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Liang-Duan Liu

Publications and source records attributed to Liang-Duan Liu.

At least 37 records · Page 2Linked to original sources

Formation of Fast-spinning Neutron Stars in Close Binaries and Magnetar-driven Stripped-envelope Supernovae

Extreme stripped-envelope supernovae (SESNe), including Type Ic superluminous supernovae (SLSNe-I), broad-line Type Ic SNe (SNe Ic-BL), and fast blue optical transients (FBOTs), are widely believed to harbor a newborn fast-spinning highly-magnetized neutron star (``magnetar''), which can lose its rotational energy via spin-down processes to accelerate and heat the ejecta. The progenitor(s) of these magnetar-driven SESNe, and the origin of considerable angular momentum (AM) in the cores of massive stars to finally produce such fast-spinning magnetars upon core-collapse are still under debate. Popular proposed scenarios in the literature cannot simultaneously explain their event rate density, SN and magnetar parameters, and the observed metallicity. Here, we perform a detailed binary evolution simulation that demonstrates that tidal spin-up helium stars with efficient AM transport mechanism in close binaries can form fast-spinning magnetars at the end of stars' life to naturally reproduce the universal energy-mass correlation of these magnetar-driven SESNe. Our models are consistent with the event rate densities, host environments, ejecta masses, and energetics of these different kinds of magnetar-driven SESNe, supporting that the isolated common-envelope formation channel could be a major common origin of magnetar-driven SESNe. The remnant compact binary systems of magnetar-driven SESNe are progenitors of some gravitational-wave transients and galactic systems.

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Bumpy Superluminous Supernovae Powered by a Magnetar-star Binary Engine

Wolf-Rayet stars in close binary systems can be tidally spun up by their companions, potentially leaving behind fast-spinning highly-magnetized neutron stars, known as ``magnetars", after core collapse. These newborn magnetars can transfer rotational energy into heating and accelerating the ejecta, producing hydrogen-poor superluminous supernovae (SLSNe). In this {\em{Letter}}, we propose that the magnetar wind of the newborn magnetar could significantly evaporate its companion star, typically a main-sequence or helium star, if the binary system is not disrupted by the {abrupt mass loss and} SN kick. The subsequent heating and acceleration of the evaporated star material along with the SN ejecta by the magnetar wind can produce a post-peak bump in the SLSN lightcurve. Our model can reproduce the primary peaks and post-peak bumps of four example observed multiband SLSN lightcurves, revealing that the mass of the evaporated material could be $\sim0.4-0.6\,M_\odot$ if the material is hydrogen-rich. {We propose that the magnetar could induce strongly enhanced evaporation from its companion star near the pericenter if the orbit of the post-SN binary is highly eccentric, ultimately generating multiple post-peak bumps in the SLSN lightcurves. This ``magnetar-star binary engine" model may offer a possible explanation for the evolution of polarization, along with the origin and velocity broadening of late-time hydrogen or helium broad spectral features observed in some bumpy SLSNe.} The diversity in the lightcurves and spectra of SLSNe may be attributed to the wide variety of companion stars and post-SN binary systems.

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The Peculiar Precursor of a Gamma-Ray Burst from a Binary Merger Involving a Magnetar

The milestone discovery of GW 170817-GRB 170817A-AT 2017gfo has shown that gravitational wave (GW) could be produced during the merger of neutron star-neutron star/black hole and that in electromagnetic (EM) wave a gamma-ray burst (GRB) and a kilonova (KN) are generated in sequence after the merger. Observationally, however, EM property before the merger phase is still unclear. Here we report a peculiar precursor in a KN-associated long-duration GRB 211211A, providing evidence of the EM before the merger. This precursor lasts $\sim$ 0.2 s, and the waiting time between the precursor and the main burst is $\sim$ 1 s, comparable to that between GW 170817 and GRB 170817A. The spectrum of the precursor could be well fit with a non-thermal cutoff power-law model instead of a blackbody. Especially, a $\sim$22 Hz Quasi-Periodic Oscillation candidate ($\sim 3σ$) is detected in the precursor. These temporal and spectral properties indicate that this precursor is probably produced by a catastrophic flare accompanying with magnetoelastic or crustal oscillations of a magnetar in binary compact merger. The strong magnetic field of the magnetar can also account for the prolonged duration of GRB 211211A. However, it poses a challenge to reconcile the rather short lifetime of a magnetar with the rather long spiraling time of a binary neutron star system only by the GW radiation before merger.

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The Red Supergiant Progenitor of Type II Supernova 2024ggi

We present a detailed analysis of the progenitor and its local environment for the recently discovered type II supernova (SN) 2024ggi at a distance of about 6.7~Mpc, by utilizing the pre-explosion images from the Hubble Space Telescope (HST) and \textit{Spitzer} Space Telescope. The progenitor is identified as a red, bright variable star, with absolute $F814W$-band magnitudes being $-$6.2 mag in 1995 to $-$7.2 mag in 2003, respectively, consistent with that of a normal red supergiant (RSG) star. Combining with the historical mid-infrared light curves, a pulsational period of about 379~days can be inferred for the progenitor star. Fitting its spectral energy distribution with stellar spectral models yields the stellar parameters of temperature, radius and bolometric luminosity as $T_*=3290_{-27}^{+19}$~K, $R_*=887_{-51}^{+60}$~R$_{\odot}$, and log($L$/L$_{\odot}$)$=4.92_{-0.04}^{+0.05}$, respectively. The above parameters indicate that the progenitor of SN 2024ggi is consistent with the stellar evolutionary track of a solar-metallicity massive star with an initial mass of $13_{-1}^{+1}$~M$_{\odot}$. Moreover, our analysis indicates a relatively low mass loss rate (i.e., $< 3\times10^{-6}$~M$_{\odot}$~yr$^{-1}$) for the progenitor compared to that inferred from the flashed spectra and X-ray detection (i.e., $10^{-2}$$-$$ 10$$^{-5}$~M$_{\odot}$~yr$^{-1}$), implying a significant enhancement in mass loss within a few years prior to the explosion.

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Magnetar Flare-Driven Bumpy Declining Light Curves in Hydrogen-poor Superluminous Supernovae

Recent observations indicate that hydrogen-poor superluminous supernovae often display bumpy declining light curves. However, the cause of these undulations remains unclear. In this paper, we have improved the magnetar model, which includes flare activities. We present a systematic analysis of a well-observed SLSNe-I sample with bumpy light curves in the late-phase. These SLSNe-I were identified from multiple transient surveys, such as the Pan-STARRS1 Medium Deep Survey (PS1 MDS) and the Zwicky Transient Facility (ZTF). Our study provides a set of magnetar-powered model light curve fits for five SLSNe-I, which accurately reproduce observed light curves using reasonable physical parameters. By extracting essential characteristics of both explosions and central engines, these fits provide valuable insights into investigating their potential association with gamma ray burst engines. We found that the SLSN flares tend to be the dim and long extension of the GRB flares in the peak luminosity versus peak time plane. Conducting large-scale, high cadence surveys in the near future could enhance our comprehension of both SLSN undulation properties and their potential relationship with GRBs by modeling their light curve characteristics.

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A Population Study on the Radio Emission of Fast Blue Optical Transients

Despite the fact that the progenitor of fast blue optical transients (FBOTs) is still up for debate, FBOTs are sometimes suggested to originate from the core-collapse of ultra-stripped stars and be powered by a spinning-down neutron star. Following this consideration, it is expected that the late-time evolution of the progenitor stars can leave important imprints in the circumstellar material (CSM) of the FBOTs, due to the strong mass loss of the stars. The interaction of the FBOT ejecta with the CSM can drive a long-lasting shock to generate radio emission, which thus enables us to probe the CSM properties through radio observation although such observations are still rare. Within the framework of the magnetar-powered model, Liu et al.(2022) fitted the multi-band optical light curves of 40 FBOTs and, hence, the statistical distributions of the FBOT magnetar and ejecta parameters were obtained. Based on these FBOT population results, we investigate the dependence of the radio emission on the mass-loss rate of the progenitors and evaluate the detectability of radio emission from FBOTs with current and future telescopes. It is found that the distribution of the peak time and peak luminosity of the emission at 8.4 GHz are primarily in the regions of $t_{\rm{peak},ν}=10^{2.12\pm0.63}$ days and $L_{\rm{peak},ν}=10^{28.73\pm0.83}$ erg s$^{-1}$ Hz$^{-1}$, respectively. A joint detection of the Zwicky Transient Facility and Very Large Array could achieve success in about 8.7% FBOTs of $z\leq1$. Furthermore, if considering a joint observation of the Chinese Space Station Telescope and Square Kilometer Array, this fraction can be increased to about 23.9%.

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Magnetar Engines in Fast Blue Optical Transients and Their Connections with SLSNe, SNe Ic-BL, and lGRBs

We fit the multi-band lightcurves of 40 fast blue optical transients (FBOTs) with the magnetar engine model. The mass of the FBOT ejecta, the initial spin period and polar magnetic field of the FBOT magnetars are respectively constrained to $M_{\rm{ej}}=0.18^{+0.52}_{-0.13}\,M_\odot$, $P_{\rm{i}}=9.4^{+8.1}_{-3.9}\,{\rm{ms}}$, and $B_{\rm p}=7^{+16}_{-5}\times10^{14}\,{\rm{G}}$. The wide distribution of the value of $B_{\rm p}$ spreads the parameter ranges of the magnetars from superluminous supernovae (SLSNe) to broad-line Type Ic supernovae (SNe Ic-BL; some are observed to be associated with long-duration gamma-ray bursts), which are also suggested to be driven by magnetars. Combining FBOTs with the other transients, we find a strong universal anti-correlation as $P_{\rm{i}}\propto{M_{\rm{ej}}^{-0.45}}$, indicating them could share a common origin. To be specific, it is suspected that all of these transients originate from collapse of extreme-stripped stars in close binary systems, but with different progenitor masses. As a result, FBOTs distinct themselves by their small ejecta masses with an upper limit of ${\sim}1\,M_\odot$, which leads to an observational separation in the rise time of the lightcurves $\sim12\,{\rm d}$. In addition, the FBOTs together with SLSNe can be separated from SNe Ic-BL by an empirical line in the $M_{\rm peak}-t_{\rm rise}$ plane corresponding to an energy requirement of a mass of $^{56}$Ni of $\sim0.3M_{\rm ej}$, where $M_{\rm peak}$ is the peak absolute magnitude of the transients and $t_{\rm rise}$ is the rise time.

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iPTF14hls in the circumstellar medium interaction model: A promising candidate for a pulsational pair-instability supernova

iPTF14hls is a luminous Type II supernova (SN) with a bumpy light curve that remains debated for its origin. It maintains roughly a constant effective temperature and luminosity since discovery for about 600 days, followed by a slow decay. On $\sim 1000$\ days post discovery the light curve transitions to a very steep decline. A spectrum taken during this steep decline phase shows clear signatures of shock interaction with dense circumstellar medium (CSM). Here we explore the possibility of iPTF14hls as an interaction-powered SN. The light curve of iPTF14hls can be fitted with wind-like CSMs. Analytic modeling indicates that iPTF14hls may have undertaken six episodes of mass loss during the last $\sim 200\mathrm{yr}$. Assuming that the 1954 eruption triggered the last mass-loss episode, the stellar-wind velocity is determined to be $40-70\mathrm{km}\mathrm{s}^{-1}$, depending on different models. Mass loss rates are in the range $% 0.4-3.3M_{\odot }\mathrm{yr}^{-1}$. The inferred total mass of ejecta and CSMs ($M_{\mathrm{ej}}+M_{\mathrm{CSMs}}\simeq 245M_{\odot }$) supports the idea that iPTF14hls may be a candidate for a (pulsational) pair-instability SN. Discovery and observations of more similar stellar explosions will help understand these peculiar SNe.

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The effects of a magnetar engine on the gamma-ray burst-associated supernovae: Application to double-peaked SN 2006aj

A millisecond magnetar engine has been widely suggested to exist in gamma-ray burst (GRB) phenomena, in view of its substantial influences on the GRB afterglow emission. In this paper, we investigate the effects of the magnetar engine on the supernova (SN) emission which is associated with long GRBs and, specifically, confront the model with the observational data of SN 2006aj/GRB 060218. SN 2006aj is featured by its remarkable double-peaked ultraviolet-optical (UV-opt) light curves. By fitting these light curves, we demonstrate that the first peak can be well accounted for by the breakout emission of the shock driven by the magnetar wind, while the primary supernova emission is also partly powered by the energy injection from the magnetar. The magnetic field strength of the magnetar is constrained to be $\sim 10^{15}$ G, which is in good agreement with the common results inferred from the afterglow emission of long GRBs. In more detail, it is further suggested that the UV excess in the late emission of the supernova could also be due to the leakage of the non-thermal emission of the pulsar wind nebula (PWN), if some special conditions can be satisfied. The consistency between the model and the SN 2006aj observation indicates that the magnetar engine is likely to be ubiquitous in the GRB phenomena and even further intensify their connection with the phenomena of superluminous supernovae.

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Diagnosing Circumburst Environment with Multiband Gamma-Ray Burst Radio Afterglows

It has been widely recognized that gamma-ray burst (GRB) afterglows arise from interactions between GRB outflow and circumburst medium, while their evolution follows the behaviors of relativistic shock waves. Assuming the distribution of circumburst medium follows a general power-law form, that is, $n = A_{\ast} R^{-k}$, where $R$ denotes the distance from the burst, it is obvious that the value of density-distribution index $k$ can affect the behaviors of the afterglow. In this paper, we analyze the temporal and spectral behaviors of GRB radio afterglows with arbitrary $k$-values. In the radio band, a standard GRB afterglow produced by forward shock exhibits a late-time flux peak, and the relative peak fluxes as well as peak times at different frequencies show dependencies on $k$. Thus with multi-band radio peak observations, one can determine the density profile of circumburst medium by comparing the relations between peak flux/time and frequency at each observing band. Also, the effects of trans-relativistic shock waves, as well as jets in afterglows are discussed. By analyzing 31 long and 1 short GRBs with multi-band data of radio afterglows, we find that nearly half of them can be explained with uniform interstellar medium ($k=0$), $\sim 1/5$ can be constrained to exhibiting stellar wind environment ($k=2$), while less than $\sim 1/3$ samples show $0< k< 2$.

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A hot and luminous source at the site of the fast transient AT2018cow at 2-3 years after its explosion

We report the discovery of a luminous late-time source at the position of the fast blue optical transient (FBOT) AT2018cow on images taken by the Hubble Space Telescope (HST) at 714 d and 1136 d after its explosion. This source is detected at both UV and optical wavelengths and has prominent H$α$ emission. It has a very stable brightness between the two epochs and a very blue spectral energy distribution (SED) consistent with $f_λ$ $\propto$ $λ^{-4.1 \pm 0.1}$, i.e. the Rayleigh-Jeans tail of a hot blackbody with a very high temperature of log($T$/K) $>$ 4.6 and luminosity of log($L$/$L_\odot$) $>$ 7.0. This late-time source is unlikely to be an unrelated object in chance alignment, or due to a light echo of AT2018cow. Other possible scenarios also have some difficulties in explaining this late-time source, including companion star(s), star cluster, the survived progenitor star, interaction with circumstellar medium (CSM), magnetar, or delayed accretion in a tidal disruption event (TDE). Long-term and multi-wavelength monitoring will help to resolve its nature and finally reveal the origin of the "Cow".

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An environmental analysis of the Type Ib SN 2019yvr and the possible presence of an inflated binary companion

SN 2019yvr is the second Type Ib supernova (SN) with a possible direct detection of its progenitor (system); however, the spectral energy distribution (SED) of the pre-explosion source appears much cooler and overluminous than an expected helium-star progenitor. Using Hubble Space Telescope (HST) images and MUSE integral-field-unit (IFU) spectroscopy, we find the SN environment contains three episodes of star formation; the low ejecta mass suggests the SN progenitor is most likely from the oldest population, corresponding to an initial mass of 10.4$^{+1.5}_{-1.3}$ $M_\odot$. The pre-explosion SED can be reproduced by two components, one for the hot and compact SN progenitor and one for a cool and inflated yellow hypergiant (YHG) companion that dominates the brightness. Thus, SN 2019yvr could possibly be the first Type Ib/c SN for which the progenitor's binary companion is directly detected on pre-explosion images. Both the low progenitor mass and the YHG companion suggest significant binary interaction during their evolution. Similar to SN 2014C, SN 2019yvr exhibits a metamorphosis from Type Ib to Type IIn, showing signatures of interaction with hydrogen-rich circumstellar material (CSM) at >150 days; our result supports enhanced pre-SN mass loss as an important process for hydrogen-poor stars at the low mass end of core-collapse SN progenitors.

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Searching for gravitationally lensed gamma-ray bursts with their afterglows

Gamma-ray bursts (GRBs) at high redshifts are expected to be gravitationally lensed by objects of different mass scales. Besides a single recent claim, no lensed GRB has been detected so far by using the gamma-ray data only. In this paper, we suggest that the multi-band afterglow data might be an efficient way to search for lensed GRB events. Using the standard afterglow model we calculate the characteristics of the lensed afterglow lightcurves under the assumption of two popular analytic lens models: point mass and Singular Isothermal Sphere (SIS) model. In particular, when different lensed images cannot be resolved, their signals would be superimposed together with a given time delay. In this case, the X-ray afterglows are likely to contain several X-ray flares of similar width in linear scale and similar spectrum, and the optical afterglow lightcurve will show rebrightening signatures. Since the lightcurves from the image arriving later would be compressed and deformed in the logarithmic time scale, the larger time delay (i.e. the larger mass of the lens), the easier is to identify the lensing effect. We analyzed the archival data of optical afterglows and found one potential candidate of the lensed GRB (130831A) with time delay $\sim$500 s, however, observations of this event in gamma-ray and X-ray band seem not to support the lensing hypothesis. In the future, with the cooperation of the all-sky monitoring gamma-ray detectors and multi-band sky survey projects, our method proposed in this paper would be more efficient in searching for strongly lensed GRBs.

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No Detectable Kilonova Counterpart is Expected for O3 Neutron Star-Black Hole Candidates

We analyse the tidal disruption probability of potential neutron star--black hole (NSBH) merger gravitational wave (GW) events, including GW190426_152155, GW190814, GW200105_162426 and GW200115_042309, detected during the third observing run of the LIGO/Virgo Collaboration, and the detectability of kilonova emission in connection with these events. The posterior distributions of GW190814 and GW200105_162426 show that they must be plunging events and hence no kilonova signal is expected from these events. With the stiffest NS equation of state allowed by the constraint of GW170817 taken into account, the probability that GW190426_152155 and GW200115_042309 can make tidal disruption is $\sim24\%$ and $\sim3\%$, respectively. However, the predicted kilonova brightness is too faint to be detected for present follow-up search campaigns, which explains the lack of electromagnetic (EM) counterpart detection after triggers of these GW events. Based on the best constrained population synthesis simulation results, we find that disrupted events account for only $\lesssim20\%$ of cosmological NSBH mergers since most of the primary BHs could have low spins. The associated kilonovae for those disrupted events are still difficult to be discovered by LSST after GW triggers in the future, because of their low brightness and larger distances. For future GW-triggered multi-messenger observations, potential short-duration gamma-ray bursts and afterglows are more probable EM counterparts of NSBH GW events.

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Thermonuclear Explosions and Accretion-induced Collapses of White Dwarfs in Active Galactic Nucleus Accretion Disks

White dwarfs (WDs) embedded in gaseous disks of active galactic nucleus (AGNs) can rapidly accrete materials from the disks and grow in mass to reach or even exceed the Chandrasekhar limit. Binary WD (BWD) mergers are also believed to occur in AGN accretion disks. We study observational signatures from these events. We suggest that mass-accreting WDs and BWD mergers in AGN disks can lead to thermonuclear explosions that drive an ejecta shock breakout from the disk surface and power a slow-rising, relatively dim Type Ia supernova (SN). Such SNe Ia may be always outshone by the emission of the AGN disk around the supermassive black hole (BH) with a mass of $M_{\rm SMBH}\gtrsim 10^8\,M_\odot$. Besides, accretion-induced collapses (AICs) of WDs in AGN disks may occur sometimes, which may form highly-magnetized millisecond neutron stars (NSs). The subsequent spin-down process of this nascent magnetar can deposit its rotational energy into the disk materials, resulting in a magnetar-driven shock breakout and a luminous magnetar-powered transient. We show that such an AIC event could power a rapidly evolving and luminous transient for a magnetic field of $B\sim10^{15}\,{\rm G}$. The rising time and peak luminosity of the transient, powered by a magnetar with $B\sim10^{14}\,{\rm G}$, are predicted to have similar properties with those of superluminous supernovae. AIC events taking place in the inner parts of the disk around a relatively less massive supermassive BHs ($M_{\rm SMBH}\lesssim10^8\,M_\odot$) are more likely to power the transients that are much brighter than the AGN disk emission and hence easily to be identified.

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Kilonova Emission From Black Hole-Neutron Star Mergers. II. Luminosity Function and Implications for Target-of-opportunity Observations of Gravitational-wave Triggers and Blind Searches

We present detailed simulations of black hole-neutron star (BH-NS) mergers kilonova and gamma-ray burst (GRB) afterglow and kilonova luminosity function, and discuss the detectability of electromagnetic (EM) counterpart in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity observations, and time-domain blind searches. The predicted absolute magnitude of the BH-NS kilonovae at $0.5\,{\rm days}$ after the merger falls in $[-10,-15.5]$. The simulated luminosity function contains the potential viewing-angle distribution information of the anisotropic kilonova emission. We simulate the GW detection rates, detectable distances and signal duration, for the future networks of 2nd/2.5th/3rd-generation GW detectors. BH-NSs tend to produce brighter kilonovae and afterglows if the BH has a higher aligned-spin, and a less massive NS with a stiffer EoS. The detectability of kilonova is especially sensitive to the BH spin. If BHs typically have low spins, the BH-NS EM counterparts are hard to discover. For the 2nd generation GW detector networks, a limiting magnitude of $m_{\rm limit}\sim23-24\,{\rm mag}$ is required to detect the kilonovae even if BH high spin is assumed. Thus, a plausible explanation for the lack of BH-NS associated kilonova detection during LIGO/Virgo O3 is that either there is no EM counterpart (plunging events), or the current follow-ups are too shallow. These observations still have the chance to detect the on-axis jet afterglow associated with an sGRB or an orphan afterglow. Follow-up observations can detect possible associated sGRB afterglows, from which kilonova signatures may be studied. For time-domain observations, a high-cadence search in redder filters is recommended to detect more BH-NS associated kilonovae and afterglows.

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Magnetar-Driven Shock Breakout Revisited and Implications for Double-Peaked Type I Superluminous Supernovae

The discovery of early bumps in some type-I superluminous supernovae (SLSNe-I) before the main peaks offers an important clue to their energy source mechanisms. In this paper, we updated an analytic magnetar-powered model for fitting the multi-band light curves of double-peaked SLSNe-I: the early bump is powered by magnetar-driven shock breakout thermal emission, and the main peak is powered by a radiative diffusion through the SN ejecta as in the standard magnetar-powered model. Generally, the diffusive luminosity is greater than the shock breakout luminosity at the early time, which makes the shock breakout bumps usually not clearly seen as observed. To obtain a clear double-peaked light curve, inefficient magnetar heating at early times is required. This model is applied to three well-observed double-peaked SLSNe-I (i.e., SN2006oz, LSQ14bdq, and DES14Xtaz). We find that a relative massive SN ejecta with $M_{\mathrm{ej}} \simeq 10.2-18.1 M_{\odot}$ and relative large kinetic energy of SN ejecta $E_{\mathrm{sn}} \simeq (3.8-6.5) \times 10^{51}$ erg are required, and the thermalization efficiency of the magnetar heating is suppressed before $t_{\mathrm{delay}}$, which are in the range of $\simeq 15- 43$ days. The model can well reproduce the observed light curves, with a reasonable and similar set of physical parameters for both the early bump and the main peak, strengthening support for magnetar-powered model. In the future, modeling of the double-peaked SLSNe-I will become more feasible as more events are discovered before the early bump.

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Special supernova signature from BH-NS/BH progenitor systems

The gravitational-wave detection by the LIGO-Virgo scientific collaboration shows that the black hole and neutron star (BH-NS) or BH-BH systems with a BH mass of tens of solar masses widely exist in the universe. Two main types of scenarios have been invoked for the formation of BH-NS/BH systems, including isolated binary evolution in galactic fields and dynamical interactions in dense environments. Here we propose that if the BH-NS/BH systems are formed from isolated binary evolution, the supernova (SN) signal associated with the second core collapse would show some identifiable features, due to the accretion feedback from the companion BH. Depending on the binary properties, we show that the SN lightcurve could present a sharp peak around $\sim10$ days, with luminosity even at the level of the super luminous SNe ( e.g. $\sim10^{44}~\rm erg~s^{-1}$) or present a plateau feature lasting for several tens of days with regular luminosity of core collapse SNe. Comparing the event rate density of these special SN signals with the event rate density of LIGO-Virgo detected BH-NS/BH systems could help to distinguish the BH-NS/BH formation channel.

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