All Figures

$\begin{figure} \par\includegraphics[width=7cm,clip]{cvir.eps} \end{figure}$ Figure 1: The dependence of $c_{\rm vir}$ on the halo mass M, at z=0, as in the Bullock et al. toy model (solid line) and in the ENS toy model (dashed line); predictions are compared to a few sets of simulation results in different mass ranges. A flat, vacuum-dominated cosmology with $\Omega _{\rm M} = 0.3$ , $\Omega _{\Lambda } = 0.7$ , h = 0.7 and $\sigma _8 = 1$ is assumed here.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{halofit.eps}\par\vspace*{3mm} \includegraphics[width=6.5cm,clip]{halofit3.eps} \end{figure}$ Figure 2: We show the 1 $\sigma$ , 2 $\sigma$ and 3 $\sigma$ contours as derived from the $\chi ^2_r$ variable in Eq. (19), for the Navarro et al. halo profile, Eq. (2), ( upper panel) and for the Diemand et al. halo profile, Eq. (3) ( lower panel). Also shown are mean values for the correlation between $M_{\rm vir}$ and $c_{\rm vir}$ as in the toy models of Bullock et al. (2001) (solid line) and that of Eke et al. (2001) (dashed line).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{halofit2.eps} \end{figure}$ Figure 3: We show here the 1 $\sigma$ , 2 $\sigma$ and 3 $\sigma$ contours as derived from the $\chi ^2_r$ variable introduced in the text, for the Burkert profile, Eq. (4).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{delta2ms.eps} \end{figure}$ Figure 4: Scaling of the average enhancement in source functions due to a subhalo of mass $M_{\rm s}$ . We show result implementing the three halo profiles introduced, i.e. the N04, D05 and Burkert profile, the two toy models for the scaling of concentration parameter with mass, i.e. the Bullock et al. and the ENS, and two sample values of the ratio between concentration parameter in subhalos to concentration parameter in halos at equal mass $F_{\rm s}$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{delta2.eps}\hspace*{5mm} \includegraphics[width=7cm,clip]{delta2int.eps} \end{figure}$ Figure 5: Left: scaling of the weighted enhancement in source functions due to subhalos versus the ratio between concentration parameter in subhalos to concentration parameter in halos at equal mass $F_{\rm s}$ . Results are shown the three halo profiles introduced, i.e. the N04, D05 and Burkert profile, the two toy models for the scaling of concentration parameter with mass, i.e. the Bullock et al. and the ENS. Right: fractional contribution per logarithmic interval in subhalo mass $M_{\rm s}$ to $\Delta ^2$ in four sample cases. A normalization of the fluctuation spectrum $\sigma _8 = 0.89$ is adopted.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{npairs.eps} \end{figure}$ Figure 6: The number density of neutralino pairs (neutralino mass set to $M_{\chi }=100$ GeV) as a function distance for the center of Coma for the three halo profiles introduced, i.e. the N04, D05 and Burkert profile in their best fit model, and a sample configuration for the subhalo parameters.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{source.eps} \end{figure}$ Figure 7: The spectral shape of the electron source function in case of three sample final states (see text for details).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{E_ele.eps}\hspace*{5mm} \includegraphics[width=6cm,clip]{E_gam.eps} \end{figure}$ Figure 8: Left: The electrons flux $({\rm d}N_{\rm e}/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the electron energy. Right: the gamma-rays flux $({\rm d}N_\gamma/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the photon energy.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{E_neu.eps}\hspace*{5mm} \includegraphics[width=6cm,clip]{E_pro.eps} \end{figure}$ Figure 9: Left: the neutrinos flux $({\rm d}N_\nu/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the neutrino energy. Right: the protons flux $({\rm d}N_{\rm p}/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the proton energy.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{radioflux.eps} \end{figure}$ Figure 10: Best fit models for the radio flux density spectrum, in case of a soft spectrum due to a $b\bar b$ annihilation final state (solid line, model with $M_{\chi } = 40$ GeV) and of a hard spectrum due to a W⁺ W^- channel (dashed line, model with $M_{\chi } = 81$ GeV); values of all parameters setting the model are given in the text. The datasets is from Thierbach et al. (2003).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.6cm,clip]{radiobr2.eps}\hspace*{3mm} \includegraphics[width=6.6cm,clip]{radiobr.eps} \end{figure}$ Figure 11: Surface brightness distribution at frequency $\nu = 1.4$ GHz, within a beam equal to $9\hbox {$.\mkern -4mu^\prime $ }35$ (HPBW), for the lightest WIMP model displayed in Fig. 10. In the left panel we show the predictions for a model with magnetic field that does not change with radius, and in the limit in which spatial diffusion for electrons and positrons has been neglected (solid line) or included (dashed line). In the right panel we consider a model with magnetic field taking a radial dependence $B(r) = B_0 \left ( 1 + {r \over r_{c1}}\right )^2 \cdot \left [ 1 + \left ( {r \over r_{c2}}\right )^2\right ]^{-\beta }$ with B₀ = 0.55 $\mu$ G , $\beta = 2.7$ , $r_{c1}=3^\prime$ , $r_{c2}=17\hbox {$.\mkern -4mu^\prime $ }5$ in order to reproduce the measured surface brightness. In both cases, the contributions from the smooth dark matter halo component only and from substructures only are also displayed. The dataset is from Deiss et al. (1997).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{RMComa.ps} \end{figure}$ Figure 12: The observed absolute RM of background sources in the Coma field are shown as a function of projected radius $\theta$ in arcmin. The blue curve is the prediction of a model with $B= \rm const$ . The red dashed curve is the prediction of a model with B(r) decreasing monotonically towards large radii and the solid red curve is the prediction of our model that fits the Coma radio-halo surface brightness. Data on positive (filled dots) and negative (empty dots) RMs are from Kim et al. (1990).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{bbarmx.eps}\hspace*{3mm} \includegraphics[width=6cm,clip]{wpwmmx.eps} \end{figure}$ Figure 13: Isolevel curves for reduced $\chi ^2$ from the fit of the Coma radio flux density spectrum, for a given mass (50-100-150 GeV) and annihilation channel. The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{bbarmxb.eps}\includegraphics[width=6.4cm,clip]{wpwmmxb.eps} \end{figure}$ Figure 14: Isolevel curves for minimum reduced $\chi ^2$ from the fit of the Coma radio flux density spectrum, obtained by varying the magnetic field within $1 ~\mu {\rm G} \le B_\mu \le 20~ \mu \rm G$ , for a given annihilation channel. The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{grid_soft.eps}\includegraphics[width=7cm,clip]{grid_hard.eps} \end{figure}$ Figure 15: A scatter plot of SUSY models, consistent with all available phenomenological constraints, giving a relic abundance in the 2- $\sigma$ WMAP range (green filled circles) or below it (low, relic density models, red circles), for soft ( left panel) and hard ( right panel) annihilation spectra.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{multiflux.eps}\includegraphics[width=6.5cm,clip]{multiflux2.eps} \end{figure}$ Figure 16: Multi-wavelength spectrum of the two best fit models for the radio flux shown in Fig. 10 (see text for details). The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.7cm,clip]{sz_coma_tot_mx40_planck.ps} \end{figure}$ Figure 17: The SZ effect produced by the $b\bar b$ model with $M_{\chi } = 40$ GeV (black solid curve) and by the W⁺W^- model with $M_{\chi } = 81$ GeV (black dashed curve) in Coma are shown in comparison with the thermal SZ effect of Coma (blue curve). The red curves represent the overall SZ effect. Notice that the DM-induced SZ effect has a very different spectral behavior with respect to the thermal SZ effect. SZ data are from OVRO (magenta), WMAP (cyan) and MITO (blue). The sensitivity of PLANCK (18 months, 1 $\sigma$ ) is shown for the LFI detector at 31.5 and 53 GHz channels (cyan shaded regions) and for the HFI detector 143 and 217 GHZ channels (green and yellow shaded areas, respectively).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{sz_coma_ratio_multifreq.ps} \end{figure}$ Figure 18: The ratio between the DM-induced and the thermal SZ effect in Coma is shown for the model with $M_{\chi } = 40$ GeV (red curve) and for the model with $M_{\chi } = 81$ GeV (blue curve). The model with $M_{\chi } = 40$ GeV produces an SZ effect which could be detected with the next coming microwave experiments.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{heating_mx40_81.ps} \end{figure}$ Figure 19: Left: the specific heating rate is plotted against the radial distance from the center of Coma. Right: the specific heating rate multiplied by the volume element is plotted against the radial distance from the center of Coma.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{multiflux3.eps}\hspace*{5mm} \includegraphics[width=6.2cm,clip]{bbarmag.eps} \end{figure}$ Figure 20: Scaling of the multi-wavelength spectrum and of relative bounds on the particle physics model with the assumed value for the mean magnetic field in Coma. Left panel: we have chosen a few sample values for the magnetic field and varied freely pair annihilation cross section and WIMP mass to minimize the $\chi ^2$ for the fit of radio data (a $b~\bar{b}$ final state is assumed); the decrease in the magnetic field must be compensated by going to larger $M_\chi$ and $\langle\sigma v\rangle_0$ , with a net increase in $\langle\sigma v\rangle_0/M_\chi^2$ , as it can be seen from the increase in the $\pi ^0$ component. The increase in the IC component is, at large values for the magnetic field, significantly more rapid, since for large values of the magnetic field synchrotron losses are the main energy loss mechanism for electrons and positrons and tend to decrease the number density for the equilibrium population. Right panel: upper limit on $\langle\sigma v\rangle_0$ as a function of the assumed value for the mean magnetic field in Coma; at each wavelength the limit is derived assuming that the predicted flux should be lower than the upper limit from each individual data point (slight overestimate of the limit from radio data, but we do not need to decide the cut on the reduced $\chi ^2$ marking the overshooting of the radio flux). Two sample values of $M_\chi$ are assumed. The lines marked GLAST refer to the GLAST projected sensitivity assuming no other $\gamma$ -ray component is present. In both panels the halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{multiflux4.eps}\hspace*{5mm} \includegraphics[width=6cm,clip]{wpwmmag.eps} \end{figure}$ Figure 21: The analogous of Fig. 20, but now for the W⁺ W^- final state and fixing the WIMP mass to 81 GeV. In the left panel, for each value of the magnetic field, the value of $\langle\sigma v\rangle_0$ is obtained by normalizing the radio flux at the value of the flux at the highest frequency point in the available dataset. Note again that on fair fit of the full radio dataset can be derived for this hard channel.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{haloscan.eps}\includegraphics[width=6.5cm,clip]{haloscan3.eps} \end{figure}$ Figure 22: Scaling of fluxes with the assumptions on the halo model for Coma. In the plane $c_{\rm vir}$ - $\Delta ^2$ we plot isolevel curves for fluxes normalized to the corresponding values within the setup as for the N04 profile in Fig. 6, marked with a dot in the left panel, i.e. the halo model we have assumed so far as reference model; the model marked with square in the right panel corresponds to the Burkert profile selected in Fig. 6. For all examples displayed we have fixed $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and a 50% mass in substructures. The left panel refers to N04 profiles, the right panel to Burkert profiles; reference values for $c_{\rm vir}$ and $\Delta ^2$ , as obtained by fitting the corresponding halo profiles and from our discussion on the substructure role, are marked on the axis. Switching to one of the halo models displayed here is equivalent to shifting all values of $\langle\sigma v\rangle_0$ plotted in figures to $\langle\sigma v\rangle_0$ divided by the scaling value shown here.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{multiflux5.eps} \end{figure}$ Figure 23: Multi-wavelength spectra for the four benchmark models described in the text. The prediction is shown for the best fit N04 profile, and our reference choice for subhalo parameters, and for a mean magnetic field equal to $2 ~\rm \mu G$ .
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{deltav.eps}\hspace*{5mm} \includegraphics[width=6.7cm,clip]{ghat.eps} \end{figure}$ Figure A.1: Left: the figure shows the distance $(\Delta v)^{1/2}$ which, on average, a electron covers while losing energy from its energy at emission $E^{\prime }$ and the energy when it interacts E, for a few values of E: 30 GeV, 10 GeV, 5 GeV and 1 GeV, and for a few values of the magnetic field (in $\mu$ G); we are focusing on a WIMP of mass 100 GeV, hence cutting $E^{\prime } < 100$ GeV. Right: green function $\widehat{G}$ as a function of $(\Delta v)^{1/2}$ , for a few values of the radial coordinate r (in kpc) and in case the DM halo of Coma is described by a N04 profile with $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ .

In the text

$\begin{figure} \par\includegraphics[width=6.6cm,clip]{ghat2.eps}\hspace*{4mm} \includegraphics[width=6.6cm,clip]{ghat3.eps} \end{figure}$ Figure A.2: Green function $\widehat{G}$ as a function of $(\Delta v)^{1/2}$ , for a few values of the radial coordinate r (in kpc) and in case the DM halo of Coma is described by a cored Burkert profile with $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ and for the Diemand et al. profile with the same parameters.

In the text

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{losses_1Mpc_b1.ps} \end{figure}$ Figure A.3: A comparison among the time scales for the energy losses due to various mechanisms (as labeled in the figure) and the time scale for diffusion (black solid curve) in a cluster of size $r_{\rm h}=1$ Mpc. A uniform magnetic field of value $B = 1~ \mu$ G and a thermal gas density $n=1.3 \times 10^{-3}$ cm^-3 have been assumed in the computations.

In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{eq_spectra.ps} \end{figure}$ Figure A.4: The electron equilibrium spectra calculated at the center of Coma as obtained for a soft spectrum due to a $b\bar b$ annihilation final state (solid line, model with $M_{\chi } = 40$ GeV) and of a hard spectrum due to a W⁺ W^- channel (dashed line, model with $M_{\chi } = 81$ GeV).

In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{cvir.eps} \end{figure}$	Figure 1: The dependence of $c_{\rm vir}$ on the halo mass M, at z=0, as in the Bullock et al. toy model (solid line) and in the ENS toy model (dashed line); predictions are compared to a few sets of simulation results in different mass ranges. A flat, vacuum-dominated cosmology with $\Omega _{\rm M} = 0.3$ , $\Omega _{\Lambda } = 0.7$ , h = 0.7 and $\sigma _8 = 1$ is assumed here.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{halofit2.eps} \end{figure}$	Figure 3: We show here the 1 $\sigma$ , 2 $\sigma$ and 3 $\sigma$ contours as derived from the $\chi ^2_r$ variable introduced in the text, for the Burkert profile, Eq. (4).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{npairs.eps} \end{figure}$	Figure 6: The number density of neutralino pairs (neutralino mass set to $M_{\chi }=100$ GeV) as a function distance for the center of Coma for the three halo profiles introduced, i.e. the N04, D05 and Burkert profile in their best fit model, and a sample configuration for the subhalo parameters.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{source.eps} \end{figure}$	Figure 7: The spectral shape of the electron source function in case of three sample final states (see text for details).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6cm,clip]{E_ele.eps}\hspace*{5mm} \includegraphics[width=6cm,clip]{E_gam.eps} \end{figure}$	Figure 8: Left: The electrons flux $({\rm d}N_{\rm e}/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the electron energy. Right: the gamma-rays flux $({\rm d}N_\gamma/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the photon energy.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6cm,clip]{E_neu.eps}\hspace*{5mm} \includegraphics[width=6cm,clip]{E_pro.eps} \end{figure}$	Figure 9: Left: the neutrinos flux $({\rm d}N_\nu/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the neutrino energy. Right: the protons flux $({\rm d}N_{\rm p}/{\rm d}E)\langle \sigma v\rangle_0$ as a function of the proton energy.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{radioflux.eps} \end{figure}$	Figure 10: Best fit models for the radio flux density spectrum, in case of a soft spectrum due to a $b\bar b$ annihilation final state (solid line, model with $M_{\chi } = 40$ GeV) and of a hard spectrum due to a W⁺ W^- channel (dashed line, model with $M_{\chi } = 81$ GeV); values of all parameters setting the model are given in the text. The datasets is from Thierbach et al. (2003).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6cm,clip]{bbarmx.eps}\hspace*{3mm} \includegraphics[width=6cm,clip]{wpwmmx.eps} \end{figure}$	Figure 13: Isolevel curves for reduced $\chi ^2$ from the fit of the Coma radio flux density spectrum, for a given mass (50-100-150 GeV) and annihilation channel. The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{bbarmxb.eps}\includegraphics[width=6.4cm,clip]{wpwmmxb.eps} \end{figure}$	Figure 14: Isolevel curves for minimum reduced $\chi ^2$ from the fit of the Coma radio flux density spectrum, obtained by varying the magnetic field within $1 ~\mu {\rm G} \le B_\mu \le 20~ \mu \rm G$ , for a given annihilation channel. The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{grid_soft.eps}\includegraphics[width=7cm,clip]{grid_hard.eps} \end{figure}$	Figure 15: A scatter plot of SUSY models, consistent with all available phenomenological constraints, giving a relic abundance in the 2- $\sigma$ WMAP range (green filled circles) or below it (low, relic density models, red circles), for soft ( left panel) and hard ( right panel) annihilation spectra.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{multiflux.eps}\includegraphics[width=6.5cm,clip]{multiflux2.eps} \end{figure}$	Figure 16: Multi-wavelength spectrum of the two best fit models for the radio flux shown in Fig. 10 (see text for details). The halo profile is the best fit N04 profile: $M_{\rm vir} = 0.9 \times 10^{15}~ M_{\odot}~h^{-1}$ and $c_{\rm vir} = 10$ , with subhalo setup as in Fig. 6.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.8cm,clip]{sz_coma_ratio_multifreq.ps} \end{figure}$	Figure 18: The ratio between the DM-induced and the thermal SZ effect in Coma is shown for the model with $M_{\chi } = 40$ GeV (red curve) and for the model with $M_{\chi } = 81$ GeV (blue curve). The model with $M_{\chi } = 40$ GeV produces an SZ effect which could be detected with the next coming microwave experiments.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.4cm,clip]{heating_mx40_81.ps} \end{figure}$	Figure 19: Left: the specific heating rate is plotted against the radial distance from the center of Coma. Right: the specific heating rate multiplied by the volume element is plotted against the radial distance from the center of Coma.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6.5cm,clip]{multiflux5.eps} \end{figure}$	Figure 23: Multi-wavelength spectra for the four benchmark models described in the text. The prediction is shown for the best fit N04 profile, and our reference choice for subhalo parameters, and for a mean magnetic field equal to $2 ~\rm \mu G$ .
Open with DEXTER