Magnetar Central Engine Research Articles

The Type I superluminous supernova catalogue I: light-curve properties, models, and catalogue description

ABSTRACT We present the most comprehensive catalogue to date of Type I superluminous supernovae (SLSNe), a class of stripped-envelope supernovae (SNe) characterized by exceptionally high luminosities. We have compiled a sample of 262 SLSNe reported through 2022 December 31. We verified the spectroscopic classification of each SLSN and collated an exhaustive data set of ultraviolet, optical, and infrared photometry totalling over 30 000 photometric detections. Using these data, we derive observational parameters such as the peak absolute magnitudes, rise and decline time-scales, as well as bolometric luminosities, temperature, and photospheric radius evolution for all SLSNe. Additionally, we model all light curves using a hybrid model that includes contributions from both a magnetar central engine and the radioactive decay of $^{56}$Ni. We explore correlations among various physical and observational parameters, and recover the previously found relation between ejecta mass and magnetar spin, as well as the overall progenitor pre-explosion mass distribution with a peak at $\approx 6.5$ M$_\odot$. We find no significant redshift dependence for any parameter, and no evidence for distinct subtypes of SLSNe. We find that only a small fraction of SLSNe, $\lt 3$ per cent, are best fit with a significant radioactive decay component $\gtrsim 50$ per cent. We provide several analytical tools designed to simulate typical SLSN light curves across a broad range of wavelengths and phases, enabling accurate K-corrections, bolometric scaling calculations, and inclusion of SLSNe in survey simulations or future comparison works.

Origin of the Twice-90° Rotations of the Polarization Angle in GRB 170114A and GRB 160821A

The observed abrupt twice-90° rotations of the polarization angle (PA) in the prompt phase of gamma-ray bursts (GRBs) are difficult to understand within the current one-emitting-shell models. Here, we apply a model with multiple emitting shells to solve this new challenging problem. Two configurations of large-scale ordered magnetic fields in the shells are considered: toroidal and aligned. Together with the light curves and the spectral peak energy evolutions, the twice-90° PA rotations in GRB 170114A and GRB 160821A could be well interpreted with the multishell aligned magnetic field configuration (MFC). Our numerical calculations also show that the multiple shells with the toroidal MFC could not explain the observed twice-90° PA rotations. An aligned MFC in the GRB outflow usually indicates the preference of a magnetar central engine, while a toroidal field configuration is typically related to a central black hole. Therefore, the magnetar central engines for the two GRBs are favored.

The enigmatic double-peaked stripped-envelope SN 2023aew

We present optical and near-infrared photometry and spectroscopy of SN 2023aew and our findings on its remarkable properties. This event, initially resembling a Type IIb supernova (SN), rebrightens dramatically sim 90 d after the first peak, at which time its spectrum transforms into that of a SN Ic. The slowly evolving spectrum specifically resembles a post-peak SN Ic with relatively low line velocities even during the second rise. The second peak, reached 119 d after the first peak, is both more luminous ($M_r = -18.75 mag) and much broader than those of typical SNe Ic. Blackbody fits to SN 2023aew indicate that the photosphere shrinks almost throughout its observed evolution, and the second peak is caused by an increasing temperature. Bumps in the light curve after the second peak suggest interaction with circumstellar matter (CSM) or possibly accretion. We consider several scenarios for producing the unprecedented behavior of SN 2023aew. Two separate SNe, either unrelated or from the same binary system, require either an incredible coincidence or extreme fine-tuning. A pre-SN eruption followed by a SN requires an extremely powerful, SN-like eruption (consistent with sim 1051 erg) and is also disfavored. We therefore consider only the first peak a true stellar explosion. The observed evolution is difficult to reproduce if the second peak is dominated by interaction with a distant CSM shell. A delayed internal heating mechanism is more likely, but emerging embedded interaction with a CSM disk should be accompanied by CSM lines in the spectrum, which are not observed, and is difficult to hide long enough. A magnetar central engine requires a delayed onset to explain the long time between the peaks. Delayed fallback accretion onto a black hole may present the most promising scenario, but we cannot definitively establish the power source.

Black Hole Activity Imprints on the Internal Plateau and the Subsequent Sharp Decay

A stellar-mass black hole (BH) or a millisecond magnetar is believed to be born as the central engine of gamma-ray bursts (GRBs). The presence of plateaus in the X-ray extended emission or afterglow of GRBs is widely accepted as an indicator of a magnetar central engine, particularly those with a sharp decay (faster than t −3), the so-called internal plateau. However, an alternative model, by taking the evolution of the magnetic flux at the BH horizon into account, suggests that an internal plateau can also arise from a jet powered by the Blandford–Znajek (BZ) mechanism (hereafter, a BZ jet). In this study, we propose that a precessional BZ jet would manifest a quasiperiodic oscillation (QPO) signature on the internal plateau and the subsequent sharp decay. Such lightcurves cannot be readily explained by the activity of a short-lived, supermassive magnetar, thus favoring a Kerr BH as the central engine. The X-ray afterglow of GRB 050904, comprising nine flares, is characterized by a QPO-modulated plateau and sharp decay, which can be well reproduced by a precessional BZ jet model. Therefore, one potential clue for distinguishing between these two engines lies in whether the QPO signature is present throughout the entire plateau and the subsequent sharp decay, as the magnetar scenario suggests a collapse at the end of the plateau.

Can Fallback Accretion on the Magnetar Model Power the X-Ray Flares Simultaneously Observed with Gamma Rays of Gamma-Ray Bursts?

The prompt emission, X-ray plateau, and X-ray flares of gamma-ray bursts (GRBs) are thought to be from internal dissipation, and the magnetar as the central engine with propeller fallback accretion is proposed to interpret the observed phenomena of GRBs. In this paper, by systematically searching for X-ray emission observed by Swift/X-ray Telescope, we find that seven robust GRBs include both X-ray flares and plateau emissions with measured redshift. More interestingly, the X-ray flares/bumps for those seven GRBs are simultaneously observed in the gamma-ray band. By adopting the propeller fallback accretion model to fit the observed data, it is found that the free parameters of two GRBs (140512A and 180329B) can be constrained very well, while in the other five cases, more or less, they are not all sufficiently constrained. On the other hand, this requires the conversion efficiency of the propeller to be two or three times higher than that of the spindown dipole radiation of the magnetar. If this is the case, it is contradictory to the expectation from the propeller model: namely, a dirtier ejecta should be less efficient in producing gamma-ray emissions. Our results hint that at least the magnetar central engine with propeller fallback accretion model cannot interpret very well both the GRB X-ray flares simultaneously observed in the gamma-ray band and the X-ray flares of GRBs with a high Lorentz factor.

The Progenitor and Central Engine of a Peculiar GRB 230307A

Recently, a lack of supernova-associated with long-duration gamma-ray burst (GRB 230307A) at such a low redshift z = 0.065, but associated with a possible kilonova emission, has attracted great attention. Its heavy element nucleosynthesis and the characteristic of soft X-ray emission suggest that the central engine of GRB 230307A is a magnetar that is originated from a binary compact star merger. The calculated lower value of ε ∼ 0.05 suggests that GRB 230307A seems to have an ambiguous progenitor. The lower value of f eff = 1.23 implies that GRB 230307A is not likely to be from the effect of “tip of iceberg.” We adopt the magnetar central engine model to fit the observed soft X-ray emission with varying efficiency and find that the parameter constraints of the magnetar falls into a reasonable range, i.e., B < 9.4 × 1015 G and P < 2.5 ms for Γsat = 103, and B < 3.6 × 1015 G and P < 1.05 ms for Γsat = 104. Whether the progenitor of GBR 230307A is from the mergers of neutron star–white dwarf (NS–WD) or neutron star–neutron star (NS–NS) remains unknown. The difference of GW radiation between NS–NS merger and NS–WD merger may be a probe to distinguish the progenitor of GRB 230307A-like events in the future.

Anisotropic energy injection from magnetar central engines in short GRBs

ABSTRACT A long-lived magnetar, potentially originating from a binary neutron star system, has been proposed to explain the extended emission observed in certain short-duration gamma-ray bursts (sGRBs), and is posited as a potential central engine to power the engine-fed kilonovae. Previously, the process by which energy is injected into the surrounding ejecta/jet was widely believed to be nearly isotropic. In this study, we employ special relativity magnetohydrodynamic (SRMHD) simulations to investigate the wind injection process from a magnetar central engine. We explore the dynamics and energy distribution within the system and found that the parameter α = uA/uMWN can be used to indicate the collimation of the magnetar wind energy injection, where uA is the local Alfven four-speed and uMWN is the four-speed of the magnetar wind nebular (MWN) formed from wind-ejecta collision. A significant portion of the injected energy from the magnetar spin-down wind will be channeled to the jet axis due to collimation within the MWN. Achieving isotropic energy injection requires a significantly small α that necessitates either an ultra-relativistic expanding MWN or an extremely low magnetization MWN, both of which are challenging to attain in sGRBs. Consequently, a considerably reduced energy budget (i.e. energy per solid angle reduced by a factor of up to 10 with respect to the value under isotropic assumption) is anticipated to be injected into the ejecta for engine-fed kilonovae. Engine-fed kilonovae would appear fainter than originally anticipated.

UV Signatures of Magnetar Formation and Their Crucial Role for GW Detection

The emission from shock breakouts (SBOs) represents the earliest electromagnetic (EM) signal emitted by cataclysmic events involving the formation or the merger of neutron stars (NSs). As such, SBOs carry unique information on the structure of their progenitors and on the explosion energy. The characteristic SBO emission is expected in the UV range, and its detection is one of the key targets of the ULTRASAT satellite. Among SBO sources, we focus on a specific class involving the formation of fast-spinning magnetars in the core-collapse of massive stars. Fast-spinning magnetars are expected to produce a specific signature in the early UV supernova light curve, powered by the extra spin energy quickly released by the NS. Moreover, they are considered as optimal candidates for the emission of long-transient gravitational wave (GW) signals, the detection of which requires early EM triggers to boost the sensitivity of dedicated GW search pipelines. We calculate early supernova UV light curves in the presence of a magnetar central engine, as a function of the explosion energy, ejecta mass, and magnetar parameters. We then estimate the ULTRASAT detection horizon (z < 0.15) as a function of the same physical parameters, and the overall expected detection rate, finding that magnetar-powered SBOs may represent up to 1/5 of the total events detected by ULTRASAT. Moreover, at the expected sensitivity of the LIGO/Virgo/Kagra O5 science run, one such event occurring within 5 Mpc will provide an ideal trigger for a GW long-transient search. Future GW detectors like the Einstein Telescope will push the horizon for joint EM-GW detections to 35–40 Mpc.

Hard X-Ray Observations of the Hydrogen-poor Superluminous Supernova SN 2018hti with NuSTAR

Some hydrogen-poor superluminous supernovae are likely powered by a magnetar central engine, making their luminosity larger than common supernovae. Although a significant amount of X-ray flux is expected from the spin-down of the magnetar, direct observational evidence is still to be found, giving rise to the “missing energy” problem. Here we present NuSTAR observations of nearby SN 2018hti 2.4 yr (rest frame) after its optical peak. We expect that, by this time, the ejecta have become optically thin for photons more energetic than ∼15 keV. No flux is detected at the position of the supernova down to F 10–30 keV = 9.0 × 10−14 erg cm−2 s−1, or an upper limit of 7.9 × 1041 erg s−1 at a distance of 271 Mpc. This constrains the fraction of bolometric luminosity from the putative spinning down magnetar to be f X ≲ 36% in the 10–30 keV range in a conservative case, f X ≲ 11% in an optimistic case.

Luminous Supernovae: Unveiling a Population between Superluminous and Normal Core-collapse Supernovae

Stripped-envelope core-collapse supernovae can be divided into two broad classes: the common Type Ib/c supernovae (SNe Ib/c), powered by the radioactive decay of 56Ni, and the rare superluminous supernovae (SLSNe), most likely powered by the spin-down of a magnetar central engine. Up to now, the intermediate regime between these two populations has remained mostly unexplored. Here, we present a comprehensive study of 40 luminous supernovae (LSNe), SNe with peak magnitudes of M r = −19 to −20 mag, bound by SLSNe on the bright end and by SNe Ib/c on the dim end. Spectroscopically, LSNe appear to form a continuum between Type Ic SNe and SLSNe. Given their intermediate nature, we model the light curves of all LSNe using a combined magnetar plus radioactive decay model and find that they are indeed intermediate, not only in terms of their peak luminosity and spectra, but also in their rise times, power sources, and physical parameters. We subclassify LSNe into distinct groups that are either as fast evolving as SNe Ib/c or as slow evolving as SLSNe, and appear to be either radioactively or magnetar powered, respectively. Our findings indicate that LSNe are powered by either an overabundant production of 56Ni or by weak magnetar engines, and may serve as the missing link between the two populations.

On the diversity of magnetar-driven kilonovae

ABSTRACT A non-negligible fraction of binary neutron star mergers are expected to form long-lived neutron star remnants, dramatically altering the multimessenger signatures of a merger. Here, we extend existing models for magnetar-driven kilonovae and explore the diversity of kilonovae and kilonova afterglows. Focusing on the role of the (uncertain) magnetic field strength, we study the resulting electromagnetic signatures as a function of the external dipolar and internal toroidal fields. These two parameters govern, respectively, the competition between magnetic-dipole spin-down and gravitational-wave spin-down (due to magnetic-field deformation) of the rapidly rotating remnant. We find that even in the parameter space where gravitational-wave emission is dominant, a kilonova with a magnetar central engine will be significantly brighter than one without an engine, as this parameter space is where more of the spin-down luminosity is thermalized. In contrast, a system with minimal gravitational-wave emission will produce a kilonova that may be difficult to distinguish from ordinary kilonovae unless early epoch observations are available. However, as the bulk of the energy in this parameter space goes into accelerating the ejecta, such a system will produce a brighter kilonova afterglow that will peak in shorter times. To effectively hide the presence of the magnetar from the kilonova and kilonova afterglow, the rotational energy inputted into the ejecta must be ≲10−3to 10−2Erot. We discuss the different diagnostics available to identify magnetar-driven kilonovae in serendipitous observations and draw parallels to other potential magnetar-driven explosions, such as superluminous supernovae and broad-line supernovae Ic.

The Zwicky Transient Facility phase I sample of hydrogen-rich superluminous supernovae without strong narrow emission lines

ABSTRACT We present a sample of 14 hydrogen-rich superluminous supernovae (SLSNe II) from the Zwicky Transient Facility (ZTF) between 2018 and 2020. We include all classified SLSNe with peaks Mg &amp;lt; −20 mag with observed broad but not narrow Balmer emission, corresponding to roughly 20 per cent of all hydrogen-rich SLSNe in ZTF phase I. We examine the light curves and spectra of SLSNe II and attempt to constrain their power source using light-curve models. The brightest events are photometrically and spectroscopically similar to the prototypical SN 2008es, while others are found spectroscopically more reminiscent of non-superluminous SNe II, especially SNe II-L. 56Ni decay as the primary power source is ruled out. Light-curve models generally cannot distinguish between circumstellar interaction (CSI) and a magnetar central engine, but an excess of ultraviolet (UV) emission signifying CSI is seen in most of the SNe with UV data, at a wide range of photometric properties. Simultaneously, the broad H α profiles of the brightest SLSNe II can be explained through electron scattering in a symmetric circumstellar medium (CSM). In other SLSNe II without narrow lines, the CSM may be confined and wholly overrun by the ejecta. CSI, possibly involving mass lost in recent eruptions, is implied to be the dominant power source in most SLSNe II, and the diversity in properties is likely the result of different mass loss histories. Based on their radiated energy, an additional power source may be required for the brightest SLSNe II, however – possibly a central engine combined with CSI.

Tale of GRB 171010A/SN 2017htp and GRB 171205A/SN 2017iuk: Magnetar origin?

We present late-time optical follow-up observations of GRB 171010A/SN 2017htp (z = 0.33) and low-luminosity GRB 171205A/SN 2017iuk (z = 0.037) acquired using the 4K×4K CCD Imager mounted at the 3.6 m Devasthal Optical Telescope (3.6 m DOT) along with the prompt emission data analysis of these two interesting bursts. The prompt characteristics (other than brightness) such as spectral hardness, T90, and minimum variability time-scale are comparable for both the bursts. The isotropic X-ray and kinetic energies of the plateau phase of GRB 171205A are found to be less than the maximum energy budget of magnetars, supporting magnetar as a central engine powering source. The new optical data of SN 2017htp and SN 2017iuk presented here, along with published ones, indicate that SN 2017htp is one of the brightest and SN 21017iuk is among the faintest GRB associated SNe (GRB–SNe). Semi-analytical light-curve modelling of SN 2017htp, SN 2017iuk and only known GRB associated superluminous supernova (SLSN 2011kl) are performed using the MINIM code. The model with a spin-down millisecond magnetar as a central engine powering source nicely reproduced the bolometric light curves of all three GRB–SNe mentioned above. The magnetar central engines for SN 2017htp, SN 2017iuk, and SLSN 2011kl exhibit values of initial spin periods higher and magnetic fields closer to those observed for long GRBs and H-deficient SLSNe. Detection of these rare events at such late epochs also demonstrates the capabilities of the 3.6 m DOT for deep imaging considering longitudinal advantage in the era of time-domain astronomy.

Bumpy Declining Light Curves Are Common in Hydrogen-poor Superluminous Supernovae

Recent work has revealed that the light curves of hydrogen-poor (Type I) superluminous supernovae (SLSNe), thought to be powered by magnetar central engines, do not always follow the smooth decline predicted by a simple magnetar spin-down model. Here we present the first systematic study of the prevalence and properties of “bumps” in the post-peak light curves of 34 SLSNe. We find that the majority (44%–76%) of events cannot be explained by a smooth magnetar model alone. We do not find any difference in supernova properties between events with and without bumps. By fitting a simple Gaussian model to the light-curve residuals, we characterize each bump with an amplitude, temperature, phase, and duration. We find that most bumps correspond with an increase in the photospheric temperature of the ejecta, although we do not see drastic changes in spectroscopic features during the bump. We also find a moderate correlation (ρ ≈ 0.5; p ≈ 0.01) between the phase of the bumps and the rise time, implying that such bumps tend to happen at a certain “evolutionary phase,” (3.7 ± 1.4)t rise. Most bumps are consistent with having diffused from a central source of variable luminosity, although sources further out in the ejecta are not excluded. With this evidence, we explore whether the cause of these bumps is intrinsic to the supernova (e.g., a variable central engine) or extrinsic (e.g., circumstellar interaction). Both cases are plausible, requiring low-level variability in the magnetar input luminosity, small decreases in the ejecta opacity, or a thin circumstellar shell or disk.

Optical Observations and Modeling of the Superluminous Supernova 2018lfe

We present optical imaging and spectroscopy of SN 2018lfe, which we classify as a Type I superluminous supernova (SLSN-I) at a redshift of z = 0.3501 ± 0.0004 with a peak absolute magnitude of M r = −22.1 ± 0.1 mag, one of the brightest SLSNe discovered. SN 2018lfe was identified for follow-up using our FLEET machine-learning pipeline. Both the light curve and the spectra of SN 2018lfe are consistent with the broad population of SLSNe. We fit the light curve with a magnetar central engine model and find an ejecta mass of M ej ≈ 3.8 M ⊙, a magnetar spin period of P ≈ 2.9 ms, and a magnetic field strength of B ⊥ ≈ 2.8 × 1014 G. The magnetic field strength is near the top of the distribution for SLSNe, while the spin period and ejecta mass are near the median values of the distribution for SLSNe. From late-time imaging and spectroscopy we find that the host galaxy of SN 2018lfe has an absolute magnitude of M r = −17.85 ± 0.24, (L B = 0.029 ± 0.007L*), and an inferred metallicity of Z ≈ 0.3 Z ⊙ and star formation rate of ≈0.8 M ⊙ yr−1.

X-ray flares raising upon magnetar plateau as an implication of a surrounding disk of newborn magnetized neutron star

The X-ray flares have usually been ascribed to long-lasting activities of the central engine of gamma-ray bursts (GRBs), e.g., fallback accretion. The GRB X-ray plateaus, however, favor a millisecond magnetar central engine. The fallback accretion can be significantly suppressed due to the propeller effect of a magnetar. Therefore, if the propeller regime cannot resist the mass flow onto the surface of the magnetar efficiently, the X-ray flares raising upon the magnetar plateau would be expected. In this work, such peculiar cases are connected to the accretion process of the magnetars, and an implication for magnetar-disc structure is given. We investigate the repeated accretion process with multi-flare GRB 050730, and give a discussion for the accretion-induced variation of the magnetic field in GRB 111209A. Two or more flares exhibit in the GRB 050730, 060607A and 140304A; by adopting magnetar mass M = 1.4 M ⊙ and radius R = 12 km, the average mass flow rates of the corresponding surrounding disk are 3.53 × 10−4 M ⊙ s−1, 4.23 × 10−4 M ⊙ s−1, and 4.33 × 10−4 M ⊙ s−1, and the corresponding average sizes of the magnetosphere are 5.01 × 106 cm, 6.45 × 106 cm, and 1.09 × 107 cm, respectively. A statistic analysis that contains eight GRBs within 12 flares shows that the total mass loading in single flare is ∼ 2 × 10−5 M ⊙. In the lost mass of a disk, there are about 0.1% used to feed a collimated jet.

Late-time Hubble Space Telescope Observations of a Hydrogen-poor Superluminous Supernova Reveal the Power-law Decline of a Magnetar Central Engine

Abstract The light-curve diversity of hydrogen-poor superluminous supernovae (SLSNe) has kept open the possibility that multiple power sources account for the population. Specifically, pair-instability explosions (PISNe), which produce large masses of 56Ni, have been argued as the origin of some slowly-evolving SLSNe. Here we present detailed observations of SN 2016inl (=PS16fgt), a slowly-evolving SLSN at z = 0.3057, whose unusually red spectrum matches PS1-14bj, an SLSN with an exceptionally long rise time consistent with a PISN. Ground-based and Hubble Space Telescope data, spanning about 800 rest-frame days, reveal a significant light-curve flattening, similar to that seen in SN 2015bn and much slower than the decline rate expected from radioactive decay of 56Co. We therefore conclude that despite its slow evolution, SN 2016inl is inconsistent with a PISN. Instead, the light-curve evolution matches the expected power-law spindown of a magnetar central engine, but with a shallower power law (L ∝ t −2.8) compared to that in SN 2015bn, indicating a possible difference in the γ-ray opacity between the two events. Analytical modeling indicates typical magnetar engine parameters, but one of the highest ejecta masses (≈20 M ⊙) inferred for an SLSN. Our results indicate that monitoring the late-time light-curve evolution of SLSNe provides a powerful diagnostic of their energy source.

ASASSN-18am/SN 2018gk: an overluminous Type IIb supernova from a massive progenitor

ABSTRACT ASASSN-18am/SN 2018gk is a newly discovered member of the rare group of luminous, hydrogen-rich supernovae (SNe) with a peak absolute magnitude of MV ≈ −20 mag that is in between normal core-collapse SNe and superluminous SNe. These SNe show no prominent spectroscopic signatures of ejecta interacting with circumstellar material (CSM), and their powering mechanism is debated. ASASSN-18am declines extremely rapidly for a Type II SN, with a photospheric-phase decline rate of ∼6.0 mag (100 d)−1. Owing to the weakening of H i and the appearance of He i in its later phases, ASASSN-18am is spectroscopically a Type IIb SN with a partially stripped envelope. However, its photometric and spectroscopic evolution shows significant differences from typical SNe IIb. Using a radiative diffusion model, we find that the light curve requires a high synthesized 56Ni mass $M_{\rm Ni} \sim 0.4\, \rm {M_{\odot }}$ and ejecta with high kinetic energy Ekin = (7–10) × 1051 erg. Introducing a magnetar central engine still requires $M_{\rm Ni} \sim 0.3\, \rm {M_{\odot }}$ and Ekin = 3 × 1051 erg. The high 56Ni mass is consistent with strong iron-group nebular lines in its spectra, which are also similar to several SNe Ic-BL with high 56Ni yields. The earliest spectrum shows ‘flash ionization’ features, from which we estimate a mass-loss rate of $\dot{M}\approx 2\times 10^{-4} \, \rm \rm {M_{\odot }}\,yr^{-1}$. This wind density is too low to power the luminous light curve by ejecta–CSM interaction. We measure expansion velocities as high as 17 000 $\rm {\, km\, s^{-1}}$ for Hα, which is remarkably high compared to other SNe II. We estimate an oxygen core mass of 1.8–3.4 M⊙ using the [O i] luminosity measured from a nebular-phase spectrum, implying a progenitor with a zero-age main-sequence mass of 19–26 M⊙.

The electromagnetic and gravitational-wave radiations of X-ray transient CDF-S XT2

Binary neutron star (NS) mergers may result in remnants of supra-massive or even stable NS, which have been supported indirectly by observed X-ray plateau of some gamma-ray burst (GRB) afterglows. Recently, Xue et al. () discovered an X-ray transient CDF-S XT2 that is powered by a magnetar from merger of double NS via X-ray plateau and following stepper phase. However, the decay slope after the plateau emission is slightly larger than the theoretical value of spin-down in electromagnetic (EM) dominated by losing its rotation energy. In this paper, we assume that the feature of X-ray emission is caused by a supra-massive magnetar central engine for surviving thousands of seconds to collapse into a black hole. Within this scenario, we present the comparisons of the X-ray plateau luminosity, break time, and the parameters of magnetar between CDF-S XT2 and other short GRBs with internal plateau samples. By adopting the collapse time to constrain the equation of state (EOS), we find that three EOSs (GM1, DD2, and DDME2) are consistent with the observational data. On the other hand, if the most released rotation energy of magnetar is dominated by GW radiation, we also constrain the upper limit of ellipticity of NS for given EOS, and its range is [0.32-1.3] × 10−3. Its GW signal cannot be detected by Advanced LIGO or even for more sensitive Einstein Telescope in the future.

Interpreting the X-ray afterglows of gamma-ray bursts with radiative losses and millisecond magnetars

ABSTRACT The spin-down energy of millisecond magnetars has been invoked to explain X-ray afterglow observations of a significant fraction of short and long gamma-ray bursts. Here, we extend models previously introduced in the literature, incorporating radiative losses with the spin-down of a magnetar central engine through an arbitrary braking index. Combining this with a model for the tail of the prompt emission, we show that our model can better explain the data than millisecond-magnetar models without radiative losses or those that invoke spin-down solely through vacuum dipole radiation. We find that our model predicts a subset of X-ray flares seen in some gamma-ray bursts. We can further explain the diversity of X-ray plateaus by altering the radiative efficiency and measure the braking index of newly born millisecond magnetars. We measure the braking index of GRB061121 as $n=4.85^{+0.11}_{-0.15}$ suggesting the millisecond-magnetar born in this gamma-ray burst spins down predominantly through gravitational-wave emission.