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REVIEW 5 major objections 5 minor 121 references

Measuring the electric dipole moment of the neutron using neutron star spin-down

T0 review · 5 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The spin-down energy budget of PSR J0437-4715 can constrain the neutron's CP-odd moments, yielding a 90th-percentile bound $|M_n^0| < 7.47\times 10^{-38}\,e\,\mathrm{cm}^2$ and an equivalent $|d_n| < 4.42\times 10^{-25}\,e\,\mathrm{cm}$.

desk verdict A novel proof-of-concept for an astrophysical nEDM channel, but the headline bound is 25x weaker than lab and rests on an r_pol prior and a N_pol/spin-down covariance that a referee must probe. read the letter →

arxiv 2608.06593 v1 pith:54AUP5QY submitted 2026-08-06 astro-ph.HE

Abriana Lyda This is my paper · ORCID
classification astro-ph.HE
keywords neutronelectricdipolemomentCPviolationstrongproblemmillisecondpulsarsPSRJ0437-4715pulsarspin-downmagneticquadrupolestarmagnetosphere
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 tries to show that a well-measured millisecond pulsar can act as a macroscopic laboratory for the neutron electric dipole moment, a CP-violating quantity that laboratory searches bound directly. Using PSR J0437-4715, it builds a star-specific model: mass and radius from X-ray pulse-profile modeling, a magnetic-field normalization from radio polarization propagation rather than from the standard $P\dot P$ torque, and a surface geometry from X-ray hot-spot observations. It then subtracts the modeled electromagnetic and gravitational-wave losses from the observed spin-down, interprets the leftover positive power as a CP-odd radiation channel, and converts that into limits. The headline result is a 90th-percentile bound on an effective neutron magnetic quadrupole moment, $|M_n^0| < 7.47\times 10^{-38}\,e\,\mathrm{cm}^2$, translating to $|\bar{\theta}| < 2.99\times 10^{-9}$ and $|d_n| < 4.42\times 10^{-25}\,e\,\mathrm{cm}$. The limits are weaker than ultracold-neutron experiments, so the paper's significance is the method: a source-specific energy budget can probe strong-CP physics astrophysically.

What carries the argument

The engine is a residual-power identity, $\Delta = \dot E_{\rm int} - L_{\rm dip} - L_{\rm GW}$, where the force-free dipolar luminosity $L_{\rm dip} = \mu_{\rm dip}^2\Omega^4(1+\sin^2\alpha)/c^3$ is evaluated from a propagation-informed surface field multiplied by the dipole fraction of a spherical-harmonic decomposition, not from the standard $P\dot P$ field. The residual is carried by $N_{\rm pol}$, the number of inner-crust free neutrons weighted by local polarization response, and by the quadrupolar surface-field fraction $f_{\ell=2} \simeq 0.18$-$0.23$ obtained from fitting low-order field families to X-ray hot-spot geometry. For the magnetic-quadrupole bound, the radiation formula is $P_{\rm MQM} = K_{\rm quad}\omega_{\rm rad}^6 (f_{\ell=2}N_{\rm pol}M_n^0)^2/c^5$ with $K_{\rm quad}=1/(60\pi)$ and $\omega_{\rm rad}=2\pi\nu_{\rm OPM}$, where $\nu_{\rm OPM}=2.472$-$2.680$ GHz is the frequency at which orthogonal polarization modes merge into a stable high-frequency branch. The polarization-limiting radius prior $r_{\rm pol} = 0.15$-$0.22\,R_{\rm LC}$ carries the field inference through $B_{\rm surf}\propto r_{\rm pol}^3$.

What would settle it

Recompute the same spin-down budget under an outer freeze-out branch, r_pol > 0.30 R_LC (for example 0.50-0.59 R_LC): the paper's own scaling B_surf proportional to $r_pol^{3}$ raises the field to roughly $10^{9}$-$10^{10}$ G, the modeled magnetic torque exceeds the pulsar's spin-down, and both the electric-dipole-radiation and magnetic-quadrupole bounds disappear. A direct measurement of r_pol from single-pulse polarization-angle sweeps across the OPM transition would decide whether the fiducial branch survives.

Watch

Extended reading notes

Core claim

The central claim is that the present-day spin-down power of PSR J0437-4715, after standard losses are subtracted with a field normalization that does not come from the torque law being tested, leaves a positive residual that any nonstandard CP-odd radiation channel must fit inside. An unscreened assignment to coherent electric-dipole radiation gives the benchmark $|d_n| < 5.783\times 10^{-25}\,e\,\mathrm{cm}$ at the 90th percentile of the positive branch. Because crustal electrons and magnetospheric plasma screen static electric dipoles, the paper instead promotes a screening-aware channel: an effective neutron magnetic quadrupole moment radiating at the observed orthogonal-polarization-mode transition frequency. With the aligned inner-crust neutron reservoir and the quadrupolar surface-field fraction, the residual gives $|M_n^0| < 7.47\times 10^{-38}\,e\,\mathrm{cm}^2$; assuming a pure-$\bar{\theta}$ origin, this becomes $|\bar{\theta}| < 2.99\times 10^{-9}$ and an equivalent $|d_n| < 4.42\times 10^{-25}\,e\,\mathrm{cm}$. The paper is explicit that these are conditional, effective bounds, not screening-independent measurements.

Load-bearing premise

The argument hinges on the assumed polarization-limiting radius: if the radio polarization freezes out farther than about a third of the light-cylinder radius, the inferred magnetic field is large enough that ordinary magnetic-dipole spin-down alone exceeds the pulsar's measured spin-down, wiping out the residual that the bounds are built on.

Editorial extensions

If this is right

  • If the residual-power logic is right, any well-timed pulsar with independent mass, radius, and field constraints can be audited for nonstandard CP-odd energy losses, not just PSR J0437-4715.
  • The direct electric-dipole-radiation bound is only as good as the unscreened assumption; under crustal or magnetospheric screening the same spin-down corresponds to a larger microscopic neutron electric dipole moment.
  • The magnetic-quadrupole channel sidesteps electrostatic Schiff screening, so the MQM bound is the more robust output of the framework.
  • Because the field posterior scales as $r_{\rm pol}^3$, constraining the polarization-limiting radius is the single highest-leverage observational step; without it the positive residual can vanish.

Reading between the lines

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

  • Editorial extension: since the inferred $d_n$ scales roughly as $\sqrt{\Delta}/N_{\rm pol}$, a better inner-crust microphysical calculation that raises the reliably aligned neutron reservoir has a direct linear payoff, and a factor-of-ten reduction in residual uncertainty would tighten the bound by about a factor of 3.2.
  • Editorial extension: if future single-pulse polarimetry places $r_{\rm pol}$ outside the fiducial interval, the paper's own logic says the branches should not be averaged; a physical measurement of the freeze-out radius would select which branch applies.
  • Editorial extension: applying the same budget to a younger, higher-field star could improve the bound only if the larger aligned-neutron reservoir outgains the larger torque systematics; the paper identifies this as an open question rather than a prediction.
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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

5 major / 5 minor

Summary. The paper develops a source-specific framework for translating the measured spin-down of PSR J0437-4715 into a constraint on CP-odd neutron electromagnetic moments. It combines a reduced-form density model (Ch. 2), a propagation-informed surface field from UWL polarimetry (Ch. 3), and NICER hot-spot geometry fits (Ch. 4) to construct a present-day luminosity budget. The residual Δ = Ė_int − L_dip − L_GW (Eq. 5.24) is first assigned to coherent electric-dipole radiation (Ch. 5) and then to an effective magnetic-quadrupole channel whose radiating frequency is identified with the OPM transition (Ch. 6). The central numerical results are the conditional 90th-percentile limits |M_n^0| < 7.47×10^-38 e cm^2, |θ̄| < 2.99×10^-9, and |d_n| < 4.42×10^-25 e cm (Eqs. 6.21–6.23), which the paper itself notes are weaker than the current laboratory bound.

Significance. If the method were validated, it would demonstrate that neutron-star spin-down can provide a complementary astrophysical probe of strong-CP violation, albeit one that is not competitive with ultracold-neutron experiments. The paper deserves credit for attempting a P-dot-independent magnetic-field estimate, for propagating many source-specific uncertainties in a Monte Carlo framework, and for being unusually explicit about screening, coherence, and branch-dependence caveats. However, no code or data products are shipped, so the numerical Monte Carlo results cannot be independently checked. More importantly, the central bound is not yet supported: the polarized-neutron inventory in the denominator of the estimator is not shown to be independent of the spin-down budget being analyzed, and the headline branch depends on an underived polarization-limiting-radius prior whose outer-branch alternatives eliminate the positive residual. The work is therefore more convincing as a methodological exercise than as a measurement, and the abstract's quoted limits should not be taken at face value without substantial additional validation.

major comments (5)
  1. [§5.2, Eqs. (2.3)–(2.6), (5.18)–(5.28)] The polarized-neutron inventory is not shown to be independent of the spin-down budget. Chapter 2 defines 𝒫_req = μ_NS/(N_n,crust |μ_n|) with μ_NS obtained from the timing-based B_p of Eq. (2.3). Section 5.2 then introduces the adjusted polarization fraction f_pol^adj = 1.26×10^-4 in Eq. (5.21) and uses it in Eq. (5.18) to obtain N_pol. The text does not derive f_pol^adj from an independent crustal-magnetization calculation; it appears to inherit the Chapter 2 timing calibration. Because the final estimator Q = 3c^3Δ/(2N_pol^2Ω^4 sin^2 α) has N_pol in the denominator while Δ = Ė_int − L_dip − L_GW, a common dependence on Ė_int can create or erase the positive residual. The manuscript must either derive f_pol from local microphysics or report the correlation between N_pol and Δ and demonstrate that the quoted 90th percentile is robust to this covariance.
  2. [§3.2, §3.6, Eqs. (3.7), (3.32), (3.33)] The polarization-limiting radius is a load-bearing prior that is not derived. The adopted r_pol = 0.15–0.22 R_LC (Eq. 3.7) is described as a 'trimmed interior subset' of the emission-height ladder, and the paper explicitly states that it does not follow from a theorem requiring r_pol < 0.30 R_LC. Since B_surf ∝ r_pol^3 (Eq. 3.32), the outer edge of the emission envelope raises the median field by ≈4.3 and an outer freeze-out branch by factors of 20–33; as §3.6 notes, those fields make L_dip exceed Ė_int and remove the positive residual on which both the EDR and MQM bounds depend. The central 90% limits are therefore conditional on a branch that the paper's own sensitivity analysis shows is not excluded. A physics-based derivation of r_pol, or a quantitative report of the final limits under the outer-branch systematics, is required before the headline numbers can be assessed.
  3. [§5.3.1, Eqs. (5.29)–(5.32)] The reported bound is the 90th percentile of the positive-residual subsample, not a 90% upper limit over the full model. Equation (5.29) gives P(Q>0)=0.787, so 21.3% of Monte Carlo draws produce Δ<0, meaning the modeled standard losses already exceed the observed spin-down. Conditioning on Q>0 selects the branch on which the prior stack leaves power; it does not provide posterior coverage for the null hypothesis of no CP-odd channel. The paper should report the full signed posterior, including the mass associated with Δ<0 realizations, before using '90% upper limit' language.
  4. [§6.3, Eqs. (6.15)–(6.18), (6.16)–(6.17)] The magnetic-quadrupole channel is an invented effective model rather than a derived neutron property. The luminosity formula introduces an effective single-neutron MQM M_n^0 with K_quad = 1/(60π) and sets the radiating mode frequency to ω_rad = 2πν_OPM without a microscopic calculation connecting a GHz magnetospheric scale to a CP-odd neutron quadrupole. The paper is transparent about this prescription, but the consequence is that Eqs. (6.21)–(6.23) are not measurements of d_n; they are conversions of an assumed residual power through an unvalidated channel. The manuscript should either provide a microscopic derivation or present the numerical values explicitly as an illustrative translation rather than as a bound.
  5. [§3.3–3.4, Eq. (3.16)] The propagation-based field is not fully independent of the spin-down budget. The pair-luminosity prior L_pair = 10^-2 Ė_int (Eq. 3.16) enters κ and Γ± in Eq. (3.24), so B_surf inherits timing dependence even though B_sd is not used. The paper acknowledges 'limited timing dependence,' but this dependence is load-bearing because the same Ė_int defines the residual that the field is used to interpret. The sensitivity of the final limit to the 10^-2 normalization and to the ±0.25 dex width should be quantified explicitly.
minor comments (5)
  1. [Eq. (2.1)] The piecewise density profile is written with explicit r^4 factors and, in the core branch, a leading 4π^2; as printed the equation has inconsistent dimensions unless the coefficients are understood to absorb all scales. Please rewrite in a dimensionally transparent form and define the units of a, b, c, d.
  2. [Table 3.2 and §3.4] The ray–field angle θ is listed as an adopted input θ=15°, but §3.4 derives it as 11.9°–14.9° from dipolar geometry for the fiducial r_pol branch. The table should state whether θ is a derived quantity or an independently assigned prior.
  3. [Fig. 5-2 and §5.3.1] The notation '90% C.L.' is used for a percentile of a conditional positive branch; consider using '90th percentile of the Q>0 subsample' throughout to avoid implying standard frequentist coverage.
  4. [Eqs. (5.28), (5.31)] Q is introduced first as a signed estimator and then as d_n^2 on the positive branch; the figure and text should define Q90 consistently and make clear that Q has units of (e cm)^2.
  5. [§7.1.1] The statement that 'the large fraction of unphysical Monte Carlo draws' suggests the force-free normalization over-assigns power is important; please move this caveat into the main results section rather than leaving it only in the future-work section.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the residual-power bound is a model-dependent physical conversion, not a restatement of its inputs.

full rationale

The paper's derivation chain does not reduce, by its own equations, to its own inputs. The central estimator Q = 3c^3 Δ / (2 N_pol^2 Ω^4 sin^2 α) (Eq. 5.28) combines a signed residual Δ = E_dot_int − L_dip − L_GW with a polarized-neutron reservoir N_pol that is constructed from the density profile and a local polarization response f_pol (Eqs. 5.17–5.22). The paper explicitly refuses to use the P Pdot-derived field B_sd for the torque subtraction (Chapter 3, opening paragraph), and the adopted field posterior is anchored to radio OPM propagation rather than to the spin-down torque law. The signed Monte Carlo distribution retains 21.3% negative realizations (Eq. 5.29), so the positive branch is not forced by construction. The MQM channel assigns the same signed residual to a specified radiation formula (Eq. 6.15) and translates it to theta-bar and d_n using external conversion coefficients (Eqs. 6.19–6.20); this is a physical hypothesis with stated assumptions, not a tautology. The only near-input dependence is the pair-luminosity prior L_pair = 10^-2 E_dot_int (Eq. 3.16), which feeds B_surf through the pair-multiplicity parameter κ. The paper discloses this as 'limited timing dependence' (Chapter 1 summary, Chapter 3.1), and it does not exhibit any explicit reduction of N_pol or L_dip to a rescaling of E_dot_int. The reader's suggested covariance between the numerator and denominator is not demonstrated in the text: f_pol^adj is presented as a Monte Carlo-propagated outcome, not as a fit to the spin-down-inferred dipole of Eq. 2.6. Because the specific reduction required for circularity cannot be quoted from the paper's equations, the finding is no significant circularity.

Assumptions & free parameters 9 free parameters · 9 assumptions · 2 invented entities

The central chain rests on a large stack of adopted priors and fitted calibrations. The most consequential are the r_pol freeze-out prior (B_surf proportional to r_pol^3), the pair-luminosity prior that retains timing dependence, the N_pol calibration to the spin-down-inferred dipole, and the ad hoc nu_eff = nu_OPM identification. None of these is validated against an independent measurement of the same quantity; the paper discloses most of them explicitly. The conversion coefficients from M_n^0 to bar_theta and d_n are external literature inputs.

free parameters (9)
  • density-profile shape parameters (a, b, c, d) and normalizations = not reported numerically
    Eq. (2.1) fits the piecewise density profile to the measured M and R and to the saturation/drip floor constraints; the fitted values are not quoted with uncertainties, though the gray band in Fig. 2-3 propagates (M, R) and density-choice uncertainties.
  • polarization-limiting radius prior r_pol = 0.15 to 0.22 R_LC (median 50.8 km, 90% interval +-8.7 km)
    Adopted freeze-out prior, deliberately trimmed from the Gangadhara-Thomas altitude ladder; B_surf is proportional to r_pol^3, the dominant sensitivity of the field inference (Chapter 3, Table 3.2).
  • pair-luminosity prior L_pair / Edot_int = 10^(-2.0 +- 0.25)
    Central value from MSP pair-cascade literature [83]; width is adopted. Retains 'limited timing dependence' through Edot_int and feeds the field normalization (Chapter 3).
  • ray-field angle theta = 15 deg
    Adopted as rounded upper-end dipolar value for the fiducial branch, not a measured parameter (Chapter 3).
  • effective mode frequency nu_eff = 2.472 to 2.680 GHz (= nu_OPM)
    Phenomenological identification of the MQM radiation frequency with the OPM-core transition scale, adopted in Chapter 6; the MQM bound scales as omega^6.
  • polarized neutron reservoir N_pol via adjusted polarization fraction f_pol^adj = N_pol = 2.14(+1.26/-0.84)e51; f_pol^adj = 1.26e-4
    Calibrated so inner-crust neutron magnetic moments account for the spin-down-inferred dipole of Eqs. (2.3)-(2.6); this timing-linked calibration sets the denominator of the final bound (Chapter 5).
  • gravitational-wave priors (ellipticity epsilon, r-mode amplitude alpha_r) = epsilon = 1e-9 +- 0.5e-9; alpha_r = 1e-10 +- 0.5e-10
    Adopted Monte Carlo priors for subdominant loss channels (Chapter 5).
  • OPM transition interval nu_OPM = 2.472 to 2.680 GHz
    Composite of four logistic-fit diagnostics (Table 3.1); the interval edges combine selected diagnostics and the PA-coherence break is excluded, so the interval involves interpretive choices.
  • quadrupolar surface-field fraction f_l=2 = 0.18 to 0.23 (0.232 offset-dipole; 0.183 dipole+quadrupole)
    Fitted to the NICER hot-region posterior; enters the MQM bound linearly through the participation factor (Chapter 4, Eq. 6.15).
assumptions (9)
  • domain assumption Global charge neutrality with a density jump at the core-crust interface
    Chapter 2 adopts the Belvedere et al. global-neutrality picture; the density model allows a small upward density jump at R_core, affecting R_core and crust thickness.
  • domain assumption Crust-confined magnetic field
    Chapter 2 assumes the large-scale field can reside in the crust for ordinary/MSP pulsars, justified by the computed P_req << 1; the whole polarized-reservoir calculation lives in the inner crust.
  • domain assumption Free-neutron reservoir is the only meaningful polarized population
    Chapter 5 asserts bound neutrons are locked into nuclei whose internal spin structure strongly cancels any net alignment; outer-crust nuclei are argued to be spin-zero in Chapter 2.
  • domain assumption Force-free magnetospheric torque law (Spitkovsky)
    Eq. (5.6) uses L_dip = mu^2 Omega^4/c^3 (1+sin^2 alpha) as the standard-loss normalization; Chapter 7 admits the fiducial force-free normalization may over-assign the available spin-down power.
  • domain assumption Cold-pair propagation scaling of Eqs. (3.20)-(3.29)
    Maps the OPM transition to B_surf; the paper warns it is a convention with eta_prop set to unity, not an empirical field prior.
  • ad hoc to paper Maximally coherent collective dipole D_eff = N_pol d_n
    Eqs. (6.5)-(6.8): the default assumption is full phase coherence across the inner crust; the paper itself presents the random-walk sqrt(N_pol) alternative as an extreme diagnostic.
  • ad hoc to paper MQM radiation model P_MQM = K_quad omega^6 (f_l=2 N_pol M_n^0)^2/c^5 with K_quad = 1/(60 pi)
    Eq. (6.15), described by the paper as 'a geometry-weighted participation prescription, not a microscopic derivation of quadrupolar ordering in dense matter'.
  • domain assumption Conversion coefficients M_n^0 = 2.5e-29 bar_theta e cm^2 [104] and d_n = 1.48e-16 bar_theta e cm [106]
    Adopted hadronic conversions from the cited literature; the reported d_n is a pure-bar_theta comparison value, not a direct measurement (Chapter 6).
  • standard math Standard TOV and pulsar electrodynamics background
    TOV equations, Goldreich-Julian density, Thomas-Fermi screening, and vacuum versus force-free torque formulas are used as textbook inputs.
invented entities (2)
  • Effective single-neutron CP-odd magnetic quadrupole moment M_n^0 acting as a bulk radiating channel
    purpose: Absorbs the residual spin-down power in a channel not suppressed by electrostatic Schiff screening, converting the energy budget into a bar_theta/d_n limit.
    The paper introduces M_n^0 as a phenomenological bulk observable (Eq. 6.15) with no independent detection channel; it is constrained only through the residual power and the adopted conversion coefficients.
  • Effective magnetospheric mode frequency omega_eff = 2 pi nu_OPM
    purpose: Sets the radiation frequency for the MQM channel; the bound scales as omega^6.
    Identified with the OPM-core transition scale as 'a phenomenological mode prescription rather than a microscopic derivation' (Chapter 6).

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Pith. "Pith review of Measuring the electric dipole moment of the neutron using neutron star spin-down." pith.science (2026). https://pith.science/paper/54AUP5QY

@misc{pith2026260806593,
  author       = {Pith},
  title        = {Pith review of: Measuring the electric dipole moment of the neutron using neutron star spin-down},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/54AUP5QY}},
  note         = {Machine review of arXiv:2608.06593}
}
abstract

The neutron electric dipole moment (nEDM) is a sensitive probe of CP violation beyond the Standard Model. We develop a source-specific framework for constraining CP-odd neutron structure using the nearby millisecond pulsar PSR J0437-4715. Mass and radius measurements are used to construct a stellar-structure model and estimate the polarized inner-crust neutron reservoir. Wideband radio polarimetry provides a propagation-informed surface-field posterior that is not obtained from the conventional $P\dot P$ magnetic-field estimate, while published NICER hot-region constraints are used to test low-order surface-field geometries and isolate the dipolar component entering the electromagnetic torque. These inputs are propagated through a present-day spin-down budget including electromagnetic and gravitational-wave losses. The remaining positive residual is first interpreted as an unscreened electric-dipole-radiation benchmark. Crustal and magnetospheric screening then motivate an effective CP-odd magnetic-quadrupole channel. Conditional on the adopted screening, coherence, and effective-mode-frequency prescriptions, the positive-residual branch gives a 90th-percentile bound $|M_n^0|<7.47\times10^{-38}$ e cm$^2$. With the adopted QCD conversion coefficients, this corresponds to $|\bar{\theta}|<2.99\times10^{-9}$ and an equivalent $|d_n|<4.42\times10^{-25}$ e cm. Although weaker than laboratory nEDM limits, the result demonstrates how source-specific neutron-star structure, radio propagation, magnetic geometry, and spin-down energetics can be combined to test nonstandard CP-odd radiation channels.

Figures

Figures reproduced from arXiv: 2608.06593 by the authors.

Figure 1-1
Figure 1-1. Illustration of the discrete-symmetry argument for a permanent neutron [PITH_FULL_IMAGE:figures/full_fig_p020_1-1.png] view at source ↗
Figure 1-2
Figure 1-2. Illustration depicting the recycling process of a millisecond pulsar, specifi [PITH_FULL_IMAGE:figures/full_fig_p022_1-2.png] view at source ↗
Figure 2-1
Figure 2-1. Model of PSR J0437-4715 using the density model described below. This [PITH_FULL_IMAGE:figures/full_fig_p030_2-1.png] view at source ↗
Figures from the paper (12 more)
Figure 2-2
Figure 2-2. Figure 2-2: Period and period derivative diagram for all stars in the ATNF catalog [PITH_FULL_IMAGE:figures/full_fig_p032_2-2.png]
Figure 2-3
Figure 2-3. Figure 2-3: Density model of J0437-4715 with documented mass [PITH_FULL_IMAGE:figures/full_fig_p034_2-3.png]
Figure 2-4
Figure 2-4. Figure 2-4: Diagram depicting the neutron, proton, and electron density breakdown [PITH_FULL_IMAGE:figures/full_fig_p035_2-4.png]
Figure 2-5
Figure 2-5. Figure 2-5: Moment of inertia of an 11.36 km star for masses varying from [PITH_FULL_IMAGE:figures/full_fig_p038_2-5.png]
Figure 2-6
Figure 2-6. Figure 2-6: Polarization for stars with documented mass, as well as all stars from [PITH_FULL_IMAGE:figures/full_fig_p040_2-6.png]
Figure 3-1
Figure 3-1. Figure 3-1: Diagram depicting the geometry used for the propagation-based magnetic [PITH_FULL_IMAGE:figures/full_fig_p046_3-1.png]
Figure 3-2
Figure 3-2. Figure 3-2: Magnetic-field diagnostics for PSR J0437–4715. (a) Folded-profile [PITH_FULL_IMAGE:figures/full_fig_p054_3-2.png]
Figure 4-1
Figure 4-1. Figure 4-1: Diagram depicting the geometric parameters being fit. [PITH_FULL_IMAGE:figures/full_fig_p063_4-1.png]
Figure 4-2
Figure 4-2. Figure 4-2: Posterior distributions for the hotspot-geometry model used in the field [PITH_FULL_IMAGE:figures/full_fig_p064_4-2.png]
Figure 4-3
Figure 4-3. Figure 4-3: Low-order surface radial-field geometries compatible with the published [PITH_FULL_IMAGE:figures/full_fig_p069_4-3.png]
Figure 5-1
Figure 5-1. Figure 5-1: Schematic structure of the neutron-star crust and core-crust interface. The [PITH_FULL_IMAGE:figures/full_fig_p081_5-1.png]
Figure 5-2
Figure 5-2. Figure 5-2: Histogram of the signed Monte Carlo estimator [PITH_FULL_IMAGE:figures/full_fig_p084_5-2.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.