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REVIEW 4 major objections 6 minor 98 references

Insights into Solar Wind Flow Speeds from the Coronal Radio occultation Experiment: Findings from the Indian Mars Orbiter Mission

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Spectral broadening of a single spacecraft radio signal can directly measure solar wind speed in the middle corona.

desk verdict New MOM occultation data and a quiet-period electron density profile, but the velocity formula is built on circular reasoning: the 'angular broadening' is refractive bending computed from the same spectral broadening it is supposed to complement, so the derived speeds are mostly geometry plus a weak sixth-root scaling. read the letter →

arxiv 2502.09512 v1 pith:UYCUWIRR submitted 2025-02-13 astro-ph.SR

Keshav Aggarwal , R. K. Choudhary , Abhirup Datta , Roopa M. V. , Bijoy K. Dai This is my paper · ORCID
classification astro-ph.SR
keywords solarwindradiooccultationspectralbroadeningcoronaMarsOrbiterMissionelectrondensitycoronalturbulencecycle25
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

This paper tries to establish that the Doppler spectral width of a single radio signal passing through the solar corona is sufficient, together with the occultation geometry, to measure the speed of the solar wind in the middle corona. Using S-band signals from the Mars Orbiter Mission during its October 2021 solar conjunction, it obtains wind speeds between 100 and 150 km/s at heliocentric distances of 5-8 solar radii, and electron densities near $10^{10}$ $m^{-3}$. The authors introduce a simplified equation, their Eq. 15, that turns one observed spectral width into a perpendicular wind speed, and they argue this is a general tool for single-station radio occultation campaigns. The measured density falloff agrees with earlier models but sits at the low edge, which the paper attributes to the unusually quiet phase of solar cycle 25.

What carries the argument

The load-bearing object is the Doppler spectral width B_s, the second moment of a Gaussian fit to the 1-second radio power spectrum, after subtracting broadening caused by line-of-sight Doppler changes. The argument chains four relations around B_s: (i) an empirical Kolmogorov-spectrum relation TEC = f (B_s/c_0)^(5/6) (Eq. 6); (ii) the spherical-corona estimate N_e = TEC/(r [ESP]) (Eq. 7); (iii) the Coles-Harmon angular broadening formula $\theta$ = (1/2) r_e $lambda^{2}$ N_e r RSP/(1+RSP) (Eq. 11); and (iv) Woo's relation between wind speed, spectral broadening, and angular broadening (Eqs. 12-13). Substituting (i)-(iii) into (iv) collapses everything but geometry and B_s^(1/6) into the constant k0 = 1.687, producing Eq. 15. The 1/6 exponent also becomes the error propagation law: a given fractional error in B_s shrinks to one sixth in velocity.

What would settle it

Re-derive wind speeds for the same MOM days using an electron density obtained independently of B_s (for example from the Doppler-shift column-density fluctuations via Eq. 10, or from white-light polarized brightness reconstructions) and compare with Eq. 15; a systematic divergence in the 5-8 R_sun range would falsify the reduction. A cleaner test is a synthetic propagation simulation with known wind speed and turbulence parameters: if Eq. 15 does not recover the injected velocity to within its stated error, the formula is not a measurement of wind speed.

Watch

Extended reading notes

Core claim

The central discovery is a direct proportionality between solar wind speed and the sixth root of the spectral broadening of an occulted radio signal: v_perp = k0 [r REP (1+RSP)^2/RSP] Bs^(1/6), with k0 = 1.687 for S-band (Eq. 15). The paper derives this by chaining an empirical TEC-to-broadening relation, a spherical-corona electron density estimate, the Coles-Harmon angular broadening formula, and Woo's velocity-broadening relation, and then simplifying. Applying it to MOM observations from October 2-14, 2021, it finds solar wind velocities of roughly 100-150 km/s in the 5-8 R_sun region, consistent with an accelerating slow solar wind during a quiet phase of solar cycle 25. The paper presents the reduced equation as a general formula: any radio occultation with known geometry can recover the perpendicular solar wind speed from a single spectral-width measurement, without needing multi-station interferometry or separate density data.

Load-bearing premise

The derivation assumes a spherically symmetric, steady corona whose density irregularities follow a standard power-law (Kolmogorov) spectrum, so that the mean electron density read off from the spectral width can be inserted into the angular-broadening formula; if the turbulent density fluctuation level or spectral index differs from that assumption, Eq. 15 will not recover the true wind speed.

Editorial extensions

If this is right

  • The 100-150 km/s values place the MOM measurements in the slow solar wind regime and show the wind still accelerating in the 5-8 R_sun middle corona.
  • Future single-station occultation experiments can derive solar wind speed directly from spectral broadening and known geometry, without multi-station interferometry, separate density soundings, or in situ crossings.
  • Because Eq. 15 has only B_s plus geometry, the velocity error is one sixth of the spectral-width error, giving per-point uncertainties of about 7-10 percent in the MOM campaign.
  • The measured electron density profile matching the shape but sitting at the low edge of previous models indicates that radio occultation can track solar-cycle variations in coronal density during extended quiet periods.
  • The method is offered as a general equation transferable to other spacecraft and bands, so archived occultation spectra can be re-analyzed for wind speeds in the acceleration region.

Reading between the lines

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

  • Beyond the paper: a natural test is to recompute Eq. 15 using an independently measured electron density (e.g., from the Doppler-shift-derived column fluctuations in Eq. 10) instead of the density implied by B_s; where the two velocities diverge, the Kolmogorov-spectrum assumption is doing the work.
  • Beyond the paper: applying Eq. 15 to archived single-station occultation recordings from earlier missions could produce a uniform multi-decade record of middle-corona wind speeds, filling the 2-10 R_sun acceleration gap that in situ probes cannot routinely cover.
  • Beyond the paper: simultaneous S-band and X-band occultation of the same ray path would test the frequency dependence built into k0, because the empirical constant was derived specifically for S-band conditions.
  • Beyond the paper: the error budget quoted in the paper treats geometry and k0 as exact; a fuller uncertainty analysis that folds in the solar wind and magnetic-field alignment assumptions would likely widen the error bars beyond the stated 7-10 percent.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper analyzes S-band radio occultation observations of the Indian Mars Orbiter Mission (MOM) during October 2-14, 2021, a quiet phase of solar cycle 25, for solar offset distances of about 5-8 solar radii. From the Doppler spectral broadening of the received signal, the authors estimate electron densities through an empirical TEC-broadening relation and then propose a simplified equation, Eq. (14)/(15), that directly relates the solar wind speed perpendicular to the line of sight, v_perp, to the sixth root of the spectral broadening Bs and to the occultation geometry. They report solar wind velocities of 100-150 km/s in this region, compare their electron density profiles with several published models, and attribute lower densities to the weak solar activity during the observations. The central claim is that spectral broadening alone, combined with geometry, yields a general single-station method for measuring solar wind speed in the middle corona.

Significance. The manuscript has positive features: it uses a relatively rare, well-documented MOM solar conjunction dataset; the data reduction includes Gaussian spectral fitting, correction for line-of-sight Doppler changes, and comparison with a wide range of published density models and velocity measurements. If Eq. (14)/(15) were physically sound, the proposed method would be attractive because it would require only a single spectral-width measurement plus geometry. However, the central derivation is not sound: the quantity called angular broadening in Eq. (11) is actually the refractive bending angle due to the mean density gradient, not the turbulent angular broadening required by Woo's formula; and the electron density used in Eq. (11) is obtained from the same spectral broadening Bs through Eqs. (6)-(7), making the resulting velocity essentially a rescaled power of the assumed TEC-broadening relation. The two proposed final formulas, Eqs. (14) and (15), are not equivalent as written. These issues affect the paper's primary result and cannot be repaired by local editing.

major comments (4)
  1. [Section 3.2, Eq. (11)] The quantity θ defined in Eq. (11) is the single-ray refractive bending angle produced by the mean coronal density gradient, not the turbulent angular broadening required in Woo's Eq. (12)/(13). The expression is linear in the mean density Ne and scales as λ^2, whereas turbulent angular broadening is controlled by the variance and spatial spectrum of the density fluctuations and, for a Kolmogorov spectrum, scales as λ^{11/5}. The paper's statement that Coles & Harmon's 'angular position shift of the source' is equivalent to angular broadening conflates two distinct physical effects; the authors themselves note the definition. Using Eq. (11) in Eq. (13) therefore invalidates the derived velocity formula.
  2. [Section 3.2, Eqs. (6), (7), (11), (13)] The derivation is circular. The electron density Ne entering Eq. (11) is not measured independently; it is obtained from the same spectral broadening Bs through the empirical TEC-Bs relation of Eq. (6) and the geometric relation of Eq. (7). As a result, θ ∝ Bs^{5/6}, and Eq. (13) reduces to v ∝ Bs^{1/6} times a geometric factor. The reported velocities are therefore a rescaled version of the assumed TEC-broadening relation rather than an independent measurement of solar wind speed. A concrete test of independence would require an independent estimate of the density fluctuation level, for example from C_N^2 or from a separate angular-broadening observation.
  3. [Section 3.2, Eqs. (14)-(16)] The two final formulas are not equivalent. Eq. (14) contains the geometric factor [ESP] REP (1+RSP)/RSP^2, while Eq. (15) contains r REP (1+RSP)^2/RSP. The manuscript states no relation between [ESP] and r that turns one expression into the other; both standard small-angle relations, r ≈ RSP [ESP] and r ≈ REP [ESP], give different powers of the geometric variables. In addition, the spatial wavenumber k appearing in Eq. (13) is never specified or eliminated, and the constant k0 in Eq. (16) contains no k or θ. The reduction from Eq. (13) to Eqs. (14)-(15) cannot be followed or reproduced as written.
  4. [Section 3.4, Table 5] The error budget includes only the uncertainty in Bs^{1/6}, but if Eqs. (11)-(13) were the correct model, the dominant uncertainties would enter through the electron-density and turbulence assumptions used to construct θ. The reported errors of about 7-10% therefore understate the actual model uncertainty and give a misleading impression of precision, especially given the circular dependence of θ on Bs.
minor comments (6)
  1. [Figure 4 caption] The caption text appears to swap the panel descriptions: the left panel is described as showing 'Doppler broadening due to rate of change of LOS Doppler velocity,' but the figure displays observed versus corrected broadening; also, '04 Dec 2021' in the text should be '04 Oct 2021.'
  2. [Equation (10)] The definition of ΔΩ and the sign convention for ΔTEC are not stated, and the units of κ and fHz are not made explicit; as written, the dimensional consistency of the equation is unclear.
  3. [Section 2, FFT description] The text says that after applying the FFT, 'converting the signal power information from the time domain to the frequency domain'; more precisely, the FFT is applied to the complex time series and the squared magnitude yields the power spectrum, so the wording should be corrected.
  4. [Table 2 and Eq. (8)] The table columns use notation such as A/r^α, B/r^β, and C/r^γ, but the table entries omit the exponents for some models and do not state the units of N0; the table should be made consistent with Eq. (8).
  5. [References] Several reference entries contain garbled or duplicated author fields, for example 'RichardWoo, J. W.A. 1979' and the two identical 'Jain etal. 2024a' and 'Jain etal. 2024b' entries; the bibliography should be cleaned.
  6. [Section 3.2, paragraph after Eq. (16)] The statement that 'the broadening component acts as a scaling factor' is itself an admission that the spectral-width measurement has a weak influence on the derived velocity; this point should be reconciled with the paper's claim that spectral broadening directly yields solar wind velocity.

Circularity Check

2 steps flagged · score 6.0 of 10

The claimed velocity measurement reduces by construction to an assumed equivalence between refractive angular position shift and turbulent angular broadening, with the same spectral width Bs used twice: once to build theta via Eqs. 6-7-11 and once in Woo's Eq. 13.

  1. self definitional [Section 3.2, Eq. 11 and the following sentence]
    "Angular broadening in the radio signals can be expressed after Coles & Harmon (1989) as θ = 1/2 reλ2NerRSP/(1+RSP) ... It is worth mentioning here that Coles & Harmon (1989) define θ as the angular position shift of the source in radians, which is equivalent to the angular broadening."

    Eq. 11 is a deterministic single-ray refractive angular shift produced by the mean coronal density gradient and is linear in the mean density Ne, whereas Woo's Eq. 13 requires the stochastic turbulent angular broadening that depends on density fluctuations and the spatial wavenumber k. By declaring the two quantities 'equivalent', the paper substitutes into Eq. 13 a θ that was itself obtained from the same Bs through Eqs. 6 and 7. The same measured quantity therefore enters both as the direct numerator Bs and as the inverse denominator θ, reducing the velocity formula to a rescaled Bs^{1/6} expression of the assumed TEC-Bs calibration plus geometry. This is a definitional substitution, not an independent measurement.

  2. other [Section 3.2, Eqs. 13-15 and the paragraph following Eq. 15]
    "Using the above equations 4, 6, 7, 11 in 13, the final reduced form ... v⊥ = k0 × [ESP] × REP × (1+RSP)/R2SP × B^{1/6}_S ... It is important to note that while the geometry factor predominantly determines the solar wind velocities, the broadening component acts as a scaling factor."

    In the reduction to Eq. 15, the spatial wavenumber k, which carries the turbulence-scale dependence in Woo's Eq. 13, is eliminated with no stated substitution, and the measured spectral width survives only through the 1/6 power. The paper's own sentence concedes that the geometry factor, not the spectral broadening, predominantly sets the velocities. Consequently the headline result, 'using spectral broadening of the received signals, we obtained velocities of solar wind,' is largely forced by the imported empirical TEC-Bs relation and the geometric configuration; the spectral measurement acts mainly as a weak scaling factor.

full rationale

The circularity is localized but central. Eq. 15 follows algebraically only if one accepts Eq. 11 as 'angular broadening' and accepts the Ho et al. TEC-Bs relation. The problem is that Eq. 11 is, by the paper's own citation, the angular position shift of the source due to refraction, not the turbulent angular broadening required by Woo's Eq. 13; the assertion of equivalence is a definitional step that makes the derivation self-fulfilling. In addition, Ne in Eq. 11 is derived from the same Bs that appears in Eq. 13, so the final dependence on the measured spectral width is only Bs^{1/6}; the velocity is essentially a geometric scaling of the empirical TEC-Bs calibration. This is why the paper can state that geometry predominantly determines the velocities. The comparison with external datasets (Woo et al. 1978, Parker Solar Probe, etc.) is a genuine consistency check and shows the numbers are plausible, but it does not cure the internal reduction; it would also be consistent with a geometric formula that contains almost no spectral-width information. Self-citations (Jain et al., Tripathi & Choudhary) are used for data processing and Allan-variance corrections and are not load-bearing for the central velocity formula. The missing substitution for k is an additional non-circular gap: without specifying k, the step from Eq. 13 to Eq. 14 is incomplete. On balance, one or more central 'predictions' reduce by construction, so the score is 6 rather than 8 because the final values are checked externally and the algebraic derivation is transparent once the suspect equivalence is granted.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The velocity pipeline imports several calibrated constants and modeling assumptions from prior work: c0 in the TEC-broadening relation, the Kolmogorov spectral index, the 5.77 scaling factor, and the choice Q=1. The only parameter fit to this paper's own data is the electron density power law in Eq. 9. There are no invented physical entities, but the use of mean electron density for angular broadening is an ad hoc domain assumption.

free parameters (5)
  • c0 in TEC-Bs relation = 1.14e-24
    Empirical constant from Ho et al. 2002 relating total electron content to spectral broadening; inserted in Eq. 6 and propagates into the velocity through Eqs. 14 and 15.
  • Kolmogorov spectral index p = 11/3
    Assumed power-law index for density irregularities in Eq. 6; not measured in this work.
  • 5.77 scaling factor = 5.77
    Constant in the Woo 1977 velocity-broadening relation, dependent on field geometry and broadening pattern; used to define k0 in Eq. 16.
  • Q, gamma, phi = Q=1, gamma=0, phi=0
    Chosen to reduce Eq. 12 to Eq. 13 by assuming isotropic turbulence and solar wind parallel to the magnetic field.
  • Ne power-law fit coefficients A and B = A=0.296, B=0.865, exponents 6 and 2.150, N0=1e12
    Power-law coefficients fit to this paper's own derived electron densities in Eq. 9 and Table 2.
assumptions (5)
  • domain assumption Electron density irregularities follow a Kolmogorov power law with spectral index p=11/3.
    Needed for the empirical TEC-broadening relation in Eq. 6; no verification is provided for this study's conditions.
  • domain assumption Coronal density is spherically symmetric and the outflow is steady.
    Assumed before Eq. 7 to convert TEC into electron density and in Eq. 11 for the angular broadening geometry.
  • ad hoc to paper Angular broadening can be computed by inserting mean electron density into the Coles and Harmon formula (Eq. 11).
    The paper uses Ne from TEC as the Ne in the angular broadening formula instead of measuring angular broadening or using turbulent fluctuation strength; this is the load-bearing assumption.
  • domain assumption After removing LOS Doppler corrections and smoothing, the remaining spectral broadening is dominated by coronal density fluctuations and solar wind outflow.
    Basis of the whole analysis; other broadening sources are assumed negligible in Section 2 and Figure 4.
  • domain assumption The empirical TEC-broadening relation from Ho et al. 2002 remains valid for the MOM S-band geometry at 5-8 solar radii.
    Eq. 6 extrapolates a calibration from earlier missions to MOM conditions with no independent check.

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Cite this review

Pith. "Pith review of Insights into Solar Wind Flow Speeds from the Coronal Radio occultation Experiment: Findings from the Indian Mars Orbiter Mission." pith.science (2026). https://pith.science/paper/UYCUWIRR

@misc{pith2026250209512,
  author       = {Pith},
  title        = {Pith review of: Insights into Solar Wind Flow Speeds from the Coronal Radio occultation Experiment: Findings from the Indian Mars Orbiter Mission},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UYCUWIRR}},
  note         = {Machine review of arXiv:2502.09512}
}
read the original abstract

Using data collected by the Indian Mars Orbiter Mission in October 2021, we investigated coronal regions of the Sun by analyzing the Doppler spectral width of radio signals to estimate solar wind velocity. A simplified equation is introduced to directly relate these two parameters. The study focuses on observations conducted from October 2 to October 14, 2021, a relatively quiet phase of solar cycle 25. The analysis targeted the coronal region within heliocentric distances of 5-8 RSun, near the ecliptic plane. In this region, solar wind velocities ranged from 100 to 150 kms^-1, while electron densities were on the order of 10^10 m^(-3). We also compared our results with electron density observations and models derived from previous studies. Though the decrease in the electron densities with respect to increasing helio-centric distance matches quite well with the theoretical models, MOM estimates fall at the lower edge of the distribution. This difference may be attributed to the prolonged weak solar activity during the MOM observations, in contrast to prior studies conducted during periods of comparatively higher solar activity in earlier solar cycles.

Figures

Figures reproduced from arXiv: 2502.09512 by the authors.

Figure 1
Figure 1. Graphical representation of the geometry during a radio occultation experiment. (2009, Wexler etal. (2019)); Rosetta, MEX, and VEX (2010, Paetzold etal. (1996)); Akatsuki (2011, Miyamoto etal. (2014); Ando etal. (2015); Wexler etal. (2020a); Jain etal. (2023, 2024a)); MAVEN (2014, Withers etal. (2020a,b)); and the Indian Mars Orbiter Mission (MOM) (2015, Jain etal. (2022, 2024b)) have contributed to these investigat… view at source ↗
Figure 2
Figure 2. This graphic displays the position of MOM (marked by colored boxes) in its orbit around Mars in relation to the Sun (composite image made using SDO-AIA 171 and SOHO-LASCO C2/C3 white light images), as observed from Earth on dates of experiment. The specific dates of observation are identified by the numbers near each colored box. in part to the relative paucity of measurements available in the mid-coronal gap, and t… view at source ↗
Figure 3
Figure 3. Gaussian fit to the spectrogram of the received signal for a 1-s data frame. experiments (Tripathi & Choudhary 2022; Tripathi etal. 2022b; Jain etal. 2022, 2023, 2024a). Since S(ω) cannot be directly obtained in practice, statistical estimates are derived at a finite discrete set of N frequencies, S(ωi). The following estimators are employed to compute these three parameters: P = X N i=1 S ′ (ωi) (2) Ω = 1 P X N i=1… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: (a) Electron number density compared with other models present in literature (2 to 10 R⊙). The red points represent the derived values from our study. (b) Column electron density fluctuations as measured for the region of study [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Our results compared against the solar wind measurements done across a period of more than 50 years, using a variety of methods from in-situ to remote sensing observations. The velocity profile of the solar wind within a polar coronal hole having a cross-sectional area…

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