Pith Number

pith:42P2ZMO7

pith:2026:42P2ZMO7ZF2GXCHGGJO6O4IWRU

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Acoustic instability at shock-wave precursors

Antonio Capanema, Emanuele Sobacchi, Pasquale Blasi

With realistic Mach numbers and cosmic-ray efficiencies, the acoustic instability grows small density perturbations into large nonlinear structures as plasma crosses a shock precursor.

arxiv:2604.12514 v1 · 2026-04-14 · astro-ph.HE · hep-ph · physics.plasm-ph

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Claims

C1strongest claim

Adopting more realistic values of Mach number and cosmic-ray acceleration efficiency than previously assumed in the literature, we show that the acoustic instability can transform small density perturbations into large nonlinear structures while the fluid crosses the precursor region of a cosmic-ray-modified shock.

C2weakest assumption

That an externally assigned cosmic-ray pressure gradient accurately captures the self-consistent precursor structure of a cosmic-ray-modified shock and that two-dimensional simulations suffice to capture the essential nonlinear evolution and resulting turbulence.

C3one line summary

Numerical simulations show acoustic instability transforms small density perturbations into nonlinear structures across realistic cosmic-ray-modified shock precursors, generating turbulent magnetic fluctuations.

References

4 extracted · 4 resolved · 0 Pith anchors

[1] For density fluctuations, the field isf=δρ/ρ 0, and we chooseC=1 such thatX n Eδρ/ρ0(¯kn)∆kn = X ab ∆2k P(kab)=ξ(0) = 1 A X i j ∆x∆y " δρ ρ0 (xi j) #2 = δρrms ρ0 !2 ,(B.12) whereδρ rms /ρ0 is the RMSδ

[2] In other words, δBrms(¯kn)= q 8πEturb,mag(¯kn)∆kn (B.14) is the RMS value of magnetic field fluctuations with charac- teristic scaleℓ=2π/ ¯kn

[3] For velocity fields,e.g.δu, we chooseC=ρ 0/2 such that X n Eδu(¯kn)∆kn = 1 A X i j ∆x∆y ρ0|δu(xi j)|2 2 = ρ0δu2 rms 2 . (B.15) Analogously to the magnetic field case, the RMS amplitude of velocity per

[4] For studies of compressible turbulence, it is common to consider the density-weighted velocityw= √ρuto de- fine kinetic energy spectra (Kida & Orszag 1990; Grete et al. 2017). Letδwbe its fluctuations 1990

Receipt and verification

First computed	2026-05-29T02:05:44.914830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e69facb1dfc9746b88e6325de771168d175b5826d50d7304c2120b8c110ba418

Aliases

arxiv: 2604.12514 · arxiv_version: 2604.12514v1 · doi: 10.48550/arxiv.2604.12514 · pith_short_12: 42P2ZMO7ZF2G · pith_short_16: 42P2ZMO7ZF2GXCHG · pith_short_8: 42P2ZMO7

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/42P2ZMO7ZF2GXCHGGJO6O4IWRU \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e69facb1dfc9746b88e6325de771168d175b5826d50d7304c2120b8c110ba418

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0d8fb9d17501986b8980ae10051b634e7dfbff480638a28f34f4274c90ee1c5",
    "cross_cats_sorted": [
      "hep-ph",
      "physics.plasm-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.HE",
    "submitted_at": "2026-04-14T09:47:55Z",
    "title_canon_sha256": "813e3f398b596bf67f158f55edd4fe91c1ff9ddb695226cf5b43f3e8de9a85b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12514",
    "kind": "arxiv",
    "version": 1
  }
}