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Resolved and Integrated Stellar Masses in the SDSS-IV/MaNGA Survey, Paper I: PCA spectral fitting & stellar mass-to-light ratio estimates

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A six-number spectral basis recovers stellar mass-to-light ratios to about 0.1 dex, and the paper uses it to map 1,773 MaNGA galaxies.

desk verdict Solid methods paper with a real product; the reliability claim is well-tested inside one SPS library but the absolute scale awaits Paper II. read the letter →

arxiv 1908.02330 v1 pith:QUQNHKGB submitted 2019-08-06 astro-ph.GA astro-ph.IM

Zachary J. Pace , Christy Tremonti , Yanmei Chen , Adam L. Schaefer , Matthew A. Bershady , Kyle B. Westfall , Joel Brownstein , Niv Drory
show 4 more authors
Mederic Boquien Kate Rowlands Brett Andrews David Wake
This is my paper · ORCID
classification astro-ph.GAastro-ph.IM
keywords spectralfittingprincipalcomponentanalysisstellarmass-to-lightratioMaNGAintegral-fieldspectroscopypopulationsynthesisresolvedmassBayesianposterior
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that an optical galaxy spectrum can be compressed to six numbers --- its amplitudes on six principal-component vectors learned from 40,000 synthetic spectra --- without losing what is needed to estimate stellar mass-to-light ratio. Fitting each MaNGA spaxel in that six-dimensional space and weighting the training models by likelihood gives resolved estimates of $\log \Upsilon_i^*$. On held-out mock spectra with known values, median deviations are about 0.05--0.1 dex over the signal-to-noise range of most MaNGA spaxels, and the reported uncertainties track the actual scatter. If this transfers to real galaxies, the resolved mass-to-light maps for the 1,773 MPL-8 galaxies become usable for stellar-mass science at that accuracy.

What carries the argument

The load-bearing object is the six-dimensional principal-component basis $\mathbf{E}$ built from 40,000 synthetic composite stellar-population spectra: 4,000 star formation histories, each subsampled ten times in stellar velocity dispersion, dust optical depth, and related parameters. An observed spectrum is median-normalized, de-redshifted, emission-line masked, and projected onto the six eigenspectra; each training model is then compared with the observation by Mahalanobis distance in PC space using a total covariance that combines PCA reconstruction residuals, MaNGA spectrophotometric covariance, and pixel noise. The resulting likelihoods weight the training models, producing a posterior PDF whose 16th, 50th, and 84th percentiles are the quoted mass-to-light estimates and uncertainties.

What would settle it

Fit the same set of MaNGA spaxels with an independent full-spectral-fitting code that uses an empirical stellar library, bin the recovered values of $\log \Upsilon_i^*$ by stellar metallicity and $D_n4000$, and check the median offset against the quoted uncertainties; a median offset larger than those uncertainties would show that the mock-based accuracy claim does not extend to real data.

Watch

Extended reading notes

Core claim

The central claim is that resolved stellar mass-to-light ratio can be recovered from optical spectra alone, and more accurately than from color-based calibrations, by projecting each spectrum onto six PCA eigenspectra and forming a posterior PDF over the training models. In tests on synthetic spectra generated identically to the training library but held out from it, the median offset between inferred and true $\log \Upsilon_i^*$ is typically $\sim 0.05$ dex at signal-to-noise above 10, and the normalized deviation $\Delta\log\Upsilon_i^*/\sigma_{\log\Upsilon_i^*}$ is consistent with a unit-Gaussian distribution, which the authors take as evidence that both the estimates and their uncertainties are reliable across a range of signal-to-noise ratios, stellar metallicities, and dust attenuation conditions. The same training library shows that color--mass-to-light relations carry intrinsic scatter of about 0.1 dex even at infinite signal-to-noise and systematics of 0.2--0.4 dex in low-metallicity or heavily attenuated cases, which motivates the use of the full spectral shape.

Load-bearing premise

All training and validation spectra are generated from the same theoretical stellar library with solar alpha-element abundances, so if that library misrepresents real stellar populations, the roughly 0.1 dex accuracy measured on mock spectra will not transfer to actual MaNGA galaxies.

Editorial extensions

If this is right

  • Resolved stellar mass surface-density maps can be built for thousands of MaNGA galaxies without spatial binning, enabling spaxel-by-spaxel mass gradients and dynamical comparisons.
  • Because posterior widths are provided, downstream studies can carry the 16th--84th percentile range as a real error budget instead of assuming a fixed 0.1 dex floor.
  • The six-dimensional projection is fast enough to fit all spaxels in a datacube at once, so the same machinery can scale to the full 10,000-galaxy MaNGA sample and to comparable integral-field surveys.
  • The comparison with color--mass-to-light relations implies that even a six-number spectral summary captures information that colors cannot, especially for low-metallicity and dusty populations.
  • Aperture-corrected total stellar masses built from these maps can be checked against integrated photometric masses and dynamical masses, which the companion paper carries out.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the validation mocks come from the same synthetic stellar library used for training, their agreement mostly demonstrates internal consistency; a stronger external test would fit the same galaxies with an independent empirical-library full-spectral fit and look for offsets correlated with stellar metallicity.
  • Editorial inference: the paper itself reports an H$\\delta$ absorption offset at high $D_n4000$ and notes that alpha-element enhancement is not modeled, so the brightest central spaxels of early-type galaxies are the most plausible places where the claimed accuracy degrades.
  • Editorial inference: training separate PC bases for sub-populations --- for example, alpha-enhanced or higher-redshift spectra --- would test whether a single basis is the source of the residual deviations.
  • Editorial inference: the method's speed makes it practical to embed in survey pipelines, producing mass-to-light maps while observations are still being taken.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper presents a PCA-based spectral fitting method for SDSS-IV/MaNGA integral-field spectra. A training library of ~40,000 synthetic spectra is built from 4,000 stochastically generated star formation histories, passed through FSPS with Padova 2008 isochrones and the C3K theoretical stellar library, and subsampled over dust attenuation and velocity dispersion. The first six principal components are used as a reduced basis; each observed spaxel is down-projected into this basis, and a likelihood-weighted posterior over training models yields resolved estimates of the i-band stellar mass-to-light ratio with 16th–84th percentile uncertainties. The method is applied to 1,773 MPL-8 MaNGA galaxies, and the paper presents validation on held-out synthetic spectra across bins of signal-to-noise, color, metallicity, and attenuation, along with a planned Value-Added Catalog and public software.

Significance. If the method works as advertised, this is a useful contribution: it provides resolved stellar mass-to-light ratio maps for thousands of MaNGA galaxies, with a publicly released fitting code and a carefully documented noise model that includes MaNGA spectrophotometric covariance, masking tests, sky-residual checks, and model-count convergence tests. The held-out mock validation is thorough within its chosen forward model, and the normalized-deviation analysis is a genuine attempt to verify uncertainty calibration rather than simply report scatter. The main limitation, acknowledged by the authors, is that the validation is internal: the mocks are generated with the same SPS library, alpha-element assumption, and SFH prior as the training data, so the absolute accuracy against real stellar populations remains unconstrained. The planned comparison with DiskMass dynamical masses in Paper II is therefore a necessary external check, not an optional extra.

major comments (2)
  1. [§4.10, Appendix B, and §5.1] The mock validation is generated 'identically to the CSP training library' (Section 4.10) using the same FSPS+Padova 2008+C3K theoretical stellar library, solar alpha-element abundances, and the same SFH prior. This establishes internal self-consistency within one forward model, but it does not calibrate the dominant systematic, which the paper itself identifies in Section 5.1 as 'the most uncertain systematic in this work.' Section 3.2 and Figure 8 show an HδA offset between models and MaNGA spectra that grows with Dn4000 and is attributed to stellar models; since Dn4000 and HδA are age-sensitive, this mismatch could plausibly propagate into log Upsilon* at the 0.1 dex level for the oldest, alpha-enhanced populations. The abstract's unqualified statement that the mass-to-light estimates are 'reliable' should be restricted or reframed as reliability conditional on the adopted SPS prescription, with an explicit statement that alternate-library or external dynamical validation is required before the VAC values are used for absolute stellar mass calibration.
  2. [§4.10, Tables 6–11, Figures 28–29] The reliability claim is also stronger than the paper's own validation in several parameter-space corners. At low signal-to-noise and high stellar metallicity, Section 4.10 states that the deviation is 'not reflected in the associated uncertainties,' and Figure 28/Table 10 show a skewed distribution with overestimates reaching roughly 0.15–0.3 dex; Figure 29/Table 11 show similar behavior for high attenuation. The normalized-deviation distributions in Table 9 (e.g., P50(ΔY/σY) ≈ 0.7 for blue, low-S/N spectra) imply that the quoted posterior widths understate the true scatter in bins that include low-surface-brightness, dusty, or edge-on spaxels. The text should either add explicit caveats and data-quality flags for these regimes, or enlarge the quoted uncertainties (or both); as written, the abstract's claim that the estimates and their uncertainties are reliable overstates the support.
minor comments (6)
  1. [§3.2] The sentence beginning 'An attempt to replace HδA with the sum of HδA and HγA...' is a grammatical fragment and should be rewritten as a complete sentence.
  2. [§3.1.1] The definition of the burst number distribution contains a malformed expression '0.5×(t0−min({tt),tf orm}))/t0' with mismatched braces and a typo; please rewrite it in unambiguous notation.
  3. [§4.9] The text refers to 'Appendix 4.7.1' and 'Appendix 4.8.1,' but these are sections, not appendices; please correct the cross-references.
  4. [Table 4] The row for C(Z) lists its dimension as '((p))' with no row dimension, and the description of the regression coefficients is unclear; please clarify whether C is a vector or a matrix.
  5. [§4.5, step 4] The emission-line mask width is described as '1.5 times the line-width (velocity dispersion),' but the units of the line-width are not specified; please state whether the mask offset is in velocity or wavelength units.
  6. [Appendix B] The first sentence of Appendix B says the procedure is 'as described in Appendix B,' which is self-referential; it should refer to Section 4.10 or to the list that follows.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: mock validation is self-consistent within the adopted SPS model, and the paper explicitly flags the synthetic stellar library as the dominant systematic.

full rationale

The paper's central claim is that PCA-based posterior PDFs for log Upsilon* recover true values on held-out synthetic spectra with typical deviations of about 0.05-0.1 dex and with calibrated uncertainties. I examined the derivation chain for circular reductions. The method constructs eigenspectra from a synthetic composite-stellar-population library, projects observed spectra onto them, and weights library models by likelihood (Equations 12-13); the Upsilon* estimate is a percentile of the posterior formed from known library values. The validation mocks are 'generated identically to the CSP training library' (Section 4.10) and therefore test self-consistency within the FSPS + Padova 2008 + C3K forward model, not the absolute fidelity of that model to real stellar populations. This is a real limitation, and the paper explicitly acknowledges it: 'The use of a synthetic stellar library represents the most uncertain systematic in this work' (Section 5.1). However, recovering a known input value from a held-out spectrum is not an equation-level identity: the estimate is obtained by likelihood weighting and is not equal to the truth by construction. No fitted parameter is renamed as a prediction; the SFH prior is data-tuned to reproduce the Dn4000-Hdelta distribution of MaNGA spaxels, but the validation does not use observed masses as inputs and the claimed reliability is explicitly conditional on the model library. The method follows Chen et al. (2012), a self-citation by overlapping authors, but the present paper re-derives the PCA system, recomputes the spectrophotometric covariance for MaNGA, and independently tests the method; the citation is methodological context rather than load-bearing evidence for the central reliability claim. Thus no circular step meeting the quoted-evidence standard is present; the main caveat is a model-fidelity systematic, not a circularity.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the fidelity of the synthetic library and the choice of SFH priors. There are no fitted constants in the final mass-to-light estimator; instead, the method propagates the library's assumptions through a likelihood-weighted average. The most consequential assumptions are (1) C3K/Padova/FSPS model correctness, (2) non-evolving metallicity, (3) the Charlot-Fall dust model, and (4) the data-tuned SFH prior. The regularization and q=6 choice are internal tuning parameters of the PCA system.

free parameters (6)
  • SFH prior hyperparameters (tform, EFTU, burst rate, transition probability) = tform ~ N(5,4) Gyr; EFTU ~ logN(0.4,0.4); p_transition=0.25; mean burst rate 0.256 per SFH
    Chosen to match the Dn4000-HdeltaA distribution of MaNGA spectra (Section 3.2); these priors shape the posterior PDF for log Upsilon*_i and thus the mass-to-light estimate.
  • Stellar metallicity prior = 80% linear-uniform, 20% log-uniform over [Z]
    Tuned to approximate the SDSS MPA-JHU gas-phase oxygen abundance distribution (Section 3.1.2, Figure 7); affects which library templates get weight.
  • Dust attenuation prior = tauV*mu ~ N(0.4,0.2), mu ~ N(0.3,0.2), truncated
    Chosen to roughly match Charlot & Fall (2000) and Brinchmann et al. (2004); attenuation changes the effective mass-to-light ratio and the CMLR scatter.
  • Blue horizontal branch and blue straggler frequency priors = fBHB ~ Beta(2,7); SBSS ~ 10*Beta(1,4)
    Adopted permissive priors because these populations are poorly constrained (Section 3.1.2); they can shift log Upsilon* by ~0.1 dex for intermediate-age populations.
  • Number of retained principal components q = 6
    Selected via broken-stick criterion (Section 4.2); fixes the dimensionality of the fit and hence the size of the theoretical residual covariance Kth.
  • Regularization strength alpha = ~1e-3
    Added to the main diagonal of Kobs to maintain a minimum KPC dispersion at high S/N (Section 4.7); tuning this changes the covariance and thus the PDF widths.
assumptions (7)
  • domain assumption C3K theoretical stellar library accurately represents stellar spectra over the MaNGA wavelength range and the age/metallicity range of MaNGA galaxies.
    Invoked in Section 3 to generate all training and test spectra; the authors note in Section 5.1 it is the most uncertain systematic, with solar alpha abundance fixed.
  • domain assumption FSPS with Padova 2008 isochrones and Kroupa IMF gives correct stellar masses and luminosities for real stellar populations.
    Basis of the mass-to-light ratios in the training library; errors in isochrones or IMF normalization translate directly into Upsilon* offsets.
  • domain assumption Non-evolving stellar metallicity is sufficient to model the relevant stellar populations.
    Adopted in Section 3.1.2 citing Gallazzi & Bell (2009); real galaxies have metallicity histories, and this simplification is not tested against external data.
  • domain assumption The randomized SFH prescription (delayed-tau with bursts, cutoffs, rejuvenation) spans the real SFH diversity of MaNGA spaxels.
    Required for the PCA basis and the posterior PDF to be well-populated; the paper checks Dn4000-HdeltaA and MWA distributions but notes a younger mode than observed MWA distributions.
  • domain assumption Two-component Charlot & Fall (2000) dust model approximates attenuation in MaNGA spaxels.
    Used to redden all model spectra; deviations from this dust law can change effective mass-to-light ratios in a way the paper shows is not parallel to CMLRs.
  • domain assumption Kobs from multiply-observed MaNGA galaxies characterizes spectrophotometric covariance for all spaxels.
    Computed in Section 4.4 and used in KPC; if the covariance is misestimated, the likelihood weights and uncertainties change.
  • ad hoc to paper Regularization alpha = 1e-3 is a small perturbation that does not bias results.
    Introduced in Section 4.7 as a 'softening parameter' to maintain a minimum dispersion at high S/N; its value is not derived from data.

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Cite this review

Pith. "Pith review of Resolved and Integrated Stellar Masses in the SDSS-IV/MaNGA Survey, Paper I: PCA spectral fitting & stellar mass-to-light ratio estimates." pith.science (2026). https://pith.science/paper/QUQNHKGB

@misc{pith2026190802330,
  author       = {Pith},
  title        = {Pith review of: Resolved and Integrated Stellar Masses in the SDSS-IV/MaNGA Survey, Paper I: PCA spectral fitting & stellar mass-to-light ratio estimates},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QUQNHKGB}},
  note         = {Machine review of arXiv:1908.02330}
}
abstract

We present a method of fitting optical spectra of galaxies using a basis set of six vectors obtained from principal component analysis (PCA) of a library of synthetic spectra of 40000 star formation histories (SFHs). Using this library, we provide estimates of resolved effective stellar mass-to-light ratio ($\log \Upsilon^*$) for thousands of galaxies from the SDSS-IV/MaNGA integral-field spectroscopic survey. Using a testing framework built on additional synthetic SFHs, we show that the estimates of stellar mass-to-light ratio are reliable (as are their uncertainties) at a variety of signal-to-noise ratios, stellar metallicities, and dust attenuation conditions. Finally, we describe the future release of the resolved stellar mass-to-light ratios as a SDSS-IV/MaNGA Value-Added Catalog (VAC) and provide a link to the software used to conduct this analysis.

Figures

Figures reproduced from arXiv: 1908.02330 by the authors.

Figure 1
Figure 1. The distributions of median spectral signal-to￾noise ratio for all MaNGA spaxels (blue) and those spax￾els for which none of the MaNGA DRP data-quality flags indicate potential problems with the estimates obtained in this work (orange)—see Section 4.9 for descriptions of data￾quality diagnostics, and how channel-specific quality flags inform reliability of mass-to-light ratio estimates. In order to generate the eige… view at source ↗
Figure 2
Figure 2. The distributions of the inputs provided to FSPS described in more detail in Section 3.1.1, left to right and top to bottom: formation time, e-folding time, transition time, transition strength, transition slope, number of bursts, stellar metallicity, stellar velocity dispersion, attenuation, specific frequency of blue straggler stars, and fraction of blue horizontal branch stars. There is no covariance between thes… view at source ↗
Figure 3
Figure 3. The distributions of five absorption indices in our synthetic training data: Dn4000, HδA, HγA, Mgb, and Fe5270. zero in the domain 0 < θ ≤ π 6 . If pt dictates there is no burst, θ is set to zero, but does not impact the SPS because tt is set to the age of the universe. • Cutoff slope is an arctan-re-parametrization of θ, scaled in units of the maximum of a pure delayed￾τ model Φmax per Gyr. Therefore, γ = 0 corre￾s… view at source ↗
Figures from the paper (27 more)
Figure 4
Figure 4. Figure 4: The distributions of eight derived parameters which are secondarily obtained from the SPS, using the distributions of inputs shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Ten sample SFHs generated using the random prescription given in Section 3 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: The distribution of the log of mass-weighted mean stellar age for all of the template SFHs. As in Gallazzi et al. (2008), the distribution has a broad peak around log MWA ∼ 9.8. Unlike Gallazzi et al. (2008), though, the distribution extends with significant power belo…
Figure 7
Figure 7. Figure 7: Comparison of the solar-normalized oxygen abun￾dance ([ O H ]) inferred from SDSS nebular emission (green) with the adopted metallicity prior. An offset of approxi￾mately -.29 dex is applied to re-scale the SFH library’s metal￾licity range ([Z], based on mass) to the n…
Figure 8
Figure 8. Figure 8: The distribution of the training models in Dn4000-HδA space (separated by stellar metallicity: super-solar metallicity in blue contours, slightly sub-solar in orange contours, and very sub-solar in green contours); plus data points for individual models with composite …
Figure 9
Figure 9. Figure 9: Left-hand panel: effective i-band stellar mass-to-light ratios (in solar units) for model spectra generated above, plotted against rest-frame g − r color, and colored by stellar metallicity; in red, the CMLR obtained from a least-squares fit to the CSP library; in mage…
Figure 10
Figure 10. Figure 10: As [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: Top panel: the normalized mean spectrum of the training data. Panels 2–7: principal component vectors 1–6 of the training data. the root-mean-square (RMS) residual between the vali￾dation data and their PC representations. The inclusion of noise in the observed spectr…
Figure 12
Figure 12. Figure 12: In blue: training data variance described by each successive principal component; in black: the fractional variance expected from the broken-stick method (randomly￾apportioned variance) [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: In light blue, the dependence of RMS recon￾struction residual on the number of PCs retained. Recon￾struction is carried out on a sample of 4000 held-out (“val￾idation”) spectra. The black dashed line denotes an RMS reconstruction error of 2%. As in C12, we wish to dev…
Figure 14
Figure 14. Figure 14: Selected directly-modelled parameters (σ, log Z Z , τV , and τV µ) and derived parameters (log Υ∗ i , Dn4000, HδA, and log mass-weighted stellar age), versus principal component amplitudes. Each scatter-subplot plots the amplitude of the PC corresponding to its column…
Figure 15
Figure 15. Figure 15: MaNGA’s observational covariance matrix Kobs, which arises due to imperfect spectrophotometric flux￾calibration of MaNGA spectra. See [PITH_FULL_IMAGE:figures/full_fig_p020_15.png]
Figure 16
Figure 16. Figure 16: In blue, the RMS value of 10,000 noise vectors drawn from the BOSS covariance matrix; and in orange, the RMS value of 10,000 noise vectors drawn from the MaNGA covariance matrix [PITH_FULL_IMAGE:figures/full_fig_p020_16.png]
Figure 17
Figure 17. Figure 17: Each panel shows the difference in EW of Balmer absorption (left to right: Hα, Hβ, Hγ, Hδ) between the corrected and corrected-then-fit spectra: in the top row, “corrected” refers to flagged elements being replaced with the corresponding values in M (S0, equivalent to…
Figure 18
Figure 18. Figure 18: dEW = EWHβ abs(Ofit) − EWHβ abs(Otrue) versus (left to right) EWHβ abs(Otrue), median signal-to-noise ratio (SNR), and DAP equivalent width of the Hα, using the fiducial (top row) and the alternative (bottom row) strategies. Pixels are colored according to the logarit…
Figure 19
Figure 19. Figure 19: A comparison in the vicinity of the first five Balmer absorption lines (Hα, Hβ, Hγ, Hδ, and H) of the principal component basis set resulting from flag-and-replacement (blue) and no flag-and-replacement (black). The overall spectral shape is largely preserved, especi…
Figure 20
Figure 20. Figure 20: The standard diagnostic figure produced for the center spaxel (coordinates 37, 37) of MaNGA galaxy 8566-12705. Top-left frame: map of the galaxy’s i-band luminosity (the “hole” in the map signifies where data have been masked due to either a foreground star or data-qu…
Figure 21
Figure 21. Figure 21: In each subplot, the change in principle component amplitude dAi (ordinate axis) induced by sky residuals at a level RMSsky (color) relative to a normalized, observed spectrum, at some redshift (abscissa). At residual RMS below 10%, the effects on PC amplitudes are ge…
Figure 22
Figure 22. Figure 22: Variability in mass-to-light estimate (50th percentile of marginalized posterior PDF) associated with changing the number of models used to populate the distribution. Each color point represents a single spectrum with the specified number of models. At low signal-to-n…
Figure 23
Figure 23. Figure 23: The cumulative distribution of log ∆p σp for values of N between 101 and 106 , under the assumption of imperfect estimation of A. The model library used in this work has N = 40000, reliably within the locus of trials with low dp σp . by un-subtracted sky at the 10% (R…
Figure 24
Figure 24. Figure 24: Distributions of deviations of PCA-inferred stel￾lar mass-to-light ratio (∆ log Υ∗ i ), binned into vertical sub￾plots according to median signal-to-noise ratio, and then within each subplot according to g − r color. Stellar mass￾to-light ratio estimates become slight…
Figure 25
Figure 25. Figure 25: Distributions of uncertainty in PCA-inferred stellar mass-to-light ratio (σlog Υ∗ i ) for mock observations of synthetic spectra, binned into vertical subplots accord￾ing to median signal-to-noise ratio, and then within each subplot according to g − r color. The overa…
Figure 27
Figure 27. Figure 27: As [PITH_FULL_IMAGE:figures/full_fig_p035_27.png]
Figure 28
Figure 28. Figure 28: As [PITH_FULL_IMAGE:figures/full_fig_p037_28.png]
Figure 30
Figure 30. Figure 30: A selection of three early-type galaxies: In the left-hand column, the SDSS cutout with a purple hexagon denoting the approximate spatial grasp of the IFU. In the middle column, an image of the resolved estimate of i-band stellar mass-to￾light ratio, taken as the 50th…
Figure 31
Figure 31. Figure 31: As [PITH_FULL_IMAGE:figures/full_fig_p041_31.png]
Figure 32
Figure 32. Figure 32: Full diagnostic figure for synthetic data based on the test galaxy 8566-12705. Same format as [PITH_FULL_IMAGE:figures/full_fig_p046_32.png]

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