All Figures

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f1}\end{figure}$ Figure 1: The time evolution of the wind particle spectrum in the case $\gamma _1=1.5$ , $\gamma _2=2.2$ , $L_{\rm pairs}=L_B=10^{39}\ {\rm erg}\ {\rm s}^{-1}$ . The different curves refer to different epochs after the supernova explosion: $t=1~ {\rm yr}$ (solid), $t=10~ {\rm yr}$ (dotted), $t=100 ~{\rm yr}$ (dashed), $t=500~ {\rm yr}$ (dot-dashed). The points trace, at each time, the approximation given in the text.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f2}\end{figure}$ Figure 2: The time evolution of $f^\mu$ for different values of the pulsar luminosity, of the remnant expansion velocity and of the wind Lorentz factor. The curves plotted in different panels are computed for different values of the wind Lorentz factor. The different curves in each panel are marked as explained below. Empty triangles: $L[{\rm erg}/{\rm s}]=3 \times 10^{39}$ , $v[\rm km~s^{-1}]=10^3$ . Empty squares: $L[{\rm erg}/{\rm s}]=3 \times 10^{39}$ , $v[\rm km~s^{-1}]=10^4$ . Filled triangles: $L[{\rm erg}/{\rm s}] =3 \times 10^{40}$ , $v[\rm km~s^{-1}]=10^3$ . Filled squares: $L[{\rm erg}/{\rm s}] =3 \times 10^{40}$ , $v[\rm km~s^{-1}]=10^4$ . The vertical lines represent the time at which the optical depth for neutrinos drops below 1 in the case when $v=10^3\ \rm km~s^{-1}$ (solid) and when $v=10^4\ \rm km~s^{-1}$ (dashed).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f3}\end{figure}$ Figure 3: The time evolution of $f^\nu$ for the highest energy pions corresponding to different values of the pulsar luminosity, of the remnant expansion velocity and of the wind Lorentz factor. Same notation as in Fig. 2.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f4}\end{figure}$ Figure 4: The time evolution of $f^\pi$ for different values of the pulsar luminosity, of the remnant expansion velocity and of the wind Lorentz factor. The solid curves refer to the efficiency of nuclear collisions while the dashed ones show the efficiency of photo-meson production. Curves referring to different values of the pulsar luminosity and remnant expansion velocity are marked according to the same notation as for Figs. 2 and 3.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f5}\end{figure}$ Figure 5: Electromagnetic spectrum of a "young Crab'' at different times after the supernova explosion. The thick curves correspond to the synchrotron (at low energies) and ICS (at higher energies) emission of the wind pairs, while the lighter curves refer to the emission of the pion decay products. The different panels correspond to different values of the wind Lorentz factor $\Gamma$ and the different line types refer to different times.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f6}\end{figure}$ Figure 6: Neutrino spectrum of a "young Crab''. The notation is the same as for Fig. 5. The solid thick line is the detection threshold for ICE-cube (Hill 2001), while the dot-dashed line is the atmospheric neutrino background in a $2^\circ \times 2^\circ$ bin.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f7}\end{figure}$ Figure 7: The flux of neutrinos expected from the Crab Nebula as a function of energy, for different values of the parameter $\mu$ and for different values of the wind Lorentz factor $\Gamma$ . The different curves in each panel correspond to $\mu =1$ (solid), $\mu =5$ (dotted), $\mu =10$ (dashed) and $\mu =20$ (long-dashed). The considered values of $\Gamma$ range from 10⁴ to 10⁷, as specified in each panel. The solid thick line is the detection threshold for IceCube (Hill 2001), while the dot-dashed line is the atmospheric neutrino background in a $2^\circ \times 2^\circ$ bin. We assume 60% of the pulsar wind energy to be carried by protons.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f8}\end{figure}$ Figure 8: The flux of high energy photons expected from the Crab Nebula, for different values of the parameter $\mu$ and of the wind Lorentz factor $\Gamma$ . The notation is the same as in Fig. 7. The expected fluxes are compared with the available data and upper limits (de Jager et al. 1996; Aharonian et al. 2000 and references therein). Also shown as a thick curve in each panel is the ICS flux computed based on this model.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f9}\end{figure}$ Figure 9: Consequences of pion production on the electromagnetic spectrum of the Crab Nebula. The thick curve and the points represent the observed emission, while the thin curves are fluxes from our model. At low frequencies the model flux is due to synchrotron emission associated to secondary electrons and positrons, while the contribution at high frequencies is the same shown in Fig. 8 and comes from $\pi ^0$ decay. The different panels refer to the emission computed for different values of the wind Lorentz factor while the different line-types are associated to different values of the parameter $\mu$ as specified in the each panel.
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In the text

$\begin{figure} \par\includegraphics[width=6.9cm,clip]{2873.f10}\end{figure}$ Figure 10: The allowed parameter space for $\Gamma$ and $L_{\rm p}/L_{\rm Tot}$ as constrained through the comparison with observations of the photon fluxes from pion decay computed within the framework of our model. The allowed regions for each of the considered value of $\mu$ are the ones lying under the curve of corresponding type: $\mu =5 \rightarrow$ solid, $\mu =10 \rightarrow$ dashed, $\mu =20 \rightarrow$ dot-dashed. No constraints can be put on the wind parameters for $\mu =1$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f11}\end{figure}$ Figure 11: The maximum number of muons per year that would be produced by neutrinos coming from the Crab Nebula in a ${\rm km}^2$ detector. Also shown, as a dot-dashed line, are the background counts, assuming an angular resolution of $(1^\circ )^2$ , such as IceCube should have.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f3}\end{figure}$	Figure 3: The time evolution of $f^\nu$ for the highest energy pions corresponding to different values of the pulsar luminosity, of the remnant expansion velocity and of the wind Lorentz factor. Same notation as in Fig. 2.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f6}\end{figure}$	Figure 6: Neutrino spectrum of a "young Crab''. The notation is the same as for Fig. 5. The solid thick line is the detection threshold for ICE-cube (Hill 2001), while the dot-dashed line is the atmospheric neutrino background in a $2^\circ \times 2^\circ$ bin.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2873.f11}\end{figure}$	Figure 11: The maximum number of muons per year that would be produced by neutrinos coming from the Crab Nebula in a ${\rm km}^2$ detector. Also shown, as a dot-dashed line, are the background counts, assuming an angular resolution of $(1^\circ )^2$ , such as IceCube should have.
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