Photon-photon dispersion of TeV gamma rays and its role for photon-ALP conversion

The propagation of TeV gamma rays can be strongly modified by $B$-field induced conversion to axionlike particles (ALPs). We show that, at such high energies, photon dispersion is dominated by background photons—the only example where photon-photon dispersion is of practical relevance. We determine the refractive index for all energies and find that, for fixed energy density, background photons below the pair-production threshold dominate. The cosmic microwave background alone provides an “effective photon mass” of $m_{\gamma }^2=-(1.01\mathrm{neV}\times \omega /\mathrm{TeV}{)}^2$ for $\omega \lesssim 1000\mathrm{TeV}$. The extragalactic background light is subdominant, but local radiation fields in the Galaxy or the source regions provide significant contributions. Photon-photon dispersion is small enough to leave typical scenarios of photon-ALP oscillations unscathed, but big enough to worry about it case by case.

Figure 1

Photon-photon dispersion as a function of energy. Black line: Absorptive part $f(\omega /{\omega }_0)$ defined in Eq. (7). Blue line: Dispersive part for background photons with fixed energy and fixed direction, $g_0(\omega /{\omega }_0)$, defined in Eq. (9). Green line: Angle average for isotropic distribution with fixed energy ${\omega }_{\mathrm{B}}$, $g_1(\omega /{\omega }_1)$, defined in Eq. (10). Red line: Thermal, isotropic average, $g_2(\omega /{\omega }_2)$, defined in Eq. (11).

Figure 2

Interstellar radiation field in the Galaxy near the Sun [61, 62], consisting of the CMB, IR and SL. (Extracted from the GALPROP code [63] and available in Ref. [64].)

Figure 3

Photon-photon dispersion in the solar neighborhood based on the EM radiation field components shown in Fig. 2.