Thermal Recoil Jets in High-Energy & Astro Physics

• Thermal Recoil Jets are emergent jet-like structures produced when a thermal medium, such as a quark-gluon plasma, redistributes energy and momentum from primary particles.
• They exhibit exponential momentum spectra and broad angular profiles that clearly differentiate them from conventional hard jets in high-energy collisions.
• Their analysis via kinetic transport models and experimental observables advances our understanding of jet-medium coupling in both heavy-ion physics and astrophysical contexts.

Thermal recoil jets are emergent jet-like objects produced by the collective response of a hot medium—such as a quark-gluon plasma (QGP) or radiative environment—when energy and momentum are deposited by primary energetic particles or asymmetric thermal emission. Unlike conventional jets directly associated with hard primary partons or magnetically-launched flows, thermal recoil jets manifest distinct dynamical, kinematic, and structural features that reflect their origin in the medium’s thermal degrees of freedom. Their study, particularly in heavy-ion collisions and high-precision astrodynamics, has revealed new aspects of jet-medium coupling, energy redistribution, and the role of thermal processes in jet formation and modification.

1. Fundamental Mechanisms and Definitional Distinctions

Hard jets originate from initial hard scatterings—high-virtuality partons that fragment via parton showers into collimated sprays of hadrons, typically exhibiting power-law transverse momentum ($p_{T}$) spectra and energy concentrated near the jet axis. In contrast, thermal recoil jets are generated as a secondary, medium-driven response to energy-momentum deposition in a thermalized plasma. In the context of heavy-ion collisions, they are composed almost entirely of thermal medium partons (“recoils”) that have been accelerated out of the medium by scatterings with the traversing jet, often populating jet cones at low $p_{T, \rm jet} \lesssim 20$ GeV and large jet radii $R \gtrsim 0.4$ (Jing et al., 14 Dec 2025).

In astrodynamical applications, the term “thermal recoil jet” refers to net forces arising when anisotropic thermal radiation, due to non-uniform heating or surface properties, imparts momentum to an object such as a spacecraft, transforming isotropic emission into a directed “jet” of momentum flow (Toth et al., 2009).

2. Kinetic Theory and Theoretical Frameworks

The formation and evolution of thermal recoil jets in QGP are described using kinetic transport equations, chiefly the linearized Boltzmann transport (LBT) equation for the parton phase-space densities $f_a(x, p)$:

$$p_a \cdot \partial f_a(x, p) = E_a \left[ C_a^{\rm el}[f] + C_a^{\rm inel}[f] \right],$$

where $C^{\rm el}$ encodes $2 \to 2$ elastic scatterings and $C^{\rm inel}$ describes in-medium radiative processes. In elastic collisions, thermal medium partons receive momentum kicks, creating recoils, while the “negative” back-reaction is handled via subtraction procedures to maintain energy-momentum conservation (He et al., 2015). Both recoil and negative partons are evolved under the same kinetic equation until reaching the hadronization boundary, with clusters of recoil hadrons reconstructable as thermal recoil jets if they satisfy jet-finding criteria (Jing et al., 14 Dec 2025).

In the AMY/MARTINI formalism, recoil production is treated via coupled transport and rate equations, with explicit generation of recoil partons whenever their post-collision momentum exceeds a thermal threshold (Park et al., 2018).

In radiative recoil contexts (e.g., spacecraft), the net thermal recoil force is given by the radiation stress-tensor framework. The fundamental surface integral,

$$\mathbf{F}_{\mathrm{recoil}} = \frac{1}{c} \int_S \int_{\Omega^+} I(\mathbf{r}, \hat{n}) \hat{n} \, d\Omega \, dA,$$

quantifies the momentum carried by anisotropic photon emission (Toth et al., 2009).

3. Observable Signatures and Phenomenology

Thermal recoil jets possess unambiguous signatures in their spectrum, topology, and substructure:

• Yield and Kinematics: The inclusive yield in heavy-ion (A+A) relative to proton-proton (p+p) collisions, $I_{AA}(p_{T,\rm jet}, R)$, can exceed unity for low $p_{T,\rm jet}$ and large $R$, reflecting the presence of excess soft, wide-angle jets from thermal recoils (Jing et al., 14 Dec 2025). The analytic spectrum for purely thermal recoil jets is exponential in $p_{T,\rm jet}$, in contrast to the power-law of hard jets.
• Jet Shape and Radial Profile: The energy profile $\rho(r)$ as a function of distance from the jet axis exhibits a rising distribution for thermal recoil jets, with energy increasing toward the cone edge—a reversal of the behavior seen in hard jets, which are most collimated at the core (Jing et al., 14 Dec 2025, Park et al., 2018).
• Constituent Spectra: The momentum spectrum of jet constituents within recoil jets follows a near-Boltzmann form: $dN/(m_T^2 dm_T) \propto e^{-m_T/T_{\rm eff}}$, where $T_{\rm eff} \approx T_{\rm QGP}$, signifying a thermal-like composition (Jing et al., 14 Dec 2025).
• Experimental Correlates: ALICE and STAR have reported enhanced large-angle, low-$p_T$, large-$R$ recoil yields in central heavy-ion collisions—consistent with theoretical predictions for thermal recoil jets (Jing et al., 14 Dec 2025).
• Jet Mass and Peripheral Enhancement: Including recoils in jet reconstruction recovers broader jet shapes and higher jet mass distributions in agreement with LHC data. Absence of recoil contributions leads to artificially quenched, narrow jets (Park et al., 2018).

4. Transport Coefficients and Quantum Corrections

Key transport parameters governing the evolution and characterization of thermal recoil jets in QGP are:

• Transverse-Momentum Broadening ($\hat{q}$): Defined as

$$\hat{q}_R(\mu_\perp) = \int^{\mu_\perp} \frac{d^2 k_\perp}{(2\pi)^2} k_\perp^2 \mathcal{C}_R(k_\perp),$$

$\hat{q}$ quantifies the rate of transverse momentum diffusion per unit length, capturing the impacts of the thermal medium on jet broadening (Weitz, 2023).

• Asymptotic Thermal Mass ($m_\infty$): A forward-scattering induced mass shift, defined by

$m_{\infty,R}^2 = g^2 (C_R Z_g + 2 T_F N_F Z_f),$

which enters dispersion relations and controls in-medium formation times and LPM suppression for jet constituents at high energies (Weitz, 2023).

• Quantum Corrections and Double Logarithms: Next-to-leading order corrections introduce double-logarithmic enhancements to $\hat{q}$, infrared-regulated by the thermal scale $\omega_T$ (Weitz, 2023). The interplay of $\hat{q}$ and $m_\infty$ underpins the formation, angular distribution, and substructure of thermal recoil jets.
• Jet-Induced Medium Excitation: Propagating both leading and recoil partons in kinetic models produces Mach cones and diffusion wakes in energy density, with angular spectra initially exhibiting double peaks that broaden with successive scatterings (He et al., 2015).

5. Astrophysical and Macroscopic Contexts

Beyond high-energy QCD, thermal recoil jets have critical importance in astrophysical and space-science contexts:

• Radiative Recoil in Spacecraft: The net momentum carried by anisotropic thermal photon emission forms a thermal recoil jet, acting as a small but cumulative force influencing spacecraft trajectories and necessitating careful modeling for precision navigation. The formalism connects internal thermal power sources ($B_i$), spacecraft geometry, and emission properties to net force via

$$F_\parallel(t) = \frac{1}{c} \sum_{i=1}^n \xi_i B_i(t),$$

with $\xi_i$ geometrical/emissivity efficiency coefficients (Toth et al., 2009).

• Thermal Acceleration in Astrophysical Jets: In relativistic outflows from active galactic nuclei (AGN), thermal pressure-driven acceleration (“thermal recoil acceleration”) can dominate jet dynamics at parsec scales when internal energies are large, extending the acceleration regions beyond traditional magnetocentrifugal limits. The relativistic Bernoulli constant governs the transformation of enthalpy into bulk Lorentz factor, making thermal acceleration relevant in the spine of AGN jets such as NGC 315 (Ricci et al., 2023).
• Scaling Laws and Dominance Criteria: The competition between thermal ($\Theta$) and magnetic ($\sigma$) energy densities shapes jet acceleration, with thermal dominance achieved for $F_I/F_j \gg F_M/F_j$. Thermal acceleration may account for the observed collimation and Lorentz-factor profiles in parsec-scale jets, especially when the plasma is relativistically hot (Ricci et al., 2023).

6. Experimental and Computational Strategies

Identification and characterization of thermal recoil jets require:

• Jet Yield Mapping: Differential measurements of $I_{AA}(p_T, R, \Delta\phi)$, with fine binning to separate thermal recoil-enhanced yields at low $p_T$, large $R$, and large azimuthal separation (Jing et al., 14 Dec 2025).
• Substructure and Energy Profile Studies: Direct comparison of jet shapes and constituent spectra (thermal exponential vs. power-law) allows discrimination between hard and thermal recoil jets.
• Fractional Thermal Energy: At the partonic level, the observable

$$\xi_{\rm th} = \frac{|\vec p_T^{\,\rm recoil}-\vec p_T^{\rm negative}|}{|\vec p_T^{\,\rm recoil}-\vec p_T^{\rm negative}|+p_T^{\rm shower}}$$

quantifies the “thermal” fraction in reconstructed jets (Jing et al., 14 Dec 2025).

• Monte Carlo Simulations and Hydrodynamics: Frameworks such as LBT, MARTINI+hydro, and real-time quantum kinetic theory enable ab initio predictions and systematic inclusion of recoil effects in jet observables, often validated directly against LHC and RHIC data (He et al., 2015, Park et al., 2018).

7. Significance and Broader Impact

Thermal recoil jets challenge conventional paradigms of jet formation and modification, mandating the inclusion of medium response and recoil contributions for accurate interpretation of jet substructure, energy loss, and angular distributions in both high-energy nuclear collisions and precise astrodynamics. Their properties—exponential momentum spectra, broad angular profiles, and sensitive dependence on medium parameters—provide stringent tests for theoretical models of finite-temperature QCD, jet quenching, and radiative transfer.

In astrophysical applications, recognition of the persistent role of thermal acceleration necessitates a revision of jet-launching and collimation scenarios, particularly in AGN and blazar systems, with direct implications for interpreting observed Lorentz factors and opening angles on parsec and sub-parsec scales (Ricci et al., 2023). In space navigation, accurate modeling of thermal recoil jets is essential for trajectory prediction and the interpretation of Doppler anomalies (Toth et al., 2009).

Thermal recoil jets thus constitute a unifying concept linking microphysical interactions in hot, dense plasmas to macroscopic momentum transfer phenomena across vastly disparate energy and length scales.