1. Light bending by a black body radiation J.Y. Kim and T. Lee, arXiv:1310.6800[hep-ph] Jin Young Kim (Kunsan National Univ.) 10 th CosPA Meeting, Hawaii

2. Outline of the talk Nonlinear property of QED vacuum Velocity shift of light in radiation background Trajectory equation based on geometric optics Calculate the bending angle of a light ray when the energy density of radiation emitted by a black body dilutes spherically and cylindrically. Assuming a neutron as an isothermal black body, estimate the order of magnitude for the bending angle and compare it with the bending by other sources.

3. Nontrivial QED vacua In classical electrodynamics vacuum is defined as the absence of charged matter. In QED vacuum is defined as the absence of external currents. VEV of electromagnetic current can be nonzero in the presence of non-charge-like sources. electric or magnetic field, temperature, … nontrivial vacua = QED vacua in presence of non-charge- like sources If the propagating light is coupled to this current, the light cone condition is altered. The velocity shift can be described as the index of refraction in geometric optics.

4. Nonlinear Properties of QED Vacuum Euler-Heisenberg Lagrangian: low-energy effective action of multiple photon interactions Strong electric or magnetic field can cause a material-like behavior by quantum correction.

5. Speed of light under electric and magnetic field the correction to the speed of light In the presence of a background EM field, the nonlinear interaction modifies the dispersion relation and results in a change of speed of light.

6. Speed of light in general nontrivial vacua Light cone condition for photons traveling in general nontrivial QED vacua effective action charge [Dittrich and Gies (1998)] For small correction,, and average over the propagation direction For EM field, two-loop corrected velocity shift agrees with the result from Euler-Heisenberg lagrangian

7. Light velocity in radiation background Light cone condition for non-trivial vacuum induced by the energy density of electromagnetic radiation null propagation vector Velocity shift averaged over polarization

8. Differential bending by non-uniform refractive index When the index of refraction is non-uniform, light ray can be bent by the gradient of index of refraction. Calculate the bending by geometrical optics.

9. Trajectory equation When the correction to the index of refraction is small, approximate the trajectory equation to the leading order.

10. Bending by electric field [Kim and Lee, MPLA (2010)] Total bending angle can be obtained by integration with boundary condition

11. Bending by magnetic field [Kim and Lee, JCAP(2011)] Contrary to Coulomb case, the bending by a magnetic dipole depends on the orientation of dipole relative to the direction of the incoming photon. Maximal bending for a ray passing the pole

12. Bending by a spherical BB As a source of lens, consider a spherical BB emitting energy in steady state. In general the temperature of an astronomical object may different for different surface points. For example, the temperature of a magnetized neutron star on the pole is higher than the equator. For simplicity, consider the mean effective surface temperature as a function of radius assuming that the neutron star is emitting energy isotropically as a black body in steady state.

13. Index of refraction as a function of radius Energy density of free photons emitted by a BB at temperature T (Stefan’s law) Dilution of energy density: Index of refraction, to the leading order, can be replaced by (critical temperature of QED)

14. Trajectory equation Take the direction of incoming ray as +x axis on the xy-plane. Index of refraction: Trajectory equation: Boundary condition:

15. Bending angle Leading order solution with Bending angle from

16. Bending by a cylindrical BB Take the axis of cylinder as z-axis. Energy density: Index of refraction: Trajectory equation: Solution: Bending angle:

17. Dependence on the impact parameter Dependence on impact parameter is imprinted by the dilution of energy density

18. Order-of-magnitude estimation for a neutron star Surface temperature: Surface magnetic field: Mass: The magnetic bending is bigger than the thermal bending for, while the thermal bending is bigger than the magnetic bending for. However, both the magnetic and thermal bending angles are still small compared with the gravitational bending.