Absorption of very high energy gamma rays in the Milky Way

Galactic gamma ray astronomy at very high energy ($E_{\gamma }\gtrsim 30\mathrm{TeV}$) is a vital tool in the study of the nonthermal universe. The interpretation of the observations in this energy region requires the precise modeling of the attenuation of photons due to pair production interactions ($\gamma \gamma \to e^{+}{e}^{-}$) where the targets are the radiation fields present in interstellar space. For gamma rays with energy $E_{\gamma }\gtrsim 300\mathrm{TeV}$ the attenuation is mostly due to the photons of the cosmic microwave background radiation. At lower energy the most important targets are infrared photons with wavelengths in the range $\lambda \simeq 50–500\mu \mathrm{m}$ emitted by dust. The evaluation of the attenuation requires a good knowledge of the density, and energy and angular distributions of the target photons for all positions in the Galaxy. In this work we discuss a simple model for the infrared radiation that depends on only few parameters associated to the space and temperature distributions of the emitting dust. The model allows to compute with good accuracy the effects of absorption for any space and energy distribution of the diffuse Galactic gamma ray emission. The absorption probability due to the Galactic infrared radiation is maximum for $E_{\gamma }\simeq 150\mathrm{TeV}$, and can be as large as $P_{\text{abs}}\simeq 0.45$ for distant sources on lines of sight that pass close to the Galactic center. The systematic uncertainties on the absorption probability are estimated as $\mathrm{\Delta }{P}_{\text{abs}}\lesssim 0.08$.

Figure 1

Pair production cross section plotted as a function of the variable $x=s/(4m_e^2)$. ${\sigma }_{\mathrm{T}}$ is the Thomson cross section.

Figure 2

Number density of the different radiation components in the solar neighborhood, plotted in the form $ϵn_{\gamma }(ϵ)$ versus the photon energy $ϵ$.

Figure 3

Energy density of the radiation fields in the solar neighborhood, plotted in the form $u_{\lambda }\lambda$ versus the wavelength $\lambda$. The points are measurements by COBE-FIRAS [19] and IRAS [21].

Figure 4

Absorption coefficient in the solar neighborhood (averaged over the photon direction) for the different components of the radiation field.

Figure 5

Absorption coefficient in the solar neighborhood due to the dust emitted radiation. The solid curve is calculated assuming an isotropic angular distribution of the photons. The other lines are calculated assuming the angular distribution observed at $100\mu \mathrm{m}$ by the IRAS satellite, and for photons traveling radially from and towards the Galactic center.

Figure 6

Space dependence of the angle integrated energy density ($u_{\lambda }\lambda$) of the infrared radiation for wavelength $\lambda =100\mu \mathrm{m}$, shown as a function of the cylindrical coordinates $r$ and $z$ in the Galaxy system.

Figure 7

Energy density (times wavelength) of the infrared radiation for $\lambda =100\mu \mathrm{m}$ as a function of $r$ for different values of $z$.

Figure 8

Angle integrated spectra of the dust emitted radiation in the vicinity of the Sun and at the Galactic center. The spectra are shown in the form $\lambda u_{\lambda }$ plotted as a function of the wavelength $\lambda$. The spectrum in the solar neighborhood is compared to the observations of COBE-FIRAS [19] (at $\lambda =100$, 150, 200, 250, 300, 400 and $600\mu \mathrm{m}$) and IRAS [21] (for $\lambda =60$ and $100\mu \mathrm{m}$).

Figure 9

Energy flux of the infrared radiation at $\lambda =100\mu \mathrm{m}$ at the Sun position as a function of the Galactic longitude, compared with the IRAS data (averaged over 10° in longitude).

Figure 10

Energy flux of the infrared radiation at $\lambda =100\mu \mathrm{m}$ at the Sun position as a function of the Galactic latitude, compared with the IRAS data (averaged over 1° in latitude).

Figure 11

Photon number density [$ϵn_{\gamma }(ϵ)$ versus the energy $ϵ$] for points on the Galactic plane at different distances from the GC. The CMBR and EBL are shown separately and are independent from the position. The other curves represent the sum of the stellar and dust spectra.

Figure 12

Survival probability of gamma rays for a trajectory from the GC to the Sun, plotted as a function of the gamma ray energy. The contributions of different radiation fields are shown. The inset shows the contributions of starlight, infrared radiation with wavelength $\lambda <50\mu \mathrm{m}$ and EBL.

Figure 13

Survival probability of gamma rays for three different trajectories in the Galactic plane, plotted as a function of the gamma ray energy. The inset shows the position of the sources.

Figure 14

Survival probabilities of gamma rays of energy 150 TeV and 2 PeV as a function of the source distance, for lines of sight with different Galactic longitudes and fixed latitude $b=0°$.

Figure 15

Survival probabilities of gamma rays of energy 150 TeV and 2 PeV as a function of the source distance, for lines of sight with different Galactic latitudes and fixed longitude $l=0°$.

Figure 16

Survival probability for gamma ray traveling from the Galactic center to the Sun, and from the Sun to the Galactic center, as a function of the gamma ray energy, calculated taking into account only the effects of dust emitted radiation. The solid curve shows the survival probability calculated assuming an isotropic distribution of the target photons.

Figure 17

Survival probabilities for gamma rays traveling from the GC to the Sun (taking into account only dust and star emitted radiation). The different curves show our calculation and those of MPS [11] and ES [15].