Implications of strong intergalactic magnetic fields for ultrahigh-energy cosmic-ray astronomy

We study the propagation of ultrahigh-energy cosmic rays in the magnetized cosmic web. We focus on the particular case of highly magnetized voids ($B\sim \mathrm{nG}$), using the upper bounds from the Planck satellite. The cosmic web was obtained from purely magnetohydrodynamical cosmological simulations of structure formation considering different power spectra for the seed magnetic field in order to account for theoretical uncertainties. We investigate the impact of these uncertainties on the propagation of cosmic rays, showing that they can affect the measured spectrum and composition by up to $\simeq 80\%$ and $\simeq 5\%$, respectively. In our scenarios, even if magnetic fields in voids are strong, deflections of 50 EeV protons from sources closer than $\sim 50\mathrm{Mpc}$ are less than 15° in approximately 10–50% of the sky, depending on the distribution of sources and magnetic power spectrum. Therefore, UHECR astronomy might be possible in a significant portion of the sky depending on the primordial magnetic power spectrum, provided that protons constitute a sizeable fraction of the observed UHECR flux.

Figure 1

Power spectrum of the initial magnetic field at $z\simeq 53$ (left) and $z\approx 0$ (right panel) as a function of the comoving wave number $h^{-1}k$.

Figure 2

Cumulative filling factors for all the runs analyzed in the present work (solid thick lines), together with a few models found in the literature [18, 19, 20, 22, 25, 26].

Figure 3

All-particle spectra for the different runs, assuming that sources follow the large-scale distribution of matter. The injected composition is assumed to be purely proton (left panel) and iron (right panel). Measurements by Auger [54] (circles) and TA [55] (squares) are shown for comparison. Curves are arbitrarily normalized to Auger data at $E=6\mathrm{EeV}$. Spectral parameters are, for the case of pure proton injection, ${\alpha }_{\mathrm{p}}=2$ and $E_{\max ,\mathrm{p}}=500\mathrm{EeV}$, and ${\alpha }_{\mathrm{Fe}}$ and $E_{\max ,\mathrm{Fe}}=156\mathrm{EeV}$ for the pure iron injection scenario.

Figure 4

Difference between the spectra for the different runs, assuming that sources follow the large-scale distribution of matter. The injected composition is assumed to be purely proton (left) and iron (right panel). Spectral parameters are the same as in Fig. 3.

Figure 5

Average of the logarithm of the mass number ($⟨\ln A⟩$, left panel) and its standard deviation ($\sigma (\ln A)$, right panel) for the case of pure iron injection assuming sources following the large-scale distribution of matter. Spectral parameters are the same as in Fig. 3.

Figure 6

Distribution of propagation times for the different runs, assuming that sources follow the large-scale distribution of matter. The composition is assumed to be purely proton (left) and iron (right panel). Spectral parameters are the same as in Fig. 3.

Figure 7

Average deflection as a function of the energy, and their corresponding standard deviations (hatched regions) for uniformly distributed sources (left) and sources following the simulated baryon density (right panel), emitting protons with the spectrum given by Eq. (1). Spectral parameters are the same as in Fig. 3.

Figure 8

Average deflection as a function of the energy, and their corresponding standard deviations (hatched regions) for sources emitting protons with spectrum given by Eq. (1). Sources are assumed to follow the simulated baryon density, and are distant 0–10 Mpc (left panel) and 10–20 Mpc (right panel). Spectral parameters are the same as in Fig. 3.

Figure 9

Fraction ($f$) of the sky with deflections ($\delta$) larger than a given value (${\delta }_0$). Sources are assumed to be emitting protons with spectrum given by Eq. (1), and either to follow the simulated baryon density (right) or to be uniformly distributed (left panel). The energy range considered here is $E>50\mathrm{EeV}$. Spectral parameters are the same as in Fig. 3.

Figure 10

Average deflection as a function of the energy, and their corresponding standard deviations (hatched regions) for an observer in a void (left) and in a cluster (right panel), assuming that sources following the baryon density of the cosmic web are emitting protons with spectrum given by Eq. (1). Deflections are calculated at a distance of 10 Mpc. Spectral parameters are the same as in Fig. 3.