1 . 0 × 10 − $^{6}$− 6 . 89 × 10 8 h − $^{1}$M ⊙ (referred to as “UnH”); and finally, (iii) the contribution of unresolved subha- los in the same mass range as in the case (ii) (compo- nent “UnS”). 

## 3.1. Resolved halos and subhalos (ReHS) 

In Fig. 2, we show full sky maps of the the γ -ray emission of all main halos and subhalos that are de- tected in the MS-II; this corresponds to an essentially perfectly complete sample of all halos above a mass limit of 6 . 89 × 10 8 h − $^{1}$M ⊙ . In the top panel of Fig. 2, a partial map at low redshift (corresponding to the first shell at z = 0) is shown in order to illustrate typical foreground structure, whereas the bottom panel gives an integrated map out to z = 10, which is approxi- mately the full EGB from annihilation. The maps in Fig. 2 are for E$_{γ,}$$_{0}$ = 10 GeV. In the color scale used for the maps, red corresponds to the highest and black to the lowest values of the specific intensity. 

## 3.2. Unresolved halos (UnH) 

The maps shown in Fig. 2 are complete down to the minimum mass in the MS-II that we can trust, ∼ 6 . 89 × 10 8 h − $^{1}$M ⊙ . In order to make a prediction of the full EGB coming from dark matter annihilations, we extrapolate the γ -ray flux to account for the con- tribution of all missing dark matter halos down to the cutoff mass 10 − 6 h − $^{1}$M ⊙ . For this purpose we use ex- trapolations of the power law behavior found for the total gamma-ray luminosity of host halos as a func- tion of mass. This is an analysis that we present in detail in section 4.1 of Zavala et al. [2009]. 

The way we incorporate this extrapolated contribu- tion in the γ -ray maps is the following. We assume that the EGB radiation from the missing halos in the mass range 10 − 6 h − $^{1}$M ⊙ to ∼ 6 . 89 × 10 8 h − $^{1}$M ⊙ is distributed on the sky in the same way as the one from the smallest masses we can resolve in the sim- ulation, which we adopt as the mass range between 1 . 4 × 10 8 h − $^{1}$M ⊙ and ∼ 6 . 89 × 10 8 h − $^{1}$M ⊙ . Hence, we compute the value of a boost factor b$_{h}$ with which each resolved halo in the mass range 1 . 4 − 6 . 89 × 10 8 h − $^{1}$M ⊙ needs to be multiplied such that the luminosity of the unresolved main halos is accounted for as well. We found that b$_{h}$ ∼ 60, and that its value is nearly inde- pendent of redshift up to the highest redshift we can reliable make the extrapolation, which is z ∼ 2 . 1. 

## 3.3. Unresolved subhalos (UnS) 

To add the contribution of unresolved substructures to the γ -ray maps, we first assume that the identified subhalo population is complete down to a mass limit 

of M$_{sub}$ = 6 . 89 × 10 8 h − $^{1}$M ⊙ . Below this mass we compute the gamma-ray luminosity of subhalos using extrapolations of the power law behavior of the con- tribution of these subhalos to the luminosities of their host halos. The parameters of the power law are given in detail in section 4.2 of Zavala et al. [2009]. We add this contribution in different ways for the following two cases. 

In the case of resolved main halos with more than 100 particles, we distributed the extra luminosity com- ing from unresolved substructures among the subhalos of the main host, assuming in this way that unresolved subhalos are distributed in the same way as the re- solved ones. If the main halos have no subhalos, the extra luminosity is given directly to them. 

For the second case of all main halos with masses less than 6 . 89 × 10 8 h − $^{1}$M ⊙ , we use the following strat- egy. From the results described in the last subsection we can get the total luminosity coming from all main halos with masses between the damping scale limit and 6 . 89 × 10 8 h − $^{1}$M ⊙ . Thus, we can compute the boost factor b$_{sub}$ for which this luminosity needs to be multiplied in order to include the full contribution of all subhalos of the main halos in this mass range. We found that b$_{sub}$ is roughly independent of redshift. Using the range of values found for the power laws de- scribed before, we obtain that b$_{sub}$ ≈ 2 − 60. We take the extreme values of this range in the following results as the minimum and maximum values that reflect the uncertainties in our extrapolation method and should bracket the true result. 

## 3.4. Isotropic and anisotropic components of the EGB from dark matter annihilation 

The upper panel of Fig. 3 shows the mean value of the specific intensity Δ I$_{γ,}$$_{0}$ divided by the comoving thickness of the shell at E$_{γ,}$$_{0}$ = 10 GeV as a function of redshift. Recall that each partial map represents the total specific intensity in a shell of constant comoving thickness, so this provides information about where the signal is coming from. The black line is for the ReHS case, while the dashed line is for main halos only (resolved and unresolved, including the boost factor b$_{h}$ = 60). The remaining lines are for the resolved and unresolved main halos and their subhalos, boosted to include the contribution of structures all the way down to the damping scale limit; here the blue line is for the “minimum boost” with b$_{sub}$ = 2 whereas the red line is for the “maximum boost” with b$_{sub}$ = 60, but both include the boost b$_{h}$ = 60 for unresolved main halos. 

In all cases, the contribution from partial maps up until z ∼ 1 is almost constant, indicating that the increasing number of sources for shells at higher red- shifts, due to the larger volume seen behind each pixel, is approximately compensated by the distance factor 

