An analysis of a simulated gravitational-arc setup found that assigning each measurement a position from its contributing light recovered an input neutral-hydrogen profile more closely than assigning it to the geometric centre of the same spatial element. The study asks whether a flux-contribution formalism can reconstruct where the light in each IFU spaxel comes from and define effective impact parameters, the estimated distances used in the comparison.
The calculation used the T21 arc-light distribution, the adopted point-spread function (PSF), which describes image blurring, and the study’s spaxel configuration. It then tested recovery of an exponential neutral-hydrogen profile.
The hidden shift inside a spatial pixel
A geometric approach assigns each measurement to its spaxel centre. The alternative built sensitivity maps and normalized flux-contribution weights for each selected spaxel, then compared the resulting flux-weighted coordinates with geometric centres using the same selected measurements.
The gap between those two positions depended on how much arc light overlapped a spaxel. For on-arc spaxels, the study described the displacement as decreasing linearly with the overlap fraction and summarized it as the PSF scale multiplied by one minus that fraction; off-arc spaxels had displacements of roughly a PSF scale or more.
The resulting impact-parameter bias was not one fixed offset. In the T21 system, it depended on the displacement’s direction relative to galaxy G1 and on local lensing magnification, scaling with the inverse square root of that magnification. The bias ranged from 0 to 3.3 kiloparsecs for on-arc spaxels and reached about 5 kiloparsecs for off-arc spaxels, with the largest effect when the displacement pointed toward or away from G1.
The test’s clearest result
The clearest comparison came from a noiseless benchmark. The input profile had a scale length of 5.0 kiloparsecs and a central column density of log N0/cm² = 20.3. The spaxel-centre fit returned 5.7 ± 0.3 kiloparsecs and 20.14 ± 0.05, with a mean absolute residual of 0.13 dex. Flux-weighted coordinates returned 4.99 ± 0.07 kiloparsecs and 20.31 ± 0.02, with a residual of 0.01 dex.
Taken together, those fits show the geometric-centre estimate moving toward a flatter, renormalized profile, while the flux-weighted estimate stayed close to the input values. The profiles were compared with orthogonal distance regression, a fitting method that included uncertainty in impact parameter and assigned zero modeled error to the column density in this noiseless test.
Adding mock uncertainties preserved the contrast. Flux-weighted fitting recovered the input parameters within 1 sigma, with a mean absolute residual of 0.11 dex and reduced chi-squared of about 1. The spaxel-centre fit was within 1.7 sigma for the scale length and 1 sigma for the central column density, but its residual rose to about 0.17 dex and its reduced chi-squared to about 4.
The result survived several checks
The flux-weighted result was also tested against a misspecified PSF. Varying the PSF full width at half maximum by plus or minus 10 percent shifted the recovered scale length by less than 1 percent and the central column density by no more than about 0.02 dex; reduced chi-squared stayed near 1 in every case.
The fiducial test used 69 selected spaxels, with more than 50 percent integrated arc-flux overlap and integrated signal-to-noise above 2 required for selection. Changing those thresholds did not remove the geometry-driven scatter in the spaxel-centre analysis: higher overlap fractions improved the shape of that fit, but tighter signal-to-noise cuts did not remove the artificial scatter.
Finer spatial sampling led to the same broad result. It did not eliminate the spaxel-centre bias, while flux-weighted fits continued to recover the input parameters.
A result tied to one simulated system
The result remains a method test inside one data-driven configuration. The simulation was tied to the T21 arc-light distribution, adopted PSF and spaxel setup, and its profile benchmark used fixed parameters for an exponential neutral-hydrogen profile; the evidence therefore describes behavior under that setup rather than performance across a population of observed systems.
The profile benchmark also treated N(b) as optically thin to isolate geometric bias. The paper says saturated magnesium-II lines require explicit optical-depth modeling, so this test should not be read as validation of saturated-line column densities.
The reported impact-parameter ranges are specific to the tested configuration. The bias depends on displacement orientation relative to G1 and local lensing magnification, rather than following a single universal correction.
A practical proposal, not a universal correction
Within those boundaries, the authors present flux-weighted coordinates as a better-motivated primary analysis or robustness check for IFU absorption-line tomography using extended background sources. They interpret coherent, geometry-driven residuals from spaxel-centre coordinates as something that can mimic intrinsic circumgalactic-medium structure, while tracking the contributing light gives the profile fit a more direct spatial basis.
The authors state that the Python implementation of the formalism and the presented simulation are publicly available on GitHub. The supplied front matter identifies an Astronomy & Astrophysics manuscript labeled Letter to the Editor and gives arXiv:2608.25364v1 dated 26 August 2026.
Paper data and sources
Original title: Recovering the effective impact parameters in integral-field absorption-line tomography
Authors: J. A. Hernández-Guajardo, L. F. Barrientos, C. Ledoux et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text