# Spectrophotometry

Improved flux-calibration: a new set of stellar templates is now used to fit absorption lines of standard stars in the flux calibration process. Flux calibration residuals were reduced by a factor of 2 in the blue spectrograph (3600 to 6000 Å).

Improved extraction algorithm: the background flux inside the spectrographs is now modeled prior to the extraction of the flux from individual fibers. This change improved the stability of extraction, mitigated fiber-to-fiber crosstalk from bright objects, and removed some features observed in quasar spectra. While these changes did not significantly reduce the spectroscopic classification success rates, they represent an improvement in the overall data quality.

Improved flux-calibration: atmospheric differential refraction is now corrected on a per-exposure basis following recipe described in Margala et al. 2016. Most quasar fibers were placed in the focal plane such that the light is optimized at 4000 Angstroms instead of 5400 Angstroms for standard stars. The calibration was therefore wrong for these quasars. Throughput corrections for these offset targets are computed based on the altitude, observing time, seeing, etc. In DR14, these corrections are applied to individual frames and stored in spXYthrucorr (FITS) files. The frames are co-added after this correction is applied. See Figure 1 in Jensen et al. 2016 that compares spectro versus photometric magnitudes.
Improved co-addition of individual exposures: the previous procedure to co-add individual exposures into final spectra was biased at the low signal-to-noise regime. In DR14, this was fixed with a more stable routine, yielding more reliable correction vectors (see Figure 4 of Hutchinson et al. 2016).

## Updates in DR9, unchanged for DR10 through DR12

In SDSS, the spectra were observed through 3 arcsecond fibers, while in BOSS, they are 2 arcsecond. A number of standard stars (chosen by color to be F stars) are observed on each plate: fitting the absorption lines to stellar models gives a model for their true spectral energy distribution, which is used to make a model for the conversion of counts to flux density as a function of wavelength and position on the plate. Because the standard stars are observed simultaneously, spectrophotometry is possible even in the presence of clouds and differential chromatic aberration.

The spectrophotometry is normalized to PSF magnitudes for point sources.

The spectrophotometric algorithms were improved throughout SDSS-I/II. The calibrations for spectroscopic data released in DR7 and SEGUE2 (i.e., with the original SDSS spectrographs) are unchanged for DR9. The rms difference between PSF g and r magnitudes, and the synthesized g and r magnitudes from the calibrated spectra, is of order 4% for stars in DR7.

With its smaller fibers, BOSS spectrophotometry is not as accurate, with an rms difference between the imaging photometry and integrated spectrophotometry of stars of about 6%. Note that the imaging data now include the quantity fiber2flux, the flux of each object in each filter, measured through a 2 arcsecond circular aperture.

There is also a systematic error in the calibration of quasar targets in BOSS spectroscopy. In order to maximize signal-to-noise ratio in the blue part of the spectra, the holes in plugplates corresponding to quasars are drawn to the expected position of the 4000 Å light (given atmospheric dispersion), and washers are added to the plate to move the focus appropriate for that wavelength. However, the standard stars (like the galaxies) are drilled for light at 5400 Å, and are therefore not on the same system. This means that the quasar spectra are biased blue, by an amount depending on airmass and position on the plate, but is of order 0.4 in spectral index.

Here we describe some of the details of previous improvements to the spectrophotometric calibration.

The following pipeline updates are specific to SEGUE observations with the original SDSS spectrograph, and are not applied to observations with the BOSS spectrograph released in DR9 through DR12.

### Correction of Instability in the Spectroscopic Flats

Spectroscopic flatfields for the blue camera in the first spectrograph contain an interference pattern produced by the dichroic. The thickness of the dichroic coating is believed to be sensitive to the ambient humidity, and moisture which enters the system during plate changes affects the instrument response, shifting the interference pattern in wavelength in unpredictable ways on timescales comparable to the 900 s exposure time.

The flats applied in processing were exposed several minutes prior to, or after, the science frames and therefore were not always representative of the true instrument response at the time of exposure. The interference pattern is most pronounced in the 3800-4100 Å region of the spectrum and, when shifted during exposure, causes significant distortion of the H and K Calcium lines in stellar spectra, systematically affecting estimates of metallicities and surface temperatures.

Flats obtained under different conditions were used to identify and model the stable and unstable (shifting) components of the flat, as shown in the Figure A (Figure 7 of the Data Release 7 paper*).

With this model in hand, we looked for shifts in the interference pattern over the typically 45 minute time a given plate was observed by comparing the results of the individual 15-minute exposures for each object. Thus, we took ratios of the extracted spectra from the separate exposures, and medianed them over all objects on a plate, giving results like those on the left-hand side of Figure B (Figure 8 of the Data Release 7 paper*)).

We fit this ratio to the results expected from a shifting interference pattern (essentially a derivative of the shifting component in Figure A), with the only free parameter being the amount of shift, and divided out this remaining component in each spectrum. The right-hand panel of Figure B shows that this technique removes the majority of the effects of the shifting interference.

An example is shown in Figure C (Figure 9 of the Data Release 7 paper*)), the spectrum of an A star observed on a place where the interference term was particularly bad, as is seen in DR6 and DR7. The shapes of the absorption lines, especially Hε at 3970 Å, is much more regular in the new reductions.

Figure A: The decomposition of the flat field of the first blue spectrograph (upper curve) into stable (lower curve, offset slightly for clarity) and unstable (interference) components. The unstable component is close to zero, but shows wiggles at wavelengths that shift from one exposure to another.
Figure B: Median flux ratios over all objects in the three exposures of plate 1916, before (left) and after (right) correction for the moving interference filters. The ratio is fit to the derivative of the interference component of the flat field (Figure A) after allowing for an arbitrary wavelength shift.
Figure C: The spectrum of SDSSJ172637.26+264127.6, an A0 star observed as part of SEGUE. The strong broad lines are due to Balmer absorption. The red spectrum is that available in DR6, while the black spectrum is from DR7.

The following pipeline updates are specific to SEGUE observations with the original SDSS spectrograph, and are not applied to observations with the BOSS spectrograph released in DR9 through DR12.

The pipeline that extracts, combines, and calibrates the SDSS spectra of individual objects from the two-dimensional spectrograms (idlspec2d) was originally designed to obtain meaningful redshifts for galaxies and quasars. However, there were several ways in which the code was inadequate, especially in light of the stellar focus of the SEGUE project, and the recognition of the rich stellar data available among the spectra of the main SDSS survey. The spectrophotometry was tied to the fiber magnitudes of stars, whose relation to the true, PSF magnitudes of stars is seeing-dependent. In addition, the SEGUE spectroscopy includes "bright plates" which contain substantial numbers of stars as bright as ifiber = 14.2, and scattered light from these stars caused systematic errors in the sky subtraction on these plates. Finally, there were errors in the wavelength calibration as large as 15 km/s on some plates, acceptable for most extragalactic science, but a real limitation for SEGUE spectroscopy. These concerns and others have caused us to substantially revise and improve the idlspec2d pipeline; the results of this improvement are included in DR6.

The new code has a different spectrophotometric calibration flux scale. The fiber magnitude reported by the photometric pipeline is the brightness of each object, as measured through a 3" diameter aperture corrected to 2" seeing to match the entrance aperture of the fibers (see the discussion in the EDR paper). However, the relationship between the fiber magnitudes of stars and the PSF magnitudes (which, for unresolved objects, is our best determination of a true, total magnitude) is dependent on seeing; this is made worse because the colors of stars measured via fiber magnitudes will be sensitive to the different seeing in the different filters (although cases in which the seeing is dramatically different in the different bands are fairly rare). With this in mind, the pipeline used in DR6 determines the spectrophotometric calibration on each plate such that the flux of the spectrum of standard stars integrated over the filter curve matches the PSF magnitude of the stars as measured from their imaging. This calibration is determined for each of the four cameras (two in each spectrograph) from observations of standard stars. Additional corrections to handle large-scale astrometric and chromatic terms are measured from isolated stars and galaxies of high S/N, and are then applied to all the objects on the plate.

## Unchanged since DR2/DR3

### Introduction

The color selection of the SDSS standard stars. Red points represent stars selected as spectroscopic standards. (Most are flux standards; the very blue stars in the right hand plot are "hot standards" used for telluric absorption correction.)

### Selection of spectroscopic standard stars

On each spectroscopic plate, 16 objects are targeted as spectroscopic standards. These objects are color-selected to be F8 subdwarfs, similar in spectral type to the SDSS primary standard BD+17 4708.

Throughput curves for the red and blue channels on the two SDSS spectrographs

The flux calibration of the spectra is handled by the idlspec2d pipeline. It is performed separately for each of the 2 spectrographs, hence each half-plate has its own calibration. In the EDR and DR1 idlspec2d calibration pipelines, fluxing was achieved by assuming that the mean spectrum of the stars on each half-plate was equivalent to a synthetic composite F8 subdwarf spectrum from Pickles (1998). In the reductions included in DR2/DR3, the spectrum of each standard star is spectrally typed by comparing with a grid of theoretical spectra generated from Kurucz model atmospheres (Kurucz 1992) using the spectral synthesis code SPECTRUM (Gray & Corbally 1994; Gray, Graham, & Hoyt 2001). The flux calibration vector is derived from the average ratio of each star (after correcting for Galactic reddening) and its best-fit model. Since the red and blue halves of the spectra are imaged onto separate CCDs, separate red and blue flux calibration vectors are produced. These will resemble the throughput curves under photometric conditions. Finally, the red and blue halves of each spectrum on each exposure are multiplied by the appropriate flux calibration vector. The spectra are then combined with bad pixel rejection and rebinned to a constant dispersion.

### Note about galactic extinction correction

In the EDR and DR1, the spectroscopic data were nominally corrected for galactic extinction. The spectrophotometry since DR2 is vastly improved compared to DR1, but the final calibrated spectra in DR2 and beyond are not corrected for foreground Galactic reddening (a relatively small effect; the median E(B-V) over the survey is 0.034). Users of spectra should note that the fractional improvement in spectrophotometry from DR1 to DR2 and beyond was much greater than the extinction correction itself. As the SDSS includes a substantial number of spectra of galactic stars, a decision has been taken not to apply any extinction correction to spectra, since it would only be appropriate for extragalactic objects, but to report the observational result of the SDSS, namely, the spectrum including galactic extinction.

## DR9 Flux to Photons

This section documents how to convert the pipeline outputs from flux (ergs/s/cm2/Å) back to photons (electrons) as extracted from the original CCD images. This is useful for modeling noise for mocks and alternate weighting schemes when coadding.

Note: the per-object spec files have this calibration precomputed as the "calib"column of the individual exposures. The following describes how to perform this calibration when using the per-plate files such as spCFrame.

The final calibrated spectra in spPlate (coadded spectra) and spCFrame (individual exposures) are in flux: 10-17 ergs/s/cm2/Å. The individual spectra are wavelength sampled to the native pixel grid of the CCD (unique to each exposure), while the coadded spectra are wavelength sampled at a constant &dELTA;log10 &LAMBDA; = 10-4. As a result of this different wavelength sampling, you can't directly add them, but they are in the same units -- i.e. you can overplot or interpolate them and they should agree between the individual spectra and the coadded spectrum.

The individual extracted spectra in spFrame are in units of flat-fielded electrons per CCD row. They have the same wavelength sampling as the spCFrame files, i.e. registered to the native pixel spacing of the CCDs.

To convert these spFrame spectra back to electrons (i.e. photons), you need to undo the flat-fielding with both the fiber-flat (spFlat HDU 0) and the superflat (spFrame HDU 8):

 eflux     = spFrame HDU 0 superflat = spFrame HDU 8 fiberflat = spFlat  HDU 0 electrons = eflux * superflat * fiberflat

So to form the correction vector to convert from flux back to electrons,

 flux = spCFrame HDU 0 calib = flux / electrons = flux / (eflux * superflat * fiberflat) = spCFrame[0] / (spFrame[0] * spFrame[8] * spFlat[0])

Notes:

• Each exposure has a unique calibration vector for each fiber.
• The b-channel spCFrame arrays have different dimensions than the equivalent arrays in spFrame. They are just padded with zeros; trim them back to the same size before dividing, etc.
• In principle, the sky flux (spFrame/spCFrame HDU 6) has a different calibration vector than the object flux, since the sky light isn't affected by guider errors, misaligned holes, etc. In practice, the quoted sky flux uses the same calibration vectors as the objects. Thus the spCFrame sky calibration is actually wrong, but if you use the same flux calibration vectors to get back to electrons, you'll have the correct object: sky ratio in electrons as extracted from the CCD.
• To convert a flux model or the coadded spectra back into electrons, you need to resample it to the same wavelength grid as one of the calibration vectors, and then apply that calibration vector.
• The in-progress "per-object" format will do this calculation for you. For each exposure, you will get the flux in ergs/s/cm2/Å and the calibration vector necessary to turn it back to electrons.

Example IDL Code: starting in riemann \$BOSS_SPECTRO_REDUX/v5_4_40/4444/

 ;; Define the input files flat_file   = 'spFlat-b1-00123584.fits.gz'coadd_file  = 'spPlate-4444-55538.fits'frame_file  = 'spFrame-b1-00123586.fits.gz'cframe_file = 'spCFrame-b1-00123586.fits';; Load the data flux      = mrdfits(cframe_file, 0) eflux     = mrdfits(frame_file, 0) superflat = mrdfits(frame_file, 8) fiberflat = mrdfits(flat_file, 0) ;; b spectra have different dimensions pre/post calib n = size(eflux, /dim) flux  = flux[0:n[0]-1, 0:n[1]-1] electrons = eflux * superflat * fiberflat calib = flux / electrons ;; Plot fiber 261 plot, electrons[*,261] plot, flux[*,261] plot, calib[*,261]

## Footnotes

*Text and figures on this page come from an author-created, un-copyedited version of the SDSS Data Release 7 paper, Abazajian et al. (2009). IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.