Fermi large area telescope observations of the cosmic-ray induced $\gamma$-ray emission of the Earth’s atmosphere

We report on measurements of the cosmic-ray induced $\gamma$-ray emission of Earth’s atmosphere by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope. The Large Area Telescope has observed the Earth during its commissioning phase and with a dedicated Earth limb following observation in September 2008. These measurements yielded $\sim 6.4\times {10}^6$ photons with energies $>100\mathrm{MeV}$ and $\sim 250$ hours total live time for the highest quality data selection. This allows the study of the spatial and spectral distributions of these photons with unprecedented detail. The spectrum of the emission—often referred to as Earth albedo gamma-ray emission—has a power-law shape up to 500 GeV with spectral index $\Gamma =2.79\pm 0.06$.

Figure 1

Two-dimensional maps of exposure (top row) and intensity (bottom row) for three different energy bands. The coordinate system in these maps is a polar representation such that the nadir direction (i.e., looking down towards the center of the Earth) with ${\Theta }_{\mathrm{nadir}}=0°$ is at the center of the plot. ${\Theta }_{\mathrm{nadir}}$ is increasing in radial direction with the edge of the plot towards the horizon at ${\Theta }_{\mathrm{nadir}}=90°$. The north pole is to the top and west is to the left. The exposure maps are given in units of ${\mathrm{cm}}^2\mathrm{s}$, the intensity maps in units of ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$.

Figure 2

The top panel shows the differential energy spectrum for the $\gamma$ rays produced in the Earth’s atmosphere taken in different ${\Theta }_{\mathrm{nadir}}$ bands. The spectrum of the limb (open circles) shows a power-law behavior. Also shown are $\gamma$-ray spectra for the inner parts of the Earth’s disk (filled circles and points). Indicated are both statistical and systematic errors (grey band), the latter derived from studies of the Vela pulsar. The inset shows a comparison to previous data by the SAS-2 satellite [13]. To allow for a direct comparison, the limb spectrum is also shown for a larger integration region ($58°<{\Theta }_{\mathrm{nadir}}<78°$) corresponding to the SAS-2 measurement. The bottom panel shows the limb spectrum multiplied by energy to the power 2.75.

Figure 3

Photon intensity as a function of azimuth for 4 different energy bands along the limb ($60°<{\Theta }_{\mathrm{nadir}}<75°$). Systematic errors as derived from LAT data on the Vela pulsar are shown as grey bands. A modulation is apparent in the low-energy bands which fades away at higher energies (see text for more details).

Figure 4

Average intensity as a function of nadir angle in wedges towards the different directions (north, west, south, east) for 4 different energy bands. The narrowing of the emission with increasing energy is seen as well as the change in shape (with a broad tail towards the center of the Earth for low energies) and a very narrow limb for the high energies. The comparison of the PSF calculated for the lower bound of the energy bin (averaged between front- and back-converting events) is shown as a dashed line. Note that the range of the histogram and the binning is different for the two high-energy bands.

Figure 5

Comparison between the integrated column density with the LAT-detected gamma-ray intensity as a function of nadir angle for events above 3.6 GeV. Two different model atmospheric profiles have been used: a simple barometric atmosphere with scale height of 6.8 km [22] shown as a solid line and a more realistic atmospheric model from [23]. Shown are the measured gamma-ray intensity (solid circles) and the gamma-ray intensity deconvolved by the PSF of the median energy (4.7 GeV) of this data set (open circles). A good correspondence between the $\gamma$-ray intensity and the column density can be seen at angles ${\Theta }_{\mathrm{Nadir}}\gtrsim 68.3°$. For these angles the atmosphere is thin enough (column density $<10\mathrm{g}{\mathrm{cm}}^{-2}$) so that no significant attenuation occurs and the $\gamma$ rays are directly related to the amount of target material for the incoming cosmic rays. The absolute level of the $\gamma$-ray intensity has been scaled to match the column density for the barometric atmosphere model.

Figure 6

A comparison of the measured gamma-ray intensity for the angular interval $68.6°<{\Theta }_{\mathrm{nadir}}<69.6°$ (thin-target case, gamma-ray attenuation is insignificant) with the scaled cosmic-ray proton intensity (see text for details). The inset shows the ratio between the $\gamma$-ray data and the scaled proton data and shows the general good match between the two measurements. The data have been taken from Sanuki et al. [18] and Ryan, Ormes, and Balasubrahmanyan [17].

Figure 7

Energy intensity for the Earth-originating $\gamma$ rays from keV to 500 GeV energies. The measurements from different instruments are not readily comparable since they have been taken in different points in the solar cycle and are also integrated over different areas of the Earth. Data points are taken from Ryan et al. [7] Share and Murphy [12], Ajello et al. [26], Frontera et al. [27], Schwartz and Peterson [28], Churazov et al. [29], Gehrels [30].