Pith. sign in

REVIEW 3 major objections 5 minor 74 references

The paper argues that dust in the unstable neutral medium—not the warm or cold gas—dominates the polarized foreground that CMB experiments must subtract, and that its EE/BB ratio of about 2 explains Planck's measurements.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-03 08:25 UTC pith:LJDHUL6A

load-bearing objection Solid phase-decomposed polarization study, but the UNM-dominance claim rests on untested uniform grain alignment and an EE/BB gap to Planck that the abstract overstates. the 3 major comments →

arxiv 2601.17255 v2 pith:LJDHUL6A submitted 2026-01-24 astro-ph.GA

Galactic Dust Polarization in Turbulent Multiphase ISM: On the Origin of the EE/BB Asymmetry

classification astro-ph.GA
keywords interstellar mediumdust polarizationEE/BB asymmetryMHD turbulencecosmic microwave backgroundinterstellar magnetic fieldsneutral interstellar phasesforeground subtraction
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper uses a high-resolution 3D magnetohydrodynamic simulation of the multiphase interstellar medium, post-processed with polarized radiative transfer, to generate synthetic dust polarization maps. Splitting the gas into the warm (WNM), unstable (UNM), and cold (CNM) neutral media, it finds that each phase has distinct turbulence properties and a distinct EE/BB polarization ratio: the WNM gives about 3, the UNM about 2, and the CNM about 1.3. Only the UNM matches both the EE/BB ratio and the spectral slope measured by Planck at high Galactic latitudes, and since the UNM holds the largest mass fraction, the paper concludes it is the dominant contributor to the polarized dust foreground. This matters because a mis-modeled foreground could be mistaken for the faint primordial B-mode signal that CMB experiments are searching for.

Core claim

The central claim is that the observed EE/BB asymmetry in Galactic dust polarization is not a single homogeneous signal but a phase-weighted mixture. In the trans-Alfvénic, transonic WNM and UNM, density filaments align tightly with the local magnetic field, which projects power into E-modes and pushes EE/BB to 2–3; in the supersonic, super-Alfvénic CNM, shocks tangle the field and nearly erase the asymmetry, driving the ratio toward 1.3. The full mixture lands near 1.6, and the UNM is the only phase whose spectral slope (about −2.6) matches Planck's measured B-mode slope. The paper therefore identifies the UNM as the dominant high-latitude polarized foreground and attributes the small-scale

What carries the argument

The load-bearing machinery is the phase decomposition of synthetic polarization maps. A 3D magnetohydrodynamic simulation on a 2048³ grid evolves gas, turbulence, and magnetic fields across a 100 pc box, and a polarized radiative transfer code converts the resulting density and field structure into Stokes Q and U maps. These maps are then Fourier-decomposed into E and B modes, and the EE/BB power ratio—the 'asymmetry'—serves as the observable diagnostic tying each phase's turbulence regime to the measured foreground. Structure-function slopes and gradient alignment angles are used to verify that the WNM, UNM, and CNM indeed occupy the claimed dynamical regimes.

Load-bearing premise

The dust composition, size distribution, and grain alignment efficiency are assumed identical across all ISM phases; if cold-medium grains align less efficiently or have different intrinsic properties, the CNM's polarization contribution shrinks and the case for the UNM as the dominant foreground weakens.

What would settle it

Re-run the synthetic polarization with dust grain alignment efficiency in the cold phase artificially reduced by a factor of 2–3 while keeping all other parameters fixed; if the total predicted EE/BB ratio and B-mode spectral slope still match Planck, then the claim that the CNM drives the flattening and lowers the ratio is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • CMB foreground models that assume a single dust population will misestimate B-mode power; models should weight the unstable neutral medium as the dominant phase at high latitudes.
  • The small-scale flattening of the B-mode spectrum is a diagnostic of cold dense gas along the line of sight; masking or modeling CNM regions could recover a steeper, smoother foreground spectrum.
  • The synthetic 150 GHz predictions provide concrete expected slopes and EE/BB ratios for next-generation CMB surveys, giving a template for component separation.
  • Because the EE/BB ratio is nearly frequency-independent under uniform dust properties, a measured frequency dependence in future data would directly indicate variations in dust grain properties or temperature, not in the turbulence.
  • The convergence of the low CNM ratio at 2048³ resolution rules out insufficient resolution as the cause of the reduced ratio in earlier numerical studies.

Where Pith is reading between the lines

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

  • If the UNM truly dominates the foreground, the dust polarization signal should vary with the local UNM fraction: regions with more cold gas should show flatter spectra and lower EE/BB ratios—a prediction testable across the sky with Planck and future CMB data.
  • The uniform grain-alignment assumption is the principal unknown; allowing phase-dependent alignment efficiency (weaker alignment in dense cold gas) would change the CNM contribution and could shift the global ratio, so this is where the paper's conclusions are most sensitive.
  • The same phase-decomposition approach could be inverted: observed EE/BB ratios and spectral slopes might be used to estimate the thermal phase mix of the ISM, turning a foreground nuisance into a probe of interstellar physics.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper uses a 2048^3 AthenaK MHD simulation of a turbulent multiphase ISM (100 pc box, ~0.05 pc resolution) post-processed with the POLARIS radiative transfer code to generate synthetic dust polarization maps at 353 and 150 GHz. The authors separate emission into WNM, UNM, and CNM based on gas temperature and analyze turbulence anisotropy, structure functions, and E/B-mode power spectra. They find that the WNM and UNM are trans-Alfvénic/transonic with strong magnetic-field alignment and high EE/BB ratios (≈2.9 and ≈2.05), while the CNM is super-Alfvénic/supersonic with weak alignment and EE/BB ≈1.35. The total synthetic EE/BB peaks at ≈1.59, below the Planck value of ≈2, a gap the authors attribute to the CNM. They conclude that UNM dust, having the largest mass fraction, could be the dominant contributor to the high-latitude polarized foreground.

Significance. If the conclusions hold, this work provides a physically motivated explanation for the observed EE/BB asymmetry in Galactic dust polarization and offers phase-dependent, testable predictions for CMB foreground subtraction at 150 GHz. The study's strengths include a very high-resolution 2048^3 simulation with a dedicated resolution convergence check (Appendix B), a beam-smoothing test (Appendix A), and a forward model that is not fitted to Planck EE/BB data. The central result, however, depends on the assumption that dust composition, size distribution, and RAT alignment efficiency are spatially uniform across all ISM phases, and the claim that UNM is the dominant contributor is not backed by a quantitative amplitude decomposition. These limitations currently make the headline conclusion less secure than the abstract suggests.

major comments (3)
  1. [Section 2.2, §3.3.2] The uniform RAT alignment efficiency across phases is load-bearing. The text states 'the dust composition and size distribution are considered to be uniform across multi-phase ISM components' and that all grains above a_align are perfectly aligned (ideal RAT model). This fixes the CNM's polarization efficiency equal to the WNM/UNM. The total synthetic EE/BB peaks at ~1.6 (Table 2), and the paper attributes the deficit relative to Planck (~2) to the CNM. If CNM grains align less efficiently, as physically plausible due to ISRF attenuation and higher gas damping, the CNM polarization power would decrease, the total EE/BB would rise toward Planck, and the conclusion that CNM lowers the ratio while UNM matches Planck would be quantitatively altered. The paper provides no sensitivity analysis varying CNM alignment efficiency. Please include such a test, or at least a robust bound on how much
  2. [Section 3.3.2, Table 2] The claim that UNM is the dominant contributor is not supported by quantitative power amplitudes. Table 2 lists per-phase EE/BB peak ratios and spectral slopes, but not the absolute C_EE or C_BB amplitudes. The text states 'the overall contribution of the WNM to the total power is relatively minor, likely due to its lower density' but no phase-decomposed amplitude comparison is shown. Since the integrated polarization signal depends on column density and the line-of-sight magnetic field structure, mass fraction alone does not establish dominance. Please provide the phase-decomposed C_EE (and ideally C_BB) amplitudes, or the fractional contribution of each phase to the total C_EE at the scales of interest, to substantiate the 'dominant contributor' claim.
  3. [Abstract, §3.3.2] The abstract states 'Our synthetic observations reproduce the polarization power spectra measured by Planck,' but the quantitative agreement is partial. The total synthetic EE/BB peaks at ~1.59 (Table 2), below the Planck value of ~2, and the total C_BB slope is -2.22, while the Planck reference slope is -2.54 (Fig. 6 top panel). The text in §3.3.2 appropriately says 'qualitatively consistent,' but the abstract overstates the match. Please revise the abstract to 'qualitatively consistent' or explicitly quantify the discrepancy and the scales where agreement holds.
minor comments (5)
  1. [Appendix B] The first sentence of Appendix B says 'Fig. 9 displays the ratio...' but the referenced figure for the resolution study is Fig. 10, while Fig. 9 shows the beam-size test. Please correct the cross-reference.
  2. [Section 4, item 5] The conclusion says 'dust polarization from the WNM and UNM yields an EE/BB ratio (≈2)... suggesting it is a dominant contributor,' but earlier §3.3.2 singles out the UNM as the dominant contributor. Clarify whether the claim applies to UNM alone or to the combined WNM+UNM, and make the wording consistent throughout.
  3. [General] There are several typos, e.g., 'flucutations' in the conclusion, 'thr turbulent kinetic energy' in §3.1.1, and 'CMBB-mode' in the conclusion. A final proofread is recommended.
  4. [Figure 7 caption] The caption for the top panel says 'cold gas (T<200K) excluded' but the bottom panel shows all phases. Clarify the relationship between the top and bottom panels, and define the dashed vertical line if it indicates k_inj/k_dis.
  5. [Section 2.2] The paper says 'for the multi-phase ISM with n<100 cm^-3, the magnetic alignment by RATs is efficient,' but CNM densities in the simulation may approach 100 cm^-3. Specify the maximum density in the CNM and whether the alignment efficiency is assumed constant at the upper end of this range.

Circularity Check

0 steps flagged

No significant circularity: synthetic EE/BB spectra are benchmarked against Planck with no parameters fitted to the target ratio; self-citations are code/alignment inputs, not derived from this paper's target result.

full rationale

The paper's derivation chain is a forward model: an AthenaK MHD simulation with stated initial conditions (B≈3 µG, σ_v≈10 km/s, 100 pc box, cooling/heating terms) is post-processed with POLARIS to produce synthetic Stokes Q/U maps, from which E/B power spectra and EE/BB ratios are computed. No model parameter is fitted to the Planck EE/BB data; the paper explicitly reports that its total ratio is lower than Planck's (`Although our peak value (∼1.6) is lower than the Planck value, this difference is primarily attributable to the presence of supersonic and super-Alfvénic CNM`). The phase-separated ratios for WNM, UNM, and CNM are direct outputs of the same radiative-transfer calculation, not quantities reconstructed from the Planck values. The 150 GHz maps are likewise direct outputs of the same simulation with no additional fitting, so calling them predictions is legitimate. The self-citations are not load-bearing in a circular sense: Hu (2025) is cited for the AthenaK-based multiphase simulation setup, whose equations and parameters are stated in Section 2.1 and are not tuned to the Planck polarization result; Hoang & Truong (2024) is cited for RAT alignment efficiency, which is an independent grain-alignment modeling result, not derived from the present paper's EE/BB target. No uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in solely by citation: the ideal-RAT model is stated explicitly in Section 2.2. The main modeling limitation is the stated uniformity assumption (`The dust composition and size distribution are considered to be uniform across multi-phase ISM components`; `intrinsic dust properties are kept spatially uniform`), especially a single RAT alignment prescription across CNM and WNM. That is a robustness/sensitivity concern, not a circularity: changing CNM alignment efficiency would alter the quantitative conclusion, but it would not make the argument self-referential. The paper is self-contained against the external Planck benchmark and its central claim is not forced by construction; the appropriate circularity score is therefore 0.

Axiom & Free-Parameter Ledger

0 free parameters · 7 axioms · 0 invented entities

No parameters were fitted to the Planck data; the model inputs (B0=3 μG, sigma_v=10 km/s, cooling/heating, dust properties) are prior observational or theoretical constraints. The main loading is on the uniformity of dust properties across phases and the representativeness of the simulated phase fractions.

axioms (7)
  • domain assumption The Koyama & Inutsuka cooling/heating functions (Eq. 2-3) reproduce the multiphase thermal structure of the ISM.
    Used in the AthenaK simulations; if the cooling curve is wrong, phase fractions and turbulence properties would change.
  • domain assumption Dust grains are perfectly aligned via RATs for sizes > a_align, with uniform dust properties across phases.
    Adopted in Section 2.2; this is the weakest premise for the phase-dependent EE/BB ratios.
  • domain assumption Temperature thresholds (T<200 K CNM, 200-5000 K UNM, >5000 K WNM) correctly separate the ISM phases.
    Standard definition used in Section 3.1; the phase fractions and derived statistics depend on these cuts.
  • domain assumption The simulation's phase mass fractions represent high-latitude ISM conditions.
    The paper compares to Kalberla & Haud (2018); if the real CNM fraction is smaller, the total EE/BB would be closer to Planck, undermining the CNM explanation.
  • domain assumption The flat-sky approximation for E/B decomposition is valid for the 100 pc box.
    Used in Section 3.3.1; curvature and projection effects are neglected.
  • domain assumption Ideal MHD and neglect of thermal conduction are adequate at resolved scales.
    Stated in Section 2.1; thermal conduction scale is subdominant.
  • domain assumption Polarized dust emission is optically thin, so phase-masked decomposition is valid.
    Invoked in Section 3.3.1 to justify masking by temperature when generating phase-separated Stokes maps.

pith-pipeline@v1.3.0-alltime-deepseek · 11 in / 14252 out tokens · 129528 ms · 2026-08-03T08:25:18.392997+00:00 · methodology

0 comments
read the original abstract

Polarized thermal emission from Galactic dust is the dominant foreground for CMB polarization measurements at high frequencies, with its statistical properties shaped by the interplay between turbulence and magnetic fields in the multiphase interstellar medium (ISM). Variations in turbulence regime and density-magnetic-field alignment across the warm (WNM), unstable (UNM), and cold (CNM) neutral media should imprint distinct signatures on the power spectra and $EE/BB$ power ratio, yet the relative contributions of these phases remain poorly constrained. Using high-resolution 3D magnetohydrodynamic simulations of a turbulent multiphase ISM coupled with synthetic dust polarization maps, we quantify phase-dependent turbulence, anisotropy, and alignment properties. We find that the trans-Alfv\'enic and transonic WNM and UNM are strongly anisotropic, exhibiting tight alignment of density and velocity structures with the local magnetic field. In contrast, the super-Alfv\'enic and supersonic CNM displays reduced anisotropy and weak alignment. These dynamical differences are reflected in the statistical scaling of fluctuations: the square root of the second-order velocity structure function exhibits a slope near $1/3$ in the WNM, near $1/2$ in the CNM, and intermediate in the UNM. Comparing our synthetic polarization power spectra with \textit{Planck} measurements, we find that polarization from UNM dust yields spectral slopes closest to the \textit{Planck}-inferred values, whereas WNM and CNM dust produce steeper and shallower spectra, respectively. The WNM yields $EE/BB>2$, the UNM gives $EE/BB\sim2$, and the CNM yields $EE/BB\approx1$. These results suggest that UNM dust may be an important contributor to the polarized foreground under typical high-latitude ISM conditions. We present predictions at 150 GHz to inform foreground modeling and separation.

Figures

Figures reproduced from arXiv: 2601.17255 by Bao Truong, Le Ngoc Tram, Thiem Hoang, Yue Hu.

Figure 1
Figure 1. Figure 1: Distributions of number density n, temperature T, and turbulent plasma beta βtur in the multiphase ISM simulation. Shown is a two-dimensional slice from the 20483 simulation, displaying the number density (top), temperature (middle), and turbulent plasma beta βtur = ρv2 /(B 2 /8π) (bottom), where ρ is the gas mass density and v is the local turbulent velocity. For visualization purposes, only half of each … view at source ↗
Figure 2
Figure 2. Figure 2: Panels (a), (b), and (c): Distributions of the relative angle θρ, θv, and θB between the local magnetic field and the rotated (by 90 degrees) density gradient ∇ρ, velocity gradient ∇v, and magnetic field strength gradient ∇B, respectively. The relative angles are evaluated separately for the warm neutral medium (WNM; T > 5000 K), unstable neutral medium (UNM; 200 K < T < 5000 K), and cold neutral medium (C… view at source ↗
Figure 3
Figure 3. Figure 3: Statistical properties of scale-dependent fluctuations of velocity (1st column), magnetic field (2nd column), and number density (3rd column) in different ISM phases. The fluctuations are computed as the square root of the second-order structure function for each quantity, shown separately for the WNM (T > 5000 K), UNM (200 K < T < 5000 K), CNM (T < 200 K), and the total ISM (including all phases). Dashed … view at source ↗
Figure 4
Figure 4. Figure 4: Statistical properties of scale-dependent velocity and magnetic field fluctuations decomposed into components parallel and perpen￾dicular to the local magnetic field in different ISM phases. Fluctuations are computed as the square root of the second-order structure function. They are shown separately for the WNM, UNM, CNM, and the total ISM (including all phases). Dashed and dash-dotted grey lines represen… view at source ↗
Figure 5
Figure 5. Figure 5: Distributions of the Stokes parameters I (left), Q (middle), and U (right) for synthetic dust polarization. We consider two distinct frequencies: 353 GHz (top), corresponding to Planck observations, and 150 GHz (bottom), a primary target for future CMB experiments [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: E-mode and B-mode power spectra, C EE and C BB, calculated from synthetic dust polarization. Top panel: The power spectra C EE and C BB computed from synthetic dust polarization maps. The gray solid line indicates a reference slope of −2.54, which was the C BB spectral slope measured by Planck at 353 GHz. The subscripts “353” and “150” represent two distinct frequencies: 353 GHz and 150 GHz. kinj means the… view at source ↗
Figure 7
Figure 7. Figure 7: Ratio of C EE to C BB from synthetic dust polarization at 353 GHz. Top panel: EE and BB power spectra computed from synthetic dust polarization maps with cold gas (T < 200 K) excluded. The shaded gray region denotes the range of C EE/CBB ratios measured by Planck. kinj means the injection wavenumber of turbulence and kdis is the numerical dissipation wavenumber. Bottom panel: Same as the top panel, but sho… view at source ↗
Figure 8
Figure 8. Figure 8: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ratio of C EE to C BB from synthetic dust polarization with all phases included. Two different beam sizes ∼ 0.05 pc (left) and ∼ 0.5 pc (right) are included. kinj means the injection wavenumber of turbulence and kdis is the numerical dissipation wavenumber. To evaluate the impact of finite angular resolution on our statistics, we compare the power spectra derived using two distinct beam sizes: ∼ 0.05 pc (c… view at source ↗
Figure 10
Figure 10. Figure 10: Ratio of C EE to C BB for synthetic 353 GHz dust polarization from CNM. Three different numerical grid resolutions 5123 , 10243 , and 20483 are included [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 12 canonical work pages · 1 internal anchor

  1. [1]

    2019, JCAP, 2019, 056, doi: 10.1088/1475-7516/2019/02/056

    Ade, P., Aguirre, J., Ahmed, Z., et al. 2019, JCAP, 2019, 056, doi: 10.1088/1475-7516/2019/02/056

  2. [2]

    G., Lazarian, A., & Vaillancourt, J

    Andersson, B. G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A, 53, 501, doi: 10.1146/annurev-astro-082214-122414

  3. [3]

    R., & Federrath, C

    Beattie, J. R., & Federrath, C. 2020, MNRAS, 492, 668, doi: 10.1093/mnras/stz3377 BICEP2 Collaboration, Ade, P. A. R., Aikin, R. W., et al. 2014, PhRvL, 112, 241101, doi: 10.1103/PhysRevLett.112.241101

  4. [4]

    2018, JCAP, 2018, 049, doi: 10.1088/1475-7516/2018/08/049

    Boulanger, F., Enßlin, T., Fletcher, A., et al. 2018, JCAP, 2018, 049, doi: 10.1088/1475-7516/2018/08/049

  5. [5]

    2019, ApJ, 870, 87, doi: 10.3847/1538-4357/aaf383

    Brandenburg, A., Bracco, A., Kahniashvili, T., et al. 2019, ApJ, 870, 87, doi: 10.3847/1538-4357/aaf383

  6. [6]

    2010, ApJ, 710, 853, doi: 10.1088/0004-637X/710/1/853

    Chepurnov, A., & Lazarian, A. 2010, ApJ, 710, 853, doi: 10.1088/0004-637X/710/1/853

  7. [7]

    Cho, J., & Vishniac, E. T. 2000, ApJ, 539, 273, doi: 10.1086/309213

  8. [8]

    Crutcher, R. M. 2012, ARAA, 50, 29, doi: 10.1146/annurev-astro-081811-125514

  9. [9]

    Draine, B. T. 2011, Physics of the Interstellar and Intergalactic Medium

  10. [10]

    T., & Hensley, B

    Draine, B. T., & Hensley, B. S. 2021, ApJ, 919, 65, doi: 10.3847/1538-4357/ac0050

  11. [11]

    Federrath, C., & Klessen, R. S. 2012, ApJ, 761, 156, doi: 10.1088/0004-637X/761/2/156

  12. [12]

    2025, arXiv e-prints, arXiv:2510.12203, doi: 10.48550/arXiv.2510.12203

    Federrath, C., & Offner, S. 2025, arXiv e-prints, arXiv:2510.12203, doi: 10.48550/arXiv.2510.12203

  13. [13]

    C., Hoang, T., Kim, J.-G., & Tram, L

    Giang, N. C., Hoang, T., Kim, J.-G., & Tram, L. N. 2023, MNRAS, 520, 3788, doi: 10.1093/mnras/stad020

  14. [14]

    J., & Scannapieco, E

    Gray, W. J., & Scannapieco, E. 2017, ApJ, 849, 132, doi: 10.3847/1538-4357/aa9121

  15. [15]

    2022, ApJ, 934, 7, doi: 10.3847/1538-4357/ac76bf

    Ha, T., Li, Y ., Kounkel, M., et al. 2022, ApJ, 934, 7, doi: 10.3847/1538-4357/ac76bf

  16. [16]

    S., & Draine, B

    Hensley, B. S., & Draine, B. T. 2023, The Astrophysical Journal, 948, 55, doi: 10.3847/1538-4357/acc4c2

  17. [17]

    W., Yuen, K

    Ho, K. W., Yuen, K. H., Flauger, R., & Kritsuk, A. G. 2025, PhRvD, 112, L101302, doi: 10.1103/vhhn-33jw

  18. [18]

    W., Yuen, K

    Ho, K. W., Yuen, K. H., & Lazarian, A. 2023, MNRAS, 521, 230, doi: 10.1093/mnras/stad481 —. 2024, arXiv e-prints, arXiv:2407.14199, doi: 10.48550/arXiv.2407.14199

  19. [19]

    2025, ApJ, 994, 115, doi: 10.3847/1538-4357/ae0a1a

    Hoang, T. 2025, ApJ, 994, 115, doi: 10.3847/1538-4357/ae0a1a

  20. [20]

    2008, MNRAS, 388, 117, doi: 10.1111/j.1365-2966.2008.13249.x

    Hoang, T., & Lazarian, A. 2008, MNRAS, 388, 117, doi: 10.1111/j.1365-2966.2008.13249.x

  21. [21]

    2016, ApJ, 831, 159

    Hoang, T., & Lazarian, A. 2016, ApJ, 831, 159

  22. [22]

    2024, ApJ, 965, 183, doi: 10.3847/1538-4357/ad2a56

    Hoang, T., & Truong, B. 2024, ApJ, 965, 183, doi: 10.3847/1538-4357/ad2a56

  23. [23]

    Hopkins, P. F. 2025, arXiv e-prints, arXiv:2509.07104, doi: 10.48550/arXiv.2509.07104

  24. [24]

    2025, ApJ, 986, 62, doi: 10.3847/1538-4357/add731

    Hu, Y . 2025, ApJ, 986, 62, doi: 10.3847/1538-4357/add731

  25. [25]

    2020, ApJ, 901, 162, doi: 10.3847/1538-4357/abb1c3

    Hu, Y ., Lazarian, A., Li, Y ., Zhuravleva, I., & Gendron-Marsolais, M.-L. 2020, ApJ, 901, 162, doi: 10.3847/1538-4357/abb1c3

  26. [26]

    2025a, ApJ, 988, 188, doi: 10.3847/1538-4357/ade701

    Hu, Y ., Scannapieco, E., Buie, II, E., et al. 2025a, ApJ, 988, 188, doi: 10.3847/1538-4357/ade701

  27. [27]

    2024, Nature Communications, 15, 1006, doi: 10.1038/s41467-024-45164-8

    Hu, Y ., Stuardi, C., Lazarian, A., et al. 2024, Nature Communications, 15, 1006, doi: 10.1038/s41467-024-45164-8

  28. [28]

    2025b, ApJ, 983, 32, doi: 10.3847/1538-4357/adbe68

    Hu, Y ., Whittingham, J., Lazarian, A., et al. 2025b, ApJ, 983, 32, doi: 10.3847/1538-4357/adbe68

  29. [29]

    2021, ApJ, 911, 37, doi: 10.3847/1538-4357/abea18

    Hu, Y ., Xu, S., & Lazarian, A. 2021, ApJ, 911, 37, doi: 10.3847/1538-4357/abea18

  30. [30]

    M., & Hopkins, P

    Hu, Y ., Xu, S., Lazarian, A., Stone, J. M., & Hopkins, P. F. 2025c, ApJ, 994, 142, doi: 10.3847/1538-4357/ae1127

  31. [31]

    M., & Lazarian, A

    Hu, Y ., Xu, S., Stone, J. M., & Lazarian, A. 2022, ApJ, 941, 133, doi: 10.3847/1538-4357/ac9ebc

  32. [32]

    H., & Lazarian, A

    Hu, Y ., Yuen, K. H., & Lazarian, A. 2018, MNRAS, 480, 1333, doi: 10.1093/mnras/sty1807 —. 2019a, ApJ, 886, 17, doi: 10.3847/1538-4357/ab4b5e

  33. [33]

    H., Lazarian, V ., et al

    Hu, Y ., Yuen, K. H., Lazarian, V ., et al. 2019b, Nature Astronomy, 3, 776, doi: 10.1038/s41550-019-0769-0

  34. [34]

    M., Rotti, A., & Collins, D

    Huffenberger, K. M., Rotti, A., & Collins, D. C. 2020, ApJ, 899, 31, doi: 10.3847/1538-4357/ab9df9

  35. [35]

    2014, Progress of Theoretical and Experimental Physics, 2014, 06B109, doi: 10.1093/ptep/ptu065

    Ichiki, K. 2014, Progress of Theoretical and Experimental Physics, 2014, 06B109, doi: 10.1093/ptep/ptu065

  36. [36]

    Jokipii, J. R. 1966, ApJ, 146, 480, doi: 10.1086/148912

  37. [37]

    R., & Parker, E

    Jokipii, J. R., & Parker, E. N. 1969, ApJ, 155, 777, doi: 10.1086/149909

  38. [38]

    Kalberla, P. M. W., & Haud, U. 2018, A&A, 619, A58, doi: 10.1051/0004-6361/201833146

  39. [39]

    Kalberla, P. M. W., & Kerp, J. 2009, ARA&A, 47, 27, doi: 10.1146/annurev-astro-082708-101823

  40. [40]

    Kamionkowski, M., & Kovetz, E. D. 2016, ARA&A, 54, 227, doi: 10.1146/annurev-astro-081915-023433

  41. [41]

    2018, MNRAS, 478, 530, doi: 10.1093/mnras/sty1115 18

    Kandel, D., Lazarian, A., & Pogosyan, D. 2018, MNRAS, 478, 530, doi: 10.1093/mnras/sty1115 18

  42. [42]

    2002, ApJL, 564, L97, doi: 10.1086/338978

    Koyama, H., & Inutsuka, S.-i. 2002, ApJL, 564, L97, doi: 10.1086/338978

  43. [43]

    G., Flauger, R., & Ustyugov, S

    Kritsuk, A. G., Flauger, R., & Ustyugov, S. D. 2018, PhRvL, 121, 021104, doi: 10.1103/PhysRevLett.121.021104

  44. [44]

    R., Burkhart, B., Forbes, J

    Krumholz, M. R., Burkhart, B., Forbes, J. C., & Crocker, R. M. 2018, MNRAS, 477, 2716, doi: 10.1093/mnras/sty852

  45. [45]

    Evidence for dust emission in the Warm Ionised Medium using WHAM data

    Lagache, G., Haffner, L. M., Reynolds, R. J., & Tufte, S. L. 2000, A&A, 354, 247, doi: 10.48550/arXiv.astro-ph/9911355

  46. [46]

    Larson, R. B. 1981, MNRAS, 194, 809, doi: 10.1093/mnras/194.4.809

  47. [47]

    2007, MNRAS, 378, 910, doi: 10.1111/j.1365-2966.2007.11817.x

    Lazarian, A., & Hoang, T. 2007, MNRAS, 378, 910, doi: 10.1111/j.1365-2966.2007.11817.x

  48. [48]

    Lazarian, A., & Vishniac, E. T. 1999, ApJ, 517, 700, doi: 10.1086/307233

  49. [49]

    2021, ApJ, 923, 53, doi: 10.3847/1538-4357/ac2de9

    Lazarian, A., & Xu, S. 2021, ApJ, 923, 53, doi: 10.3847/1538-4357/ac2de9

  50. [50]

    Lazarian, A., & Yuen, K. H. 2018, ApJ, 853, 96, doi: 10.3847/1538-4357/aaa241

  51. [51]

    H., Lee, H., & Cho, J

    Lazarian, A., Yuen, K. H., Lee, H., & Cho, J. 2017, ApJ, 842, 30, doi: 10.3847/1538-4357/aa74c6

  52. [52]

    Lehner, N., & Howk, J. C. 2011, Science, 334, 955, doi: 10.1126/science.1209069

  53. [53]

    2022, MNRAS, 510, 4952, doi: 10.1093/mnras/stab3783

    Liu, M., Hu, Y ., & Lazarian, A. 2022, MNRAS, 510, 4952, doi: 10.1093/mnras/stab3783

  54. [54]

    S., Mezger, P

    Mathis, J. S., Mezger, P. G., & Panagia, N. 1983, ˚a, 128, 212

  55. [55]

    S., Rumpl, W., & Nordsieck, K

    Mathis, J. S., Rumpl, W., & Nordsieck, K. H. 1977, Astrophysical Journal, 217, 425

  56. [56]

    M., Stanimirovi´c, S., & Rybarczyk, D

    McClure-Griffiths, N. M., Stanimirovi´c, S., & Rybarczyk, D. R. 2023, ARA&A, 61, 19, doi: 10.1146/annurev-astro-052920-104851

  57. [57]

    F., & Ostriker, E

    McKee, C. F., & Ostriker, E. C. 2007, ARA&A, 45, 565, doi: 10.1146/annurev.astro.45.051806.110602

  58. [58]

    F., & Ostriker, J

    McKee, C. F., & Ostriker, J. P. 1977, ApJ, 218, 148, doi: 10.1086/155667 OpenAI. 2022, Introducing ChatGPT, doi: https://openai.com/index/chatgpt/ Planck Collaboration, Abergel, A., Ade, P. A. R., et al. 2014a, A&A, 571, A11, doi: 10.1051/0004-6361/201323195 —. 2014b, A&A, 566, A55, doi: 10.1051/0004-6361/201323270 Planck Collaboration, Ade, P. A. R., Agh...

  59. [59]

    E., Peek, J

    Putman, M. E., Peek, J. E. G., & Joung, M. R. 2012, ARA&A, 50, 491, doi: 10.1146/annurev-astro-081811-125612

  60. [60]

    H., & Bieber, J

    Qin, G., Matthaeus, W. H., & Bieber, J. W. 2002, ApJL, 578, L117, doi: 10.1086/344687

  61. [61]

    2016, A&A, 593, A87, doi: 10.1051/0004-6361/201424930

    Reissl, S., Wolf, S., & Brauer, R. 2016, A&A, 593, A87, doi: 10.1051/0004-6361/201424930

  62. [62]

    2017, ApJ, 837, 150, doi: 10.3847/1538-4357/aa61a0

    Scoville, N., Lee, N., Vanden Bout, P., et al. 2017, ApJ, 837, 150, doi: 10.3847/1538-4357/aa61a0

  63. [63]

    A., Collins, D

    Stalpes, K. A., Collins, D. C., & Huffenberger, K. M. 2024, ApJ, 972, 26, doi: 10.3847/1538-4357/ad571b

  64. [64]

    Snowden, S. L. 1999, MNRAS, 302, 417, doi: 10.1046/j.1365-8711.1999.02013.x

  65. [65]

    M., Mullen, P

    Stone, J. M., Mullen, P. D., Fielding, D., et al. 2024, arXiv e-prints, arXiv:2409.16053, doi: 10.48550/arXiv.2409.16053

  66. [66]

    G., Sormani, M

    Tress, R. G., Sormani, M. C., Girichidis, P., et al. 2024, A&A, 691, A303, doi: 10.1051/0004-6361/202450035

  67. [67]

    2025, The Astrophysical Journal, 981, doi: 10.3847/1538-4357/adb423 Van Rossum, G., & Drake, F

    Truong, B., & Hoang, T. 2025, The Astrophysical Journal, 981, doi: 10.3847/1538-4357/adb423 Van Rossum, G., & Drake, F. L. 2009, Python 3 Reference Manual (Scotts Valley, CA: CreateSpace) V´azquez-Semadeni, E. 2025 V´azquez-Semadeni, E., Gazol, A., & Scalo, J. 2000, ApJ, 540, 271, doi: 10.1086/309318

  68. [68]

    N., Li, Y ., Ha, T., et al

    Velguth, B. N., Li, Y ., Ha, T., et al. 2025, ApJ, 990, 165, doi: 10.3847/1538-4357/adf5c0

  69. [69]

    2023, MNRAS, 526, 224, doi: 10.1093/mnras/stad2680

    Whittingham, J., Sparre, M., Pfrommer, C., & Pakmor, R. 2023, MNRAS, 526, 224, doi: 10.1093/mnras/stad2680

  70. [70]

    G., Hollenbach, D., McKee, C

    Wolfire, M. G., Hollenbach, D., McKee, C. F., Tielens, A. G. G. M., & Bakes, E. L. O. 1995, ApJ, 443, 152, doi: 10.1086/175510

  71. [71]

    G., McKee, C

    Wolfire, M. G., McKee, C. F., Hollenbach, D., & Tielens, A. G. G. M. 2003, ApJ, 587, 278, doi: 10.1086/368016

  72. [72]

    2019, ApJ, 878, 157, doi: 10.3847/1538-4357/ab21be

    Xu, S., Ji, S., & Lazarian, A. 2019, ApJ, 878, 157, doi: 10.3847/1538-4357/ab21be

  73. [73]

    2020, ApJ, 894, 63, doi: 10.3847/1538-4357/ab8465

    Xu, S., & Lazarian, A. 2020, ApJ, 894, 63, doi: 10.3847/1538-4357/ab8465

  74. [74]

    2001, PhRvD, 64, 103001, doi: 10.1103/PhysRevD.64.103001

    Zaldarriaga, M. 2001, PhRvD, 64, 103001, doi: 10.1103/PhysRevD.64.103001