Challenges in constraining dust properties from starlight polarization

Raphael Skalidis (Caltech)

REVIEW 4 major objections 5 minor 2 cited by

Challenges in constraining dust properties from starlight polarization

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Line-of-sight averaging over multiple magnetic-field orientations biases most published starlight-polarization constraints on dust by about 10 percent.

desk verdict Solid contamination analysis on the largest catalog; the 10% bias claim and the projection reinterpretation of the pmax/E(B-V) break are plausible but not nailed down. read the letter →

arxiv 2411.08971 v1 pith:KYHHRK62 submitted 2024-11-13 astro-ph.GA

Raphael Skalidis (Caltech) This is my paper · ORCID

classification astro-ph.GA

keywords interstellarduststarlightpolarizationSerkowskirelationgrainalignmentmagneticfieldsline-of-sightprojectioneffectsefficiency3Dextinction

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

The paper argues that when starlight polarization is measured toward a star, the signal usually sums contributions from several clouds along the line of sight, and those clouds often have different magnetic-field orientations. That averaging can mimic or distort the wavelength-dependent polarization curve even when the polarization angles look constant across bands. The author fits the empirical Serkowski curve—the standard relation between polarization fraction and wavelength—to the largest multi-band catalog, flags sightlines with variable polarization angles, and uses 3D dust maps and stellar distances to identify lines of sight with multiple clouds. The conclusion is that the majority of existing multi-band sightlines are contaminated, that fitted Serkowski parameters are biased by roughly 10 percent, and that only diffuse sightlines with $E(B-V)$ below about 0.5 mag give trustworthy constraints on intrinsically aligned dust grains. If right, published constraints on grain sizes and alignment efficiency need revision, and the well-known drop in polarization efficiency at high reddening is a projection artifact rather than a change in grain alignment.

What carries the argument

The machinery is the Serkowski relation, the empirical curve $p_{\lambda} = p_{\max}\,\exp[-K\ln^2(\lambda_{\max}/\lambda)]$ describing how the starlight polarization fraction varies with wavelength, whose fitted parameters are the standard readout for dust grain properties. The paper combines it with a polarization-angle variability diagnostic $\Delta\theta$, Bayesian fits in both $p$–$\lambda$ and Stokes $q$–$u$ space, 3D dust extinction maps, Gaia parallaxes, and a molecular-gas map to identify lines of sight where the signal is built from multiple clouds. The critical interpretive move is comparing cumulative polarization efficiency with stellar distance: a drop that tracks distance is attributed to projection and averaging over multiple magnetic-field geometries rather than to intrinsic loss of grain alignment.

What would settle it

Take a single isolated high-extinction cloud, with $E(B-V)$ near 1 mag or more, and measure $p_{\max}/E(B-V)$ for background stars at several distances all behind that same cloud; if the efficiency is already suppressed for every background star, the suppression is intrinsic to the cloud, whereas if it appears only when additional background clouds enter the line of sight, it is a projection effect.

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Extended reading notes

Core claim

The central claim is that line-of-sight integration effects contaminate the majority of the existing multi-band starlight polarization dataset, biasing the derived Serkowski parameters—the peak polarization $p_{\max}$, the peak wavelength $\lambda_{\max}$, and the width parameter $K$—by approximately 10 percent. The paper shows that constant polarization angles with wavelength do not guarantee a clean sightline: multiple clouds with similar sky-plane magnetic-field orientations can add constructively, inflating $K/\lambda_{\max}$ and pushing measurements off the Wilking relation, while slightly misaligned clouds can suppress $p_{\max}$ without obviously breaking the Serkowski fit. It further argues that the observed suppression of polarization efficiency $p_{\max}/E(B-V)$ near $E(B-V)\approx 0.5$ mag is a projection effect, because the cumulative efficiency declines with stellar distance, whereas intrinsic alignment loss would not. The paper also finds that all measurements respect the 13 percent efficiency limit inferred from polarized dust emission. The reliable part of the data for grain-property studies is therefore the diffuse regime with $E(B-V)\lesssim 0.5$ mag, where the number of line-of-sight clouds is small.

Load-bearing premise

The claim that the efficiency drop is a projection effect depends on assuming that true loss of grain alignment would suppress the polarization-to-reddening ratio equally at every stellar distance; since faraway stars also tend to sit behind more dust, distance and reddening are degenerate, and if real alignment loss also grows over longer sightlines the reinterpretation would fail.

Editorial extensions

If this is right

Constraints on grain size distributions drawn from the Wilking relation in the aggregated multi-band catalog are systematically biased; the intrinsic Galactic averages may be $\lambda_{\max}\approx 0.63$–$0.65\,\mu$m and $K\approx 1.0$, about 10 percent off previous values.
The $p_{\max}/E(B-V)$ break near 0.5 mag should not be read as a drop in grain alignment efficiency, so observational tests of radiative alignment theory that rest on that break need re-examination.
At low reddening the $\lambda_{\max}$ distribution is bimodal with modes near 0.4 and 0.6 $\mu$m, suggesting the intrinsic aligned-grain size distribution may itself be bimodal.
Polarized dust emission, which integrates signal along the entire line of sight, should be even more sensitive to the same projection effects, so similar 3D checks are needed there.
A constant polarization angle across wavelengths is not sufficient evidence of a single-cloud sightline; future surveys must combine polarimetry with 3D extinction and distance information.

Reading between the lines

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

If the projection explanation is correct, per-cloud Serkowski parameters could in principle be recovered tomographically by pairing multi-band polarimetry with 3D dust maps, inverting the line-of-sight averaging rather than discarding contaminated sightlines.
The paper's picture predicts a quantitative scaling: the inflation of $K/\lambda_{\max}$ should grow with the number of clouds and with the degree of magnetic-field coherence along the line of sight, which could be tested with mock sightlines built from a 3D magnetic-field model.
A natural testable extension is to compare starlight and emission polarization on the same diffuse sightlines; if the 13 percent efficiency limit holds in both, that supports a common intrinsic alignment efficiency and confines strong projection effects to structured, multi-cloud sightlines.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Bottom line: this is a useful paper with one strong qualitative result, one weaker quantitative inference, and one interpretation that goes past the data. The strong result is that LOS integration contaminates Serkowski fits for most of the Panopoulou et al. catalog, and that constant EVPA does not guarantee a single-cloud sightline. The Berkeley 59, Taurus/Perseus, and NGC 6823 case studies, combined with 3D extinction profiles, make that case convincingly. This extends the mechanism demonstrated in Mandarakas et al. 2024 to the largest available dataset, and that is worth having.

The weak parts are the 10% bias estimate and the reinterpretation of the pmax/E(B-V) break at E(B-V) ~ 0.5 mag as a projection effect rather than an alignment-efficiency change. The 10% figure is a difference in posterior medians between diffuse and molecular subsamples, with no uncertainty attached to the bias itself. And Fig. 11, which shows median pmax/E(B-V) decreasing with stellar distance, does not break the distance-reddening degeneracy: E(B-V) is computed along the line of sight to each star, so high-extinction sightlines are preferentially more distant. An intrinsic alignment-efficiency drop with extinction or reddening would produce a very similar distance trend. The paper's claim that alignment loss would be distance-independent is asserted, not derived, and the figure alone cannot distinguish the two. The qualitative contamination result is solid; the efficiency-break reinterpretation is plausible but not definitive.

One more thing: the recovered Wilking slope of 1.58 in Eq. 16 is partly prior-imposed, because the prior fixes K = alpha * lambda_max with alpha centered at 1.66. The text admits this, and the deviating-sightline criterion is anchored to the same prior. That does not kill the paper, but it does mean the quantitative slope claim should be read as prior-driven, and the circularity concern raised by the reader is real even though disclosed.

Who is this for: anyone using Serkowski parameters from the Panopoulou et al. catalog, and anyone modeling grain alignment from pmax/E(B-V) statistics. It deserves a serious referee. The referee should push on the distance-reddening degeneracy, ask for an uncertainty on the 10% bias, and request a model that treats alignment loss as an explicit alternative to projection. I would cite it for the contamination caveat, not for the efficiency-break reinterpretation.

Referee Report

4 major / 5 minor

Summary. The paper fits the Serkowski relation to 258 multi-band starlight polarization sightlines from the Panopoulou et al. (2023) catalog, using Bayesian methods with an informative prior linking K to lambda_max. It combines these fits with Gaia distances and 3D dust extinction maps to argue that line-of-sight (LOS) averaging over multiple clouds with different magnetic field geometries contaminates Serkowski-parameter constraints, biasing them by about 10%. The paper further analyzes pmax/E(B-V), finds a break near E(B-V)=0.5 mag, and attributes that break to projection effects rather than to an intrinsic loss of grain alignment efficiency.

Significance. If the conclusions hold, the paper would imply that published Serkowski-parameter constraints from the largest current starlight-polarization catalog are systematically biased, and that the widely discussed suppression of polarization efficiency at moderate reddening is a geometric/projection artifact rather than a direct signature of grain alignment physics. The case studies toward Berkeley 59, Taurus/Perseus, and NGC 6823 are valuable: they combine distance-resolved extinction profiles with pmax and EVPA behavior and make a convincing qualitative case that LOS integration can modify K and lambda_max even when the Serkowski fit is formally good and the EVPAs are constant. The Bayesian fitting machinery, the explicit treatment of Rice-distributed polarization likelihoods, and the conservative 0.1% uncertainty floor are also strengths. However, the quantitative claims about the size of the bias and the specific reinterpretation of the pmax/E(B-V) break are not yet established at the same level as the qualitative contamination effect.

major comments (4)

[§3.1.2 and §4, Eq. (16)] The prior in §3.1.2 fixes K = alpha*lambda_max with alpha drawn from a Gaussian of mean 1.66, so the recovery of a linear K-lambda_max relation in Eq. (16) is guaranteed by construction. The text acknowledges this, but the same prior-dominated posterior is later used to infer an intrinsic slope K/lambda_max ~ 1.58, intrinsic values lambda_max ~ 0.63 and K ~ 1.0, and a deviating-sightline criterion K/lambda_max >= 1.75. This makes the quantitative 10%-bias claim partly circular. The authors should either repeat the analysis with a prior on K that is not tied to lambda_max, or demonstrate explicitly how strongly the posterior medians of K depend on the assumed alpha distribution.
[§5, Fig. 11] The central reinterpretation of the pmax/E(B-V) break rests on the claim that if the suppression were due to intrinsic alignment loss it would be independent of stellar distance. That premise is asserted but not derived, and Fig. 11 does not break the distance-reddening degeneracy: E(B-V) is integrated along the line of sight to the star, so high-reddening sightlines are preferentially more distant. An intrinsic-alignment model in which polarization efficiency declines with reddening or with the reddening of the radiation field would also produce a decreasing pmax/E(B-V) versus distance. To support the projection interpretation, the authors need to control for E(B-V) when showing the distance trend (for example, by binning in E(B-V) at fixed distance or by fitting a joint model).
[§5, Fig. 12 and §7] The quantitative intrinsic values lambda_max ~ 0.63 micron and K ~ 1.0, and the resulting '10% off' statement, are posteriors-median summaries for subsamples defined by an E(B-V) cut. No uncertainty is quoted for the 10% bias itself, and the diffuse and molecular subsamples differ simultaneously in reddening, distance, and cloud multiplicity. The authors should report the dispersion and sampling uncertainty of these medians and test whether the difference between the E(B-V)<0.5 and E(B-V)>0.5 subsamples is significant after accounting for the informative prior used in the fits.
[§4.2 and §7, Abstract] The abstract and conclusions state that LOS integration effects contaminate 'the majority' of the existing dataset, but the paper does not supply a quantitative statistic for the fraction of the 258 sightlines that are contaminated. The detailed case studies demonstrate the effect convincingly for selected regions, and the statement that most sightlines contain multiple clouds is attributed to Mandarakas et al. (2024), but the present sample is not systematically scored with an objective criterion based on the 3D extinction profiles. A per-sightline contamination metric, or at least a statistical estimate with an uncertainty, is needed to support the majority-contamination claim.

minor comments (5)

[§4.1.2] The region is referred to as 'Chameleon I'; the standard astronomical name is 'Chamaeleon I'. The spelling should be made consistent with the literature.
[§5] The paper reports lambda_max ~ 0.63 micron and K ~ 1.0 against previous lambda_max ~ 0.55 micron and K ~ 0.9. These are approximately 15% and 11% differences respectively; the paper should state which quantity is meant by the '10%' bias.
[§4.2, Fig. 9] The text refers to the 'top left panel' when describing the extinction profile toward NGC 6823, but Fig. 9 is a three-column figure without an explicit top-left layout in the caption; the reference should be clarified.
[§2.1, Eq. (4)] The definition of Delta_theta as [max(theta_lambda)-min(theta_lambda)] divided by the quadrature sum of the uncertainties of only those two extreme bands should be justified more explicitly; it is not obvious that this is the optimal way to quantify EVPA variability across more than two bands.
[Fig. 5 caption] The caption contains the typo 'Galatic Longitude'; it should read 'Galactic Longitude'.

Circularity Check

2 steps flagged · score 6.0 of 10

The recovery of the Wilking relation (Eq. 16) is admitted to be a consequence of the K = alpha lambda_max prior adopted in Sect. 3.1.2, and the 'majority contaminated' premise is imported from a co-authored paper; the projection reinterpretation itself is not circular but is confounded by distance-reddening coupling.

self definitional [Sect. 3.1.2 (prior) and Sect. 4 (Wilking relation), Eq. (16)]
"We assumed that K linearly correlates with λmax as: K = αλ max. We assumed that α follows a Gaussian distribution with an average value equal to 1.66, as the optical data suggests (Wilking et al. 1980; Whittet et al. 1992; Whittet 2022). [...] Similarly to past works (Wilking et al. 1980; Whittet et al. 1992), we find a linear correlation between K and λmax. This was expected because it was assumed in the distribution of priors (Sect. 3.1.2)."

The prior enforces the relation that Sect. 4 reports as a constraint. Each K posterior is sampled with log-prior containing K = alpha lambda_max and alpha centered at 1.66 with 20% variance, so the ensemble of (lambda_max, K) medians must scatter around that line; the recovered slope 1.58 +/- 0.37 and zero intercept are the prior re-emerging, not an independent property of the data. The paper concedes this: 'This was expected because it was assumed in the distribution of priors.' Thus 'we find a linear correlation between K and lambda_max' is not a test of the Wilking relation, and downstream claims that use the resulting slope, such as the K/lambda_max >= 1.75 'deviating' criterion, inherit the same prior.
self citation load bearing [Sect. 4.2, final paragraph; supported by Sect. 5 and Sect. 7]
"As noted by Mandarakas et al. (2024), the majority of LOSs in the compiled catalogue (Panopoulou et al. 2023) include multiple clouds along a LOS. Thus, existing constraints on the Serkowski parameters are biased due to projection effects."

The quantitative scope of the central claim, that the majority of sightlines are contaminated and Serkowski parameters are biased, is not derived from the present sample. The case studies (Berkeley 59, Chamaeleon I, Taurus, NGC 6823/6709/1502) demonstrate LOS effects in specific regions, but they do not quantify the 'majority' fraction. That statistic is imported from Mandarakas et al. (2024), whose authors include the present author (Skalidis); the projection interpretation additionally leans on Skalidis et al. (2024) for the rising cloud-multiplicity probability at E(B-V) >= 0.3 mag. The central premise therefore rests on a same-author citation chain rather than on an independent rederivation in this paper.

full rationale

The overall circularity is partial, so the score is 6. Step 1 is an admitted construction: the K - lambda_max prior fixes the recovered Wilking relation, and because the S/N in K is low, the diffuse-ISM median K about 1.0 is also prior-dominated. Step 2 shows that the 'majority contaminated' premise relies on a co-authored citation, although the individual case studies and 3D extinction profiles are independent evidence that LOS effects exist. The projection reinterpretation of the pmax/E(B-V) break is not circular: it uses Gaia distances and the Edenhofer et al. (2024) and Green et al. (2018) 3D maps, and a projection effect genuinely predicts a distance trend. The skeptic's distance-reddening degeneracy is a real confound, since Fig. 11 does not separate distance from E(B-V) and an intrinsic-alignment-loss model would also produce a declining trend with distance, but that is a correctness risk, not a reduction of the claim to its inputs. The Monte Carlo test of the deviating points is similarly independent of the prior mean. For these reasons the paper is not scored 8-10; it retains substantial external and independent content despite the admitted prior-driven Wilking-relation result.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The contamination claim rests on external 3D dust maps and Gaia distances; the quantitative Serkowski-parameter results additionally rest on a prior that encodes the very K-lambda_max correlation the paper reports. The projection-effect interpretation of the polarization efficiency break relies on an asserted distance-independence of intrinsic alignment physics. No new physical entities are introduced.

free parameters (4)

Prior slope alpha of K-lambda_max relation = Gaussian mean 1.66, 20% variance (chosen)
Sect. 3.1.2 fixes K = alpha * lambda_max with alpha drawn from a Gaussian of mean 1.66 and inflated variance 20%. This imposes the Wilking relation on every posterior, so the recovered slope in Eq. 16 is a prior echo.
EVPA variability cut Delta_theta = kept only Delta_theta <= 1
Sect. 2.1 excludes sightlines with variable EVPAs and keeps only Delta_theta <= 1, giving the 258-star sample that underlies all contamination statistics. The threshold shapes the 'majority contaminated' claim.
Deviating-point threshold K/lambda_max = at least 1.75 at lambda_max about 0.55 micron
Sect. 4 defines the roughly 8% 'deviating' subsample using these ad hoc criteria, anchored to the prior-mean Wilking slope; the subsequent line-of-sight analysis is applied to this subsample.
Polarization uncertainty floor = 0.1%
Sect. 2 sets all sigma_p smaller than 0.1% to 0.1%, a conservative calibration floor that affects chi-square values and posterior widths.

assumptions (6)

domain assumption The Serkowski relation (Eq. 1) is the correct functional form for optical starlight polarization spectra.
Used throughout Sect. 3 for fitting; it is empirical and not derived in this paper.
standard math The Rice distribution applies to observed polarization fractions (Eq. 7).
Adopted from Vaillancourt (2006) to handle low S/N asymmetries in the polarization likelihood.
ad hoc to paper K and lambda_max are linearly related with slope about 1.66 (Wilking/Whittet), used as a prior.
Sect. 3.1.2 imports this relation from Wilking et al. (1980) and Whittet (2022) and hardwires it into the Bayesian prior; the paper's own Eq. 16 then recovers it.
domain assumption 3D dust extinction maps (Green et al. 2018; Edenhofer et al. 2024) and Gaia parallaxes trace the line-of-sight dust distribution accurately enough to identify separate cloud contributions.
Used in Sects. 4 and 5 to associate high-K sightlines with background clouds, e.g., Taurus/Perseus and Berkeley 59.
ad hoc to paper If the pmax/E(B-V) suppression were due to intrinsic alignment loss, it would be independent of stellar distance.
Sect. 5, Fig. 11: this premise drives the paper's key argument separating projection effects from alignment physics, and it is asserted without a quantitative model of density-dependent alignment.
domain assumption NH/E(B-V) = 5.8 x 10^21 cm^-2 (Bohlin et al. 1978) converts reddening to column density.
Used in Sect. 5 to associate E(B-V) = 0.5 mag with the onset of the molecular hydrogen regime.

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Cite this review

Pith. "Pith review of Challenges in constraining dust properties from starlight polarization." pith.science (2026). https://pith.science/paper/KYHHRK62

@misc{pith2026241108971,
  author       = {Pith},
  title        = {Pith review of: Challenges in constraining dust properties from starlight polarization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KYHHRK62}},
  note         = {Machine review of arXiv:2411.08971}
}

read the original abstract

Dust polarization, which comes from the alignment of aspherical grains to magnetic fields, has been widely employed to study the interstellar medium (ISM) dust properties. The wavelength dependence of the degree of optical polarization, known as the Serkowski relation, was a key observational discovery that advanced grain modeling and alignment theories. However, it was recently shown that line-of-sight (LOS) variations in the structure of the ISM or the magnetic field morphology contaminate the constraints extracted from fits to the Serkowski relation. These cases can be identified by the wavelength-dependent variability in the polarization angles. We aim to investigate the extent to which we can constrain the intrinsic dust properties and alignment efficiency from dust polarization data, by accounting for LOS variations of the magnetic field morphology. We employed archival data to fit the Serkowski relation and constrain its free parameter. We explored potential imprints of LOS variations of the magnetic field morphology in these constraints. We found that these LOS integration effects contaminate the majority of the existing dataset, thus biasing the obtained Serkowski parameters by approximately 10%. The constancy of the polarization angles with wavelength does not necessarily guarantee the absence of 3D averaging effects. We examined the efficiency of dust grains in polarizing starlight, as probed by the ratio of the degree of polarization to dust reddening, E(B-V). We found that all measurements respect the limit established by polarized dust emission data. A suppression in polarization efficiencies occurs at E(B-V) close to 0.5 mag, which we attribute to projection effects and may be unrelated to the intrinsic alignment of dust grains.

Figures

Figures reproduced from arXiv: 2411.08971 by the authors.

**Figure 1.** Characteristic examples of good fits (χ 2 ≤ 1). The top two rows shows stars with variable EVPAs (∆θ > 3), while bottom rows shows stars with constant EVPAs (∆θ < 1). The third row star (identified as BD+26746), has a higher K / λmax ratio than predicted by the Wilking relation. Stars that deviate from the Wilking relation, likely due LOS integration effects, tend to have relatively high degrees of polarization, pma… view at source ↗

**Figure 2.** Analytical examples of the Serkowski relation (Eq. 1). The colored curves have different K but fixed pmax, and λmax at 1% and 0.6 µm respectively. The black curve is typical of the ISM, while other curves, such as red, and green, are extreme cases that are unlike to observe in our Galaxy. Fitting models with only a few data around λmax, leads to a spectrum of K solutions, which can favor extreme (unphysical) values… view at source ↗

**Figure 4.** The Wilking relation derived from our fits. Colored points correspond to the median values of the K and λmax posterior distributions. Our obtained slope, 1.570.31 −0.39, (solid line) is statistically consistent with previous constraints (dashed line). The colorbar shows pmax for each measurement. Close to 0.5 µm a group of points maximally deviates from the linear relation. These measurements have high pmax, and K … view at source ↗

Figures from the paper (8 more)

**Figure 3.** Figure 3: A typical example of the correlations between the posteriors of the free parameters. This case corresponds to a star identified as HD 283643, whose fit is shown in the first row of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

**Figure 5.** Figure 5: The target sightlines overplotted on a full-sky molecular column density map of our Galaxy (Skalidis et al. 2024). Sightlines with typical λmax are shown as magenta points. These measurements are primarily encountered in diffuse molecular clouds. Blue triangles show si…

**Figure 6.** Figure 6: Cumulative extinction, obtained from Edenhofer et al. (2024), versus distances towards the Berkeley 59 star cluster, which is located at ∼ 1 kpc. Colored curves correspond to different LOSs. Extinction steeply rises from 0.2 to 1.0 kpc. Polarization data suggests that …

**Figure 8.** Figure 8: Cumulative extinction, obtained from Edenhofer et al. (2024), versus distance toward four different LOSs in the Taurus molecular cloud complex. Colored lines corresponds to measurements with different polarization properties. The legend shows K / λmax, pmax, and the d…

**Figure 9.** Figure 9: Variations in dust extinction and polarization properties as a function of the distance of several stars. The left, middle, and right columns correspond to measurements toward the star clusters NGC 6823, 6709, and 1502, respectively. Shaded regions in the K / λmax prof…

**Figure 10.** Figure 10: Maximum polarization fraction, obtained from our fits, versus dust reddening. The black, and blue lines correspond to the 13%, and 9% upper limits respectively. Colorbar shows our obtained Wilking relation slopes. Points with high K/λmax (red stars) tend to have maxi…

**Figure 11.** Figure 11: Cumulative polarization efficiency with distance. The decrease in polarization efficiency with distance strongly suggests that the observed reduction of pmax / E(B − V) at E(B − V) > 0.5 mag ( [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: Cumulative median profiles of λmax, and K with E(B−V). K has been normalized with the value of the Wilking slope for vizualization purposes. For E(B − V) ≲ 0.5 mag, the average λmax ≈ 0.63 µm, while the average K ≈ 1.0. Both averages are slightly higher than previous …

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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, " * write output.state after.block = add.period write newline

ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

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write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

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