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By making use of an explicit representation for the imaginary part of thephoton polarization tensor in terms of transitions between the Landau levels oflight quarks, we study the angular dependence of direct photon emission from astrongly magnetized quark-gluon plasma. Because of the magnetic field, theleading order photon rate comes from the three processes of the zeroth order inthe coupling constant $\alpha_s$: (i) the quark splitting ($q\rightarrowq+\gamma $), (ii) the antiquark splitting ($\bar{q} \rightarrow \bar{q}+\gamma$), and (iii) the quark-antiquark annihilation ($q + \bar{q}\rightarrow\gamma$). In a wide range of moderately high temperatures, $T\gtrsim m_\pi$,and strong magnetic fields, $|eB|\gtrsim m_\pi^2$, the direct photon productionis dominated by the two splitting processes. We show that the Landau-levelquantization of quark states plays an important role in the energy and angulardependence of the photon emission. Among other things, it leads to a nontrivialmomentum dependence of the photon ellipticity coefficient $v_2$, which takesnegative values at small transverse momenta and positive values at largetransverse momenta. The crossover between the two regimes occurs around$k_T\simeq \sqrt{|eB|}$. In application to heavy-ion collisions, this suggeststhat a large value of $v_2$ for the direct photons could be explained in partby the magnetic field in the quark-gluon plasma.

Ellipticity of photon emission from strongly magnetized hot QCD plasma