Radio polarization from runaway star bowshocks-I. The general case

M Pohl; M.V. del Valle; R Santos-Lima

REVIEW 4 major objections 5 minor 1 cited by

Radio polarization from runaway star bowshocks-I. The general case

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper predicts that radio polarization from runaway-star bowshocks is weak, typically 8–10 percent, because thermal emission and magnetic turbulence dilute the synchrotron signal.

desk verdict First bowshock polarization synthesis, but the headline numbers are hostage to an assumed turbulence amplitude. read the letter →

arxiv 2505.06777 v1 pith:ITXXSH36 submitted 2025-05-10 astro-ph.SR astro-ph.GAastro-ph.HE

M.V. del Valle , R Santos-Lima , M Pohl This is my paper · ORCID

classification astro-ph.SRastro-ph.GAastro-ph.HE

keywords bowshocknebulaerunawaymassivestarssynchrotronpolarizationradiomagnetohydrodynamicscosmic-rayelectronsFaradayrotationthermalfree-freeemission

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 models radio emission and linear polarization from the bowshocks of runaway massive stars, combining magnetohydrodynamic simulations of the wind-ISM collision with transport of relativistic electrons and radiative transfer. It aims to show that, although synchrotron emission is intrinsically up to about 70 percent polarized, the observable degree of polarization is severely reduced by two effects: unpolarized thermal free-free emission from the photoionized bowshock and surroundings, and depolarization by a turbulent magnetic field. The central quantitative prediction is that the maximum polarization reaches roughly 40 percent at 1.4 GHz in localized spots, while the most feasible value within the brightest regions is 8–10 percent. If correct, low or absent polarization measurements from these sources should not be interpreted as evidence against particle acceleration.

What carries the argument

The central object is a set of synthetic polarization maps built in three stages: a three-dimensional magnetohydrodynamic steady-state simulation of the colliding stellar wind and interstellar medium, a two-dimensional axisymmetric diffusion-advection-loss transport calculation for electrons injected at the reverse shock with a power-law spectrum, and integration of the Stokes parameters Q and U along lines of sight that includes Faraday rotation and a superimposed Kolmogorov turbulent magnetic field. The polarization fraction Π = sqrt(Q²+U²)/Itot, with Itot including both synchrotron and thermal free-free intensity, is what carries the argument that thermal contamination and turbulence, not the absence of relativistic electrons, dominate the observed polarization.

What would settle it

Deep radio-polarimetric mapping of a known nonthermal bowshock at 4.86 GHz with sensitivity below a few percent: if the polarization in the brightest regions exceeds roughly 40 percent, or if the typical value inside the 0.8 Imax contour is well above 10 percent, the assumed turbulence level or the thermal-to-synchrotron ratio would be ruled out.

Watch

Extended reading notes

Core claim

Using a fiducial O-type runaway star with a fast wind moving through a typical interstellar medium, the paper constructs synthetic intensity and polarization maps at 1.40 and 4.86 GHz. It finds that thermal bremsstrahlung from the ionized gas can outshine the synchrotron component, and that internal Faraday rotation is not negligible at the lower frequency, so the observed polarization position angle does not reliably trace the magnetic field direction. With a fiducial turbulent magnetic field amplitude of δBturb/Breg = 0.5, the degree of linear polarization drops dramatically, peaking near 40 percent only in rare spots and lying around 8–10 percent inside the regions of maximum total intensity. The contribution from background Galactic cosmic-ray electrons is minor. The paper concludes that a bowshock can still be accelerating particles even when its radio emission looks unpolarized or thermal-dominated.

Load-bearing premise

The degree of unresolved magnetic turbulence in the source, set to a fiducial value of δBturb/Breg = 0.5, is essentially unconstrained, and if the real turbulence is weaker the predicted polarization would be much higher, up to about 70 percent.

Editorial extensions

If this is right

Low or null radio polarization detections from stellar bowshocks should not be taken as evidence against particle acceleration; a bowshock can be a particle accelerator even when its emission looks thermal.
Observing at higher radio frequencies such as 4.86 GHz is more promising than at 1.4 GHz because internal Faraday rotation and thermal contamination are weaker there.
For most viewing angles and magnetic-field orientations, the most polarized regions do not coincide with the intensity peaks, so searches for polarization should target the inner bright contours of a bowshock rather than its outer shell.
Spectral-index maps will show spatial variation from roughly -0.5 in the inner nonthermal region to about -0.1 in the thermal-dominated shocked interstellar medium, so classifying a bowshock as nonthermal requires multi-frequency, spatially resolved data.
Background cosmic-ray electrons contribute only modestly to the synchrotron intensity and do not strongly change the local polarization degree, meaning the accelerated electron population dominates within the inner bowshock.

Reading between the lines

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

If the unknown turbulence level is lower than the assumed δBturb/Breg = 0.5, the predicted polarization could rise substantially toward the intrinsic synchrotron value of about 70 percent, so the model effectively predicts that bowshock polarization measurements can be used to constrain the turbulent magnetic-field amplitude.
The model suggests a testable environmental correlation: bowshocks in denser interstellar media, where thermal emission is stronger, should show systematically lower polarization fractions than bowshocks in tenuous media.
By analogy with colliding-wind binaries, several radio-detected bowshocks currently classified as thermal emitters may harbor hidden nonthermal components; spectral-index mapping at two frequencies could reveal these hidden particle accelerators.
Because the polarization position angle is distorted by Faraday rotation and by the mismatch between high-field and high-emissivity regions, two-frequency polarimetry offers a way to isolate the true magnetic-field geometry and even locate the acceleration site.

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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

Two things to know. The paper gives the first synthetic radio polarization maps for runaway star bowshocks, including internal Faraday rotation and turbulent depolarization. It is a solid, honest modeling effort. The second thing: the headline numbers—maximum polarization ~40%, most feasible 8–10% in the bright regions—rest on an unconstrained amplitude for the turbulent magnetic field, δB/B=0.5, and they would jump to ~70% (pure synchrotron) or ~25% (after free-free dilution) if the field were ordered. So the quantitative predictions are illustrative, not robust.

What is genuinely new: nobody has done synthetic Stokes maps for bowshocks before. The pipeline is standard—MHD with PLUTO, particle transport in the diffusion approximation, then radiative transfer—and the qualitative conclusions follow from the simulations and are likely robust: internal Faraday rotation matters at 1.4 GHz, thermal free-free can outshine synchrotron, the position angle is not a direct field tracer, and the Galactic background electrons contribute little. These are useful anchoring expectations for the ~700 cataloged bowshocks and for interpreting the one deep polarization measurement (BD+43 3654) that found <0.5%.

The soft spots are real but proportionate. The turbulence amplitude is the load-bearing one. The paper acknowledges it is unknown and just asserts a high degree of turbulence. Figures 5 and 8 show the drop from ~70% to 8–10% when δB/B goes from 0 to 0.5, so the central quantitative claim is essentially a function of that parameter. The authors also 'arbitrarily choose a representative snapshot' from a time-varying MHD solution, and the electron transport is done on azimuthally averaged 2D fields while emission is computed in the full 3D fields. Those choices add uncertainty to the maps, though they are unlikely to overturn the qualitative conclusions. No code or data are released, which is a minor but not fatal omission for an astrophysics modeling paper.

This paper is for people interpreting radio observations of bowshocks and anyone modeling nonthermal emission from wind-ISM interactions. It deserves a serious referee: the framework is solid, the caveats are largely stated, and the paper will be a useful reference. I would push the authors to quantify sensitivity to the snapshot and to δB/B, and to release the simulation setup if possible. Engage with it; send it out.

Referee Report

4 major / 5 minor

Summary. This paper presents a three-stage forward model of radio synchrotron and free-free emission and linear polarization from runaway O-type star bowshocks. First, 3D MHD simulations of the wind-ISM interaction are run to a quasi-steady state for three orientations of the ambient magnetic field (alpha = 0, 30, 90 degrees). Second, relativistic electrons injected at the reverse shock, plus a Galactic cosmic-ray electron background, are transported in a 2D axisymmetric approximation with a diffusion-advection-loss equation. Third, synchrotron and free-free emissivities are integrated along lines of sight through the full 3D magnetic field, including internal Faraday rotation and a superimposed Kolmogorov turbulent field, to produce synthetic intensity, spectral-index, polarization-degree, and position-angle maps at 1.40 and 4.86 GHz. The paper's main conclusions are that internal Faraday rotation is non-negligible at about 1.4 GHz, that polarization position angle is not a reliable magnetic-field tracer, that thermal free-free emission can outshine synchrotron emission and strongly reduces the polarization degree, that background cosmic-ray electrons contribute little, and that the most feasible polarization degree inside the brightest regions is about 8-10% with maxima of order 40-45%.

Significance. If the quantitative predictions hold, this would be the first self-consistent set of synthetic radio polarization maps for stellar bowshock nebulae and a useful interpretation framework for current upper limits (e.g., the <0.5% limit on BD+43 3654) and future SKA observations. The work is not circular: no model parameters are fit to polarization data, and the maps are genuine forward-model predictions with a concrete, falsifiable content. The systematic exploration of viewing angle theta and field orientation alpha, the inclusion of free-free dilution, internal Faraday rotation, and the Galactic electron background are strengths. However, the headline polarization numbers are controlled to a large degree by an uncalibrated turbulence amplitude and by several acknowledged approximations, so the quantitative claims should be read as scenario-dependent rather than robust predictions.

major comments (4)

[Section 2.3; Figures 5 and 8; Conclusion 8] The central quantitative prediction is controlled by an unconstrained parameter. Section 2.3 sets the fiducial turbulent-to-ordered magnetic field ratio to deltaBturb/Breg = 0.5 with the justification 'we expect a high degree of turbulence', without deriving it from the MHD simulation or from an observational constraint. The paper itself shows the sensitivity: with deltaB/B = 0 the 1.4 GHz total-emission polarization reaches about 25% (Fig. 5, lower left) and the 4.86 GHz peak is about 14% (Fig. 8, left panel), whereas with deltaB/B = 0.5 the 4.86 GHz peak is about 8% (Fig. 8, middle panel) and the 'most feasible' value inside the 0.8 Imax contour at 1.4 GHz is 8-10% (Section 3.5). Varying this single free parameter over the range already shown in the paper changes the headline number by more than a factor of two, and by a larger factor if one compares with the intrinsic synchrotron limit. Conclusion 8 therefore is not robust unless the authors either constrain deltaB/B for bowshock environments or present all quantitative predictions as explicit functions of this parameter.
[Section 2.1 and Section 2.3] The quoted polarization numbers are drawn from a single arbitrarily chosen MHD snapshot and, apparently, a single realization of the turbulent magnetic field. Section 2.1 states that the MHD fields oscillate in time and that a representative snapshot is 'arbitrarily choose[n]', while Section 2.3 adds an isotropic Kolmogorov turbulent component whose particular realization is not described as averaged. Because depolarization is highly sensitive to the small-scale field structure, the peak values and the 8-10% estimate could carry significant realization noise. Multiple snapshots or multiple turbulent realizations should be used to establish that the quoted numbers are representative rather than specific to one draw.
[Sections 2.2 and 2.3] There is a dimensionality inconsistency between the transport and the emission calculations. The electron distribution is computed from a 2D axisymmetric transport equation using azimuthally averaged magnetic fields (Section 2.2), but the Stokes parameter maps are then integrated using the full 3D magnetic field from the MHD simulation (Section 2.3). For lines of sight that break the assumed axisymmetry (theta not equal to 0), this mixes a symmetric electron density with an asymmetric magnetic field, which can introduce artificial structure in the Q and U maps and in the resulting position angles. The authors should either use the azimuthally averaged fields consistently in both stages for the maps shown, or justify and quantify the error introduced by this hybrid approach.
[Section 2.3; Conclusions 4 and 5] The free-free treatment is too crude to support the quantitative polarization predictions. The optical path is taken arbitrarily from -8 to +8 pc, and the free-free emission from the Strömgren sphere outside this path is replaced by a uniform medium; the authors themselves estimate the resulting error as 'a factor close to unity'. Because thermal dilution is one of the two main mechanisms that reduce the polarization degree (Conclusions 4 and 5), an order-unity uncertainty in the free-free intensity translates directly into an order-unity uncertainty in the predicted polarization percentage. The qualitative conclusion that thermal emission can dominate is solid, but the numerical values quoted in Conclusion 8 require a more accurate treatment of the ionized surroundings, or a stated range reflecting this systematic uncertainty.

minor comments (5)

[Introduction, paragraph 4] There is a typo in 'A special case is the the bowshock of the massive runaway star BD+43 3654'; 'the the' should read 'the'.
[Figure 2 caption] The caption describes the free-free emissivity as 'evaluated from the steady state MHD fields used with the transport equation', but free-free emissivity depends on the thermal plasma and not on the relativistic electron transport; the wording is confusing and should be clarified.
[Section 4 versus Conclusion 8] There is a small numerical inconsistency: Section 4 states that the maximum polarization degree is 'about 45% in very localized spots' for alpha = 90 and theta = 90, while Conclusion 8 quotes a maximum of 'about 40%'. The color scale of the corresponding panel in Figure 11 saturates at 40%, so the text and conclusion should be checked for consistency.
[Section 3.5] The sentence 'In all cases, a polarization degree of approximately 30%, is encircled inside the I = 0.2 Imax contour' has a misplaced comma; also, 'approximately' should be 'less than or approximately' to match the displayed ranges, since several maps show values above 30% inside the contour.
[Section 2.2] The expression for the maximum electron energy, E < 3 e B_shock V_shock l / c, would benefit from a brief derivation or a reference specifying the numerical pre-factor and the assumed shock geometry; as written, the pre-factor appears without justification.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the polarization numbers are forward-model outputs under stated assumptions; the unconstrained turbulence amplitude is a robustness caveat, not a fitted input.

full rationale

The derivation chain is forward-modeling rather than circular. The MHD structure is obtained by solving Eqs. (1)-(5) with PLUTO; the electron distribution comes from solving Eq. (9); the polarized intensity is obtained from Eq. (10) with Stokes integration; and the polarization fraction is defined as Pi = sqrt(Q^2+U^2)/Itot with Itot = Isync + IBrems. No model parameter is fitted to an observed polarization target; the headline numbers in Conclusion 8 are read off the synthetic maps under the stated assumptions. The largest quantitative sensitivity is to the turbulent-field amplitude introduced in Section 2.3: "The degree of magnetic turbulence in the source is unknown, however we expect a high degree of turbulence. Here we assume a fiducial value deltaBturb/Breg = 0.5." This is an unconstrained input, and Fig. 8 shows that setting deltaB/B = 0 raises the peak from about 8% to about 14% (or about 25% after thermal dilution at 1.4 GHz); that is a robustness limitation, not a circular reduction, because the prediction is not defined to be the input and the paper does not tune the amplitude to force the 8-10% result. The paper cites the authors' prior transport code and a "Galactic-like" diffusion coefficient in Section 2.2, but these are explicitly stated numerical modeling choices rather than imported uniqueness theorems, and they do not by themselves determine the conclusion. Likewise, the statements that thermal emission can outshine synchrotron and dilute polarization follow from the definition of Pi once the computed IBrems is included, but the actual spatial distributions and magnitudes are computed, so the conclusions are properties of the model output, not restatements of the inputs. No significant circularity is present.

Assumptions & free parameters 8 free parameters · 8 assumptions · 0 invented entities

The central predictions rest on a handful of hand chosen inputs, the most consequential being the turbulence amplitude δB/B=0.5, the electron injection efficiency, and the assumed diffusion coefficient. None of these is fitted to the target observable (polarization), but they set the normalization and the spatial morphology of the maps. Standard physical formulas (synchrotron, free-free, transport) are taken from the literature.

free parameters (8)

Turbulent to ordered magnetic field ratio δBturb/Breg = 0.5 (fiducial), 1.0 for comparison
Assumed in Section 2.3; directly controls the predicted polarization degree, which drops from roughly 70 percent at zero turbulence to 8-10 percent at 0.5.
Electron injection efficiency ζ = 0.01
Fraction of wind mechanical power converted into relativistic electrons (Section 2.2); sets the overall synchrotron normalization.
Maximum electron energy Emax = 10 GeV
Derived from the acceleration region size using Bohm diffusion (Section 2.2); affects the synchrotron spectrum near the modeled frequencies.
Diffusion coefficient D(E) = 10^25 (E/10 GeV)^1/2 cm^2 s^-1
Assumed Galactic-like, isotropic and homogeneous diffusion (Section 2.2); sets the spatial distribution of electrons and therefore the morphology of the maps.
Ambient ISM density nISM = 0.57 cm^-3
Fiducial ambient density in Table 1; determines the size of the bowshock and the strength of free-free emission.
Ambient magnetic field BISM = 5 μG
Fiducial ISM field strength in Table 1; compressed at the shock to roughly 20 μG, setting the synchrotron emissivity and Faraday depth.
Stellar space velocity V⋆ = 40 km s^-1
Fiducial runaway velocity in Table 1; sets the shock Mach number and the bowshock geometry.
Turbulence outer scale = 1 pc
Assumed injection scale of the Kolmogorov turbulent field (Section 2.3); affects depolarization along the line of sight.

assumptions (8)

domain assumption Ideal MHD equations with radiative cooling and heating describe the wind-ISM interaction.
Used in Section 2.1 to compute the steady state structure; assumes the plasma behaves as a single-fluid ideal MHD gas.
domain assumption Diffusive shock acceleration produces a power-law electron spectrum with index 2 at the reverse shock.
Injection spectrum Q proportional to E^-2 assumed in Section 2.2; a different mechanism or index would change the synchrotron spectral index and maps.
domain assumption Bohm diffusion determines the maximum electron energy.
Used to set Emax = 10 GeV in Section 2.2.
standard math The wind magnetic field follows the Parker spiral model (Equations 6 and 7).
Taken from Ignace et al. 1998; valid for weak, flow-dominated fields in the stellar wind.
domain assumption The galactic cosmic ray electron flux parametrization of Potgieter et al. 2015 represents the background.
Used in Section 3.5 to set boundary conditions for background electrons.
ad hoc to paper Turbulent magnetic field is isotropic with a Kolmogorov spectrum and outer scale 1 pc.
Introduced in Section 2.3 to model depolarization; the amplitude is unconstrained and chosen as a fiducial value.
standard math Polarization angle follows standard synchrotron radiative transfer with Faraday rotation (Equation 10).
Standard synchrotron polarization formulas from Rybicki & Lightman 1979.
ad hoc to paper Free-free emission from the ionized Strömgren sphere can be approximated as uniform outside the 16 pc optical path.
Assumed in Section 2.3 to account for thermal emission beyond the simulation domain; the authors estimate a factor of order unity error from this choice.

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Cite this review

Pith. "Pith review of Radio polarization from runaway star bowshocks-I. The general case." pith.science (2026). https://pith.science/paper/ITXXSH36

@misc{pith2026250506777,
  author       = {Pith},
  title        = {Pith review of: Radio polarization from runaway star bowshocks-I. The general case},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ITXXSH36}},
  note         = {Machine review of arXiv:2505.06777}
}

read the original abstract

High velocity stars move through the interstellar medium with V > 30 km/s. When the star has powerful winds, under the appropriate conditions, the interaction of the wind with the interstellar material produces a system of shocks. The outer shock, called the bowshock, perturbs the ambient medium, heating and compressing the gas. The dust in the compressed bowshock cools, producing infrared radiation. This emission appears as extended coma-shape structures. The discovery of radio nonthermal emission from two stellar bowshock nebulae indicates that these sources might be accelerating electrons up to relativistic energies. The produced nonthermal radio emission is most probably synchrotron which has a high degree of polarization. In this work we model the synchrotron emission of runaway massive star bowshocks aiming to produce synthetic radio emission and polarization maps for two frequencies: 1.40 and 4.86 GHz. We model the interacting plasmas in a steady-state regime by means of magnetohydrodynamics simulations and we compute the injection and transport of the relativistic electrons in the diffusion approximation. We include in the model the most important depolarization effects. Our main conclusions are i) the effects of Faraday rotation within the source are important at the lowest frequency considered, ii) inferring the local magnetic field direction from polarization measurements only can be misleading, iii) thermal radio emission produced by ionized plasma within the bowshock structure and surroundings can surpass the polarized one for the considered frequencies, and iv) the contribution from the background electrons is minor.

Figures

Figures reproduced from arXiv: 2505.06777 by the authors.

**Figure 1.** Maps of density (left) and magnetic field magnitude (right), for the plane y = 0, corresponding to the “steady state” solution of the collision of the wind of a massive star moving at V⋆ = 40 km s−1 with the ISM. The white arrows in the right panel show the magnetic field direction. No turbulent magnetic field component is superimposed to the magnetic field in these maps (that is, they correspond to the models δBtur… view at source ↗

**Figure 2.** Emissivity distributions at ν = 1.40 GHz for the plane y = 0, for our models with α = 0◦ and δBturb/Breg = 0. Left: Free-free (Bremsstrahlung) jBREMS evaluated from the “steady state” MHD fields used with the transport equation (Eq. 9; see also § 2.1 and [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Specific intensity maps for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ). The panels on the left correspond to ν = 1.4 GHz, and those on the right to ν = 4.86 GHz. The maps on the top correspond to synchrotron, the middle plots correspond to Bremsstrahlung, and the maps on the bottom show the sum of both contributions. The blue iso-intensity curves correspond to the values I = 0.8 (dark-blue), 0.… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Spectral index map for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ). The blue isointensity curve corresponds to the values I = 0.8 (dark-blue), 0.5 (light-blue), and 0.2 Imax (cyan), for the total intensity at 1.40 GHz. appearing between the polar…

**Figure 5.** Figure 5: Polarization degree maps for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ). The panels on the left correspond to ν = 1.4 GHz, and those on the right to ν = 4.86 GHz. The maps on the top correspond to the polarization degree considering synchrotron em…

**Figure 6.** Figure 6: Polarization direction rotated 90◦ (red vectors) for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ). The blue vectors show the direction of the average magnetic field along the line of site. See the text for further details. Data is shown only inside …

**Figure 7.** Figure 7: Intensity synchrotron maps for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ) in the presence of a turbulent magnetic field component with δBturb/Breg = 0.5 . The panel on the left corresponds to ν = 1.4 GHz, and that on the right to ν = 4.86 GHz. The…

**Figure 8.** Figure 8: Polarization degree and position angle maps for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ) at ν = 4.86 GHz. The panels show the polarization degree considering the total emission (thermal + nonthermal) and a turbulent component of the magnetic fie…

**Figure 9.** Figure 9: Top: Specific intensity synchrotron map at ν = 1.4 GHz, for the bowshock region projected onto the POS (θ = 30◦ and α = 0◦ ) produced by the background cosmic ray electrons. Bottom: Polarization degree map at ν = 1.4 GHz and position angle (rotated by 90◦ ) for the tot…

**Figure 10.** Figure 10: Intensity maps at ν = 1.4 GHz for the total emission (the contribution from the cosmic rays is also considered), for 3 projection angles θ = 0, 30 and 90◦ (left, middle, and right column, respectively) and for 3 values of α (angle between BISM and −V⋆): 0◦ (upper pane…

**Figure 11.** Figure 11: Polarization degree maps at ν = 1.4 GHz for the total emission (the contribution from the cosmic rays is also considered), for 3 projection angles θ = 0, 30 and 90◦ (left, middle, and right column, respectively) and for 3 values of α (angle between BISM and −V⋆): 0◦ (…

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Cited by 1 Pith paper

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