Finding a 24-day orbital period for the X-ray binary 1A 1118-616

0.27 MB·English

by  R. Staubert

Astronomy&Astrophysicsmanuscriptno.astro-ph˙15737˙v2 (cid:13)c ESO2011
January17,2011
Finding a 24-day orbital period for the X-ray binary 1A 1118-616
R.Staubert1,K.Pottschmidt2,3,V.Doroshenko1,J.Wilms4,S.Suchy5,R.Rothschild5,andA.Santangelo1
1 Institutfu¨rAstronomieundAstrophysik,AbteilungAstronomie,Universita¨tTu¨bingen(IAAT),Sand1,72076Tu¨bingen,Germany
2 NASA-GoddardSpaceFlightCenter,AstrophysicsScienceDivision,Code661,Greenbelt,MD20771,USA
3 CenterforSpaceScienceandTechnology(CRESST),UniversityofMarylandBaltimoreCounty,1000HilltopCircle,Baltimore,
MD21250,USA
4 Dr.KarlRemeis-SternwarteandErlangenCenterforAstroparticlePhysics,Universita¨tErlangen-Nu¨rnberg,Sternwartstr.7,96049
Bamberg,Germany
5 CenterforAstrophysicsandSpaceSciences(CASS),UniversityofCaliforniaSanDiego,LaJolla,CA92093-0424,USA
1
1
Received10.09.2010;accepted02.11.2010
0
2
ABSTRACT

n
a WereportthefirstdeterminationofthebinaryperiodandorbitalephemerisoftheBeX-raybinarycontainingthepulsar1A1118-616
J (35yearsafterthediscovery ofthesource). Theorbital periodisfound tobeP =24.0±0.4days. Thesource wasobserved by
orb
RXTEduringitslastlargeX-rayoutburstinJanuary2009,whichpeakedatMJD54845.4,bytakingshortobservationseveryfew
4
days,coveringanelapsedtimecomparabletotheorbitalperiod.Usingthephaseconnectiontechnique,pulsearrivaltimedelayscould
1
bemeasuredandanorbitalsolutiondetermined.Thedataareconsistentwithacircularorbit,andthetimeof90degreeslongitude

wasfoundtobeT =MJD54845.37(10),whichiscoincidentwiththatofthepeakX-rayflux.
] π/2
E
Key words.stars:binaries:general–stars:neutron–X-rays:general –X-rays:Bebinaries–X-rays:individuals:1A1118-616 –
H
Ephemerides
.
h
p
- 1. Introduction
o
r TheX-raytransient1A1118−61wasdiscoveredduringanout-
t
s burst in 1974 by the Ariel-5satellite in the 1.5–30keV range
a (Eylesetal. 1975). The modulation with a period of 6.75min
[
found in the data used by Ivesetal. (1975) was initially inter-

2 pretedastheorbitalperiodoftwocompactobjects.Fabianetal.
v (1975) then suggested that the observed period may be due
9 to a slowly spinning accreting neutron star in a binary sys-
5 tem. The optical counterpart was identified as the Be-star He
4 3-640/Wray793byChevalier&Ilovaisky(1975)andclassified
2
as an O9.5IV-Ve star with strong Balmer emission lines and
.
2 an extended envelope by Janot-Pachecoetal. (1981). The dis-
1 tancewasestimatedtobe5±2kpc(Janot-Pachecoetal.1981).
0 The classification anddistance was confirmedby Coe&Payne
1 (1985)usingUVobservationsofthesource. Fig.1. The light curve of the outburst of 1A 1118-616 as ob-
v: A second strong X-ray outburst occurred in January 1992, served by RXTE/PCA (4–40keV) in January 2009. The time
i which was observed by CGRO/BATSE (Coeetal. 1994). The resolutionis 16s. Thecontinuouscurveisthe dailylightcurve
X measuredpeakfluxwas∼150mCrabforthe20-100keVenergy as seen by RXTE/ASM (scaled to the PCA count rate and
r range,similartothatofthe1974outburst.Thisoutburstwasfol- smoothedbytakingtherunningmeanoffiveconsecutivedays).
a
lowedbyenhancedX-rayactivityfor∼60days,withtwoflare-
likeeventsabout∼25dand∼49dafterthepeakoftheoutburst
(seeCoeetal.1994, Fig.1).Pulsationswith ∼406.5swerede-
tectedupto100keVandthepulseprofileshowedasinglebroad clusion is supported by pulsations from the source also being
peak, close to a sinusoidal modulation with little change with detectedinquiescence(Rutledgeetal.2007).
photonenergy.Aspin-upwitharateof0.016s/daywasobserved The source remained quiescentuntil January4, 2009 when
duringthedecayoftheoutburst.Multi-wavelengthobservations a third outburst was detected by Swift (Manganoetal. 2009;
revealed a strong correlation between the H equivalent width Mangano2009).Pulsationswithaperiodof407.68±0.02swere
α
and the X-ray flux. This led Coeetal. (1994) to conclude that reported by Mangano (2009). The complete outburst was reg-
expansionofthe circumstellardisk oftheopticalcompanionis ularly monitored by RXTE. INTEGRAL observed the source
mainlyresponsiblefortheincreasedX-rayactivity,includinga after the main outburst (Leyderetal. 2009). Suzaku observed
largeoutburstifthereisenoughmatterinthesystem.Thiscon- 1A 1118−61 twice, once during the peak of the outburst and
also∼20dayslaterwhenthefluxreturnedto itspreviouslevel.
Sendoffprintrequeststo:[email protected] Doroshenkoetal.(2010)analyzedRXTE/PCAdataofthemost
2 R.Staubertetal.:Findinga24-dayorbitalperiodfortheX-raybinary1A1118-616
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Fig.2. An example of a pulse profile (with 32 phase bins) of Fig.3.Anexamplelightcurvewith 16s resolutionofonecon-
1A1118-616asobservedin∼2.5ksbyRXTE/PCA(normalized tinuousobservationbyRXTE/PCAinthe4–40keVinterval,to-
toameanfluxof1.0),correspondingtothefoldingof6pulses getherwiththebest-fitcosinefunction.
withapulseperiodof∼407.7s.Thecenteroftheobservingtime
isMJD54844.375.Theprofileisrepeatedsuchthattwophases Table1.Orbitalelements,P andP˙ of1A1118-616.The
pulse pulse
areshown.Thisprofilewasusedasatemplateinmeasuringrel- uncertaintiesare1σ(68%)fortwoparametersofinterest.
ativephaseshiftsofprofilesfromotherintegrationintervalsand
thecorrespondingpulsearrivaltimes. T [MJD(TDB)] = 54845.37±0.10
π/2
P [d] = 24.01±0.43
orb
asini[lt-s] = 54.85±1.4
recent outburst with emphasis on spectral analysis, detecting a eccentricityǫ = 0.01
cyclotronresonantscatteringfeature(CRSF)at∼55keV. Ω[deg] = 360.01
In this letter, we report on an in-depth timing analysis of P [s]atT 2 = 407.6546±0.0011
pulse ref
RXTE/PCA data overthe entire outburst in January 2009,and P˙ [ss−1]atT 2 = (−1.8±0.2)×10−7
pulse ref
thediscoveryofanorbitalperiodof24.0d.Thissolutionissup- 1Theseparameterswerekeptfixed(seetext),2T =54841.2593913
ref
ported by the timing of the three large X-ray outbursts seen in seetextregardingthisuncertainty
historyandbytheanalysisofpulsearrivaltimesoftheJanuary
1992BATSEobservations.
tion intervals ranged from ∼1500s to ∼15000s, corresponding
tobetweenfourand38pulses.Nineteenpulseprofiles(with32
2. Observations phasebins)werethenconstructedbyepoch-foldingbarycenter-
corrected event times (since the Earth is always moving with
Weusedtwodatasets.First,andmostimportantly,weanalyzed respect to the source, the event arrival times are referenced to
data obtained by RXTE/PCA during a 27-day monitoring of thecenterofthesolarsystem).Fig.2showsoneofthesepulse
1A 1118-616, which started on January 7, 2009, covering the profilesproducedbyaccumulatingsix pulses(centeredatMJD
completeoutburst.Theresultinglightcurve(4–40keV)isshown 54844.375).Usingthisprofile,thepulsearrivaltimes(inMJD)
in Fig. 1. The source flux peaked on January 14 and decayed for the other profiles were determined by template fitting. The
over∼15days.Thedatastructureisdefinedbytheorbitsofthe uncertainties of these arrivaltimes are of the order of 10sec
RXTEsatellite, with 29RXTEpointings of a typical duration (∼2.5%ofthepulseperiod).
ofaroundonehour.Atotalexposureof87kswasobtained.The For the case of no binary modulation and non-zero first
PCA data were all taken ineventmode(”Good Xenon”), pro- andsecondderivativesofthe pulse period,the expectedarrival
vidingarrivaltimesforindividualevents.Thedatawerereduced timesas a function of pulse number n are given by (see, e.g.,
usingHEASOFTversion6.8. Kelleyetal.1980;Nagase1989;Staubertetal.2009)
A second data set consists of pulse profiles generatedfrom
1 1
archivaldataoftheobservationoftheJanuary1992outburstby t =t +nP + n2 P P˙ + n3 P2P¨ +... (1)
CGRO/BATSE,coveringabout12days. n 0 s 2 s s 6 s s
With the given accuracy, it was possible to phase-connect the
19 pulse arrival times and determine values for the pulse pe-
3. Timinganalysisofpulsearrivaltimes riodanditsfirstderivativebyapplyinga quadraticfitinn.The
sondderivativeP¨ wasnotconstrainedandsettozero.Inthisfit,
3.1.RXTE/PCA-2009 s
significantsystematicresidualsremainedwithasine-likeshape
Some timing analysis of the RXTE data was performed ear- andanamplitudeofseveraltensofseconds,indicativeofpulse
lier byDoroshenkoetal. (2010),who determinedthe pulsepe- arrival-timedelaysduetoorbitalmotion.Addingtheadditional
riod and an initial value of its derivative but failed to identify term
the orbital modulation. Here, a more rigorous analysis is per-
+ asin i×cos[2π(t−T )/P ] (2)
formed,which beginsin a similar way by selecting 19integra- π/2 orb
tion intervals of the 29 pointings according to the time struc- yieldedanacceptablefitasexpectedforacircularbinaryorbit,
tureoftheindividualsatellitepointings(Fig.1).Theseintegra- asini being the projected radius of the orbit in light-seconds,
R.Staubertetal.:Findinga24-dayorbitalperiodfortheX-raybinary1A1118-616 3
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Fig.4.Delaysofthepulsearrivaltimesin1A1118-616forthe Fig.5.Delaysofthepulsearrivaltimesin1A1118-616forthe
outburstofJanuary2009asobservedbyRXTE/PCAandbest- outburstinJanuary1992asobservedbyCGRO/BATSE.
fitsinecurveforcircularorbitalmotionwithaperiodof24.0d.
Thedotsaroundzeroaretheresidualstothebest-fitsolution.
3.2.CGRO-1992
The second data set is from observations of the January
1992 outburst by CGRO/BATSE. This outburst is described
well in Coeetal. (1994). Pulse profiles were generated using
and T (= T ) in MJD being the time at which the mean
π/2 90 phase/energy channel matrices for all eight BATSE detectors
orbital longitude of the neutron star is 90◦, corresponding to
which are stored at the HEASARC archive. 1 For each detec-
the maximum delay in pulse arrival time. We found that asini
tor,eventsinthe20–40keVenergyrange(accordingto theen-
∼55light-s,P ∼24d,T MJD∼54845,P ∼407.7s,and
orb 90 pulse ergy calibration provided) were selected and sorted into com-
P˙ ∼−1.9×10−7ss−1.
s mon pulse profiles with 128 phase bins. This was done for 12
Wethenrealizedthatbyusingtheoriginallightcurve,asam- differentintegrationintervals, coveringabout12daysof obser-
ple ofwhichisshownin Fig. 3, we were ableto determinethe vation (MJD 48621–48633). Pulse arrival times in MJD were
pulsearrivaltimesmoreaccurately,whenfittedpiecewisewitha determinedbytemplatefitting.Fig.5showsthedelaysofpulse
cosinefunction(keepingthepulseperiodfixedatthepreviously arrival times as found from a pulse phase connection analysis.
foundbest-fitvalues,andleavingthemeanflux,theamplitude, Assumingan orbitalperiodof 24.0d, the best-fitsolutionfor a
and the zero phase as free parameters). The same 19 integra- circularorbitleadstotheparametersofP =406.53±0.02s,
pulse
tionintervalsasbeforewereused.Thephaseconnectionanaly- P˙ =(−3.1±0.9)×10−7ss−1,andT =MJD48633.5±2.5d.
pulse π/2
sisofthepulsearrivaltimesdeterminedinthiswaythenleadsto WhenthedifferencebetweentheT valuefromtheRXTEob-
π/2
the orbital elements and pulse period information summarized servation(seeTable1)andtheonefromtheBATSEobservation
in Table 1. The pulse delay times and the residuals against the is divided by the orbital period of 24.0d, we find a separation
expecteddelaysforthebest-fitcircularorbitisshowninFig.4. of258.83orbitalcycles.If,inturn,wedividetheseparationby
Theχ2ofthisbestfitwas21.0for15dof(degreesoffreedom). 259 cycles, we determinea cycle length of 23.98d. The corre-
In finding this solution, we assumed a vanishing eccentric- spondinguncertaintyinthisvalueis0.01d.However,wecannot
ity and a fixed value of 24.0d for the orbital period.When the be certain wether the separation is really 259 cycles, since the
orbitalperiodwasleftasafreeparameter,wefoundthatP = previouslyfounduncertaintyof0.4dintheorbitalperiodwould
orb
24.0±0.4d. This uncertaintyis expected to be large since our permitanycyclenumberbetween255and263.
observationscoveronly27days,littlemorethanoneorbitalcy-
cle.
4. Othersupportforthe24.0dorbitalperiod
Finally, we attempted a properorbitalsolution with the ec-
centricityǫandthelongitudeofperiastronpassageΩincludedas 4.1.TimingoflargeX-rayoutbursts
freeparametersbysolvingKepler’sequation.Thedatadoallow
ThreelargeX-rayoutburstsof1A1118-616havebeenobserved
one to define a pair of parameters with reasonably constrained
uncertaintiesofǫ =0.10±0.02andΩ=(310±30)◦.However, sofar.Thefirstoneoccurredin December1974,leadingtothe
originaldiscoveryofthesourcebyARIEL-5(Eylesetal.1975;
weconsidertheevidenceofanon-zeroeccentricityasmarginal.
Ivesetal. 1975). At this time, a modulation with a period of
Byintroducingthesetwoadditionalfreeparameters,theχ2 was
6.75min was also discovered. The second burst was observed
reducedfrom21.0(15dof)to16.4for(13dof).AnF-testyielded
by CGRO/BATSE in January 1992 (Coeetal. 1994), with en-
aratherlargeprobabilityof∼22%fortheimprovementtohave
hancedX-rayactivityfor∼80days.Thethird,mostrecentout-
occuredbychance.Furthermore,nosystematicuncertaintiesof
burst occurred in January 2009 and was observed by several
anykindwereconsidered.
X-ray satellites: Swift (Manganoetal. 2009; Mangano 2009),
Wenotethatthevaluesforthepulseperiodanditsderivative
RXTE (Doroshenkoetal. 2010), INTEGRAL (Leyderetal.
given in Table 1 differ from those stated by Doroshenkoetal.
(2010) because of the missing orbital correctionsin the earlier 1 ftp://heasarc.gsfc.nasa.gov/compton/data/batse/pulsar/
analysis. groundfolded/A1118-6
4 R.Staubertetal.:Findinga24-dayorbitalperiodfortheX-raybinary1A1118-616
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#’(!! #’)!! #’*!! #’+!! ##!!! !’! !’( &’! &’( "’!
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Fig.6.AsectionoftheX-raylightcurveof1A1118-616asob- Fig.7.FrequencyhistogramofASMsmallflareswithpeakflux
servedbytheRXTE/ASM(smoothedusinga runningmeanof >0.5cts/s(fromsmootheddailylightcurves)asafunctionofthe
five consecutivedays).The large burstof January2009,reach- 24.012dphase.
ing a peak flux of 7.6cts/s at MJD 54845.4 is included. The
shortverticallinesareatphase0.0withrespecttotheephemeris
with P = 24.012d and the arrowspoint to those small flares 4.3.TimingofsmallX-rayflares
orb
with peak fluxes>0.5cts/s (dottedhorizontalline), which hap-
InthesectionoftheASMlightcurveshowninFig.6,threesmall
penclosetophase0.0(severalothersappeartohappencloseto
peaksbeforethebigburst(highlightedbysmallarrows)happen
phase0.5).
quite close to phase zero. There are also flares at other phases,
but counting the numberof flares with peak fluxes higherthan
0.5cts/soverthecompleteASMlightcurve(MJD50087-MJD
55315),wefind39outof86flares(45%)betweenphase-0.15
and+0.15.Therestarealmostuniformlydistributedwithaslight
2009), and Suzaku. Also in this case, the source continued to enhancementaroundphase0.5.Theanalysisofexcursionswith
exhibit high activity for about 70days after the large outburst. fluxes>1.0cts/sconfirmsthisresult:15outof32eventsbetween
Fromthecitedpublications,wedeterminedthetimeofthepeak phase -0.15and +0.15.Fig. 7 showsthe frequencydistribution
fluxes in these outbursts to be MJD 42407.0, MJD 48626.0, for the case of the >0.5cts/s peaks. When the same analysis is
and MJD 54845.4, respectively, with an estimated uncertainty repeated with orbital periods corresponding to separations be-
of ±1day in all cases. Taking the abovevalue of 24.0d for the tween the large outbursts other than 259 orbital cycles (that is
orbital period, the outbursts in December 1974 and the one in between 255 and 263), the rate of coincidencesof small flares
January 2009 occurred 259 orbits before and after the one in with phase zero is significantly less. We take this as an indica-
January1992.But,again,becauseoftheuncertaintyinPorb the tion,notproof,that259isprobablytherightnumber.
separations could range from 255 to 263 orbital cycles, corre-
When a simple epoch folding of the long-term light curve
spondingtoaseriesofperiodvaluesseparatedbyabout0.1d.In of1A1118-616asobservedbyRXTE/ASMisdone,nosignif-
Section4.3,however,wepresentevidencethat259maybe the icant peak is found at ∼24d. This is not inconsistent with the
correct number. Assuming that this is indeed so, a linear fit to
above considerations of medium size and small X-ray flares:
the threeoutbursttimes leadsto a periodof (24.012±0.003)d
there are only very few (not well aligned) medium size flares,
(thesmalluncertaintybeingduetothelongbaselineintime). occurringafterthebigoutbursts,andthesmallflares(>0.5cts/s)
have such low fluxes that both types of flares are completely
buriedinthe”noise”representedbythedailyfluxmeasurements
4.2.Timingofmedium-sizeX-rayflares
<0.5cts/s. When a dynamicalpowerdensityspectrum (PDS)
(seee.g.Wilmsetal.2001)isgenerated(withanindividualdata
Asalreadymentioned,thesourceremainsparticularlyactiveaf-
set length of 2000d and a step size of 10d), a weak signal in
terthesecondaswellasafterthethirdlargeoutburstforseveral
the form of a broad peak between 22d and 25d is found. The
tens of days. Fig. 1 in Coeetal. (1994) shows this for the sec-
PDSiscapableofdetectingquasi-periodicsignalsallowingfor
ond large burst (observedbyCGRO/BATSE in January 1992):
frequencyvariationswithtime.
thereishighlystructuredX-rayemissionwithseveralpeaks,the
largest of which are around ∼26d and ∼49d after the peak of
thelargeburst(withpeakfluxes∼0.5and∼0.4ofthebigburst,
5. Inclinationandmassfunction
respectively). In Fig. 6, we show the light curve in the vicin-
ity of the third large burst (of January 2009) as observed by Usingtheorbitalelementsdeterminedaboveandanestimateof
RXTE/ASM(inasmoothedversionofthedailylightcurvewith themassoftheopticalcompanion,wecanconstraintheinclina-
arunningmeanoffiveconsecutivedays).Threepeakscanalso tionofthebinaryorbitof1A1118/He3-640.Theopticalcom-
beidentifiedwithin∼70d ofthethelargeburst,noneofwhich panionwasclassifiedbyJanot-Pachecoetal.(1981)asanO9.5
correspondsexactlyto phasezero,butthe secondandthe third III-Ve star with strong Balmer emission lines and an extended
one are close (the mean of the three separations- starting with envelope.Motchetal.(1988)assumedamassof18 M forthe
⊙
thelargeburst-is∼23d). opticalcompanion.WhenthecalibrationofO-starparametersof
R.Staubertetal.:Findinga24-dayorbitalperiodfortheX-raybinary1A1118-616 5
Martinsetal.(2005)isused,thevalueof18M isconfirmed(in- shortnessofthelargeroutburstsmayhavehelpedthe24dorbital
⊙
terpolatingthevaluesforO9.5ofTables4and5ofMartinsetal. periodescapedetectionfor35yrsafterthesource’sdiscoveryin
2005).Adoptingthisvalueandassuming1.4M forthemassof 1975. 1A 1118-616 is indeed at the edge of the Be star distri-
⊙
theneutronstar,Kepler’sthirdlawleadstoaphysicalradiusof butiontowardstheregionwherewind-fedSGXRBs(supergiant
the (circular) orbit of a = 219.1light-s. The observed a sin i = X-raybinaries) accumulate,and the secondmostoffset Be star
54.85light-sthenleadsto sin i= 0.25andto the inclinationof after SAX J2103.5+4545.For the latter, Reigetal. (2004) had
i = 14.5◦. This value is consistent with no eclipses being ob- discussed a physical reason for the slow spin at a rather short
served. The mass function is f(M) = (m sin i)3 / (m +m )2 = orbital period, namely that long episodes of quiescence in Be
2 1 2
1.14×10−4. X-ray systems can cause a spin down to an equilibriumperiod
thatisexpectedforwind-drivenaccretion.Thismayalsoapply
to 1A 1118-616 and is consistent with the observed moderate
6. Discussion
spin-uprate(∼1.1Hzs−1)duringitsoutburstsinJanuary2009.
The detection of the period of 24days for the binary orbit of A discussion of variousalternative ways of reaching very long
1A1118-616restsmainlyontheobservationandanalysisofor- spinperiodsisgiveninFarrelletal.(2008)inthecontextofin-
bitaldelaysofthearrivaltimesoftheX-raypulses(withapulse vestigatingtheextremelyslow(∼2.7h)pulsar2S0114+650.
period of ∼407s). The main data set is from observations by
RXTE/PCA,whichsampledthelargeX-rayoutburstofJanuary Acknowledgements. We acknowledge the support through DLR grant
50 OR 0702. RSt likes to thank Klaus Werner and Dima Klochkov for
2009. Fortunately, the duration of the outburst as well as the
discussions about the optical companion and the analysis of the ASM light
length of the observations were long enough to cover slightly curve,respectively.RERandSSacknowledgethesupportunderNASAcontract
morethanonecompleteorbit.Itwasalsofortunatethatthesam- NAS5-30720. Wethank Robin Corbet forpointing us to SAX J2103.5+4545
plingpatternwasdenseenoughtoallowpulsephaseconnection andforhisdatacollectionoftheCorbet-diagram.
betweenthesamplingintervals.However,withdataforonlyone
orbitthedeterminationoftheorbitalperiodusingthesedatahas
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the two phenomena with each other, which is clearly justified
Staubert,R.,Klochkov,D.,&Wilms,J.2009,A&A,500,883
by examples of these associations in other Be X-ray binaries Wilms,J.,Nowak,M.,Pottschmidt,K.,Heindl,W.,&Dove,J.B.andBegelman,
(Grundstrometal.2007;Kizilogluetal.2009;Reigetal.2010). M.C.2001,MNRAS,320,327
WithrespecttothetimingofthethreeobservedlargeX-ray
bursts, we emphasize that the two separations are the same at
17.04yrs. Motchetal. (1988) already concluded that the enve-
lopeofHe3-640isprobablynotinastationarystatebutunder-
goesexpansionandcontractionphasesonatimescaleofseveral
years.”We suggestthatthe17yrsbetweenthelargeX-rayout-
burstsisacharacteristicperiodfortheoscillationoftheenvelope
ofHe3-640.
Finally, we look at the position of 1A 1118-616 in the
Corbet-diagram,whichrelatestheorbitalperiodtothespinpe-
riod (see e.g., Reigetal. 2004; Rodriguezetal. 2009). For Be
binaries,thereisconsiderablescatteraroundameancorrelation
trend,which was quantifiedby Corbet(1986) by the following
formula:P = 10 days× (1−e)−2/3 (P /1 s)1/2. According
orb spin
to this formula, an orbital period of ∼200d or more had been
expected(e.g., Motchetal. 1988), a prediction that in addition
tothegenerallylowleveloftheX-rayfluxandtherarenessand