Lightcurve Features of Magnetar-Powered Superluminous Supernovae with Gravitational-Wave Emission and High-Energy Leakage

TL;DR

This paper investigates magnetar-powered Type I SLSNe, focusing on how gravitational-wave emission and high-energy leakage modify the bolometric lightcurves. It develops an analytic, one-zone framework with three spin-down channels: Case I (pure EM spin-down), Case II (EM+GW with ellipticity $\varepsilon$), Case III (EM+GW with r-mode amplitude $\alpha$), deriving the spin-down relations and leakage treatment (including $d\Omega/dt$ and $L_{\mathrm{EM}}$, $L_{\mathrm{GW,e}}$, $L_{\mathrm{GW,r}}$) and the leakage factor $\eta(t)$ that governs energy deposition. It finds that for millisecond initial spins, GW losses suppress early luminosity but, together with leakage, enhance late-time emission and delay the peak; the magnitude of these effects depends on the NS EOS through $R$ and $I$, as well as on the GW amplitudes $\varepsilon$ and $\alpha$. These results provide a theoretical handle to diagnose central-engine properties in SLSNe and motivate future surveys like LSST to constrain magnetar parameters and NS EOS from observed lightcurves.

Abstract

Superluminous supernovae (SLSNe) are a distinct class of stellar explosions, exhibiting peak luminosities 10-100 times brighter than those of normal SNe. Their extreme luminosities cannot be explained by the radioactive decay of $^{56}\mathrm{Ni}$ and its daughter $^{56}\mathrm{Co}$ alone. Consequently, models invoking newly formed millisecond magnetars have been widely proposed, capable of supplying additional energy through magnetic dipole radiation. For these rapidly rotating magnetars, however, gravitational-wave (GW) emission may also contribute significantly to the spin-down, particularly during their early evolutionary stages. While high-energy photons initially remain trapped within the optically thick ejecta, they will eventually escape as the ejecta becomes transparent during the expansion, thereby influencing the late-time lightcurve. In this work, we adopt an analytical framework to systematically explore the combined effects of GW emission and high-energy leakage on the lightcurve of SLSNe. Compared to scenarios that neglect these processes, we find that for magnetars with initial spin periods of millisecond, the combined influence suppresses early-time luminosities but enhances late-time emission. We further investigate the effects of the neutron-star equation of state to the lightcurve, GW emission efficiency, ejecta mass, and other relevant quantities. Our results highlight the complex interplay between GW-driven spin-down and radiative transport in shaping the observable features of SLSNe, offering new insights into diagnosing the nature of their central engines.

Figures (8)

• Figure 1: Evolution of the magnetar spin period. Different colors denote different energy-loss scenarios (see Section \ref{[' subsec:magnetar ']}). We fix $\varepsilon = 10^{-3}$ for Case II and $\alpha = 0.1$ for Case III. Solid lines correspond to an initial spin period of $P_0 = 1 \rm ~ms$, while dashed lines correspond to $P_0 = 10\rm ~ms$. Other parameters are fixed at $M = 1.4 ~\rm M_\odot$, $R = 10 \mathrm{~km}$, $I = 10^{45} \mathrm{~g ~cm^2}$, and $B=1 \times 10^{14} \mathrm{~G}$. When $P_0 = 10\rm ~ms$, GW emission becomes negligible, causing the evolution of spin period nearly overlaps with each other.
• Figure 2: The bolometric SLSN lightcurves (top) in different energy-loss scenarios, and the evolution of the $\gamma$-ray trapping factor $\eta$ and ejecta radius $R_\mathrm{ej}$ (bottom). Red, blue, and green curves correspond to Case I, II, and III, respectively. Solid lines represent an initial spin period of $P_0 = 1 \rm ~ms$, while dashed lines correspond to $P_0 = 10\rm ~ms$. In the top panel, dotted lines show the effective injected power, $\eta L_{\mathrm{EM}}$, for each case. The upper-right subpanel provides a zoomed-in view. For comparison, the black solid line shows the SN lightcurve powered solely by the radioactive decay of ${ }^{56} \mathrm{Ni}$ with a mass of $0.1\,\mathrm{M}_{\odot}$1994ApJS...92..527NArnett:1996ev. In the bottom panel, thick lines trace the evolution of $\eta(t)$ (vertical axis on the left), while thin lines indicate the ejecta expansion $R_{\mathrm{ej}}(t)$ (vertical axis on the right). Other parameters are fixed at $M = 1.4~\rm M_\odot$, $R = 10^6\mathrm{~cm}$, $I = 10^{45}\mathrm{~g\,cm^2}$, $B = 10^{14}\mathrm{~G}$, $M_{\mathrm{ej}} = 5~\rm M_\odot$, $\varepsilon = 10^{-3}$, and $\alpha = 0.1$. Some cases are indistinguishable in the plot for $P_0 = 10\,$ms.
• Figure 3: The $M$--$R$ (top) and $I$--$M$ (bottom) relations for five representative NS EOSs: MS0, BSK21, ENG, APR, and WFF1 Lattimer:2000nx. The 1-$\sigma$ confidence intervals of two precisely measured NS masses from PSRs J0740+6620 Fonseca:2021wxt and J0348+0432 Saffer:2024tlb are shown as shaded regions in the top panel. In the bottom panel, the dimensionless moment of inertia $I_{45}$ is defined as $I_{45} \equiv I / 10^{45}~\mathrm{g\,cm^2}$.
• Figure 4: Bolometric SLSN lightcurves for three spin-down scenarios with five different NS EOSs. Different colors represent different EOS models. Solid, dashed, and dotted lines correspond to Cases I, II, and III, respectively. Other parameters are fixed at $P_0 = 1\rm ~ms$, $M = 1.4~\rm M_\odot$, $M_{\mathrm{ej}} = 5~\rm M_\odot$, $B = 10^{14}\mathrm{~G}$, $\varepsilon = 10^{-3}$, and $\alpha = 0.1$.
• Figure 5: Ratios of the bolometric SLSN luminosity between Case I and Case II (upper), and between Case I and Case III (lower). Different colors represent different EOS models. The horizontal dashed black line marks a ratio of unity.