Simulations of black hole air showers in cosmic ray detectors

We present a comprehensive study of TeV black hole events in Earth’s atmosphere originated by cosmic rays of very high energy. An advanced fortran Monte Carlo code is developed and used to simulate black hole extensive air showers from ultrahigh-energy neutrino-nucleon interactions. We investigate the characteristics of these events, compare the black hole air showers to standard model air showers, and test different theoretical and phenomenological models of black hole formation and evolution. The main features of black hole air showers are found to be independent of the model considered. No significant differences between models are likely to be observed at fluorescence telescopes and/or ground arrays. We also discuss the tau “double-bang” signature in black hole air showers. We find that the energy deposited in the second bang is too small to produce a detectable peak. Our results show that the theory of TeV-scale black holes in ultrahigh-energy cosmic rays leads to robust predictions, but the fine prints of new physics are hardly to be investigated through atmospheric black hole events in the near future.

Figure 1

Number of $e^{+}{e}^{-}$ vs slant depth for the longitudinal development of 50 air showers with $E_{\nu }={10}^7\mathrm{TeV}$. The BH air showers for the benchmark model (solid lines) and the ${\nu }_e$-CC air showers (dashed lines) are shown. The air shower maxima are $X_m=1566\pm 6\mathrm{g}{\mathrm{cm}}^{-2}$ for the BH benchmark model and $X_m=1780\pm 9\mathrm{g}{\mathrm{cm}}^{-2}$ for the ${\nu }_e$-CC, respectively. The difference in the air shower maxima is $\Delta X_m=214\pm 12\mathrm{g}{\mathrm{cm}}^{-2}$. The left panel has both air showers with identical first interaction point, $X_0({\nu }_e\mathrm{\text{−}}\mathrm{CC})=X_0(BH)=780\mathrm{g}{\mathrm{cm}}^{-2}$. The right panel shows the same air showers with a shift in $X_0({\nu }_e\mathrm{\text{−}}\mathrm{CC})$ such that $X_m({\nu }_e\mathrm{\text{−}}\mathrm{CC})\simeq X_m(BH)$.

Figure 2

Number of ${\mu }^{+}{\mu }^{-}$ at various atmospheric depths $X_m+\Delta X$ vs the number of $e^{+}{e}^{-}$ at $X_m$ for 50 benchmark model BH air showers (filled circles) and 50 ${\nu }_e$-CC air showers (empty circles). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The observation depth of the muons increases from left to right panel and from top to bottom panel.

Figure 3

Number of ${\mu }^{+}{\mu }^{-}$ vs number of $e^{+}{e}^{-}$ at various depths $X_m+\Delta X$. The comparison is between 50 BH benchmark model air showers (filled circles) and 50 ${\nu }_e$-CC air showers (empty circles) with $E_{\nu }={10}^7\mathrm{TeV}$. The observation depth of the muons and electrons increases from left to right panel and from top to bottom panel.

Figure 4

Longitudinal development of 50 air showers for the BH benchmark model (solid curves) vs two different choices of BH parameters (dashed curves). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The left panel shows the difference between the benchmark model ($M_{\star }=1\mathrm{TeV}$) and $M_{\star }=3\mathrm{TeV}$. The average difference in the air shower maxima is $\Delta X_m=21\pm 9\mathrm{g}{\mathrm{cm}}^{-2}$. The right panel shows the benchmark case ($n=6$) and $n=3$. The average difference in $X_m$ is $\Delta X_m=15\pm 10\mathrm{g}{\mathrm{cm}}^{-2}$.

Figure 5

Longitudinal development of 50 air showers for the BH benchmark model (solid curves) vs two different choices of BH parameters (dashed curves). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The left panel shows the difference between the benchmark model ($M_{\min }=2M_{\star }$) and $M_{\min }=10M_{\star }$. The average difference in the air shower maxima is $\Delta X_m=20\pm 10\mathrm{g}{\mathrm{cm}}^{-2}$. The right panel shows the benchmark case ($Q_{\min }=M_{\star }$) and $Q_{\min }=2M_{\star }$. The average difference in $X_m$ is $\Delta X_m=7\pm 10\mathrm{g}{\mathrm{cm}}^{-2}$.

Figure 6

Longitudinal development of 50 air showers for the BH benchmark model (solid curves) vs two different choices of BH parameters (dashed curves). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The left panel shows the difference between the benchmark model (final decay in 2 quanta) and BH evolution with final electrically neutral remnant. The average difference in the air shower maxima is $\Delta X_m=17\pm 10\mathrm{g}{\mathrm{cm}}^{-2}$. The right panel shows the benchmark case and BH evolution with final electrically charged remnant. The average difference in $X_m$ is $\Delta X_m=2\pm 10\mathrm{g}{\mathrm{cm}}^{-2}$.

Figure 7

Longitudinal development of 50 air showers for the BH benchmark model (solid curves) vs two different choices of BH parameters (dashed curves). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The left panel shows the difference between the benchmark model (black disk) and the YN graviton loss model. The average difference in the air shower maxima is $\Delta X_m=19\pm 11\mathrm{g}{\mathrm{cm}}^{-2}$. The right panel shows the benchmark case and the improved YR graviton loss model. The average difference in $X_m$ is $\Delta X_m=19\pm 8\mathrm{g}{\mathrm{cm}}^{-2}$. There is virtually no difference between the YN and YR models.

Figure 8

Longitudinal development of 50 air showers for the BH benchmark model (solid curves) and a BH evolution model with minimum length $l_{\min }=2\alpha M_{\star }^{-1}$ (dashed curves). The energy of the primary neutrino is $E_{\nu }={10}^7\mathrm{TeV}$. The average difference in the air shower maxima is $\Delta X_m=47\pm 13\mathrm{g}{\mathrm{cm}}^{-2}$.

Figure 9

Longitudinal development of 50 BH air showers containing at least one $\tau$ decaying at an altitude $X>0.75(X_g-X_0)$. The air showers are started at an altitude of 20 km, corresponding to a slant depth of $X_0=160\mathrm{g}{\mathrm{cm}}^{-2}$. The left panel shows the profile of all the particles in the air shower. The right panel shows only the profile of the secondary particles from the $\tau$ decay. Note that the y axis of the right panel is magnified 10 times w.r.t the left panel. The peaks between $500\mathrm{g}{\mathrm{cm}}^{-2}$ and $1500\mathrm{g}{\mathrm{cm}}^{-2}$ are originated by multiple $\tau$ events with one $\tau$ decaying high in the atmosphere.