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arxiv: 2606.31629 · v1 · pith:NDEPLQNCnew · submitted 2026-06-30 · 🌌 astro-ph.CO · astro-ph.GA· gr-qc· hep-ph

Ultralight dark matter mixed with primordial black holes

Xing-Yu Yang This is my paper

Pith reviewed 2026-07-01 03:57 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GAgr-qchep-ph
keywords ultralight dark matterprimordial black holesmixed halossolitoneigenmodesshot noiseSchrödinger-Poisson
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The pith

A one percent fraction of primordial black holes changes the soliton structure in ultralight dark matter halos by about twenty percent.

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

This paper studies halos containing both ultralight dark matter particles and primordial black holes. It divides the black hole effects into a smooth average background and random discrete positions. The average background alters the overall gravitational potential only slightly yet shifts how the dark matter waves organize in the dense central soliton by tens of percent. Discrete position fluctuations drive very slow shifts between different wave patterns that take billions of years to matter. As a result the smooth contribution dominates the dynamics on relevant timescales.

Core claim

For mixed halos with ultralight dark matter of mass 10^{-22} eV, total mass around 10^{10} solar masses, and one percent primordial black holes, the continuum black hole contribution changes the background density and potential at the sub-percent level but produces a twenty percent change in the radial mode participation within the soliton. The discrete shot-noise component induces mode transitions with the shortest timescale around 10^9 Gyr for solar-mass black holes, rendering it negligible. Thus the continuum term is the primary effect while discreteness can be ignored on galactic timescales.

What carries the argument

Separation of the primordial black hole contribution into a continuum term entering the averaged Schrödinger-Poisson background equation and a perturbative discreteness term inducing eigenmode transitions.

If this is right

  • Sub-percent modifications to the background density produce tens-of-percent responses in the soliton region.
  • The radial mode participation in the soliton changes by about twenty percent.
  • Mode transition timescales reach 10^9 Gyr, far longer than galactic evolution times.
  • The continuum contribution dominates over discrete effects for the fiducial parameters.

Where Pith is reading between the lines

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

  • This suggests that models of ultralight dark matter can incorporate a small black hole fraction through a simple adjustment to the background potential without needing to track individual objects.
  • Future observations of central halo densities or wave interference patterns might reveal such mixed compositions if the soliton alteration is detectable.
  • The negligible role of discreteness implies that primordial black holes in this mass range do not disrupt ultralight dark matter coherence over cosmic time.

Load-bearing premise

The treatment of discrete primordial black holes as a small perturbation whose shot noise does not trigger significant nonlinear back-reaction on the ultralight field remains accurate.

What would settle it

A direct measurement of the central density profile or the number of radial nodes in the soliton of a 10^{10} solar mass halo known to contain about one percent stellar-mass black holes, compared against pure ultralight dark matter simulations.

read the original abstract

Dark matter candidates span many orders of magnitude in mass, from ultralight bosonic fields to massive compact objects. In this work, we connect these two extremes by investigating ultralight dark matter (ULDM) mixed with primordial black holes (PBHs). We study mixed ULDM-PBH halos by separating the continuum PBH contribution from the shot-noise fluctuation generated by discrete PBHs. The continuum contribution enters the averaged Schr\"odinger-Poisson background, while the discreteness contribution is treated as a perturbation that induces ULDM eigenmode transitions and soliton heating. The two contributions have distinct parametric dependencies: continuum effects scale with PBH fraction, whereas discreteness-driven transition rates scale with the product of PBH fraction and individual PBH mass in the perturbative regime. For a fiducial mixed halo with ULDM particle mass $10^{-22}\,\mathrm{eV}$, virial mass of order $10^{10}\,M_{\odot}$, and PBH fraction $1\%$, the continuum PBH component modifies the background density, gravitational potential, and low-lying ULDM eigenvalues only at the sub-percent level. Nevertheless, this percent-level continuum PBH contribution produces a tens-of-percent response in the coherent soliton region, changing the radial mode participation by about $20\%$. For stellar-mass PBHs, the discrete shot-noise fluctuation induces extremely slow ULDM mode transitions, with the fastest low-lying multiplet transition having a timescale of order $10^9\,\mathrm{Gyr}$ for solar-mass PBHs. In this regime, the leading PBH effect is the continuum contribution, while discrete PBH shot noise is dynamically negligible on galactic timescales.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates mixed ultralight dark matter (ULDM) and primordial black hole (PBH) halos by separating the averaged continuum PBH density contribution to the Schrödinger-Poisson system from the perturbative shot-noise fluctuations due to discrete PBHs. For a fiducial model with ULDM particle mass 10^{-22} eV, virial mass ~10^{10} M_⊙, and PBH fraction 1%, it reports that the continuum PBH component modifies the background density, potential, and low-lying eigenvalues at the sub-percent level yet produces a ~20% response in the coherent soliton region (radial mode participation), while discrete shot-noise induces extremely slow eigenmode transitions with the fastest low-lying multiplet transition timescale ~10^9 Gyr for solar-mass PBHs, rendering discreteness negligible on galactic timescales.

Significance. If the perturbative separation and quantitative scalings hold, the work supplies a useful parametric framework distinguishing continuum effects (scaling with PBH fraction) from discreteness-driven rates (scaling with fraction times individual PBH mass). This connects two disparate dark-matter candidates and indicates that even percent-level PBH admixtures can produce amplified structural responses in ULDM solitons while leaving discreteness dynamically irrelevant for stellar-mass PBHs. The explicit separation of scaling behaviors is a clear analytical strength.

major comments (2)
  1. [Abstract] Abstract (paragraph on the two contributions): the central quantitative claims (sub-percent background shift yet ~20% soliton response; 10^9 Gyr transition timescale) rest on treating the averaged PBH density as a fixed modification while modeling discreteness as a linear perturbation; no explicit bound on the size of neglected second-order back-reaction terms is supplied for the fiducial parameters (m=10^{-22} eV, f_PBH=0.01, M_PBH~M_⊙), which is load-bearing for the conclusion that discreteness is negligible.
  2. [Abstract] Abstract (fiducial model paragraph): the reported ~20% change in radial mode participation arising from sub-percent continuum modifications lacks any derivation steps, eigenvalue-shift calculation, or comparison to the pure-ULDM limit, so the amplification cannot be verified from the supplied text.
minor comments (1)
  1. The abstract would benefit from a brief parenthetical definition or reference to the precise quantity used for 'radial mode participation' in the 20% figure.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph on the two contributions): the central quantitative claims (sub-percent background shift yet ~20% soliton response; 10^9 Gyr transition timescale) rest on treating the averaged PBH density as a fixed modification while modeling discreteness as a linear perturbation; no explicit bound on the size of neglected second-order back-reaction terms is supplied for the fiducial parameters (m=10^{-22} eV, f_PBH=0.01, M_PBH~M_⊙), which is load-bearing for the conclusion that discreteness is negligible.

    Authors: We agree that an explicit bound on the neglected second-order back-reaction terms would strengthen the justification for the perturbative treatment. In the revised manuscript we will add a dedicated estimate for the fiducial parameters, showing that the quadratic corrections remain at least an order of magnitude smaller than the retained linear terms and do not alter the conclusion that discreteness is negligible on galactic timescales. revision: yes

  2. Referee: [Abstract] Abstract (fiducial model paragraph): the reported ~20% change in radial mode participation arising from sub-percent continuum modifications lacks any derivation steps, eigenvalue-shift calculation, or comparison to the pure-ULDM limit, so the amplification cannot be verified from the supplied text.

    Authors: The ~20% shift in radial mode participation is obtained by numerically solving the eigenvalue problem for the modified background potential that includes the continuum PBH density and then decomposing the resulting ground-state wavefunction into the pure-ULDM eigenbasis. The sub-percent eigenvalue shifts and the resulting mode-weight changes are reported in Section 3, together with the direct comparison to the f_PBH=0 case. To make the abstract self-contained we will add a brief clause noting the comparison to the pure-ULDM limit while retaining the quantitative claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper models mixed ULDM-PBH halos by explicitly separating the averaged continuum PBH density (entering the Schrödinger-Poisson background) from discrete shot-noise treated as a linear perturbation driving eigenmode transitions. The reported outcomes—sub-percent shifts in background density/potential/eigenvalues, ~20% change in soliton radial mode participation, and ~10^9 Gyr transition timescales—are presented as computed results for stated fiducial parameters (m=10^{-22} eV, M_vir~10^{10} M_⊙, f_PBH=0.01) under the stated perturbative decomposition. No equations reduce these outputs to inputs by construction, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or imported uniqueness theorems appear in the provided text. The central claims rest on the modeling assumptions rather than tautological redefinitions.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

Abstract relies on the validity of the perturbative treatment and the clean separation of continuum and shot-noise terms; no new particles or forces introduced.

free parameters (3)
  • PBH fraction = 0.01
    Input parameter set to 1% for fiducial halo
  • ULDM particle mass = 10^{-22} eV
    Input parameter set to 10^{-22} eV for fiducial halo
  • Virial mass = ~10^{10} M_⊙
    Input parameter set to order 10^{10} solar masses for fiducial halo
axioms (1)
  • domain assumption Continuum and discrete PBH contributions can be cleanly separated with distinct scaling
    Invoked when stating that continuum scales with fraction while discreteness scales with fraction times mass

pith-pipeline@v0.9.1-grok · 5832 in / 1425 out tokens · 51087 ms · 2026-07-01T03:57:41.699748+00:00 · methodology

discussion (0)

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