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arxiv: 2606.30129 · v1 · pith:6HU45VOAnew · submitted 2026-06-29 · 🌌 astro-ph.GA

The Impact of Non-Gaussian Line Spread Functions on Stellar Kinematic Recovery: Consequences for Dynamical Models

David A. Simon This is my paper

Pith reviewed 2026-06-30 04:55 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords stellar kinematicsline spread functionnon-Gaussian profilesintegral field spectroscopydynamical modelsGauss-Hermite momentsvelocity dispersion
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The pith

Non-Gaussian line spread functions introduce up to 7 percent uncertainty in stellar velocity dispersion even at 300 km/s.

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

The paper tests how real, non-Gaussian shapes of a spectrograph's line spread function affect the extraction of stellar velocities, dispersions, and higher-order moments from spectra. It shows that treating the LSF as Gaussian when it is not produces systematic offsets in the recovered kinematics. A practical method is presented for matching the LSF shape of template spectra to the observed target spectrum, which removes most of the bias. Accurate kinematics underpin dynamical mass models, so uncorrected LSF mismatch directly limits what can be learned about galaxy structure.

Core claim

Even in the high-dispersion regime of 300 km s^{-1}, non-Gaussian LSF profiles create up to 7 percent uncertainty in the recovered velocity dispersion and biases of up to ±0.1 in the Gauss-Hermite moments h3 and h4. A method that explicitly matches the LSF of the template spectra to the LSF of the target spectrum reduces the dispersion bias to less than 1 percent all the way down to the instrumental resolution limit.

What carries the argument

An LSF-matching procedure that adjusts template spectra so their effective line spread function matches the (possibly non-Gaussian) LSF of the target spectrum before kinematic fitting.

If this is right

  • Stellar kinematic maps from integral-field surveys carry previously unquantified systematic errors unless non-Gaussian LSF shapes are accounted for.
  • Higher-order Gauss-Hermite moments are more sensitive to LSF mismatch than the first two moments.
  • The matching technique allows kinematic recovery to remain reliable down to the native instrumental resolution.
  • Public code implementing the matching step makes the correction immediately usable on existing datasets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Many published velocity-dispersion maps may need re-reduction with LSF-matched templates before being used in dynamical models.
  • Reporting only the resolving power R is insufficient; full LSF profiles should become standard metadata for future instruments.
  • The same matching logic could be tested on emission-line or absorption-line fitting in other wavelength regimes.

Load-bearing premise

The particular mock spectra and non-Gaussian LSF shapes examined are representative of actual integral-field spectrograph data and do not hide extra systematics when the matching method is used.

What would settle it

Apply the LSF-matching method and the standard Gaussian assumption to the same set of real galaxy spectra that also have independent, high-resolution kinematic measurements; the two approaches should converge once matching is performed.

Figures

Figures reproduced from arXiv: 2606.30129 by David A. Simon.

Figure 2
Figure 2. Figure 2: — Sample of three LSF profiles taken from the SINFONI handbook (Hau 2017, [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: — Recovered pPXF σ with M = 2 for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spectrum is convolved with the winged LSF profile. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . The dispersion is always recovered to within 8 percent accuracy. 50 100 150 200 250 300 True Dispers… view at source ↗
Figure 6
Figure 6. Figure 6: — Recovered pPXF h3 for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spectrum is also convolved with the winged LSF profile. The MUSE instru￾mental dispersion is the dashed gray line at σ = 51.4 km s−1 . The true value is only recovered (within ±0.02) for h3 when σ is 100 km/s, twice the instrumental disper… view at source ↗
Figure 7
Figure 7. Figure 7: — Recovered pPXF h4 for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spec￾trum is also convolved with the winged LSF profile. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . We see that the true value is only recovered (within ±0.02) for h4 when σ is 200 km/s, four times the in… view at source ↗
Figure 8
Figure 8. Figure 8: — Recovered pPXF LOSVD shapes with M = 4 for an underlying stellar LOSVD that is a pure Gaussian with σ = 200 km s−1 . The true LOSVD is shown in gray. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spectrum is also convolved with the winged LSF profile. Plots along the diagonal naturally give the best recovery while off diagonal plots have stronger err… view at source ↗
Figure 11
Figure 11. Figure 11: — Recovered pPXF h4 for an underlying stellar LOSVD with h3 = −0.1 and h4 = 0.1. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . LSFs involving the winged profile are systematically too large or too small, with h4 dropping to the smallest possible value of -0.3 when the template spectrum is convolved with it. The remaining choices recover h4 close to the instrumental resoluti… view at source ↗
Figure 13
Figure 13. Figure 13: — Recovered pPXF dispersion for an underlying stellar LOSVD that is Gaussian. The LSF of the template spectrum is a pure Gaussian whereas the LSF of the target spectrum is a GH series with h4 given by the x axis. Shaded regions are drawn at the 99 percent and 95 percent accuracy levels. most of the SAMI survey would not be significantly im￾pacted by the non-Gaussian shape of the LSF. I repeat this test bu… view at source ↗
Figure 14
Figure 14. Figure 14: — Recovered pPXF velocity for an underlying stellar LOSVD that is Gaussian. The LSF of the template spectrum is a pure Gaussian whereas the LSF of the target spectrum is a GH series with h3 given by the x axis. of all of the spaxels within a given aperture. In the case where there are spatial variations in the LSF, this would require making multiple pointings so that light from the star is in all spaxels … view at source ↗
Figure 15
Figure 15. Figure 15: — Recovered pPXF velocity for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the tem￾plate spectrum is also convolved with the winged LSF profile. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . The velocity is recovered everywhere to within ±0.05 km s−1 . 50 100 150 200 250 300 True Dispers… view at source ↗
Figure 16
Figure 16. Figure 16: — Recovered pPXF σ for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spec￾trum is also convolved with the winged LSF profile. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . The dispersion is recovered to better than one percent down to the instrumental dispersion percent at ha… view at source ↗
Figure 17
Figure 17. Figure 17: — Recovered pPXF h3 for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the template spectrum is also convolved with the winged LSF profile. The MUSE instru￾mental dispersion is the dashed gray line at σ = 51.4 km s−1 . h3 is perfectly recovered down to twice the instrumental dispersion. At the instrumental dispersion it … view at source ↗
Figure 18
Figure 18. Figure 18: — Recovered pPXF h3 and h4 for an underlying LOSVD that is a pure Gaussian. The notation W-W means the target spectrum is convolved with the winged LSF profile and the tem￾plate spectrum is also convolved with the winged LSF profile. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . h4 is perfectly recovered down to twice the instrumental dispersion. At the instrumental dispers… view at source ↗
Figure 20
Figure 20. Figure 20: — Fractional uncertainty in the dispersion as a function of the true stellar dispersion for different values of the fractional error in the LSF width. The MUSE instrumental dispersion is the dashed gray line at σ = 51.4 km s−1 . Errors are typically on the order of a few percent. both template and target LSF have the same morphol￾ogy ( [PITH_FULL_IMAGE:figures/full_fig_p013_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: — Recovered pPXF σ with M = 2 for an underlying LOSVD that is a pure Gaussian. The full MARCS library with a Salpeter IMF is fit. These results are largely unchanged from [PITH_FULL_IMAGE:figures/full_fig_p014_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: — Recovered pPXF σ for an underlying LOSVD that is a pure Gaussian. The LSF of the template and target spectrum are both taken to be Gaussian with constant FWHM equal to 2.61 ˚A for the target and 2.51 ˚A for the template. For the curves labeled ’step’ the template FWHM is 2 ˚A and 2.5 ˚A on the left and right hand halves of the spectrum, respectively. In the case that the LSF of the template is matched t… view at source ↗
Figure 23
Figure 23. Figure 23: — The true velocity (or mean) of Equation B4 as a function of the stellar dispersion σ∗. The blue curve shows Equation C4 whereas the orange and green curves break this down into the contributions from just the h1 term and the h3 term. The h1 term slowly increases before decreasing whereas the h3 term uniformly decreases. Fitting a Gaussian to Equation B4 gives the dashed red curve. lower order term in th… view at source ↗
read the original abstract

The line spread function (LSF) of a spectrograph encodes the inherent broadening of a single spectral line. It is typically reported as a single number, the resolving power $R = \lambda/\Delta\lambda$ with $\Delta \lambda$ the FWHM of the LSF. In standard pipelines for extracting stellar kinematics the LSF is assumed to be a wavelength dependent Gaussian. However, detailed LSF measurements from real integral field spectrographs reveal a variety of shapes, some close to Gaussian, others with large wings or that appear boxy. I have studied the impact that these non-Gaussian LSF profiles have on the recovery of the stellar kinematics of a mock spectrum and find that even in the high dispersion case of 300 km s$^{-1}$, there is up to a 7 percent uncertainty in the dispersion due to non-Gaussian LSF profiles. Additionally, higher order Gauss-Hermite moments $h_3$ and $h_4$ can be biased by up to $\pm$0.1. To resolve this bias, I developed a method to match the LSF of the template spectra to the LSF of a target spectrum when the LSF of either one or both is non-Gaussian and show that it can reduce bias in the dispersion to less than a percent down to the instrumental resolution. A Python implementation of this method has been made publicly available.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that non-Gaussian line spread functions (LSFs) in integral-field spectrographs introduce biases in stellar kinematic recovery from mock spectra, with up to 7% uncertainty in velocity dispersion and ±0.1 bias in Gauss-Hermite moments h3 and h4 even at 300 km s^{-1}. It presents a method to match non-Gaussian LSFs between templates and targets that reduces dispersion bias to <1% down to instrumental resolution, and releases a public Python implementation.

Significance. If the tested LSF profiles and mocks prove representative, the work identifies a relevant systematic for kinematic measurements that underpin dynamical galaxy models. The open-source code release is a concrete strength that could facilitate adoption of the matching approach.

major comments (2)
  1. [Mock spectra construction and LSF application (methods/results sections)] The central quantitative claims (7% dispersion uncertainty and ±0.1 bias in h3/h4 at 300 km s^{-1}) rest on the representativeness of the chosen non-Gaussian LSF profiles and mock spectra for real IFS data. The manuscript must supply explicit validation—such as direct comparisons to observed LSFs from instruments, tests of wavelength dependence, and spatial variation across the field—to establish that these profiles capture the dominant systematics rather than serving as illustrative cases only.
  2. [LSF matching method description and validation tests] The performance of the LSF-matching method (bias reduced to <1%) requires additional tests that include realistic template mismatch, noise properties, and cases where both template and target LSFs are non-Gaussian; without these, it is unclear whether the reported improvement generalizes or introduces compensating systematics.
minor comments (1)
  1. [Abstract] The abstract reports bias magnitudes but does not list the exact functional forms or parameter ranges of the non-Gaussian LSFs tested; adding this would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough and constructive comments. We address each major point below and have revised the manuscript to incorporate additional validation as requested.

read point-by-point responses

  1. Referee: [Mock spectra construction and LSF application (methods/results sections)] The central quantitative claims (7% dispersion uncertainty and ±0.1 bias in h3/h4 at 300 km s^{-1}) rest on the representativeness of the chosen non-Gaussian LSF profiles and mock spectra for real IFS data. The manuscript must supply explicit validation—such as direct comparisons to observed LSFs from instruments, tests of wavelength dependence, and spatial variation across the field—to establish that these profiles capture the dominant systematics rather than serving as illustrative cases only.

    Authors: We agree that explicit validation strengthens the claims. The revised manuscript adds a dedicated subsection with direct comparisons of the tested LSF shapes to published measurements from instruments including MUSE and SAMI. We also include new tests of wavelength dependence and a discussion of spatial LSF variations, showing that position-dependent matching can be applied. These additions confirm the profiles capture representative systematics. revision: yes

  2. Referee: [LSF matching method description and validation tests] The performance of the LSF-matching method (bias reduced to <1%) requires additional tests that include realistic template mismatch, noise properties, and cases where both template and target LSFs are non-Gaussian; without these, it is unclear whether the reported improvement generalizes or introduces compensating systematics.

    Authors: The original work already covers cases with non-Gaussian LSFs on both template and target. In response, the revised manuscript adds tests incorporating realistic template mismatch (via alternate stellar libraries) and representative noise levels. These confirm the dispersion bias remains below 1% with no significant compensating systematics introduced. The public code release has been updated to support such extended tests. revision: yes

Circularity Check

0 steps flagged

Numerical experiment on mock spectra exhibits no circular derivation

full rationale

The paper's central results (quantified biases up to 7% in dispersion and ±0.1 in h3/h4, plus a matching method reducing bias to <1%) arise from direct numerical experiments on constructed mock spectra with chosen non-Gaussian LSF profiles. No derivation chain, parameter fitting, or uniqueness claim reduces by construction to its own inputs; the reported quantities are simulation outputs, not self-referential definitions or renamed fits. The representativeness assumption is a standard external-validity concern, not a circularity issue.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The work relies on standard assumptions of stellar kinematic extraction (Gauss-Hermite expansion, template fitting) that are not enumerated here.

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