# On a Possible Origin of the Gamma-ray Excess around the Galactic Center
## 2 Modeling the CR Interaction with Molecular Clouds
Indeed, we assumed that all molecular clouds are located at the distance of \(R=8\) kpc and ignored the contribution of clouds that are located in the vicinity. In the case of electrons, we can also argue that their density in the galactic center is much higher than their local density [19]. We also plotted the ICS emission from the modulated spectrum of electrons due to the scattering of soft photons with energy of 1 eV. To calculate this, we used Equation (9), where we replaced factor \(\frac{M}{m_{p}}\) with \(eV\). Here, \(\varepsilon\) is the average energy density of soft photons in the galaxy and \(V\) is the total volume involved in the emission. The differential cross section of the ICS emission is taken from Blumenthal and Gould [21]. If we assume that \(\varepsilon=10\) eV\(\cdot\)cm\({}^{-3}\)[27], we need the volume to be equal to \(V=7\times 10^{65}\) cm\({}^{3}\) to match the data points and assuming that the region is spherical with a radius of about \(r=2\) kpc. This is larger than the size of the the CMZ and CND; however, we can argue that soft photon density is much higher in the central regions of the galaxy. As one can see from Figure 1, modulation of CR flux due to self-generated turbulence indeed produces the deficit of gamma-ray photons at the required energies below several GeV. Thus, our model is able to justify the explanation of GC excess (see [16]). One can assume that the analysis performed by, e.g., [PERSON] et al. [15] used standard assumptions (incorporated by GALPROP) to calculate the emissivity of MCs and did not take into account self-modulation of the CRs. Therefore, they overestimated the intensity of all the key emission components coming from MCs: hadronic due to proton-proton interactions, and bremsstrahlung and ICS from electrons at energies below several GeV. Although the intercloud diffuse gas emissivity in our model is not modified, the modification of the part of total emission coming from MCs is potentially able to change the ratio of all components significantly. The deficit of gamma-ray intensity from MCs below several GeV would require in turn an increase in the GC excess intensity at those energies in order to preserve the whole balance. The GC excess brightening at low energies in turn would make its spectrum more monotonous, i.e., less bumpy. Furthermore, this kind of power-law spectrum is then relatively easy to \"absorb\" into the overall diffuse gas or point sources (both resolved and unresolved) spectra, which have the similar shape close to a power law, by their slight renormalization towards higher levels. Such procedure would remove the GC excess as a separate emission component merging the former with the known components. Finally, we would like to notice that our model curves in Figure 1 are not intended to fit the GC excess directly. They only illustrate that reasonable parameter values for MCs and ISM are able to produce the spectral break in intensity of MCs at an energy near the GC excess peak, allowing the excess below this energy to \"brighten\" up to the state (ideally) where the whole excess spectrum is close to a monotonous power law.