arXiv:2108.01349v1 [astro-ph.HE] 3 Aug 2021 osaln-ie enn eto treitatrsotgam short after exist star neutron remnant long-lived a Does 00 rnt&Sr 02.Acmayn ihtejtlaunch- Li of jet & mass the Chevalier non-relativistic with 1998; a Accompanying ing, 2002). al. et Sari Sari & Granot t 1997; 2000; (ES) Rees Meszar & & shock devi- Mészáros (Rees external afterglows 1992; not 2011; the an long-lasting with drive al. does broad-band et jet can produce (Rezzolla the axis medium of much jet interstellar interaction too The bient the 2015). 2007). direction al. if Earth Nakar et Paschalidis observed the 1992; be from al. et ate can Narayan (Paczyn SGRB 1989; jet The j the al. et in relativistic Eichler dissipations collimated 1986; internal bu of the gamma-ray short-duration through pair a (SGRB) generate a to launched merger, be could a After tectors. egr fdul eto tr DS)adbakhole- gravitation of black sources and important aLIGO (DNSs) for are stars (GW) binaries wave neutron star double neutron of Mergers Introduction 1. iedcy fthe radioac- of the Then, decays 1982). t Schramm be tive & Schr through can Symbalisty & universe 1976; Lattimer ejecta, 1974, (r-process; the merger nearl process in neutron-rich neutron-capture iron that rapid these than suggested heavier in is elements synthesized It the of feedback. e half accretion the and to squeeze, due widely more h jcat eeaeabih hra msin hc was which emission, thermal Paczy & bright Li by a predicted generate first to ejecta the ue l 03 rsmne l 04 eze io2014; Piro & Metzger typical 2013; 2014; the Hotokezaka al. of & et Tanaka Grossman that 2017; 2013; 2013; of Kasen 2015, al. & times et Barnes Yu 2013, 2011; thousand al. al. et few e et Kasen (Roberts is a luminosity phenomena no be peak nova is its to emission since “kilonova", thermal pected as transient termed This usually (2010). al. et Metzger uut4 2021 4, August Astronomy ugse oepanteA 07f iooaeiso nthe in emission kilonova 2017gfo AT the explain to suggested a nedb elcnitn ihteosrainldt.T data. observational the with consistent well be indeed can by contributed be can component emission non-thermal form a the that to lead could (DNSs) stars neutron double of Mergers ee ymdln h fego ih uvsadsetao G of spectra a and to curves light believed afterglow widely the modeling is GR by kilonova to Here, Similar candidate NS. A remnant Th (SGRBs). the ejecta. of bursts merger existence preceding the the for with evidence an NS remnant the from wind aei h N egreet n,tu,teeuto fstate of equation the thus, and, events merger DNS the in rare e words. Key 3 1 2 eateto srnm,Sho fPyis eigUnivers Peking Physics, of School Astronomy, of Department nttt fAtohsc,CnrlCiaNra Universit Normal e-mail: China Central Astrophysics, of Institute e aoaoyo ur n etnPyis(eta hn No China (Central Physics Lepton and Quark of Laboratory Key & Astrophysics [email protected] rvttoa ae am-a us:idvda GB160 (GRB individual burst: gamma-ray – waves Gravitational r poeseeet a e can elements -process / ig n te rudbsdG de- GW ground-based other and Virgo ff aucitn.ms210731 no. manuscript cso ia irpin collision disruption, tidal of ects si(98 n usqetyby subsequently and (1998) nski ´ ∼ 10 − un-e Wu Guang-Lei 4 − 10 − 2 us R 160821B? GRB burst M ⊙ ff a eejected be can cieyheat ectively 1 , 2 u-e Yu Yun-Wei , amm ABSTRACT ,Whn407,China 430079, Wuhan y, i a niaeta h omto fasal asv Scou NS massive stable a of formation the that indicate may his am- B102B efidta h noigo o-hra W emis PWN non-thermal a of invoking the that find we 160821B, RB ski ets rst fteps-egrNssol esti be should NSs post-merger the of he os x- usrwn eua(W) hc eut rmteinteracti the from results which (PWN), nebula wind pulsar a aosG101 vn.Fra NS-a an For event. GW170817 famous 787,GB102Bi looeo h ers hr gamma- short nearest the of one also is 160821B GRB 170817A, B w al pa nteutailtotclifae fegoso G of afterglows ultraviolet-optical-infrared the in ppear to faln-ie asv enn S hc a enprev been has which NS, remnant massive long-lived a of ation o y t,Biig107,China 100871, Beijing ity, n h icvr fsc o-hra W msincnprov can emission PWN non-thermal a such of discovery the en, mlUiest) iityo dcto,Whn407,Chi 430079, Wuhan Education, of Ministry University), rmal S hc tlatlse o e udeso milliseconds, of associat be hundreds only few can a hole hypermassive black for a immediately-formed lasted be an to least since likely at very which is event NS, in pr GW170817 merger component th the the “purple" detail, of that a uct indicated more also further In emission maybe NS. 2017gfo AT and the one “blue" contain a prog least of the existence at that should suggests which binary ejecta, itor merger t the indicated o 2017gfo of AT an existence of from observations jet SGRB the the Meanwhile, of view. structure angular the possi origi explore became to it can Moreover, mergers. SGRBs binary compact robustly that from afterglows nate hypothesis its long-standing and the 2 170817A confirmed al. 20 GRB et Tanvir al. of 2017; 2017; et observations al. Nicholl al. et The et 2017; Soares-Santos Hu 2017; al. 2017; al. et et 2017; Lipunov al. Smartt et 2017; al. Covino et al. Evans 2017 et 2017; Kilpatrick al. 2017; al. et et Arcavi al. Coulter et 2017; Cowperthwaite 2017; al. et al. as Andreoni et well Chornock 2017c; as al. and ultraviolet-optical-infrar et al. 2019) (Abbott the et al. in Troja et 2017gfo AT Ghirlanda kilonova 2017; et 2018; the Lazzati al. 2019; al. et al. et Lyman et Margutti Ghirlanda 2018; 2018; 2017; al. et D’Avanzo al. 2017; et Hallinan e di (Alexander X-rays in 2017; to radio emission the afterglow from follo bands of 2017; the electromagnetic number monitored al. large et the a observations Goldstein subsequently, up and, 2017a), 2017b; 2018) al. al. sig- al. et et et Zhang (Abbott (Abbott GW170817 170817A Virgo the GRB and by after s LIGO 1.7 Fermi by 2017a; About detected 2017. Metzger nal August, 2016; 17 on Yu & Li al. et 2015; Perego 2020). al. 2014; et al. Zhu et al. Martin et Wanajo 2014; 2014; Fernández & Metzger 1 h rtmlimsegrG vn a endiscovered been had event GW multi-messenger first The , 2 n i-igZhu Jin-Ping and , 2B tr:nurn usr:general pulsars: neutron– stars: – 821B) am-a us oio a ucsflytriggered successfully was Monitor Burst Gamma-ray 3 ff enough. ff ce iooa ti expected is it kilonova, ected ril ubr ae1o 6 of 1 page number, Article B160821B. RB db not be ld no the of on ma-ray © iously S 2021 ESO na sion ray ide dband ed ff ff 017). erent -axis al. t od- 17; en- ble w- al. ed he e - ; A&A proofs: manuscript no. ms210731 with a “red" kilonova1 (Cowperthwaite et al. 2017; Perego et al. nario can provide a natural explanation for the AT2017gfoemis- 2017; Tanaka et al. 2017; Tanvir et al. 2017; Villar et al. 2017; sion. Therefore, in our opinion, this situation could also appear Kawaguchi et al. 2018). Therefore, in summary, the progenitor in the case of GRB160821B. Then, this paper is devoted to test of the GW170817 event can be identified as a DNS system, whether there is a non-thermalemission component arising from which is consistent with the result of the GW analysis. the interaction between the NS wind and the merger ejecta, just However, strictly speaking, in the radioactive power model, as mentioned above for AT2017gfo. the observationally required mass and opacity of the merger ejecta actually cannot fall in an acceptable parameter region predicted by the merger simulations. Therefore, alternatively, 2. The Model Yu et al. (2018) and Li et al. (2018) hadmodeledthe AT2017gfo As a result of the collision of a relativistic NS wind with a emission by invoking a long-lived post-merger NS. Such a rem- preceding ejecta, a termination shock (TS) can be formed in nant NS can naturally provide an extra energy source for the the wind to decelerate the wind material, while the ejecta can kilonova emission and thus reduce the requirement on the ejecta be heated by absorbing the radiation from the shocked wind. mass. Simultaneously, the remnant NS can also influence the Such an interaction has been previously studied in some semi- opacity of the merger ejecta, due to the possible ionization of analytical works for GRBs (Dai 2004; Yu & Dai 2007), superlu- lanthanides by the hard emission from the NS. About 155days minous supernovae (Kotera et al. 2013), mergernovae(Ren et al. after GRB170817A, Piro et al. (2019) discovered a possible X- 2019), and even accretion-induced collapses of white dwarfs ray flare, which somewhat implied independently the existence (Yu et al. 2019). In this paper we employ the model proposed in of the remnant NS. Furthermore, by considering of the interac- Yu et al. (2019) and Ren et al. (2019), which is most relevant to tion between the merger ejecta and the relativistic wind from the the situation concerned here. I.e., a relativistic wind from a mil- remnant NS, it is expected that a non-thermal emission com- lisecond pulsar is blocked by a low-mass optically thick ejecta. ponent could be generated by the shocked NS wind (i.e., the pulsar wind nebula; PWN), in addition to the thermal kilonova emission from the merger ejecta (Kotera et al. 2013; Yu et al. 2.1. The PWN emission 2019). Very encouragingly, such a non-thermal emission com- The energy luminosity carried by a NS wind can usually be esti- ponent had indeed been resolved from the AT2017gfo data, as mated by the luminosity of magnetic dipole radiation of the NS, presented in Ren et al. (2019), which can improve the fitting to which reads the AT2017gfo data significantly. In view of the ultrahigh mass of the merger product around B2R6 4 p s 2π 42 2 6 −4 −1 2.5 M⊙, it is undoubtedly necessary and important to further test Lmd = = 9.6 × 10 B R P− erg s (1) 6c3 P ! p,12 s,6 3 the existence of post-merger NSs, which can provide a robust constraint on the equation of state of the NS matter and then pro- with Bp, Rs, and P are the polar magnetic field strength, ra- mote our understandingof the low-energyfeature of strong inter- dius, and spin period of the NS, respectively, and c is the speed action. Besides the GRB 170817A/AT2017gfo event, searchings x of light. Hereafter, the conventional notation Qx = Q/10 is for possible kilonova emission have already been implemented adopted in cgs units. The temporal evolution of this wind lumi- in the afterglowsof many SGRBs since 2013 (Berger et al. 2013; nosity is determined by the spin-down behavior of the NS, which Tanvir et al. 2013; Yang et al. 2015; Jin et al. 2015, 2016, 2018, can be written as 2020; Gao et al. 2015, 2017; Kasliwal et al. 2017). Among the − SGRBs owning a kilonova candidate, GRB160821B is one of t α the lowest redshift of z = 0.162. From its optical/nIR afterglow, Lmd(t) = Lmd,i 1 + , (2) tsd ! an obvious excess was found. Because of its near distance, the kilonova emission associated with GRB 160821B is in princi- where the initial value of the luminosity Lmd,i is given for an ple detectable and can provide a natural explanation for the ob- initial spin period Pi. About the temporal index, we can take served optical/nIR excess (Lamb et al. 2019; Troja et al. 2019). α = 2 when the spin-down is dominated by the magnetic dipole In view of its luminosity lower than AT2017gfo, the kilonova radiation. On the other hand, the NS’s rotation could sometimes after GRB160821B can in principle be modeled with a pure ra- be braked primarily by a GW radiation, if the NS is deformed dioactive power. However, it could still be necessary to mention with a sufficiently high ellipticity ǫ, which leads to α = 1. For that a significant internal plateau had appeared in the early X- these two different braking effects, the spin-down timescale of ray afterglow during the first few hundreds of seconds (see the the NS can be expressed as insert in Figure 1), which indicated that a post-merger NS also − exists in this event. According to these observations, Ma et al. 3Ic3 2π 2 t = = 2 × 103I R−6B−2 P2 s (3) (2020) suggested that the post-merger NS could collapse intoa sd,md 2 6 45 s,6 p,15 i,−3 B R Pi ! black hole and then the subsequent kilonova could be powered p s by the accretion onto the black hole. Nevertheless, alternatively, and as suggested by Yu et al. (2018), the steep decay after the inter- nal plateau may not represent the collapse of the NS, but just 5P4c5 t = i = 9.1 × 105ǫ−2I−1P4 s, (4) be caused by the suppression of the magnetic dipole radiation sd,gw 2048π4GIǫ2 −4 45 i,−3 of the NS. In this case, the spin-down of the NS of a relatively low luminosity can still power the kilonova emission, which can respectively, where I is the inertia moment and G is the gravita- be generally called as mergernovae (Yu et al. 2013). This sce- tional constant. When the relativistic wind drives a TS by colliding with the 1 The reason of this judgement is that the neutrino emission from the preceding merger ejecta, a PWN (i.e., the shocked wind region) remnant NS can suppress the synthesization of lanthanides in a part of can be formed between the TS and the merger ejecta. Denoting merger ejecta and reduce its opacity. the bulk Lorentz factor of the unshockedwind by Γw, the internal

Article number, page 2 of 6 Guang-Lei Wu et al.: Does a long-lived remnant neutron star exist after short gamma-ray burst GRB 160821B? energy density of the PWN can be expressed by according to the with a distribution index of δ, where Mej is the total mass of the shock jump condition ejecta, Rmin and Rmax are the minimum and maximum radii, re- spectively. Since the internal energy of the ejecta is usually much ′2 ′ 2 ξLmd ets = 4Γ n mec = , (5) smaller than its kinetic energy, we assume that the ejecta expands ts w πR2 c 4 ts homologously. Therefore, the maximum and minimum ejecta ′ where Γ = Γw/2 is the Lorentz factor of the TS measured in the radii for a given time t can be expressed as Rmax = vmaxt and ts ′ rest frame of the injecting unshocked wind, nw is the comoving Rmin = vmint, by invoking the maximum and minimum velocities. number density of the wind electron/positrons, me is the electron Following Metzger (2017a), we separate the merger ejecta into n rest mass, Rts is the radius of the TS, and the fraction ξ is intro- mass layers and denote the layers by the subscript i = 1, 2, ···, n, duced due to a possible fact that the energy released from the NS where i = 1 and n represent the bottom and the head layers, re- is collimated in the jet direction. In our calculations, the value spectively. Then, the evolution of the internal energy Eint,i of the of ets is actually obtained according to the mechanical equilib- i−th layer can be determined by the energy conservation law as rium between the PWN and the merger ejecta at the contact dis- (Kasen & Bildsten 2010) continuity surface (see Eq. 20). Then, by using Eq. (5), we can reversely obtain the evolution of the TS radius, which is deter- dEint,i Eint,i dRi = Lh,i + miq˙r,iηth − − Le,i, (10) mined by the motion of the inner boundary of the merger ejecta, dt Ri dt The electrons and positrons in the PWN can initially be ac- celerated by the TS to distribute with their random Lorentz fac- where Lh,i is the heating rate due to the absorption of the PWN ∝ −p − − ′ emission by the layer,q ˙ is the radioactive power per unit mass, tors as dNe/dγ γ for γ > γm = [(p 2)/(p 1)]Γts, where r p is a constant spectral index. At a time of t, the total number of ηth is the thermalization efficiency of the radioactive power, mi the accelerated electrons can be estimated by and Ri are the mass and radius of the layer, Le,i is the observed ξL t luminosity contributed by this layer. The specific expressions of N ≈ N˙ t = md . the terms in Equation (10) would be introduced as follows. e e 2 (6) Γwmec First of all, the energy injection rate from the PWN to the Here, we multiply Lmd as a function of time to the time t di- i−th layer can be calculated by rectly but do not integrate Lmd over t, because the electrons accelerated at early times can be cooled to be non-relativistic pwn −τν,i ∆τν,i Lh,i = Lν e e − 1 dν, (11) very quickly via their synchrotron radiation and, sometimes, fur- Z ther via synchrotron self-Compton scattering. For calculating the   pwn synchrotron radiation, we estimate the stochastic magnetic field where the value of Lν is given by Eq. (8) and the optical depths 1/2 in the PWN by Bts = (4πǫBets) with a magnetic equiparti- are defined as tion factor ǫB. At the very beginning, the stochastic magnetic field in the PWN could be very high, which can lead the cooling Ri τ = κ ρ (r)dr (12) timescale of relativistic electrons (i.e., γ & 2) to be much shorter ν,i ν ej ZRmin than the dynamical timescale. In this case, the number of the rel- ativistic electrons that can contribute to the synchrotron radiation and should be discounted by a fraction of tcol/t, which yields Ri tcol ∆τν,i = κνρej(r)dr. (13) Ne,rel = Ne × min[1, ], (7) t ZRi−1 2 where tcol = 3πmec/σTB is taken for γ ∼ 2 and σT is the Thom- → ∞ → n ts When n and thus ∆τi 0, we can get Lh = Σi=1Lh,i = son cross section. pwn − L (1 − e τν,tot ) dν from Eq. (11), where τ is the optical Following Sari et al. (1998), we can analytically calculate ν ν,tot depthR of the whole ejecta for a given frequency. In our cal- the synchrotron radiation spectrum of relativistic electrons by culations, Eq. (17) in Yu et al. (2019) is adopted to describe

ν 1/3 the frequency-dependent opacity κν, which was obtained by fit- ν , ν<νl; ting the numerical results presented in Figure 8 of Kotera et al. l − − pwn pwn ×   ν  (q 1)/2 Lν = Lν,max  , νl <ν<νh; (8) (2013). Secondly, the radioactive power per unit mass reads  νl  −(q−1)/2 −p/2 (Korobkin et al. 2012)   νh ν  , νh < ν,  νl νh  1.3      pwn 1 1 t − t − − where the peak luminosity is given by Lν,max = q˙ = 4 × 1018 − arctan 0 erg s 1 g 1 (14) 2 r Ne,relmec σT Bts/(3qe) with qe is the electron charge. For "2 π  σ # the braking frequencies and the spectral index, we have with t = 1.3s and σ = 0.11s, and the thermalization efficiency νl = min[νm, νc], νh = max[νm, νc], and q = 2 for νc < νm 0 2 is given by (Barnes et al. 2016; Metzger 2017b) and q = p for νc > νm, where νm = qeBtsγm/2πmec, 2 νc = qeBtsγc /2πmec, and the cooling Lorentz factor is defined 2 ln 1 + 0.34t0.74 as γc = max[2, 6πmec/σTBtst]. day ηth = 0.36 exp −0.56tday + (15)   0.34t0.74     day  2.2. The kilonova emission     with tday = t/day. Thirdly, the luminosity of the thermal emis- For the merger ejecta, as usual, we take a power-law density pro- sion of the i−th layer can be determinedby the radiativediffusion file as (Nagakura et al. 2014) as − − 3−δ 1 −δ (δ 3)Mej Rmin R Ei ρej(R, t) = − 1 (9) L = , (16) πR3  R !  R ! e,i 4 max  max  max max Ri/c, td,i       Article number, page 3 of 6 A&A proofs: manuscript no. ms210731 where the radiation diffusion timescale of the i-th layer is the particle number density of the medium, and mp is the mass n of proton. A half-opening angle θj of the jet is taken in our calcu- 3κes lation. When the Lorentz factor of the jet decreases to be smaller t = m ′ , (17) − d,i 4πR c i than θ 1, the analytical results given by Eq. (8) should be fur- i Xi′=i j −2 ther multiplied by an extra suppression factor Γ θ , which is where κ = 0.2 cm2 g−1 is the electron-scattering opacity since j j es ff the ejecta thermal emission is mainly in the UV/optical bands. called as a jet break. Sometimes, the Newtonian e ect should Under this treatment, the propagation of the PWN emission in also be taken into account. the ejecta and the radiative transfer of the ejecta heat can be gen- erally described by a set of independent equations for different 3. Comparison with the GRB 160821B observations layers. As described, the electromagnetic emission after a DNS merger After the calculations of all layers, we can finally obtain the total luminosity of the ejecta thermal emission as is contributed by three components as tot jet kn pwn −τν,tot n Lν = Lν + Lν + Lν e , (22) Le = Le,i, (18) which can be used to fit the multi-wavelength afterglow emission Xi=1 of GRB160821B.In view of the limited number of the afterglow data, in this paper we do not seek for a completed constraint on which corresponds to a black-body temperature of Teff = / the model parameters. Alternatively, we just try to test the com- 2 1 4 Le/4πσRph , where σ is the Stephan-Boltzmann constant, patibility of the model with the observations. A tentative mod- and Rph is the photosphere radius where the electron-scattering eling of the light curves and spectra are presented in Figures1 optical depth satisfies (τes,tot −τes,i) = 1. If Rph < Rmin, we simply and 2, respectively. The used parameter values are listed in Ta- set Rph = Rmin. For an effective black-body spectrum, the lumi- ble 1, which are all typical for SGRBs including GRB170817A. nosity of the kilonova emission at a frequency ν can be given by To be specific, firstly, the X-ray afterglow for t > 103 s can be easily accounted for by the emission from the jet ES, which was 2 2 ′3 8π Rph hν not influenced by the energy release from the remnant NS be- Lkn = (1 + z) , (19) cause of the huge kinetic energy of the jet. Moreover, a jet break ν c2 exp (hν′/kT ) − 1 eff could happen at a few days after GRB160821B. It should also where h is the Planck constant, k is the Boltzmann constant, and been mentioned that the very early plateau in the X-ray after- ′ ν = (1 + z)ν. Meanwhile, by using the internal energy of the glow has not been modeled. This plateau can probably be at- innermost layer Eint,1 and according to the the mechanical equi- tributed to the PWN emission at the jet direction before the NS’s librium between the PWN and the merger ejecta, we can obtain surface magnetic field was buried (see Yu et al. (2018) and ? for the internal energy density of the PWN by related discussions). Secondly, for the radio afterglow, the upper limit appearing at t ∼ 1 day indicated that the two observational E e = int,1 , data could not have the same origin, as previously suggested by ts 2 (20) 4πRmin∆R Troja et al. (2019) and Lamb et al. (2019). Then, while the late data at ∼ 10 day is ascribed to the ES emission, the early data where ∆R = (R − R )/n. Then, we can finally combine the max min at ∼ 0.1 day is probably contributed by another emission region, calculations for the PWN emission and the kilonova together. e.g., a reverse shock propagating into the GRB jet (Troja et al. 2019). Finally, for the optical/nIR data, by subtracting the con- 2.3. The jet ES emission tribution from the jet ES, we can naturally attribute the excesses to the kilonova and PWN emission. The multi-wavelength afterglows of GRB 160821B must be pri- In more detail, the peak time of the kilonova emission is marily contributed by the ES driven by the GRB jet decelerating found to be around ∼ 1 day, which can be naturally explained into the interstellar medium. In principle, the relativistic wind 1/2 from the remnant NS can also interact with the GRB jet and by the diffusion timescale of tp = κesMej/4πvejc for a typical thus influence the emission of the ES, which can be described ejecta mass of Mej ∼ 0.01M⊙ and a typical electron-scattering 2 −1 by the model of Dai (2004) and Yu & Dai (2007). Nevertheless, opacity of κes ∼ 0.2cm g . Although a large number of lan- by considering that the wind luminosity is probably only com- thanides are believed to be synthesized in the merger ejecta, parable to the luminosity of the kilonova, the influence of the the required small opacity can still be understood, by consid- NS wind on the jet ES can be basically neglected in the case of ering that the merger ejecta could be deeply ionized by the early GRB160821B, unless the wind energy is extremely highly col- PWN emission before the surface magnetic field of the NS is limated in the jet direction (i.e., ξ ≪ 1). Therefore, we simply suppressed. The radioactive power corresponding to the ejecta employ the standard ES model introduced in Sari et al. (1998) mass Mej ∼ 0.01M⊙ can be comparable to the emission lumi- and Huang et al. (2000); Huang & Cheng (2003). In short, while nosity of the PWN. This indicates the kilonova emission after the dynamical evolution of the jet is described by the classical GRB160821B was powered by hybrid energy sources, which is formula as the same to the situation of AT2017gfo (Yu et al. 2018). In any 1/8 case, the crucial effect of the remnant NS is mainly displayed 17Ej Γ t = , in the appearance of the non-thermal PWN emission, which can j( ) 5 3 (21) 1024πn0mpc t ! help to explain the relatively slow decay of the excess emission. Such a non-thermalPWN emission can also be clearly seen from jet the synchrotron luminosity Lν of the ES emission can also be the evolving spectra presented in Figure 2. As shown, while the determined by using Eq. (8) for corresponding parameters and thermal component shifts from the UV to the IR quickly, the characteristic quantities. Here, Γj and Ej are the Lorentz factor synchrotron emission from the PWN gradually increased to be and the isotropically-equivalent kinetic energy of the jet, n0 is dominated about 10days after GRB160821B.

Article number, page 4 of 6 Guang-Lei Wu et al.: Does a long-lived remnant neutron star exist after short gamma-ray burst GRB 160821B?

Table 1. The adopted parameter values for the tentative fitting of the observations of GRB 160821B

jet external shock Ej n0 ǫe ǫB p θj 1050erg 1.58 × 10−3 cm−3 0.5 0.006 2.3 14◦ kilonova ξLmd,i tsd Mej κes vmin vmax δ 41 −1 5 −2 10 erg s 8.64 × 10 s 0.01 M⊙ 0.2g cm 0.1 c 0.4 c 1.5 PWN Γw ǫe ǫB p 105 0.99 0.01 2.5

3 3 3 Data Data Data 2 X-ray (1keV) Upper limit 2 g band Upper Limit 2 F606W Upper Limit Total Total Total 3 Jet External Shock Jet External Shock 1 2 1 1 1 Kilonova Kilonova Jy) PWN PWN

/ 0 Jy) 0 Jy) 0 Jy) 0 F -1 ( / / / 10 -2 log F -3 F F ( -1 ( -1 ( -1

10 -4 10 10 -3 -2 -1 0 1 2 log -2 t log -2 log -2 log10( /day)

-3 -3 -3

-4 -4 -4

-2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 t t t log10( /day) log10( /day) log10( /day) 3 3 3 Data Data Data 2 r band Upper Limit 2 i band Upper Limit 2 z band Total Total Total Jet External Shock Jet External Shock Jet External Shock Kilonova 1 1 1 Kilonova Kilonova PWN PWN PWN Jy) 0 Jy) 0 Jy) 0 / / / F F F

( -1 ( -1 ( -1 10 10 10

log -2 log -2 log -2

-3 -3 -3

-4 -4 -4

-2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 t t t log10( /day) log10( /day) log10( /day) 3 3 3 Data Data 2 F110W Upper limit 2 F160W Upper limit 2 Radio Total Total Jet External Shock Jet External Shock 1 1 1 Kilonova Kilonova PWN PWN Jy) 0 Jy) 0 Jy) 0 / / / F F F

( -1 ( -1 ( -1 10 10 10

log -2 log -2 log -2

-3 -3 -3 Data Upper limit -4 -4 -4 Total

-2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 t t t log10( /day) log10( /day) log10( /day) Fig. 1. The multi-wavelength light curves of the afterglow emission of GRB 160821B for different electromagnetic bands as labeled. The ob- servational data are taken from (Lamb et al. 2019; Troja et al. 2019) and Swift. The dotted, dash-dotted, dashed, and solid lines correspond to the emissions from the jet external shock, the thermal kilonova, the PWN, and their combination, respectively. The insert shows the early X-ray afterglow plateau, which may indicate the remnant NS could be intrinsically a magnetar before its surface magnetic field is buried.

4. Summary a result of the interactionbetween the pulsar wind and the merger ejecta. Such a situation has been previously suggested to appear It is of fundamental importance to determine the nature of the in the GRB170817A/AT2017gfo event. And in this paper, by merger product of DNSs. The existence of a long-lived remnant resolving the non-thermal PWN emission component from the NS can leave many imprints in the kilonova emission after the kilonova data, we further find that the remnant NS scenario can GW event, by reducing the opacity of the merger ejecta, provid- also be consistent with the afterglow emission of GRB 160821B. ing energy injection for the thermal kilonova emission, and, in Although a stringent constraint on the model is still difficult be- particularly, contributing a non-thermal emission by the PWN as

Article number, page 5 of 6 A&A proofs: manuscript no. ms210731

0.5 t = 1day 0.5 t = 2day 0.5 t = 3.5day Data Data Upper Limit Upper Limit 0.0 0.0 0.0 Total Total Jet External Shock Jet External Shock

Jy) Jy) Kilonova Jy) Kilonova

/ -0.5 / -0.5 PWN / -0.5 PWN F F F ( ( ( 10 10 10

log -1.0 log -1.0 log -1.0

Data -1.5 Total -1.5 -1.5 Jet External Shock Kilonova -2.0 -2.0 -2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 2.2 2.4 2.6 2.8 3.0 3.2 3.4 2.2 2.4 2.6 2.8 3.0 3.2 3.4 log10( / nm) log10( / nm) log10( / nm)

0.5 t = 4.5day 0.5 t = 10day 0.5 t = 20day Data Data Upper Limit Upper Limit Upper Limit Total 0.0 0.0 0.0 Total Total Jet External Shock Jet External Shock Jet External Shock PWN

Jy) Kilonova Jy) Kilonova Jy) μ μ

/ -0.5 PWN / -0.5 PWN / -0.5 ν ν F F F ( ( ( 10 10 10

log -1.0 log -1.0 log -1.0

-1.5 -1.5 -1.5

-2.0 -2.0 -2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 2.2 2.4 2.6 2.8 3.0 3.2 3.4 2.2 2.4 2.6 2.8 3.0 3.2 3.4

log10( / nm) log10(λ / nm) log10(λ / nm)

Fig. 2. The ultraviolet-optical-infrared spectra of the afterglow emission of GRB 160821B for different times as labeled. The observational data are taken from (Lamb et al. 2019; Troja et al. 2019). The dotted, dash-dotted, dashed, and solid lines correspond to the emissions of the jet external shock, the thermal kilonova, the PWN, and their combination, respectively. cause of the very limited number of the afterglowdata, our result Jin, Z.-P., Hotokezaka, K., Li, X., et al. 2016, Nature Communications, 7, 12898 still indicates that the formation of a long-lived massive NS is Jin, Z.-P., Li, X., Cano, Z., et al. 2015, ApJ, 811, L22 Jin, Z.-P., Li, X., Wang, H., et al. 2018, ApJ, 857, 128 probably not rare in the DNS merger events, which implies the Kasen, D., Badnell, N. R., & Barnes, J. 2013, ApJ, 774, 25 equation of state of the post-merger NSs should be stiff enough. Kasen, D. & Bildsten, L. 2010, ApJ, 717, 245 Kasen, D., Fernández, R., & Metzger, B. 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