Enhanced Disruption of Axion Minihalos by Multiple Stellar Encounters in the Milky Way

Chris Gordon; Ian DSouza; John C. Forbes

REVIEW 3 major objections 6 minor 1 cited by

Enhanced Disruption of Axion Minihalos by Multiple Stellar Encounters in the Milky Way

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper argues that accounting for relaxation between successive stellar encounters makes stellar disruption of axion minihalos roughly twice as destructive as previously estimated, with only about 30% of the original minihalo mass…

desk verdict Solid Monte Carlo update on axion minihalo disruption, but the headline 30% survival fraction sits on a parameter from the authors' own prior paper and needs a sensitivity analysis before I'd trust the number. read the letter →

arxiv 2411.16166 v3 pith:SMOQ2O5F submitted 2024-11-25 astro-ph.CO hep-ph

Ian DSouza , Chris Gordon , John C. Forbes This is my paper · ORCID

classification astro-ph.COhep-ph

keywords axionminihalosstellardisruptiondarkmattersubstructureQCDmassfunctionhaloscopedetectiondynamicalrelaxationMilkyWayencounters

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 repeated stellar encounters in the Milky Way destroy axion minihalos more efficiently than earlier work concluded, because what matters is whether a minihalo has time to re-form between successive hits. The authors combine the energy injections from consecutive Galactic disk crossings with $p=1$ when the gap exceeds the minihalo's dynamical time and $p=2$ when it does not, a rule they call the hybrid method. For an axion mass of $25\,\mu\mathrm{eV}$ and a minimum adiabatic-halo mass of $10^2\,M_\odot$, they find that only about 30% of the original minihalo mass survives at the solar radius, compared with about 58% under the earlier linear-addition method. If that is right, more axion dark matter sits in inter-minihalo space, the local axion density at Earth is higher, and haloscope searches become more promising than previously estimated. The paper also presents the disrupted mass function and checks that updating the dynamical time after each pass changes the result by only a few percent.

What carries the argument

The load-bearing object is the effective energy injection parameter $E_{\mathrm{frac}}=\Delta E/E_{\mathrm{bind}}$ for a single stellar encounter, combined across many encounters by $E_{\mathrm{frac,eff}}=\left(\sum_i E_{\mathrm{frac},i}^{p/2}\right)^{2/p}$. The exponent $p$ encodes the physical state of the halo: $p=2$ when encounters arrive so quickly that the minihalo cannot change between them, and $p=1$ when the minihalo fully relaxes in between, a value parameter-fitted in Paper 1 and adopted as a conservative choice. The decision is made by comparing the time between consecutive disk passages to the dynamical time $t_{\mathrm{dyn}}=\sqrt{3\pi/(16G\bar\rho_{\mathrm{vir}})}$; the hybrid method applies $p=1$ or $p=2$ separately to each consecutive pair of passages. Feeding the resulting effective $E_{\mathrm{frac}}$ and the concentration parameter $c$ into the survival-fraction relation of Paper 1, over a Monte Carlo population of orbits evolved in the Galactic potential, produces the disrupted mass function and the 30% survival figure.

What would settle it

A controlled $N$-body experiment would settle it: take an NFW minihalo, apply two identical impulsive stellar kicks separated by waiting times of $0.5$, $1$, $2$, and $5$ dynamical times, and measure the final bound mass in each case. If the fully relaxed cases do not match the $p=1$ prediction, or if the transition from linear to nonlinear addition occurs at a different threshold than one dynamical time, the 30%-versus-58% contrast will not be reproduced.

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Extended reading notes

Core claim

The central claim is a mechanism and a number: when a minihalo is struck twice with enough time to relax in between, the second encounter acts on a looser object, so the two energy injections should be added nonlinearly ($p=1$) rather than linearly ($p=2$). Using Monte Carlo orbits drawn from a singular isothermal sphere so that the minihalo population is found at the solar neighborhood today, and summing the energy injected on every disk passage with the $p=1$/$p=2$ hybrid rule, the authors obtain a surviving mass fraction $M_{\mathrm{surv}}/M_{\mathrm{ori}}=30\%$ for $m_a=25\,\mu\mathrm{eV}$ and $M_{\mathrm{min}}=10^2\,M_\odot$, against roughly 58% for linear addition. Their Table II gives 29-30% for axion masses $1.25,25,500\,\mu\mathrm{eV}$ at that $M_{\mathrm{min}}$, and 37-38% for $M_{\mathrm{min}}=10^{-2}\,M_\odot$. Since Earth is more likely inside a minivoid than inside a minihalo, the extra disrupted mass raises the expected local axion density and strengthens haloscope detection prospects. The disrupted mass function is more suppressed than in the linear case and its peak shifts toward lower masses.

Load-bearing premise

The load-bearing premise is that one dynamical time is enough for a minihalo to fully relax after a stellar encounter, so that a later encounter combines with the earlier one through the $p=1$ rule; if real relaxation needs several dynamical times, or if the relaxed rule is closer to $p=2$, the drop from about 58% to about 30% largely disappears.

Editorial extensions

If this is right

The stellar-disrupted minihalo mass function is roughly halved in area relative to the $p=2$ case, and its peak shifts toward lower masses, which directly changes predictions for any probe that counts compact dark-matter subhalos.
More axion mass ends up in inter-minihalo space; since Earth is more likely inside a minivoid than inside a minihalo, the expected local axion density at a haloscope is higher than previous estimates.
Haloscope detection prospects improve relative to the linear-addition estimate, with the same qualitative conclusion across axion masses $1.25$, $25$, and $500\,\mu\mathrm{eV}$ and across the two assumed adiabatic-halo mass cutoffs.
Updating the dynamical time after each disk pass instead of holding it fixed changes $M_{\mathrm{surv}}/M_{\mathrm{ori}}$ by at most about 1-3%, so the main conclusion is stable against that simplification.

Reading between the lines

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

One consequence left implicit is that gravitational-lensing and pulsar-timing searches for small-scale dark-matter structure should expect a deficit of roughly $10^{-12}$ to $10^{-3}\,M_\odot$ halos relative to disruption-free predictions, turning the mass-retention ratio into an observable target.
The hybrid relaxation rule is independently testable in controlled $N$-body setups with two impulsive kicks separated by $0.5$ to $5$ dynamical times, which would calibrate where the $p=1$/$p=2$ transition actually sits.
The same relaxation logic should apply to other self-gravitating substructures that repeatedly cross stellar disks, so the factor-of-two reduction in retained mass could be a general feature of substructure evolution rather than an axion-specific one.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new thing here is the hybrid treatment of multiple stellar encounters: they simulate realistic orbits in a Milky Way potential, decide per gap whether the minihalo had time to relax, and combine energy injections with p=1 or p=2 accordingly. That is a real step beyond S2024's pure linear addition, and the machinery is described carefully enough to reproduce. The p=2 limit matches S2024, they checked convergence, and the code and data are public. Credit where due: this is a transparent, well-scoped simulation paper.

The soft spot is exactly where the headline comes from. The 30% versus ~60% survival difference is driven almost entirely by the switch to p=1 for relaxed encounters. That rule is not derived here; it is a fitted parameter from their own Paper 1, quoted as p ≲ 1 and then rounded down as a conservative choice. The threshold between relaxed and unrelaxed is a hard step at one dynamical time. The paper never shows what happens if the true p is 1.2 or 1.5, or if relaxation takes three dynamical times instead of one. The stress-test concern is legitimate: if either knob moves modestly, the 30% number slides back toward S2024's ~54%. The qualitative conclusion that multiple encounters are more destructive than linear addition would survive, but the quantitative claim would need rescaling.

Two smaller things. First, the detection-inference paragraph says the local axion density in minivoids increases, but they never compute that density; it is a plausible hand-wave, not a result. Second, there is a section-numbering typo in the introduction (Sec. III appears twice). Both are minor and fixable.

Who is this for? People working on axion substructure and haloscope detection strategies. It deserves a serious referee. The referee should ask for a sensitivity scan over p and over the relaxation-time threshold, plus ideally an independent check of the p=1 rule against direct N-body simulations of relaxing minihalos. Conditional acceptance is the right verdict: the framework is sound, the headline number is not yet firm.

Referee Report

3 major / 6 minor

Summary. The paper studies the disruption of QCD axion minihalos by stellar encounters in the Milky Way, extending the recent analysis of S2024. The authors Monte Carlo simulate minihalo orbits in a singular isothermal sphere potential, weight them by a pre-infall mass function from X2021, and track energy injections from passages through a two-component stellar disk. Their new element is a hybrid rule for summing energy injections from multiple encounters: p = 2 when consecutive encounters are separated by less than the minihalo dynamical time, and p = 1 when the minihalo has time to relax between encounters (Sec. V, Eqs. (6)-(9)). With this hybrid rule, they find Msurv/Mori ≈ 30% for ma = 25 µeV and Mmin = 10^2 M_sun, compared with ≈ 58% in S2024, and they argue that the extra mass in inter-minihalo space raises the local axion density and improves haloscope detection prospects. The p = 2 limit of their simulation reproduces S2024's results at the level of the published curves.

Significance. If the central quantitative claim holds, the paper makes a meaningful correction to estimates of the present-day minihalo mass function and to predictions for axion direct detection. The methodology is transparent: the orbit sampling is described in detail, the code and data are openly available, the comparison to S2024 in the p = 2 limit is shown, and the authors explicitly quantify a number of secondary effects (not updating the dynamical time, response-function differences, and Monte Carlo convergence). The key strength is that the paper isolates the one physical ingredient that changes the answer, namely how repeated energy injections combine when halos relax between encounters. The main limitation is that this ingredient is not independently derived or calibrated in the present work; it is a parameter fit from a companion paper with overlapping authorship, and the final survival fraction is highly sensitive to it.

major comments (3)

[Sec. V, Eqs. (6)-(8) and Table II] The headline result, Msurv/Mori = 29.6% for ma = 25 µeV and Mmin = 10^2 M_sun in Table II, is driven almost entirely by the choice p = 1 for relaxed encounters. The value p = 1 is not derived here; it is taken from a parameter fit in Paper 1 (Ref. [47]), where the authors found p ≲ 1 and then rounded to p = 1 'to be conservative.' Since Eq. (8) makes the effective energy injection grow as the square of the sum of sqrt(E_frac,i), the difference between the hybrid result and S2024's p = 2 result is a direct consequence of this fitted exponent. If the true combination exponent for relaxed encounters is, say, p = 1.5, or if complete relaxation requires several dynamical times rather than one, the survival fraction will move substantially upward, toward S2024's 53.5% for the same parameters. The paper should either provide a first-principles derivation or direct N-body calibration of the relaxed-encounter combination rule, or systematically vary p and the relaxation threshold and show how the headline number changes. Without this, the quantitative 30%-vs-60% claim is not robustly established, even though the qualitative direction (more disruption than linear addition) is plausible.
[Sec. V, step-function threshold at tdyn] The hybrid method applies a sharp step: encounters separated by more than tdyn are combined with p = 1, and encounters separated by less than tdyn are combined with p = 2. Gravitational relaxation is a continuous process, and a halo that has only partially relaxed between encounters should presumably be treated with an intermediate combination rule. Because early disk passages, when the minihalo is most concentrated and tdyn is short, fall on the p = 1 side of the switch, this step could systematically overstate the amount of relaxation. The authors note in Sec. IX and Appendix G that updating tdyn changes the result by only a few percent, but that estimate does not test the sharpness of the p = 1/p = 2 transition itself. A concrete sensitivity test, for example using a smooth interpolation in Delta t/tdyn or a threshold at 2-3 tdyn, would directly address this concern.
[Sec. IX, Figs. 5-6 and Table II] The reported values of Msurv/Mori are quoted to one decimal place and the text says the Monte Carlo result is stable at the 0.1% level, but this stability is only with respect to re-drawing orbits for the same grid and model choices. The dominant uncertainty is model uncertainty in p, the relaxation threshold, and the assumed constant value (250 km/s)^2 for sigma_*^2 + v_mh^2 in Eq. (19). The paper would be considerably stronger if Table II or Fig. 6 included a propagation of these modeling uncertainties, rather than only Monte Carlo sampling noise. This is a presentation and completeness issue for the central claim.

minor comments (6)

[Sec. I, organization paragraph] The introduction states that the undisrupted mass function is derived in 'Sec. III' and then later refers to 'Sec. III' again for a different topic; the section numbering in the introduction should be corrected.
[Sec. II, sentence after Eq. (B4)] The text 'In Sec. III, we derive the undisrupted mass function...' appears to duplicate the section label; the actual derivation appears in the second Sec. III (or should be renumbered).
[Sec. V, footnote 1] The overlap between the authors of this paper and Paper 1 is disclosed in a footnote, but the main text could more explicitly state that the p ≲ 1 result is from that companion paper and is not independently checked here.
[Eq. (23) and surrounding text] There is a typo: 'assummed' should be 'assumed' in the sentence defining rc.
[Sec. IX, text near Fig. 4] The phrase 'It is a good match to the analogous dashed gray curve in the top panel of Fig. 10 of 2024' should explicitly refer to S2024 rather than just '2024'.
[Sec. VI, Eq. (11)] The definition of E via Phi(robs) and the random variable R1 is clear, but the relation to the sampled energy distribution would benefit from one sentence explaining why the expression has the log term; currently it is only justified by the reference to Ref. [62].

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the p=1 combination rule is an openly adopted input from a disclosed companion paper, and the paper's survival-fraction calculation is a model propagation of that input rather than a circular prediction.

full rationale

The paper's derivation chain is not circular. The central new ingredient is the hybrid method in Sec. V, which selects p=2 for unrelaxed encounters and p=1 for relaxed encounters based on the dynamical-time comparison of Eq. (9). The p=1 value is explicitly disclosed as a parameter fit from Paper 1, a companion paper with overlapping authors (footnote 1 and Sec. V: 'in Paper 1, we parameter-fit the value of p in Eq. (6) to various such multiple encounter cases... To be on the conservative side, we choose p = 1'). The paper does not present p as a first-principles derivation, and it does not fit Msurv/Mori to any data; instead, the survival fraction is computed by Monte Carlo propagation of stellar encounters through Eqs. (17)-(36). The result is therefore sensitive to the p=1 input, but sensitivity to a disclosed fitted input is model dependence, not circularity. External benchmarks anchor the other major ingredients: the minihalo mass function from X2021, the concentration-mass-redshift relation and disk-pass energy formula from S2024, and the combination formula from Stücker et al. Appendix G's estimate of the effect of updating tdyn is a consistency check, not a disguised fit. Footnote 1 and Appendix G disclose the self-citation and the dynamical-time approximation, which should be weighed as correctness risk, but no equation reduces to its own input and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim depends on several inputs imported from prior literature (mass function, concentration relation, energy injection formula, disk model) and on the hybrid relaxation criterion introduced for this paper, which uses a parameter fitted in the authors' own previous work.

free parameters (3)

p (combination exponent for relaxed encounters) = =1 (conservative; Paper 1 fitted p<=1)
Controls how energy injections from well-separated encounters are combined; the headline 30% survival fraction is sensitive to this value.
sigma_*^2+v_mh^2 = (250 km/s)^2
Assumed constant in the stellar encounter energy injection formula Eq. (19); affects the magnitude of Efrac.
Survival fraction response function = Parameterized from Paper 1's numerical simulations
Maps (Efrac, c) to mass loss; adopted from overlapping prior work and used for interpolation.

assumptions (5)

domain assumption Minihalos have NFW profiles and follow the mass-concentration relation tabulated by S2024.
Used to assign concentration c for each (M, z) grid point in the Monte Carlo simulation, following S2024's tabulation.
domain assumption The stellar encounter energy injection formula of S2024 (Eq. 19) is accurate for a single disk pass.
Adopted without re-derivation; this formula is the input for Efrac for each disk crossing.
domain assumption The Galactic potential is a singular isothermal sphere with VC=200 km/s and r0=10 kpc.
Used both for sampling orbits and for evolving them with the LBparticles code; the disk potential is ignored.
domain assumption The pre-infall minihalo mass function is given by the modified Sheth-Tormen fit of X2021 with the CAMB growth function.
Underlies the undisrupted mass function dnf/dM and the weights wij in the Monte Carlo integration.
ad hoc to paper A minihalo relaxes completely between encounters if the time between them exceeds tdyn, enabling Eq. (8) with p=1.
This hybrid threshold is the paper's central modeling choice; the p=1 rule was fitted in prior work by the same group.

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Cite this review

Pith. "Pith review of Enhanced Disruption of Axion Minihalos by Multiple Stellar Encounters in the Milky Way." pith.science (2026). https://pith.science/paper/SMOQ2O5F

@misc{pith2026241116166,
  author       = {Pith},
  title        = {Pith review of: Enhanced Disruption of Axion Minihalos by Multiple Stellar Encounters in the Milky Way},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SMOQ2O5F}},
  note         = {Machine review of arXiv:2411.16166}
}

read the original abstract

If QCD axion dark matter formed post-inflation, axion miniclusters emerged from isocurvature fluctuations and later merged hierarchically into minihalos. These minihalos, potentially disrupted by stellar encounters in the Milky Way, affect axion detectability. We extend prior analyses by more accurately incorporating multiple stellar encounters and dynamical relaxation timescales, simulating minihalo orbits in the Galactic potential. Our results show stellar interactions are more destructive than previously estimated, reducing minihalo mass retention at the solar system to ~30%, compared to earlier estimates of ~60%. This enhanced loss arises from cumulative energy injections when relaxation periods between stellar encounters are accounted for. The altered minihalo mass function implies a larger fraction of axion dark matter occupies inter-minihalo space, potentially increasing the local axion density and improving haloscope detection prospects. This work highlights the significance of detailed modeling of stellar disruptions in shaping the axion dark matter distribution.

Figures

Figures reproduced from arXiv: 2411.16166 by the authors.

**Figure 2.** FIG. 2: Orientation of a minihalo’s initial velocity [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3: The minihalo is in orbit around the Galactic [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4: The mass function for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: FIG. 5: The value of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: for a plot of these values. X. CONCLUSIONS In this work, we have investigated the disruption of axion minihalos due to stellar encounters in the Milky Way galaxy. We extended previous analyses by incorporating a more accurate treatment of multiple stellar encounters, …

**Figure 7.** Figure 7: FIG. 7: The isocurvature growth function [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: FIG. 8: The 95% contour lines of the joint probability [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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