SDSS-IV MaNGA: Modeling the Spectral Line-spread Function to Subpercent Accuracy

The spectral LSF of the MaNGA data is first estimated using 4 s observations of a Neon–Mercury–Cadmium arc-lamp spectrum taken at the beginning of each series of MaNGA observations of a given plate and roughly every 2 hr thereafter. This arc frame provides a well-populated series of bright unresolved emission lines spanning the wavelength range of the instrument. Since the wavelength zero-point is curved along the pseudo-slit (see, e.g., Figure 22 of Law et al. 2016), this means that a given arc line lies at a range of different "pixel phases" (i.e., centroid locations within a pixel) for different fibers, and as the relative fiber-to-fiber wavelength solution is accurate to better than 0.024 pixels rms (see Section 10.3 of Law et al. 2016), it is therefore possible to combine the observed spectra from multiple fibers to obtain a super-sampled realization of the arc-line profile.

As shown in Figure 2, these line profiles are well described by a simple Gaussian model for both the blue and red cameras across a wide range of wavelengths. While the residuals from the simple Gaussian fit show evidence for intrinsic kurtosis in the line profile (consistent with expectations for the convolution of a 2D Gaussian with the circular image of the optical fiber), the peak amplitude of this residual is sufficiently small (∼5% relative to the peak intensity of the line) that it is expected to have a negligible effect on our analysis.¹⁷ We therefore fully characterize the shape of the LSF by a single value ω¹⁸ giving the 1σ width of a Gaussian profile fit to the observed pixel values (after first subtracting off the small continuum signal using the median in a 100-pixel window surrounding the line).

Zoom In Zoom Out Reset image size

As illustrated by Figure 3, ω varies over each of the four detectors as a complicated function of both wavelength and fiberid along the pseudo-slit. Similarly, it can change from exposure to exposure with varying telescope/spectrograph focus, gravitational flexure, and changing observing conditions. The DRP therefore constructs a model of ω in pixel units using the individual arc lines in each calibration frame that will be used as the base calibration for nearby science exposures (the median science exposure is within 34 minutes of the nearest arc frame, 86% of exposures are within 1 hr, and 99.5% are within 2 hr).

Zoom In Zoom Out Reset image size

First, we assume that any variation in ω for a given arc line should be approximately linear within a given v-groove block of fibers mounted to the pseudo-slit. This is because all fibers in a given block will have a common telecentricity with common alignment errors, and should vary in profile only smoothly with the gradual curvature of the slithead. Figure 3 (left-hand panels) shows that this is the case; while individual measurements for a given fiber are noisy, they describe smooth well-defined trends within a given block with discrete jumps between adjacent blocks corresponding to alignment differences in their mounting on the pseudo-slit. We therefore replace the individual measurements of each arc line in a given fiber with the linear polynomial fit to the fibers in each block; this polynomial fit reduces the typical ω uncertainty by a factor of about $\sqrt{30}$ (as there are roughly 30 fibers in each block), corresponding to an improvement from ∼1% to ∼0.2% in the wavelength range λλ6500–7000 Å. This replacement also has the added benefit of allowing us to be robust against occasional critical failures of the Gaussian-fitting algorithm (resulting, e.g., from bad pixels or cosmic rays).

Next, we assume that ω within each fiber should vary smoothly as a function of wavelength within the range λλ3500–6300 Å (blue cameras) and λλ5900–10300 Å (red cameras). We therefore fit the linearly interpolated ω in each fiber with an nth-order polynomial, where n = 5/6 for the blue/red cameras, respectively.¹⁹ As illustrated in Figure 3 (middle panels), these trace-sets can be evaluated throughout the entire MaNGA wavelength range, and they do a good job of reproducing the observed widths at individual arc lines. In the 6000–7000 Å range, the density of arc lines is particularly high, and ω varies particularly slowly with wavelength; the scatter of individual arc lines about the model relation suggests that the overall uncertainty of the fit in the Hα wavelength regime is about 0.5%.

Figure 3 (right panels) illustrates the resulting arc-lamp model for ω across the blue and red cameras; we note that while ω in the red cameras is relatively flat as a function of both fiberid and wavelength (rms ∼0.01 pixels below 9000 Å), ω in the blue cameras shows significantly more structure (rms ∼0.03–0.04 pixels between 4000 and 6000 Å), corresponding both to the overall curvature of the focal plane and global alignment differences between blocks of fibers. The details of this structure are cartridge-dependent since the slithead on each of the six cartridges has its own mechanical alignment. Generally, however, fibers ∼25% and 75% of the way along each slit have up to a factor ∼2 lower and more constant ω with wavelength, while fibers near the middle or ends of the slit show larger variations.

As indicated by Figure 3, MaNGA is nearly critically sampled since spectrally unresolved arc lines typically have a 1σ width of about ω = 1.0–1.2 pixels (2.4–2.8 pixels per FWHM). As discussed extensively by Robertson (2017, see their Figure 16), such pixels are sufficiently large compared to the intrinsic LSF delivered by the telescope/spectrograph optics that the effective LSF is broadened by the convolution with the top-hat response of the detector pixels. Our post-pixellized measurements of ω that were obtained by simply evaluating a Gaussian profile model at the midpoint of each pixel are therefore systematically biased relative to the "true" intrinsic instrumental dispersion before convolution with the pixel response function (i.e., the pre-pixellized ω).

We compute the magnitude of this effect using Monte Carlo simulations in which we constructed 10x over-sampled Gaussian models of known width, convolved them with the pixel response function at a variety of pixel phases, and then measured the resulting profiles using the commonly available Gaussian-fitting techniques that simply evaluate the Gaussian function at the pixel midpoints. As illustrated in Figure 4, post-pixellized widths are systematically broader than the pre-pixellized values by ∼1%–10%, and they define an extremely tight mathematical relation in which the pixel-sampling phase drives the scatter but is of negligible importance (<0.1%) in the range of line widths observed by MaNGA. The DRP therefore computes pre-pixellized estimates of the MANGA LSF (ω_PRE) from the measured post-pixellized values (ω_POST) using a fourth-order polynomial fit to this relation (red line in Figure 4).

Zoom In Zoom Out Reset image size

As motivated and discussed in Section 4, the MaNGA DAP adopts these pre-pixellized estimates of ω and rigorously accounts for pixel convolution. However, since many third-party analysis routines ignore pixel convolution and instead rely on simple Gaussian-fitting approximation, the DRP provides both ω_POST and ω_PRE with all of the survey data products.

In practice, differences in the telescope focus (due to, e.g., changing weather conditions), gravitational flexure of the spectrographs, and various other effects mean that the LSFs derived from arc-lamp exposures are only an approximation to the actual LSF of any given science exposure. We therefore use the well-known bright sky emission-line features to refine the LSF estimate for each individual science exposure.²⁰

Unlike the arc spectra, however, the night-sky emission features are not ideally distributed in wavelength (there are very few bright skylines at blue wavelengths), and they can frequently be biased by continuum emission and blends of multiple atomic and/or molecular transitions. While such blending may be weak, even weak blending can bias apparent measurements of the LSF at the few-percent level. Rather than re-deriving the LSF solution from the skylines, the DRP therefore uses them to simply make low-order adjustments to the arc-line model.

Using the extracted, flat-fielded science frame spectra, we fit each skyline in our list of reliable lines (see Table 2) with a post-pixellized Gaussian model that includes a linear polynomial term to account for wavelength gradients in the sky continuum level. We then compute the difference Δω = ω_sky − ω_arc, where ω_arc is the arc-line LSF model evaluated at the wavelength of the skyline features. Even in the cases for which the sky and arc line measurements differ substantially, the difference Δω between the measurements shows an extremely smooth variation along the slit with no noticeable block-to-block jumps and only statistical noise from the individual fiber measurements (Figure 5). We therefore fit (unmasked) values of Δω with a cubic basis spline with breakpoints every 150 fibers to obtain our initial estimate of the difference between skyline and arc line LSF models.

Zoom In Zoom Out Reset image size

In the blue camera (λλ = 3600–6300 Å), only the bright O i λ5577.339 skyline is deemed to be a reliable LSF calibrator since all of the other lines used to adjust the MaNGA wavelength solution are marginally blended at the few-percent level, and the Δω derived from this line is therefore assumed to be constant for all wavelengths. In the red camera (λλ = 5900–10300 Å), there are multiple skylines, but since we observe no unambiguous trends in Δω with wavelength, we simply median combine each of the estimates to obtain our final correction value. The resulting sky-adjusted LSF models are typically different from the original arc-line models by less than 0.01 pixels, although in some extreme cases can differ by around 0.05 pixels (Figure 6, middle and right-hand panels, respectively). Based on the >22,000 individual science exposures in MPL-10, we note that the arc-line model tends to systematically underestimate the observed skyline width by ∼0.5% on average in the b1, r1, and r2 cameras, and overestimates the skyline width by about the same amount in the b2 camera (Figure 6, left-hand panels), possibly due to systematic differences in optical alignment between the cameras. In contrast, the skyline-adjusted models have a negligible systematic offset from the skyline measurements and a significantly smaller width to the distribution that is dominated by the uncertainty in individual lines.

Zoom In Zoom Out Reset image size

As discussed in detail by Law et al. (2016), the MANGA DRP processes each camera of data independently up to the point of producing flux-calibrated, sky-subtracted spectra for each fiber. Once all four cameras have been thus processed, the DRP stitches together the natively sampled spectra from the blue and red cameras across the dichroic break to produce final calibrated spectra for each fiber that cover the entire MaNGA wavelength range. This is achieved via high-order cubic basis spline modeling of the blue and red spectra with a tapered inverse variance weighting²¹ in the 5900–6300 Å dichroic window to provide a smooth transition between the cameras. This spline model is evaluated on two different output grids: a linear solution with a constant Δλ = 1 Å and a logarithmic wavelength solution with a constant Δlog (λ/Å) = 10⁻⁴. While the linear wavelength solution products are used for some MaNGA value added catalogs (e.g., Pipe3D; Sánchez et al. 2016), the MaNGA DAP (Section 4) uses the products with a logarithmic wavelength solution.

The combination of the per-camera LSF vectors onto the final rectified wavelength grid uses the same algorithm as for the spectra themselves. In the 5900–6300 Å dichroic overlap region, the gradual tapering of the weights applied to the blue/red cameras serves to produce a smooth transition between the LSF solutions of the individual cameras, but the spectra are nonetheless a composite of individual spectra whose LSF widths differ from each other by about 15%. As we show in Figure 7 however, the non-Gaussianity introduced as a result is insignificant, especially compared to the known intrinsic line profile (Figure 2).

Zoom In Zoom Out Reset image size

In addition to simply mapping the LSF onto the output wavelength grid however, the wavelength rectification also broadens the effective LSF slightly compared to the original spectra that were sampled by the native detector pixels. We compute the magnitude of this broadening using a series of Monte Carlo simulations for a statistically large grid of Gaussian "comb" spectra, in which artificial spectra with emission lines of known width are created every 100 Å throughout the MaNGA wavelength range. These artificial spectra are produced using the wavelength solution of a typical natively sampled exposure and then combined together across the dichroic to produce composite spectra using the spline algorithm described above. The widths of the resulting lines are then computed via Gauss-fitting techniques to compare to the known input widths. By repeating this experiment across the 700+ fibers per MaNGA spectrograph, shifting the input line centroids by sub-pixel values to consider ten different input pixel phases, and covering a range of 12 different input widths from 0.9 to 2.0 pixels, we are therefore working with a grid of >6 million simulated lines.

As shown in Figure 8, the effective broadening factor (post-pixel to post-pixel) is a strong function of wavelength, increasing from near unity at the shortest wavelengths in both the blue and red cameras to a ∼10% effect at the longest wavelengths in the red camera for input ω_POST = 1.0 pixels. The exact correction factor is strongly dependent on the input pixel phase, particularly for values of ω_POST ≤ 1.0 pixel. Since any DRP correction to the LSF cannot take pixel phase into account (since this will be different for every emission line in the science data in a manner that cannot easily be modeled), we fit the median relation as a function of wavelength²² for each of our 12 input widths with a cubic basis spline to compute a grid of correction factors for both the logarithmic and linear wavelength solutions. The DRP then corrects the composite LSF vectors for each fiber by the appropriate value interpolated from this reference grid (applying the same factor to both ω_PRE and ω_POST estimates). Given the typical range of ω_POST = 1.1–1.2 pixels in the vicinity of Hα, the range of correction factors across different pixel phases indicated by Figure 8 suggests that the rms uncertainty of the applied correction is typically around 1%.

Zoom In Zoom Out Reset image size

The corrected pre-pixel instrumental LSFs for all individual calibrated exposures (∼30 million individual fiber spectra) in MPL-10 are shown in Figure 9. We conclude that the typical instrumental resolution improves from 80 to 90 km s⁻¹ at the bluest wavelengths to about 55 km s⁻¹ at the red end of the MaNGA wavelength range, with the largest rms variation between fibers around 5000–6000 Å and the smallest rms variation of just a few percent around Hα.

Zoom In Zoom Out Reset image size

The DRP additionally reformats the calibrated fiber spectra into a rectilinear data cube in which the individual fiber spectra have been coadded to produce a single 3D data cube with two spatial axes and one spectral axis. Working with these data cubes is significantly easier than working directly with the individual calibrated fiber spectra (provided by the DRP as "row-stacked spectra," or RSS) as the latter suffer from chromatic differential refraction while the spectra in the rectified data cubes are directly associated with a specific location on the sky. For this reason, the vast majority of the MaNGA science team has thus used the composite data cubes for science analyses, as does the MaNGA DAP.

However, the algorithm used to construct these data cubes produces complications of its own. In addition to introducing strong spatial covariance between adjacent data cube spaxels, as explored in detail by Law et al. (2016, Section 9) and Westfall et al. (2019, Section 6), the data cube construction also combines spectra with a variety of different spectral resolutions. Since the effective LSF can vary strongly from fiber to fiber, exposure to exposure, and night to night, the range of input resolutions contributing to any given data cube spaxel can be non-negligible.

Figure 10 shows a density plot of the rms variation in ω of all fibers contributing to a given data cube as a function of wavelength for all 10,523 data cubes in MPL-10. As discussed in Law et al. (2016), typical IFUs show variability at the 1%–2% level in the blue cameras with rare worst-case outliers at about 10%–15% at some wavelengths for IFUs on the edges of the slit. In contrast, driven by the flatter focal plane across the CCDs, the focus in the red cameras is significantly flatter than in the blue, with the majority of all data cubes showing <1% variability in the component fiber spectra. Given this relatively small LSF variability, we avoid the complexity of attempting to convolve all fiber spectra to the same resolution (i.e., the difficulty in making such small adjustments to the wavelength-dependent resolution, the loss of information by degrading the majority of the data cube spectra, and the introduction of more spectral covariance; see, e.g., Pace et al. 2019) and instead construct an LSF width metric for the combined spectra. In other words, assuming a Gaussian function for the astrophysical line-of-sight velocity distribution (LOSVD), we want a simple metric that can be used to accurately remove the influence of the LSF on our measurement of the astrophysical velocity dispersion.

Zoom In Zoom Out Reset image size

To understand the influence of the LSF metric, we perform an experiment by constructing two Gaussian profiles, each with a width defined by perturbing ω by a small percentage above and below 70 km s⁻¹ (e.g., we denote a 1% change as δω/ω = 0.01). We then construct an "observed" profile by summing these two Gaussian profiles and convolving the result with a third Gaussian with dispersion σ_in that represents the LOSVD of the gas in the galaxy. We then fit a fourth Gaussian to the result, mimicking the typical procedure when fitting galaxy data. The dispersion of the best-fitting Gaussian is then corrected for the LSF width to produce σ_out; any difference between σ_in and σ_out indicates a measurement bias. The experiment is performed with highly over-sampled noiseless profiles so as to explore the intrinsic bias in each approach.

In Figure 11, we show the results of this test for four values of δω/ω (differentiated by line color) and three different methods of estimating the combined LSF metric: (1; dotted lines) the second moment of the summed profile ${\omega }^{2}=({\omega }_{\mathrm{lo}}^{2}+{\omega }_{\mathrm{hi}}^{2})/2$, where ${\omega }_{\mathrm{lo}}^{2}$ and ${\omega }_{\mathrm{hi}}^{2}$ are the values for the narrow and broad Gaussian components, (2; solid lines) the mean ω of the two components, and (3; dashed lines) the width of a new Gaussian profile fit directly to the summed profile.

Zoom In Zoom Out Reset image size

Figure 11 demonstrates that when the range in LSF widths for combined spectra is ≲1% (true for the majority of MaNGA data cubes, particularly for λ ≳ 6000 Å), the method used to estimate the combined LSF is largely irrelevant; any bias is <1% for σ_in > 10 km s⁻¹ for all methods. For larger differences in the LSF widths, fitting the composite LSF to define ω is generally better than the other two definitions. However, given that this method requires significantly more computational overhead—requiring us to construct the composite profile and fit a Gaussian for every pixel with valid spectral data in the full MaNGA data set—and the fact that it indeed introduces biases of its own, we instead adopt the simple mean method, which performs modestly better than using the second moment. Combined with Figure 10, we expect that this simple mean method of combining the fiber LSFs will rarely introduce more than a 1 km s⁻¹ bias for σ ≳ 20 km s⁻¹ even in the extreme case of 5% variation in the fiber ω, and will more typically be <0.1 km s⁻¹ (far below the typical uncertainty in the individual measurements; see Figure 15). As illustrated by Figure 7, differences in the LSF of the input spectra at such levels will have a negligible impact on the overall Gaussianity of the composite spectrum.

We therefore construct LSF data cubes using the same algorithm and weighting scheme as adopted to construct the science data cube. That is, with the modified Shepard algorithm, the image of the galaxy at a given wavelength slice is a weighted sum of the input fiber spectra at that wavelength, and the LSF "image" is constructed from the same weights applied to the LSF vectors of the individual fibers.

The MaNGA DRP provides both a summary averaged LSF vector for each data cube (as small variations will be unimportant to science cases studying astrophysical line widths in excess of 100 km s⁻¹), as well as a full 3D LSF data cube so that downstream analysis programs can use the effective LSF appropriate for each spaxel in the cube. For illustrative purposes, we show in Figure 12 examples with 1%, 2%, and 6% LSF variation across the face of the IFU as calculated by the DRP. Such spatial variation in the effective LSF of integral-field data is well known for slit-type and lenslet-type spectrographs as well (see, e.g., Figure 6 of Law et al. 2018) and must be taken into account when measuring velocity dispersions near the instrumental resolution or below. As suggested by Figure 10, 99.9% of cubes resemble the 1% or 2% rms examples at red wavelengths, while 80% resemble these examples at blue wavelengths.

Zoom In Zoom Out Reset image size

As the MaNGA DRP has evolved over the survey, the estimated instrumental LSF too has changed. Rather than representing significant changes in the data, as outlined in the previous sections, this instead reflects our evolving understanding of the instrument and improvements to our methods of characterizing the data. These changes are summarized in Figure 13, which plots the ratio between ω for all MPL-10 fiber spectra that were included in four of the major internal/external MaNGA data releases and shows that the MaNGA LSF estimates have generally been converging over the lifetime of the survey.

Zoom In Zoom Out Reset image size

Relative to MPL-10, MaNGA's initial public data release (DR13, released Summer 2016) systematically overestimated the pre-pixellized LSF in the far blue by 10%–15% while underestimating it in the red by 5%–10%. This changed with the release of DR14 (Summer 2017), which made an initial correction to broaden the pre-pixellized LSF measurements to post-pixellized values during the skyline adjustment stage, in addition to including a term to account for the broadening factor contributed by the wavelength rectification of fiber spectra (see Abolfathi et al. 2018). These changes generally improved performance at red wavelengths but were an overcorrection, leading to a ∼5% effective overestimate of the LSF around Hα.

DR15 (Summer 2018) for the first time provided simultaneous measurements of the pre-pixellized and post-pixellized LSF in full cube format, fixed the LSF overestimate in the far blue (by rejecting the partially blended Cd i λλ3610 and low-quality Hg ii λλ3984 arc-lamp lines and substituting Hg i λλ3663 instead), and implemented a Gaussian-comb solution for measuring the broadening due to wavelength rectification (instead of relying upon measurements of individual lines). As illustrated by Figure 13, the combination of these changes brought all wavelengths relatively well in line with MPL-10, but with a ∼4% underestimate of the LSF around Hα. Minor additional changes to polynomial fitting orders and rejection of additional skylines implemented in MPL-9 in turn decreased this difference to around 2%–3%.

Relative to MPL-9, MPL-10 completely overhauled many aspects of the LSF estimation. Most fundamentally, instead of using legacy C code dating back to the original SDSS spectro survey to measure the pre-pixellized LSF (and later bootstrap the corresponding post-pixellized LSF), it instead uses new code to measure the post-pixellized LSF and later bootstraps the pre-pixellized values based on extensive Monte Carlo simulations (Section 3.2). Additionally, MPL-10 introduced further modifications to the reference arc and skyline lists and polynomial fitting orders.

The scientific impact of this evolution in the estimated LSF will depend on the range of astrophysical velocity dispersions considered by a given analysis. Above σ_Hα = 100 km s⁻¹, the systematic error in recovered velocity dispersions after correcting for the instrumental resolution will be less than 3%. At velocity dispersions far below the instrumental resolution though, the changes in the estimated LSF become increasingly important, and around σ_Hα = 30 km s⁻¹, analyses using DR13, DR14, or DR15 data will have derived values that are systematically too high by ∼30%, too low by ∼30%, and too high by ∼20%, respectively compared to MPL-10.

The pPXF approach operates on the fundamental assumption that a galaxy spectrum is composed of a linear combination of template spectra convolved with a template-dependent LOSVD. Ignoring any multiplicative (e.g., attenuation, flux-calibration) or additive (e.g., sky-subtraction) effects and explicitly including the convolution by the pre-pixel spectral-resolution kernel, ${ \mathcal R }(\lambda )$, and the pixel-sampling kernel, ${ \mathcal S }(\lambda )$, we can write the underlying pPXF assertion as (see Cappellari 2017, Equation (11)):

$$\begin{eqnarray}&&{G}_{j}\equiv {G}^{{\prime} }\ast {{ \mathcal R }}_{j}\ast { \mathcal S }\approx \displaystyle \sum _{i}{w}_{i}({T}_{i}^{{\prime} }\ast {{ \mathcal L }}_{i}^{{\prime} }\ast {{ \mathcal R }}_{j}\ast { \mathcal S }),\end{eqnarray} \tag{ 1 }$$

where ∗ denotes a wavelength-dependent convolution, ${{ \mathcal L }}_{i}^{{\prime} }$ is the intrinsic LOSVD kernel, G' and ${T}_{i}^{{\prime} }$ are the intrinsic spectra of the galaxy and template object, respectively, and the summation runs over each of the individual template objects. We have additionally subscripted the observed galaxy spectrum, G, and the associated spectral-resolution kernel with the index j to emphasize that MaNGA observations have a range in spectral resolution that vary both between observations and between spaxels in a given data cube (Figure 12). Except for templates based on theoretical models, the ${T}_{i}^{{\prime} }$ are not generally known; instead we have observed spectra that are taken with their own spectral-resolution and sampling kernels; i.e., ${T}_{i}\equiv {T}_{i}^{{\prime} }\ast {{ \mathcal R }}_{i}\ast {{ \mathcal S }}_{i}$. Solving for ${T}_{i}^{{\prime} }$, Equation (1) becomes

$$\begin{eqnarray}&&{G}_{j}\approx \displaystyle \sum _{i}{w}_{i}\left\{{T}_{i}\ast {{ \mathcal L }}_{i}^{{\prime} }\ast ({{ \mathcal R }}_{j}\ \overline{\ast }\ {{ \mathcal R }}_{i})\ast ({ \mathcal S }\ \overline{\ast }\ {{ \mathcal S }}_{i})\right\},\end{eqnarray} \tag{ 2 }$$

where we use $\overline{\ast }$ to signify a wavelength-dependent deconvolution. Although pPXF allows for template spectra with a pixel sampling that is a fixed integer factor smaller than the sampling of the galaxy spectrum,²³ any differences in the (pre-pixelized) spectral resolution of the templates and the galaxy data are ignored.

Standard practice is to use templates that have been convolved to exactly the same spectral resolution as the galaxy data, either by observing templates with the same instrument setup or by degrading the spectral resolution of a set of templates to match the resolution of the galaxy data. As we note in Westfall et al. (2019), however, this is hard to do in practice for many reasons: the reproducibility of the instrument setup, the uncertainty in the determination of the wavelength-dependent LSF for both the galaxy and template spectra, and the redshift difference between the galaxy and template objects. Moreover, an analysis of the relevant error propagation implies that it is almost always better to use templates with higher spectral resolution than the galaxy spectra (Westfall et al. 2019, Appendix B). In the MaNGA DAP, we therefore chose to use pPXF to fit the galaxy data using templates at their native spectral resolution. This means that we must construct a correction that accurately removes the effect of the template-galaxy spectral-resolution difference to recover the parameters of the astrophysical LOSVD. In terms of Equation (2), our approach is to have pPXF fit ${{ \mathcal L }}_{{ij}}={{ \mathcal L }}_{i}^{{\prime} }\ast ({{ \mathcal R }}_{j}\ \overline{\ast }\ {{ \mathcal R }}_{i})$—the kernel composed of the astrophysical LOSVD convolved with the template-galaxy instrumental resolution difference—and then we construct a correction to ${{ \mathcal L }}_{{ij}}$ that yields ${{ \mathcal L }}_{i}^{{\prime} }$. The details of how the DAP constructs the corrections are different for the ionized gas and the stars; however, both currently assume that the template LSF, the MaNGA LSF, and the LOSVD are single-component Gaussian profiles. This means that the only parameter of ${{ \mathcal L }}_{{ij}}$ that requires correction is the velocity dispersion.

The key difference between the velocity-dispersion corrections derived for the stars and ionized gas is that the former ignores the wavelength dependence of $({{ \mathcal R }}_{j}\ \overline{\ast }\ {{ \mathcal R }}_{i})$, whereas the latter is effectively treated on a line-by-line, wavelength-dependent basis.

The construction of the emission-line templates is described in detail by Westfall et al. (2019, Section 9.1). Taking advantage of the analytic Fourier transform of a Gaussian line profile (Cappellari 2017), we set the spectral resolution of the emission-line templates to match the resolution of the MaNGA data cube up to a quadrature offset in ω_PRE, to first order. This is only done once per data cube, meaning that there are second-order differences between the resolution of the emission-line templates and the data given the spaxel-to-spaxel variations in the LSF and the spectral variation in the LSF over the velocity scale of the galaxy's internal motions. That is, $({{ \mathcal R }}_{j}\ \overline{\ast }\ {{ \mathcal R }}_{i})$ is nearly constant for the emission-line templates. Regardless, the DAP fits the velocity dispersion of each line (except for the line doublets listed in Section 4.2.2) independently, which allows pPXF to account for the second-order LSF effects during the fit. Moreover, by adding the template-line velocity dispersion to the pPXF measurement in quadrature, the measurement reported by the DAP for each emission line is exactly the pre-pixelized velocity dispersion of the observed line profile (${{ \mathcal L }}_{i}^{{\prime} }\ast {{ \mathcal R }}_{j}$ from Equation (1)).²⁴ The corrections needed (and provided by the DAP) to calculate the velocity dispersion of ${{ \mathcal L }}_{i}^{{\prime} }$ consist of, therefore, the pre-pixelized width, ω_PRE, of the instrumental line profile (${{ \mathcal R }}_{j}$ from Equation (1)) at exactly the best-fitting centroid of the line. Specifically, the corrected velocity dispersion of, e.g., the Hα line is:

$$\begin{eqnarray}&&{\sigma }_{{\rm{H}}\alpha }=\sqrt{{\sigma }_{{\rm{H}}\alpha ,\mathrm{obs}}^{2}-{\omega }_{\mathrm{PRE}}^{2}},\end{eqnarray} \tag{ 3 }$$

where σ_Hα,obs is the pre-pixelized velocity dispersion of the observed line.

In DR15 and subsequent MPLs, the templates used to measure stellar kinematics are based on a set of 42 composite spectra generated by the hierarchical clustering of the 985 empirical stellar spectral of the MILES library (Falcón-Barroso et al. 2011; Sánchez-Blázquez et al. 2006), i.e., the "MILES-HC" library (Westfall et al. 2019, Section 5). The MaNGA spectra are fit only over the MILES spectral range (3575 Å < λ_rest < 7400 Å). We adopt a wavelength-independent instrumental resolution of Δλ = 2.5 Å for the MILES library (Falcón-Barroso et al. 2011, see, by way of comparison, Beifiori et al. 2011).²⁵ Given the MaNGA resolution from Figure 9, $({{ \mathcal R }}_{j}\ \overline{\ast }\ {{ \mathcal R }}_{i})$—and therefore ${{ \mathcal L }}_{{ij}}$— is wavelength dependent; however, we use pPXF to instead fit a wavelength-independent parameterization of ${{ \mathcal L }}_{{ij}}$. Given the complications involved in allowing for a wavelength-dependent ${{ \mathcal L }}_{{ij}}$ and the fact that the stellar kinematics are determined by all of the absorption features in the MaNGA spectra, we adopt a simple correction for the stellar velocity dispersion derived from the average difference in the pre-pixelized MaNGA and MILES resolution over the fitted spectral range. The corrected velocity dispersion of the stars is therefore:

$$\begin{eqnarray}&&{\sigma }_{* }=\sqrt{{\sigma }_{* ,\mathrm{obs}}^{2}-\langle {\omega }_{\mathrm{PRE}}^{2}-{\omega }_{\mathrm{MILES}}^{2}{\rangle }_{\lambda }},\end{eqnarray} \tag{ 4 }$$

where σ_*,obs is the velocity dispersion of ${{ \mathcal L }}_{{ij}}$, ω_MILES is the pre-pixelized instrumental dispersion of the MILES spectra, and the average quadrature difference in the instrumental dispersion ($\langle {\omega }_{\mathrm{PRE}}^{2}-{\omega }_{\mathrm{MILES}}^{2}{\rangle }_{\lambda }$) is computed over the fitted wavelength range. This approach is shown to be sufficiently accurate for our purposes (Figure 17 from Westfall et al. 2019, see also Section 6.2).

Since DR15 we have made a few key improvements to the DAP compared to the algorithms described by Westfall et al. (2019) and Belfiore et al. (2019). Here we update this information briefly before discussing the reliability of the velocity-dispersion measurements in Section 4.3.

4.2.1. Updated Stellar-continuum Templates during Emission-line Modeling

4.2.2. Updated Line List and Tied Parameters

Using a combination of idealized recovery simulations and analysis of repeat observations (i.e., galaxies observed on more than one plate and processed into independent data cubes), in Westfall et al. (2019, Section 7.5) and Belfiore et al. (2019, Section 3) we explored the precision and accuracy of the observed line width measurements σ₀ for the stars and emission lines, respectively. Specifically, we found that the formal uncertainties ε₀ reported by the DAP²⁶ were generally reliable based on comparison with repeated observations, albeit somewhat underestimated at S/N > 100 due to small uncertainties in the astrometric registration of individual MaNGA exposures (see discussion by Belfiore et al. 2019).

However, neither Westfall et al. (2019) nor Belfiore et al. (2019) explored the propagation of these uncertainties in the observed line widths (along with uncertainties in the estimated spectral LSF) to the effective uncertainties in the underlying astrophysical LOSVD. Here, we explore the influence of the LSF measurements on the accuracy of the emission-line and absorption-line velocity dispersions, and specifically target the accuracy of astrophysical measurements of the LOSVD σ_Hα (Equation (3)) and σ_* (Equation (4)). The uncertainty ε_rec of these astrophysical widths will be a strong function of both the total S/N and the astrophysical width itself (as measurements will become less reliable far below the instrumental resolution).

In Figure 14, we plot the error in the observed velocity dispersion as a function of the S/N for both the Hα line and the stellar continuum. For the Hα line, there is a very tight correlation between the fractional error and the S/N—i.e., ε₀ ∝ σ₀(S/N)⁻¹—as expected when fitting a Gaussian line profile. The distribution for σ_* is more complicated because ε₀ becomes increasingly independent of σ₀ as σ₀ becomes small relative to the instrumental resolution; this effect is illustrated by analysis of both idealized simulations and repeat observations by Westfall et al. (2019, Figures 19 and 20).

Zoom In Zoom Out Reset image size

We use the tight relationship between the fractional error in ε₀/σ₀ and S/N for the emission lines to explore the precision and accuracy of the astrophysical measurements of σ_Hα using a series of Monte Carlo simulations. The input for each simulation is the astrophysical LOSVD σ_Hα (for which we adopt a grid from 1 to 100 km s⁻¹ stepped every 1 km s⁻¹), the emission-line S/N (for which we adopt a range from S/N = 5–100), the instrumental LSF ${\omega }_{\mathrm{PRE}}$ (which, for simplicity, we fix to be 67.6 km s⁻¹, the median at the wavelength of Hα for the MPL-10 sample), the fractional error in the observed line width ε₀/σ₀ at a given S/N from the relation shown in Figure 14, and an estimated 3% statistical uncertainty in the LSF (see Section 6.3). For each combination of σ_Hα and S/N, we draw 10⁵ samples from the error distributions²⁷ for both σ₀ and ω_PRE, and compute the mean (σ_rec) and rms (ε_rec) of the 10⁵ astrophysical velocity dispersions recovered following Equation (3).

The stellar velocity dispersions are significantly more complicated to model in detail as they are derived from a simultaneous fit across a wide range of different wavelengths. However, we obtain a rough estimate of their reliability by performing a similar series of Monte Carlo simulations using ω_PRE = 74 km s⁻¹ (i.e., an average value throughout the wavelength range of interest), combined with the observed error distribution in the observed stellar line widths.

As illustrated by Figure 15, the recovered line widths are most reliable at high S/N and high intrinsic astrophysical velocity dispersions, and the effective errors ε_rec in the recovered line width increase dramatically toward lower S/N. In addition, below the instrumental resolution, we note a systematic positive bias in the recovered velocity dispersions whose strength increases toward lower S/N and lower σ_Hα or σ_*. This expected behavior arises because of the asymmetric error distribution; namely, data points whose measured line widths (after application of mock measurement errors) are less than the instrumental line width produce imaginary astrophysical widths following Equations (3) or (4) and are thus preferentially lost from the sample.

Zoom In Zoom Out Reset image size

In a per-spectrum sense, Figure 15 can be interpreted as giving the S/N cut required in order for the measurements to reach a given accuracy. In order to obtain velocity dispersions at σ_Hα = 20 km s⁻¹ for which all data points have less than 1 km s⁻¹ systematic error, for instance, the spaxel sample must be restricted to those with Hα S/N > 50, for which the typical statistical uncertainty ε_rec will be about 5 km s⁻¹. Although more stringent cuts in S/N would produce samples with less systematic bias, the gain in such cases must be weighed against the dramatically decreased sample size at larger S/N thresholds.

We note that similar analyses have been performed for both the SAMI and CALIFA surveys, for which qualitatively similar trends are observed. Falcón-Barroso et al. (2017), for instance, note that the recovered stellar velocity dispersions in CALIFA are systematically larger than expected below σ_* = 40 km s⁻¹, at which point the random typical uncertainty in individual measurements is about 20%. Likewise, Fogarty et al. (2015) and van de Sande et al. (2017) find that systematic uncertainties in the instrumental resolution dominate the SAMI error budget for stellar velocity dispersions below σ_* = 35 km s⁻¹ and recommend a variety of quality cuts in both S/N and σ_* accordingly.

In Belfiore et al. (2019, see their Figure 21) we noted that the astrophysical velocity dispersions computed from a variety of nebular emission lines were broadly consistent with those estimated using Hα. In Figure 16 we repeat this exercise for the MPL-10 data products and plot LOSVD ratios as a function of σ_Hα for all star-forming spaxels²⁸ in which both emission line are detected with S/N > 50. Given the large wavelength difference between [O II] and Hα, we additionally restrict [O II] observations to those with a Balmer decrement indicative of minimal dust attenuation (f_Hα/f_Hβ < 3.5).

Zoom In Zoom Out Reset image size

We find that [O II], Hβ, [O III], [N II], and [S II] velocity dispersions all match σ_Hα to within a few percent, suggesting that there are no significant wavelength-dependent errors in the MaNGA LSF compared to the performance around Hα. Indeed, for σ_Hα > 30 km s⁻¹, the small offsets that we see between the dispersions of different ions may be genuinely astrophysical in origin as the relative offset appears to be correlated with the ionization energy. The S⁺ ion for instance has an ionization energy of 10.4 eV, and median σ_{[S II]}/σ_Hα = 0.989, while the H⁺ and O⁺ ions (both with 13.6 eV ionization energy) have median σ_Hβ/σ_Hα = 1.004 and σ_{[O II]}/σ_Hα = 1.014, respectively. Likewise, the N⁺ and O⁺⁺ ions have ionization energies of 14.5 and 35.2 eV, respectively, and median σ_{[N II]}/σ_Hα = 1.027 and σ_{[O III]}/σ_Hα = 1.038.

We note, however, that all four lines except [O III] show a ∼10% turnup in their velocity dispersion relative to Hα at the lowest values of σ_Hα ∼ 20 km s⁻¹. If this were due to a systematic error in the LSF, it would imply a ∼0.8% offset relative to Hα. However, this appears implausible given the small separation between Hα and [N II] in wavelength, and the well-sampled, well-behaved LSF in this range (see, e.g., Figure 9). Likewise, interpolation of the positivity bias from Figure 15 due to the differential S/N of Hα and the other emission lines suggests that this could account for at most a 1% deviation rather than the 10% observed.

The few-percent trends visible in Figure 16 may therefore be telling us more about the ionization structure of H II regions in the MaNGA galaxy sample rather than any low-level, systematic, and wavelength-dependent uncertainty in the spectral LSF of the instrument. Indeed, as we demonstrate in a forthcoming contribution (Law et al. 2020), typical gas-phase velocity dispersions can vary substantially depending on the selection method since these kinematics are strongly correlated with the ionization mechanism as traced by line ratios such as [N II]/Hα, [S II]/Hα, and [O III]/Hβ.

As a part of the MaStar stellar library program, we observed six bright stars (HD 284248, HD 37828, NGC 2682 108, NGC 6838 1009, HD 23924, and [W71b] 008-03) that had previously been observed at higher spectral resolution by X-Shooter. Since these stars have visual magnitudes g = 6–13 that are significantly brighter than typical MaNGA/MaStar targets, observations were made using custom 10–250 s exposures instead of the usual 900 s exposures. Since night skylines are too faint to be observed reliably in such short exposures, the DRP skips the skyline adjustment step (Section 3.3) for these observations and relies entirely upon the arc-lamp LSF solution.

We compared the final 1D spectra of these six stars produced by the DRP to high-resolution template spectra drawn from the X-Shooter Spectral Library (XSL; Chen et al. 2014). Spectra for HD 284248 and HD 37828 were taken from XSL DR1 (Chen et al. 2014) and have been processed with a unified resolution of R = 7000 across the wavelength range λ = 3000–10185 Å, while the remaining four stars were taken from XSL DR2 (Gonneau et al. 2020) and have spectral resolution R = 9793/11573 in the MaNGA blue/red wavelength ranges, respectively. After converting the X-Shooter templates to the MaStar vacuum rest-frame wavelength solution and rebinning them to a constant pixel size of 30 km s⁻¹, we broke the spectra into 200–400 Å windows stepped every 100 Å and measured the effective spectral resolution based on a convolution of the high-resolution templates. After rejecting wavelength regions for which the MaStar and X-Shooter spectra do not match each other well (e.g., due to differences in the correction from telluric absorption bands), we plot the X-Shooter-derived LSF of the MaStar spectra against the DRP estimates in Figure 18.

Zoom In Zoom Out Reset image size

As indicated by Figure 18, the effective spectral LSF derived from the X-Shooter spectra is generally in excellent agreement with the DRP-estimated LSF throughout the entire wavelength range. Although there are small systematic deviations for some of the stars (e.g., 12185–3703), these are generally within the uncertainty of the convolution technique given calibration differences between the spectra.

While Section 6.1 qualitatively suggested that the MaNGA LSF estimate was reasonable in the case of a single object with extant high-resolution data, the MaSTAR stellar spectral library provides an opportunity to test the pipeline-estimated LSF in a statistical manner as well. Barring unusual broadening due to stellar rotation and atmospheric features, the observed absorption-line width in a given MaSTAR spectrum should be similar to other stars of similar spectral type. Hence, comparing these MaSTAR spectra to those from a spectral template set with an established LSF we can test the robustness of the MaNGA LSF measurements.

For this test we conduct full-spectrum fitting of a large sample of MaSTAR spectra using the pPXF algorithm (Cappellari 2017) and the MILES-HC spectral template set (see Section 4.1, and Section 5 of Westfall et al. 2019). Since the LSF of the MILES stellar library is both well studied (ω_MILES = 2.54 Å FWHM; Beifiori et al. 2011) and has slightly higher resolution than MaSTAR, a strong test of the accuracy of the MaNGA LSF estimate can be provided by comparing the broadening required to reproduce the MaSTAR spectra using the MILES-HC templates:

$$\begin{eqnarray}&&A=\sqrt{{\omega }_{\mathrm{Fit}}^{2}-{\omega }_{\mathrm{MILES}}^{2}}\end{eqnarray} \tag{ 5 }$$

against the expected broadening factor based on ω_MILES and the pipeline-reported LSF ω_PRE:

$$\begin{eqnarray}&&B=\sqrt{{\omega }_{\mathrm{PRE}}^{2}-{\omega }_{\mathrm{MILES}}^{2}}.\end{eqnarray} \tag{ 6 }$$

In this test we compute A for a random sample of 5000 spectra from the MaSTAR sample of "Good Visit" spectra, which are single-visit observed spectra without extinction issues, having a median S/N per pixel greater than 15 and that pass a visual inspection for other quality problems (Yan et al. 2019). Due to the limited wavelength coverage of the MILES stellar library (and hence the MILES-HC templates), for this test we fit the MaSTAR spectra within a wavelength range of 3620–7400 Å. The full-spectrum fit is conducted using eight additive and multiplicative polynomials in order to account for issues of flux-calibration errors, reddening, template mismatch, etc. (see, e.g., Westfall et al. 2019).

Defining ${\omega }_{\mathrm{Fit}}={\omega }_{\mathrm{PRE}}(1+\delta )$ for some small δ, we can then write

$$\begin{eqnarray}&&\displaystyle \frac{{A}^{2}}{{B}^{2}}=\displaystyle \frac{{\omega }_{\mathrm{PRE}}^{2}{(1+\delta )}^{2}-{\omega }_{\mathrm{MILES}}^{2}}{{\omega }_{\mathrm{PRE}}^{2}-{\omega }_{\mathrm{MILES}}^{2}}.\end{eqnarray} \tag{ 7 }$$

Dropping terms ${ \mathcal O }({\delta }^{2})$, we can solve Equation (7) for δ and find

$$\begin{eqnarray}&&\delta =\displaystyle \frac{{\omega }_{\mathrm{PRE}}^{2}-{\omega }_{\mathrm{MILES}}^{2}}{2{\omega }_{\mathrm{PRE}}^{2}}\left(\displaystyle \frac{{A}^{2}}{{B}^{2}}-1\right).\end{eqnarray} \tag{ 8 }$$

In Figure 19, we show the distribution of ${\omega }_{\mathrm{PRE}}{/\omega }_{\mathrm{Fit}}=\tfrac{1}{1+\delta }$ for the 5000 MaSTAR spectra in our sample. For MPL-9, we find that the distribution has a sigma-clipped mean of 0.97 and 1σ width of 0.05; i.e., suggesting that the the MPL-9 LSF is underestimated by about 3%. In contrast, for MPL-10, the distribution has a sigma-clipped mean of 0.99 and a 1σ width of 0.04, indicating that both the scatter of the distribution has decreased and the overall agreement between the pipeline and MILES estimates has improved to within 1%.³² This result is broadly consistent with Figure 13, which found that the MPL-9 LSF estimate was ∼2%–3% narrower than the MPL-10 estimate in the wavelength range covered by the MILES library.

Zoom In Zoom Out Reset image size

We note a few important caveats to this result however. First, the stellar absorption-line kinematics are the product of a convolution across a wide range of wavelengths across which the MaNGA LSF varies substantially. As such, the actual accuracy of the pipeline LSF at a given wavelength may be better or worse than 1%, depending on the effective weight of that wavelength range in driving the stellar population model fit. Likewise, our result is predicated upon the assumption that the MILES spectral resolution itself has <1% systematic error (statistical uncertainties are known to be ∼3%, see Falcón-Barroso et al. 2011), and that there are negligible systematic differences due to template mismatch between MILES-HC and the MaSTAR sample.

Perhaps the strongest possible test of the MaNGA LSF model for emission-line kinematics is to compare the derived galaxy-resolved velocity-dispersion profile σ_Hα in the face of LSF variations, beam smearing, and other factors against prior observations of the same galaxies from higher-resolution IFU observations. We therefore compared the MaNGA data against Hα observations³³ from the DiskMass survey (Bershady et al. 2010a, 2010b; Westfall et al. 2011, 2014; Martinsson et al. 2013), which used the SparsePak IFU (Bershady et al. 2004, 2005) on the 3.5 m WIYN telescope to obtain R ∼ 10,000 (σ_inst = 12.7 km s⁻¹) fiber spectroscopy of 176 spiral galaxies oriented nearly face-on to the line of sight. SparsePak fibers have 47 diameters. As of MPL-10, MaNGA has observed seven galaxies in common with DiskMass (see Table 4), which can be identified via targeting bit 2¹⁶ in the ancillary target flag MANGA_TARGET3.

We compare the MaNGA and DiskMass samples by extracting kinematic data for all good-quality spaxels with S/N > 50 in the common region of overlap 4'' < r < 15''. This radial cut is designed to exclude the central regions of the galaxies for which beam smearing is most significant and for which at least one galaxy (UGC 4368) exhibits Seyfert-I type AGN contributions to the Hα emission. In Figure 20 we plot a histogram³⁴ of the raw DiskMass and MaNGA measurements (i.e., uncorrected for beam smearing) for both MPL-9 and MPL-10. As illustrated in the left-hand panel, MPL-9 is appreciably biased with respect to the DiskMass data, peaking at 23.3 km s⁻¹ instead of 16.7 km s⁻¹, indicative of a 2.9% systematic underestimate in the LSF. In contrast, the MPL-10 histogram peaks at 18.2 km s⁻¹, matching the DiskMass data to within a 0.6% systematic error in the LSF around Hα. If we account for the expected positivity bias in the MaNGA observations from Figure 15, this agreement improves further to about 17.4 km s⁻¹, or about 0.3% systematic error in the LSF. Similarly, this level of agreement is largely insensitive to whether or not we apply a beam smearing correction to the MaNGA data; following the method described in Section 5, the corrected MPL-10 data matches the DiskMass observations to within 0.3%, and we obtain a comparable result if we instead estimate the beam smearing correction using a Bayesian forward model of a disk-like rotation curve.

Zoom In Zoom Out Reset image size

We can also use the relative widths of the DiskMass and MaNGA MPL-10 distributions to assess the statistical error in individual estimates of the LSF. Assuming that the DiskMass histogram represents the true astrophysical range of σ_Hα³⁵ , we construct a Monte Carlo simulation with line width values drawn from the DiskMass distribution and convolve them with our median LSF of 68.5 km s⁻¹ to create a mock set of observations. We then perturb these values by random errors combining the DAP-reported uncertainties in individual measurements (accounting for the plateau at high S/N discussed in Section 4.3) and some statistical uncertainty in the LSF. After subtracting the LSF from these perturbed values in quadrature, we compare the width of the simulated distribution to the MPL-10 observations. This exercise suggests that the statistical uncertainty in the LSF around Hα for a given spaxel is about 2%, corresponding to 1.4 km s⁻¹ (i.e., comparable to the uncertainty in the measured line widths at high S/N).

As a final consistency check, we additionally compare the MaNGA data against similar observations obtained by the SAMI survey (Bryant et al. 2015) using the Sydney-AAO integral field spectrograph (Croom et al. 2012) on the Anglo-Australian Telescope. While SAMI has a similar spectral resolution to MaNGA in its blue arm, around Hα, SAMI has a spectral resolution R ∼ 4300 delivering a 1σ LSF ω_SAMI = 30 km s⁻¹.

In MPL-10 we find that there are 74 targets observed in common between MaNGA and SAMI DR2 (Scott et al. 2018), and we select the 23 that have been observed with MaNGA's largest IFU bundle size (12 of which have significant Hα emission) for comparison. For each of these 12 galaxies, we extract the DAP kinematic measurements for all good-quality spaxels with S/N > 50 in the common radial range 3'' < r < 75, where the upper boundary is set by the size of the SAMI field coverage. Similarly, we extract all of the Hα kinematic measurements for these same galaxies provided by the SAMI DR2 public data products, introducing a limiting flux cut of 2 × 10⁻¹⁷ erg s⁻¹ cm⁻² Å⁻¹ spaxel⁻¹, which visual inspection suggests selects a nearly identical range of spaxels for SAMI as the S/N > 50 cut does for MaNGA.

As we demonstrate in Figure 21 (top panels), despite the 2.3x higher spectral resolution of SAMI, the MaNGA MPL-10 Hα velocity dispersions are in excellent agreement with the values provided by SAMI DR2, with the centroids of the respective histograms matching each other to within 0.7 km s⁻¹. As expected, the MPL-9 velocity dispersions are, in contrast, systematically too large by about 7 km s⁻¹, consistent with our comparison against the DiskMass observations.

Zoom In Zoom Out Reset image size

In addition to the statistical agreement between the MaNGA MPL-10 and SAMI DR2 velocity dispersions, we note also the excellent agreement in terms of the resolved spatial structures. In Figure 21 (bottom panels), we show an illustrative example of the Hα flux, velocity, and velocity-dispersion maps produced independently by the two surveys. The level of agreement between the two is exquisite, with even small and apparently insignificant features in the dispersion map appearing nearly identically in both sets of observations.