Quark Corona: Non-Thermalized Parton Dynamics

• Quark Corona is the non-equilibrated ensemble of quarks and gluons produced when local density is too low for complete thermalization.
• Dynamical core–corona models utilize local density criteria and transverse momentum dependence to distinguish fluidized core from string-fragmented corona.
• This framework explains multiplicity scaling, strangeness enhancement, and flow variations, impacting QGP transport extraction and astrophysical observations.

A "Quark Corona" is the non-equilibrated component of partons—quarks and gluons—produced in high-energy systems where the local density is too low for complete thermalization with the bulk medium. This concept primarily arises in the context of high-energy nuclear collisions and dense astrophysical environments, providing a quantitative and phenomenological description of energy partition, hadronization, and observable multiplicity dependencies. Within the dynamical core-corona initialization frameworks developed for collider and astrophysical phenomenology, the quark corona stands in contrast to the thermalized core, and its interplay with the core underlies key features seen in hadron yield ratios, flow observables, and electromagnetic signatures.

1. Core–Corona Separation: Dynamical Criteria and Physical Origins

In high-energy nuclear collisions, the produced system is naturally decomposed into two spatially distinct regions:

• The core consists of locally dense zones where partons quickly deposit sufficient energy and momentum to achieve thermal and chemical equilibrium. This equilibrated plasma is described by relativistic hydrodynamics and undergoes hadronization via the Cooper–Frye prescription at decoupling temperature $T_{\rm dec}\approx160$ MeV (Kanakubo et al., 2019, Kanakubo, 2022).
• The corona comprises regions of lower parton density where the environment remains too dilute for significant thermalization. Partons traversing these regions escape without equilibrating and ultimately hadronize by string fragmentation rather than statistical hadronization (Steinheimer et al., 2011, Kanakubo et al., 2022).

Rather than a sharp threshold, the core–corona distinction is made dynamically using local density criteria: $$\rho_i(\mathbf{x}_i(t)) = \sum_{j\neq i} G\left(\mathbf{x}_i(t)-\mathbf{x}_j(t)\right)$$ where $G$ is a Gaussian kernel with widths $\sigma_\perp$ and $\sigma_{\eta_s}$ in transverse and longitudinal directions, respectively. Thermalization probability and fluidization rate for each parton are weighted by local spatial density and (in DCCI2) by transverse momentum. Partons with high $\rho_i$ are absorbed into the core; those with low $\rho_i$ comprise the corona (Kanakubo et al., 2019, Kanakubo, 2022, Kanakubo et al., 2022).

2. Mathematical Frameworks in Collider Phenomenology

The dynamical core-corona initialization (DCCI/DCCI2) models implement the following coupled dynamical equations:

• Hydrodynamic evolution of the core:

$\partial_\mu T_{\rm fluid}^{\mu\nu}(x) = J^\nu(x)$

$$T_{\rm fluid}^{\mu\nu} = (e+P)u^\mu u^\nu - P g^{\mu\nu}$$

with $J^\nu(x)$ denoting the energy–momentum source term extracted from localized parton fluidization (Kanakubo et al., 2019).

• Parton-by-parton fluidization criterion:

$$\frac{d p_i^\mu}{dt}(t) = -a_0 \frac{\rho_i(\mathbf{x}_i(t))}{(p_{T,i})^2} p_i^\mu(t)$$

where $a_0$ is a tunable parameter calibrating fluidization intensity, and $p_{T,i}$ is the parton’s transverse momentum (Kanakubo et al., 2019).

• Fraction of fluidized (core) energy:

$$R(\langle dN_{\rm ch}/d\eta \rangle) \equiv \frac{dE_{\rm fluid}/d\eta_s}{dE_{\rm tot}/d\eta_s}\Big|_{\eta_s=0}$$

This observable grows with event multiplicity and saturates to unity in very high-multiplicity (central) collisions (Kanakubo et al., 2019, Kanakubo, 2022).

These models allow unambiguous tagging of each final hadron as originating from the core or corona and support direct extraction of core/corona fractions as continuous functions of charged-particle multiplicity $N_{\rm ch}$ (Kanakubo et al., 2022). In the UrQMD hybrid model, separation is established by assigning each particle to core or corona based on local scalar quark-number density exceeding a cut-off $\rho_q^{\rm cut}$ (Steinheimer et al., 2011).

3. Experimental and Simulated Observables: Multiplicity Scaling and Strangeness Enhancement

Multiplicity scaling—a signature outcome of the core–corona paradigm—is observed in strange-to-non-strange hadron yield ratios across $pp$, $p$Pb, and PbPb collisions. The DCCI/DCCI2 frameworks reproduce a smooth, system-independent rise in ratios such as $\Xi/\pi$, $K/\pi$, or $\Lambda/K$ as a function of $\langle dN_{\rm ch}/d\eta \rangle$: $$\frac{K}{\pi}(\langle dN_{\rm ch}/d\eta\rangle) =\frac{N_{K}^{\rm core} +N_{K}^{\rm corona}}{N_{\pi}^{\rm core} +N_{\pi}^{\rm corona}}$$ The core contribution overtakes the corona at high multiplicity, resulting in universal saturation at chemical equilibrium values (Kanakubo et al., 2019, Kanakubo et al., 2022). This matches ALICE observations that these ratios depend exclusively on final-state multiplicity, not on collision system or beam energy.

In UrQMD, partial equilibration described via $f_{\rm core}(E_{\rm lab})$ accounts for features such as the strangeness horn in $K^+/\pi^+$ and centrality-dependent enhancement of $\Lambda$, $\Xi$ yields, interpolating between pure transport (corona) and full hydrodynamics (core) (Steinheimer et al., 2011).

Observable	Core–Dominated	Corona–Dominated	Transition Region
$K/\pi$, $\Xi/\pi$	Statistical hadronization	String fragmentation	Smooth rise, saturation at equilibrium value
$p_T$ spectra	Exponential ($p_T<1$ GeV)	Power-law ($p_T>3$ GeV)	Corona "bump" at low $p_T$ (partially quenched)

4. Impact on Flow, Spectra, and QGP Transport Extraction

Corona hadrons, lacking collective hydrodynamic flow, dilute key flow-sensitive measurements such as $v_n$, multi-particle cumulants, and mean transverse mass $\langle m_T \rangle$. Even in central PbPb collisions, 5–10% of all hadrons commonly originate from non-equilibrated corona, lowering $v_2$ and $c_2\{4\}$ by a factor $\sim f_{\rm corona}$ (Kanakubo et al., 2022, Kanakubo, 2022).

Consequently, if pure hydrodynamics is fitted to experimental data without explicit corona subtraction, inferred QGP transport coefficients (such as $\eta/s$) are systematically biased—typically underestimating the true viscosity. Inclusion of the corona restores agreement with the observed slopes of low-$p_T$ spectra and collective observables (Kanakubo, 2022).

A plausible implication is that hybrid core–corona models must be used for sophisticated QGP property extraction, with corona fractions determined dynamically from the underlying parton density and event activity.

5. Extensions to Astrophysical and Exotic Environments

The quark corona concept also manifests in models of axion quark nugget (AQN) dark matter and accreting quark-cluster stars:

• In the solar context, the AQN paradigm proposes that coronal nanoflare heating is powered by annihilation of antimatter AQNs in the solar atmosphere. Simulations yield correct energy injection rates and altitude profiles, matching the observed EUV (soft X-ray) luminosity ($L_{\rm EUV}\sim10^{27}$ erg s$^{-1}$) and a peak heating height at $\sim 2000$ km (the Transition Region). Testable signatures include spatial distribution of nanoflares, uniform EUV excess, and axion emission accompanying energetic events (Raza et al., 2018).
• For accreting strange quark-cluster stars, a circumstellar corona mediates the interaction between wind-accreted ions and the self-bound surface, creating observable phenomena like redshifted O VIII lines and variable blackbody radius in X-ray binaries such as 4U 1700+24. Two regimes—low-density collisionless and high-density collisional—are distinguished by a critical density $\rho_c$. Gravitational redshift and hydrostatic equilibrium models allow extraction of star masses and emission profiles unique to quark-cluster stars (Xu, 2014).

6. Model Calibration, Limitations, and Future Refinements

Calibration of the dynamical frameworks relies on tuning of smearing widths ($\sigma_\perp$, $\sigma_{\eta_s}$), initialization/freezeout times ($\tau_{00}$, $\tau_0$), and parton fluidization intensity ($a_0$). Multiplicity scaling yields robust, system-independent behavior but model realism can be improved by:

• Implementing viscous hydrodynamics with $\delta f$ corrections,
• Incorporating in-medium string fragmentation,
• Refining the thermalization criterion via kinetic theory,
• Performing global Bayesian fits to extract threshold parameters across multiple collision systems and energies (Kanakubo, 2022, Kanakubo et al., 2022).

For the astrophysical scenarios, predictions await observational tests—such as Parker Solar Probe signatures for the AQN model and high-resolution X-ray spectroscopy for quark-cluster stars.

7. Unified Physical Interpretation

The quark corona is understood as the non-equilibrated ensemble of quarks and gluons that, due to insufficient local density or rapid outward propagation, never join the perfect-fluid QGP core. This non-equilibrium component leaves observable imprints on hadron ratios, flow, and emission spectra, and its share traces a continuous transition from fragmentation-dominated to statistically equilibrated chemistry. The concept generalizes across collision energies, centrality, system size, and even to astrophysical domains where supra-nuclear matter is present.

The dynamical core–corona picture not only corrects for edge effects in hybrid models but unifies the interpretation of systematics in strangeness enhancement, collective flow, and energy deposition, rendering the quark corona a central construct for modern high-density QCD phenomenology (Kanakubo et al., 2019, Kanakubo, 2022, Kanakubo et al., 2022, Steinheimer et al., 2011).