Photon production from gluon mediated quark-anti-quark annihilation at confinement

Heavy ion collisions at RHIC produce direct photons at low transverse momentum, $p_{T}$ from 1-3 GeV/c, in excess of the $p$$+$$p$ spectra scaled by the nuclear overlap factor, $T_{AA}$. These low $p_{T}$ photons have a large azimuthal anisotropy, $v_{2}$. Theoretical models, including hydrodynamic models, struggle to quantitatively reproduce the large low $p_{T}$ direct photon excess and $v_{2}$ in a self-consistent manner. This paper presents a description of the low $p_{T}$ photon flow as the result of increased photon production from soft-gluon mediated $q$-$\bar{q}$ interactions as the system becomes color-neutral. This production mechanism will generate photons that follow constituent quark number, $n_{q}$, scaling of $v_{2}$ with an $n_{q}$ value of two for direct photons. $\chi^{2}$ comparisons of the published PHENIX direct photon and identified particle $v_{2}$ measurements finds that $n_{q}$-scaling applied to the direct photon $v_{2}$ data prefers the value $n_{q}=1.8$ and agrees with $n_{q}=2$ within errors in most cases. The 0-20% and 20-40% Au$+$Au direct photon data are compared to a coalescence-like Monte Carlo simulation that calculates the direct photon $v_{2}$ while describing the shape of the direct photon $p_{T}$ spectra in a consistent manner. The simulation, while systematically low compared to the data, is in agreement with the Au$+$Au measurement at $p_{T}<3$ GeV/c in both centrality bins. Furthermore, this model predicts that higher order flow harmonics, $v_{n}$, in direct photons will follow the modified $n_{q}$-scaling laws seen in identified hadron $v_{n}$ with an $n_{q}$ value of two.