Influence of interstellar environment near the solar system on cosmic-ray spectra and dipole anisotropy

Siming Liu; Zhangxi Xue

REVIEW 3 major objections 5 minor 73 references

Influence of interstellar environment near the solar system on cosmic-ray spectra and dipole anisotropy

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper argues that the cosmic-ray dipole anisotropy's energy dependence is naturally explained by a three-component source model once local interstellar transport and the Compton-Getting effect are included.

desk verdict A plausible local-transport fix for the CR dipole problem, but the sub-TeV fit leans on an assumed background anisotropy direction; worth refereeing, not yet convincing. read the letter →

arxiv 2507.07057 v1 pith:4VT2SGEL submitted 2025-07-09 astro-ph.HE

Zhangxi Xue , Siming Liu This is my paper · ORCID

classification astro-ph.HE

keywords cosmicraysdipoleanisotropylocalinterstellarmediumcosmic-raytransportCompton-Gettingeffectthree-componentmodelprotonandheliumspectramagneticfieldwandering

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 establish that the cosmic-ray anisotropy problem goes away once the local interstellar environment is taken seriously. It models proton and helium spectra from a few GV to several PV as the sum of three components — a Galactic-disk background, a nearby source associated with the Geminga supernova remnant, and a Galactic-center source — and adds the Compton-Getting effect from the heliosphere's motion through the Local Interstellar Cloud, along with anisotropic diffusion in the cloud's magnetic field. The computed dipole amplitude and position angle then track the observed energy dependence from sub-TeV to above 100 TeV. If correct, the anisotropy is not a sign of exotic global source structure but a local transport phenomenon, making cosmic-ray measurements a probe of the interstellar medium within a few parsecs of the Sun.

What carries the argument

The central object is the flux-weighted anisotropy sum in Eq. (15): $\xi(E) = (3/v)C\mathbf{u}_{\rm HC} + \sum_z (J_{zn}\xi_n + J_{zb}\xi_b + J_{zc}\xi_c)/J(E)$, where the first term is the Compton-Getting effect from the heliosphere's motion through the Local Interstellar Cloud and the remaining terms are the projected dipole anisotropies of the background, nearby-source, and Galactic-center components, weighted by their flux contributions. The local transport parameters ($u_{\rm LSR}$, $u_{\rm HC}$, magnetic field $\mathbf{B}$, cloud size $x$, and the critical rigidity $R_{\rm cr}=3$ PV) enter through the diffusion tensor and suppress the nearby-source anisotropy because the cloud moves nearly perpendicular to the magnetic field.

What would settle it

A more precise measurement of the dipole amplitude and position angle between roughly 10 GeV and 10 TeV with full-sky coverage would falsify the model if it does not show the predicted low-energy near-cancellation and the phase swing across the TeV range; independently, a determination of the local interstellar velocity that disagrees with the adopted $u_{\rm HC}=25.4$ km/s (RA 74.9°, Dec 17.6°) and $V_\odot=15.5$ km/s would break the fit.

Watch

Extended reading notes

Core claim

The paper claims that the energy dependence of the cosmic-ray dipole anisotropy — a persistent problem because the amplitude is far smaller than expected and the position angle changes with energy — is a natural outcome of local interstellar transport. In the model, three components produce the proton and helium fluxes from a few GV to several PV: a Galactic-disk background, an instantaneous nearby source identified with the supernova remnant that formed the Geminga pulsar, and an instantaneous source at the Galactic center. Adding the Compton-Getting effect produced by the heliosphere's motion through the Local Interstellar Cloud, and projecting each component's anisotropy onto the large-scale magnetic field, the sum in Eq. (15) reproduces the observed dipole amplitude and position angle from sub-TeV to above 100 TeV. The same local environment that shapes the spectra also shapes the anisotropy: because the cloud moves nearly perpendicular to the magnetic field, the nearby-source anisotropy is suppressed, and its direction matches observations.

Load-bearing premise

The fit below ~100 TeV treats the background cosmic-ray anisotropy as a free parameter with magnitude $\delta_b = 0.0006$ and direction perpendicular to the Galactic plane; if the real background anisotropy has a different direction or magnitude, the near-cancellation with the Compton-Getting effect that produces the observed low-energy amplitude and position angle is lost.

Editorial extensions

If this is right

Below ~100 TeV, the dipole amplitude and position angle become controlled by measurable local quantities — the heliosphere's velocity in the local cloud, the cloud's velocity in the local standard of rest, the magnetic-field direction and strength, and the cloud's size — so cosmic-ray anisotropy can be inverted to constrain those quantities.
The earlier three-component model without local-environment effects predicted position angles more than 30 degrees away from the observed values; the local-transport terms close that gap, so local propagation is essential rather than a minor correction.
Above ~100 TeV the anisotropy swings toward the Galactic center, and a minimum in the dipole amplitude appears just above 100 TeV where the nearby and center contributions balance.
The model rejects an earlier determination of the heliosphere's velocity in the local cloud ($u_{\rm HC} = 23.2$ km/s with RA 78.5°, Dec 18.0°), implying cosmic-ray data can discriminate between competing local-ISM velocity measurements.
New anisotropy measurements in the 1–100 TeV range and new local-ISM measurements should agree with the best-fit parameter set ($u_{\rm HC}=25.4$ km/s, $V_\odot=15.5$ km/s, $B=3\,\mu$G, $x=1.6$ pc) if the model is right.

Reading between the lines

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

One consequence the authors leave implicit: if this model is correct, the sub-TeV cosmic-ray dipole is largely a kinematic cancellation, so it should vary on timescales of decades if the heliosphere's velocity in the cloud changes appreciably — a testable prediction for long-running muon and neutron monitors.
The model's success would also mean that global cosmic-ray transport models that omit the local cloud are missing a dominant anisotropy effect below 100 TeV; incorporating a local-ISM zone into such models should reproduce the observed phase swing without special global source distributions.
Extending the computation to heavier nuclei and to the full composition data near the knee would test whether the same three-component framework holds above a few hundred TeV, where the current proton–helium treatment is acknowledged to be incomplete.

Share X Bluesky LinkedIn Reddit HN

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

The new thing here is real: the authors add the LIC's motion in the local standard of rest as an advective term in the diffusion solution and handle the Compton-Getting effect properly. That fixes the old >30 degree position-angle mismatch in the three-component model, and it makes a specific, testable claim: below ~100 TeV the dipole amplitude and phase are controlled by local parameters like V_sun, u_HC, and the LIC size. That is a genuine step for the anisotropy problem, not a repackaging of earlier fits.

The paper is also honest about its own limits. The authors state explicitly that delta_b is a free parameter from an approximate treatment, they admit they do not attempt to reproduce the recent LHAASO all-particle spectrum, and they put parameter-sensitivity figures in the appendix. Those are good practices.

Now the soft spots, in proportion. The stress-test concern holds up: the sub-TeV anisotropy is a delicate near-cancellation between the Compton-Getting vector and an assumed background anisotropy whose direction (north Galactic pole) is fixed ad hoc and whose magnitude is free. Equation (14) projects that vector onto the local field and discards the perpendicular part; only the magnitude is varied in Appendix A.1, not the direction. If the real background anisotropy has a different direction, the cancellation changes and the clean match in Fig. 2 goes away. So the central claim of a "natural" explanation is not yet secured. That is a load-bearing issue, but it is fixable: constrain delta_b's direction and magnitude jointly from the data, or derive it from a physical model of the background propagation.

Second, the fits are by eye. There are 17+ free parameters, no uncertainties, no chi-squared or similar. The reader cannot tell whether the good-looking agreement in Figs. 1 and 2 is meaningful or the result of flexibility. That is a soundness problem for a paper whose main output is a multi-parameter fit.

The equations themselves look standard and the parameter choices are within observed ranges. The citation pattern is appropriate, including credit to the prior model they improve on. This is a serious, clearly argued paper, not a crank claim. It just needs a lot more statistical discipline before the "naturally explain" wording is justified.

For a referee: yes, send it to review. The local-transport mechanism is worth the community's time, and the fixable statistical issues are exactly what referees should ask for. I would not cite it in my own work until the background-anisotropy direction is constrained rather than assumed. Worth a reading-group slot as a good example of how to turn a fit failure into an improved model.

Referee Report

3 major / 5 minor

Summary. The paper proposes a three-component model for cosmic-ray proton and helium spectra—a Galactic background, a nearby Geminga-related source, and a Galactic center source—and combines them with local interstellar transport effects to fit the observed dipole anisotropy amplitude and phase from sub-TeV to PeV energies. The model explicitly includes the Compton-Getting effect from the Sun's motion in the Local Interstellar Cloud and the anisotropy induced by the LIC's motion in the local standard of rest, and it demonstrates sensitivity to parameters such as the heliosphere velocity, the LIC velocity, the magnetic field strength, and the LIC size. Two variants are presented, one using kinetic diffusion theory and one including magnetic field wandering, and both are shown to reproduce the available spectra and anisotropy data to visual accuracy.

Significance. If the central mechanism is correct, the paper offers a unified explanation of the cosmic-ray anisotropy problem by linking sub-TeV anisotropy to a cancellation between the Compton-Getting effect and a background dipole, and TeV-to-PeV anisotropy to the nearby and Galactic center sources. The work is valuable for its explicit analytic formulas, a complete parameter table, and falsifiable predictions that can be tested with LHAASO and IMAP. The sensitivity studies in Appendices A and B are a clear strength, as is the authors' candid acknowledgment of limitations such as the lack of a fit to LHAASO's knee-region data and the exclusion of heavier elements. However, the sub-TeV result rests heavily on an unconstrained background anisotropy, and the fits are not quantified statistically, which currently limits the strength of the central claim.

major comments (3)

[Section II B, Eq. (14)] The background dipole anisotropy δ_b is treated as a free parameter with its direction fixed perpendicular to the Galactic plane, and its magnitude is chosen as 0.0006 to cancel the Compton-Getting effect at sub-TeV energies. Since Fig. 3 shows the fit depends on this near-cancellation, the central claim that the observed energy dependence is 'naturally explained' is not yet secure: the low-energy amplitude and phase are essentially determined by an assumed vector that is neither derived from the transport model nor measured independently. Appendix A.1 varies only the magnitude of δ_b, not its direction. The authors should either derive δ_b from an independent physical model, constrain it from data in a way that includes its direction, or demonstrate that the fit is robust to the assumed direction of the background anisotropy.
[Section II, Table I] The model has 18 fitted parameters, yet the paper reports no quantitative goodness-of-fit measure, no uncertainties on the best-fit values, and no comparison of the two model variants (kinetic diffusion versus magnetic field wandering) beyond visual inspection of Fig. 4. With this many degrees of freedom, the agreement shown in Figs. 2 and 4 is not by itself evidence for the model. The authors should provide a chi-square or likelihood statistic for the spectra and anisotropy data, and at least rough confidence intervals for the key physical parameters (δ_b, V_⊙, uHC, x, Rcr, B) discussed in Appendix A.
[Section III, Eqs. (16)-(17)] The magnetic-field-wandering variant is introduced without explicit definitions of D‖ and D⊥ or an explanation of which rigidity dependences they follow, despite being the basis for the claim that this variant 'has fewer parameters.' The text states that the same parameters are used except r⊥ and Q0c, but it is not clear whether k0‖, MA, or the relation κ⊥ = κ‖/[1+(ωτ)^2] are modified. Without these definitions, the comparison between Eq. (6)/(11) and Eq. (16)/(17) cannot be checked, and the physical interpretation of the second model remains ambiguous.

minor comments (5)

[Abstract and Table I] The abstract uses 'GV to several PV' but PV is never defined; if it denotes peta-volt rigidity, this should be stated explicitly, otherwise the unit may be confused with PeV.
[Eq. (4)] The variable R' is introduced but not explicitly defined; please state that R' is the rigidity at the observer after solar modulation.
[Appendix A.3] The left panel of Fig. 7 uses uHC = 23.2 km/s from reference [4], but the main text describes uHC = 25.4 km/s from reference [51]; a sentence clarifying the provenance of each value would prevent confusion.
[Section III] The notation switches from κxx in Eq. (6) to Dxx in Eq. (16), and from κ‖/κ⊥ to D‖/D⊥, without a table relating the two sets; please unify the notation or explicitly state the correspondence.
[Fig. 2 caption] The data label 'UG-μ' is not explained; please spell out the experiment name (e.g., underground muon detector) or cite the original paper in the caption.

Circularity Check

1 steps flagged · score 6.0 of 10

Sub-TeV dipole 'explanation' is partly a fit: the background anisotropy magnitude δb is a free parameter tuned so that Eq. (15) cancels the Compton-Getting term, so the low-energy amplitude is not independently predicted.

fitted input called prediction [Section II B, Eq. (14); Table I; Appendix A.1]
"For the background component, we assume that the background CRs come from the Galactic disc and propagate perpendicular to it into the LIC, and the dipole anisotropy magnitude is a free parameter δb = 0.0006. ... Then, we project δb to the direction of the magnetic field, i.e., ξb = δb cos θb bhat ... In our model, δb is a free parameter due to our approximate treatment of the background component. ... Such a component plays a crucial role in canceling out the Compton-Getting effect at low energies, leading to the observed low amplitudes and position angles."

The quantity the paper claims to explain—the sub-TeV dipole amplitude and position angle—is itself parametrized by δb, which is not derived from transport theory or from an independent measurement. Setting δb = 0.0006 and assuming its direction at Galactic latitude 90° makes the ξb term in Eq. (15) nearly cancel the Compton-Getting vector, so the low-energy match in Fig. 2 is imposed by the free parameter rather than predicted. Appendix A.1 varies only the magnitude of δb and confirms that the observed low amplitude is achieved precisely by this cancellation. Thus the central 'natural explanation' of the energy-dependent anisotropy is, at sub-TeV energies, a one-parameter fit to the very observable being explained.

full rationale

The paper's central claim is that a three-component spectrum plus local interstellar transport effects naturally explain the energy dependence of the CR dipole anisotropy. For the TeV and higher-energy ranges, the anisotropy has non-trivial derived content: the nearby-source term in Eq. (11) depends on the measured uLSR and on the diffusion tensor, and the Galactic-center term in Eq. (12) follows from Fick's law, with the energy dependence of the total anisotropy then coming from the relative weightings Jn/J, Jb/J, Jc/J. Those parts are not circular. However, the sub-TeV band is dominated by the background component, and there the model's agreement is achieved by the explicitly free parameter δb: Eq. (14) injects δb cosθb bhat into Eq. (15), and δb = 0.0006 is selected so that this vector cancels the Compton-Getting anisotropy. The paper is transparent about this, but transparency does not remove the circularity: the fitted parameter is the background dipole amplitude, which is the same observable whose low-energy value is then presented as reproduced. A minor self-citation issue also exists—the three-component model and Geminga source parameters are taken from the authors' prior work [38]—but that is a normal extension of published modeling and is not scored as load-bearing circularity. Weighing the genuinely predictive TeV/PeV structure against the fitted sub-TeV background anisotropy, the central claim is partially circular, giving a score of 6.

Assumptions & free parameters 19 free parameters · 7 assumptions · 0 invented entities

The model fits about 19 parameters, including three source normalizations, two cutoffs, the solar modulation, the diffusion coefficient, the injection index, and a free background anisotropy. Several physically motivated parameters (uHC, B, V_odot, x) are taken from measurements, but are also varied in the appendices. The advection treatment and the background anisotropy direction are the most ad hoc elements.

free parameters (19)

Q0b,p = 4.6e52 GV^-1
Background proton source normalization, fitted to AMS/DAMPE/CREAM spectra.
Q0b,He = 6.9e51 GV^-1
Background helium normalization.
Q0n,p = 4.7e52 GV^-1
Nearby (Geminga) proton normalization.
Q0n,He = 7.05e51 GV^-1
Nearby helium normalization.
Q0c,p = 5e57 GV^-1
Galactic center proton normalization.
Q0c,He = 8e56 GV^-1
Galactic center helium normalization.
Rcut = 4 PV
Cutoff rigidity for background and nearby sources.
Rcutc = 100 PV
Cutoff rigidity for Galactic center source.
phi = 0.97 GV
Solar modulation potential (force-field approximation).
D0 = 2.15e28 cm2/s
Diffusion coefficient normalization outside LIC.
Gamma_p = 2.6
Injection spectral index of protons.
delta_b = 0.0006
Magnitude of background dipole anisotropy, free parameter; direction assumed perpendicular to Galactic plane.
V_odot = 15.5 km/s
Solar azimuthal velocity component; bracketed by 10-20 km/s in Appendix A.2.
x = 1.6 pc
Characteristic size of the LIC; upper limit few pc.
uHC = 25.4 km/s
Heliosphere velocity in the LIC; taken from Schwadron et al. 2015, but also varied in Appendix A.3.
Rcr = 3 PV
Critical rigidity where Bohm diffusion is assumed in the LIC.
B = 3 uG
Local interstellar magnetic field strength.
r_par = 250 pc
Distance along magnetic field from Geminga to solar neighborhood, adopted from [38].
r_perp = 18.5 pc (kinetic) / 20 pc (wandering)
Perpendicular distance of Geminga, adjusted between the two diffusion models.

assumptions (7)

domain assumption Leaky-box approximation for the background component
Eq. 1 models the background CRs as confined in a galactic disk with constant escape; a common simplification.
domain assumption Force-field approximation for solar modulation
Eqs. 3-4 relate interstellar and observed fluxes via a single potential phi; valid at low energies, approximate at TeV.
domain assumption Neglect of the antisymmetric part of the diffusion tensor
Section II A: kappa_T is neglected assuming a uniform large-scale magnetic field; this drops drift effects that could affect anisotropy.
ad hoc to paper 1D advection factor for the nearby source in the LIC
Eq. 6 inserts exp(-uLSR x / kappa_xx) into the instantaneous diffusion solution; this assumes a uniform flow across the LIC and ignores boundary effects.
ad hoc to paper Galactic center instantaneous source with age 4 Myr
Eq. 9 posits an unobserved burst 8.5 kpc away; no independent identification is given in this paper, only a speculative link to the LHAASO PeV component.
ad hoc to paper Background anisotropy direction fixed perpendicular to the Galactic plane
Eq. 14 assumes the background dipole points at Galactic latitude 90 degrees; not derived from any model or independent measurement.
standard math Compton-Getting coefficient C = 1.6
From the spectral index, C = (Gamma+2)/3 roughly; taken from Schwadron et al. 2014.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Influence of interstellar environment near the solar system on cosmic-ray spectra and dipole anisotropy." pith.science (2026). https://pith.science/paper/4VT2SGEL

@misc{pith2026250707057,
  author       = {Pith},
  title        = {Pith review of: Influence of interstellar environment near the solar system on cosmic-ray spectra and dipole anisotropy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4VT2SGEL}},
  note         = {Machine review of arXiv:2507.07057}
}

abstract

Properties of interstellar environment near the solar system have been probed by missions like IBEX, Voyager over the last two decades. Although it has been well recognized that properties of cosmic rays up to the PeV energy can be affected by the local interstellar environment, detailed modeling has not been done. We show that a three component model for the cosmic ray proton and helium spectra from GV to several PV can naturally explain the energy dependence of the dipole anisotropy of cosmic ray fluxes by considering effects of the local interstellar environment on cosmic ray transport, addressing the so-called cosmic ray anisotropy problem. In particular, it is shown that the dipole amplitude and position angle below $\sim 100$ TeV are very sensitive to the velocity of the heliosphere in the local interstellar cloud and the motion of the local interstellar cloud in the local standard of rest. Better measurement of cosmic ray flux anisotropy by experiments like LHAASO and properties of the local interstellar environment by future missions like IMAP will be able to test this model.

Figures

Figures reproduced from arXiv: 2507.07057 by the authors.

**Figure 2.** FIG. 2. Upper: The best fit of dipole anisotropy amplitude [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Sky map in equatorial coordinates. The circle-cross [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. The fitting results considering magnetic field wan [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5. Influences of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Influences of V [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: FIG. 7. Influences of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 9.** Figure 9: FIG. 9. Influences of [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

**Figure 10.** Figure 10: FIG. 10. Influences of the magnetic field strength [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]

**Figure 11.** Figure 11: FIG. 11. The fitting of KASCADE proton and helium spectra [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

73 extracted references · 67 canonical work pages

[1]

76×1057 GV−1

1×1058 GV−1, and Q0c,He = 1. 76×1057 GV−1. Due to more contribution from the nearby source toward higher energies, contributions from the Galactic center compo- nent needs to be enhanced to ﬁt the CR dipole anisotropy. This modeling has fewer parameters and the ﬁtting re- sults are shown in Fig. 4. 6 IV. CONCLUSION The dipole anisotropy of CR ﬂux shows co...

work page
[2]

Fig- ure 6 shows both the spectra and dipole anisotropy are very sensitive to solar velocity in the direction of Galac- tic rotation V ⊙ in the local standard of rest frame

Dependence on solar motion in the direction of Galactic rotation V⊙ Contribution from the nearby source is very sensitive to properties of the local interstellar environment due to CR transport processes in the solar neighborhood. Fig- ure 6 shows both the spectra and dipole anisotropy are very sensitive to solar velocity in the direction of Galac- tic ro...

work page
[3]

4×105 yr. The CRs diﬀuse along a large scale magnetic ﬁeld from this source to the solar neighborhood with a distance along the magnetic ﬁeld r‖ = 250 pc and per- pendicular to the magnetic ﬁeld r⊥ = 18 . 5 pc so that the total energy of injected CRs above 1 GV is about 1050 ergs for the best ﬁt model [38]. What’s more, con- sidering the fact that the LIC...

work page
[4]

Figure 5 shows that it can be well constrained by observations and mostly aﬀect the overall anisotropy in the sub-TeV en- ergy range where the background component dominates

Dependence on the magnitude of the background dipole anisotropy δb In our model, δb is a free parameter due to our approx- imate treatment of the background component. Figure 5 shows that it can be well constrained by observations and mostly aﬀect the overall anisotropy in the sub-TeV en- ergy range where the background component dominates. Such a compone...

work page
[5]

Figure 7 shows that an earlier measurement of uLSR [4] can be 7 ruled out based on our model

Dependence on the solar velocity in the LIC uHC The velocity of the Sun in the LIC uHC not only aﬀects the Compton-Getting eﬀect, but also the velocity of the LIC in the local standard of rest frame uLSR. Figure 7 shows that an earlier measurement of uLSR [4] can be 7 ruled out based on our model. ◆◆◆◆◆◆◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ...

work page
[6]

Figure 8 shows the de- pendence of CR properties on x

Dependence on the characteristic size of the LIC x The characteristic size of the LIC x also aﬀects ﬂuxes of CRs from the nearby source. Figure 8 shows the de- pendence of CR properties on x. Since a high value of x will suppress contribution to CRs from the nearby source, an upper limit of a few pc can be derived for x, which is consistent with the obser...

work page
[7]

For a given magnetic ﬁeld B, a lower value of Rcr implies a smaller diﬀusion coeﬃcient k‖ and a higher turbulence intensity

Dependence on the critical rigidity Rcr and the magnetic ﬁeld B We introduce the critical rigidity Rcr, where Bohm dif- fusion is achieved, to characterize the level of turbulence in the LIC. For a given magnetic ﬁeld B, a lower value of Rcr implies a smaller diﬀusion coeﬃcient k‖ and a higher turbulence intensity. Figure 9 shows that turbulence in the LI...

work page
[8]

K. C. Hsieh and E. M¨ obius, Neutral-atom Astronomy: Plasma Diagnostics from the Aurora to the Interstellar Medium (World Scientiﬁc, 2022)

work page 2022

Show all 73 references

[9]

Redﬁeld and J

S. Redﬁeld and J. L. Linsky, The Astrophysical Journal 534, 825 (2000)

2000
[10]

J. L. Linsky, S. Redﬁeld, and D. Tilipman, The Astro- physical Journal 886, 41 (2019)

2019
[11]

Schwadron, F

N. Schwadron, F. Adams, E. Christian, P. Desiati, P. Frisch, H. Funsten, J. Jokipii, D. McComas, E. Moe- bius, and G. Zank, Science 343, 988 (2014)

2014
[12]

A. M. Hillas, Journal of Physics G Nuclear Physics 31, R95 (2005)

2005
[13]

S. Liu, H. Zeng, Y. Xin, and Y. Zhang, Reviews of Mod- ern Plasma Physics 6, 19 (2022)

2022
[14]

Z. Cao, F. Aharonian, Axikegu, Y. X. Bai, Y. W. Bao, D. Bastieri, X. J. Bi, Y. J. Bi, W. Bian, A. V. Buke- vich, Q. Cao, W. Y. Cao, Z. Cao, J. Chang, J. F. Chang, A. M. Chen, E. S. Chen, H. X. Chen, L. Chen, L. Chen, L. Chen, M. J. Chen, M. L. Chen, Q. H. Chen, S. Chen, S. H. ...

2024
[15]

Aguilar, D

M. Aguilar, D. Aisa, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen, L. Arruda, N. Attig, P. Azzarello, A. Bach- lechner, et al., Physical review letters 115, 211101 (2015)

2015
[16]

Aguilar, D

M. Aguilar, D. Aisa, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen, L. Arruda, N. Attig, P. Azzarello, A. Bach- lechner, et al., Physical review letters 114, 171103 (2015)

2015
[17]

collaboration, Q

D. collaboration, Q. An, R. Asfandiyarov, P. Azzarello , P. Bernardini, X. Bi, M. Cai, J. Chang, D. Chen, H. Chen, et al. , Science advances 5, eaax3793 (2019). 9

2019
[18]

Alemanno, Q

F. Alemanno, Q. An, P. Azzarello, F. Barbato, P. Bernar- dini, X. Bi, M. Cai, E. Catanzani, J. Chang, D. Chen, et al. , Physical Review Letters 126, 201102 (2021)

2021
[19]

Y. S. Yoon, T. Anderson, A. Barrau, N. Conklin, S. Coutu, L. Derome, J. Han, J. Jeon, K. Kim, M. Kim, et al. , The Astrophysical Journal 839, 5 (2017)

2017
[20]

Munakata, T

K. Munakata, T. Kiuchi, S. Yasue, C. Kato, S. Mori, K. S. Hirata, K. Kihara, Y. Oyama, M. Mori, K. Fu- jita, S. Hatakeyama, M. Koga, T. Maruyama, A. Suzuki, T. Ishizuka, K. Miyano, H. Okazawa, Y. Fukuda, T. Hayakawa, K. Inoue, K. Ishihara, H. Ishino, S. Joukou, T. Kajita, S. K...

1997
[21]

Bartoli, P

B. Bartoli, P. Bernardini, X. Bi, Z. Cao, S. Catalanotti , S. Chen, T. Chen, S. Cui, B. Dai, A. D’Amone, et al. , The Astrophysical Journal 809, 90 (2015)

2015
[22]

Bartoli, P

B. Bartoli, P. Bernardini, X. Bi, Z. Cao, S. Catalanotti , S. Chen, T. Chen, S. Cui, B. Dai, A. D’Amone, et al. , The Astrophysical Journal 861, 93 (2018)

2018
[23]

Amenomori, S

M. Amenomori, S. Ayabe, S. Cui, L. Ding, X. Ding, C. Feng, Z. Feng, X. Gao, Q. Geng, H. Guo, et al. , The Astrophysical Journal 626, L29 (2005)

2005
[24]

Amenomori, X

M. Amenomori, X. Bi, D. Chen, T. Chen, W. Chen, S. Cui, L. Ding, C. Feng, Z. Feng, Z. Feng, et al. , The Astrophysical Journal 836, 153 (2017)

2017
[25]

Aglietta, B

M. Aglietta, B. Alessandro, P. Antonioli, F. Arneodo, L. Bergamasco, M. Bertaina, A. Bosio, A. Castellina, C. Castagnoli, A. Chaivasa, et al. , in 24th Interna- tional Cosmic Ray Conference, Vol. 2, held August 28- September 8, 1995 in Rome, Italy. Edited by N. Iucci and E. La...

1995
[26]

Aglietta et al

M. Aglietta et al. (EAS-TOP), Astrophys. J. 470, 501 (1996)

1996
[27]

Aglietta, V

M. Aglietta, V. Alekseenko, B. Alessandro, P. Antoniol i, F. Arneodo, L. Bergamasco, M. Bertaina, R. Bonino, A. Castellina, A. Chiavassa, et al. , The Astrophysical Journal 692, L130 (2009)

2009
[28]

Abbasi, Y

R. Abbasi, Y. Abdou, T. Abu-Zayyad, J. Adams, J. Aguilar, M. Ahlers, K. Andeen, J. Auﬀenberg, X. Bai, M. Baker, et al. , The Astrophysical journal letters 718, L194 (2010)

2010
[29]

Abbasi, Y

R. Abbasi, Y. Abdou, T. Abu-Zayyad, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, M. Allen, D. Altmann, K. Andeen, et al. , The Astrophysical Journal 746, 33 (2012)

2012
[30]

Aartsen, R

M. Aartsen, R. Abbasi, Y. Abdou, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, D. Altmann, K. An- deen, J. Auﬀenberg, et al. , The Astrophysical Journal 765, 55 (2013)

2013
[31]

Aartsen, K

M. Aartsen, K. Abraham, M. Ackermann, J. Adams, J. Aguilar, M. Ahlers, M. Ahrens, D. Altmann, T. Ander- son, I. Ansseau, et al. , The Astrophysical Journal 826, 220 (2016)

2016
[32]

W. Apel, J. Arteaga-Vel´ azquez, K. Bekk, M. Bertaina, J. Bl¨ umer, R. Bonino, H. Bozdog, I. Brancus, E. Cantoni, A. Chiavassa, et al. , The Astrophysical Journal 870, 91 (2019)

2019
[33]

A. Aab, P. Abreu, M. Aglietta, I. Albuquerque, J. M. Albury, I. Allekotte, A. Almela, J. A. Castillo, J. Alvarez- Mu˜ niz, G. A. Anastasi,et al. , The Astrophysical Journal 891, 142 (2020)

2020
[34]

McComas, F

D. McComas, F. Allegrini, P. Bochsler, M. Bzowski, E. Christian, G. Crew, R. DeMajistre, H. Fahr, H. Ficht- ner, P. Frisch, et al. , Science 326, 959 (2009)

2009
[35]

Schwadron, M

N. Schwadron, M. Bzowski, G. Crew, M. Gruntman, H. Fahr, H. Fichtner, P. Frisch, H. O. Funsten, S. Fuse- lier, J. Heerikhuisen, et al. , Science 326, 966 (2009)

2009
[36]

Heerikhuisen, N

J. Heerikhuisen, N. Pogorelov, G. Zank, G. Crew, P. Frisch, H. O. Funsten, P. Janzen, D. McComas, D. B. Reisenfeld, and N. Schwadron, The Astrophysical Jour- nal Letters 708, L126 (2009)

2009
[37]

Funsten, R

H. Funsten, R. DeMajistre, P. Frisch, J. Heerikhuisen, D. Higdon, P. Janzen, B. Larsen, G. Livadiotis, D. McCo- mas, E. M¨ obius, et al. , The Astrophysical Journal 776, 30 (2013)

2013
[38]

M¨ obius, K

E. M¨ obius, K. Liu, H. Funsten, S. Gary, and D. Winske, The Astrophysical Journal 766, 129 (2013)

2013
[39]

Zirnstein, J

E. Zirnstein, J. Heerikhuisen, H. Funsten, G. Livadio- tis, D. McComas, and N. Pogorelov, The Astrophysical Journal Letters 818, L18 (2016)

2016
[40]

Z. Cao, F. Aharonian, Axikegu, Y. Bai, Y. Bao, D. Bastieri, X. Bi, Y. Bi, W. Bian, A. Bukevich, et al. , Physical Review Letters 132, 131002 (2024)

2024
[41]

Tomassetti, The Astrophysical Journal Letters 752, L13 (2012), arXiv:1204.4492 [astro-ph.HE]

N. Tomassetti, The Astrophysical Journal Letters 752, L13 (2012), arXiv:1204.4492 [astro-ph.HE]

2012 arXiv
[42]

Zhang, S

Y. Zhang, S. Liu, and Q. Yuan, The Astrophysical Jour- nal Letters 844, L3 (2017)

2017
[43]

M. A. Malkov and I. V. Moskalenko, Astrophys. J. 911, 151 (2021), arXiv:2010.02826 [astro-ph.HE]

2021 arXiv
[44]

Yuan, B.-Q

Q. Yuan, B.-Q. Qiao, Y.-Q. Guo, Y.-Z. Fan, and X.-J. Bi, Frontiers of Physics 16, 1 (2021)

2021
[45]

Zhang, S

Y. Zhang, S. Liu, and H. Zeng, Monthly Notices of the Royal Astronomical Society 511, 6218 (2022)

2022
[46]

M. A. Malkov and I. V. Moskalenko, Astrophys. J. 933, 78 (2022), arXiv:2105.04630 [astro-ph.HE]

2022 arXiv
[47]

M. A. Forman and L. Gleeson, Astrophysics and Space Science 32, 77 (1975)

1975
[48]

Mertsch and S

P. Mertsch and S. Funk, Physical Review Letters 114, 021101 (2015)

2015
[49]

B. E. Wood, J. L. Linsky, and G. P. Zank, The Astro- physical Journal 537, 304 (2000)

2000
[50]

D’Ettorre Piazzoli, S.-M

B. D’Ettorre Piazzoli, S.-M. Liu, D. della Volpe, Z. Cao, A. Chiavassa, Y.-Q. Guo, L. T. Ksenofontov, O. Martineau-Huynh, D. Martraire, L.-L. Ma, X.-H. Ma, Y. Stenkin, Q. Yuan, H.-D. Zeng, S.-S. Zhang, Y. Zhang, and H. Zhu, Chinese Physics C 46, 030004 (2022)

2022
[51]

Gleeson and W

L. Gleeson and W. Axford, Astrophysical Journal, vol. 154, p. 1011 154, 1011 (1968)

1968
[52]

Redﬁeld and J

S. Redﬁeld and J. L. Linsky, The Astrophysical Journal 673, 283 (2008)

2008
[53]

P. C. Frisch and J. D. Slavin, Astrophysics and Space Sciences Transactions 2, 53 (2006)

2006
[54]

Yan and A

H. Yan and A. Lazarian, Astrophys. J. 673, 942 (2008), arXiv:0710.2617 [astro-ph]

2008 arXiv
[55]

R.-Y. Liu, H. Yan, and H. Zhang, Phys. Rev. Lett. 123, 221103 (2019), arXiv:1904.11536 [astro-ph.HE]

2019 arXiv
[56]

Y. Hu, A. Lazarian, and S. Xu, MNRAS 512, 2111 (2022), arXiv:2111.15066 [astro-ph.GA]

2022 arXiv
[57]

Lee and L

K. Lee and L. Lee, The Astrophysical Journal 904, 66 (2020). 10

2020
[58]

Schwadron, E

N. Schwadron, E. M¨ obius, T. Leonard, S. Fuselier, D. Mc- Comas, D. Heirtzler, H. Kucharek, F. Rahmanifard, M. Bzowski, M. Kubiak, et al. , The Astrophysical Jour- nal Supplement Series 220, 25 (2015)

2015
[59]

Dehnen and J

W. Dehnen and J. J. Binney, Monthly Notices of the Royal Astronomical Society 298, 387 (1998)

1998
[60]

Piskunov, N

A. Piskunov, N. Kharchenko, S. R¨ oser, E. Schilbach, and R.-D. Scholz, Astronomy & Astrophysics 445, 545 (2006)

2006
[61]

M. Reid, K. Menten, X. Zheng, A. Brunthaler, L. Moscadelli, Y. Xu, B. Zhang, M. Sato, M. Honma, T. Hirota, et al. , The Astrophysical Journal 700, 137 (2009)

2009
[62]

M. Reid, K. Menten, A. Brunthaler, X. Zheng, T. Dame, Y. Xu, Y. Wu, B. Zhang, A. Sanna, M. Sato, et al. , The Astrophysical Journal 783, 130 (2014)

2014
[63]

Xu, L.-G

Y. Xu, L.-G. Hou, and Y.-W. Wu, Research in Astronomy and Astrophysics 18, 146 (2018)

2018
[64]

Sch¨ onrich, J

R. Sch¨ onrich, J. Binney, and W. Dehnen, Monthly No- tices of the Royal Astronomical Society 403, 1829 (2010)

2010
[65]

T. K. Gaisser, R. Engel, and E. Resconi, Cosmic rays and particle physics (Cambridge University Press, 2016)

2016
[66]

Antoni, W

T. Antoni, W. Apel, A. Badea, K. Bekk, A. Bercuci, J. Bl¨ umer, H. Bozdog, I. Brancus, A. Chilingarian, K. Daumiller, et al. , Astroparticle physics 24, 1 (2005)

2005
[67]

Asakimori, T

K. Asakimori, T. Burnett, M. Cherry, K. Chevli, M. Christ, S. Dake, J. Derrickson, W. Fountain, M. Fuki, J. Gregory, et al. , The Astrophysical Journal 502, 278 (1998)

1998
[68]

Amenomori, S

M. Amenomori, S. Ayabe, D. Chen, S. Cui, L. Ding, X. Ding, C. Feng, Z. Feng, X. Gao, Q. Geng, et al. , Physics Letters B 632, 58 (2006)

2006
[69]

Giacalone and J

J. Giacalone and J. Jokipii, The astrophysical journal 520, 204 (1999)

1999
[70]

Ahlers and P

M. Ahlers and P. Mertsch, Progress in Particle and Nu- clear Physics 94, 184 (2017)

2017
[71]

A. H. Compton and I. A. Getting, Physical Review 47, 817 (1935)

1935
[72]

Ahlers, Physical Review Letters 117, 151103 (2016)

M. Ahlers, Physical Review Letters 117, 151103 (2016)

2016
[73]

Swaczyna, M

P. Swaczyna, M. Bzowski, J. Heerikhuisen, M. Kubiak, F. Rahmanifard, E. Zirnstein, S. Fuselier, A. Galli, D. McComas, E. M¨ obius,et al. , The Astrophysical Jour- nal 953, 107 (2023)

2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

76×1057 GV−1

1×1058 GV−1, and Q0c,He = 1. 76×1057 GV−1. Due to more contribution from the nearby source toward higher energies, contributions from the Galactic center compo- nent needs to be enhanced to ﬁt the CR dipole anisotropy. This modeling has fewer parameters and the ﬁtting re- sults are shown in Fig. 4. 6 IV. CONCLUSION The dipole anisotropy of CR ﬂux shows co...

work page

[2] [2]

Fig- ure 6 shows both the spectra and dipole anisotropy are very sensitive to solar velocity in the direction of Galac- tic rotation V ⊙ in the local standard of rest frame

Dependence on solar motion in the direction of Galactic rotation V⊙ Contribution from the nearby source is very sensitive to properties of the local interstellar environment due to CR transport processes in the solar neighborhood. Fig- ure 6 shows both the spectra and dipole anisotropy are very sensitive to solar velocity in the direction of Galac- tic ro...

work page

[3] [3]

4×105 yr. The CRs diﬀuse along a large scale magnetic ﬁeld from this source to the solar neighborhood with a distance along the magnetic ﬁeld r‖ = 250 pc and per- pendicular to the magnetic ﬁeld r⊥ = 18 . 5 pc so that the total energy of injected CRs above 1 GV is about 1050 ergs for the best ﬁt model [38]. What’s more, con- sidering the fact that the LIC...

work page

[4] [4]

Figure 5 shows that it can be well constrained by observations and mostly aﬀect the overall anisotropy in the sub-TeV en- ergy range where the background component dominates

Dependence on the magnitude of the background dipole anisotropy δb In our model, δb is a free parameter due to our approx- imate treatment of the background component. Figure 5 shows that it can be well constrained by observations and mostly aﬀect the overall anisotropy in the sub-TeV en- ergy range where the background component dominates. Such a compone...

work page

[5] [5]

Figure 7 shows that an earlier measurement of uLSR [4] can be 7 ruled out based on our model

Dependence on the solar velocity in the LIC uHC The velocity of the Sun in the LIC uHC not only aﬀects the Compton-Getting eﬀect, but also the velocity of the LIC in the local standard of rest frame uLSR. Figure 7 shows that an earlier measurement of uLSR [4] can be 7 ruled out based on our model. ◆◆◆◆◆◆◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ◆ ...

work page

[6] [6]

Figure 8 shows the de- pendence of CR properties on x

Dependence on the characteristic size of the LIC x The characteristic size of the LIC x also aﬀects ﬂuxes of CRs from the nearby source. Figure 8 shows the de- pendence of CR properties on x. Since a high value of x will suppress contribution to CRs from the nearby source, an upper limit of a few pc can be derived for x, which is consistent with the obser...

work page

[7] [7]

For a given magnetic ﬁeld B, a lower value of Rcr implies a smaller diﬀusion coeﬃcient k‖ and a higher turbulence intensity

Dependence on the critical rigidity Rcr and the magnetic ﬁeld B We introduce the critical rigidity Rcr, where Bohm dif- fusion is achieved, to characterize the level of turbulence in the LIC. For a given magnetic ﬁeld B, a lower value of Rcr implies a smaller diﬀusion coeﬃcient k‖ and a higher turbulence intensity. Figure 9 shows that turbulence in the LI...

work page

[8] [8]

K. C. Hsieh and E. M¨ obius, Neutral-atom Astronomy: Plasma Diagnostics from the Aurora to the Interstellar Medium (World Scientiﬁc, 2022)

work page 2022