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Acta Polytechnica Vol. YY No. X/ZZZZ Search for gravitational waves from supernovae and long GRBs Maurice H.P.M. van Putten1 1Korea Institute for Advanced Study, Hoegiro, Dongdaemun-gu, Seoul 130-722, Korea, and Department of Astronomy, Sejong University, 98 Gunja-Dong Gwangin-gu, Seoul 143-747, Korea Corresponding author: [email protected] 3 1 0 2 Abstract n We report on evidence for black hole spindown in the light curves of the BATSE catalogue of 1491 long GRBs by a application of matchedfiltering. This observation pointstoastronginteraction oftheblack holewith surroundinghigh J densitymatterattheISCO,inducingnon-axisymmetricinstabilitiessustainedbycoolingingravitationalwaveemission. 6 Opportunities for LIGO-Virgo and the recently funded KAGRA experiments are highlighted, for long GRBs with and ] without supernovae and for hyper-energetic core-collapse supernovae within a distance of about 35 Mpc in the Local E Universe. H . Keywords: Core-collapsesupernovae-longGRBs-framedragging-Kerrblackholes-gravitationalradiation-BATSE h - BeppoSax - matched filtering - LIGO-Virgo - KAGRA. p - o r t 1 Introduction s the Earth’s angular momentum J. By this scaling a property,these experimentsequivalentlymeasuredω [ Gamma-ray bursts (GRBs) and core-collapse super- around a maximally spinning Kerr black hole at a 1 novae (CC-SNe) are by far the most energetic and distance of about 5.3 million Schwarzschildradii. v enigmatic transient events associated with neutron As partofthe gravitationalfield, the frame drag- 4 stars and mass black holes. A key objective is to gingangularvelocityω isacleananduniversalagent 6 9 identify the nature of their explosion mechanism. inducing non-thermal radiation processes in space- 0 Extremely powerful events are unlikely powered time around rotating black holes. Relativistic frame . by their presumably prodigious output in MeV neu- draggingis encounteredas ω approachesthe angular 1 0 trinos. They may, instead, be powered by rota- velocity ΩH of the black hole itself. 3 tion (e.g. [4]). GRB 030329/SN 2003dh and GRB Frame dragging around rapidly rotating black 1 031203/SN2003lwarehyper-energeticevents,requir- holes enables transfer of a major fraction of its spin : v ing anenergyreservoirthat exceeds the maximalro- energytosurroundingmatterviaaninnertorusmag- i tational energy of a proto-neutron star (PNS) by an netosphere simultaneously with transfer of a minor X order of magnitude [27]. These anomalous super- fraction to infinity in the form of ultra-relativistic r a novae - of “Type I X” - practically rule out PNS as outflowsalongthespinaxis. Thefirstcanbeseenby universalinnerenginetoallcore-collapsesupernovae. an equivalence in poloidal cross-section of the inner Inlightofthesehyper-energeticeventsandthedi- and outer faces of a torus in suspended accretion to versity in GRBs in durations and associations (with the magnetospheres of neutron stars [19, 23]. The and without supernovae, e.g., listed in [27]), we here second is described by a potential energy E = ωJ p turn to inner engines hosting a rotating black hole for test particles with angular momentum J . Here, p surrounded by high-density matter. These systems E assumesenergiesontheorderofUltraHighEnergy appearnaturallyinmergersofneutronstarswithan- Cosmic Rays (UHECRs) for particles in superstrong other neutron star or companion black hole, as well magnetic fields, typical for the catastrophic events as in core-collapse of relatively mass stars. underconsideration[25]. Framedraggingisherebya causal mechanism for the onset of a two-component outflow,comprisingabaryon-richwindfromaninner 1.1 Frame dragging induced outflows disk or torus collimating the latter in the form of a According to the Kerr metric, the angular momen- baryon-poor jet. tum of rotating black holes induces frame dragging. A two-component outflow with different baryon Frame dragging has recently been measured by the loading is advantageous for GRB-supernovae, whose LAGEOSII[6]andGravityProbeB[10]satelliteex- GRB emissions are generally attributed to dissipa- periments around the Earth, manifest in an angular tion of ultra-relativistic baryon-poor outflows and velocity ω ∼ J/r3 at an orbital radius r and given whose supernovae can be attributed to irradiation Acta Polytechnica Vol. YY No. X/ZZZZ from within [23], such as by impulsive momentum energyemissionproducedbydissipationoftheafore- transferofinternalmagneticwindsontotheremnant mentioned baryon poor outflows is a characteristic stellar envelope. The efficiency of the latter favors imprint of black hole spindown. relativelybaryon-richwinds[27],whichgenerallywill The above suggests extracting a normalizedlight produceasphericalexplosions. Thesetwo-component curve(nLC)oflongGRBs,toidentifytheanticipated outflows circumvent the limitations of neutron stars late time, exponentialdecay. Here,we reportonthis withapproximatelyuniformbaryon-loadingthrough- study using a recent implemented matched filtering out their wind, rendering these less amenable to [25], to identify a model light curve in the complete making hyper-energeticsupernovaewith a successful BATSE catalogue of 1491 long GRBs. Matched fil- GRB. tering allows for an accurate extraction of a normal- izedlightcurve,inwhichfluctuations onallinterme- diate time scales are filtered out, that can be used 1.2 If not a pulsar, how to identify to validate model templates. We apply this to vari- rotation? ousmodeltemplates representingspindown,ofblack holes and (proto-)neutron stars. In our model, the T90 durations of long GRBs is attributed to the lifetime of rapid spin of the black 1.3 EM priors to GW searches hole. It sets the duration for energy and angular momentum transfer from the black hole mostly onto Properties of the inner engine of hyper-energetic su- the surrounding matter. When the black hole has pernovaeandlongGRBsintheelectromagneticspec- slowed down sufficiently, this interaction ceases, and trum of radiation can provide valuable priors to theinneraccretiondiskortoruswillfallin,heralding searches for their gravitational wave emissions. By the end of the GRB. That is, a long GRB ends with theverynatureofthesecatastrophicevents,thehigh hyper-accretion onto a slowly spinning black hole, density matter at nuclear densities orbiting at about whoseangularvelocityisapproximatelyequaltothat the Schwarzschildradius of the central engine, is ex- of the ISCO as prescribed by the Kerr metric. pectedtodevelopanon-axisymmetricmassdistribu- Furthermore, our model considers the aforemen- tion in response to exceptionally large energy fluxes. tioned two-component outflow. Any time-variability Ifso,significantemissioningravitationalwavesisin- in the collimated torus wind - in strength or orien- evitable for a sustained period of time, provided by tation-inevitablymodulatestheinnerjetproducing a balance between heating, apparent in MeV neu- the GRB with possibly quasi-periodic variations in trino emission, and cooling, by aforementioned mag- the light curve. The frequency scale of these vari- netic disk winds and gravitational radiation. This ations are those associated with the ISCO around outlook offers some novel opportunities for the ad- the black hole, i.e., on the order of 1 kHz, possibly vanceddetectorsLIGO-VirgoandKAGRAcurrently higher if multipole mass moments are involved and under construction, that are expected to be opera- possibly lower by precession. A search for such high tional within this decade. frequency QPOs requires the highest sampling fre- quencies available for GRB light curves,well beyond 12 normal mean =4.72e+003 10 the64mssamplingintervalintheBATSEcatalogue. σ = 659 8 Following the above, we consider the problem of N6 tracking the evolution of black hole spin, as deter- 4 mined by its interaction with a surrounding torus. 2 Attributedtoframedraggingasindicatedabove,the 30000 3500 4000 4500 5000 5500 6000 6500 7000 vα [km/s] count rate of gamma-ray photons observed should 4 show a near-exponential decay as the angular velocity approaches the fixed point Ω =Ω . 3 BL H ISCO Theevolutionofaninitiallyrapidlyrotatingblack N2 mean =5.68e+003 σ = 860 hole that ensues is mostly in a decrease in its angu- 1 lar momentum and less so in a decrease of its total 0 mass [24, 26]. Since ω and hence E decrease along 3000 3500 4000 4500 5000 5500 6000 6500 7000 vα [km/s] with Ω , the luminosity ofthe baryon-pooroutflows H willdecreaseintheprocessofblackholespindownin Figure 1: Shown are the histograms of the ejection approaching a fixed point ΩH = ΩD. Here, ΩD de- velocities of the sample of [14] of CC-SNe with nar- notes the angular velocity of the inner disk, which is row(top)andbroad(bottom)lineemissionlines. The expectedto closelytrackthe angularvelocityΩISCO mean of the latter is larger than that of the former of the Inner Most Stable Circular Orbit (ISCO), as by 3.9σ. described by the Kerr metric. Thus, an asymptoti- callyexponentialdecayinthe lightcurveofanyhigh Of particular interest are priors to identifying Acta Polytechnica Vol. YY No. X/ZZZZ blackholesorPNS,inviewoftheir dramaticallydif- loss of mass that forms an accretion disk, for which ferent outlook in gravitational wave emission. The we estimate latteroffersabroadrangeofpossibleradiationchan- nels which, however, remain hitherto somewhat un- a 2 R = =0.5963, 0.7303, 0.8433 (1) certain. Examples are acoustic modes, convection, M 5sRg differentialrotation,andmagneticfields[17,15,7,8, 2, 11, 9, 1, 18]. If an electromagnetic prior is found forMNS =3, 2, 1.5M⊙. Thesevaluesareinremark- able agreement with numerical simulations, showing to rule out a PNS, we can direct our attention to black holes as a probable alternative. An attractive a/M = 0.74−0.84 for MNS = 1.5M⊙ [3]. In the merger of a neutron star with black hole compan- possibility, for example, is a prolonged quasi-period ion, an accretion disk will form from tidal break-up emissionbyquadrupolemassinhomogeneitiesornon- aroundthe latter if the black hole is not too massive axisymmetric instabilities in the inner disk or torus (the limit for which is relaxed if it spins rapidly). In attwice the orbitalfrequency, particularlysoif pow- this event, the spin of the black hole is unchanged ered by the spin energy of the black hole. from its spin prior to the merger. Consequently, the rotation of the black hole may be diverse, given by Table 1: Selected supernovae with kinetic energies thediversityspininneutronstar-blackholebinaries. E in units of 1051 erg. Required energy reservoir SN In considering GRBs from rotating black holes, E is expressed in Eˆ =E /E , E =3×1052 erg rot rot c c we associate long/short GRBs with rapidly/slowly (adapted from [27]). spinningblackholes. Theaboveleadstotheperhaps counter-intuitive conclusion that mergers of neutron GRB SN E η Eˆ Prior star-neutron star binaries produce long GRBs, more SN likely so than short GRBs [24]. They may further 2005ap >10 1 >0.3 indet be produced by mergers of neutron stars with black 2007bi >10 1 >0.3 indet holecompanions(e.g. [16,12]), especiallythosewith 980425 1998bw 50 1 1.7 BH rapid spin [19]. Consequently, long GRBs are expected to occur 031203 2003lw 60 0.25 10 BH both with and without supernovae involving rapidly 060218 2006aj 2 0.25 0.25 indet rotating black holes. Notable examples are given in 100316D 2010bh 10 0.25 1.3 BH Table 1 of [27], e.g., GRB 060614with T90 =102 s. 030329 2003dh 40 0.25 5.3 BH 3 A light curve of long GRBs 2 Diversity out of universality Toleadingorder,the evolutionofrotatingblackhole interactingwithsurroundingmatterviaatorusmag- netosphereisdescribedbyconservationofenergyand IncontrasttoTypeIasupernovae,CC-SNearenotof angular momentum associated with the black hole one kindwith both narrowandbroademissionlines, luminosity L , its mass M and angular momentum shown in the histograms of ejection velocities (Fig. H J , satisfying [19] 1) of a sample of CC-SNe compiled by [14]. Those H of broad emission line events are higher on average L =−M˙ , J˙ =−T, (2) H H that those of narrow emission line emission events with a statistical significance in excess of 4 σ. The where L = Ω T associated with the torque T = H H explosionsofthe formerappeartoberelativelymore κ(Ω −Ω ). Here, κ incorporates the physical and H D energetic. geometrical properties of the inner torus magneto- Rapidly rotating black holes (Ω > Ω , sphere, and Ω is taken to be tightly correlated to H ISCO D a/M > 0.36) can form in CC-SNe and mergers of Ω mentioned earlier. Upon numerical integra- ISCO two neutron stars. If the progenitor of the former is tion of (2), a model light curve can be calculated amemberofashortperiodbinary,arapidlyrotating fromthe resulting baryon-pooroutflow as a function blackholeisformedwitharotationalenergybetween ofΩ =Ω (t) andθ =θ (t) in its dependence on H H H H about one- and two-thirds of the extremal value for the radius R = R of the inner disk. For our D ISCO Kerrblackholes. Inparticular,dimensionlessspecific intended leading order analysis, we assume that the angular momenta a/M = 0.7679 and a/M = 0.9541 photoncountrateisproportionaltotheluminosityin are found with E /Emax = 0.3554 and, respec- the baryon poor outflow. Fig. 2 shows the resulting rot rot tively, E /Emax = 0.6624. Neutron star-neutron template, scaled to a duration of about one minute. rot rot starmergersformrapidlyrotatingblackholesofrela- Afinitepolarcapsupportsanopenmagneticflux tivelysmallmass,M,essentiallythesumofthemass tube to infinity, while the remainder of the black M of individual neutron stars except for a minor hole event horizon is connected to the inner disk or NS Acta Polytechnica Vol. YY No. X/ZZZZ torus via an inner torus magnetosphere. The time- quasi-periodic, in the BATSE data (Fig. 3) that are averaged luminosity of the jet along the open mag- notrepresentativefortheevolutionoftheblackhole. netic flux tube that results from the action of frame These include, without being exhaustive, precession dragging, satisfies the angular scaling [23] of the disk or black hole and instabilities, in the accretion disk, the inner torus magnetosphere and in 4 hL (t)i∼1051 M1 θH(t) erg s−1 (3) the interface between baryon-poor jet and the sur- j (cid:18)T90/30s(cid:19)*(cid:18) 0.5 (cid:19) + rounding baryon-rich disk winds, as well as fluctuations in the dissipative fronts due to turbulence. To with further dependence on the angular velocity of this end, anormalizedlightcurve(nLC) is extracted the black hole according to L ∝Ω2 z2E , E ∝ j H k,T k,D by an ensemble average of individually normalized (Ω R )2e(z), e(z)= 1− 2 , R ≡zM. Here, we light curves defined by a best-fit to a template upon D D 3z T consider the geometricqalansatz θ4 ∝zn with n=2. scaling and translation of time and count rate. H (Here,n=2correspondstotheexpansionofthesur- faceareaAH =A1z+A2z2+···ofthepolarcapasa functionoftheradiusoftheinnerdisk.) Fig. 2shows the model light curve produced by (3) following (2). 1 1 0.9 0.9 (a.u.)LGRB0000....5678 θθ/max()HH000...678 0.4 0.5 0.3 0.4 0 20 40 60 0 20 40 60 time [s] time [s] 1 1 0.9 0.9 u.)0.8 u.)0.8 a.0.7 a.0.7 (RB0.6 (RB0.6 G G L0.5 L0.5 0.4 0.4 0.3 0.3 0.2 0.4 a0/.M6 0.8 1 0.4 0(.θ6/max(θ0.)8 1 Figure 3: Compilationof the complete BATSE cata- H H logue of 1491 light curves of long GRBs, sorted by 2 Figure 2: The template light curve in gamma-rays s <T90 < 1307 s. Each light curve shown represents for an initially extremal black hole, shownas a func- the sum of the photon count rate in all four BATSE tion of time (top left), dimensionless angular mo- energychannels,issmoothedwithatimescaleof2.56 mentum (bottom left), and the associated horizon s and is plotted as a function of time normalized to half-opening angle θH (right). During initial spin- T90. (Reprinted from [28].) down,theriseisduetoamarkedincreaseofθ with H the expansion of the ISCO, leading to a maximal lu- Fig. 4 shows the results along with the residuals, minosity at about 16% of the duration of the burst. showingconvergenceforverylongbursts(T90 >20s) There is anaccompanyingdecreaseinthe totalmass to Template A (Fig. 2). The results are sub-optimal of the black hole [24, 27]. forothermodeltemplates,hereTemplateBforspin- down against surrounding matter beyond the ISCO Thus, the light curve (2) is based on two posi- 1 satisfyingΩ = Ω ,andTemplateC,forspindown tive correlations, in the GRB luminosity with ω and D 2 H of a PNS. θ with the radius of the ISCO. For the latter we H The preferred match to Template A establishes use the Ansatz n=2, a choice among a few integers confidenceinthenaturalinviewofspindownagainst by insisting on analyticity. We now seek validation matter at the ISCO,that representsa suspended ac- of this Model A in the BATSE light curves of long cretionstatewithaluminousoutputingravitational GRBs by application of matched filtering. radiation [20]. A detailed analysis points to a sensitivity distance of about 35 Mpc by the advanced 4 Normalized GRB light curve gravitational wave detectors LIGO-Virgo and KA- GRA [26], by extrapolating the sensitivity distance To extract an intrinsic light curve of long GRBs, determinedfrommodelinjectionsintothestrainam- we set out to filter out all fluctuations, randomly or plitude noise of the TAMA 300, shown in Fig. 5. Acta Polytechnica Vol. YY No. X/ZZZZ 2 s < T90 < 20 s T90 > 20 s 0.2 0.2 1 1 count rate (a.u.)0.5 nTLeCmAp l a t e A 0.01 d± e3vσiation count rate (a.u.)0.5 nTLeCmAp l a t e A 0.01 d± e3vσiation 0 −0.1 0 −0.1 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 0.4 0.4 1 1 count rate (a.u.)0.5 nTLeCmBp l a t e B 0.02 d± e3vσiation count rate (a.u.)0.5 nTLeCmBp l a t e B 0.02 d± e3vσiation 0 −0.2 0 −0.2 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 0.5 0.5 1 1 count rate (a.u.)0.5 nTLeCmCp l a t e C 0 d± e3vσiation count rate (a.u.)0.5 nTLeCmCp l a t e C 0 d± e3vσiation 0 −0.5 0 −0.5 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 −1 0 1 2 3 normalized time normalized time normalized time normalized time Figure 4: Shown are the nLC (thick lines) generated by model templates AC (thin lines) for the ensemble of 531 long duration bursts with 2 s < T90 < 20 s (left) and the ensemble of 960 long bursts with T90 >20 s (right) and the associated deviations for Templates AC. Here, the standard deviation σ is calculated from the square root of the variance of the photon count rates in the ensemble of individually normalizedlight curves as a function of normalized time. (Reprinted from [28].) D=0.07 Mpc to a similar suspended accretion state catalyzing 2000 1800 mTSoMdeFl ( M = 1 0 Mο) black hole spin energy into powerful winds. eLISO TSMF± 1σ 1600 may test for suspended accretion by searches for 1400 an accompanying low-frequency emission in gravita- frequency [Hz]11802000000 tfliaornianlgwianvetsh,enogtaalabclyticfrommicSrgorqAua*s.aTrhGeRTSyp1e9B15X+-1ra0y5 600 may further illustrate the suspended accretion state 400 in a galactic microquasar [22]. 200 Fig. 4 validates our model for black hole spin- 00 5 10 tim1e5 [s] 20 25 30 downmostlikely againstmatter atthe ISCO,rather than further out or the spindown of (proto-)neutron Figure 5: The long duration negative chirp can be stars. As a corollary, some of the neutron star- searched for using a dedicated time-sliced matched neutron star mergers are expected to long GRBs, filtering procedure, here illustrated following signal more likely so than short GRBs. injection in TAMA 300 noise data. It points to a Ourresultspointtospecifichigh-frequencychirps sensitivity distance of about 35 Mpc for the upcom- bothinGWsofinteresttoLIGO-VirgoandKAGRA, ing advanced detectors. (Reprinted from [26].) and in intensity modulations in prompt GRB emissions to some of the gamma-ray satellite missions. For the first, we estimate a sensitivity distance to be 5 Discussion and conclusions about 35 Mpc for the advanced generation of gravitational wave detectors, indicated in Fig. 5. Some hyper-energetic supernovae - of Type I X - appear to require an energy reservoir that exceeds Acknowledgement the maximal rotational energy of a PNS. GRB- supernovae ideally has an inner engine that pro- TheauthorthanksM.DellaValleandthe organizers duces simultaneously a baryon-rich wind to power fortheinvitationtoparticipateatthisworkshopand the supernova and a baryon-poor jet to power the the referee for constructive comments. GRB.These andotherconsiderationspointto auni- versal inner engine in the form of a rotating black References hole, whose diversity in spin [19] can account for short/long GRBs from hyper- and suspended accre- [1] Andersson, N., Ferrari, V., Jones, D. I., et al. tion [23]. 2011, Gen. Rel. Gravit., 43, 409 TheFanaroff-RileyclassI andIIradio-loudAGN may represent a closely related dichotomy for super- [2] Arras, P., Flanagan, E. E., Morsink, S. M., et massive black holes, where the latter may be related al. 2003,ApJ, 591, 1129 Acta Polytechnica Vol. YY No. X/ZZZZ [3] Baiotti, Giacomazzo & Rezzolla, 2008, Phys. [27] vanPutten,M.H.P.M.,DellaValle,M.,&Levin- Rev. D, 78, 084033 son, A., 2011, A&A, 535, L6 [4] Bisnovatyi-Kogan, G.S., 1970, Astron. Zh., 47, [28] van Putten, M.H.P.M., 2012, Prog. Theor. 813 Phys., 127, 331 [5] Bromberg, O., Levinson, A., & van Putten, M.H.P.M., 2006, NewA, 11, 619 DISCUSSION [6] Ciufollini, I., & Pavils, E.C., 2004, Nature, 431, 958 J. Beal: Is there anisotropy in the emitted gravitational radiation? [7] Cutler, C. 2002, Phys. Rev. D, 66, 084025 M. van Putten: The anisotropy in quadrupole [8] Cutler, C., & Thorne, K. S. 2002, Proc. emissions is known to be small, about a factor of GR16, Durban, South Africa, 2001 1.58 at most. [arXiv:astro-ph/0204090] [9] DallOsso, S., Shore, S. N., & Stella, L. 2009, B. Czerny: (a) GW efficiency will depend strongly MNRAS, 38, 1869 on the m in azimuthal modes. Are low m more im- portant in the Papaloizou-Pringle instability? (b) [10] Everitt, C.W.F., et al., 2011, Phys. Rev. Lett., Why don’t you use the term “hyper nova”? (c) How 106, 221101 sensitive are your GRB templates to the detailed as- [11] Howell,E.,Coward,D.,Burman,R.,etal.2004, sumptions that go into BZ efficiency? MNRAS, 351, 1237 M. van Putten: (a)In [5], we consideredthe prob- [12] Klu´zniak,W.,&Lee,W.H.,1998,ApJ,494,L53 lem of the spectrum in gravitational wave emission using a toy model for a magnetized disk. The re- [13] Kumar, P., Narayan, R., Johnson, J.L., 2008, sults indicate a dominantemissioninm=2. In[21], Science, 321, 376, ibid. MNRAS, 388, 1729 I extended the PP instability analysis to tori with [14] Maurer, J. I., Mazzali, P. A., Deng, J., et al. finite width, andfoundthatthe lowm modes (start- 2010, MNRAS, 402, 161 ing with m = 1) become unstable first in response to thermal or magnetic pressures. Both results are [15] Owen, B. J., Lindblom, L., Cutler, C., et al. fortunate, pointing to major emission in quadrupole 1998, Phys. Rev. D, 58, 084020 radiation,thatfallswithin the limitedbandwidthof [16] Paczynski, B. 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Lett., cific to serve as a prior on the inner engine. 87, 091101 (c) BZ proposed an open model for a black hole luminosityentirelyinopenoutflows,sustainedbyac- [21] van Putten, M.H.P.M., 2002, ApJ, 575, L71 cretion of magnetized flows with no feedback onto [22] van Putten, M.H.P.M., & Eikenberry, S., the inner accretion disk. The black hole evolves ac- arXiv:astro-ph/0304386 cording to the net result of losses (in energy and angular momentum) in magnetic outflow and gain by [23] van Putten, M.H.P.M., & Levinson, A., 2003, accretion. Hyper-accretionwilllikelycausetheblack ApJ, 584, 937 hole to spin up continuously up to close to maximal [24] van Putten, M.H.P.M., 2008, ApJ, 684, L91 rotation [13]. In associating the duration of hyper- accretionwiththeobservedT90ofthebursts,amodel [25] vanPutten,M.H.P.M.,&Gupta,A.,2009,MN- light curve from a baryon poor jet along the black RAS, 396, L81 holespinaxisshouldbeincreasing,followedbyarel- [26] van Putten, M.H.P.M., Kanda, N., Tagoshi, H., atively sharp drop off when accretion ceases. This is Tatsumi,D.,Masa-Katsu,F.,&DellaValle,M., atodds with the gradualandextendeddecayseenin 2011, Phys. Rev. D, 83, 044046 the nLC obtained by Templates A-C (Fig. 4).