GRB 210610B:The Internal and External Plateau as Evidence for the Delayed Outflow of Magnetar

After launching a jet,outflows of magnetar were used to account for the achromatic plateau of afterglow and the early X-ray flux plateau known as“internal plateau”.The lack of detecting magnetic dipole emission together with the energy injection feature in a single observation poses confusion until the long gamma-ray burst(GRB)210610B is detected.GRB 210610B is presented with an optical bump following an early X-ray plateau during the afterglow phase.The plateau followed by a steep decline flux overlays in the steadily decaying X-ray flux with indexα_(X,1)~2.06,indicating an internal origin and that can be fitted by the spin-down luminosity law with the initial plateau luminosity log_(10)L_(X)~48.29 erg s~(-1)and the characteristic spin-down timescale T~2818 s.A subsequent bump begins at~4000 s in the R band with a rising indexα_(R,1)~-0.30 and peaks at~14125 s,after which a decay indexα_(R,2)~0.87 and finally transiting to a steep decay withα_(R,3)~1.77 achieve the closure relation of the external shock for the normal decay phase as well as the magnetar spin-down energy injection phase,provided that the average value of the photon indexΓ_γ=1.80 derived from the spectral energy distributions(SEDs)between the X-ray and optical afterglow.The closure relation also works for the late X-ray flux.Akin to the traditional picture of GRB,the outflow powers the early X-ray plateau by dissipating energy internally and collides with the leading decelerating blast burst as time goes on,which could interpret the exotic feature of GRB 210610B.We carry out a Markov Chain Monte Carlo simulation and obtain a set of best parameters:■.The artificial light curve can fit the afterglow data well.After that,we estimated the average Lorentz factor and the X-ray radiation efficiency of the later ejecta are 35%and 0.13%,respectively.

GRB 200612A:An Ultralong Gamma-Ray Burst Powered by Magnetar Spinning Down

GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to~1020 s and the true timescale of the central engine activity t_(burst)≥4×10^(4) s.The late X-ray light curve with a decay index ofα=7.53 is steeper than the steepest possible decay from an external shock model.We propose that this X-ray afterglow can be driven by dipolar radiation from the magnetar spindown during its early stage,while the magnetar collapsed into the black hole before its spindown,resulting in a very steep decay of the late X-ray light curve.The optical data show that the light curve is still rising after 1.1 ks,suggesting a late onset.We show that GRB 200612A’s optical afterglow light curve is fitted with the forward shock model by Gaussian structured off-axis jet.This is a special case among GRBs,as it may be an ultralong gamma-ray burst powered by a magnetar in an off-axis observation scenario.

GRB 210323A:Signature of Long-lasting Lifetime of Supra-massive Magnetar as the Central Engine from the Merger of Binary Neutron Star

Theoretically,a supra-massive neutron star or magnetar may be formed after the merger of binary neutron stars.GRB210323A is a short-duration gamma-ray burst(GRB)with a duration of lasting~1 s.The light curve of the prompt emission of GRB 210323A shows a signal-peaked structure and a cutoff power-law model can adequately fit the spectra with E_p=1826±747.More interestingly,it has an extremely long-lasting plateau emission in the X-ray afterglow with a duration of~10^(4)s,and then follows a rapid decay with a decay slope~3.2.This temporal feature is challenging by invoking the external shock mode.In this paper,we suggest that the observed long-lasting X-ray plateau emission is caused by the energy injection of dipole radiation from supra-massive magnetar,and the abrupt decay following the longlasting X-ray plateau emission is explained by supra-massive magnetar collapsing into a black hole.It is the short GRB(SGRB)with the longest X-ray internal plateau emission powered by a supra-massive neutron star.If this is the case,one can estimate the physical parameters of a supra-massive magnetar,and compare with other SGRBs.We also discuss the possible gravitational-wave emission,which is powered by a supra-massive magnetar and its detectability,and the possible kilonova emission,which is powered by r-process and magnetar spin-down to compare with the observed data.

GRB 220408B:A Three-episode Burst from a Precessing Jet

Jet precession has previously been proposed to explain the apparently repeating features in the light curves of a few gamma-ray bursts(GRBs).In this paper,we further apply the precession model to a bright GRB 220408B by examining both its temporal and spectral consistency with the predictions of the model.As one of the recently confirmed GRBs observed by our GRID CubeSat mission,GRB 220408B is noteworthy as it exhibits three apparently similar emission episodes.Furthermore,the similarities are reinforced by their strong temporal correlations and similar features in terms of spectral evolution and spectral lags.Our analysis demonstrates that these features can be well explained by the modulated emission of a Fast-Rise-Exponential-Decay(FRED)shape light curve intrinsically produced by a precessing jet with a precession period of 18.4_(-0.2)~(+0.2)s,a nutation period of11.1_(-0.2)~(+0.2)s and viewed off-axis.This study provides a straightforward explanation for the complex yet similar multiepisode GRB light curves.

GRB 130310A: very high peak energy and thermal emission

The special GRB 130310 A was observed by Fermi Gamma-Ray Burst Monitor and Large Area Telescope,with T90~2.4 s.With a combination of a Band function and a blackbody(BB)function,the time-resolved spectral analysis of GRB 130310 A confirmed that there is a sub-dominate thermal component in the early period(e.g.,slice T0+[4.03-4.14]s)spectrum with BB temperature(kT)being~7~5 keV,which can be interpreted as photosphere emission.The precursor of GRB 130310 A can be fitted well with a BB component with kT~45 keV,which is higher than that of the main burst.It suggests that the radiation of GRB 130310 A is in transition from thermal to non-thermal.Such a transition is an indication of the change in jet composition from a fireball to a Poynting-flux-dominated jet.A very high peak energy is obtained in the first time bin,with the peak energy E_(p) of the Band component for Band+BB and Band model being~8.5~5.2 MeV and~11.1~7.4 MeV,respectively.Afterwards,the E_(p) drops to~1 MeV.The E_(p) evolution patterns with respect to the pulses in the GRB 130310 A light curves show a hard-to-soft evolution.The interpretation of the high peak energy E_(p) within the photosphere and internal shock model is difficult.It also suggests that at least for some bursts,the Band component must invoke a non-thermal origin in the optically thin region of a GRB outflow.Assuming the redshift is z~0.1~8,the radius of the jet base r_(0)~10^(9) cm to allow(1+σ_(15))>1 in line with the calculation results of the magnetization parameter at~1015 cm(σ_(15)).However,the value of(1+σ_(15))is■1 in the zone z around 3 for r_(0)~10^(9) cm,suggesting the non-excluded possibility that the origin is from ICMART with a low value.The photosphere-internal shock seems capable of interpreting the high peak energy,which requires electron Lorentz factorγe~60 andεe~0.06.

Probing the Progenitor of High-z Short-duration GRB 201221D and its Possible Bulk Acceleration in Prompt Emission

The growing observed evidence shows that the long-and short-duration gamma-ray bursts(GRBs) originate from massive star core-collapse and the merger of compact stars,respectively.GRB 201221 D is a short-duration GRB lasting~0.1 s without extended emission at high redshift z=1.046.By analyzing data observed with the Swift/BAT and Fermi/GBM,we find that a cutoff power-law model can adequately fit the spectrum with a soft E=113keV,and isotropic energy E=1.36× 10erg.In order to reveal the possible physical origin of GRB 201221 D,we adopted multi-wavelength criteria(e.g.,Amati relation,ε-parameter,amplitude parameter,local event rate density,luminosity function,and properties of the host galaxy),and find that most of the observations of GRB 201221 D favor a compact star merger origin.Moreover,we find that α is larger than 2+βin the prompt emission phase which suggests that the emission region is possibly undergoing acceleration during the prompt emission phase with a Poynting-flux-dominated jet.

A two-step energy injection explanation for the rebrightenings of the multi-band afterglow of GRB 081029

The afterglow of GRB 081029 showed unusual behavior, with a signifi- cant rebrightening being observed at the optical wavelength at about 3000 s after the burst. One possible explanation is that the rebrightening resulted from an energy in- jection. Here we present a detailed numerical study of the energy injection process and interpret the X-ray and optical afterglow light curves of GRB 081029. In our model, we have assumed two periods of energy injection, each with a constant injec- tion power. One injection starts at 2.8 × 10^3 s and lasts for about 2500 s, with a power of 7.0 × 10^47 erg s-1. This energy injection mainly accounts for the rapid rebrighten- ing at about 3000 s. The other injection starts at 8.0 × 10^3 s and lasts for about 5000 s. The injection power is 3.5 × 10^47 erg s-1. This energy injection can help to explain the slight rebrightening at about 10 000 s. It is shown that the observed optical after- glow, especially the marked rebrightening at about 3000 s, can be reproduced well. In the X-ray band, the predicted amplitude of the rebrightening is much shallower, which is also consistent with the observed X-ray afterglow light curve. It is argued that the two periods of energy injection can be produced by clumpy materials falling onto the central compact object of the burster, which leads to an enhancement of accretion and gives rise to a strong temporary outflow.

GRB 190530A:From Precursor,Prompt Emission to Afterglow all Originated from Synchrotron Radiation

GRB 190530A was jointly observed by the High Energy X-ray Telescope of the Hard X-ray Modulation Telescope(Insight-HXMT/HE)and the Ground-Based Wide-Angle Camera network(GWAC-N)with the extremely large field of view.After triggered by Insight-HXMT/HE and Fermi/GBM,we observed the optical emission of GRB 190530A,using the 30 cm telescope of GWAC(GWAC-F30)to search and locate its position.Subsequent observation of the late afterglow of GRB 190530A was made with the 2.16 m telescope at Xinglong Observatory.In this paper,we make a detailed exploration of the origin of GRB 190530A.In the prompt emission,a“double-tracking”pattern is presented both for the low-energy spectral indexαand the peak energy Epin the Band function with Insight-HXMT/HE and Fermi/GBM data;the results of GRB 190530A are consistent with the Amati and Yonetoku correlations;the spectral lag(τ)versus energy(E)can be estimated withτ=-3.0±0.06+(0.17±0.03)logE.The synchrotron radiation can account for the origin of GRB190530A prompt emission behaviors.Theαand Epof the precursor are essentially the same as that of the main prompt emission,implying that they have the same origin.For the afterglow,it can be described with the external forward shock model in ISM circumburst medium.In summary,from precursor,prompt emission to afterglow of GRB 190530A all originated from synchrotron radiation.

A magnetically driven origin for the low luminosity GRB 170817A associated with GW170817

The gamma-ray burst GR170817 A associated with GW170817 is subluminous and subenergetic compared with other typical short gamma-ray bursts. It may be due to a relativistic jet viewed off-axis, or a structured jet or cocoon emission. Giant flares from magnetars may possibly be ruled out.However, the luminosity and energetics of GRB 170817 A are coincident with those of magnetar giant flares. After the coalescence of a binary neutron star, a hypermassive neutron star may be formed. The hypermassive neutron star may have a magnetar-strength magnetic field. During the collapse of this hypermassive neutron star, magnetic field energy will also be released. This giant-flare-like event may explain the luminosity and energetics of GRB 170817 A. Bursts with similar luminosity and energetics are expected in future neutron star-neutron star or neutron star-black hole mergers.

Physical origin of multi-wavelength emission of GRB 100418A and implications for its progenitor

Swift GRB 100418A is a long burst at z = 0.624 without detection of any associated supernova （SN）. Its light curves in both the prompt and afterglow phases are similar to GRB 060614, a nearby long GRB without an associated SN. We analyze the observational data of this event and discuss the possible origins of its multiwavelength emission. We show that its joint light curve at 1 keV derived from Swift BAT and XRT observations is composed of two distinguished components. The first component, whose spectrum is extremely soft （Γ = 4.32）, ends with a steep decay segment, indicating the internal origin of this component. The second component is a slowly-rising, broad bump which peaks at ～ 10 5 s post the BAT trigger. Assuming that the late bump is due to onset of the afterglow, we derive the initial Lorentz factor （Γ 0 ） of the GRB fireball and find that it significantly deviates from the relation between the Γ 0 and isotropic gamma-ray energy derived from typical GRBs. We also check whether it follows the same anti-correlation between X-ray luminosity and the break time observed in the shallow decay phase of many typical GRBs, which is usually regarded as a signal of late energy injection from the GRB central engine. However, we find that it does not obey this correlation. We propose that the late bump could be contributed by a two-component jet. We fit the second component with an off-axis jet model for a constant medium density and find the late bump can be represented by the model. The derived jet half-opening angle is 0.30 rad and the viewing angle is 0.315 rad. The medium density is 0.05 cm 3 , possibly suggesting that it may be from a merger of compact stars. The similarity between GRBs 060614 and 100418A may indicate that the two GRBs are from the same population and the late bump observed in the two GRBs may be a signal of a two-component jet powered by the GRB central engine.

Shallow Decay of X-ray Afterglows in Short GRBs:Energy Injection from a Millisecond Magnetar?

With the successful launch of Swift satellite, more and more data of early X-ray afterglows from short gamma-ray bursts have been collected. Some interesting features such as unusual afterglow light curves and unexpected X-ray flares are revealed. Especially, in some cases, there is a flat segment in the X-ray afterglow light curve. Here we present a simplified model in which we believe that the flattening part is due to energy injection from the central engine. We assume that this energy injection arises from the magnetic dipole radiation of a millisecond pulsar formed after the merger of two neutron stars. We check this model with the short GRB 060313. Our numerical results suggest that energy injection from a millisecond magnetar could make part of the X-ray afterglow light curve flat.

GRB 170817A: a short GRB seen off-axis

The angular distribution of gamma-ray burst（GRB）jets is not yet clear.The observed luminosity of GRB 170817A is the lowest among all known short GRBs,which is best explained by the fact that our line of sight is outside of the jet opening angle,θ_（obs）〉θ_j,whereθ_（obs） is the angle between our line of sight and the jet axis.As inferred by gravitational wave observations,as well as radio and X-ray afterglow modeling of GRB 170817A,it is likely that θ_（obs）~20°–28°.In this work,we quantitatively consider two scenarios of angular energy distribution of GRB ejecta：a top-hat jet and a structured jet with a power law index s.For the top-hat jet model,we get a large θ_j（e.g.,θ_j〉10°）,a rather high local （i.e., z 〈 0.01） short GRB rate ~8–15×10~3 Gpc^（-3）yr~（-1（（estimated to be 90~1850 Gpc^（-3）yr^（-1） in Fong et al.）and an extremely high（on-axis,V（~500 ke V for a typical short GRB）.For the structured jet model,we use θ_（obs） to give limits on s and θ_j for typical on-axis luminosity of a short GRB（e.g.,10^（49）erg s（-1） 1051erg s（-1））,and a low on-axis luminosity case（e.g.,1049erg s（-1））gives more reasonable values of s.The structured jet model is more feasible for GRB170817A than the top-hat jet model due to the rather high local short GRB rate,and the extremely high on-axis E_（peak,0） almost rules out the top-hat jet model.GRB 170817A is likely a low on-axis luminosity GRB（1049erg s（-1））with a structured jet.

X-ray afterglow of GRB 050712: multiple energy injections into the external shock

As indicated by observed X-ray flares, a great amount of energy can be in- termittently released from the postburst central engine of gamma-ray bursts （GRBs）. As a natural consequence, the GRB＇s external shock could be repeatedly energized. With such a multiple energy injection model, we explore the unique X-ray afterglow light curve of GRB 050712, which exhibits four shallow decay plateaus. Together with three early X-ray flares, the celatral engine of GRB 050712 is believed to have released energy at least seven times after the burst. Furthermore, we find that the ener- gies released during the four plateaus are all on the same order of magnitude, but the luminosity significantly decreased with time. These results may provide some inter- esting implications for the GRB central engine.

Optical light curve of GRB 121011A:a textbook for the onset of GRB afterglow in a mixture of ISM and wind-type medium

We report the optical observations of GRB 121011 A by the 0.8m TNT facility at Xinglong observatory, China. The light curve of the optical afterglow shows a smooth and featureless bump during the epoch of;30 s and;000 s with a rising index of 1.57 ± 0.28 before the break time of 539 ± 44 s, and a decaying index of about 1.29 ± 0.07 up to the end of our observations. Moreover, the X-ray light curve decays in a single power-law with a slope of about 1.51 ± 0.03 observed by XRT onboard Swift from 100 s to about 10 000 s after the burst trigger. The featureless optical light curve could be understood as an onset process under the external-shock model. The typical frequency has been below or near the optical one before the deceleration time, and the cooling frequency is located between the optical and X-ray wavelengths. The external medium density has a transition from a mixed stage of ISM and wind-type medium before the peak time to the ISM at the later phase. The joint-analysis of X-ray and optical light curves shows that the emissions from both frequencies are consistent with the prediction of the standard afterglow model without any energy injections, indicating that the central engine has stopped its activity and does not restart anymore after the prompt phase.

X-Ray Afterglows of GRBs 050318 and 060124 and their External Shock Origin

The observations with Swift X-ray telescope （XRT） challenge the conventional gamma-ray burst model in many aspects. The XRT light curves are generally composed of four consecutive segments, i.e., a steep decay segment, a shallow decay segment, a normal decay segment, a jet-like steep decay segment, and sometimes erratic flares as well. The physical origin of the X-ray emission is highly debatable. We focus here on the physical origin of the X-ray emissions of GRBs 050318 and 060124. We present the XRT light curves and spectra of the two bursts. The light curve decay slopes of the two bursts are normal, and their relations to the spectral indices are consistent with the prediction of the standard forward shock model. The multi-wavelength light curves at 0.5 keV, 1.0 keV, 2.0 keV and 4.0 keV can be reproduced by this model with an isotropic kinetic energy Ek = 2.2 × 10^52 erg, εe = 0.04, εB = 0.01 for GRB 050318 and Ek = 4.2 × 10^53 erg, εe = 0.05, εB = 0.01 for GRB 060124. These facts suggest that the normal decay phases of the X-rays for the two bursts are of the forward shock origin.

Energy Conservation in the Thin Layer Approximation: IV. The Light Curve for Supernovae

The light curves (LC) for Supernova (SN) can be modeled adopting the conversion of the flux of kinetic energy into radiation. This conversion requires an analytical or a numerical law of motion for the expanding radius of the SN. In the framework of conservation of energy for the thin layer approximation, we present a classical trajectory based on a power law profile for the density, a relativistic trajectory based on the Navarro-Frenk-White profile for the density, and a relativistic trajectory based on a power law behaviour for the swept mass. A detailed simulation of the LC requires the evaluation of the optical depth as a function of time. We modeled the LC of SN 1993J in different astronomical bands, the LC of GRB 050814 and the LC GRB 060729 in the keV region. The time dependence of the magnetic field of equipartition is derived from the theoretical formula for the luminosity.

Relativistic Motion with Viscosity: II Stokes’s Law of Resistance

The deduction of a relativistic and mildly relativistic equation of motion in the presence of a drag force proportional to the velocity is presented. The obtained results are used to model the trajectory of the supernova SN1993J and the light curves of gamma-ray bursts.

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 111209 A.Two or more flares exhibit in the GRB 050730,060607 A and 140304 A;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 5.01×10^(6)cm,6.45 x 10^(-6)cm,and 1.09×10^(-7)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.

Relativistic Motion with Viscosity. I Newton’s Law of Resistance

The equation of motion for a relativistic neutral particle that moves in a medium characterized by a friction proportional to the square of the velocity is analyzed. The relativistic trajectory is derived in a numerical way and in the form of a Taylor series. The astrophysical applications cover the trajectory of SN 1993J and the light curve of gamma ray bursts.