arXiv:1605.04660v1 [astro-ph.HE] 16 May 2016 t erdcdwt omlcnrlegn,wiebrt with bursts while engine, central normal a with reproduced on htbrt ihduration on with Based th bursts simulations, that numerical features. found and curve analysis light observational both X-ray aforementioned the a aeaseilcnrlegn,sc sasrnl magne- strongly GRBs a ultra-long as the On such that engine, central proposed special also durations. a radii is have long may it larger unusually hand, 2001; much other the the their explain Rees supergiant-like & considering naturally (Mészáros blue could 2013), GRBs a al. et ultra-long proposed Nakauchi al. et for Nakauchi 2014) 2013; progenitor al. et al. Levan et F (Gendre special 2014). 2013; a authors al. et either some (Levan have progenitor instance, special may a GRBs or engine ultra-long central the that sidered 20 2015). al. Mészáros et & (Zhang Gao population “ultra-long” the to classified be a fego ih uvs hypooet een the redefine to propose They X- early the as decay in curves. duration 2007) shallow burst light al. 2005a; and et afterglow Liang al. 2011) ray 2007; et al. (Burrows al. et et flares Margutti (Troja plateaus time 2006; by activity al. indicated et engine Zhang GRBs, central tak- prolonged some GRBs, the “ultra-long" of account defining for into measure ing reliable a not larger a ézrs21) nteohrhn,agethat argue 2014; hand, al. other et the (Zhang on authors 2015), Some Mészáros & 2014). Gao al. et Levan 2013; nsm eeecs h utaln"GB eee othe to 2015). refered al. GRBs et Greiner “ultra-long" the 2014; with 2013 GRBs references, al. al. et et Levan some Virgili 2013; In 2013; al. al. et et (Gendre Stratta attention been have great seconds), of paid ( (tens GRBs activity typical engine to central compared hours) long unusually with (GRBs) bursts burst ua,407,China. 430074, Wuhan, 085 China 100875, [email protected] [email protected] [email protected]; 3 vntog ako la ento,i sgnrlycon- generally is it definition, clear a of lack though Even eety utaln uss,asbls fgamma-ray of subclass a bursts”, “ultra-long Recently, rpittpstuigL using typeset Preprint D lhuhn la onayln a endfie yet. defined been has line boundary clear no Although LC OECNRLEGN O LR-OGGMARYBRT11 BURST GAMMA-RAY ULTRA-LONG FOR ENGINE CENTRAL HOLE BLACK ATVERSION RAFT 2 1 > colo hsc,Hahn nvriyo cec n Techn and Science of University Huazhong Physics, of School eateto srnm,BiigNra nvriy Beiji University, Normal Beijing Astronomy, of Department 3 10 Gnr ta.21;Vriie l 03 tat tal. et Stratta 2013; al. et Virgili 2013; al. et (Gendre lc oe h mlctoso u eut sdiscussed. is headings: results supergiant, our Subject blue of of implications The instead star hole. Wolf-Rayet black progenit a the likely of radius more and is mass f total accretion the fall-back as with such fall-bac model parameters, broad-ban collapsar 121027A-like the a GRB propose inspect a thus We we exhibits paper, lightcurve this p X-ray the In time investigate to GRBs. us ultra-long enables for which 2011kl, 111209A/SN GRB 4 eety h rtascainbtena lr-oggamma ultra-long an between association first the Recently, eur netne eta nieatvt,may activity, engine central extended an require s γ ryduration -ray O t burst A CTOBER T E tl mltajv 5/2/11 v. emulateapj style X 1. ytkn noacutboth account into taking by INTRODUCTION 6 2018 16, T 111209A) crto,aceindss-bakhl hsc gamma-ray - physics hole black - disks accretion accretion, 90 xedn to extending T H 90 E fodr10 order of G AO 1 W , ∼ EI 10 -H 3 3 γ rf eso coe 6 2018 16, October version Draft UA reven or s a be can s UENV 2011KL SUPERNOVA ryand -ray L T ology, EI 90 ABSTRACT 14; 2 ey ng or Z , ∼ is ; HI -Q IANG fGB110AS 01li eto .I eto ,we 5, section implication. data In the broadband discuss and 4. the results section to our in given model summarize briefly 2011kl this is 111209A/SN apply model GRB we accretion of and fall-back 3 111209A. the section GRB of in section of picture In features general observational 2011kl. A the SN describe of gi we luminosity to 2, high ejecta supernova unusually the the accre into rise revived energy the momentum depositing from en- angular disc, magnetically central tion and extracted long be energy unusually also the the could rise timescale; give fall spin activity the to would gine tapping envelope BH BH, the the the of in onto energy accretion materials the the reactive of and is back fraction engine central a 111209A/SN GRB BH; the GRB a model: of collapsar data the broadband within we 2011kl work, to the this reservoir interpret In energy to ? the 2011kl intend SN is as luminous question serve abnormally The the engine power magnetar. central more a BH of is ra- the instead 111209A could (BH) dipole GRB hole the of black obey engine a than like central rather fall- the 2013), 121027A-like profile, al. diation GRB et a (Wu exhibits bump 111209A back lig GRB X-ray of late-time curve the that especially 2011kl, 111209A/SN a be might 111209A GRB thu of magnetar. They engine millisecond central required. the is that input energy propose additional an but 2011kl, that suggest they 2011), al. et 56 Quimby SN super- 2012; (Gal-Yam overlumi- super-luminous novae of canonical and supernovae luminosity Nev- between GRB-associated high intermediate nous 111209A. is unexpected GRB which the and 2011kl, for on progenitor interpretation based supergiant blue ertheless, disruption light a and tidal out spectra ob- rule its a as they the such on su- shape, 2011kl, Based curve a SN of and 2011kl. properties GRB 111209A/SN served GRB ultra-long i.e., an pernova, between association covered GRBs. of of progenitor understanding and our engine ultr promote central of the origin potentially physical would the GRBs on Research long 2015). 20 al. al. et et (Levan Greiner magnetar) (a star neutron millisecond tized rsa,sgetta h rgntro R 111209A GRB of progenitor the that suggest star, or ii o epnil o oeigtelmnst fSN of luminosity the powering for responsible not is Ni rGB110AS 01l h eurdmodel required The 2011kl. 111209A/SN GRB or osdrn h opeesv bevtoso GRB of observations comprehensive the Considering dis- first the reported (2015) al. et Greiner recently, Most n h eta nieo hsutaln us sa is burst ultra-long this of engine central the and rybrt(R)adasproai eotd i.e., reported, is supernova a and (GRB) burst -ray up ugsigabakhl eta engine. central hole black a suggesting bump, k aao R 129/N21k.Telate- The 2011kl. 111209A/SN GRB of data d Y OU yiso eta nie ree progenitors even or engines central of hysics 2. 1 BEVTOA ETRSO R 111209A GRB OF OBSERVATIONAL FEATURES AND W EI X IE 29 N T ASSOCIATED ITS AND 1209A 2 us:idvda (GRB individual burst: 14; ve ht a- s - 2

GRB 111209Awas discovered at T0 = 2011:12:09-07:12:08 of the mass in the core part collapses into a rapidly spinning UT on 9 December 2011 by the Burst Alert Telescope (BAT) black hole (BH), and the rest mass forms a surroundingaccre- on board Swift, and was later accurately located by XRT at tion disc. The GRB prompt emission can be powered by the a position of RA(J2000)=00h 57m 22.63s and Dec(J2000)=- Blandford-Znajek (1977, hereafter BZ) mechanism, in which 46d 48′ 03.8′′, with an estimated uncertainty of 0.5 arc- the spin energy of the BH is extracted via the open field lines sec (Hoversten et al. 2011) . GRB 111209A showed an ex- penetrating the event horizon. An alternative mechanism for traordinarily long prompt duration, and was monitored up powering GRB jet is the neutrino annihilation process, which to T0 + 1400 s until BAT entering the orbital gap region. It is too “dirty” and inffective to account for long-term activ- was also detected by the Konus detector on the WIND space- ity of GRB, like ultra-long GRBs (Fan et al. 2005; Lei et craft (Golenetskii et al. 2011). As shown in the ground data al. 2009, 2013; Liu et al. 2015). The energy and angu- analysis of the Konus-Wind instrument, GRB 111209A was lar momentum could also be extracted magnetically from ac- recorded with a continuous coverage extending from 5,400 s cretions discs, by field lines that leave the disc surface and before to 10,000 s after the Swift trigger T0. extend to large distance, centrifugally launching a baryon- Both Very Large Telescope (VLT)/X-shooter (2011 Decem- rich wide wind/outflow through the Blandford-Payne (Bland- ber 10 at 1:00 UT) and Gemini-N/GMOS-N detected the early ford & Payne 1982, hereafter BP) mechanism. The bound- spectroscopy of the transient optical light of GRB 111209A. ing shock responsible for the associated supernova and the A redshift of z = 0.677 was suggested by the identify of BP outflow would transfer kinetic energy to the envelope ma- absorption lines and emission lines from the host galaxy terials. During the fall-back, only a portion of the fall-back (Vreeswijk et al. 2011). Based on the Konus-Wind results, mass accretes onto the BH, while the rest is ejected in a disc GRB 111209Ahad a fluence of (4.86±0.61)×10−4 erg cm−2 wind (Kumar et al. 2008a,b). The more energetic the super- (Golenetskii et al. 2011), inferring an isotropic gamma-ray nova shock, the less envelope material falls back into the cen- 2 53 ter. For a parcel of gas of the progenitor star at radius r , the energy release Eγ,iso =4πD fγ /(1 + z)=5.54 ± 0.70 × 10 fb L 2 3 1/2 erg. Here we adopt the concordance cosmology with Ωm = fall-back time could be estimated as tfb ∼ (π rfb/8GM•) , 0.27, ΩΛ =0.73 and h0 =0.71. where M• is the BH mass. The fall-back of the envelope ma- Swift/XRT observations started at 425 s after the BAT terials may form a new accretion disc, powering the shallow trigger (Hoversten et al. 2011), revealing a bright afterglow decay phase or late flares seen in X-ray afterglow. The BP mainly with several components: outflow from the new disc would further deposit energy into the supernova ejecta. • An initial plateau phase overlapping with the prompt Based on some analytical and numerical calculations, γ-ray emission; the fall-back accretion rate initially increases with time ˙ ∝ 1/2 • After an observational gap, from 3 × 103 s to ∼ 104 as Mearly t until it reaches a peak value at tp s, the light curve rapidly rise back and then gradually (MacFadyen et al. 2001; Zhang et al. 2008; Dai & Liu 2012). steepen to a “steep decay" phase with decay index of And then the late-time fall-back accretion behavior would fol- ˙ ∝ −5/3 ∼ 5, behaving very likely the GRB 121027A-like fall- lows Mlate t , as suggested by Chevalier (1989) until time te, when most of the fall back materials fuel out and the accre- back bump (Wu et al. 2013). ˙ −α tion behavior could be described with Mfinal ∝ t , where α • At very late time (∼ 105 s), the tail of steep decay phase depends on the stellar structure and rotation rate of progenitor is superposed by another power-law component with star4. We use a three-segments-broken-power-lawfunction of decay index of ∼ 1.5, which is usually denoted as “nor- time to describe the evolution of the fall-back accretion rate mal decay" phase in the canonical picture of X-ray af- as terglow (Zhang et al. 2006). −1 − −1/2 − 5/3 ˙ ˙ 1 t t0 1 t t0 The afterglow of GRB 111209A was also clearly detected M = Mp + 2 t −t 2 t −t in the optical-UV band by Swift/UVOT and other ground "  p 0   p 0  # based instruments, such as the TAROT-La Silla (Klotz et al. − −1 t −t α 5/3 2011) and the seven-channel optcial/near-infrared imager × + 0 1 − , (1) GROND (Kann et al. 2011). After the prompt optical flashes, " tb t0 # the earlier optical afterglow shows a normal power-law decay   until day 15. And then, the optical light curve starts to de- where t0 is the starting time of fall-back accretion (henceforth, viate from the power-law decay and remains essentially flat time is defined in the cosmologically local frame). between days 15 and 30. After day 30, the light curve starts Consider a Kerr black hole with mass M• and (or dimen- to decay again, approaching the host-galaxy level. Most re- sionless mass m• = M•/M⊙) and angular momentum J•. The cently, based on its temporal and spectral features, this excess BZ jet power is (Lee et al. 2000; Li 2000; Wang et al. 2002; emission is identified as a supernova, designated SN 2011kl, McKinney2005; Lei et al. 2008; Lei & Zhang2011; Lei et al. associated with GRB 111209A (Greiner et al. 2015). The 2013) bolometric peak luminosity of SN 2011kl is intermediate be- 50 2 2 2 −1 tween canonical over-luminous GRB-associated supernovae LBZ =1.7 × 10 a•m•B•,15F(a•) erg s , (2) and super-luminous supernovae. 2 where a• = J•c/(GM•) is the BH spin parameter, and F(a•)= 3. FALL-BACK ACCRETION MODEL 2 2 2 [(1 + q )/q ][(q + 1/q)arctanq − 1] with q = a•/(1 + 1 − a•). In this work, we intend to use the collapsar model to in- B• is the magnetic field strength threading the BH horizon. terpret the broadband afterglow data of GRB 111209A. The p physical picture is as follows: the progenitor star has a core- 4 In this work, the value of α is inferred from the X-ray afterglow steep envelope structure, as is common in stellar models. The bulk decay index. 3

Since the magnetic field on the BH is supported by the sur- where κ, Mej and v are the Thomson electron scattering opac- roundingdisc, one can estimate its value by equating the mag- ity, the ejecta mass, and the expansion velocity of the ejecta. netic pressure on the horizon to the ram pressure of the accre- β ≃ 13.8 is a constant that accounts for the density distri- tion flow at its inner edge (e.g. Moderski et al. 1997), bution of the ejecta (Wang et al. 2015a,b). Linj is the gen- − eralized energy source. 1 − e τγ(t) reflects the γ-ray trap- B2 Mc˙ • ∼ 2 ∼ −2 = Pram ρc 2 (3) ping rate, with τγ (t) = At being the optical depth to γ- 8π 4πr• rays (Chatzopoulos et al. 2009, 2012).
Provided that the SN 3 2 ejecta has a uniform density distribution (M = (4/3)πρR , where r• =(1+ 1 − a )r is the radiusof the BH horizon,and ej • g 2 2 EK = (3/10)Mejv ), the characteristic parameter A could be rg = GM•/c . We can then rewrite the BZ power as a function of mass accretionp rate as estimated as 53 2 −1 3κγMej L =9.3 × 10 a mX˙ (a•) erg s , (4) A = BZ • 4πv2 and 13 κγ 2 2 =4.75 × 10 − X(a•)= F(a•)/(1 + 1 − a ) . (5) 0.1 cm2 g 1 •   q M v −2 The the observed X-ray luminosity is connected to the BZ × ej 2 9 −1 s , (13) power via the X-ray radiation efficiency η and the jet beaming M⊙ 10 cm s    factor fb, i.e., where κ is the opacity to γ-rays. ηL = f L (6) γ BZ b X,iso As argued in Greiner et al. (2015), radioactive 56Ni decay The BP outflow luminosity could be estimated as could not be responsible for the luminosity of SN 2011kl. (Armitage & Natarajan 1999) Here we take that

(BP )2r4 Ω2 Linj ≃ LBP. (14) L = ms ms ms (7) BP 32c 4. APPLICATION TO GRB 111209A P Ω where Bms and ms are the poloidal disk field and the Ke- plerian angular velocity at inner stable circular orbit radius In the following, we apply the above fall-back accretion (r ). Here we define R = r /r as the radius of the model to fit the broad-band data of GRB 111209A, as pre- ms ms ms g sented in Figure 1. Table 1 summarize the values of the pa- marginally stable orbit in terms of rg. The expression for Rms is (Bardeen et al. 1972), rameters adopted in the model. We find that the broadband data of GRB 111209A could be well explained with all stan- 1/2 Rms =3 + Z2 − [(3 − Z1)(3 + Z1 + 2Z2)] , (8) dard parameter values. The early X-ray light curve (from 3000s to 5 × 104s) + − 2 1/3 + 1/3 + − for 0 ≤ a• ≤ 1, where Z1 ≡ 1 (1 a•) [(1 a•) (1 could be well interpreted with the BZ power induced by the 1/3 2 + 2 1/2 Ω a•) ], Z2 ≡ (3a• Z1) . The quantity ms is given by fall-back disc. We focus on the overall shape of the X- ray lightcurve. The flare-like variations during this phase 1 Ω = (9) could be due to the fragmentation during the fall-back phase ms 3 3 + M•/c (χms a•) (King et al. 2005). The contribution from the GRB afterglow emission is initially outshone by the BZ power and emerge where ≡ r M . Following Blandford & Payne 1982, χms ms/ • later (> 5 × 104s) to account for the late time normal decay BP could be estimated as ms p light curve. As shown in Figure 1, the early optical data may P −5/4 come from the GRB afterglow emission, while the late optical Bms = B•(rms/rH ) (10) data, i.e., the SN 2011kl component, could be dominated by where r = M (1 + 1 − a2) is the horizon radius of the black the emission from a BP process powered supernova. H • • In the interpretation for the afterglow component, the jet hole. 52 The photosphericp luminosity of SNe powered by a variety isotropic kinetic energy Ek of 7.6 × 10 erg and the ambient −3 5 of energy sources (e.g. radioactive 56Ni decay, BP power in- medium density n of1 cm are adopted . The fitting results Γ jection, etc) could be expressed as (Arnett 1982; Wang et al. depend weakly on the values of initial Lorentz factor ( 0) and 2015a,b) half opening angle (θ) of the jet. The microphysics shock pa- rameters (e.g., ǫe, ǫB, and p) are all chosen as their commonly ′ ′ − t2 + 2R0t t t 2 + 2R0t used values in GRB afterglow modeling. (Gao et al. 2013; 2 τ2 vτ2 −τ (t) τ2 vτ2 L(t)= e  m m  1 − e γ e m m  Kumar & Zhang 2015, for a review). To compare with the τ m Z0 observations of X-ray bump in GRB 111209A, we carried out ′
R0 t ′ ′ −1 numerical calculation for the time evolution of the BZ power. × + Linj(t )dt erg s , (11) vτm τm The radiation efficiency η =0.05 is taken in our calculation.   The BH is initially set up with a mass m• =3 and a spin a• = where R0 is the initial radius of the progenitor, which could 0.9. The fall-back accretion starts at t0 = 3000/(1 + z) s, peaks be taken as zero to largely simplify the above equation since 5 it is very small compared to the radius of the ejecta. τm is the It is worth noting that the fitness of the GRB afterglow emission could be effective light curve timescale, which reads also achieved by simultaneously enhancing the kinetic energy but reducing 53 the medium density, which means Ek could be equal or larger than 10 erg 1/2 (Nakauchi et al. 2013), matching with the isotropic gamma-ray energy re- 2κMej τ = , (12) lease Eγ,iso in order of magnitude. m βvc   4

2 −8 10 10 ) 2 1 −10 10 10 Jy) µ ( ν F

0

Flux (erg/s/cm −12 10 10

−14 −1 10 10 4 5 6 7 5 6 7 10 10 10 10 10 10 10 Time (s) Time (s) Figure 1. Modeling results for the XRT range (left panel) and r band (right panel) light curve of GRB 111209A. The observed data are exhibited with points, and the theoretical modeling are shown with solid lines. The thin-dash line denotes the external shock component and the dash-dotted line in left (right) panel denotes the BZ powered radiation according to the fall-back disc (the BP outflow powered supernova component). For optical data, a constant host galaxy emission is invoked (Greiner et al. 2015).

4 at tp = 8000/(1+z)s and fuels outaround tb =1.8×10 /(1+z) optical observations could be well explained. In our interpre- s. The outermost radius of the fallback material could be es- tation, the central BH mass, the fallback material mass and the 2 2 1/3 11 sentially estimated as rfb ∼ (8GM•tb /π ) =3.2 × 10 cm, supernova ejecta mass are adopted as 3 M⊙, ∼ 2.6 M⊙ and which is smaller than the typical radius of blue supergiant star 3 M⊙ respectively, inferring that the total mass of the progen- (Nakauchi et al. 2013). To achieve the fitness of the data, the itor star is in order of 10 M⊙. Moreover, the outermost radius 11 late time accretion rate decay index α = 5 is required. For of the fallback material is estimated as rfb ∼ 3.2 × 10 cm, 5 the supernova ejecta, we take the standard values for its mass times of solar radius. Therefore, we suggest that the progeni- (Mej ∼ 3M⊙), initial velocity (vi =0.06c) and the effective tor of GRB 111209A is more likely a Wolf-Rayet star instead opacity κ =0.06 cm2 g−1 (Lyman et al. 2016). Note that these of blue supergiant star, which is consistent with the obser- ejecta parameters suffer severe degeneracy, which could be vational implications from Greiner et al. (2015), although we justified by equation 12. argue that the central engine of this ultra-long burst is a BH From Eqs.(3) and (6), the maximum angular velocity and rather than a magnetar. The required magnetic field strength magnetic field strength around BH could be estimated as around BH is ∼ 1014 G, similar to the magnetar magnetic − 14 3 field properties ( 6 9 × 10 G) as proposed by Greiner et al. c a• 5 −1 Ω• = ≃ 1.01 × 10 m• q rad/s. (15) (2015). But the black hole spin period is around 0.3 ms, al- 2 GM• 2(1 + 1 − a•) most 2 orders of magnitude faster than the assumed magnetar spin (∼ 12 ms). and p If our interpretation is correct, the following implications 14 1/2 −1 −2 −1/2 −1/2 1/2 can be inferred. B•,p ≃ 2.4 × 10 LX iso 49m• qa• X (a•)η−2 fb −2G. (16) , , , Under the framework of collapsar model, the central en- With initial setup values, e.g., m• =3 and a spin a• =0.9, we gine (BH) activity timescale could have a wide range, de- 14 4 have B•,p ∼ 10 G and Ω• ∼ 2.1 × 10 rad/s. In this case, the pending not only on the size of the progenitor star, but also BH spin period is around 0.3 ms. on the stellar structure and rotation rate of the progenitor star From Eqs. (9) and (10), the initial angular velocity and (Kumar et al. 2008a,b). The latter property would mainly af- magnetic field at rms could be estimated as fect the fallback process of the envelope material, which could largely extend the central engine activity time, having chance Ω 5 −1 3 + −1 ms ≃ 2.03 × 10 m• (χms a•) rad/s. (17) to give rise to the ultra-long GRBs. On the other hand, the and bounding shock responsible for the associated supernova and the BP outflow from the initial accretion disc would transfer 14 1/2 −5/4 −1 −2 −1/2 −1/2 1/2 Bms,p ≃ 2.4×10 LX,iso,49(rms/rH ) m• qa• X (a•)η−2 fb,−2G.kinetic energy to the envelope materials. If the injected kinetic (18) energy is less than the potential energy of the envelop mate- 14 With initial setup values, we have Bms,p ∼ 0.5 × 10 G and rial, the starting time of the fallback would be delayed, which 4 Ωms ∼ 1.5 × 10 rad/s. may even prolong the burst duration. However, if the injected kinetic energy is larger, which might be the majority cases, the 5. CONCLUSION AND DISCUSSION fallback process is vanished and the central engine activity is As the first reported association between ultra-long GRB relatively short, corresponding to the normal long GRBs. It is and supernova, GRB 111209A/SN 2011kl system provides us worth noting that besides GRB 111209A, the other GRB that a good chance to study the properties of central engines or exhibits a fall-back bump in X-ray light curve, namely GRB even progenitors for ultra-long GRBs. In this work, we apply 121027A, is also an ultra-long burst (Wu et al. 2013). a fallback accretion scenario within the collapsar model to in- Regardless of the fallback process, BP outflow would al- terpret the broadband data of GRB 111209A/SN 2011kl. We ways deliver additional energy to the supernova ejecta, which find that with all standard parameter values, both X-ray and may explain the fact that GRB associated supernovae is usu- 5

Table 1 Parameters for interpreting the broadband data of GRB 111209A.

BH and ejecta parameters 2 −1 M• (M⊙) a• Mej (M⊙) v/c κ (cm g ) 3 0.9 3 0.06 0.06 GRB afterglow parameters −3 Ek (erg) Γ0 n (cm ) θ (rad) ǫe ǫB p − 7.6 × 1052 200 1 0.4 0.1 10 4 2.5 Other parameters ˙ −1 2 −1 η t0 (s) tp (s) tb (s) Mp (M⊙s ) α κγ (cm g ) − 0.05 3000/(1 + z) 8000/(1 + z) 1.8 × 104/(1 + z) 2.5 × 10 4 5 0.1 ally a energetic hypernovae (Li et al. 2016, for details). For Chatzopoulos, E., Wheeler, J. C., & Vinko, J. 2009, ApJ, 704, 1251 ultra-long GRBs, where fallback accretion might perform, Chatzopoulos, E., Wheeler, J. C., & Vinko, J. 2012, ApJ, 746, 121 the associated supernovae could be even brighter, like SN Chen, W.-X., & Beloborodov, A. M. 2007, ApJ, 657, 383 Chevalier, R. A. 1989, ApJ, 346, 847 2011kl, since the BP outflow injection is largely prolonged. Dai, Z. G., & Liu, R.-Y. 2012, ApJ, 759, 58 It is worth noticing that given the ejecta properties, such as Fan, Y. Z., Zhang, B., Proga, D. 2005, ApJ, 635, L129 its radial density profile, metallicity content and so on, the Gal-Yam, A. 2012, Science, 337, 927 supernova spectrum is essentially determined by the total in- Gao, H., Lei, W.-H., Zou, Y.-C., Wu, X.-F., & Zhang, B. 2013, New A Rev., jected energy from the central engine, no matter the central 57, 141 Gao, H., & Mészáros, P. 2015, ApJ, 802, 90 engine is magnetar or black hole. For the case of SN 2011kl, Gendre, B., Stratta, G., & on behalf of the FIGARO collaboration 2013, Greiner et al. (2015) have carefully reproduced its spectrum arXiv:1305.3194 within the magnetar central engine scenario and interpreted Golenetskii, S., Aptekar, R., Mazets, E., et al. 2011, GRB Coordinates the observations. With the parameters presented in Table 1, it Network, 12663, 1 6 Greiner, J., Mazzali, P. A., Kann, D. 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