THE DATA REDUCTION PIPELINE FOR THE SDSS-IV MaNGA IFU GALAXY SURVEY

The MaNGA hardware design is described in detail by Drory et al. (2015); here we provide a brief summary of the major elements that most closely pertain to the DRP. MaNGA uses the BOSS optical fiber spectrographs (Smee et al. 2013) installed on the Sloan Digital Sky Survey 2.5 m telescope (Gunn et al. 2006) at Apache Point Observatory (APO) in New Mexico. These two spectrographs interface with a removable cartridge and plugplate system; each of the six MaNGA cartridges contains a full complement of 1423 fibers that can be plugged into holes in pre-drilled plug plates ∼0.7 m (3°) in diameter and which feed pseudo-slits that align with the spectrograph entrance slits when a given cartridge is mounted on the telescope.

These 1423 fibers are bundled into IFUs ferrules with varying sizes; each cartridge has 12 seven-fiber IFUs that are used for spectrophotometic calibration and 17 science IFUs of sizes varying from 19 to 127 fibers (see Table 2). As detailed by D. Wake et al. (in preparation), this assortment of sizes is chosen to best correspond to the angular diameter distribution of the MaNGA target galaxy sample. The orientation of each IFU on the sky is fixed by use of a locator pin and pinhole a short distance west of the IFU. Additionally, each IFU ferrule has a complement of associated sky fibers (see Table 2) amounting to a total of 92 individually pluggable sky fibers.

Each fiber is 150 μm in diameter, consisting of a 120 μm glass core surrounded by a doped cladding and protective buffer. The 120 μm core diameter subtends 1.98 arcsec on the sky at the typical plate scale of ∼217.7 mm degree⁻¹. These fibers are terminated into 44 V-groove blocks with 21–39 fibers each that are mounted on the two pseudo-slits. As illustrated in Figure 1, the sky fibers associated with each IFU are located at the ends of each block to minimize crosstalk from adjacent science fibers. In total, spectrograph 1 (2) is fed by 709 (714) individual fibers.

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Within each spectrograph a dichroic beamsplitter reflects light blueward of 6000 Å into a blue-sensitive camera with a 520 l/mm grism and transmits red light into a camera with a 400 l/mm grism (both grisms consist of a VPH transmission grating between two prisms). There are therefore four "frames" worth of data taken for each MaNGA exposure, one each from the cameras b1/b2 (blue cameras on spectrograph 1/2) and r1/r2 (red cameras on spectrograph 1/2). The blue cameras use blue-sensitive 4K × 4K e2V CCDs while the red cameras use 4K × 4K fully depleted LBNL CCDs, all with 15 micron pixels (Smee et al. 2013). The combined wavelength coverage of the blue and red cameras is ∼3600–10300 Å, with a 400 Å overlap in the dichroic region (see Table 3 for details). The typical spectral resolution ranges from 1560 to 2650, and is a function of the wavelength, telescope focus, and the location of an individual fiber on each detector (see, e.g., Figure 37 of Smee et al. 2013); we discuss this further in Sections 4.2.5 and 10.2.

While each of the IFUs is assigned a specific plugging location on a given plate, the sky fibers are plugged non-deterministically (although all are kept within 14 arcmin of the galaxy that they are associated with). Each cartridge is mapped after plugging by scanning a laser along the pseudo-slitheads and recording the corresponding illumination pattern on the plate. In addition to providing a complete mapping of fiber number to on-sky location, this also serves to identify any broken or misplugged fibers. This information is recorded in a central svn-based metadata repository called mangacore (see Section 3.3).

Each time a plate is observed, the cartridge on which it is installed is wheeled from a storage bay to the telescope and mounted at the Cassegrain focus. Observers acquire a given field using a set of 16 coherent imaging fibers that feed a guide camera; these provide the necessary information to adjust focus, tracking, plate scale, and field rotation using bright guide stars throughout a given set of observations. In addition to simple tracking, constant corrections are required to compensate for variations in temperature and altitude-dependent atmospheric refraction.

At the start of each set of observations, the spectrographs are first focused using a pair of hartmann exposures; the best focus is chosen to optimize the line spread function (LSF) across the entire detector region (see Sections 4.2.2 and 4.2.5). Twenty-five-second quartz calibration lamp flat-fields and four-second Neon–Mercury–Cadmium arc-lamp exposures are then obtained by closing the eight flat-field petals covering the end of the telescope. These provide information on the fiber-to-fiber relative throughput and wavelength calibration, respectively; since both are mildly flexure dependent they are repeated every hour of observing at the relevant hour angle and declination.

After the calibration exposures are complete, science exposures are obtained in sets of three 15 minute dithered exposures. As detailed by Law et al. (2015), this integration time is a compromise between the minimum time necessary to reach background limited performance in the blue while simultaneously minimizing astrometric drift due to DAR between the individual exposures. Since MaNGA is an imaging spectroscopic survey, image quality is important and the 56% fill factor of circular fiber apertures within the hexagonal MaNGA IFU footprint (Law et al. 2015) naturally suffers from substantial gaps in coverage. To that end, we obtain data in "sets" of three exposures dithered to the vertices of an equilateral triangle with 1.44 arcsec to a side. As detailed by Law et al. (2015), this provides optimal coverage of the target field and permits complete reconstruction of the focal plane image. Since atmospheric refraction (which is wavelength dependent, time-dependent through the varying altitude and parallactic angle, and field dependent through uncorrected quadrupole scale changes over our 3° field) degrades the uniformity of the effective dither pattern, each set of three exposures is obtained in a contiguous hour of observing.²⁵ These sets of three exposures are repeated until each plate reaches a summed signal-to-noise ratio (S/N) squared of 20 pixel⁻¹ fiber⁻¹ in g-band at g = 22 AB and 36 pixel⁻¹ fiber⁻¹ in i-band at i = 21 AB (typically 2–3 hr of total integration; see R. Yan et al. 2016b).

All MaNGA galaxy survey observations are obtained in dark or gray-time for which the moon illumination is less than 35% or below the horizon (see R. Yan et al. 2016b for details). Since MaNGA shares cartridges with the infrared SDSS-IV/APOGEE spectrograph, however (Wilson et al. 2010), both instruments are able to collect data simultaneously. MaNGA and APOGEE therefore typically co-observe, meaning that data are also obtained with the MaNGA instrument during bright-time with up to 100% moon illumination. These bright-time data are not dithered, have substantially higher sky backgrounds, and are generally used for ancillary science observations of bright stars with the aim of amassing a library of stellar reference spectra over the lifetime of SDSS-IV. These bright-time data are processed with the same MaNGA software pipeline as the dark-time galaxy data, albeit with some modifications and unique challenges that we will address in a future contribution.

The MaNGA DRP is tasked with producing fully flux-calibrated data for each galaxy that has been spatially rectified and combined across all individual dithered exposures in a multi-extension FITS format that may be used for scientific analysis. This mangadrp software is written primarily in IDL, with some C bindings for speed optimization and a variety of python-based automation scripts. Dependencies include the SDSS idlutils and NASA Goddard IDL astronomy users libraries; namespace collisions with these and other common libraries have been minimized by ensuring that non-legacy DRP routines are prefixed by either "ml_" or "mdrp_." The DRP runs automatically on all data using the collaboration supercluster at the University of Utah,²⁶ is publicly accessible in a subversion svn repository at https://svn.sdss.org/public/repo/manga/mangadrp/tags/v1_5_4 with a BSD three-clause license, and has been designed to run on individual users' home systems with relatively little overhead.²⁷ Version control of the mangadrp code and dependencies is done via svn repositories and traditional trunk/branch/tag methods; the version of mangadrp described in the present contribution corresponds to tag v1_5_4 for public release DR13. We note that v1_5_4 is nearly identical to v1_5_1 (which has been used for SDSS-IV internal release MPL-4) save for minor improvements in cosmic-ray rejection routines and data-quality-assessment statistics.

The DRP consists of two primary parts: the 2D stage that produces flux-calibrated fiber spectra from individual exposures, and the 3D stage that combines individual exposures with astrometric information to produce stacked data cubes. The overall organization of the DRP is illustrated in Figure 2. Each day when new data are automatically transferred from APO to the SDSS-IV central computing facility at the University of Utah a cronjob triggers automated scripts that run the 2D DRP on all new exposures from the previous modified Julian date (MJD). These are processed on a per-plate basis, and consist of a mix of science and calibration exposures (flat-fields and arcs).

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The 2D stage of the MaNGA DRP is largely derived from the BOSS idlspec2d pipeline (see, e.g., Dawson et al. 2013, Schlegel et al., in preparation)²⁸ that has been modified to address the different hardware design and science requirements of the MaNGA survey (we summarize the numerous differences in Appendix A). Each frame undergoes basic pre-processing to remove overscan regions and variable-quadrant bias before the one-dimensional (1D) fiber spectra are extracted from the CCD detector image. The DRP first processes all of the calibration exposures to determine the spatial trace of the fiber spectra on the detector and extract fiber flat-field and wavelength calibration vectors, and applies these to the corresponding science frames. The science exposures are in turn extracted, flatfielded, and wavelength calibrated using the corresponding calibration files. Using the sky fibers present in each exposure we create a super-sampled model of the background sky spectrum, and subtract this off from the spectra of the individual science fibers. Finally, the 12 mini-bundles targeting standard stars in each exposure are used to determine the flux calibration vector for the exposure compared to stellar templates. The final product of the 2D stage is a single FITS file per exposure (mgCFrame) containing row-stacked spectra (RSS; i.e., a 2D array in which each row corresponds to an individual 1D spectrum) of each of the 1423 fibers interpolated to a common wavelength grid and combined across the four individual detectors.

Once a sufficient number of exposures has been obtained on a given plate, it is marked as complete at APO and a second automated script triggers the 3D  stage DRP to combine each of the mgCFrame files resulting from the 2D DRP. For each IFU (including calibration mini-bundles) on the plate, the 3D pipeline identifies the relevant spectra in the mgCFrame files and assembles them into a master row-stacked format consisting of all spectra for that target. The astrometric solution as a function of wavelength for each of these spectra is computed on a per-exposure basis using the known fiber bundle metrology and dither offset for each exposure, along with a variety of other factors including field and chromatic differential refraction (see Law et al. 2015). This astrometric solution is further refined using SDSS broadband imaging of each galaxy to adjust the position and rotation of the IFU fiber coordinates. Using this astrometric information the DRP combines the fiber spectra from individual exposures into a rectified data cube and associated inverse variance and mask cubes. In post-processing, the DRP additionally computes mock broadband griz images derived from the IFU data, estimates of the reconstructed point-spread function (PSF) at griz, and a variety of quality-control metrics and reference information.

The final DRP data products in turn feed into the MaNGA Data Analysis Pipeline (DAP), which performs spectral modeling, kinematic fitting, and other analyses to produce science data products such as Hα velocity maps, kinemetry, spectral emission line ratio maps, etc., from the data cubes. DAP data products will be made public in a future release and described in a forthcoming contribution by K. Westfall et al. (in preparation).

Rather than running the full DRP in real-time at the observatory, we instead use a pared-down version of the code that has been optimized for speed that we refer to as DOS.²⁹ The DOS pipeline shares much of its code with the DRP, performing reduction of the calibration and science exposures up through sky subtraction. The primary difference is in the spectral extraction; while the DRP performs an optimized profile fitting technique to extract the spectra of each fiber (see Section 4.2.2), DOS instead uses a simple boxcar extraction that sacrifices some accuracy and robustness for substantial gains in speed.

The primary purpose of DOS is to provide real-time feedback to APO observers on the quality and depth of each exposure. Each exposure is characterized by an effective depth given by the mean S/N squared at a fixed fiber2mag³⁰ of 22 (g-band) and 21 (i-band). The S/N of each fiber is calculated empirically by DOS from the sky-subtracted continuum fluxes and inverse variances, while nominal fiber2mags for each fiber in a galaxy IFU are calculated by applying aperture photometry to SDSS broadband imaging data at the known locations of each of the IFU fibers (see Section 8.1) and correcting for Galactic foreground extinction following Schlegel et al. (1998). As illustrated in Figure 3, the S/N as a function of fiber2mag for all fibers in a given exposure forms a logarithmic relation that can be fitted and extrapolated to the effective achieved S/N at fixed nominal magnitudes g = 22 and i = 21. This calculation is done independently for all four cameras using a g-band effective wavelength range λλ4000–5000 Å and an i-band effective wavelength range λλ6910–8500 Å. As described above in Section 2.2, we integrate on each plate until the cumulative S/N² in all complete sets of exposures reaches 20 pixel⁻¹ fiber⁻¹ in g-band and 36 pixel⁻¹ fiber⁻¹ in i-band at the nominal magnitudes defined above.

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MaNGA is a complex survey that requires tracking of multiple levels of metadata (e.g., fiber bundle metrology, cartridge layout, fiber plugging locations, etc.), any of which may change on the timescale of a few days (in the case of fiber plugging locations) to a few years (if cartridges and/or fiber bundles are rebuilt). At any point, it must be possible to rerun any given version of the pipeline with the corresponding metadata appropriate for the date of observations. This metadata must also be used throughout the different phases of the survey from planning and target selection, to plate drilling, to APO operations, to eventual reduction and post-processing.

To this end, MaNGA maintains a central metadata repository mangacore, which is automatically synchronized between APO and the Utah data reduction hub using daily crontabs. Version control of files within mangacore is maintained by a combination of MJD datestamps and periodic svn tags corresponding to major data releases (v1_2_3 for DR13).

Given the volume of data that must be processed by the MaNGA pipeline (∼10 million reduced galaxy spectra and ∼100 million raw-frame spectra over the six-year lifetime of SDSS-IV³¹ ), automated quality control is essential. To that end, multiple monitoring routines are in place. The 2D and 3D stage DRP has bitmasks (MANGA_DRP2PIXMASK and MANGA_DRP3PIXMASK, respectively) associated with the primary flux extensions that can be used to indicate individual pixels (or spaxels³² in the case of the 3D data cubes) that are identified as problematic. In the 2D case (spectra of all 1423 individual fibers within a single exposure), this pixel mask indicates such things as cosmic-ray events, bad flat-fields, missing fibers, extraction problems, etc. In the 3D stage (a composite cube for a single galaxy that combines many individual exposures into a regularized grid), this pixel mask indicates things like low/no fiber coverage, foreground star contamination, and other issues that mean a given spaxel should not be used for science.

Additionally, there are overall quality bits MANGA_DRP2QUAL and MANGA_DRP3QUAL that pertain to an entire exposure or data cube, respectively, and indicate potential issues during processing. In the 2D case, this can include effects like heavy cloud cover, missing IFUs, or abnormally high scattered light. In the 3D case, this can include warnings for bad astrometry, bad flux calibration, or (rarely) a critical problem suggesting that a galaxy should not be used for science. As of DR13, 22 of the 1390 galaxy data cubes are flagged as critically problematic for a variety of reasons ranging from the severe and unrecoverable (e.g., poor focus due to hardware failure, ∼5 objects) to the potentially recoverable in a future data release (e.g., failed astrometric registration due to a bright star at the edge of the IFU bundle) to the mundane (errant unflagged cosmic-ray confusing the flux calibration QA routine).

All of these pixel-level and exposure-level data quality flags are used by the pipeline in deciding how and whether to continue to process data (e.g., flux calibration will not be attempted on an exposure flagged as completely cloudy). We provide a reference table of the key MaNGA quality-control bitmasks in Appendix B.4.

Raw data from each of the four CCDs (b1, r1, b2, r2) are in the format of 16 bit images with 4352 columns and 4224 rows (Table 3), with a 4096 × 4112 pixel active area (for the blue CCDs; 4114 × 4128 pixel active area for the red CCDs) and overscan regions along each edge of the detector. As described by Dawson et al. (2013), the CCDs are read out with four amplifiers, one for each quadrant, resulting in variable bias levels. Each exposure is preprocessed to remove the overscan regions of the detector, subtract off quadrant-dependent biases, convert from bias corrected ADUs to electrons using quadrant-dependent gain factors derived from the overscan regions,³⁴ and divide by a flat-field containing the relative pixel-to-pixel response measured from a uniformly illuminated calibration image (see Figure 4).

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A corresponding inverse variance image is created using the measured read noise and photon counts in each pixel; this inverse variance array is capped so that no pixel has a reported S/N greater than 100.³⁵ Finally, potential cosmic rays (which affect ∼ 10 times as many pixels in the red cameras as in the blue) are identified and flagged using the same algorithm adopted previously by the SDSS imaging and spectroscopic surveys. As discussed by R. H. Lupton (see http://www.astro.princeton.edu/~rhl/photo-lite.pdf), this algorithm is a first-pass approach that successfully detects most cosmic rays by looking for features sharper than the known detector PSF, but sometimes incompletely flags pixels around the edge of cosmic-ray tracks. A second-pass approach that addresses these residual features is applied later in the pipeline, as described in Section 7. The inverse variance image is combined with this cosmic-ray mask and a reference bad pixel mask so that affected pixels are assigned an inverse variance of zero (and hence have zero weight in the reductions).

All flat-field and arc calibration frames from a planfile are reduced prior to processing any science frames. These provide estimates of the fiber-to-fiber flat-field and the wavelength solution, and are also critical for determining the locations of individual fiber spectra on the detectors. Since there are four cameras, each reduced flat-field (arc) exposure corresponds to four mgFlat (mgArc) multi-extension FITS files as described in the data model in Appendix B.

4.2.1. Spatial Fiber Tracing

4.2.2. Spectral Extraction

Similarly to the BOSS survey (Dawson et al. 2013), we extract individual fiber spectra from the 2D detector images using a row-by-row optimal extraction algorithm that uses a least-squares profile fit to obtain an unbiased estimate of the total counts (Horne 1986). The counts in each row are modeled by a linear combination of N_fiber Gaussian³⁷ profiles plus a low-order polynomial (or cubic basis-spline; see Section 4.2.3) background term. As we illustrate in Figure 5 (right panel), the resulting model is an extremely good fit to the observed profile. MaNGA uses the extract_row.c code (dating back to the original SDSS spectroscopic survey), which creates a pixelwise model of the Gaussian profile integrated over fractional pixel positions (i.e., the profile is assumed to be Gaussian prior to pixel convolution), describes deviations to the line centers and widths as linear basis modes (representing the first and second spatial derivatives, respectively), and solves for the banded matrix inversion by Cholesky decomposition. An initial fit to the flat-field calibration images allows both the amplitude and the width of the Gaussian profiles in each row to vary freely, with the centroid set to the positions determined via fiber tracing in Section 4.2.1. These individual width measurements are noisy, however, and for each block of fibers we therefore fit the derived widths with a linear relation as a function of fiberid along the slit in order to reject errant values and determine a fixed set of fiber widths that vary smoothly (within a given block) with both fiberid and wavelength. As illustrated in Figure 6, low-frequency variation of the widths with fiberid reflects the telescope focus (which we choose to ensure that the widths are as constant as possible across the entire slit), while discontinuities at the block boundaries are due to slight differences in the slithead mounting. These fixed widths are then used in a second fit to the detector images in which only the polynomial background and the amplitude of the Gaussian terms are allowed to vary.

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The final value adopted for the total flux in each row is the integral of the theoretical Gaussian profile fits to the observed pixel values, while the inverse variance is taken to be the diagonal of the covariance matrix from the Cholesky decomposition. This approach allows us to be robust against cosmic rays or other detector artifacts that cover some fraction of the spectrum, since unmasked pixels in the cross-dispersion profile can still be used to model the Gaussian profile (Figure 5). Additionally, this technique naturally allows us to model and subtract crosstalk arising from the wings of a given profile overlapping any adjacent fibers, and to estimate the variance on the extracted spectra at each wavelength. This step transforms our 4096 × 4112 CCD images (4114 × 4128 for the red cameras) to RSS with dimensionality 4112 × N_fiber (4128 × N_fiber for the red cameras).

4.2.3. Scattered Light

4.2.4. Fiber Flat-field

Each flat-field calibration frame is extracted into individual fiber spectra using the above techniques and matched to the nearest (in time) arc-lamp calibration frame, which has been processed as described in Section 4.2.5. Using the wavelength solutions derived from the arc frames, we combine the individual flat-field spectra (first normalized to a median of unity) into a single composite spectrum with substantially greater spectral sampling than any individual fiber.³⁸ We fit this composite spectrum with a cubic basis-spline function to obtain the superflat vector describing the global flat-field response (i.e., the quartz lamp spectrum convolved with the detector response and system throughput). This global superflat is shown in Figure 7, and illustrates the falloff in system throughput toward the wavelength extremes of the detector (see also Figure 4 of Yan et al. 2016a).

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We evaluate the superflat spline function on the native wavelength grid of each individual fiber and divide it out from the individual fiber spectra in order to obtain the relative fiber-to-fiber flat-field spectra. So normalized, these fiber-to-fiber flat-field spectra have values near unity, vary only slowly (if at all) with wavelength, and easily show any overall throughput differences between the individual fibers. Each such spectrum is in turn fitted with a bspline in order to minimize the contribution of photon noise to the resulting fiber flats and interpolate across bad pixels. In the end, we are left with two flat-fields to store in the mgFlat files (see Table 5); a single superflat spectrum describing the global average response as a function of wavelength, and a fiberflat of size 4112 × N_fiber (4128 × N_fiber for the red cameras) describing the relative throughput of each individual fiber as a function of wavelength.

The individual MaNGA fibers typically have high throughput (see discussion by Drory et al. 2015) within 5%–10% of each other. The relative distribution of throughputs is monitored daily to trigger cleaning of the IFU surfaces when the DRP detects noticeable degradation in uniformity or overall throughput. Individual fibers with throughput less than 50% that of the best fiber on a slit are flagged by the pipeline and ignored in the data analysis. This may occur when a fiber and/or IFU falls out of the plate (a rare occurrence), or when a fiber breaks. Such breakages in the IFU bundles occur at the rate of about 1 fiber per month across the entire MaNGA complement of 8539 fibers.

4.2.5. Wavelength and Spectral Resolution Calibration

The Neon–Mercury–Cadmium arc-lamp spectra are extracted in the same manner as the flat-fields, except that they use the fiber traces determined from the corresponding flat-field (with allowance for a continuous 2D polynomial shift in the traces as a function of detector position to account for flexure differences) and allow only the Gaussian profile amplitudes to vary. These spectra are normalized by the fiber flat-field³⁹ and an initial wavelength solution is computed as follows.

A representative spectrum is constructed from the median of the five closest spectra closest to the central fiber on the CCD. This spectrum is cross-correlated with a model spectrum generated using a reference table of known strong emission features in the Neon–Mercury–Cadmium arc lamps,⁴⁰ and iterated to determine the best-fit coefficients to map pixel locations to wavelengths. These best-fit coefficients are used to contruct initial guesses for the wavelength solution of each fiber, which are then iterated on a fiber-to-fiber basis to obtain the final wavelength solutions. Several rejection algorithms are run to ensure reliable arc-line centroids across all fibers. A final sixth-order Legendre polynomial fit converts the wavelength solutions into a series of polynomial traceset coefficients. The higher order coefficients are forced to vary smoothly as a function of fiberid since they predominantly arise from optical distortions along the slit (whereas lower order terms represent differences arising from the fiber alignment). These coefficients are stored as an extension in the output mgArc file (see Table 4), and are used to reconstruct the wavelength solutions at all fibers and positions on the CCD.

The arc-lamp spectral resolution (hereafter the line spread function, or LSF) is computed by fitting the extracted spectra around the strong arc-lamp emission lines in each fiber with a Gaussian profile integrated over each pixel (note that we integrate the fitted profile shape across each pixel rather than simply evaluating the profile at the pixel midpoints; see the discussion in Section 10.2) and allowing both the width and amplitude of the profile to vary. As illustrated in Figure 8, these widths are intrinsically noisy and the DRP therefore fits them with a linear relation as a function of fiberid along the slit in order to reject errant values and determine a fixed set of line widths that vary smoothly (within a given block) with fiberid. These arc-line widths are then fit with a Legendre polynomial traceset that is stored in the mgArc files and evaluated at each pixel to compute the LSF at wavelengths between the bright arc lines.

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Both wavelength and LSF solutions derived from the arc frames are later adjusted for each individual science frame to account for instrumental flexure during and between (see discussion in Section 4.3).

All calibrations are additionally complicated in the red cameras since the middle row of pixels on these detectors is oversized by a factor of 1/3, causing a discontinuity in both the wavelength solution and the LSF for each fiber as a function of pixel number. All of the algorithms described above therefore allow for such a discontinuity across the CCD quadrant boundary. The primary impact of this discontinuity on the final data products is to produce a spike of low spectral resolution around 8100 Å, the exact wavelength of which can vary from fiber to fiber based on the curvature of the wavelength solution along the detector.

Each science frame is associated with the arc and flat pair taken closest to it in time (generally within one hour since calibration frames are taken at the start of each plate and periodically thereafter), and extracted row-by-row following the method outlined in Section 4.2.2. During this extraction only the profile amplitudes and background polynomial term are allowed to vary freely; the trace centroids are tied to the flat-field traces with a global 2D polynomial shift to account for instrument flexure, and the cross-dispersion widths are fixed to the values derived from the flat-field. The extracted spectra are normalized by the superflat and fiberflat vectors derived from the flat-field.

The wavelength solutions derived from the arcs are adjusted for each science frame to match the known wavelengths of bright night-sky emission lines in the science spectra by fitting a low-order polynomial shift as a function of detector position to allow for instrumental flexure (these shifts are typically less than a quarter pixel). The final wavelength solution for each exposure is corrected to the vacuum heliocentric restframe using header keywords recording atmospheric conditions and the time and date of a given pointing. As we explore in Section 10.3, we achieve a ∼10 km s⁻¹ or better rms wavelength calibration accuracy with zero systematic offset to within 2 km s⁻¹.

Similarly, in order to account for flexure and varying spectrograph focus with time the spectral LSF measurements derived from the arc-lamp exposures are also adjusted for each science frame to match the LSF of bright skylines that are known to be unblended in high-resolution spectra (e.g., Osterbrock et al. 1996). Starting from the original arc-line LSF model, we derive a quadrature correction term for the profile widths ${Q}^{2}={{\sigma }_{{\rm{sky}}}}^{2}-{{\sigma }_{{\rm{arc}}}}^{2}$. Q is taken to be constant as a function of wavelength for each camera, and is based on the strong auroral O i 5577 line in the blue (since the Hg i lines are too weak and broadened to obtain a reliable fit) and an average of many isolated bright lines in the red.⁴¹ The measured quadrature correction term is fitted with a cubic basis-spline to ensure that the correction applied varies smoothly with fiberid. Across the ∼1100 individual exposures in DR13 the average correction Q² = 0.08 ± 0.04 pixel² in the blue cameras and ${Q}^{2}=0.05\pm 0.02$ pixel² in the red cameras (likely due to the flatter and more stable focus in the red cameras).

The final RSS, inverse variances, pixel masks, wavelength solutions, and broadened LSF are all stored as extensions in the output mgFrame FITS file (Table 6).

Sky subtraction is performed independently for each of the four cameras using the flat-fielded, wavelength-calibrated fiber spectra contained in the mgFrame files, and is a multi-step iterative process. Broadly speaking, we build a super-sampled sky model from all of the sky fibers, scale it to the sky background level of a given block, and evaluate it on the native solution of each fiber within that block. In detail:

• 1.  
  The metadata associated with the exposure are used to identify the N_sky individual sky fibers in each frame based on their FIBERTYPE.
• 2.  
  Pixel values for these N_sky sky fibers are resorted as a function of wavelength into a single one-dimensional array of length N_sky × N_spec (where N_spec is the length of a single spectrum). Since each fiber has a unique wavelength solution, this super-sky vector has much higher effective sampling of the night-sky background spectrum than any individual fiber and provides an accurate LSF for OH airglow features. An example of this procedure is shown in Figure 10.
• 3.  
  Similarly, we also construct a super-sampled weight vector by comining individual sky fiber inverse variance spectra that have first been smoothed by a boxcar of width 100 pixels (∼100–200 Å) in the continuum and 2 pixels (∼2–3 Å) within 3 Å of bright atmospheric emission features.
• 4.  
  The super-sky spectrum is then weighted by the smoothed inverse variance spectrum (convolved with the bad-pixel mask) and fitted with a cubic basis-spline as a function of wavelength, with the number of breakpoints set to $\sim {N}_{{\rm{spec}}}$ so that high-frequency variations (due, e.g., to shot noise or bad pixels) are not picked up by the resulting model (see, e.g., green line in Figure 10).⁴² The breakpoint spacing is set automatically to maintain approximately constant S/N between breakpoints. The B-spline fit itself is iterative, with upper and lower rejection threshholds set to mask bad or deviant pixels. We note that the smoothing of the inverse variance in determining the weight function is critical as otherwise the weights (which are themselves estimated from the data) would modulate with the Poisson scatter and bias the fit toward slightly lower values, resulting in systematic undersubtraction of the sky background, especially near the wavelength extrema where the overall system throughput is low.
• 5.  
  This B-spline function is evaluated on the native wavelength solution of each of the sky fibers. Dividing the original sky fiber spectra by this functional model, and collapsing over wavelengths using a simple mean, we arrive at a series of scale factors describing the relative sky background seen by the fiber compared to all other fibers on the detector. For each harness (i.e., each IFU plus associated sky fibers) we compute the median of these scale factors to obtain a single averaged scale factor for each harness. These scale factors help account for nearly gray variations in the true sky continuum across our large field produced by a combination of intrinsic background variations and patchy cloud cover. The variability in sky background between harnesses is about 1.5% rms, with some larger deviations >5% observed during the bright-time stellar library program when pointing near a full moon can produce strong background gradients.
• 6.  
  Repeat steps 2–4 after first scaling each individual sky fiber spectrum by the value appropriate for its harness in order to obtain a super-sky spectrum in which per-harness scaling effects have been removed.
• 7.  
  Evaluate the new B-spline function on the native pixelized wavelength solution of each fiber (sky plus science), and multiply it by the scaling factor for the harness to obtain the first-pass model sky spectrum for each fiber. Subtract this from the spectra to obtain the first-pass sky-subtracted spectra.
• 8.  
  Identify deviant sky fibers in which the median sky-subtracted residual S/N² > 2 (this is extremely rare, and generally corresponds to a case where a sky fiber location was chosen poorly, or a fiber was misplugged and not corrected before observing). Eliminate these sky fibers from consideration, and repeat steps 2–7 to obtain the second-pass model sky spectrum for each fiber. We refer to this as the 1D sky model.
• 9.  
  Repeat steps 2–4, this time allowing the bspline fit to accommodate a smoothly varying third-order polynomial of values at each breakpoint as a function of fiberid (i.e., rather than requiring the model to be constant for all fibers, it is allowed to vary slowly as a function of slit position). This polynomial term is introduced in order to model variations in the LSF along each slit; empirically, increasing polynomial orders up to three results in an improvement of the skyline residuals, while no further gains are observed at greater than third order. Evaluate the new B-spline function on the native pixelized wavelength solution of each fiber (sky plus science) to obtain the 2D sky model. Notably, this 2D model does not use the explicit scaling used by the 1D model. This is partially because a similar degree of freedom is introduced by the 2D polynomial, and partially because OH features can vary in strength independently from the underlying continuum background (see, e.g., Davies 2007).
• 10.  
  The final sky model is a piecewise hybrid of the 1D and 2D models; in continuum regions it is taken to be the 1D model, and in the skyline regions (i.e., within 3 Å of any wavelength for which the sky background is >5σ above a bspline fit to the interline continuum) it is taken to be the 2D model. We opt for this hybrid model as it optimizes our various performance metrics: In the continuum far from night-sky lines, our performance is limited by the poisson-based rms of the model sky spectrum subtracted from each science fiber. Therefore, we use the 1D model that is based on all 46 sky fibers on a given spectrograph. In contrast, for near bright skylines our performance is instead limited by our ability to accurately model the shape of the skyline wings, which can vary along the slit (see, e.g., Figure 8). Therefore, in skyline regions we use the 2D model, which improves the model LSF fidelity at the expense of some S/N. There is no measurable discontinuity between the sky-subtracted spectra at the piecewise 1D/2D model boundaries.

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The final sky model is subtracted from the mgFrame spectra; these sky-subtracted spectra are stored in mgSFrame files (Table 7), which contain the spectra, inverse variances (with appropriate error propagation), pixel masks, applied sky models, etc. in a row-stacked format identical to the input mgFrame files.

We estimate the accuracy of our calibration and sky subtraction up to this point by using specially designed "all-sky" plates in which every science IFU is placed on a region of sky determined to be empty of visible sources according to the SDSS imaging data (calibration mini-bundles are still placed on standard stars so that these all-sky plates can be properly flux calibrated). The resulting sky-subtracted sky spectra can then be used to estimate the accuracy of our noise model, extraction algorithms, and sky-subtraction technique.

Working with the row-stacked mgSFrame spectra (i.e., prior to flux calibration and wavelength rectification) we construct "Poisson ratio" images for each camera by multiplying the sky-subtracted residual counts by the square root of the inverse variance (which accounts for both shot noise and detector read noise). If the sky subtraction is perfect, and the noise model properly estimated, these poisson ratio images should be devoid of structure with a Gaussian distribution of values with mean of 0 and σ = 1.0. In Figure 11 (right-hand panels) we show the actual distribution of values for the sky-subtracted science fibers for exposure 183643 (cart 4, plate 8069, MJD 56901) for each of the four cameras (solid black lines) compared to the ideal theoretical expectations (solid red line; note that this is not a fit to the data). We find that the overall distribution of values is broadly consistent with theoretical models in all four cameras (c.f. Figure 23 of Newman et al. 2013, which shows similar plots for the DEEP2 survey), albeit with some evidence for slight oversubtraction on average and a non-Gaussian wing in the blue cameras (pixels in this asymmetric wing do not correspond to particular wavelengths or fiberid).

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We examine this behavior as a function of wavelength in Figure 11 (left-hand panel) by plotting the 1σ width of the Gaussian that best fits the distribution of unflagged pixel values at a given wavelength across all science fibers.⁴³ As before, perfectly noise-limited sky subtraction with a perfect noise model would correspond to a flat distribution of σ around 1.0 at all wavelengths; we note that the blue cameras and the continuum regions of the r2 camera are close to this level of performance with up to a 3% offset from nominal (suggesting that the read noise in some quadrants may be marginally underestimated). In the r1 camera the read noise may be overestimated by ∼10% in some quadrants (as σ < 1 for r1 in the wavelength range λλ5700–7600 Å), but is otherwise well-behaved in the continuum region. In the skyline regions of the red cameras, performance is within 10% of Poisson expectations out to ∼8500 Å. Longward of ∼8500 Å (where skylines are brighter, and the spectra have greater curvature on the detectors) sky subtraction performance in skyline regions is ∼10%–20% above theoretical expectations. This is likely due to systematic residuals in the subtraction caused by block-to-block variations in the spectral LSF that are difficult to model completely. Indeed, such an analysis during commissioning revealed the OH skyline residuals were significantly worse in R1 than in the R2 camera. This led to the discovery of an optical coma in R1 that was fixed during Summer 2014 prior to the formal start of SDSS-IV, but which nonetheless affected the commissioning plates 7443 and 7495.

Overall, the results in Figure 11 indicate excellent performance from the MaNGA DR13 data pipeline sky subtraction, albeit with some room for further improvement in future data releases. Finally, we assess whether any systematics exist within the data that would prohibit stacking of multiple fiber spectra in order to reach faint surface brightness levels (e.g., in the outer regions of the target galaxies). Using the flux-calibrated, camera-combined mgCFrame data (again corresponding to exposure 183643 from MJD 56901) we compute the limiting 1σ surface brightness reached in the largely skyline-free wavelength range 4000–5500 Å as a function of the number of individual fiber spectra stacked. As shown in Figure 12, when N fibers are stacked randomly from across both spectrographs (solid black line) the limiting surface brightness decreases as $\sqrt{{N}^{-1}+{92}^{-1}}$ (i.e., improving as $\sqrt{N}$ for small N, and becoming limited by the statistics of the 92 fiber sky model as N becomes large). If fibers are stacked sequentially along the slit (dashed black line) the limiting surface brightness decreases as $\sqrt{{N}^{-1}+{46}^{-1}}$ at first (since only the 46 sky fibers on a single slit are being used in the sky model) but approaches nominal performance again once fibers from both spectrographs are included in the stack (N > 621).

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Another way to check the sky subtraction quality of the DRP is to compare its performance for a typical galaxy plate against the results obtained using the skycorr tool (Noll et al. 2014). Skycorr was designed as a data reduction tool to remove sky emission lines for astronomical spectra using physically motivated scaling relations, and has been found to consistently perform better than the popular algorithm of Davies (2007). As input, skycorr needs the science spectrum and a sky spectrum, preferably taken around the time as the science spectrum. After subtracting the continuum from both spectra, it then scales the sky emission lines from the sky spectrum to fit these lines in the science spectrum by comparing groups of sky lines that should vary in similar ways.

In Figure 13 we compare a typical sky-subtracted MaNGA science spectrum obtained using the DRP algorithms described in Section 5 with the spectrum obtained using skycorr instead. The two sky-subtracted spectra are nearly indistinguishable, indicating comparable performance between the two techniques.

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The effective location of a particular IFU fiber in any given exposure is dictated by numerous optomechanical factors. Many of these are possible to either measure or estimate for an arbitrary source, and the MaNGA basic astrometry module combines these factors into a single wavelength-dependent position vector (in R.A./decl.) for each fiber. These factors include the following.

• 1.  
  Relative and absolute fiber location within a given IFU ferrule based on the as-built fiber bundle metrology. This is measured during the manufacturing process to a typical accuracy ∼0.3 μm (relative)⁴⁵ and ∼5 μm (absolute; see Drory et al. 2015) and recorded in mangacore for each harness serial number.
• 2.  
  Offset of an IFU from its base position due to the three-point dithering pattern. We assume that the dithering exactly matches the commanded offsets; the accuracy of this assumption is limited by the ∼0.1 arcsec dithering accuracy of the telescope (see Law et al. 2015).
• 3.  
  Offset of drilled holes from the intended drilling location. Although holes can be drilled to within an accuracy of ∼9 μm rms, they are measured after the fact to an accuracy ∼5 μm. This information is recorded for each plate in mangacore.
• 4.  
  Chromatic DAR relative to the guide wavelength (∼5500 Å). This shifts the effective location of each fiber as a function of wavelength (i.e., a given fiber receives light from a different part of a target galaxy at blue versus red wavelengths). The magnitude and direction of this effect is calculated using the SDSS plate design code model (based in part on Filippenko 1982) as discussed in detail by Law et al. (2015) and depends on the altitude, the parallactic angle, and the atmospheric temperature/pressure/humidity. We calculate the expected effect at the midpoint of a given exposure for each of the 4563 wavelength channels (for the logarithmic case) given the known location of each IFU on the sky and atmospheric conditions recorded in the headers of individual exposures.
• 5.  
  Global shift of the IFU location at the guide wavelength due to field DAR. Over the 3° field of an SDSS plate there are changes in scale and rotation of the sky image (in particular, altitude-dependent compression along the altitude axis). The telescope guiding software corrects for these effects averaged over the plate, but cannot fully correct the quadrupole distortion in the effective location of a given IFU. We estimate this effect as discussed in detail by Law et al. (2015).
• 6.  
  Wavelength-dependent distortions due to the SDSS telescope optics. These are estimated based on upon optical models of the telescope in the SDSS plate design code (Gunn et al. 2006).

The final product of the basic astrometry module is a pair of two-dimensional arrays (matched in size to the mgCFrame flux array) that give the X and Y fiber positions (in units of arcseconds in the tangent plane) relative to the nominal IFU center IFURA, IFUDEC. These arrays can thereafter be used to look up the effective on-sky location corresponding to any wavelength, for any fiber.

During operations within a single dark run a MaNGA cartridge will remain plugged with a given plate until observations for that plate are complete. Since MaNGA shares carts with APOGEE-2 N, however, at the end of a dark run it is typically necessary to unplug the MaNGA IFUs from unfinished plates and replug them again the following dark run to continue observations. This replugging introduces an uncertainty into the relative centering and rotation of each IFU in its hole at the level of ∼0.5 arcsec (centering) and ∼2°–3° (rotation) from the required clearance of locator pins within their holes. The precise change cannot be measured directly and will change from plugging to plugging as it depends on the torsional stresses arising from the routing of each IFU cable through a cartridge. Such uncertainties⁴⁶ are significantly larger than any of the uncertainties derived from effects described in Section 8.1.

We therefore follow the method employed by the VENGA survey (Blanc et al. 2013) of registering the fiber spectra from each exposure against SDSS broadband imaging. In this "extended astrometry module" (EAM) we compute the synthetic broadband flux of each fiber by integrating the flux-calibrated spectrum over the corresponding transmission curve. We then search a grid in right ascension, declination, and rotation of the fiber bundle relative to the base position determined in Section 8.1 (we keep the relative positions of fibers within the bundle fixed). At each position on the grid the fiber coordinates (collapsed from the basic astrometry solution over the appropriate wavelength range) are shifted accordingly, and aperture photometry is performed on a PSF-matched SDSS broadband image using 2.0 arcsec diameter apertures for each fiber. An additional overall flux normalization is permitted according to

$$\begin{eqnarray}&&{f}_{{\rm{SDSS}}}=A\,{f}_{{\rm{MaNGA}}}+B\end{eqnarray} \tag{ 1 }$$

where f_SDSS and f_MaNGA are the SDSS broadband and MaNGA fiber fluxes, respectively, A is a multiplicative scaling factor, and B represent a zeropoint shift.⁴⁷ Yan et al. (2016a) presented a discussion of these A and B coefficients, and determined that A had a roughly Gaussian distribution centered about 1.00 (in i-band) with a sigma of 0.037 for ∼25,000 IFU-exposures obtained during the first year of operations, indicating that the spectrophotometric accuracy of the MaNGA data is about 4% with respect to the SDSS imaging data. The best-fit values of position, rotation, and flux offsets are determined via χ² minimization, with corresponding uncertainties drawn from the χ² probability maps. This exercise is repeated in each of the four g, r, i, and z bands, with the final result a biweight mean of the four bands (this provides robustness against occasional unmasked cosmic rays).

Unsurprisingly, the EAM can achieve better results for larger fiber bundles on galaxies with significant azimuthal structure than for smaller bundles on smooth and circular galaxies. In Figure 15 we show EAM results for two commissioning galaxies 7443–12703 and 7443–3702. For the large IFU on a source with significant structure (7443–12703) the measurement uncertainties on both positional shift and global rotation are small, and reveal (in this case) a ∼0.5 arcsec shift in the IFU center across a cartridge replugging. In contrast, for the small IFU on a rotationally symmetric source (7443–3702) the positional shift is still well constrained but the global rotation is almost completely unconstrained in the range of values explored by the EAM (±5°).

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In order to avoid introducing errors into our astrometry due to such noisy measurements, we therefore run the EAM iteratively. In the first pass, each exposure is fitted independently. The derived values of Δθ are then averaged across all exposures in a given plugging, and the EAM run again holding Δθ fixed at these average values in order to better determine positional shifts between exposures. Since rotation is expected to change only between repluggings (consistent with observed behavior based on galaxies with sufficient azimuthal structure to measure Δθ reliably), this allows us to mitigate the uncertainty in any individual measurement of bundle rotation. In contrast, such averaging is not justified for the positional shifts. Although such shifts are dominated by repluggings (e.g., Figure 15), smaller shifts at the ∼0.1 arcsec level are possible due to uncertainties in the applied dither offsets that we wish to correct through the EAM. On average, we find that the median astrometric uncertainty of the exposures making up the 1390 galaxies in DR13 relative to the SDSS preimaging data is ∼0.1 arcsec (1σ) based on the reduced χ² surface.

Since each set of three exposures is known to have uniform coverage (see Law et al. 2015; R. Yan et al. 2016b) sets from different pluggings of a given plate (and indeed, even between different cartridges) can therefore be combined together onto a common astrometric solution using the EAM. Since all MaNGA target galaxies are drawn from the SDSS imaging footprint, this correction is automatically applied to all MaNGA galaxies.⁴⁸

Using the RSS files and associated astrometric solutions derived in Section 8 we combine the individual fiber spectra into rectilinearly gridded cubes (with orientation R.A., decl., λ) for each IFU on both logarithmic and linearly sampled wavelength solutions. Since these input spectra have already been resampled onto a common wavelength grid, this simplifies to the two-dimensional reconstruction of a regularly gridded image from an irregularly sampled cloud of measurements of the intensity profile at a given wavelength channel.

Multiple methods exist for performing such image reconstruction (see Section 9.2); we choose to build our data cubes one image slice at a time using a flux-conserving variant of Shepard's method similar to that used by the CALIFA pipeline (Sánchez et al. 2012). At each of the 4563 wavelength channels (for the logarithmically sampled data; 6732 for the linear), we describe our input data as one-dimensional vectors of intensity f[i] and variance g[i] with length $N={N}_{{\rm{fiber}}}\times {N}_{{\rm{\exp }}}$ where N_fiber is the number of fibers in the IFU (e.g., 127) and N_exp is the total number of exposures to combine together. Similarly, we can construct vectors x and y, which describe the effective position of the center of each fiber based on the astrometric solution derived in Section 8, and converting to fractional pixel coordinates relative to some chosen origin and pixel scale. We adopt a spatial pixel scale of 0.5 arcsec pixel⁻¹ and an output grid of size X_max by Y_max taken to be slightly larger than the dithered footprint of the MaNGA IFU.

Each of the $M={X}_{{\rm{\max }}}\times {Y}_{{\rm{\max }}}$ pixels in the output image can likewise be resorted into a one-dimensional array of values, with the pixel locations given by X[j] and Y[j], respectively, for j = 1 to M. The mapping between the f[i] intensity measurements in the irregularly sampled input and the F[j] intensities in the regularly sampled output image are then determined by the weights $w[i,j]$ describing the relative contribution of each input point to each output pixel. We take this weight function to be a circular Gaussian:

$$\begin{eqnarray}&&w[i,j]=b[i]\,\exp \left(-0.5\displaystyle \frac{r{[i,j]}^{2}}{{\sigma }^{2}}\right)\end{eqnarray} \tag{ 2 }$$

where σ = 0.7 arcsec is an exponential scale length, $r[i,j]=\sqrt{{(x[i]-X[j])}^{2}+{(y[i]-Y[j])}^{2}}$ is the distance between the i'th fiber location and the j'th output grid square, and b[i] is a binary integer equal to zero where the inverse variance $g{[i]}^{-1}=0$ and one elsewhere. Essentially, b[i] functions as a mask that allows us to exclude known bad values in individual spectra from the final combined image. Additionally, we set $w[i,j]=0$ for all $r[i,j]\gt {r}_{{\rm{lim}}}=1.6$ arcsec as an upper limit on the radius of influence of any given measurement. These limiting radii and scale lengths are chosen empirically based on observed performance; the present values are found to provide the smallest reconstructed FWHM for stellar targets observed as part of commissioning (see Section 10.1) while not introducing spurious structures by shrinking the impact-radius of individual fibers too severely.

In order to conserve flux we must normalize the weights such that the sum of the weights contributing to any given output pixel is unity. The normalized weight function is therefore

$$\begin{eqnarray}&&W[i,j]=\displaystyle \frac{w[i,j]}{{\sum }_{i=1}^{N}\,w[i,j]}\end{eqnarray} \tag{ 3 }$$

where in order to avoid divide by zero errors we set $W[i,j]=0$ where $w[i,j]=0$ for all i in the range 1 to N (e.g., outside the hexagonal footprint of the IFU).

The intensity distribution of the pixels in the output image may therefore be written as the matrix product of the normalized weights and the input intensity vector:

$$\begin{eqnarray}F=\alpha \,W\times f=\alpha \left[\begin{array}{ccc}{W}_{11} & ... & {W}_{N1}\\ \vdots & \ddots & \vdots \\ {W}_{1M} & ... & {W}_{{NM}}\end{array}\right]\times \left[\begin{array}{c}{f}_{1}\\ \vdots \\ {f}_{N}\end{array}\right]\end{eqnarray} \tag{ 4 }$$

or alternatively as

$$\begin{eqnarray}&&F[j]=\alpha \displaystyle \sum _{i=1}^{N}\,f[i]\,W[i,j]\end{eqnarray} \tag{ 5 }$$

where α = 1/(4π) is a constant factor to account for the conversion from flux per unit fiber area (π arcsec²) to flux per unit spaxel area (0.25 arcsec²). The resulting F[j] may then trivially be rearranged to form the output image at this wavelength slice given the known mapping of the pixel coordinates X[j] and Y[j].

Similarly, the variance G of the rectified output image may be written as

$$\begin{eqnarray}&&G[j]={\alpha }^{2}\displaystyle \sum _{i=1}^{N}\,g[i]\,{(W[i,j])}^{2}.\end{eqnarray} \tag{ 6 }$$

This calculation therefore propagates the uncertainties in individual spectra through to the final data cube, but does not use these uncertainties in constructing the combined flux values (except for the simple masking of bad values where inverse variance is equal to zero).

These rectified images of the intensity profile and the corresponding inverse variance maps at each wavelength channel are reassembled by the DRP into three-dimensional cubes along with a 3D quality mask describing the effective coverage and data quality of each spaxel. The final manga-CUBE files are discussed further in Appendix B.2 (see also Table 11).

As stated in Section 9.1, there are multiple algorithms that we could have adopted for building our data cubes, ranging from surface-fitting techniques (e.g., thin plate spline fits) to drizzling and our adopted modified Shepard approach. Based on idealized numerical simulations performed prior to the start of the survey, we found that the surface-fitting approach provided reasonable quality reconstructed images, but was nonetheless undesirable because there is no simple means by which to propagate uncertainties in the resulting surface. In contrast, the modified Shepard approach allows for easy calculation of both the variance and covariance of the reconstructed data cubes, as described in Section 9.3.

The drizzle approach (Fruchter & Hook 2002) has been tested by ourselves and by the CALIFA (Sánchez et al. 2012) and SAMI (Sharp et al. 2015) surveys, all of whom have found that (1) it broadened the final PSF, and (2) since fiber bundle IFUs have <100% fill factor in a given exposure it can create artificial structures in the intensity distribution following the footprint of the circular fibers. To mitigate this problem the SAMI survey (see discussion by Sharp et al. 2015) adopted a weighting system based on the ratio between the original fiber area and the area covered by a final spaxel of a particular fiber (if the fiber is reduced by an arbitrary amount smaller than the original size). This in essence redistributes the flux following a weighting that depends on the distance to the centroid of the fiber and is truncated at a maximum distance controlled by the arbitrary reduction of the covered area of the fibers. This weighting function results in sharper images, but in order to smooth out the artificial structure in the intensity distribution (Sharp et al. 2015, see their Figures 7 and 9) found that a large number of dither positions (≥7) was required to sufficiently sample the galaxy.

Such an approach is not viable for MaNGA (or CALIFA) for a variety of reasons. First, the effective filling factor of the MaNGA IFUs is lower than that of SAMI (56% versus 75%; see Law et al. 2015), meaning the gaps in coverage for a given exposure are larger (although much more regular). Second, the inner diameter of the MaNGA fibers (2 arcsec) and the fiber-to-fiber spacing in the IFUs (2.5 arcsec) is large compared to the typical FWHM of the observational seeing (∼1.5 arcsec), meaning that the spatial resolution incident upon the IFU bundles is drastically undersampled in a single exposure. Most importantly, however, the MaNGA survey strategy of reaching constant depth on each target field requires a different total number of exposures depending on observational conditions and the Galactic foreground extinction. The number of exposures on a given target can therefore range from 6 to 21, obtained in sets of three dithered exposures that must achieve uniform coverage and good reconstructed image quality. Similarly, the SAMI approach also does not work for CALIFA since CALIFA often has only a single visit to a given field.

In contrast, the modified Shepard approach adopted in Section 9.1 allows for high-quality image reconstruction from just three dithered exposures that can be repeated as necessary to achieve the desired depth in a given field (see discussion in Law et al. 2015). This algorithm was found to perform well based on prior experience with the CALIFA survey, and in numerical simulations designed to optimize the choice of the scale length and truncation radius for the exponential weighting function. We note that although the MaNGA and SAMI approaches to cube building are conceptually different they are mathematically quite similar, albeit that the SAMI weighting function does not follow a Gaussian distribution and the kernel is in essence sharper (i.e., with smaller size and truncation radius).

The redistribution of intensity measurements from individual fibers into a rectilinearly sampled data cube via the equations in Section 9.1 leads to significant covariance among spatially adjacent pixels at each wavelength slice. The formal covariance matrix of each slice of the data cube can be written via matrix multiplication as

$$\begin{eqnarray}&&C={\alpha }^{2}\,W\times (g^{\prime} \times {W}^{\top })\end{eqnarray} \tag{ 7 }$$

where α is again a constant scale factor, and g' is the diagonal variance matrix

$$\begin{eqnarray}g^{\prime} =\left[\begin{array}{cccc}{g}_{1} & 0 & ... & 0\\ 0 & {g}_{2} & ... & 0\\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & ... & {g}_{N}\end{array}\right].\end{eqnarray} \tag{ 8 }$$

The diagonal elements of C represent the M elements of the variance array G[j] for the output image while the off-diagonal elements of C represent the covariance introduced between different pixels in the output image by the chosen weighting method. These may in turn be recast as the correlation matrix ρ, where ${\rho }_{{jk}}={C}_{{jk}}/\sqrt{{C}_{{jj}}{C}_{{kk}}}$ for all j and k from 1 to M. ρ is thus unity along the diagonal elements (since each pixel has unity correlation with itself). Following this exercise, we find that, generally, pixels separated by 05 (1 pixel) have correlation coefficients of ρ ≈ 0.85, decreasing to $\rho \lt 0.1$ (i.e., nearly uncorrelated) at separations of ≥2 arcsec. Spatial covariance therefore becomes important when, for example, one calculates the inverse variance in a spectrum generated by coadding many adjacent spaxels.

Although ρ is nominally a large matrix, in practice it is both symmetric and sparse, containing mostly zero-valued elements since we have truncated the weight function to be zero outside a radius of 1.6 arcsec. Since the MaNGA reconstructed PSF is only a weak function of wavelength, ρ also changes only slowly with wavelength, meaning that values of ρ at a given wavelength may generally be interpolated from adjacent wavelengths. In a future data release, the DRP will therefore include the correlation matrix at the central wavelengths of the griz bands in the final data products of the cube building algorithm. At the present time in DR13, however, these correlation matrices are not yet available, and we therefore provide a rough calibration of the typical covariance in the MaNGA data cubes following the conventions established by the CALIFA survey (Husemann et al. 2013). Specifically, we provide a calibration of the nominal calculation of the noise vector of a coadded spectrum under the incorrect assumption of no covariance to one determined from a rigorous calculation that includes covariance.

We have done so using an idealized experiment. Using five data cubes from plate 7495, one of each of the fiber-bundle sizes, we synthetically replace each RSS spectrum with unity flux and Gaussian error. We then construct the data cube identically as done for our galaxy observations. We bin the resulting spaxels using a simple boxcar of size N² where N = 1, 3, 5, 7, and 9, and calculate the mean and standard deviation in the resulting spectrum. This noise estimate is our measured error, n_measured. Alternatively, we can use the inverse-variance vectors for each spaxel in the synthetic data cube that results from the nominal calculation above to create a separate noise estimate, which instead assumes that each spaxel is independent. This calculation follows nominal error propagation, but does not account for the covariance between spaxels; we refer to this as ${n}_{{\rm{no}}{\rm{covar}}}$. The ratio of these two estimates is shown in Figure 16.

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Figure 16 demonstrates that the true error in a combined spectrum is substantially larger than an error calculated by ignoring spatial covariance. The relationship of the errors with and without covariance depends upon the number N_bin of spaxels combined. For small N_bin the values in nearby spaxels are highly correlated and the S/N is nearly constant with N_bin (i.e., both the signal and the true error increase proportionally to N_bin). At large N_bin the values in combined spaxels are nearly uncorrelated, and the S/N increases proportionally to $\sqrt{{N}_{{\rm{bin}}}}$.

We have thus fit a functional form identical to that used by Husemann et al. (2013) to our measurements in Figure 16 and find that

$$\begin{eqnarray}&&{n}_{{\rm{measured}}}/{n}_{{\rm{no}}{\rm{covar}}}\approx 1+1.62\mathrm{log}({N}_{{\rm{bin}}}),\end{eqnarray} \tag{ 9 }$$

for N_bin ≲ 100, and

$$\begin{eqnarray}&&{n}_{{\rm{measured}}}/{n}_{{\rm{no}}{\rm{covar}}}\approx 4.2\end{eqnarray} \tag{ 10 }$$

for N_bin > 100 (i.e., beyond ∼2 times the FWHM where spaxels are uncorrelated).

It is important to note that the binned spaxels must be adjacent for this calibration to hold; i.e., a random selection of spaxels across the face of the IFU will not show as significant an effect because they will not be as strongly covariant. The inset histogram shows the ratio of the data to the fitted model in Equation (9), demonstrating the calibration is good to about 30%. We have confirmed this result empirically by comparing the standard deviation of the residuals of the best-fitting continuum model for a large set of galaxy spectra, following an approach similar to Husemann et al. (2013). However, we emphasize that the test we have performed to produce Figure 16 is more idealized and controlled. We also confirm that a rigorous calculation of the covariance, following the matrix multiplication discussed at the beginning of this section, and a subsequent calculation of the noise vector in the binned spectra used in Figure 16 are fully consistent with our meausurements n_measured.

An estimate of the spatial light profile of an unresolved point source (i.e., the "reconstructed PSF") is automatically provided for each data cube using a numerical simulation tied to the specific observing conditions of each exposure. Using the known fiber locations for a given exposure, the DRP computes the flux expected to be recorded by each fiber from an unresolved point source located at the center of the IFU. This model flux is based on integration of the nominal PSF incident on the face of the IFU in the focal plane of the SDSS 2.5 m telescope. The focal-plane PSF is taken to be a double-Gaussian that accounts for chromatic distortions due to the telescope optics and observational seeing recorded by the guide camera. As detailed by Yan et al. (2016a), since the guide camera reports image FWHM systematically larger than measured by the MaNGA IFU fiber bundles, the guider seeing measurements are also "shrunk" by a scale factor determined by the flux calibration module to give an incident PSF that best matches differential fiber fluxes recorded by the 12 photometric standard star mini-bundles. These simulated fiber fluxes are reconstructed into a data cube using the same algorithm as the science data, and slices of this cube corresponding to g, r, i, and z bands are attached to each data cube.

These griz images (GPSF, RPSF, IPSF, ZPSF; see Appendix B.2) provide a reasonable estimate of the reconstructed PSF in each data cube and are reported in each of the FITS headers. We confirmed the fidelity of these reconstructed PSF models by observing a plate during survey commissioning in which every MaNGA IFU targeted bright stars with two sets of dithered observations (i.e., following the methodology of typical galaxy observations). This plate (7444) was processed by the DRP in an identical manner to standard galaxy plates, with the exception that only the basic astrometry module was used to register the fiber locations since there is no extended structure against which to use extended astrometry module.

In Figure 17 we show the profiles of stars in four of the reconstructed data cubes compared to the simulated estimates. We find that the actual reconstructed PSF of these data cubes is well described by a single 2D Gaussian function with normalized intensity

$$\begin{eqnarray}&&I(r)=\displaystyle \frac{1}{2\pi {\sigma }^{2}}\,{\rm{\exp }}(-{r}^{2}/2{\sigma }^{2})\end{eqnarray} \tag{ 11 }$$

where 2.35σ is the standard Gaussian FWHM. This profile is well matched to the model PSF estimated based on mock integrations of an artificial point source at the known fiber positions; the model FWHM estimates agree with the measured values to within 1%–2%. The measured FWHM of the reconstructed PSF for the other 13 IFUs on plate 7444 similarly lie in the range 2.4–2.5 arcsec.⁴⁹ Based on the simulations presented by Law et al. (2015) and the range of Ω uniformity values for DR13 reported by R. Yan et al. (2016b) we expect that the reconstructed PSF FWHM should vary by less than 10% across a given IFU.

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As discussed in greater detail by R. Yan et al. (2016b), the range of g-band reconstructed PSF FWHM in the 1390 DR13 galaxy data cubes is generally distributed in the range 2.2–2.7 arcsec, with a tail to about 3 arcsec (Figure 17).

As indicated in Section 4.2.5, the LSF varies along the spectrograph slit, and hence varies spatially within a given IFU. Similarly, the LSF can also vary between exposures with ambient temperature drifts and changes in the focus of the spectrograph. The typical spectral resolution for DR13 galaxies is shown in Figure 18; typical IFUs show rms variability at the level of 1%–2% (blue shaded region), while the worst-case large IFUs on the ends of the spectrograph slit can show variability as high as 8%–10% at blue wavelengths (red shaded region). This variability within the worst-case IFUs is dominated by the along-slit variability, but compounded by variations between exposures. The focus in the red cameras is significantly flatter than in the blue cameras, meaning that variation in spectral resolution longward of 6000 Å is 1% or less even for the worst-case IFUs.⁵⁰

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Each MaNGA data cube therefore has an associated extension (see Appendix B.2) describing both the mean and 1σ deviation about the mean spectral resolution for all fiber spectra contributing to the cube. Detailed information on spectral resolution of the individual fiber spectra used to create a given data cube are contained in the final RSS files.

After finalization of the DR13 data pipeline it was realized that the instrumental LSF estimates reported by the pipeline are systematically underestimated. There are two factors that contribute to this underestimation; first, the LSFs reported in DR13 correspond to native Gaussian widths prior to convolution with the boxcar detector pixel boundaries (i.e., the Gaussian function is integrated over the pixel boundaries), while many third-party analysis routines simply evaluate Gaussian models at the pixel midpoints. Although neither approach is necessarily more "correct" than the other, this nonetheless represents a systematic difference between the values quoted and the values that would be measured with most third-party routines. Second, the wavelength rectification performed in Section 7 effectively resamples the spectra and introduces a broadening into the LOG and LINEAR-format spectra that is not accounted for by the DR13 data pipeline. These issues are not unique to the MaNGA data and pipeline, but rather affect all previous generations of SDSS optical fiber spectra as well.

Efforts to address this discrepancy are ongoing (see, e.g., K. Westfall et al., in preparation) and will be detailed in a future version of the MaNGA data pipeline. In the present contribution, we note that re-analysis of ∼2500 individual exposures suggests that multiplying the DR13 LSF by a factor of 1.10 gives a reasonable first-order correction (i.e., the spectral resolution of the DR13 data products is overestimated by ∼10%). This correction factor accounts for both the pre- versus post-pixelization Gaussian difference (∼4%) and the wavelength rectification broadening (∼6%).

Based on previous calculations for the BOSS redshift survey (e.g., Bolton et al. 2012, their Figure 14), the MaNGA spectra (which share the same instrument and much of the same reduction pipeline software) should also have absolute wavelength calibration good to ∼5 km s⁻¹. We verify this estimate by comparing bright emission line features in the MaNGA data cubes against publicly available SDSS-I single-fiber spectra of each of the galaxies in DR13. For each galaxy, we obtain the corresponding SDSS-I spectrum from SkyServer,⁵¹ and determine the effective location of the spectrum from the PLUG_RA and PLUG_DEC header keywords. We then perform aperture photometry in a 2 arcsec circular radius about this location at every wavelength slice of the MaNGA data cube in order to construct a 1D MaNGA spectrum of the central pointing. Both the SDSS-I and MaNGA spectra are then fitted with single-Gaussian emission line components at the expected wavelengths of the Hβ, [O iii] λ5007, Hα, and [N ii] λ 6583 nebular emission lines given the known galaxy redshift from the NASA-Sloan Atlas (NSA; Blanton et al. 2011).⁵²

Although many of the MaNGA galaxies do not have strong emission line features in their central spectra, sufficiently many do in order to allow us to statistically compare the MaNGA and SDSS-I spectra. Considering only galaxies for which both MaNGA and SDSS fits are within 5 Å of the nominal wavelength, have σ width of 0.5–5 Å, and line fluxes >10⁻¹⁶ erg s⁻¹ cm⁻², we find that 470/670/760/1063 galaxies fulfill the criteria for Hβ, [O iii], Hα, and [N ii], respectively. In Figure 19 we plot the distribution of relative peak velocity offsets for each of these four emission lines. We conclude that there is no systematic offset between the MaNGA and SDSS-I spectra to within ∼2 km s⁻¹, and that individual galaxies are distributed nearly according to a Gaussian with 1σ width ∼10 km s⁻¹.

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This width may in part, however, reflect intrinsic velocity gradients within the galaxies combined with uncertainties at the few tenths of an arcsecond level in the effective location of the SDSS-I fibers due to hardware tolerances and DAR.⁵³ Using the MaNGA IFU spectra, we find that changes in location at the level of just 0.25 arcsec (compared to the typical MaNGA astrometric uncertainty of 0.1 arcsec; see Section 8.2) can easily result in ∼20 km s⁻¹ velocity shifts in the resulting spectra for galaxies with strong central velocity gradients (e.g., 8453–12703). The actual wavelength accuracy of the MaNGA spectra may therefore more accurately be given by the rms agreement between repeat MaNGA observations of a small sample of galaxies in DR13; indeed, although there are only ∼10 repeat observations with strong emission lines in DR13, we find a typical rms agreement of 5 km s⁻¹ between the four emission line wavelengths above.

The relative wavelength calibration accuracy of the individual fibers within a given IFU is more difficult to assess in the absence of a calibration reference. However, we can obtain a rough estimate by considering the rms scatter between the measured centroids of bright skylines and the fitted value adopted by the pipeline as described in Section 4.3. As a conservative estimate,⁵⁴ we assume that the smallest rms among the individual skyline measurements is indicative of the relative wavelength calibration accuracy. At 0.024 pixels at 8885 Å, this suggests a relative fiber-to-fiber wavelength calibration accuracy of better than 1.2 km s⁻¹ rms.

Finally, we illustrate the overall quality of the MaNGA spectral data by comparing the spectrum of the central region of galaxy 7443–12704 (aka UGC 09873) from the MaNGA commissioning plate against previous SDSS-I single-fiber and CALIFA⁵⁵ DR-2 (Sánchez et al. 2012; Walcher et al. 2014; García-Benito et al. 2015) IFU observations of the same galaxy. Such a direct comparison is intrinsically difficult as the total flux in a given circular aperture is strongly affected by both the observational seeing and chromatic differential refraction (for SDSS-I) and by the effective spatial resolution of the reconstruction data cubes (MaNGA and CALIFA), especially in regions of the galaxy where there is a strong gradient in the intrinsic surface brightness (i.e., near the center). This method is therefore good for comparing the relative shapes of spectra from different surveys, but not the overall normalization of the flux calibration (which should instead be assessed through PSF-matched broadband imaging, e.g., Yan et al. 2016a).

In this case, the SDSS-I spectrum (observed in 2004 May, and obtained from the DR12 Science Archive Server) corresponds to a circular fiber with a core diameter of 3 arcsec observed in ∼1.6 arcsec seeing. In contrast, the MaNGA and CALIFA cubes have an effective FWHM of ∼2.5 arcsec, meaning that for a centrally concentrated source there will be systematically less flux within a 3 arcsec diameter aperture within these cubes than in the original SDSS-I single-fiber spectrum. We therefore extract the corresponding MaNGA and CALIFA spectra in a five-arcsecond-diameter circular aperture about the nominal location of the SDSS-I spectrum, and additionally allow for a constant multiplicative scaling factor between all of the spectra (derived from the average ratio of the spectra interpolated to a common wavelength solution).

In Figure 20 we plot the resulting spectra for the SDSS-I (red line), SDSS-IV/MaNGA (black line), and CALIFA R ∼ 850 (green line) and R ∼ 1650 (blue line) data. Although we cannot assess the absolute flux calibration from this plot, we note that the relative flux calibration between the four spectra is in extremely good agreement. In the regions of common wavelength coverage, all four spectra show similar structure in the continuum and the emission/absorption lines, with the exception of a known downturn due to vignetting in the CALIFA low-resolution spectrum longward of 7100 Å. Figure 20 also clearly demonstrates the longer wavelength baseline and higher S/N (especially in the far blue) of the MaNGA data compared to both SDSS-I and CALIFA.

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Additionally, we estimate the typical sensitivity of the MaNGA data cubes based on the inverse variance reported by the pipeline for regions far along the minor axis away from edge-on disk galaxy 8465–12704. We estimate the typical continuum surface brightness sensitivity by taking the square root of the sum of the variances of cube spaxels within a five-arcsecond-diameter region, multiplying by a covariance correction factor based on the number of spatial elements summer (see Equation (9)), and converting the resulting 1σ flux sensitivity to a 10σ sensitivity in terms of AB surface brightness. Similarly, to determine the typical 5σ point source emission line sensitivity we sum the variance over twice the FWHM of the LSF, sum over a five-arcsecond-diameter aperture, and multiply the square root of this by a covariance correction factor. We note that both sensitivity estimates include only noise from the detector and background sky, and do not account for any additional noise that may be introduced by astrophysical sources. As illustrated in Figure 21, the derived sensitivities within a five-arcsecond-diameter aperture are strong functions of wavelength, varying from about 23.5 AB arcsec⁻² and 5 × 10⁻¹⁷ erg s⁻¹ cm⁻² at blue wavelengths to about 20 AB arcsec⁻² and 2 × 10⁻¹⁶ erg s⁻¹ cm⁻² in the vicinity of the strongest OH skylines.

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The intermediate data products are produced by the 2D stage of the MaNGA DRP. These products are output during the calibration, flux extraction, sky subtraction, and flux calibration stages of the pipeline. In Figure 22 we show examples of the primary data extension of these types of files. In Tables 4–9 we give the structure of the intermediate and calibration FITS files. For the intermediate data products, the naming convention includes the camera name (except for the camera-combined mgCFrame file), and the zero-padded exposure number. Since the MaNGA instrument has two spectrographs each with a red and blue camera, there are four camera designations: b1, r1, b2, and r2.

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B.1.1. mgArc

B.1.2. mgFlat

B.1.3. mgFrame

B.1.4. mgSFrame

B.1.5. mgFFrame

B.1.6. mgCFrame

Depending on the science case, different final summary products are desirable. The MaNGA DRP provides both RSS files and regularly gridded combined data cubes, with both logarithmic and linear wavelength solutions.

These have the naming convention of manga-[PLATEID]-[IFUDESIGN]-[BIN][MODE].fits.gz. PLATEID refers to the four- or five-digit plate identifer. IFUDESIGN refers to the design id of the IFU bundle. BIN refers to the wavelength sampling of the output data product, LOG for logarithmic sampling, or LIN for linear sampling. MODE refers to the output structure, whether an RSS file or a CUBE file. The combination of plateID-ifuDesign provides a unique identifier to a MaNGA target, and output final-DRP products. While the identifier of manga-id maps to a unique galaxy, it does not map to a unique set of output data products. If a given galaxy is observed on more than one plate, it will have different final-DRP outputs associated with it by default.

The RSS files (Table 10) are a two-dimensional array in row-stacked-spectra format with horizontal size N_spec and vertical size $N=\sum {N}_{{\rm{fiber}}}(i)$ where ${N}_{{\rm{fiber}}}(i)$ is the number of fibers in the IFU targeting this galaxy for the i'th exposure and the sum runs over all exposures. In contrast, the cubes (Table 11) are three-dimensional arrays in which the first and second dimensions are spatial (with regular 0.5 arcsec square spaxels) and the third dimension represents wavelength.

In each case, there are associated image extensions describing the inverse variance, pixel mask, and a binary table "OBSINFO" that describes full information about each exposure that was combined to produce the final file (exposure number, integration time, hour angle, seeing, etc.). This structure is appended to each file with one line per exposure (Table 12) both for quality-control purposes (so that delivered data can be tracked back to individual exposures easily), and so that future forward modeling efforts can read from this extension everything necessary to know about the instrument and observing configuration of each exposure.

Additionally, each RSS-format file has an extension listing the effective X and Y position (calculated by the astrometry module) corresponding to each element in the flux array. Because of chromatic DAR, each wavelength for a given fiber has a slightly different position, and therefore the positional arrays have the same dimensionality as the corresponding flux array. Each data cube also has four extensions corresponding to reconstructed broadband images obtained by convolving the data cube with the SDSS griz filter response functions, and four extensions illustrating the reconstructed PSF in the griz bands (see discussion in Section 10.1).

As detailed by http://www.sdss.org/dr13/manga/manga-data/data-model/ there are an assortment of FITS header keycards specifying information such as World Coordinate Systems (WCS), average reconstructed PSF FWHM in griz bandpasses, total exposure time, Milky Way dust extinction, etc. The WCS adopted for the logarithmic wavelength solution follows the CTYPE = WAVE-LOG convention (Greisen et al. 2006) convention in which

$$\begin{eqnarray}&&\lambda ={\rm{CRVALi}}\times {\rm{\exp }}(\mathrm{CDi}\_{\rm{i}}\times ({\rm{p}}-\mathrm{CRPIXi})/\mathrm{CRVALi})\end{eqnarray} \tag{ 12 }$$

• Writtenby: https://svn.sdss.org/public/repo/manga/mangadrp/tags/v1_5_4/pro/spec3d/mdrp_reduceoneifu.pro
• RSS Data Model: https://data.sdss.org/datamodel/files/MANGA_SPECTRO_REDUX/DRPVER/PLATE4/stack/manga-RSS.html
• CubeData Model: https://data.sdss.org/datamodel/files/MANGA_SPECTRO_REDUX/DRPVER/PLATE4/stack/manga-CUBE.html

The 3D-stage reductions of the MaNGA DRP (including calibration mini-bundles) are summarized in the DRPall FITS file, drpall-[version].fits. This file aggregates metadata pulled from all individual reduced data cube files (plus spectrophotometric standard stars), as well as the NSA targeting catalog. Each row in this table corresponds to an individual observation. The DRPall summary file is a convenient place to quickly look for information regarding, for example, unique cube identifiers, achieved S/N, data quality, observing conditions, targeting bitmasks and basic NSA catalog parameters. The complete data model for the DRPall summary file can be found at https://data.sdss.org/datamodel/files/MANGA_SPECTRO_REDUX/DRPVER/drpall.html.

The MaNGA DRP 2D pixel bitmasks applicable to individual reduced frames and composite RSS files are given in Table 13. These indicate the quality of entire fibers or individual pixels within these frames, accounting for cases of broken and/or unplugged fibers, cosmic rays, sky-subtraction failures, etc. A catch-all summary bit 3DREJECT is set when a given pixel should be excluded from use in building a 3D composite data cube.

The MaNGA DRP 3D spaxel masks applicable to these composite data cubes are given in Table 14. Since these cubes combine across many individual exposures, the 3D spaxel masks are necessarily less detailed than the 2D pixel masks, and indicate simply the overall quality of individual spaxels within a given data cube. This includes whether there is no coverage (i.e., outside the footprint of the IFU bundle), low coverage (near the edges of the IFU bundle), a dead fiber (which will in turn cause low and/or no coverage within the bundle), or a foreground star that should be masked for many science analyses. These foreground stars are identified manually using a combination of SDSS imaging and the MaNGA data cubes, and stored in a reference list read by the DRP. A catch-all DONOTUSE flag indicates a superset of all pixels that should not be used for science.

The progress of a given exposure through the DRP is controlled by use of the MANGA_DRP2QUAL maskbit (Table 15, which indicates any potential problems that affect the reduction of the exposure. These range from the informative for operations (RAMPAGINGBUNNY indicates dust accumulation on the IFU surfaces that must be cleaned) to the fatal (FULLCLOUD indicates that the transparency is too low to successfully flux calibrate the data).

The final quality of a given object processed by the 3D stage of the DRP is indicated by the reduction quality bit MANGA_DRP3QUAL (Table 16). This single integer refers to the quality of an entire galaxy data cube, and can indicate a variety of possible problems sorted roughly in increasing order of importance from low average depth (BADDEPTH) to a CRITICAL failure that means that the data should be treated with great caution or (conservatively) omitted from science analyses. We note that many of even the CRITICAL failure cases may represent an overly vigorous QA algorithm rather than any intrinsic problem in the data though; these routines will continue to be refined throughout SDSS-IV.

We note that additional bits may be added to each of these quality-control bitmasks over the lifetime of the survey. An online version can be found at http://www.sdss.org/dr13/algorithms/bitmasks/ for DR13, and at similar locations for future data releases.