $N({\rm H\,\scriptsize{I}})=2.2\times 10^{18}\ {\rm atoms\ cm^{-2}}$ from the Lyman lines, which corresponds to E(B − V) = 0.0005 according to the galactic average $N({\rm H\,\scriptsize{I}})/E(B-V)=4.8\times 10^{21}\ {\rm atoms\ cm^{-2}\ mag^{-1}}$ of Bohlin et al. (1978).

New models for the three fundamental primary standards GD71, GD153, and G191B2B (Bohlin 2003) are calculated with the Tübingen NLTE Model-Atmosphere Package (Werner et al. 2003; Rauch & Deetjen 2003), which includes metal line blanketing for G191B2B but only pure hydrogen for GD153 and GD71 at the G11 T_eff and log g. The model parameters for the three primary WDs appear in Table 2. Their SEDs are available via CALSPEC¹ and also from the registered Virtual Observatory service TheoSSA² that was created in the framework of the GAVO³ project. After reddening the G191B2B model by E(B − V) = 0.0005 and normalizing relative to the 5556 Å flux of for Vega, these three SEDs define the STIS absolute flux calibration and all observed STIS fluxes.

Previous to 2013 November, pure hydrogen models calculated with the Hubeny NLTE code defined the SEDs of all three stars. The switch to Rauch models results in a wavelength dependent shift of the HST flux scale by <∼1% in the STIS wavelength range. At 8 μm, the worst discrepancy with the Spitzer/IRAC fluxes (Bohlin et al. 2011) had been a 4σ difference of 12% for G191B2B. The 4% lower flux at 8 μm for the new G191B2B SED reduces the discrepancy to 8% with less than a 3σ significance.

The final Sirius fluxes adjusted to the new calibration can be found in the CALSPEC database with the file name sirius_stis_001.fits. Included in the file are the estimated systematic uncertainty of 1% and the statistical uncertainties, which determine a S/N per pixel that ranges up to 15000 at 4000–4100 Å, where 2.4 × 10⁸ electrons per pixel are extracted from the CCD spectral images.

Figure 2 compares the STIS flux for Sirius to other results, including an R = 500 resolution, original Kurucz model⁴ and an update (R. Kurucz 2013, private communication). All of the illustrated SEDs have been divided by the same theoretical smooth continuum, as normalized to the STIS flux at 6800–7700 Å, in order to display the spectral features on an expanded scale. Ratio plots of STIS/model have large and distracting, spurious dips and spikes near strong absorption line features because of small mismatches in resolution and tiny wavelength errors. The ratios of flux/continuum in Figure 2 display the nature of the absorption lines, and the irrelevant small mismatches at line centers are often off-scale and can be easily ignored. Longward of 1 μm, the 2013 Kurucz model, normalized to the STIS flux in the 6800–7700 Å range, is chosen for the composite Sirius SED. Many of the weak STIS features which are <1% correspond to spectral features in the Kurucz model. To define the final composite Sirius SED below 1675 Å, an IUE spectrum is used after normalization to the STIS flux by multiplying by 1.28. The highest speed IUE trail data used for bright stars often missed the exact slit center, making the absolute flux low; but see Section 3.4 for verification of the 1.28 factor. The blue curve in Figure 2 is from EPK, while the Cohen et al. (1992a) reference SED is green. The Cohen SED for Sirius is part of the CWW standard star network (Cohen et al. 1992b; Cohen 2007).

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The EPK curve (blue) is more than 10% low at places in the top two panels of Figure 2 but differs from the Kurucz extrapolation (red) by only a few percent in the bottom panel. The EPK fluxes are the zero-point SED from their Table 4, as scaled up by their −1.368 mag for Sirius. Below 0.9 μm, the EPK SED is based on the vintage absolute flux for 109 Vir from Tüg et al. (1977), as scaled to zero magnitude. Between 0.9 and 9 μm, EPK warp NICMOS and ISO measured flux distributions to match various photometry. From 9.4 to 35 μm, the upward trend of the blue curve in Figure 2 reflects the EPK smooth adjustment of the CWW model to closely track the MSX absolute fluxes of Price et al. (2004, PPEM).

The normalized Kurucz model (red) agrees with the observed STIS flux (black) to better than ∼1% over most of the wavelength range in the middle panel of Figure 2. The original 1993 specially tailored Kurucz model⁵ agrees with his 2013 update to <1% longward of 1800 Å; and at shorter wavelengths, the update fits the observed flux significantly better. This precise agreement of STIS and model suggests that the modeled flux could represent the true stellar flux with a similar accuracy of ∼1% longward of 1 μm.

Absolute IR flux measurements with direct reference to laboratory standards were pioneered from the ground by Selby et al. (1983), Blackwell et al. (1983), Mountain et al. (1985), and Booth et al. (1989). From space where the atmosphere does not cause complications, the SPIRIT III instrument on the MSX provided pedigreed absolute mid-IR fluxes from emissive reference spheres (ERS) that were ejected and observed as point sources with fluxes based on lab data and basic physics. Preliminary MSX results appear in Cohen et al. (2001), while PPEM present a definitive final analysis. In their Table 9, PPEM compare their new ERS based absolute fluxes to the ensemble average of a subset of the CWW network of standards. However, the uncertainties for each of the four MSX bands in that Table 9 seem to be the internal statistical precision to which the MSX flux scale can be related to the CWW average scale. For the final MSX external uncertainties of the absolute flux measures, the 1.4% from the PPEM abstract is most appropriate. Larger uncertainties of 3%–4% are quoted for the calculated ERS fluxes; but those values are reduced by an analysis of the band-to-band flux ratios, which constrain the sphere temperature. A minimum error bar arises from the two uncertainties of 2% attributed to ±1% in the sphere radii and ±1% in the distance to the ejected spheres. If each of the five ERS ejection events are independent, e.g., the 1% radius error is random and not the same for all five released spheres, then the error-in-the-mean floor for each band is $\sqrt{(4 + 4)/5)} = 1.3\%$, which is consistent with the adopted 1.4% in Table 3.

In addition to the systematic corrections to the global CWW flux scale, the CWW flux for Sirius itself was found to be offset by 1% low compared to the ensemble set of CWW program stars. Table 3 summarizes these results and includes the correction factors and final MSX in-band, effective fluxes (irradiance) for Sirius, where the negative corrections mean that the CWW flux is low and must be increased by the tabulated factors to agree with the MSX results. The fluxes in Column 5 of Table 3 are the integral fluxes over the bandpass from Table 2 of PPEM divided by Table 1 bandwidth of Cohen et al. (2001) times the correction in Column 4 of Table 3. Multiplying this total CWW correction factor by the Column 7 ratio of the green CWW to the red curve adopted for the IR extension of the HST/STIS fluxes in Figure 2 produces the ratio of MSX to the adopted IR flux. These ratios of MSX to HST/STIS are tabulated in the final Column 8 of Table 3 and are plotted with their 2σ error bars of 2.8% as the filled circles at the MSX isophotal wavelengths in Figure 2.

To normalize the Kurucz model to the MSX lab based absolute flux calibration, the illustrated normalization that is based on the 5556 Å Vega flux of Megessier (1995) would be multiplied by the average of the four factors in the final column of Table 3. However to properly weight the visible and mid-IR absolute fluxes, a weighted average correction of 0.9945% ± 0.5% includes the 5556 Å normalization at unit value ±0.7% with a 1/0.7² weight along with the four IR corrections with their 1/1.4² weights. Equivalently, to establish a new HST flux scale that is based on Vega at 5556 Å, the Megessier value should be multiplied by 0.9945. A revised, MSX weighted value of 3.46 × 10⁻⁹ × 0.9945 = 3.44 × 10⁻⁹ ± 0.5% is adopted. (Coincidentally, this new value is the same as recommended by Hayes 1985.) The most significant deviation among the five absolute flux measures is for the MSX A band, where the 0.976 offset from Table 3 is improved by the 0.9945 factor to 0.982, i.e., a deviation from unity by 1.8/1.4 = 1.3σ. The revised absolute normalization is within the uncertainty expectations of all five absolute flux measures from the visible to the mid-IR.

While the Sirius flux is difficult to model in detail in the far-UV, where the line-blanketing is severe, other modeling efforts reproduce the visible–IR shape. Figure 3 compares the best efforts of Linnell et al. (2013) and A. P. Linnell et al. (2013, private communication) and of Mészáros et al. (2012) and Sz. Mészáros et al. (2013, private communication) to the STIS fluxes by dividing by the same Kurucz continuum level as in Figure 2. The Linnell model shown in Figure 3 is slightly improved over the on-line SED. The small differences between the Kurucz and Mészáros models are probably due to different solar abundances and different updates to the synthesis code. Mészáros uses the Asplund et al. (2005) abundances and the F. Castelli version of the synthesis code, while Linnell uses the I. Hubeny line list and Synspec. The modeling of the Sirius IR SED is robust with all three independent models agreeing to better than ±1%, which increases confidence that the adopted Sirius IR flux is accurate to 1%.

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Figure 4 shows that the absolute UV flux of Sirius that is defined by IUE and STIS is confirmed by the independent lab based calibration of Snow et al. (2013) for the SOLSTICE fluxes⁶ (green) over their 1300–3000 Å range. These two measured absolute flux levels agree to ∼3%, as expected from the SOLSTICE/STIS comparison for three stars in R. C. Bohlin & K. D. Gordon (2014, in preparation). The structure of the spectral features in the STIS data (black) at R ∼ 500 often matches the Kurucz R = 500 resolution model (red) longward of 1675 Å. The R ∼ 250 IUE data (black) below 1675 Å and the R ∼ 100 SOLSTICE SEDs also nicely track the flux level of the model, but the spectral structure is smoother than the R = 500 model. In general, the observed spectral structure is remarkably well reproduced by the theoretical modeling, even with the heavy UV line-blanketing.

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Once Sirius is established as a primary flux standard, the flux of any other star is determined by just the brightness relative to Sirius. These signal ratios are free of errors in instrumental flux calibrations. For example, the ratio of Vega to Sirius is available for a few IR missions; and the total flux of Vega on the HST absolute flux scale is this ratio times the well-modeled flux of the primary IR standard, Sirius. Vega is a pole-on rapid rotator (Peterson et al. 2006) requiring a model with temperature zones in the 7900–10,150 K range (Aufdenberg et al. 2006). However longward of 4000 Å, a single temperature Kurucz model at 9400 K fits the STIS SED to 1%, as discussed by Bohlin (2007). After subtracting this CALSPEC Kurucz model for the Vega photospheric flux (T_eff = 9400 K, log g = 3.90, [M/H] = −0.5; Bohlin 2007), the remainder is the emission from the dust rings surrounding Vega, as shown in Figure 5. The photospheric Kurucz model that fits the STIS flux for Vega is the dotted line, which decreases steeply to less than the total dust emission beyond ∼40 μm.

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The measured ratios of Vega/Sirius include the four broadband MSX points of PPEM (×), i.e., the Vega flux from their Table 3 divided by the Sirius flux from their Table 2. The open circles in Figure 5 are from the IRAC ratios (Marengo et al. 2009) with their 1% error bars. The DIRBE data are from the electronic version of Table 1 in Smith et al. (2004), while Neugebauer et al. (1984) review the IRAS data.⁷ Three of the six DIRBE values (squares) in Figure 5 are low at 3.5, 12, and 60 μm, even after correcting Sirius by 0.014 mag for other stars in the 42 arcmin DIRBE beam (Su et al. 2013, hereafter Su). The 3.5 and 12 μm points are offscale in Figure 5, while the three DIRBE measures at 2.2, 4.9, and 25 μm nicely track the other experimental results. The error bars on the DIRBE points are the rms scatter divided by the square root of the number of observations (N); however, there is another quoted DIRBE uncertainty 〈err〉 due to background fluctuations. What is not clear is whether or not 〈err〉 should be reduced by $\sqrt{N}$ to get total DIRBE uncertainties. The illustrated error bars for DIRBE, IRAC, MSX, and IRAS all include a 1% uncertainty for the Sirius flux combined in quadrature with the instrumental rms scatter.

Using interferometric techniques in the K band at 2.1 μm, Absil et al. (2013) measure a 1.26% ± 0.27% dust contribution with respect to the Vega photosphere. Similarly, Defrère et al. (2011) find a 1.23% ± 0.45% contribution from small grains at the H band. These interferometric results are the filled black circles in Figure 5 and are independent of the Sirius SED.

Su models the dust with three rings at different temperatures: an inner hot ring of radius ∼15 at 2400 K, a warm 170 K ring at 2–3'', and a cold 50 K ring peaked at 11–14''. For the data analyzed here, a 270 K blackbody fits the warm component better than the 170 K of Su, while 62 K is used for the cold dust. Planck blackbody curves for the three temperatures are normalized to the observed fluxes in Figure 5. Following Su, the three blackbody curves are truncated longward of the peak with a steep λ^−x decline, where x = 2.8, 2.5, and 2.9, instead of the x = 2 for the Rayleigh–Jeans slope. The total emission from all three blackbody curves (black curve) falls within ∼1σ of the observational data, except for a ∼2σ deviation for the MSX 14.65 μm point and for the two offscale and the 60 μm DIRBE points.

The normalization of the three dust components is summarized in Table 4 and includes the ratio of the peak dust emission to photosphere in the final column. The sum of dust emission plus photosphere could be used as a standard star SED in the IR with a ∼1% photospheric uncertainty plus the tabulated uncertainty in the dust contribution. However, this total IR Vega flux is dependent on the observational aperture size, which compromises its practical utility as a standard star longward of 1 μm.

The Kurucz special photospheric models that do not include the dust contributions are in the CALSPEC database as alpha_lyr_mod_001.fits (T_eff = 9400 K, log g = 3.90, [M/H] = −0.5) and sirius_mod_001.fits (T_eff = 9850 K, log g = 4.30, [M/H] = +0.4).

EPK reported that the Hipparcos photometry H_p (van Leeuwen et al. 1997) shows that Vega is a variable star. Those data are reviewed here with the conclusion that this apparent variability is most likely caused by saturation of the pulse counting electronics in the image dissector photomultiplier tube. For the brightest stars, Figure 6 shows increasing differences between H_p⁸ and the V mag (Johnson et al. 1966) for A and F stars. For example, H_p for Sirius is ∼0.37 mag too faint, while for stars fainter than V = 1, the two magnitude measures are equal within ∼0.02. For Vega, the Hipparcos 0.087 mag is 0.06 fainter than the standard Johnson value of V = 0.03.

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Figure 7 shows that the exact effect of the pulse pileup is sensitive to environmental conditions, e.g., temperature, as the electronics attempt to discriminate between coincident pulses. Thus, the recorded count rate fluctuates the most for the brightest star, Sirius, where the rms scatter of the 160 separate measures is 0.051 mag. For Vega after removing a spurious 2.29 value, the rms of the remaining 102 values is 0.014 mag, i.e., considerably above the typical 0.004–0.005 mag rms of fainter stars, where the H_p photometry becomes linear.

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EPK state (p. 3) that while the discrepant magnitude for Vega "might be attributed to saturation effects, other, brighter stars do not show such discrepancies between V and H_p. Hence, we conclude that the faintness of Vega cannot be attributed to non-linearity in Hipparcos." This work demonstrates just the opposite: Brighter stars are discrepant and the faint H_p = 0.087 for Vega is caused by non-linearity. Furthermore, the apparent variability and gradual apparent brightening of the four brightest stars in Figure 7 is probably caused by slight variations in the exact level of pulse pileup in the detector. The Hipparcos photometry does not provide good evidence for the variability of Vega.