REVIEW
Elliptic flow in an expanding and rotating fireball
Nuclear Theory · Submitted 29 Sep 2026 · 94 references
Pith's verdict: Honest, internally consistent phenomenology: the first rotating blast-wave model, but the headline 2–10% number leans on an extrapolated freeze-out angular velocity at exactly the energy where the effect is biggest.
T0 · AI review
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Referee report
The paper
The paper claims
Rotation from the fireball's initial orbital angular momentum contributes roughly 2 to 10 percent of the observed elliptic flow in an expanding and rotating blast-wave model, with the largest share at the lowest beam energy studied.
The reading
What carries the argument
The load-bearing object is the rotating blast-wave flow $u^\mu$: a standard expanding-fireball four-velocity with a rotational piece added, built for spherical and spheroidal geometries and for two rotation profiles, one differential (position-dependent angular velocity) and one uniform. Each profile is arranged so the net orbital angular momentum points along the $y$-axis, matching off-central collision geometry, while the expansion part carries none. These flows enter the Cooper–Frye freeze-out integral, the standard prescription that converts a flow profile into particle momentum spectra; switching the expansion-anisotropy parameter $\Delta v$ and the angular velocity $\Omega$ on and off isolates how much of $v_2$ comes from each source.
Extended reading notes
Core claim
The paper claims that in a blast-wave description of an off-central heavy-ion collision, adding a rotating component to the expanding fluid velocity imprints a few-percent vorticity signal on the elliptic flow $v_2$ without visibly changing the $p_T$ spectra. Concretely, for an anisotropically expanding spheroidal fireball with freeze-out angular velocities taken from transport simulations, rotation enhances $v_2(p_T)$ by roughly $7$–$15\%$ at $\sqrt{s_{NN}}=7.7$ GeV, corresponding to about $7$–$9\%$ after averaging over $0<p_T<2$ GeV, and the enhancement falls to about $2\%$ at 39 GeV; the paper states this as a $2$–$10\%$ vorticity contribution to the observed elliptic flow. The mechanism is a centrifugal-like extra push along the transverse in-plane direction from rotation about the reaction-plane normal, which adds to the anisotropy already created by elliptical expansion. The same calculation shows that rotation alone, in a spherical fireball, cannot reach the measured $v_2$ with realistic angular velocities, so the paper concludes that anisotropic expansion dominates while vorticity is a non-negligible supplement.
Load-bearing premise
The central percentage inherits the freeze-out angular velocities $\Omega_f$, which are not derived here but taken from a transport simulation and extrapolated to low collision energies; if those values are off, the claimed $2$–$10\%$ contribution shifts with them.
Editorial extensions
If this is right
- At low collision energies, rotation contributes at the few-percent level to $v_2$, so flow analyses that omit rotation are missing a small but not negligible part of the signal.
- The rotation contribution grows as beam energy decreases, making low-energy collisions the natural place to look for vorticity signatures in collective flow.
- Because the $p_T$ spectra are almost insensitive to realistic rotation, good spectrum fits do not by themselves rule out a rotating fireball.
- The rotation effect is larger for pions than for kaons and protons, while particles and antiparticles show nearly the same fractional change, so the model predicts a species-dependent pattern in the rotation contribution.
Reading between the lines
- If the same few-percent vorticity share holds in full hydrodynamic evolution, rotation should also leave comparable, energy-dependent imprints on higher-order flow harmonics such as $v_3$ and $v_4$ and on event-plane angle correlations, which this paper does not compute.
- The paper's velocity ansatz treats expansion and rotation as additive and non-interacting; in a genuine fluid, Coriolis and centrifugal feedback could mix the two channels, so the $2$–$10\%$ figure is best regarded as the estimate that follows from the simplest superposition.
- Comparing light-to-heavy $v_2$ ratios across beam energies, with the expansion part modelled separately, would offer a direct experimental route to isolating the vorticity contribution without relying on the transport-simulation angular velocity.
Original abstract
We investigate the role of initial orbital angular momentum in generating elliptic flow in off-central heavy-ion collisions. The conventional expanding fireball picture is extended for the first time to a simultaneously expanding and rotating fireball characterized by an angular velocity. Spherical and spheroidal emission geometries with two different rotating flow profiles, reminiscent of global and differential rotation, are considered for our investigation. While the transverse-momentum spectra at midrapidity are largely insensitive to the geometry and flow profile for realistic values of angular velocity, the elliptic flow is strongly affected by anisotropic expansion and rotation. A spherical fireball generates elliptic flow solely through the momentum anisotropy induced by rotation, but its magnitude remains below the observed values for realistic angular velocities. In contrast, an anisotropically expanding and rotating spheroidal fireball exhibits a $\sim 10\%$ enhancement of elliptic flow for $\sqrt{s_{\rm NN}}=7.7$ GeV, which reduces to a $2\%$ for $\sqrt{s_{\rm NN}}=39$ GeV relative to its non-rotating counterpart. Within our fireball framework, this indicates that vorticity can contribute at the $2-10\%$ level to the observed elliptic flow.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We investigate the role of initial orbital angular momentum in generating elliptic flow in off-central heavy-ion collisions. The conventional expanding fireball picture is extended for the first time to a simultaneously expanding and rotating fireball characterized by an angular velocity. Spherical and spheroidal emission geometries with two different rotating flow profiles, reminiscent of global and differential rotation, are considered for our investigation. While the transverse-momentum spectra at midrapidity are largely insensitive to the geometry and flow profile for realistic values of angular velocity, the elliptic flow is strongly affected by anisotropic expansion and rotation. A spherical fireball generates elliptic flow solely through the momentum anisotropy induced by rotation, but its magnitude remains below the observed values for realistic angular velocities. In contrast, an anisotropically expanding and rotating spheroidal fireball exhibits a $\sim 10\%$ enhancement of elliptic flow for $\sqrt{s_{\rm NN}}=7.7$ GeV, which reduces to a $2\%$ for $\sqrt{s_{\rm NN}}=39$ GeV relative to its non-rotating counterpart. Within our fireball framework, this indicates that vorticity can contribute at the $2-10\%$ level to the observed elliptic flow.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the role of initial orbital angular momentum in generating elliptic flow in off-central heavy-ion collisions. | contribution 0.88 | 0.89 | 0.04 | unclear 0.76 |
| s1 | The conventional expanding fireball picture is extended for the first time to a simultaneously expanding and rotating fireball characterized by an angular velocity. | contribution 0.87 | 0.87 | 0.05 | asserted 1.00 |
| s2 | Spherical and spheroidal emission geometries with two different rotating flow profiles, reminiscent of global and differential rotation, are considered for our investigation. | method 0.94 | 0.73 | 0.03 | asserted 0.87 |
| s3 | While the transverse-momentum spectra at midrapidity are largely insensitive to the geometry and flow profile for realistic values of angular velocity, the elliptic flow is strongly affected by anisotropic expansion and rotation. | result 1.00 | 0.88 | 0.20 | asserted 1.00 |
| s4 | A spherical fireball generates elliptic flow solely through the momentum anisotropy induced by rotation, but its magnitude remains below the observed values for realistic angular velocities. | result 1.00 | 0.90 | 0.09 | asserted 1.00 |
| s5 | In contrast, an anisotropically expanding and rotating spheroidal fireball exhibits a $\sim 10\%$ enhancement of elliptic flow for $\sqrt{s_{\rm NN}}=7.7$ GeV, which reduces to a $2\%$ for $\sqrt{s_{\rm NN}}=39$ GeV relative to its non-rotating counterpart. | result 1.00 | 0.92 | 0.25 | asserted 1.00 |
| s6 | Within our fireball framework, this indicates that vorticity can contribute at the $2-10\%$ level to the observed elliptic flow. | interpretation 0.98 | 0.89 | 0.77 | hedged possibility 0.99 |
What was examined, and what was not
- arXiv listing abstract v1
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Figures
Figures reproduced from arXiv:2609.36649 by the authors.
References
Discussion
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