High-energy cosmic ray nuclei from tidal disruption events: Origin, survival, and implications

Tidal disruption events (TDEs) by supermassive or intermediate mass black holes have been suggested as candidate sources of ultrahigh-energy cosmic rays (UHECRs) and high-energy neutrinos. Motivated by the recent measurements from the Pierre Auger Observatory, which indicates a metal-rich cosmic-ray composition at ultrahigh energies, we investigate the fate of UHECR nuclei loaded in TDE jets. First, we consider the production and survival of UHECR nuclei at internal shocks, external forward and reverse shocks, and nonrelativistic winds. Based on the observations of Swift $\mathrm{J}1644+57$, we show that the UHECRs can survive for external reverse and forward shocks, and disk winds. On the other hand, UHECR nuclei are significantly disintegrated in internal shocks, although they could survive for low-luminosity TDE jets. Assuming that UHECR nuclei can survive, we consider implications of different composition models of TDEs. We find that the tidal disruption of main sequence stars or carbon-oxygen white dwarfs does not successfully reproduce UHECR observations, namely the observed composition or spectrum. The observed mean depth of the shower maximum and its deviation could be explained by oxygen-neon-magnesium white dwarfs, although they may be too rare to be the sources of UHECRs.

Figure 1

Photonuclear and photomeson production cross sections for five chemical species, which are used in this work: Fe, Si, O, He, and proton, as a function of NRF target photon energy [48, 54, 55, 56]. For simplicity, the superposition model is assumed for the photomeson production.

Figure 2

Various time scales for five typical chemical species (Fe, Si, O, He, and proton) in the internal shock region as a function of particle energy (measured in the observer frame). We show interaction time scales in the upper panel and energy-loss time scales in the lower panel. The thin (thick) black line represents the acceleration time scale for the proton (Fe). We show the synchrotron cooling time scale for protons as the dotted black line. The parameters are $L_{\mathrm{iso}}={10}^{48}\mathrm{erg}{\mathrm{s}}^{-1}$, $\mathrm{\Gamma }=10$, ${\epsilon }_B=0.1$, and $r=3\times {10}^{14}\mathrm{cm}$.

Figure 3

Same as Fig. 2, but the parameters are $L_{\mathrm{iso}}=10^{44.8}\mathrm{erg}{\mathrm{s}}^{-1}$, $\mathrm{\Gamma }=10$, ${\epsilon }_B=0.1$, and $r={10}^{14}\mathrm{cm}$.

Figure 4

Various time scales for five typical chemical species (Fe, Si, O, He, and proton) in the reverse shock region as a function of particle energy (measured in the observer frame). We show the interaction time scales in the upper panel and energy-loss time scales in the lower panel. The thin (thick) black line represents the acceleration time scale for the proton (Fe). We show the synchrotron cooling time scale for the proton as the dotted black line. The parameters we use are $L_{\mathrm{iso}}={10}^{47}\mathrm{erg}{\mathrm{s}}^{-1}$, $t_j={10}^6\mathrm{s}$, ${\mathrm{\Gamma }}_0=10$, ${\epsilon }_B^r=0.01$, ${\epsilon }_e^r=0.02$, and $f_e^r=0.1$.

Figure 5

Various time scales for five typical chemical species (Fe, Si, O, He, and proton) in the forward shock region as a function of particle energy (measured in the observer frame). We show the interaction time scales in the upper panel and energy-loss time scales in the lower panel. The thin (thick) black line represents the acceleration time scale for the proton (Fe). We show the synchrotron cooling time scale for the proton as the dotted black line. The parameters we use are $L_{\mathrm{iso}}={10}^{47}\mathrm{erg}{\mathrm{s}}^{-1}$, $t={10}^6\mathrm{s}$, ${\mathrm{\Gamma }}_0=10$, ${\epsilon }_B=0.015$, ${\epsilon }_e=0.03$, and $f_e=0.1$.

Figure 6

The time evolution of maximum energy (lower panel) and optical depth $f_{A\gamma }$ (upper panel) for five typical chemical species: Fe, Si, O, He, and proton in the forward shock model. The optical depth is calculated when UHECR nuclei have energy $10^{20}\mathrm{eV}$ (measured in the observer frame).

Figure 7

Various time scales for five typical chemical species (Fe, Si, O, He, and proton) in the wind model as a function of particle energy. We show the interaction time scales in the upper panel and energy-loss time scales in the lower panel. The thin (thick) black line represents the acceleration time scale for the proton (Fe). We show the synchrotron cooling time scale for protons as the dotted black line. The parameters we use are ${\mathcal{E}}_k={10}^{48}\mathrm{erg}$, $V_s=0.1c$, ${\epsilon }_B=0.1$, ${\epsilon }_e=0.1$, and $f_e=0.1$.

Figure 8

CR injection spectra for model I: MS stars tidally disrupted by SMBHs. The mass fraction is $X_{\mathrm{H}}=73.9\%$, $X_{\mathrm{He}}=24.7\%$, $X_{\mathrm{C}}=0.22\%$, $X_{\mathrm{N}}=0.07\%$, $X_{\mathrm{O}}=0.63\%$, $X_{\mathrm{Ne}}=0.17\%$, $X_{\mathrm{Mg}}=0.06\%$, $X_{\mathrm{Si}}=0.07\%$, and $X_{\mathrm{Fe}}=0.12\%$, which are taken from Ref. [86]. The maximum energy is $Z{E}_{p,\max }=2\times {10}^{19}Z\mathrm{eV}$, and the spectral index is $s_{\mathrm{esc}}=1$. The total CR injection energy is ${\mathcal{E}}_{\mathrm{CR}}={10}^{53}\mathrm{erg}$.

Figure 9

CR injection spectra for WDs disrupted by IMBHs. Upper panel: Model II-1, CO-WDs with mass fraction $X_{\mathrm{C}}=0.5$, $X_{\mathrm{O}}=0.5$. Lower panel: Model II-2, ONeMg-WDs with mass fraction $X_{\mathrm{O}}=0.12$, $X_{\mathrm{Ne}}=0.76$, $X_{\mathrm{Mg}}=0.12$. The maximum energy is $Z{E}_{p,\max }=6.3\times {10}^{18}Z\mathrm{eV}$, and the spectral index is $s_{\mathrm{esc}}=1$. The total CR injection energy is ${\mathcal{E}}_{\mathrm{CR}}={10}^{53}\mathrm{erg}$.

Figure 10

CR injection spectra for WDs disrupted by an IMBH. Upper panel: Model III-1, $0.2M_{\odot }$ helium WDs disrupted by $10^3{M}_{\odot }$ IMBHs. The mass fraction is $X_{\mathrm{He}}=77.6\%$, $X_{\mathrm{C}}=0.37\%$, $X_{\mathrm{Si}}=7.3\%$, and $X_{\mathrm{Fe}}=0.2\%$. Lower panel: Model III-2, $1.2M_{\odot }$ CO-WDs disrupted by $500M_{\odot }$ IMBHs [98]. The mass fraction is $X_{\mathrm{He}}=15.25\%$, $X_{\mathrm{C}}=3.7\%$, $X_{\mathrm{O}}=10.3\%$, $X_{\mathrm{Ne}}=0.3\%$, $X_{\mathrm{Mg}}=0.37\%$, $X_{\mathrm{Si}}=21.7\%$, and $X_{\mathrm{Fe}}=66.7\%$. The maximum energy is $Z{E}_{p,\max }=6.3\times {10}^{18}Z\mathrm{eV}$, and the spectral index is $s_{\mathrm{esc}}=1$. The total CR injection energy is ${\mathcal{E}}_{\mathrm{CR}}={10}^{53}\mathrm{erg}$.

Figure 11

Model I: MS stars with the solar composition. We use a maximum proton energy of $E_{p,\max }=2\times {10}^{19}\mathrm{eV}$ and spectral index of $s_{\mathrm{esc}}=1$.

Figure 12

Model II-1: CO-WDs with an initial mass composition, $X_{\mathrm{C}}=0.5$, $X_{\mathrm{O}}=0.5$. We use a maximum proton energy of $E_{p,\max }=6.3\times {10}^{18}\mathrm{eV}$ and spectral index of $s_{\mathrm{esc}}=1$.

Figure 13

Model II-2: ONeMg-WDs with an initial mass composition $X_{\mathrm{O}}=0.12$, $X_{\mathrm{Ne}}=0.76$, $X_{\mathrm{Mg}}=0.12$. We use a maximum proton energy of $E_{p,\max }=6.3\times {10}^{18}\mathrm{eV}$ and spectral index of $s_{\mathrm{esc}}=1$.

Figure 14

Model III-1: $0.2M_{\odot }$ (ignited) helium WDs disrupted by $10^3{M}_{\odot }$ IMBHs. We use a maximum proton energy of $E_{p,\max }=6.3\times {10}^{18}\mathrm{eV}$ and spectral index of $s_{\mathrm{esc}}=1$.

Figure 15

Model III-2: $1.2M_{\odot }$ (ignited) CO-WDs disrupted by $500M_{\odot }$ IMBHs. We use a maximum proton energy of $E_{p,\max }=6.3\times {10}^{18}\mathrm{eV}$ and spectral index of $s_{\mathrm{esc}}=1$.