Could the GRB-Supernovae GRB 031203 and XRF 060218 be Cosmic Twins?

0.34 MB·English

by  Lu Feng

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed12January2010 (MNLATEXstylefilev2.2)
Could the GRB-Supernovae GRB 031203 and XRF 060218
be Cosmic Twins?
⋆
Lu Feng & Derek B. Fox
Department of Astronomy & Astrophysics, 525 Davey Laboratory, Pennsylvania State University, UniversityPark, PA 16802, USA;
[email protected]; [email protected]
0
1
0
2 12January2010

n
a
J ABSTRACT

2
1 The gamma-ray burst (GRB) / X-ray flash (XRF) events GRB031203, discov-
eredby INTEGRAL, andXRF060218, discoveredby Swift, representtwo of only five

] GRB-SNe with optical spectroscopic confirmation of their SN components. Yet their
E
observed high-energy properties offer a sharp contrast: While GRB031203 was de-
H
tectedasashort40-sburstwithaspectrumpeakingatE >190keV,XRF060218
peak
h. was a T90 ≈ 2100-s long, smoothly evolving burst with peak energy Epeak =4.9keV.
p At the same time, the properties of the two expanding dust-scattered X-ray halos
- observedina fast-responseXMM-Newton observationofGRB031203revealthatthis
o
r event was accompanied by an “X-ray blast” with fluence comparable to or greater
t
s than that of the prompt gamma-ray event. Taking this observation as our starting
a point, we investigate the likely properties of the X-ray blast from GRB031203 via
[
detailed modeling of the XMM data, discovering a third halo due to scattering off

2 a more distant dust sheet at d = 9.94±0.39kpc, and constraining the timing of
3
v the X-ray blast relative to the GRB trigger time to be t = 11±417s. Using our
0
3
constraints, we compare the properties of GRB031203 to those of other GRB-SNe
3
in order to understand the likely nature of its X-ray blast, concluding that a bright
7
0 X-ray flare, as in GRB050502B, or shock breakout event, as in XRF060218, provide
. the mostlikelyexplanations.Inthe latter case,weconsiderthe addedpossibility that
8
0 XRF060218 may have manifested an episode of bright gamma-ray emission prior to
9 the burst observed by Swift, in which case GRB031203 and XRF060218 would be
0 “cosmic twin” explosions with nearly identical high-energy properties.
:
v
Key words: dust, extinction — gamma-rays: bursts — supernovae: general — su-
i
X pernovae: individual: SN2003lw — supernovae: individual: SN2006aj
r
a
1 INTRODUCTION anomalousintheirownway;evenconsideredasagroup,the
properties of GRB-SNethusresist ready generalisation.
The discovery of the connection between long-duration
In all, five spectroscopically confirmed GRB-SNe – a
gamma-ray bursts (GRBs) and X-ray flashes (XRFs), on
term we will use to refer to the GRB- and XRF-SNe, as
theonehand,andTypeIbcsupernovae(SNe)ontheother,
a group – have been observed to-date. SN1998bw offered
has confirmed the collapsar model as proposed by Woosley
the first direct evidence for GRB-SN association, as the
(1993) – for a recent review, see Woosley & Bloom (2006).
SN that appeared in the error box of GRB980425, with
Several distinct types of investigation provide support an explosion time consistent with the GRB trigger, was
for the GRB- (XRF-) SN connection; however, the most shown to be exceptionally luminous and energetic in the
convincing evidence has come from spectroscopic observa- optical (Galama et al. 1998), with an associated mildly rel-
tions of coincident supernovae associated with the lowest- ativistic (Γ>3) outflow thatmade it uniquelyradio-bright
redshiftGRBsandXRFs.Asisfrequentlythecaseinastron- (Kulkarniet∼al.1998).Occurringinacataloguedgalaxyata
omy, these nearby and best-studied cases have each proven distanceof just 36Mpc(z=0.0085), however, GRB980425
⋆ Currentaddress:DepartmentofPhysics,26-524,MassachusettsInstituteofTechnology,Cambridge,MA02139,USA;[email protected]
(cid:13)c 0000RAS
2 Feng & Fox
wasfourordersofmagnitudelessluminousthanthetypical and temporally apart from the GRB. To satisfy these con-
z>1 burst. straints,W06considerthepossibility thatGRB031203 was
∼ XRF020903, at z = 0.25 the first XRF with a followed by a bright X-ray flare such as that observed by
determined redshift and observed optical and radio af- Swift from GRB050502B (Burrows et al. 2005); such flares
terglow emission (Soderberg et al. 2004a), also provided –albeitrarelyasbrightasthatcase–arefamiliarfeaturesof
the first XRF-associated supernova (Soderberg et al. 2005; theGRBX-raylightcurvesnowroutinelygathered bySwift
Bersier et al.2006);itsspectrumwasultimatelyshowntobe (e.g., Chincarini et al. 2007).
similar to that of SN1998bw (Soderberg et al. 2005), con-
firmingthe deep connection between XRFsand GRBs.
XRF060218, detected by Swift (Campana et al. 2006)
GRB030329 /SN2003dh atz=0.17providedthefirst
and coincident with a z=0.033 host galaxy (Mirabal et al.
definitiveassociationofa“cosmological”GRBwithacoinci-
2006), evolved into a type Ic supernova that was ob-
dent type Ic supernova, since it had an isotropic-equivalent
served from its earliest moments, including extensive spec-
gamma-ray output of E = 1052erg (Vanderspek et al.
γ,iso troscopicobservations(Mirabal et al.2006;Pian et al.2006;
2004), within the observed range for z > 1 events. Broad-
Mazzali et al. 2006), thanks to the prompt alert and ex-
line SN Ic features were visible within∼a few days of the
tended follow-up observations of Swift. Analysis of the
GRB (Stanek et al. 2003), and the ultimate evolution of
X-ray, optical, and radio energetics of XRF060218 demon-
the supernova showed a striking similarity to SN1998bw
strate a deep similarity to SN1998bw and GRB031203
(Hjorth et al. 2003; Matheson et al. 2003), validating the
(Soderberget al. 2006); however, XRF060218 remains an
two earlier associations.
anomaly in that its prompt emission exhibited a uniquely
Later that year, GRB031203 was detected by IN-
extended evolution, having a 90%-containment duration of
TEGRAL with a duration of 40-s and a peak energy
T = 2100s and a correspondingly low peak flux F =
90 peak
of > 190keV (Sazonov et al. 2004, hereafter SLS04). Six 8.8 10−9erg cm−2 s−1(15–150keV).Thispeakfluxismore
hours after the burst, a fast-response XMM-Newton ob- ×
than an order of magnitude lower than those of all other
servation of the burst position began; a fading X-ray
GRB-SNeexceptforXRF020903,whichhadanevensofter
afterglow was quickly identified (Rodriguez-Pascual et al.
spectrum; indeed, it was only detected because of the “im-
2003), coincident with a z =0.105 galaxy (Prochaska et al.
age trigger” capability of the Swift BAT, which identified
2004). This was confirmed as the host galaxy once an
XRF060218asanuncataloguedsourceapparentinthefirst
associated type Ic supernova, SN2003lw, was discovered
64s integration taken at that pointing.
(Malesani et al. 2004). Investigation of theradio and X-ray
energetics of the event revealed further similarities to
Emission fromXRF060218 ispresentinthefirstimage
SN1998bw (Soderberget al. 2004b), although theSN itself
takenbySwift onthatparticularorbit;assuch,aGRBsim-
was somewhat subluminous by comparison (Gal-Yam et al.
ilar to GRB031203 could have occurred prior to the start
2004).
ofSwift observations.Moreover,asignificantfractionofthe
Contemporaneously,analysisoftheXMM datarevealed
promptX-rayemissionofXRF060218issuppliedbyather-
two expanding X-ray halos centred on the fading GRB af-
mal component, unobserved in other GRB-SNe, that is at-
terglow (Vaughan et al. 2004, hereafter V04); these halos
tributed to the shock breakout of the associated supernova
were convincingly interpreted as scattered photons from
(Campana et al.2006)ratherthantotherelativisticjetusu-
a bright X-ray “blast” that occurred near-simultaneously
ally invoked to explain the prompt emission. If the X-ray
with GRB031203. Modeling the properties of the X-ray
blast from GRB031203 can beexplained as a similar shock
blast,Watson et al.(2004,orW04)andWatson et al.(2006,
breakout, then these two events – despite their very differ-
or W06) argued that the prompt emission of GRB031203
ent appearances – would in fact be “cosmic twins” exhibit-
was, in fact, an X-ray flash, exhibiting greater fluence in
ing nearly identical evolution in the X-ray and gamma-ray
X-raycompared to gamma-ray, log(S /S )=
2–30keV 30–400keV
bands(see also Ghisellini et al. 2006).
0.6 0.3>0.IndependentanalysisbyTiengo & Mereghetti
±
(2006, or TM06) yielded a lower X-ray fluence estimate
which nonetheless also satisfies S >S . In this paper, we undertake a quantitative exploration
2–30keV 30–400keV
The nature of GRB031203 is not easily resolved, for ofthishypothesisbyconstrainingthepropertiesoftheX-ray
two reasons. First, the bright soft X-ray emission cannot blastin GRB031203 viadetailed modeling ofitsexpanding
be interpreted as the low-energy tail of GRB031203, as its X-ray halos; this analysis also allows us to address the al-
fluence significantly exceeds the low-energy extrapolation ternate theory that the X-ray emission from GRB031203
of the INTEGRAL spectrum (SLS04; W06; TM06). Sec- wasduetoalaterX-rayflare(W06). 2presentstheXMM
§
ond, the INTEGRAL observations themselves would have observations of the afterglow and halos of this burst and
detected the X-ray blast if it was emitted over a brief time the details of our analysis, including derivation of param-
intervalpriortoorwithin300sfollowingtheburstitself,be- eter uncertainties. 3 discusses our results in light of vari-
§
fore22:06:27 UT,whenINTEGRALbegantoslewtoanew oushypothesesregardingGRB031203andXRF060218,and
pointing.Thus,twodistinctexplosiveepisodesarerequired, places these eventsin the larger context of the known vari-
with the X-ray blast most likely occurring both physically eties of cosmic explosion. 4 summarizes our conclusions.
§
(cid:13)c 0000RAS,MNRAS000,000–000
GRB031203 and XRF060218 as Cosmic Twins 3
2 OBSERVATION AND DATA ANALYSIS to increasing Dec., as usual. The temporal coordinate t is
measured relative to the burst trigger time (t = 0), scaled
TheGRB031203 data(ObservationID0158160201), down-
such that the XMM observation begins at t = 1, 22.2ksec
loaded from the XMM-Newton archive, are processed and
(6h10m44s)after theburst.Usingthistemporal coordinate,
reduced for EPIC MOS and PN cameras through the stan-
the XMM observation extends from t = 1 (defined by the
dard procedures (tasks emchain and epchain), with stan-
earliest arrival time in our dataset, from the MOS-2 detec-
dard filtering, using the XMM Science Analysis System
tor) to t 3.61. An illustration of the resulting dataset
(SAS), version 7.1.0. The observation had start and stop ≈
is presented as an image in normalized coordinates (x/√t,
timesof04:10:18UTand20:16:20UTon4Dec2003,which
y/√t) in Fig. 1.
after standard filtering yields 57.8ksec of good time and
We represent the fading GRB afterglow using an ana-
57.3ksecnetexposureinCCD1ofEPIC-MOS1andMOS2,
lytical model for the XMM Point Spread Function (PSF),
and56.2ksecofgood timeandaCCD-dependentnetexpo-
which approximates the PSFas a Kingfunction:
sure between 53.4 and 54.0ksec in EPIC-PN. The observa-
tion was not affected bysignificant soft-proton flaring. sp(r)= απ−r21 (1+r2/rc2)−α, (1)
c
whereαistheKingslope,r istheKingcoreradius,risthe
c
2.1 Model Construction and Fitting radial distance from the source (ring centre), and the inte-
′′ grated surface brightness is normalized to unity for α > 1.
We consider a circular region with radius 311 centred on
Since we combine the data from the two MOS cameras, we
the GRB afterglow, and restrict our attention to detected
use average MOS PSF parameter values for the MOS data
counts in the energy range 0.2 to 3.0keV (0.2 to 4.0keV
for PN). We generate an exposure map with 1′′ pixel res- (rc=4.916 and α=1.442), and PN PSFvaluesfor thePN
data1 (r = 6.636 and α = 1.525). The fading of the after-
olution, using the eexpmap task, to account for PN active c
glow is parameterized as a power-law with temporal index
regions; exposure map values are treated as binary (on or
α , referenced to theburst trigger time.
off)inthesubsequentanalysis,andnoinitialexposuremap g
We represent the expanding, fading dust-scattered ha-
iscreatedfortheMOSdataasourcircularregionofinterest
los, centred on the GRB position, using a numerical model
isfullycontainedon thecentralCCD.Bright X-raysources
for ring-like sources observed with XMM that we have de-
within the region of interest are identified and all counts
′′ veloped. The derivation of this model is provided in Ap-
withinanexclusionradiusof15 ofeachsourcepositionare
pendix A; as realized in our code, this bivariate function
excluded from analysis; these exclusion regions are then in-
is precalculated on a grid and interpolated to the particu-
tegrated into exposure maps for the PN and MOS data for
lar values required for each function evaluation. Fading of
analysispurposes.Afterallexclusionsweacceptforanalysis
the halos is parameterized as a power-law with temporal
10,754countsfromtheMOS-1detector,10,535countsfrom
index α , referenced to the burst trigger time; this index
MOS-2,and 32,085 countsfrom PN. h
is assumed to be the same for all rings. In order to avoid
We construct a 16-parameter, three-dimensional (x,
complications associated with normalizing the model prob-
y, t) maximum-likelihood model including parameters to
ability density function for indices α 1 as well as for
describe the fading GRB afterglow, the expanding dust- h ≤ −
α > 1,weimposeahardlimitα 0.95onthisparam-
scattered halos, and the vignetted X-ray (and charged h − h ≥−
eterduringfitting.Initial investigations suggested that this
particle-induced) background. The total counts from all
limit was encountered in less than 5% of bootstrap trials;
model components, for the 2-MOS and PN datasets, are
however, our final analysis resulted in a somewhat greater
constrained to be equal to the observed count totals given
proportion of 9% of all trials encountering thislimit.
above. The model probability density is evaluated at the
Becausetheringsexpandbyafactorof√3.6 1.9over
positionandarrivaltimeofeachdetectedphoton,thevalue ≈
the course of the observation, and because we wish to ac-
of the probability density function is interpreted as being
curately model the background over the region of interest,
proportional to the likelihood of observing that event, and
wefindit necessary toapplyan off-axisvignettingfunction
agloballikelihoodcalculated;wethenattempttomaximize
(Lumbet al. 2003) tothe rings and background:
thegloballikelihoodusingnumericaltechniques,specifically,
the AMOEBA minimization routine (Press et al. 1995) as im- S(r)=S(0)(1 mre) (2)
plemented in the IDL programming environment. For ease −
ofmodeling,weconvertphotonangularpositionsandarrival whereS(0)isthesurfacebrightnesson-axis,S(r)isthesur-
times as follows: angular coordinates x and y are measured face brightness at off-axis distance r (measured in arcsec),
in arcsec relative to an initial estimate of the GRB posi- and m and e are the vignetting parameters for the EPIC
tion, XMM physical coordinates (26024.8, 23674.1), with cameras.Weusem=3.43 10−5 ande=1.45fortheMOS
the +x direction corresponding to decreasing R.A. and +y cameras, and m = 3.51 ×10−5 and e = 1.53 for the PN,
×
1 PSF model and parameter values are obtained from the XMM calibration document “In Flight Calibration of the PSF for the PN
Camera” by Simona Ghizzardi, located at http://xmm.vilspa.esa.es/docs/documents/CAL-TN-0029-1-0.ps.gz. See, in particular, Eq.1
andTable1inthedocument.
(cid:13)c 0000RAS,MNRAS000,000–000
4 Feng & Fox
MOS PN 1500
GRB
1000
Counts 500 H3 H2 H1
0
0 100 200 300
Normalized Radius (arcsec)
Figure1.(left)Imagesofthe2-MOSandPNcountsdatainnormalizedcoordinates(x/√t,y/√t).ThefadingGRBafterglow,
Halo 1 (outer), and Halo 2 (inner) are readily distinguished; the signature of the more distant and fainter Halo 3 (close to
the GRB) is more subtle. White streaks in the images are due to bright source exclusion regions and PN camera chip gaps,
which are incorporated into our model via MOS and PN exposuremaps.
Figure 2.(right) Histogram of 2-MOS + PN counts data(black), best-fitmodel (green), and residuals (lower panel), binned
accordingtonormalized radius,r/√t.ContributionsofthefadingGRBafterglow (GRB)andthethreeexpandinghalos(H1,
H2, H3) are individually distinguishable; the fall-off in counts at large normalized radius is due to our region of interest cut
′′
(r =311 ) as smeared out by thenormalization procedure.
max
which we find accurately models the vignetting of PN and For each trial, a new dataset is generated by drawing ran-
MOS exposure maps generated in SAS. domly,withreplacement,fromthetruedatasetuntilwehave
TheexcludedsourcesandthePNexposuremappresent thesamenumberofeventsasintheactualdata.Thefitting
discontinuities to the model probability density function, sequence,describedabove,isidenticalforeachtrial;param-
which must be normalized to yield an appropriate fit. We eter starting points are randomized based on preliminary
perform thisnormalization vianumericalintegration overa estimates(subsequentlyverifiedin ourfinalanalysis) ofthe
three-dimensional rectangular grid (x, y, t), where the grid uncertainties in each parameter. The result should approx-
spacing is 2′′ in x and y, and the temporal grid is divided imate the posterior distributions that would result from a
into 40 equal intervals. The same cuts applied to the data, fullBayesiananalysisusinguniform(non-informative)prior
includingthecircularregionofinterest,theexclusionregions distributionsforeachofthemodelparameters.Forourfinal
around identified bright sources, and (for PN only) the PN analysis, presented below, we executed 1000 trials in all.
exposure map, are applied to the grid prior to integration, The optimization of nonlinear functions in many-
and are thus(approximately) accounted for. dimensional spaces is a known hard (“NP”) computational
We maximize the likelihood function using the AMOEBA problem. We therefore point out that the bootstrap Monte
algorithm, in stages, using multiple fitting rounds at each Carlo approach is expected to yield conservative estimates
stage (with fit starting points randomized prior to each ofparameteruncertaintiesincases wherethemodelfails to
round)toensurearelativelywide-rangingexplorationofthe offer a statistically-complete representation of the data, or
parameterspace.Insequence,weexecute:(1)Tenroundsof where the underlying fitting procedure fails to identify the
fittingtheGRBcountsparametersandfadingindexα ;(2) globalminimumineachandeverytrial.Thereason isthat,
g
Tenroundsoffittingwithallringparameters(counts,radii, quite simply, the failure to identify the best possible fit is
and fading index α ) also free; and finally, (3) Five rounds robustly expected to drive the fitting routine to explore a
r
of fitting with all parameters free. larger(ratherthansmaller)regionofparameterspace.This
istrueaslongasthefittingroutineisnottrappedinasingle
Initial examination of the data suggested the presence
localminimum,repeatedly,intrialaftertrial;inouranalysis
of a third dust-scattered halo at small radius (Fig. 1). Pre-
weavoid thisnumericaldisorderbyrandomizingparameter
liminary investigation confirmed the reality of this feature,
starting values for each trial, as mentioned above.
and indicated that it should be interpreted as dueto X-ray
scattering off a third dust sheet, more distant than the two
discussed byprevious authors ( 3.2).We therefore incorpo-
§ 2.2 Results
rate this third halo into our fits, with the same burst time
t0 and fading indexαh as theothers. The results of our model fitting, including parameter un-
Uncertaintiesinourmodelparametersarederivedwith certainties quoted both as standard deviations and as
thebootstrapMonteCarlomethod,executingmultipletrials 90%-confidence intervals, are presented in Table 1. 90%-
and accumulating best-fit parameter values from each trial confidence intervals are defined as the minimum-length in-
torealizetheposteriordistributionofourmodelparameters. tervalsthatencompass90%oftheparametervaluesfromour
(cid:13)c 0000RAS,MNRAS000,000–000
GRB031203 and XRF060218 as Cosmic Twins 5
bootstrap Monte Carlo trials (e.g., 900 of 1000 parameter along the line of sight within the Milky Way. They con-
values). Associated background count totals can be derived strained the time of burst for the inner and outer rings to
by subtracting the counts of the model components given be t = 2794+2765s and t = 2005+2512s respectively, rela-
0 −3178 0 −2867
in the table from the total instrument counts of 21,289 for tivetotheINTEGRALtrigger, andbyapplyingamodelof
2-MOS and 32,085 for PN ( 2.1). the dust properties, determined that the initial soft X-ray
§
To illustrate the model goodness-of-fit, we present in eventhad a power law spectrum with photon index Γ 2.
≈
Fig. 2 a histogram of the data (2-MOS + PN counts) com- Subsequently, W04, W06, and TM06, using different
paredtoourbest-fitmodel.Inthisfigure,aswellasinFig.1, analysisapproaches,refinedthedetailsofthispicture.They
we present the data in terms of the “normalized radius,” derived more precise distances to the dust sheets (d
1
≈
which is the radial distance from the GRB afterglow po- 870pc and d 1390pc, respectively), and correspond-
2
≈
sition, divided by the square root of the normalized time ingly more precise constraints on the timing of the X-ray
(time measured from the GRB trigger, with t = 1 at the blast. The time constraint from W06 is t = 600 700s at
0
±
startoftheXMM observation).Thisnormalizationservesto 90% confidence; the inferred power-law spectral index for
highlighttheexpandinghalosasdistinctfeatures,whilenot theX-rayblastisreported aseitherΓ=2.5 0.3(W04)or
±
significantly altering the appearance of the afterglow itself Γ = 2.1 0.2 (TM06), results which are consistent at the
±
(atsmallradius);thefall-off incountsatlargeradiusisdue 1σlevel.ThetwoconclusionsastothefluenceoftheX-ray
to our region of interest cut (r =311′′), as smeared out b≈last over 1–2 keV, F = 1.5(3) 10−6erg cm−2 (W06)
max X
by the conversion to normalized units. We find the overall versus3.6(2) 10−7erg cm−2 (TM0×6),aremorediscrepant,
×
fit to be satisfactory. Specifically, although several system- whichTM06attributetotheauthors’divergingassumptions
atic features are apparent in the residuals, we have investi- on the relation between X-ray scattering optical depth and
gated these without identifying any obvious model failings extinction.
that might account for them. In particular, we have veri- In discussing their model for the dust properties, W06
fied that none of the features are due to unaccounted-for show a plot of the halo fading (their Fig. 2) which cor-
brightpoint sources orinstrumentartifacts (e.g., hot pixels responds to a temporal power-law index of α 0.6.
h
≈ −
orhotcolumns).Variationsineffectiveexposurewithinour They use this fact (along with the size of the scatter-
regionofinterest,notaccountedforbyoursimplevignetting ing halos) to derive a maximum size for the dust grains,
model, may be responsible for some of these trends. Note a =0.50 0.03µm;inaccountingfortheeffectsofsmaller
max
±
that our fittingprocedure is executed against theunbinned grainstheyuseapower-lawsizedistributionwithpower-law
data, in three dimensions, and that this figure merely rep- indexequal to 3.5.
−
resents one possible projection of the model and data onto
a one-dimensional space, for visualization purposes.
3.2 Discovery of a Third Halo
In Fig. 3 we present the full posterior distribution for
fourparametersofspecialinterest:αg,thetemporalpower- Our analysis reveals the presence of a third, faint halo
lawindexforthefadingoftheGRBafterglow;t0,thetimeof (Figs. 1, 2) in addition to the two identified by previous
zero-radiusfortheexpandinghalos;αh,thetemporalpower- authors. The presence of this halo is robust in our analy-
lawindexforthefadingoftheexpandinghalos;andthesum sis, with associated total 2-MOS + PN counts between 403
ofthe2-MOSandPNcountsforHalo3,thehaloduetothe and572at90%-confidence(Fig.3d),andwithroughlyequal
most distant scattering dust sheet, discovered in our anal- counts in the two sets of detectors, which are fit indepen-
ysis. 90%-confidence intervals on each of these parameters dently(Table 1).
are indicated. Initially, we speculated that the third halo might be
the signal of a second X-ray blast or early afterglow emis-
sion,withtheX-raysscatteringoffoneofthetwopreviously
3 DISCUSSION knowndustsheets.Ifthiswerethecase,thethirdhalowould
necessarilybeassociatedwithadistinct(later)t andwould
0
In the sections below we discuss the prior understandingof share thesame distance d as one of the otherhalos.
the GRB031203 X-ray blast phenomenon and our own re-
To investigate this possibility, we performed a distinct
sults as to the properties and timing of the event. We then
bootstrapMonteCarloanalysisof600trials,allowing t for
0
discuss the full set of observations of GRB031203 in the
the third halo to vary while fixing t =0 for the two other
0
context of the known varieties of cosmic explosion, includ-
halos. Given the angular size of the halo at the start of the
ing XRF060218. XMM observation,θ,t isdirectlyrelatedtothedistanceto
0
the dust scattering sheet by d=2c(t t )/θ2, where t t
0 0
− −
is the time from the burst to the start of XMM observa-
3.1 Previous Findings
tions. This analysis yields a 90%-confidence interval for d
3
V04 originally reported the discovery of two evolving dust- of8597 to10503pc,inconsistent with bothd 870pcand
1
≈
scattered X-ray halos centred on GRB031203 and made d 1390pc.Hence,weconcludethatthethirdhalois due
2
≈
the first attempt to model the halos and extract parame- to a third dust sheet and require t to be identical, for all
0
tersoftheX-rayblastandassociated dustscatteringsheets halos, in our full analysis.
(cid:13)c 0000RAS,MNRAS000,000–000
6 Feng & Fox
Table 1.FitparametersforGRB031203afterglowandexpandinghalos
Parameter Median σ 90%-conf.
GRBx 0.46 0.14 0.23 0.70
y 0.19 0.13 −0.04 0.40
2-MOScounts 2252.7 60.3 2157.3 2355.6
PNcounts 2340.0 125.5 2172.4 2559.2
Fadingindex,αg −0.557 0.056 −0.64 −0.46
Halost0 (s) 11.0 416.9 −620.6 722.8
Fadingindex,αh −0.77 0.10 (−0.95) −0.65
Halo1Radius(arcsec) 145.04 0.70 143.74 146.07
Distance(pc) 871.7 9.7 855.6 886.8
2-MOSCounts 1365.0 67.8 1251.1 1467.4
PNCounts 1686.4 88.8 1568.4 1855.6
Halo2Radius(arcsec) 114.93 0.63 113.90 115.94
Distance(pc) 1388. 14. 1364. 1410.
2-MOSCounts 2059.3 65.5 1952.9 2164.1
PNCounts 2229.3 108.9 2041.6 2389.5
Halo3Radius(arcsec) 42.97 0.81 41.46 44.06
Distance(kpc) 9.94 0.39 9.32 10.52
2-MOSCounts 268.5 40.7 203.4 334.1
PNCounts 219.7 32.2 177.7 274.8
Median, standard deviation about the median (σ), and 90%-confidence
intervals are derived from model fits to 1000 bootstrap Monte Carlo re-
alizations of the dataset. PN and 2-MOS counts are defined as the total
counts gatheredfromthePN(0.2to4.0keV)andtwoMOScameras(0.2
to 3.0keV), respectively. Halo radii are defined as the radius in arcsec
at the start of XMM observations. Halo distances are determined by the
best-fit halo radii and t0 values from each trial and are not independent
parameters.GRBcoordinates(x,y)areoffsetsinarcsecfromXMM phys-
icalcoordinates(26024.8,23674.1);themedianoffsetof(0.46,0.19)arcsec
corresponds to R.A. 08h02m30s.20, Dec. −39◦51′02s.8 (J2000) using the
uncorrected XMM aspect. t0 is the time of zero-radius for the expand-
ing halos relative to the INTEGRAL trigger time of 22:01:28 UT. The
modelenforcesahardlimitαh≥−0.95whichisencounteredin9%ofour
bootstraptrials.
The third dust sheet is located at greater distance and α < 0.65 that is unconstrained from below because of
h
−
greater Galactic radius (R 14.5kpc) than thetwo nearby ourhardlimit(α 0.95);Fig.3cpresentsthefullposte-
h
≈ ≥−
sheets, and nominally at greater distance from the Galac- rior distribution. Ourresult appears mildly in conflict with
tic plane as well (z 0.83kpc), given the Galactic co- the value α 0.6 from W06, with associated implica-
h
≈ − ◦ ◦ ≈ −
ordinates toward GRB031203, l = 255.7 and b = 4.8 . tions for the properties of the scattering dust particles (see
−
However, reconstructions of the three-dimensional distri- also TM06); we have not investigated these implications in
bution of neutral hydrogen density throughout the Milky detail.
Way(Kalberla et al.2007;Kalberla & Dedes2008)reveala
“warp”in thediskwhichhasanamplitudeofδz 1kpcat
≈ 3.3 Properties of the GRB031203 X-ray Blast
R=15kpc, in precisely the ( z) sense needed to place the
−
third dust sheet within or near the densest portion of the Ouranalysis yieldsa90%-confidenceintervalon thetiming
Hi disk. The existence and location of the third dust sheet of the X-ray blast which places it within roughly ten min-
is not particularly surprising in thiscontext. utesoftheGRB031203trigger,between 621sand+723s,
−
Our final analysis yields 90%-confidence intervals on with median value and standard deviation t = 11 417s;
0
±
the distances to the dust sheets as follows: d1 = 856– thefull posterior distribution for t0 is shown in Fig. 3b.
887pc, d2 = 1364–1410pc, and d3 = 9321–10523pc (Ta- Our constraint is comparable in precision to the best
ble 1); these uncertainties are inclusive of uncertainties in previous determination, t =600 700s at 90%-confidence
0
±
thevalueoft0 itself,whichwehavenotfixed(e.g.,Fig.3b). (W06). The shift of our confidence interval to earlier times
For Halo 1 and Halo 2, our values agree with those derived sharpensthecontrastbetweentheimplicationsoftheXMM
by W06 (d1 = 868+−1176pc and d2 = 1395+−1350pc) and TM06 and INTEGRAL observations: The INTEGRAL pointing
(d1=870 5pcand d2=1384 9pc);note,however,that extends to 300s after the GRB trigger, and only 22.5% of
± ±
TM06 fix t0=0s in their analysis. ourtrialsyieldt0valuesconsistentwiththisconstraint.Ifwe
The median value of the halo fading index from our assume,inaccordancewithstandardGRBmodels,thatthe
analysis is α = 0.77 with a 90%-confidence interval X-rayblastcouldnothaveprecededthegamma-raytrigger,
h
−
(cid:13)c 0000RAS,MNRAS000,000–000
GRB031203 and XRF060218 as Cosmic Twins 7
50 80
(a) (b) 10-5
40
60
?
30
N 20 N 40 s) 10-6
2/
10 20 ^
m 10-7
0 0 c
-0.G6RB Fad-in0.g5 Index, α-g0.4 -1000 -500 Halo0s t0 (s) 500 1000 gs/
100 (c) 100 (d) x (er 10-8
80 80 u
60 60 Fl 10-9
N N
40 40
10-10
20 20
-200 0 200 400 600 800
0 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 0 400 500 600 700 800 Time (s)
Halos Fading Index, αh Halo 3 Counts (2-MOS + PN)
Figure3.(left)Approximateposteriordistributionsofselectedmodelparameters,asderivedfromourbootstrapMonteCarlo
analysis.(a)TheGRBafterglowtemporalfadingindex,α ;(b)t fortheexpandinghalos,correspondingtothecharacteristic
g 0
emission timeof theX-rayblast, measuredrelativetothetrigger timeforGRB031203;(c)Thehalos temporalfadingindex,
α (note this parameter is subject to a hard limit, α 0.95); (d) The sum of 2-MOS + PN counts for the expanding
h h
≥ −
Halo 3, discovered in ouranalysis. 90%-confidenceintervals for each parameter are indicated graphically (dotted lines).
Figure 4.(right) Superposition of XRF060218 Swift BAT (green, 15–350keV) and XRT(red, 0.3–10 keV) light curves with
ahypotheticalprecursoreventhavingpropertiesidenticaltoGRB031203(black,20–200 keV).ThestartofSwift BATobser-
vationsdefinest=0;theINTEGRALlightcurveofGRB031203isobtainedfromSLS04,rebinned,correctedforredshiftand
time dilation, and offset by 70s to represent its occurrence prior to the start of Swift observations. Negative (background-
−
subtracted) fluxmeasurements are not shown on this logarithmic plot.
then our upperlimit of t <545s at 90%-confidence is also icantly flatter than the canonical α 1.3 familiar from
0 X
≈ −
relevant in thiscontext. Beppo-SAX observations at the time. In retrospect we can
An alternative approach to resolving this dilemma identify this as one of the first observations of a “plateau
would reduce the peak flux of the X-ray blast – making it phase” in GRB X-ray afterglows, now familiar from Swift
undetectableintheINTEGRALobservation–byextending observations (e.g., Nousek et al. 2006; Racusin et al. 2009).
its fluence over a significant time interval after the GRB. As we have since learned, extrapolation of this slow decay
This hypothesis is also constrained by our analysis, since toearlytimes,t<1000s,isnotparticularlyrevealingofthe
weobserve noevidencethat thehalos areradially resolved; likely X-ray flux∼at that time.
our analytical model for unresolved ring-like sources (Ap-
pendixA)providesasatisfactory fittotheradialprofilesof
3.4 Could GRB031203 and XRF060218 be
thehalos (Fig. 2).
Cosmic Twins?
WhilewehavenotconstrainedthedurationoftheX-ray
blast directly,ourresultson thetimingof theblast demon- As mentioned in 1, a GRB similar to GRB031203, as ob-
§
strate that our model is sensitive to changes of δt0 600s, served by INTEGRAL, could have occurred immediately
≈
and we expect that, in demonstrating an adequate fit with prior to Swift observations of XRF060218 without being
the unresolved “ring” model, we have constrained the du- observed by Swift. Likewise, a slow-evolving XRF similar
ration of the blast at approximately this magnitude, δt < to XRF060218 could have occurred following GRB031203
600s.GiventhattheXMM observationbegant=22.2kse∼c withoutbeingobservedbyINTEGRAL,ifitexhibitedeither
after the GRB trigger, a duration of 600s corresponds to a sufficiently low peak flux or peaked after t = 300s, when
′′
δt/t = 3% or δr1 = 4 for Halo 1, which would be most INTEGRAL began its slew to a new pointing. In this sce-
sensitive to these effects. Since the XMM PSF has a width nario,then,botheventswouldconsistoftwoseparatebursts,
′′
ofFWHM=4 ,itisreasonabletothinkthedatawouldbe one peaking at gamma-ray energies and one peaking in
sensitive to signs of broadening at this level. Moreover, the the X-ray. Importantly, while we have evidence for distinct
dust sheets themselves must be extended to some degree; gamma-ray and X-ray emission episodes in GRB031203,
anysuchextensionwouldtendtofurtherbroadentheradial in this picture only the X-ray episode was observed from
profileofthehalos,beyondanybroadeningduetothefinite XRF060218.
duration of theblast itself. A variation on this scenario, without any separate
Finally,wenotethatW04callattentiontotherelatively episode of gamma-ray emission from XRF060218, was pro-
slowfadingoftheX-rayafterglowofGRB031203duringthe posed by Ghisellini et al. (2006). These authors were con-
XMM observation, α 0.55 (Table1),which was signif- cernedwiththequestionofwhethertheprompthigh-energy
g
≈−
(cid:13)c 0000RAS,MNRAS000,000–000
8 Feng & Fox
emissions of GRB031203 and GRB980425 could be recon- as three times the energy of the prompt X-ray emission of
ciledwiththehigh-energyrelationshipsbetweenpeakenergy XRF060218 (Table 2).
and isotropic-equivalent energy output that are observed To illustrate these constraints in detail, and explore
amongthez >1GRBpopulation.Theyconcluded,aswedo otherpossibleexplanationsfortheGRB031203X-rayblast,
here,that th∼eobservation of XRF060218 bySwift suggests Table2presentsthegamma-ray andX-raypropertiesof all
stronglythatasimilarphenomenonmightberesponsiblefor five confirmed spectroscopic GRB-SNe, and the properties
the “X-ray blast” inferred from the expanding X-ray halos of two other cosmic explosions that may be interesting in
of GRB031203. thiscontext, GRB050502B and SN2008D.
To illustrate the nature of our proposal, we have gen- First, we consider the“cosmic twins” hypothesis, com-
eratedafigurethatsuperimposestheprompt-emissionlight paring the properties of GRB031203 and XRF060218.
curveofGRB031203(SLS04),appropriatelyrescaledtothe A distinct, earlier episode of high-energy emission for
redshiftandluminositydistanceofXRF060218,ontheSwift XRF060218 is readily accommodated by the total
BATandXRTlightcurvesofthepromptandearlyemission gamma-rayenergybudgetofGRB031203;inordertoavoid
of XRF060218 (Fig. 4). With t = 0 at the beginning of detection by various IPN experiments, the peak luminos-
Swift observations, it is necessary tooffset theINTEGRAL ity, peak energy, or total energy release should be some-
light curve to earlier times in order to avoid detection by what reduced from GRB031203 values. The X-ray blast
the Swift BAT; we arbitrarily choose a 70s offset. The from GRB031203 released more energy in the X-ray than
−
BATlightcurveisacombinationofthemask-weightedlight XRF060218; however, depending on the assumed relation
curve generated by the BAT standard analysis (t < 350s) between extinction and X-ray scattering optical depth, the
with data from Campana et al. (2006) (64-s integrations at additional25%(TM06)to200% (W06)energyrequirement
t > 350s). The XRT light curve (red) for XRF060218 is is not necessarily severe. Finally, the time delay from burst
obtainedfromtheSwift/XRTlightcurvesrepositoryat the triggertoX-raypeak(technically,tothecharacteristictime
Universityof Leicester2 (Evans et al. 2007, 2009). ofemission)shouldbeatleasttwiceaslongforXRF060218
As Fig. 4 shows, this “cosmic twin” to GRB031203 asforGRB031203.Noneoftheserequirementsappeartous
would haveexhibitedapeakfluxof2.7 10−6erg cm−2 s−1 prohibitive; collectively, however, they restrict the allowed
×
(20–200 keV), roughly 11 times brighter than the origi- parameter range of models considerably. The main appeal
nal event, which occurred at about three times the dis- tosatisfyingtheseconstraints,inanOccam’sRazorsense,is
tance of XRF060218. This addresses an important con- therequirement for one fewer sui generis typeof GRB-SN.
dition on our hypothesis, which is that the burst not be Next, we consider the X-ray flare explanation for the
bright enough to trigger detectors of the Interplanetary GRB031203 X-ray blast (W06). Even at the maximum in-
Network (IPN; e.g., Hurley et al. 2006), and in particular, ferred energy of 4 1049erg (2–10keV), the ratio of X-ray
×
Konus-WIND (Aptekaret al. 1995), which did not report togamma-rayenergiesforGRB031203 wouldbenogreater
any trigger associated with XRF060218. A review of the thanobservedinGRB050502B.Moreover,therelativetim-
catalogofKonus-WINDshortburstdetections3 revealsthat ing of the gamma-ray and X-ray episodes is very close to
the peak flux distribution peaks at 7.5 10−6erg cm−2 s−1 what is needed to satisfy both our time constraint, derived
×
(15–2000keV),althoughburstsaredetecteddowntoamin- from the expanding halos, and the INTEGRAL slew time
imumpeakfluxof2 10−6erg cm−2 s−1.Dependingon the constraint, t > 300s. The latter applies to any relatively
×
high-energy spectrum of GRB031203, the peak flux of its short (hence high peak flux) model for the X-ray blast. At
hypotheticalz=0.033cosmictwinwouldbefrom5.2 10−6 the same time, the X-ray flare from GRB050502B remains
to 7.9 10−6erg cm−2 s−1 (15–2000 keV), likely belo×w the anextremeexampleofitsclass(e.g.,Chincarini et al.2007),
×
regime of maximum sensitivity for this experiment. With and in this model the GRB031203 X-ray blast would be a
a peak flux falling close to threshold in the brightest case, similarly extreme case; in addition, it would be the only
relatively slight variations in the profile or spectrum of the known example of an X-rayflare from a GRB-SN.
eventwould be sufficient torender theburst undetectable. None of the other cosmic explosions listed in Table 2
An associated “classical GRB” like GRB031203 thus areknowntoexhibitstrongdistinctepisodes ofgamma-ray
seems plausible; however, our analysis indicates that the and X-rayemission. Their properties are presented to illus-
X-ray properties of the two events must differ to some trate the diversity of the GRB-SN phenomenon, and the
degree. First, we have constrained the timing of the gamma-ray and X-ray luminosities that may generally be
GRB031203 X-ray blast to fall within t = 11 417s of expected from these events on the basis of past experience.
0
±
the GRB (t < 545s at 90%-confidence; 3.3), whereas the Thus,aprompthigh-energyemissionepisodeinXRF060218
0
§
XRTlightcurveforXRF060218risesslowlyuntilitpeaksat like those seen from SN1998bw or XRF020903, and occur-
t 1000s. Second, depending on the assumed relation be- ringpriortothestartofSwift observations,wouldcertainly
≈
tweenextinctionandX-rayscatteringopticaldepth(TM06), havefallen below IPNthreshold, and if present,would help
the GRB031203 X-ray blast may have released as much tohomogenize the GRB-SNeas a class.
2 Swift/XRTlightcurvesrepository:http://www.swift.ac.uk/xrt_curves/
3 Konus-WINDshortburstcatalog: http://www.ioffe.ru/LEA/shortGRBs/Catalog/
(cid:13)c 0000RAS,MNRAS000,000–000
GRB031203 and XRF060218 as Cosmic Twins 9
Table 2.PropertiesofGRB031203 andrelatedcosmicexplosions
Event z logEγ,iso logEX,iso ∆tX−γ Interpretation Refs.
SN 1998bw 0.0085 47.8 47.1 +10 GRB-SNIc 1,2
XRF 020903 0.251 48.5 48.9 0 XRF-SNIc 3,4
GRB 030329 0.167 52.0 51.1 +3 GRB-SNIc 5
GRB 031203 0.105 50.0 49.2–49.6 ±600 GRB-SNIc+? 6,7,8,9
GRB 050502B (2.0) 51.4 51.0 +250 GRB+X-rayflare 10,11
XRF 060218 0.033 49.4 49.1 +1050 XRF-SNIc+shock 12
SN 2008D 0.0065 <46.5 46.3 – SNIcshock 13
logEγ,iso is the isotropic-equivalent gamma-ray energy over 20 keV to 2 MeV, rest-frame (ergs);
logEX,iso is the isotropic-equivalent prompt X-ray energy over 2 to 10 keV, rest-frame (ergs);
and ∆tX−γ is the mean or estimated delay between gamma-ray and X-ray emission, rest-frame
(s). A redshift of z = 2 is assumed for GRB050502B; no redshift-related corrections are ap-
plied for SN1998bw and SN2008D. The two values of logEX,iso for GRB031203 are from TM06
(49.2) and W04 (49.6), respectively. The X-ray energy and time delay for XRF060218 are de-
rived by analysis of the XRT lightcurve from the Swift XRT lightcurves repository (Evans etal.
2007, 2009). The upper limit on Eγ,iso for SN2008D is extrapolated from the Swift BAT upper
limit using an α = 1.5 power-law spectrum. References: 1Galamaetal. (1998); 2Fronteraetal.
(2000); 3Soderbergetal. (2004a); 4Sakamoto etal. (2004); 5Vanderspeketal. (2004); 6SLS04;
7W04; 8TM06; 9this work; 10Burrowsetal. (2005); 11Sakamotoetal. (2008); 12Campanaetal.
(2006);13Soderbergetal.(2008).
Finally, we note that, given that SN2008D manifests ter trigger, our findings significantly restrict the parameter
as an ordinary type Ibc SN, and that rate estimates for space of allowed models for the X-rayblast.
SN2008D-typeX-rayoutburstsareconsistentwiththetotal Weexploretheimplicationsofourfindings,inreference
rateoftypeIbcsupernovae(Soderberg et al.2008),itseems to the properties of all other spectroscopically-confirmed
likely that E 2 1046erg represents a lower boundon GRB-SNe,andconcludethattwoalternativeinterpretations
X,iso
≈ ×
theprompt X-ray energy output of any GRB-SN. seem possible. Ontheonehand (Ghisellini et al. 2006),the
X-ray blast may be the signature of a high-energy “shock
breakout”event,asobservedfromXRF060218;inthiscase,
4 CONCLUSIONS the event should exhibit roughly 2 faster evolution and
×
25% to 200% greater X-ray energy than the XRF060218
The expanding X-ray halos observed by XMM-Newton in
event.Alternatively(W06),theX-rayblast maybethesig-
association with GRB031203 providea rare opportunityto
nature of an X-ray flare that occurred during the inter-
study the prompt soft X-ray properties of a nearby GRB-
val 300s < t < 545s; if so, the ratio of X-ray flare to
0
supernova (V04). We have undertaken a detailed investiga-
gamma-ray burst energies for GRB031203 would be high
tion of these halos in hopes of clarifying the nature of the
butnot unprecedented.
“X-ray blast” (W06) whose dust-scattered X-rays are re-
WepointoutthatobservationsofXRF060218bySwift
sponsible for thehalos.
and IPN experiments allow for the presence of a “precur-
In agreement with previous authors (V04; W04; W06;
sor”gamma-ray burstasluminousas(ormorelikely,some-
TM06), we find that the properties of the halos are consis-
whatlessluminousthan)GRB031203.Inthiscase,ashock-
tent with an X-ray blast occurring simultaneously with the
breakoutoriginfortheGRB031203X-rayblastwouldmake
gamma-rayburstandsubsequentlyscatteringoffdustsheets
GRB031203andXRF060218“cosmictwin”explosionswith
atdistancesd =871.7 9.7pcandd =1388 14pcaway
1 ± 2 ± nearly-identical high-energy properties. If GRB031203 and
in the plane of the Milky Way. In addition, we discover a
XRF060218 thus represent two facets of a single type of
thirdexpandinghalothatrevealsscatteringbyathirddust
GRB-SN,detection andobservation of futurenearbyGRB-
sheet at distance d = 9.94 0.39kpc; the presence of this
3 ± SNe by Swift can be expected to yield additional examples
thirdhaloisarobustfeatureofourmodelasappliedtothe
of these events.
independent EPIC-MOS and EPIC-PN datasets, and due
to the warping of the Milky Way disk, its location is well
within thedensest Hiregions of the outerdisk.
Our constraints on the timing of the X-ray blast, t =
0 ACKNOWLEDGEMENTS
11 417s by comparison to the GRB031203 trigger time
±
(t <545s at 90%-confidence), are comparable in precision TheauthorsacknowledgestimulatingdiscussionswithJamie
0
to the previous best constraint (W06) while suggesting a Kennea, Ehud Nakar, and Avishay Gal-Yam, and valuable
greaterdegreeofsynchronizationbetweentheGRBandthe feedback from the anonymous referee, which has improved
X-rayblast. Combined with upperlimits from INTEGRAL thepaper. This work made use of data supplied bythe UK
observations of GRB031203, which extend to t 300s af- Swift Science Data Centreat the Universityof Leicester.
≈
(cid:13)c 0000RAS,MNRAS000,000–000
10 Feng & Fox
REFERENCES Nousek,J. A.et al. 2006, ApJ, 642, 389
Pian, E. et al. 2006, Nature, 442, 1011
Aptekar,R.L. et al. 1995, Space ScienceReviews, 71, 265
Press, W., Flannery, B., Teukolsky, S., & Vetterling, W.
Bersier, D. et al. 2006, ApJ, 643, 284
1995, Numerical Recipies in C (Cambridge University
Burrows, D. N.et al. 2005, Science, 309, 1833
Press)
Campana, S. et al. 2006, Nature, 442, 1008
Prochaska, J. X. et al. 2004, ApJ, 611, 200
Chincarini, G. et al. 2007, ApJ, 671, 1903
Racusin, J. L. et al. 2009, ApJ, 698, 43
Evans, P. A.et al. 2009, MNRAS,397, 1177
Rodriguez-Pascual, P., Santos-Lleo, M., Gonzalez-Riestra,
— 2007, A&A,469, 379
R., Schartel, N., & Altieri, B. 2003, GRB Coordinates
Frontera, F. et al. 2000, ApJS,127, 59
Network, 2474, 1
Gal-Yam, A. et al. 2004, ApJ,609, L59
Sakamoto, T. et al. 2008, ApJS, 175, 179
Galama, T. J. et al. 1998, Nature, 395, 670
— 2004, ApJ,602, 875
Ghisellini, G., Ghirlanda, G., Mereghetti, S., Bosnjak, Z.,
Sazonov, S. Y., Lutovinov, A. A., & Sunyaev,R. A. 2004,
Tavecchio, F., & Firmani, C. 2006, MNRAS,372, 1699
Nature, 430, 646 (SLS04)
Hjorth, J. et al. 2003, Nature, 423, 847
Soderberg, A. M. et al. 2008, Nature, 453, 469
Hurley,K. et al. 2006, ApJS,164, 124
— 2004a, ApJ, 606, 994
Kalberla, P. M. W. & Dedes,L. 2008, A&A,487, 951
Kalberla, P.M.W.,Dedes,L.,Kerp,J., &Haud,U.2007, — 2004b, Nature,430, 648
A&A,469, 511 — 2005, ApJ,627, 877
Kulkarni,S. R. et al. 1998, Nature, 395, 663 — 2006, Nature,442, 1014
Lumb,D.H.,Finoguenov,A.,Saxton,R.,Aschenbach,B., Stanek,K. Z. et al. 2003, ApJ, 591, L17
Gondoin, P., Kirsch, M., & Stewart, I. M. 2003, Experi- Tiengo, A.& Mereghetti, S.2006, A&A,449, 203 (TM06)
mentalAstronomy, 15, 89 Vanderspek,R.et al. 2004, ApJ, 617, 1251
Malesani, D. et al. 2004, ApJ, 609, L5 Vaughan,S. et al. 2004, ApJ,603, L5 (V04)
Matheson, T. et al. 2003, ApJ, 599, 394 Watson, D. et al. 2004, ApJ, 605, L101 (W04)
Mazzali, P. A.et al. 2006, Nature, 442, 1018 — 2006, ApJ,636, 967 (W06)
Mirabal, N.,Halpern, J. P., An,D., Thorstensen, J. R., & Woosley, S.E. 1993, ApJ, 405, 273
Terndrup,D. M. 2006, ApJ,643, L99 Woosley, S.E. & Bloom, J. S.2006, ARA&A,44, 507
APPENDIX A: RING SURFACE BRIGHTNESS
Inthisappendixwedevelopasemi-analyticaltreatmentofthesurfacebrightnessofring-typesourcesasobservedwithXMM.
The results are incorporated into the numerical model of expanding dust-scattered halos which is used in the main text to
analyse thesoft X-ray properties of GRB031203.
We begin with the angularly-symmetric expression for the XMM point-spread function (PSF; Eq. 1 in the main text),
expressed as a Kingfunction:
sp(r)= απ−r21 (1+r2/rc2)−α, (A1)
c
where r is the radial coordinate and the PSF parameters, core radius r and scaling index α, are functions of the incident
c
photonenergyandexhibitslightly differentfunctionalformsfortheMOS-1,MOS-2,andPNdetectors;representativevalues
for the parameters are r = 4.9′′ and α = 1.44. As expressed here, the surface brightness distribution is normalized to unit
c
integralover0<r< aslongasα>1.WenotethattheXMM PSFisknownnottobeangularly-symmetricandthatthis
∞
form is adopted strictly as a useful approximation to the actual PSF form.
Figure A1 serves to define the coordinate system we use in our analysis. We seek to describe the surface brightness at
the point x, due to a ring of radius R, as an integral over contributions from various angles, 0 φ<2π, where the angular
≤
coordinate is defined from the perspective of the ring centre. Owing to the angularly-symmetric nature of the PSF, we may
takethepoint x to lie on thex-axis, as shown, without loss of generality.
The integral we wish to solve is thusexpressed as:
sr(x)= 21π 2π απ−r21(1+r2/rc2)−α dφ, (A2)
Z0 c
where the squared distance r2 from the point x to the ring element at angle φ can be derived by simple trigonometry as
r2=R2+x2 2Rxcosφ.Insertingthisdefinitionintotheexpressionforthesurfacebrightness,andfactoringoutallcoefficients
−
on the cosφ term, we find:
sr(x)= α2−π21 rc2(α−1) (2Rx)−α 2π rc2+2RR2x+x2 −cosφ −α dφ, (A3)
Z0 (cid:18) (cid:19)
wheretheintegralisnowinaform thatcanbesolvedbyuseofoneofthehypergeometricfunctions, F .Inparticular,ifwe
2 1
(cid:13)c 0000RAS,MNRAS000,000–000