Super-knee cosmic rays from interacting supernovae

TL;DR

This work investigates interacting supernovae as progenitors of super-knee cosmic rays (CRs) in the energy window ${\sim}{\rm few}\times10^{15}$ to ${\sim}{\rm few}\times10^{17}$ eV, arguing that ISNe, especially IIn events with dense circumstellar media, can dominate the CR flux in this band. The authors develop a phenomenological, time-dependent model of SN ejecta–CSM shock interaction that includes non-resonant streaming instability–driven magnetic-field amplification, composition-dependent injection, and heavy-ion abundance enhancements, and they compute maximum energies and escaping CR spectra for several SN types. A detailed temperature/ionization treatment using Cloudy informs the ionization state and injection efficiency of nuclei, enabling realistic multi-species CR predictions. By integrating the resulting escape spectra and propagating them through the Galactic medium, the study shows that IIn SNe can account for a large fraction of the observed super-knee CR flux and naturally explain the increasing heavy composition with energy, aligning with LHAASO, TA, and IceTop measurements and offering a compelling multimessenger test bed for hadronic acceleration in ISNe.

Abstract

There is increasing evidence that, in the very late phase of stellar evolution before core collapse, massive stars have winds with large mass loss rates that give rise to a dense circumstellar medium (CSM) surrounding the progenitor star. After core collapse, a shock wave forms when the supernova ejecta interacts with this CSM. In such an interaction, the nuclei in the CSM can undergo diffusive shock acceleration and reach very high energies. We consider such a model, which includes magnetic field amplification from the non-resonant streaming instability, enhancement to the abundance of heavy-ions, and composition-dependent acceleration. Applying this to several supernova subclasses, we find that IIn supernovae can supply a dominant fraction of the observed super-knee cosmic-ray (CR) flux from $\sim{\rm few}\times10^{15}\,{\rm eV}$ to $\sim{\rm few}\times10^{17}\,{\rm eV}$ and is consistent with recent LHAASO measurements above the CR knee. This systematic model also explains the increasingly heavy nuclear composition in this energy range.

Figures (6)

• Figure 1: These panels show quantities for He nuclei in IIn supernovae in the $T2$ model. Left panel: Comparison of the acceleration and energy-limiting timescales at $t_{\rm crit}$. Note that $t_{\rm crit}$ is determined by the magnetic field amplification effect of escaping cosmic rays, but there is no corresponding timescale defined for this. For $t_{\rm pho}$, this is calculated at each time and model, since an analytic expression for $E_{i,\rm pho}$ cannot be written. Photodisintegration is the most restricting destruction process for many cases, prior to the escape time. Right panel: Maximum energies achievable for He nuclei. The shaded gray region shows when the radiation-mediated condition is not met (see Eq. \ref{['radmediatedopticaldepth']}). After this, around $3\,{\rm days}$, the shock becomes collisionless and CRs can be accelerated. Energy-limiting processes include nuclear processes, adiabatic losses, photodisintegration, geometric escape, and the current induced from escaping nuclei. Here, the dotted lines (for $E_{\rm He,esc}$ and $E_{\rm He,cur}$) represent the processes that allow accelerated nuclei to escape. Here, $s = 2.8$ and magnetic field amplification is considered. In this case, the maximum energy is limited by photodisintegration for the first $\sim22\,{\rm days}$ ($t_{\rm crit}$, the vertical gray line) before escaping upstream. After this point, the maximum energy is limited by the non-resonant streaming instability effect that leads to magnetic field amplification, giving a maximum energy of $\sim10^{16}\,{\rm eV}$. Depending on the composition and input parameters like temperature and power-law index $s$, most cosmic-rays are limited in energy by either nuclear spallation, $pp$ interactions, or photodisintegration.
• Figure 2: Predicted flux from different models compared to observed fluxes from LHAASO (and the LHAASO p- and He-only spectra), TA, and IceTop, shown in the thinner line styles. Statistical errors are shown as vertical bars and systematic errors are shown as a shaded region. We highlight the white regions in each panel where these models (thicker lines) generally provide a dominant fraction of the observed flux. All models are consistent with the recent LHAASO p- and He-only fluxes, but the relative compositions and overall flux are useful in constraining models (see also Appendix \ref{['sec:icetopresults']}). Upper left panel: shows the predicted flux for the $T1$ model, where $T\sim L^{1/4}$. Although, consistent with LHAASO results, this model overestimates the observed flux at $10^{17}\,{\rm eV}$ because of an overabundance of Fe compared to He. Upper right panel: shows the predicted flux for the $T2$ model, where $T\sim15000\,{\rm K}$. This model is consistent with recent data and naturally explains the expected composition trends, so is used as the fiducial model in additional figures. Lower left panel: shows the predicted flux for the $s=2.4$ model. In this model, heavier elements dominate more of the spectrum, so the flux peak reaches relatively higher energies. Lower right panel: finally shows the 'Amp off' where the non-resonant streaming instability is assumed not to operate (or, equivalently, $\mathcal{A}=1$). This too is consistent with data, but reaches somewhat lower energies and fluxes compared to other models.
• Figure 3: Here we break down the components of the $T2$ model's predicted fluxes. Left panel: shows the breakdown of supernova types to the overall predicted flux. IIn supernova contribute the most to the predicted flux by $\gtrsim$ an order of magnitude. This is due to the combination of physical parameters (relative to other SN subtypes, the high wind mass-loss rate, low wind velocity, and moderate rate). Right panel: shows the breakdown of contributions from H, He, CNO, and Fe nuclei. The dominant component of the predicted flux becomes increasingly heavier with energy because the maximum energies are $A$ and $Z$ dependent.
• Figure 4: The flux-weighted average of the natural log of mass number as a function of energy. Here we show the inferred energy-dependence of composition from the LHAASO, TA, and IceTop experiments compared to that predicted from various models. As with the flux data, these data's statistical errors are shown as vertical bars and systematic errors shown as shaded regions. These figures reveal a potentially large discrepancy between experiments, where the TA observed composition is notably lighter. Since these are all air-shower experiments, the average mass number is an inferred quantity and individual cosmic-rays cannot be detected. Upper left panel: shows the average mass number for the $T1$ model, in red. This predicts a significant contribution of protons to the spectrum at $10^{16}\,{\rm eV}$ while overestimating the average mass number at higher energies. Upper right panel: shows the average mass number for the $T2$ model, in green, which reasonably agrees with the measured averages between $\sim5\times10^{15}\,{\rm eV}$ and $\sim5\times10^{17}\,{\rm eV}$. Lower left panel: shows the $s=2.4$ model, in brown, which shows a similar pattern to the $T1$ result, but may be slightly more consistent with observed averages. Finally, lower right panel: shows the 'Amp off' model, which similarly is consistent with data, but has a much lower average mass number at the highest energies, compared to other models.
• Figure 5: The mean free path of X-ray photons (dashed lines) compared to the shock radius, $R_{\rm sh}$, and the Larmor radius, $r_l$, for Fe nuclei. Up to $\sim100\,{\rm days}$, the softer X-ray photons up to $\sim1\,{\rm keV}$ can be reprocessed in the acceleration region of Fe nuclei. Harder X-ray photons, however, have a longer mean free path. The net effect of this may increase the effective temperature that nuclei experience, which affects the ionization state of pre-accelerated nuclei in the CSM and ultimately affects the observed CR composition.