The strange-matter hypothesis predicts that lumps of strange quark matter (strangelets) may be absolutely stable and may be injected into the Galaxy by mergers of strange stars. A 2017 statistical-multifragmentation calculation determined source-level strangelet mass and charge spectra from strange-star-merger ejecta, but converted them to a near-Earth flux only through a homogeneous diffusion estimate, explicitly deferring realistic shock acceleration, interstellar-medium interactions, geomagnetic shielding, solar modulation, and CFL-matter source spectra. The quantitative link between strangelet production and the fluxes that direct searches (AMS-02, PAMELA, SLIM) actually test remains open: propagation frameworks exist only with generic source assumptions, the source-level mass spectrum itself is contested, the most recent merger simulations sharpen the tension with experimental limits while leaving the fragment mass distribution unsettled, and no end-to-end prediction has been performed.

Background

The strange-matter hypothesis (Bodmer-Witten-Terazawa) proposes that strange quark matter (SQM) — degenerate matter with roughly equal numbers of up, down, and strange quarks — is the true ground state of hadronic matter, more deeply bound than iron-56 nuclei. If true, macroscopic lumps called strangelets should exist, and compact stars made of SQM (strange stars) could form a second family of neutron-star-like objects. The standard phenomenological description of SQM is the MIT bag model, in which quarks are confined within a region of the QCD (quantum chromodynamics, the theory of the strong interaction) vacuum whose energy cost is set by a bag constant BB (often quoted as B1/4B^{1/4} in MeV); the model predicts the energy per baryon, the electric charge of strangelets (from the heavier strange-quark mass msm_s), and surface and curvature contributions to the energy. At yet higher density, QCD favors color-superconducting phases, in particular the color-flavor-locked (CFL) phase, where quarks of all three colors and flavors pair; CFL strangelets carry different charge-mass relations than unpaired ones.

A plausible astrophysical source of strangelets is the merger of two strange stars in a compact binary: general-relativistic simulations show lumpy SQM ejecta of order 10−4 M⊙10^{-4}\,M_{\odot} per merger that can fragment into a distribution of strangelet masses. Biswas, De, Joarder, Raha, and Syam (Phys. Rev. C 95, 045201 (2017)) modeled this fragmentation with a statistical multifragmentation model (SMM) — the framework otherwise used for the breakup of hot nuclear matter, in which a hot expanding fragmenting system populates fragment species according to statistical weights at freeze-out — including finite strange-quark mass, Coulomb charge corrections with Debye screening, and stability criteria on the energy per baryon. They obtained source-level mass spectra of stable strangelets over a range of bag constants and then estimated the near-Earth intensity with a simple homogeneous-diffusion prescription (merger rate ∼10−5 yr−1\sim10^{-5}\,\mathrm{yr}^{-1} per Galaxy, halo radius ∼10\sim10 kpc, confinement time ∼107\sim10^7 yr), finding integrated fluxes ranging from essentially zero up to ∼(2−5)×104\sim(2-5)\times10^4 particles m−2 sr−1 yr−1\mathrm{m}^{-2}\,\mathrm{sr}^{-1}\,\mathrm{yr}^{-1} depending on bag constant and freeze-out temperature.

The authors emphasize that this estimate omits the physics that a real prediction requires. Strangelets in the Galaxy must be accelerated by astrophysical (supernova-remnant) shock waves to cosmic-ray energies, and the acceleration efficiency for ultra-heavy, highly charged exotic primaries is unknown; during propagation they can undergo spallation and fragmentation in interactions with the interstellar medium and can escape the Galaxy; near Earth their flux is filtered by the geomagnetic cutoff and reshaped by solar modulation (the effect of the solar wind on low-rigidity particles, where rigidity is momentum per unit charge); and the resulting flux is what the actual instruments test — the magnetic spectrometer AMS-02 on the International Space Station, and earlier searches such as PAMELA (a satellite-borne cosmic-ray spectrometer, which set the current space-based upper limit for charges Z=1Z=1-88) and the SLIM mountain-altitude nuclear-track detector (sensitive to much larger baryon numbers). Madsen (Phys. Rev. D 71, 014026 (2005)) had earlier built precisely such a parametrized propagation framework — with shock-acceleration, interstellar-medium, escape, and solar-modulation parameters — for strangelets from compact-star collisions, but with generic source assumptions that predate any multifragmentation source spectrum; and a competing fragmentation study by Paulucci and Horvath concluded that most SMM fragments are unstable, so the source spectrum itself is disputed. The missing piece, as the source paper notes, is a combination of CFL-matter source spectra and more sophisticated galactic propagation for both strangelet types, required to arrive at a definite prediction of the strangelet flux in primary cosmic rays for AMS-02 and other potential experiments.

Problem Statement

Determine the flux and mass/charge spectrum of cosmic-ray strangelets near Earth as a definite, testable prediction, by completing the chain from strange-star-merger sources to near-Earth observation: (i) compute the source-level mass and charge distributions of strangelets produced by fragmentation of strange-star-merger ejecta, for unpaired strange quark matter and for CFL (color-flavor-locked) strange quark matter, using a finite-strange-quark-mass equation of state (bag model or its chiral extensions) with consistent surface and curvature energies; (ii) propagate these source spectra through the Galaxy with a realistic transport treatment — acceleration of ultra-heavy, highly charged primaries by astrophysical shock waves, spallation and fragmentation in interactions with the interstellar medium, and escape from the Galaxy — to obtain the strangelet intensity in the solar neighborhood with its dominant uncertainties; and (iii) account for geomagnetic shielding and solar modulation to obtain the near-Earth strangelet flux and mass/charge spectrum that is, in principle, measurable by AMS-02-class experiments. The single scientific objective uniting these components is a definite prediction of the strangelet flux in primary cosmic rays for both unpaired and CFL strangelets — one that is confronted with current experimental upper limits, whether it lands within them at a detectable level, falls below detectability, or demonstrably conflicts with them — replacing the order-of-magnitude diffusion estimates and fixed-baryon-number scalings that are all the literature currently offers.

References

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