Table Of ContentMon.Not.R.Astron.Soc.000,1–??(000) Printed11December 2013 (MNLATEXstylefilev2.2)
Signatures of magnetar central engines in short GRB lightcurves
1⋆ 2 3 2 4
A. Rowlinson , P. T. O’Brien , B. D. Metzger , N. R. Tanvir , A. J. Levan
1AstronomicalInstitute“AntonPannekoek”,UniversityofAmsterdam,Postbus94249,1090GEAmsterdam,TheNetherlands
2DepartmentofPhysics&Astronomy,UniversityofLeicester,UniversityRoad,Leicester,LE17RH,UK
3 3DepartmentofAstrophysicalSciences,PeytonHall,PrincetonUniversity,Princeton,NJ08544,USA
1 4DepartmentofPhysics,UniversityofWarwick,CoventryCV47AL,UK
0
2
n 11December 2013
a
J
3 ABSTRACT
A significant fraction of the Long Gamma-ray Bursts (LGRBs) in the Swift sample have a
] plateau phase showing evidence of ongoing energy injection. We suggest that many Short
E
Gamma-rayBursts(SGRBs)detectedbytheSwiftsatellitealsoshowevidenceofenergyin-
H jection.ExplainingthisobservationwithinthetypicalSGRBprogenitormodelischallenging
. aslatetimeaccretion,oftenusedtoexplainplateausinLGRBs,islikelytobeabsentfromthe
h
SGRBpopulation.Alternatively,itispredictedthattheremnantofNS-NSmergersmaynot
p
collapseimmediatelytoaBH(orevencollapseatall),forminginsteadanunstablemillisec-
-
o ondpulsar(magnetar)whichpowersaplateauphaseintheX-raylightcurve.
r ByfittingthemagnetarmodeltoalloftheSwiftSGRBsobserveduntilMay2012,wefind
t
s thatabouthalfcanbeclearlyfittedwithamagnetarplateauphasewhiletherestareconsistent
a
withformingamagnetarbutthedataareinsufficienttoproveaplateauphase.Moredata,both
[
atearlytimesandalargersample,arerequiredtoconfirmthis.Thismodelcanbetestedby
1 detectingthegravitationalwaveemissionfromeventsusingthenextgenerationgravitational
v waveobservatories.
9
Keywords:
2
6 Gamma-RayBursts,Magnetars
0
.
1
0
3 1 INTRODUCTION lightcurves (Nouseketal. 2006; O’Brienetal. 2006; Zhangetal.
1 2006;Evansetal.2009).Thesteepdecayphaseisassociatedwith
: Following the launch of the Swift satellite (Gehrelsetal. 2004),
v high latitude emission from the prompt emission followed by a
it has been possible to place tighter constraints on the na-
i late emission plateau giving the plateau phase (Tagliaferrietal.
X ture of short gamma-ray bursts (SGRBs). The detection of their
2005; Goadetal. 2006). The fluence of thisplateau can be com-
faint and rapidly fading X-ray afterglows has led to the iden-
r parabletothefluenceofthepromptemission(O’Brienetal.2006;
a tification of optical afterglows and in many cases candidate
Marguttietal. 2012), and typically they occur from 102 – 103 s
host galaxies (for example GRB 050509B, Gehrelsetal. 2005;
till 103 – 104 s after the trigger time. The plateau is thought to
Hjorthetal. 2005). These observations have provided significant
provideevidenceofongoingcentralengineactivity(Nouseketal.
support for the popular compact binary merger progenitor theo-
2006;Zhangetal.2006).Evansetal.(2009)studied162GRBsin
ries,i.e.thecoalescenceof twoneutronstars(NS)oraNSanda
the Swift sample identifying a “canonical” lightcurve in 42% of
black hole (BH) (Lattimer&Schramm 1976; Eichleretal. 1989;
GRBX-raylightcurves,including2(051221Aand060313)outof
Narayan,Paczynski,&Piran 1992). However, without the coin-
11SGRBsanalysed.
cident observation of gravitational waves by observatories like
LIGO (Laser Interferometry Gravitational-wave Observatory) we Although studies of flares and plateaus are typically con-
aremissingthesupporting“smokinggun”observationforthispro- ducted for LGRBs, fainter versions are evident in many SGRB
genitortheory. X-ray lightcurves suggesting a long lived central engine (e.g.
Observed features in X-ray lightcurves suggest longevity of Marguttietal.2011).ThisisproblematicforSGRBprogenitorthe-
the central engine of GRBs, for example late time flares (e.g. ories as accretion is expected to end withina few seconds (pow-
Curranetal.2008;Marguttietal.2010;Bernardinietal.2011)and eringrelativisticjets;Rezzollaetal.2011) and onlyasmall frac-
plateaus(e.g. Nouseketal.2006;Zhangetal.2006).GRBswhose tionofthemergermassisavailable(0.01–0.1M⊙ althoughthis
X-raylightcurveshaveasteepdecayandaplateauphasefollowed is dependant on the NS equation of state, Lee&Ramirez-Ruiz
byastandardafterglowphase,havebeenidentifiedas“canonical” 2007). Additionally, it is thought that the accretion disk gets de-
stroyedafterafewseconds(e.g.Metzger,Piro,&Quataert2008).
Therehavebeenstudiesoffallbackaccretion,inwhichtheNSis
⋆ E-mail:[email protected] shredded and parts (6 10% of the original disk mass) are flung
(cid:13)c 000RAS
2 A. Rowlinsonet al.
GRB α1 Γx,1 T1 α2 Γx,2 T2 α3 Γx,3 Prob.Chance
(s) (s) Improvement
2ormorebreaks
051221A 1.43+0.01 2.03+0.20 2935+714 0.059+0.22 1.91+0.23 24370+4631 1.41+0.08 2.06+0.19 1×10−4%
−0.01 −0.19 −785 −0.11 −0.22 −2823 −0.07 −0.18
060313 1.84+0.85 1.7+1.2 0.74+0.08 1.82+0.16 7467+1511 1.65+0.12 2.50+0.22 6×10−20%
−0.37 −0.9 −0.09 −0.10 −1491 −0.11 −0.28
061201 3.09+0.66 1.85+1.03 0.54+0.13 1.44+0.20 2209+802 1.84+0.17 2.26+0.38 2×10−3%
−0.46 −0.53 −0.14 −0.19 −587 −0.14 −0.42
070724 0.97+0.12 1.45+0.73 79+10 -1.13+0.69 1.66+0.24 110+2 10+0.00 1×10−5%
−0.05 −0.64 −35 −1.01 −0.23 −3 −4.33
090426 2.12+0.36 33+125 0.21+0.31 1.85+0.36 260+140 1.04+0.07 2.14+0.14 2×10−14%
−0.45 −3 −0.34 −0.24 −127 −0.06 −0.14
090515 2.76+0.55 0.30+0.00 0.28+0.07 1.85+0.17 156+9 2.51+0.59 2.12+0.39 3×10−32%
−0.10 −0.30 −0.03 −0.16 −27 −0.87 −0.33
100625A 3.63+0.01 1.90+2.40 0.36+0.36 2.09+0.30 222+52 3.15+0.94 2.66+0.53 0.11%
−0.25 −1.10 −0.63 −0.29 −50 −0.85 −0.83
100702A 1.67+0.15 0.59+0.4 0.74+0.18 2.05+0.13 194+14 4.86+0.52 2.41+0.28 2×10−43%
−0.18 −0.4 −0.18 −0.13 −6 −0.26 −0.26
101219A 0.79+0.04 1.33+0.72 195+7 10+0.00 9×10−3%
−0.04 −0.75 −12 −2.40
120305A 2.88+0.30 2.2+1.4 0.18+0.29 1.94+0.21 156+11 5.11+0.55 2.510.72 0.17%
−0.23 −0.9 −0.29 −0.20 −10 −0.52 0.44
1break
051210 0.65+0.04 1.21+0.25 137+8 3.52+0.25 3.11+0.44 1×10−8%
−0.04 −0.15 −6 −0.19 −0.65
060801 0.53+0.05 1.59+0.23 315+21 5.83+0.86 2.18+0.63 1×10−3%
−0.06 −0.22 −30 −0.76 −0.43
070714A 2.23+0.18 123+4 0.62+0.06 2.24+0.33 4×10−6%
−0.04 −45 −0.05 −0.33
070809 1.42+0.05 1.65+1.01 233+96 0.52+0.06 1.35+0.18 3×10−3%
−0.04 −0.40 −68 −0.06 −0.13
080426 1.94+0.15 15+18 1.18+0.05 2.03+0.26 0.018%
−0.14 −7 −0.05 −0.24
080905A 0.44+0.05 0.89+0.56 126+45 2.51+0.30 1.53+0.29 0.03%
−0.05 −0.41 −55 −0.25 −0.27
080919 0.86+0.04 2.31+1.01 351+195 4.83+0.77 2.35+1.01 0.02%
−0.03 −0.83 −55 −0.84 −0.83
090510 0.80+0.01 1.78+0.14 1412+136 2.18+0.17 2.22+0.20 1×10−6%
−0.01 −0.14 −192 −0.17 −0.16
090621B 4.06+0.01 5+5 0.72+0.18 3.40+1.40 3×10−5%
−0.49 −1 −0.16 −1.00
091109B 4.02+0.01 4+1 0.64+0.08 2.04+0.55 4×10−4%
−0.32 −1 −0.09 −0.37
111020A 1.63+0.62 124+38 0.76+0.05 2.18+0.49 0.02%
−0.05 −123 −0.04 −0.43
120521A 1.20+0.05 1.81+0.36 283+13 9.98+0.02 0.12%
−0.05 −0.29 −17 −2.25
Nobreaks
050509B 1.32+0.06 1.92+1.13
−0.04 −0.52
050813 1.27+0.04 2.70+4.30
−0.03 −1.20
050906 >1.28
051105 >1.33
060502B 0.95+0.04 2.10+2.77
−0.03 −0.81
061217 1.29+0.08 1.40+1.13
−0.05 −0.86
070209 >1.23
070429B 1.54+0.05 3.10+1.00
−0.04 −1.40
070729 1.29+0.05 1.62+0.86
−0.04 −0.43
070810B >1.36
071112B >0.87
080702A 1.13+0.04 1.99+0.75
−0.04 −0.67
081024A 0.99+0.03 1.82+0.64
−0.02 −0.55
081101 >1.21
081226 1.45+0.05 3.84+0.96
−0.04 −1.93
090305A 1.42+0.05
−0.04
100117A 0.97+0.01 2.59+0.48
−0.01 −0.40
100206A 1.80+0.05 3.30+3.30
−0.04 −1.30
100628A 1.00+0.01
−0.01
110112A 1.00+0.06 2.15+0.39
−0.05 −0.31
111117A 1.45+0.05 2.20+0.40
−0.06 −0.37
Table1.TheSwiftSGRBsampleandtheresultsofbrokenpowerlawfitstotheobservedBAT-XRTdatainthe0.3-10keVband(asdescribedinthetext)and
theX-rayspectralindiciesforeachregime(Γx).Thesearesubdividedintothosewith2ormoresignificantbreaksintheirlightcurves,thosewith1breakand
thosewithnosignificantbreaks.Wherevaluesareleftblanktherewasinsufficientdataavailabletoconstrainthem.Thelastcolumnshowstheprobabilitythat
thisfitisachanceimprovementonasimplermodel.
into highly eccentric orbits which accrete onto the central en- onds.Cannizzo,Troja,&Gehrels(2011)haveattemptedtoexplain
gine at late times giving flares in the X-ray lightcurve (Rosswog plateausbyintroducingabandofmaterialatalargedistancefrom
2007). Flares may also be caused by Toomre instabilities within thecentralengine.Cannizzo,Troja,&Gehrels(2011)suggestthat
theaccretiondisk(Perna,Armitage,&Zhang2006),althoughthis therequiredreservoirofmaterialcouldbeprovidedviatheaccre-
doesnotexplainplateauemissionorlatetimeflaresastheSGRB tiondiskmovingoutwards(duetohavingalargeamountofangu-
accretion disks are expected to accrete within the first few sec-
(cid:13)c 000RAS,MNRAS000,1–??
Signaturesof magnetarcentralengines inshortGRBlightcurves 3
GRB z T90 Γγ Fluence Host Hostoffset OpticalAfterglow
(s) (10−7ergcm−2s−1) (arcsec)
2ormorebreaks
051221A(1) 0.55 1.4±0.2 1.39±0.06 11.6±0.4 y 0.12±0.04 Y
060313(2) (0.72) 0.7±0.1 0.71±0.07 11.3±0.5 ? 0.4±0.6 Y
061201(3) 0.111 0.8±0.1 0.81±0.15 3.3±0.3 ? 17 Y
070724A(4) 0.46 0.4±0.04 1.81±0.33 0.30±0.07 y 0.7±2.1 N
090426(5) 2.6 1.2±0.3 1.93±0.22 1.8±0.3 y 18 Y
090515(6) (0.72) 0.04±0.02 1.60±0.20 0.21±0.04 n - Y
100625A(7) (0.72) 0.33±0.03 0.90±0.10 2.3±0.2 y 0±1.8 N
100702A(8) (0.72) 0.16±0.03 1.54±0.15 1.2±0.1 n - N
101219A(9) 0.718 0.6±0.2 0.63±0.09 4.6±0.3 y - N
120305A(10) (0.72) 0.10±0.02 1.00±0.09 2.0±0.1 n - N
120521A(11) (0.72) 0.45±0.08 0.98±0.22 0.8±0.1 n - N
1break
051210(12) (0.72) 1.4±0.2 1.10±0.30 0.8±0.1 ? 2.8±2.9 N
060801(13) 1.13 0.5±0.1 0.47±0.24 0.8±0.1 ? 2.4±2.4 N
070714A(14) (0.72) 2.0±0.3 2.60±0.20 1.5±0.2 n - N
070809(15) 0.219 1.3±0.1 1.69±0.22 1.0±0.1 y 20 Y
080426(16) (0.72) 1.7±0.4 1.98±0.13 3.7±0.3 n - N
080905A(17) 0.122 1.0±0.1 0.85±0.24 1.4±0.2 y 9 Y
080919(18) (0.72) 0.6±0.1 1.10±0.26 0.7±0.1 ? - Y
090510(19) 0.9 0.3±0.1 0.98±0.20 3.4±0.4 y 1 Y
090621B(20) (0.72) 0.14±0.04 0.82±0.23 0.7±0.1 n - N
091109B(21) (0.72) 0.30±0.03 0.71±0.13 1.9±0.2 ? 8 Y
111020A(22) (0.72) 0.40±0.09 1.37±0.26 0.7±0.1 n N
Table2.PropertiesoftheSGRBsample,includingT90,ΓγandFluence(15–150keV).Theseobservedquantities,includinghostgalaxyassociations,offsets
andopticalafterglowdetections,arefrompublishedpapersandGCNs(referenceslistedbelow),hostoffsetsarequotedwitherrorsifpublished.Whenthe
redshiftisnotknown,theaverageredshift0.72wasusedandthisisshownusingbrackets.
(1)Cummingsetal.(2005b);Soderbergetal.(2006)(2)Markwardtetal.(2006a);Romingetal.(2006)(3)Markwardtetal.(2006b);Strattaetal.(2007)
(4)Parsonsetal.(2007);Bergeretal.(2009);Kocevskietal.(2010)(5)Satoetal.(2009);Antonellietal.(2009);Xinetal.(2011)(6)Barthelmyetal.
(2009);Rowlinsonetal.(2010a)(7)Barthelmyetal.(2010a);Tanvir&Levan(2010)(8)Baumgartneretal.(2010)(9)Krimmetal.(2010);
Chornock&Berger(2011)(10)Palmeretal.(2012)(11)Cummingsetal.(2012)(12)Satoetal.(2005b);LaParolaetal.(2006)(13)Satoetal.(2006b);
Cucchiaraetal.(2006)(14)Barthelmyetal.(2007)(15)Krimmetal.(2007);Perleyetal.(2008)(16)Cummingsetal.(2008a)(17)Cummingsetal.(2008b);
Rowlinsonetal.(2010b)(18)Baumgartneretal.(2008);Immler&Holland(2008);Covinoetal.(2008)(19)Ukwattaetal.(2009);dePasqualeetal.(2010);
McBreenetal.(2010)(20)Krimmetal.(2009b)(21)Markwardtetal.(2009);Levanetal.(2009);Malesanietal.(2009)(22)Sakamotoetal.(2011b)
lar momentum) or ejecta thrown out during the merger in highly of neutron stars. Morrison,Baumgarte,&Shapiro (2004) studied
eccentricorbitsthatcircularisesforminganaccretiondisk. the effect that the equation of state of a NS and rotation would
haveontheremnant of acompact merger,i.e.whether aNSora
AnalternativetheoryisthatduringsomeGRBsamillisecond BHisformed(seealsoShibata&Taniguchi 2006).Theyshowed
pulsar (magnetar) may be formed with enough rotational energy that,evenforthehardernuclearequationsofstate,therotationof
topreventgravitationalcollapse(Usov1992;Duncan&Thompson the NS could increase the maximum mass by ∼ 50% and hence
1992;Dai&Lu1998a,b;Zhang&Me´sza´ros2001).Therotational mergerscouldoftenresultinaNS.Consideringtheparametersof
energyisreleasedasgravitationalwavesandelectromagneticradi- 6 known Galactic NS binaries and a range of equations of state,
ation, causing themagnetar tospin down. If themagnetar issuf- Morrison,Baumgarte,&Shapiro (2004) predict that the majority
ficientlymassiveitmayreachacriticalpointatwhichdifferential ofmergersoftheknownbinarieswillformaNS.
rotation is no longer able to support it, resulting in collapse to a
BH. Assuming constant radiative efficiency, the energy injection The recent discovery of an 1.97 M⊙ NS (Demorestetal.
fromthemagnetarwouldproduceaplateauintheX-raylightcurve 2010) provides further supporting evidence of thepossibilitythat
(Zhang&Me´sza´ros2001)andwouldbefollowedbyasteepdecay high mass magnetars can be formed from NS mergers (the max-
ifthemagnetarcollapsestoaBH.Theprogenitorofthissystemis imum mass of NSs is dependent on the very uncertain NS equa-
typicallythoughttobeacollapsarandLGRBcandidateshavebeen tionofstate,sothisisaconservativelowerlimitonthemaximum
identifiedbyTrojaetal.(2007)andLyonsetal.(2010).However, massofaNS).Ozeletal.(2010b)showthat,foramaximumnon-
it has also been proposed that such a magnetar could be formed rotatingNSmassofMmax =2.1M⊙,themergeroftwoNSswith
by the merger of two neutron stars (Dai&Lu 1998a; Daietal. a total mass 6 1.4M will have a delayed collapse to a BH
max
2006; Yu&Huang 2007) or via the accretion induced collapse (i.e. a magnetar phase). They also predict a regime in which the
(AIC)ofawhitedwarf(WD)(Nomoto&Kondo1991;Usov1992; merged remnant does not collapse toform aBH, inthiscase the
Levanetal. 2006; Metzger,Quataert,&Thompson 2008). A can- total mass is 6 1.2Mmax. If the maximum NS mass is 2.1 M⊙,
didateeventforthisisGRB090515withanunusualX-rayplateau thenthemergeroftwoNSsofmassesupto1.3M⊙ wouldresult
followed by a steep decay (Rowlinsonetal. 2010a). The likeli- inastablemagnetarandthemergeroftwoNSswithlargermasses
hoodofproducingthiseventisdependentontheequationofstate (upto1.5-1.7M⊙)wouldformanunstablemagnetar.Asthema-
(cid:13)c 000RAS,MNRAS000,1–??
4 A. Rowlinsonet al.
GRB z T90 Γγ Fluence Host Hostoffset OpticalAfterglow
(s) (10−7ergcm−2s−1) (arcsec)
Nobreaks
050509B(24) 0.23 0.024±0.009 1.50±0.40 0.2±0.1 y 17.9±3.4 N
050813(25) (0.72) 0.6±0.1 1.19±0.33 1.2±0.5 n - N
050906(26) (0.72) 0.13±0.02 1.91±0.42 0.6±0.3 ? - N
051105(27) (0.72) 0.028±0.004 1.38±0.35 0.2±0.05 ? - N
060502B(28) (0.72) 0.09±0.02 0.92±0.23 0.4±0.05 n - N
061217(29) (0.72) 0.3±0.05 0.96±0.28 0.46±0.08 ? - N
070209(30) (0.72) 0.1±0.02 1.55±0.39 0.11±0.03 n - N
070429B(31) (0.72) 0.5±0.1 1.71±0.23 0.63±0.1 ? - ?
070729(32) (0.72) 0.9±0.1 0.96±0.27 1±0.2 ? - N
070810B(33) (0.72) 0.08±0.01 1.44±0.37 0.12±0.03 ? - N
071112B(34) (0.72) 0.3±0.05 0.69±0.34 0.5±0.1 n - N
080702A(35) (0.72) 0.5±0.2 1.34±0.42 0.4±0.1 n - N
081024A(36) (0.72) 1.8±0.6 1.23±0.21 1.2±0.2 n - N
081101(37) (0.72) 0.2±0.02 1.25±0.20 0.62±0.1 n - N
081226(38) (0.72) 0.4±0.1 1.36±0.29 1.0±0.2 n - N
090305A(39) (0.72) 0.4±0.1 0.86±0.33 0.8±0.1 n - Y
100117A(40) (0.72) 0.30±0.05 0.88±0.22 0.9±0.1 y 0.6 Y
100206A(41) (0.72) 0.12±0.03 0.63±0.17 1.4±0.2 ? - N
100628A(42) (0.72) 0.36±0.009 1.26±0.25 0.3±0.1 y - N
110112A(43) (0.72) 0.5±0.1 2.14±0.46 0.3±0.1 y - Y
111117A(44) (0.72) 0.47±0.09 0.65±0.22 1.4±0.2 y 1.00±0.13 N
Table2–continued
(24)Barthelmyetal.(2005b);Gehrelsetal.(2005)(25)Satoetal.(2005a)(26)Parsonsetal.(2005);Levanetal.(2008),notethisisacandidateextra-galactic
magnetargiantflare(27)Cummingsetal.(2005a);Barbieretal.(2005);Klose,Laux,&Stecklum(2005)(28)Satoetal.(2006a)(29)Parsonsetal.(2006);
Ziaeepouretal.(2006)(30)Sakamotoetal.(2007a)(31)Tuelleretal.(2007);Antonellietal.(2007);Holland,dePasquale,&Markwardt(2007)
(32)Satoetal.(2007a);Berger&Kaplan(2007)(33)Sakamotoetal.(2007b);Thoeneetal.(2007)(34)Fenimoreetal.(2007)(35)Krimmetal.(2008)
(36)Barthelmyetal.(2008)(37)Barthelmyetal.(2008b)(38)AutomatedBATanalysisproducts(39)Krimmetal.(2009a);Cenkoetal.(2009)
(40)Markwardtetal.(2010);Levanetal.(2010);Fongetal.(2010)(41)Sakamotoetal.(2010);Milleretal.(2010);Levanetal.(2010);Bergeretal.(2010)
(42)Barthelmyetal.(2010b);Starling,Beardmore,&Immler(2010);Berger(2010)(43)Barthelmy,Sakamoto&Stamatikos(2011);Levan,Tanvir&Baker
(2011)(44)Sakamotoetal.(2011a);Cenko&Cucchiara(2011);Berger,Fong,&Sakamoto(2011)
jorityofobservedNSshavemasses∼1.4M⊙,itseemsreasonable magnetar (with or without collapse to a BH) which may signify
to predict that many NS mergers could result in a magnetar. The thecoalescenceoftwoNSs.Iffound,thiswouldprovideadditional
stabilityofthefinalmagnetarisdependentonthemaximumpossi- supporttothispopularprogenitortheoryalthoughformingamag-
blemassofaNSwhichisstilluncertain.Itslifetimedependsboth netarviatheAICofaWDisnotruledout.Themagnetarmodelis
ontheratethatadditionalmass(ifany)isaccretedafterformation, consideredinsection3;withadescriptionofthemodelandsample
aswellastherateatwhichangularmomentumisextractedbye.g. used and analysis of the available data. A discussion of the im-
gravitationalwavesormagnetictorques(e.g.Shibata&Taniguchi plications, e.g. for gravitational waves, is given in section 4 and
2006;Oechslin,Janka,&Marek2007). ourconclusions aregiveninsection5.Throughout thiswork,we
Inthispaper,weconsiderallSwiftdetectedSGRBs,T90 62 adopt a cosmology with H0 = 71 kms−1Mpc−1, Ωm = 0.27,
s,observeduntilMay2012withanX-rayaftergloworwhichwere ΩΛ = 0.73. Errorsarequoted at 90% confidence for X-ray data
promptly slewed to and observed by the X-ray Telescope (XRT; andat1σforfitstothemagnetarmodel.
Burrowsetal.2005).ThisallowstheinclusionofSGRBswithout
anX-rayafterglowbut whichdohaveaconstrainingupper limit.
ForalltheSGRBs,weanalysedtheBAT(BurstAlertTelescope;
2 PLATEAUPHASESINSGRBLIGHTCURVES
Barthelmyetal.2005a)databycreatinglightcurvesusingavariety
ofbinninginsignal-to-noiseratiosandtimelookingforevidence Outofoursampleof43SGRBs,showninTable1,only6didnot
ofextendedemissionatthe3σlevelwhereweconsistentlysawex- haveadetectedX-rayafterglow(GRBs050906,051105,070209,
tended emission over more than 30 s(the SGRBswithidentified 070810B 071112B and 081101). Hence, ∼86% of Swift SGRBs
extendedemissionare050724,050911,051227,060614,061006, withapromptslewhavedetectedX-rayafterglows.Theobserved
061210, 070714B, 071227, 080123, 080503, 090531B, 090715A, propertiesoftheSGRBsamplearegiveninTable2.
090916 and 111121A). This procedure recovered all of the ex- The 0.3 – 10 keV observed flux X-ray lightcurves were ob-
tended emission bursts identified by Norris,Gehrels,&Scargle tainedfromtheautomatedanalysispageforeachindividualSGRB
(2010). Hence, our selection criteria excludes SGRBs with ex- fromtheUKSwiftScienceDataCentrewebsite(Evansetal.2007,
tendedemission,whichmayshareacommonprogenitortoSGRBs 2009).TheBurstAlertTelescope(BAT)lightcurveswerecreated
but this remains uncertain. This sample is used to identify those usingstandardpipelinesintheHEASOFTpackagewith3σsignifi-
withaplateau phaseintheir lightcurvessuggesting ongoing cen- cancebins.The15–150keVBATspectrawerefittedinXSPECfor
tralengineactivity.Theseresultsarediscussedinsection2.Asub- eachSGRBandthenextrapolatedtoobtainthefluxat0.3–10keV.
samplewithsufficient dataarethenstudiedforthesignatureofa Usingthisextrapolatedfluxandthenetcount-rateintheBATspec-
(cid:13)c 000RAS,MNRAS000,1–??
Signaturesof magnetarcentralengines inshortGRBlightcurves 5
Figure1.ThesearetheBAT-XRTlightcurves(0.3–10keV,observedflux)sortedinto3groups.a)TheseGRBshave2ormorebreaksintheirlightcurve.b)
GRBswith1breakintheirlightcurve.c)andd)GRBswithnosignificantbreaksintheirlightcurve.
trum,eachcount-ratedatapointintheBATlightcurvewasscaled QDP1.Thesefitswerethenusedtoidentifythosewitha“canoni-
toan0.3–10keVfluxusingasimplepowerlawspectralmodel. cal”likelightcurve.AnXRTspectrumwascreatedforeachregion
ThesewerecombinedwiththeXRTlightcurvestomaketheBAT- ofthelightcurveusingtheautomaticdataproductsontheUKSwift
XRT lightcurves used in this analysis. For later comparison with ScienceDataCentrewebsite(Evansetal.2007,2009).TheSGRB
the magnetar model, these lightcurves were converted into unab- lightcurvesareshowninFigure1.
sorbedfluxlightcurvesandthenintorestframe1-10000keVlumi- WeassumethatF ∝ν−βt−αwhereβ =Γ−1isthespec-
ν
nositylightcurvesusingak-correction(Bloom,Frail,&Sari2001) tralindex,Γisthephotonindex(Γ isthephotonindexmeasured
γ
givinganapproximation toabolometriclightcurve. Therangeof usingBATandΓ isthephotonindexmeasuredusingXRT)and
x
k-correctionsobtainedaretypicallyconsistentwiththerange0.4- αisthetemporalindex.Wedefinethesteepdecayphasefollowing
7asobtainedbyBloom,Frail,&Sari(2001).However,therearea thepromptemissiontohaveapowerlawdecayofα ,afterwhich
1
smallnumberoflargek-corrections(particularlyforGRBs070809, thedecaycanbreaktoadecayofα andafurtherbreaktoα .We
2 3
080905Aand101219A),showingthespectrummaybepoorlyun- alwaysdefineα tobetheshallowestdecayphase, asthisallows
2
derstood at the frequency range we extrapolate to. If no redshift thedirectcomparisonofallplateauphasesinthesubsequentanal-
is known the mean SGRB redshift is used, z ∼ 0.72 (excluding ysis. All SGRBs with 1 or more breaks in their lightcurves have
the redshift for GRB 061201 as the host galaxy association re- aplateauphase. Inthreecases therearemore thantwobreaks in
mainsuncertain;Strattaetal.2007,Tunnicliffeetal.inprep),and the lightcurve. GRB 070724 has a third break at T = 152+18
3 −5
theimplicationsofchoosingthisaverageredshiftarediscussedin (α = 1.15+0.07 andΓ = 1.45+0.48),GRB090515hasathird
4 −0.06 4 −0.29
Section 3.3. All the SGRB observed BAT-XRT lightcurves were breakatT = 241+8 (α = 10+0 )andGRB101219A hasa
4 −10 4 −0.97
fittedwithmultiplepower lawsfromthe finaldecay phase inthe break at T = 241+15 (α = 1.88+0.23 and Γ = 1.63+0.37).
3 −13 3 −0.25 4 −0.49
BAT prompt emissionthroughout the total X-rayafterglow using
1 https://heasarc.gsfc.nasa.gov/docs/software/ftools/others/qdp/qdp.html
(cid:13)c 000RAS,MNRAS000,1–??
6 A. Rowlinsonet al.
Figure2.HistogramsshowingthebreaktimesfortheSGRBlightcurves Figure 3. Histograms showing the temporal indices of the SGRB
with a plateau phase. T1 is the break from the steep decay phase tothe lightcurveswithaplateauphase.α1 istheinitialsteepdecayphasefrom
plateauphasewhileT2 markstheendoftheplateau. Thebluefilledhis- thelastdecayinthepromptemission.α2aretheplateauandshallowdecay
togramscorrespondtotheSGRBsampleusedinthisPaperandoverplotted phaseslopes.α3 isthefinalafterglow decayslope.Thefilledhistograms
inredaretheLGRBvaluesdeterminedbyEvansetal.(2009). correspondtotheSGRBsampleusedinthispaperandoverplottedarethe
LGRBvaluesdeterminedbyEvansetal.(2009).
due to Earth occultation during orbits, giving further gaps in the
The6GRBswhichwereundetectedbyXRTarefittedwithlower lightcurveswhichcouldalsohidefeaturesinthelightcurves.
limitsforα usingtheshallowestdecayallowedbytheBATdata Using the broken powerlaw fit method, we find that 22
1
andtheXRTupperlimit.InTable1,weprovidethelightcurvefits SGRBs(∼50%)areconsistentwithhavingaplateauphaseintheir
for all the SGRBs in the sample. An F-test was conducted using lightcurves, although theplateau phase isnot always directly ob-
theχ2anddegreesoffreedomforeachfittodeterminetheproba- servedduetothegapinthelightcurveprior totheXRTobserva-
bilitythatthefitisachanceimprovementonasimplermodel(i.e. tions.Itishardtoruleoutplateauphasesinothercases(sincethe
anF-testbetweenthemodelprovidedinTable1andamodelwith plateauphase couldbe missedbythesamplingor lost duetothe
1lessbreakinthelightcurve).Weutilisethemethoddescribedin faintnessoftheafterglow).ThosewhichwereundetectedbyXRT
Evansetal.(2009)todeterminethebestfit,i.e.themodelthathas donotrequireextremedecayslopesrelativetotherestofthesam-
themostbreaksandtheprobabilityofbeingachanceimprovement pleofSGRBs.ThebreaktimesoftheSGRBswithplateausaretyp-
onasimplermodelas60.3%. icallyoccuringordersofmagnitude earlierthanfor thecanonical
Thereareseveralcaveatswhichneedtobeconsideredwiththe LGRBs(asshowninFigure2).Thismaybecausedbyouruseof
resultsinthisSectionandforthemagnetarfitsinSection5.3.2.As BATandXRTdatawhereasEvansetal.(2009)useonlytheXRT
SGRBafterglowsareoftenfaintandfaderapidly,theselightcurves dataandisonlyabletofindplateausattimesafterXRThasstarted
andspectracanbepoorlysampledgivinglargeerrorsontheval- observing.However,itisveryrareforXRTtonotobservethesteep
ues in Table 1. This could also cause breaks in the lightcurve to decayphaseforLGRBssotheinclusionofBATdatadoesnotaffect
bemissedduetolargebinsizes(binstypicallycontain20photons the plateau fits (e.g. O’Brienetal. 2006; Willingaleetal. 2007).
in PC mode data so bins could have long durations; Evansetal. Additionally,Evansetal.(2009)discussedwhethertheirtypeband
2007).Additionally,theSwiftsatelliteslewstoobserveGRBsaf- typecLGRBscanbe cannonical (i.e.thosewhich aresteep then
terdetection,leadingtoacharacteristicgapbetweentheBATdata shallow or shallow then steep). They conclude that they are not
andtheXRTdata,andXRTcanonlyobserveforshortwindows, basedontheplateaudecayratesandbreaktimesfortypebandthe
(cid:13)c 000RAS,MNRAS000,1–??
Signaturesof magnetarcentralengines inshortGRBlightcurves 7
Figure 5. The prompt BAT 15 – 150 keV fluence in comparison to the
shallowdecayphaseunabsorbedX-rayfluenceextrapolatedtothe15–150
keV energy band.Symbols areas definedinFigure 4andthe black line
showswheretheshallowdecayphasefluenceisequaltothepromptfluence.
theirlightcurves(bluestars,theGRBsinFigure1a),1break(green
circles,theGRBsinFigure1b) andthosewithnobreaksintheir
lightcurves(redtriangles,theGRBsinFigure1candd).
The BAT fluence (15 – 150 keV) of these GRBs is plotted
againsttheir0.3–10keVfluxat100sinFigure4a.ThoseGRBs
with a plateau tend to be clustered at somewhat higher fluences
andtheirX-rayfluxesaresignificantlyhigher at100s(∼ 10−11
– 10−9 erg cm−2 s−1). The GRBs which do not have a plateau
phase in their lightcurves tend to have faint X-ray afterglows at
100 s (6 2×10−11 erg cm−2 s−1) and relatively low fluences
(62×10−7ergcm−2).Figure4bshowsthereisawidevariation
inXRTfluxat100sforSGRBswithsimilarpromptfluxes.
O’Brienetal. (2006) and Willingaleetal. (2007) found that
Figure4.(a)TheBATfluence(15–150keV)plottedagainsttheXRTun-
thepromptfluenceiscomparabletotheplateaufluenceforLGRBs.
absorbedfluxat100s(0.3–10keV).Bluestarshave2ormoresignificant
Inordertocomparethisresulttooursample,wetooktheaverage
breaksintheirlightcurves,greencircleshave1breakandredtriangleshave
flux for the plateau phase and multiplied it by the time at which
nosignificantbreaksintheirlightcurves.(b)TheBATpeakphotonflux(15-
150keV)againsttheXRTunabsorbedfluxat100sintheobserverframe the decay broke to a more typical afterglow (assuming this com-
(0.3–10keV).Symbolsareasin(a). ponent started at the initialtrigger time) giving the 0.3 –10 keV
fluence. This fluence was then converted to a 15 – 150 keV flu-
enceusingthespectralindexandfittedabsorption.Figure5shows
relativeBATversusXRTfluxesfortypec.WhereasforSGRBs,the thepromptandplateaufluencearegenerallycomparable,whichis
BATobservationsneedincludinginordertoidentifythesteepde- consistentwiththeresultobtainedforLGRBs.Therearefoursig-
cayphase.HistogramsshowingthevariousSGRBdecayslopesfor nificantoutliers(GRBs061201,070724A,080905Aand090515),
thosewithplateauphasesareshowninFigure3withthevaluesfor lying significantly above the one-to-one line, whose plateaus are
canonical LGRBs, determined by Evansetal. (2009). The values significantlymoreenergeticthantheirpromptemission.
forα andα areconsistentwiththeLGRBsample,butthefinal Figure6shows thespectral indiciesplottedagainst thetem-
1 2
decayphase(α )istypicallysteeper thanfortheLGRBcounter- poral indicies for the lightcurves with a plateau phase (values all
3
parts(consistentwiththeresultsobtainedby Marguttietal.2012, tabulatedinTable1).Alsoplottedaretheclosurerelationsforthe
wheretheoveralldecayofSGRBsistypicallyfoundtobesteeper slowcoolingregime(greyband)andthefastcoolingregime(solid
thanLGRBs,howevertheirsampleofSGRBsusedforthisisdom- blacklines) (Zhang&Me´sza´ros 2004). Theseshow thesame be-
inatedbySGRBswithextendedemission).UsingaKolmogorov- haviour identified by Evansetal. (2009) for the canonical sam-
Smirnov test between the values for LGRBs and SGRBs, α is ple of LGRBs. In particular Figure 6b shows evidence of energy
1
consistentwithbeingdrawnfromthesamedistribution(p-value= injection during the plateau phase as described by Evansetal.
0.07),althoughthevaluesforα areunlikelytobefromthesame (2009). These figures can be compared to updated values for the
2
distribution(p-value=0.003)andα arehighlylikelytobedrawn whole GRB sample using the UK Swift Science Data Centre
3
fromcompletelydifferentdistributions(p-value=0.00007).Inthe (www.swift.ac.uk/xrt live cat;Evansetal.2009).
following analysis we consider SGRBs with2 or more breaks in Dainottietal. (2010) identified a correlation between the
(cid:13)c 000RAS,MNRAS000,1–??
8 A. Rowlinsonet al.
Figure7.(a)Theplateauphaseunabsorbedfluxversusthedurationofthis
phase.SymbolsareasdefinedinFigure4.(b)Theplateauphaseluminosity,
usingpublishedredshifts(filledsymbols)ortheaverageredshift(opensym-
bols),versustherestframedurationofthisphase.Thelightgreydatapoints
aretheDainottietal.(2010)sampleofLGRBs.Theblacklineshowsthe
correlationbetweentheluminosityanddurationfortheSGRBandLGRB
sampleswhichisconsistent withtherelationship foundbyDainottietal.
(2010).
plateauphaseluminosityanddurationforLGRBswithacanonical
lightcurve. Using redshifts where available or the average SGRB
redshift(z ∼0.72)andak-correction(Bloom,Frail,&Sari2001)
wecalculatedtheluminosityandrestframedurationsfortheSGRB
sample(XRTfluxesusedaretheobserved valueswhichhavenot
beencorrectedforabsorption).TheseresultsareplottedinFigure
7andtheluminosity–durationcorrelationisidentified.Thefitted
correlationfortheSGRBandLGRBsample,b = −1.29±0.12,
log(a)=48.74±0.44,intrinsicscatterσ =9×10−11±0.01
V
(where L = aTb and the uncertainties on each datapoint
X plateau
andanintrinsicscatterareaccountedforinthefitusingthemethod
describedin D’Agostini2005),isconsistentwiththatforobtained
the LGRB sample (−1.06 ±0.28, 51.06 ± 1.02, although they
didnotaccount fortheintrinsicscatter;Dainottietal.2010).The
SGRBplateauphasesaretypicallymoreluminousandtheplateau
Figure6.Thespectralindexβ versusthetemporalindexαforthethree
isshorterindurationthantheLGRBcounterparts.Thismaybea
regimesofthelightcurveswithaplateauphase:(a)steepdecayphase,(b)
selection affect due to the inclusion of BAT observations in this
plateau phase and (c) standard afterglow phase. Where there is no XRT
spectrumavailableforthesteepdecayphase,theBATspectrumisused.All analysis, and hence finding earlier plateaus. However, when BAT
symbolsareasdefinedinFigure4,thesolidlinesandgreyregionsshow dataareincluded inLGRBanalysistheplateauproperties donot
theclosurerelationsasdefinedbyZhang&Me´sza´ros(2004),andtheblack significantly change (O’Brienetal. 2006; Willingaleetal. 2007)
dashedlineshowswhereα=β+2.
(cid:13)c 000RAS,MNRAS000,1–??
Signaturesof magnetarcentralengines inshortGRBlightcurves 9
additionally,thereisashortageoflongdurationplateausobserved below with an underlying powerlaw component. Previously, the
intheSGRBsample.Cannizzo,Troja,&Gehrels(2011)arguethat plateaudurationandluminositywerecalculatedandtheninputinto
therelationshipidentifiedbyDainottietal.(2010)isdominatedby theequations.Inthiswork,theequationsarefitdirectlytotherest-
selectionaffectsatz>1.5asthereisanobservationalbiasagainst framelightcurves,takingintoaccounttheshapeofthelightcurve
faintplateausduetothelimitingXRTflux.However,SGRBsare (this is a comparable method to that used by Dall’Ossoetal.
typicallyatlowerredshift(theSGRBswithanobservedredshiftin 2011; Bernardinietal. 2012, who fitted a stable magnetar to the
oursamplehaveanaverageredshiftofz∼0.72)sooursamplelies lightcurvesof4LGRBs).Wecanthenusethevaluesofthemag-
wellwithintheregionwhichisnotdominatedbyselectionaffects. netic field and spin period obtained to derive the luminosity and
The plateau phases of GRB lightcurves are typically ex- plateauduration.
plained as ongoing central engine activity, for example on go-
ing accretion onto the central BH. However, ongoing accre-
T =2.05(I B−2 P2 R−6) (1)
tion is problematic for NS-NS and NS-BH merger theories as em,3 45 p,15 0,−3 6
there is insufficient surrounding material to maintain this accre- L ∼(B2 P−4 R6) (2)
0,49 p,15 0,−3 6
tion (Lee&Ramirez-Ruiz 2007). Fallback accretion from ma- B2 =4.2025I2 R−6L−1 T−2 (3)
terial on highly eccentric orbits has been postulated to re- p,15 45 6 0,49 em,3
solve this (Rosswog 2007; Kumar,Narayan,&Johnson 2008; P02,−3 =2.05I45L−0,149Te−m1,3 (4)
Cannizzo,Troja,&Gehrels 2011), however it is unclear how to
where T is the plateau duration in 103 s, L is the
producetherequiredreservoirofmaterialatafixedradius.Inthe plateaulumineomsi,t3yin1049ergs−1,I isthemomento0f,4in9ertiain
remainder of thispaper, wesuggest that theplateauphasescould 45
unitsof1045gcm2,B isthemagneticfieldstrengthatthepoles
bepoweredbyamagnetarformedviathemergeroftwoNSs. p,15
inunitsof1015G,R istheradiusoftheneutronstarin106cmand
6
P0,−3 is the initial period of the compact object in milliseconds.
Theseequationsapplytotheelectromagneticdominatedspindown
3 MAGNETARMODEL regime,asthegravitationalwavedominatedregimewouldbeex-
tremelyrapidandproduceanegligbleelectromagneticsignal.We
The magnetar model predicts a plateau phase in the X-ray
haveassumedthattheemissionis100%efficientandisotropicas
lightcurvewhichispoweredbythespindownofanewlyformed
thebeamingangleandemissionmechanismremainsveryuncertain
magnetar. This section fits the model directly to the restframe
(seehoweversection3.4.4).Theequationsofvacuumdipolespin-
SGRBlightcurves.Themagnetarcomponent isexpectedtobean
downgivenaboveneglecttheenhancedangularmomentumlosses
extra component to the typical lightcurve. Therefore, we assume
duetoneutrino-drivenmassloss,whichareimportantatearlytimes
there is a single power law decay, α , underlying the magnetar
1 afterthemagnetarforms(Metzgeretal.2011).Nevertheless,these
component.Thisvaluehasbeensettoα =Γ +1,whereΓ isthe
1 γ γ expressionsreasonablyapproximatethespin-downofveryhighly
photonindexofthepromptemission,assumingthatthedecayslope
magnetizedneutronstarsofmostrelevanceinthispaper.Isotropic
isgovernedbythecurvatureeffect(Kumar&Panaitescu2000),i.e.
emission is also a reasonable assumption for relatively powerful
that thesurrounding medium isverylow density asmight beex-
magnetarwinds,since(unlikefollowingthecollapseofamassive
pectedforneutronstarmergers.Wenotethatthesimplecurvature
star)themagnetaroutflowcannotbeconfinedefficientlybytherel-
effectassumedheredoesnotaccountforanyspectralevolution(for
ativelysmallquantityofsurroundingmaterialexpectedfollowing
exampleasthepeakenergymovesthroughtheobservationband)
aNSmergerorAIC(Bucciantinietal.2011).
howeverthisistokeepthenumberoffreeparametersfittedinthe
We use equation 5 to obtain the mass dependence of
model low. The normalisation of the power law decay fit is con-
strainedusingthelastdecayfromthepromptemission.Inasmall the model, where M1.4 = 1.4M⊙, and equation 6 (from
Zhang&Me´sza´ros2001)todeterminethetimedependenceofthe
numberofcases,thedecayslopeissignificantlydifferentfrompre-
magnetaremission.
diction and we allow α to vary. It is important to note that the
1
underlyinglightcurvecouldbesimilartootherGRBswithamore
complexafterglowlightcurve,butthisworkassumesthattheseare I ∼M R2 (5)
45 1.4 6
nakedbursts(i.e.nosurroundingISMforneutronstarmergers)and −2
T
onlythecurvatureeffectisimportant. L (T)=L 1+ (6)
Also,weexpecttheretobeflaresalsooverlyingthepowerlaw em,49 0,49(cid:18) 10−3Tem,3(cid:19)
decayandmagnetarcomponent(e.g.Marguttietal.2011).Dueto
Ifthereisasteepdecayphaseaftertheplateau,itisassumed
thelimitedstatisticsinSGRBlightcurves,wedonotattempttoex-
themagnetarhascollapsedtoaBHatthestartofthesteepdecay
cludepossibleflaresfromthelightcurvefits(exceptGRB060313,
(givingtheCollapseTimeparameter).Thedecayaftercollapseto
whichhasmultipleflaresearlyinthelightcurve)andtheunderlying
aBHassumesthesamepowerlawdecayfromthecurvatureeffect,
flareswillslightlyaffectthefitparameters.
butstartingatt =t .
0 collapse
ThismodelwasthenwrittenintoaQDPcodfile(COmponent
Definition file, used to generate new models within QDP which
3.1 Theory
can then be fitted to data sets). In this analysis, the mass (M )
1.4
ThemodelusedhereisasdescribedinZhang&Me´sza´ros(2001) and radius (R ) of the neutron star are constrained to be equal
6
and was suggested to explain GRB 051221A with a long lived to1toreducethenumberoffreeparametersinourmodel.These
magnetar(Fan&Xu2006),forseveralLGRBs(Trojaetal.2007; canonicalvaluesareconsistentwiththevaluesdeterminedbyob-
Lyonsetal. 2010; Bernardinietal. 2012) and for the short GRB servationsof threetypicalneutron stars,namelyM 6 2M⊙ and
090515(Rowlinsonetal.2010a).Thismodelisconsistentwiththe 76R611km(Ozel,Baym,&Guver2010a).Asthemodelcon-
latetimeresidual spindown phasedrivingarelativisticmagnetar siders an extreme neutron star, we note that the mass and radius
wind as described in Metzgeretal. (2011). Weuse the equations maydiffer from theseresults. However, thisonly has arelatively
(cid:13)c 000RAS,MNRAS000,1–??
10 A. Rowlinsonet al.
Figure8.SGRBBAT-XRTrestframelightcurvesfitwiththemagnetarmodel.Thelightgreydatapointshavebeenexcludedfromthefit.Thedashedline
showsthepower-lawcomponentandthedottedlineshowsthemagnetarcomponenet.
(cid:13)c 000RAS,MNRAS000,1–??
