Late-Onset Energy Injection in Type Ic SNe and W-Shaped O II Absorption in SLSNe-I

Abstract

We show that delayed (weeks-months) energy injection into expanding Type Ic supernova (SN) ejecta can reproduce the luminosity and spectral evolution of hydrogen-poor superluminous SNe (SLSNe-I). Late-time reheating sets the radiation temperature and density needed for the W-shaped OII absorption near peak, explaining its disappearance as the ejecta cools without extra excitation mechanisms. In our model, the neutron star (NS) undergoes a core phase transition to deconfined quark matter at time t_QN, triggering rapid magnetic field amplification and forming a hybrid star (HS; a QCD-magnetar). This Quark-Nova (QN) resets the central engine, weeks to months after the SN, by converting the NS rotational energy into renewed energy injection, producing two powering epochs separated by a delay determined by hadron-to-quark microphysics. The model reproduces photometric and spectroscopic evolution of SLSNe-I such as iPTF13ajg, SN2010gx, PTF09cnd, and PTF09atu. We predict a systematic offset between spectroscopic and photometric ages when pre-QN emission is below detection limits, and discuss observational signatures distinguishing QCD-magnetars from standard magnetars. Double-peaked SLSNe-I may probe the hadron-quark transition, constraining quark-matter parameters like deconfinement density and surface tension.

Figures (12)

• Figure 1: Peak luminosity (top panel), photospheric radiation temperature (middle panel), and ejecta mass (bottom panel) as functions of the HS spin period in our model. Green open stars show Monte Carlo realizations obtained by sampling $P_{\rm NS}$, $t_{\rm QN}/t_{\rm ej,d}$, and $v_{\rm ej}$ over the ranges adopted in the text (see § \ref{['sec:model']}). Red points correspond to SLSNe-I from the observational catalogue of gomez_2024, while blue symbols indicate representative best-fit parameters for four well-studied events (SN 2010gx, iPTF13ajg, PTF09cnd, and PTF09atu) within our model (see § \ref{['sec:spectroscopy-TARDIS-4SLSNe-I']}). The solid black curve in the middle panel shows the analytic scaling $L_{\rm SLSN,pk} \propto P_{\rm HS}^{-2}$ for the case $t_{\rm ej,d}=t_{\rm QN}$ (see Eq. \ref{['eq:L-SLSN-peak']}).
• Figure 2: Bolometric light curves in our model for ejecta masses $M_{\rm ej}=5M_{\odot}$ (top) and $M_{\rm ej}=10M_{\odot}$ (bottom). Colored curves show the total luminosity $L_{\rm tot}$ for different ratios $t_{\rm NS,SpD}/t_{\rm QN}$, obtained by varying the NS magnetic field strength (Eq. \ref{['eq:Ltotal']}). The HS forms at $t_{\rm QN}=40$ days after the Type Ic SN. We refer to the HS as a QCD-magnetar, with $B_{\rm HS}=10^{15}$ G and $P_{\rm HS}=P_{\rm NS}(1+t_{\rm QN}/t_{\rm NS,SpD})^{1/2}$. The thin green curve shows the purely $^{56}$Ni-powered SN component, while the blue curve indicates the intrinsic LFBOT luminosity prior to reprocessing by the ejecta. Larger $t_{\rm NS,SpD}/t_{\rm QN}$ implies more NS rotational energy available to reheat the ejecta at $t_{\rm QN}$. When $t_{\rm QN}\sim t_{\rm NS,SpD}$, the pre- and post-QN bumps have comparable brightness and width, while smaller ratios produce hotter post-QN ejecta (i.e., more luminous SLSNe) and favor the appearance of W-shaped O ii absorption features (see § \ref{['sec:spectroscopy-TARDIS']}).
• Figure 3: Time evolution of SN properties for an ejecta mass $M_{\rm ej}=5M_{\odot}$. All other parameters are fixed to the fiducial values listed in Table \ref{['table:parameters']}. Top panel: Bolometric luminosity from individual power sources and their sum. Contributions from $^{56}$Ni radioactive decay (thin green), neutron-star (NS) spin-down power (black dotted), and reprocessed LFBOT emission (red open symbols) are shown separately. The intrinsic LFBOT luminosity is shown by the dashed blue curve, and the total bolometric luminosity by the solid magenta curve. Second panel: Effective temperature $T_{\rm eff}$ computed from the total bolometric luminosity. The temperature corresponding to the intrinsic (non-reprocessed) LFBOT emission is shown for comparison. Third panel: Sobolev optical depth $\tau_{\rm w}$ of the O ii$\lambda4649$Å absorption line (dashed purple) and the number density of the 23 eV O ii level (solid purple). Thin curves show the contribution from $^{56}$Ni-powered ionization. Bottom panel: Ionization rate from $^{56}$Ni decay (solid) compared with the minimum rate required to maintain $\tau_{\rm w}=1$ (dashed). Green stars mark the epochs when $\tau_{\rm w}=1$ during the rise and decline, the time of maximum $\tau_{\rm w}$, and the epoch of peak total luminosity $L_{\rm Tot,pk}$. The shaded region in all panels indicates the interval where $\tau_{\rm w}>1$, during which the $\lambda4649$Å absorption line (and the associated W-shaped feature) is expected to be observable. Vertical lines mark $t_{\rm QN}$, the HS spin-down timescale, and the QN ejecta diffusion timescale.
• Figure 4: Same as Figure \ref{['fig:LC-5Mej']}, but for $M_{\rm ej}=10M_{\odot}$.
• Figure 5: Synthetic spectra at the epochs marked by green stars in Figures \ref{['fig:LC-5Mej']} and \ref{['fig:LC-10Mej']}, with the corresponding photospheric conditions listed in Table \ref{['table:the-Sobolev-times']}, for the $M_{\rm ej}=5M_{\odot}$ and $10M_{\odot}$ SN models. The characteristic W-shaped O ii absorption features are prominent at early times when the ejecta temperature exceeds $\sim12{,}000$ K and fade as the ejecta expands and cools, eventually revealing the underlying Type Ic spectrum.