No indications of axionlike particles from Fermi

As very high energy ($\gtrsim 100\mathrm{GeV}$) gamma rays travel over cosmological distances, their flux is attenuated through interactions with the extragalactic background light. Observations of distant gamma ray sources at energies between $\sim 200\mathrm{GeV}$ and a few TeV by ground-based gamma-ray telescopes such as HESS, however, have motivated the possibility that the universe is more transparent to very high energy photons than had been anticipated. One proposed explanation for this is the existence of axionlike particles (ALPs) which gamma rays can efficiently oscillate into, enabling them to travel cosmological distances without attenuation. In this article, we use a state-of-the-art model for the extragalactic background light (which is somewhat lower at $\sim \mu \mathrm{m}$ wavelengths than in previous models) and data from the Fermi Gamma Ray Space Telescope to calculate the spectra at 1–100 GeV of two gamma-ray sources, 1ES1101-232 at redshift $z=0.186$ and H2356-309 at $z=0.165$, in conjunction with the measurements of ground-based telescopes, to test the ALP hypothesis. We find that these observations can be well fit by an intrinsic power-law source spectrum with indices of $-1.72$ and $-2.1$ for 1ES1101-232 and H2356-309, respectively, and that no ALPs or other exotic physics is necessary to explain the observed degree of attenuation. While this does not exclude the possibility that ALPs are involved in the cosmological propagation of gamma rays, it does reduce the motivation for such new physics.

Figure 1

Representative models of the extragalactic background light (EBL) compared to various measurements. The solid black line is the model of Franceschini et al. [12], which we adopt in our calculations. The dashed (red) line denotes the model used by the HESS Collaboration in Ref. 2. The dotted (blue) line is the model of Primack et al., using the Kennicutt et al. stellar initial mass function [15, 36]. The data are as described in Ref. 12. The three rightmost data points in the far-IR (black squares) are from the analysis of the Diffuse Infrared Background Experiment (known as DIRBE) data by Madau et al. [37] and the reanalysis of that data ([red] squares) by Lagache et al. [38]. The two lower limits given at 70 and $160\mu \mathrm{m}$ (shaded [cyan] circles) come from a stacking analysis of Spitzer data described in Ref. 39. The mid-IR data points at 15 and $24\mu \mathrm{m}$ are the resolved fraction of the EBL by the deep Infrared Space Observatory’s ISOCAM (Isolated Camera) Guaranteed Time Extragalactic Surveys, known as IGTES [40, 41]. The near-IR data point at $8\mu \mathrm{m}$ (upper open triangle) is from Ref. 12, while the three lower wavelength points (lower open triangles) are from Ref. 42, using the integration of the IRAC galaxy counts. The far-UV/optical/near-IR points from $0.25\mu \mathrm{m}$ to $2.5\mu \mathrm{m}$ (open squares) are from an analysis of Ref. 37 based on deep galaxy counts.

Figure 2

The attenuation factor for gamma rays due to electron-positron pair production for sources at redshifts of $z=0.1$, $z=0.2$, $z=0.3$, $z=0.4$, and $z=0.5$, from right to left. The dashed and solid curves denote the attenuation for the EBL models of Franceschini et al. [12] and Primack et al. [15, 36], respectively (see Fig. 1).

Figure 3

The gamma-ray spectrum at Earth from a source with an injected spectrum of $dN/dE\propto E^{-2}$, after propagation over a distance of $z=0.2$ (top) and $z=0.5$ (bottom). Results are shown with (solid curve) and without (dashed curve) the effects of photon-ALP oscillations. The ALP-photon mixing mitigates the impact of absorption via pair production and leads to a plateau in the spectrum at high energies. We have calculated the effects of ALP-photon mixing assuming a source conversion probability of $1/3$ and a Milky Way reconversion probability of 0.1. The vertical axis is in arbitrary units.

Figure 4

The spectra of gamma-ray sources 1ES1101-232 at $z=0.186$ (top frame) and H2356-309 at $z=0.165$ (bottom frame) as determined from Fermi data (black circles) and as measured by HESS (black squares). The curves shown are the calculated best fits to the data assuming absorption of gamma rays via electron-positron pair production interactions with the EBL. The intrinsic source spectra are taken to be of the form $dN/dE\propto E^{-\Gamma }$. The best-fit values for the power-law indices are $\Gamma =1.72$ for 1ES1101-232 and $\Gamma =2.1$ for H2356-309. The EBL model used is that of Franceschini et al. [12]. See text for more details.