Implications of the X-ray Variability for the Mass of MCG-6-30-15

5 Pages·0.09 MB·English

by  Michael A. Nowak

SUBMITTED1999JUNE23;ACCEPTED2000JANUARY12
PreprinttypesetusingLATEXstyleemulateapjv.04/03/99
IMPLICATIONSOFTHEX-RAYVARIABILITYFORTHEMASSOFMCG- 6-30-15
MICHAELA.NOWAK1ANDJAMESCHIANG1
Submitted1999June23;Accepted2000January12
ABSTRACT
The brightSeyfert1 galaxyMCG- 6-30-15shows large variabilityon a variety of time scales. We study the
<∼3daytimescalevariabilityusingasetofsimultaneousarchivalobservationsthatwereobtainedfromRXTEand
theAdvancedSatelliteforCosmologyandAstrophysics(ASCA).TheRXTEobservationsspannearly106secand
0 indicatethattheX-rayFourierPowerSpectralDensityhasanrmsvariabilityof16%,isflatfromapproximately
0 10- 6–10- 5Hz,andthensteepensintoapowerlaw∝ f- αwithα>∼1.Afurthersteepeningtoα≈2occursbetween
0 10- 4–10- 3Hz. TheshapeandrmsamplitudearecomparabletowhathasbeenobservedinNGC5548andCygX-
2 1,albeitwithbreakfrequenciesthatdifferbyafactorof10- 2 and104, respectively. Ifthebreakfrequenciesare
indicativeofthecentralblackholemass,thenthismassmaybeaslowas106 M . Anupperlimitof∼2ksfor
n ⊙
a therelativelagbetweenthe0.5–2keVASCAbandcomparedtothe8–15keVRXTEbandwasalsofound. Again
J byanalogywithNGC5548andCygX-1,thislimitisconsistentwitharelativelylowcentralblackholemass.

4 Subjectheadings:galaxies:individual(MCG- 6-30-15)—galaxies:Seyfert—X-rays:galaxies
1

2 1. INTRODUCTION mains constant. Iwasawa et al. (1999) suggest that multiple,
v Thetype1SeyfertgalaxyMCG- 6-30-15hasinrecentyears localizedX-rayflares occuronthe disk surfacenear the inner
1 edge and illuminate onlya relativelysmall regionof the disk.
beenthesubjectofintensestudyowingtothediscoverybythe
7 Thesesmallregionsmakecontributionstonarrowrangesinline
AdvancedSatelliteforCosmologyandAstrophysics(ASCA)of
3 redshiftandthusproduceverycomplextemporalbehavior.
a resolved, broad iron Kα fluorescent line in its hard X-ray
6 In supportof this interpretation,Iwasawa et al. (1999)con-
spectrum (Tanaka et al. 1995). The shape of the line is con-
0 sider the iron line associated with a very short, bright flare
9 sistentwithagravitationallyandDopplershiftedemissionline from MCG- 6-30-15 observed during 1997 August by ASCA
9 whichoriginatesfromneartheinneredgeofanaccretiondisk
/ aroundablackhole. IntheX-rays,MCG- 6-30-15isalsoone (see Fig. 1). The line was very redshiftedand had little or no
h emissionbluewardof6keV.Itsshapewasconsistentwithhav-
ofthebrighterandmorevariabletype1Seyferts.Itistherefore
p ingoriginatedentirelyfromasmallregionatr≃5GM/c2 on
hopedthatbyexaminingthecorrelatedvariabilitybetweenthe
- the approaching side of the disk. The flare lasted about 4ks,
o ionizing X-ray continuum and various components of the Fe
whichisalsoapproximatelytheorbitalperiodatthisradiusfor
r Kαline,onecanobtainasizescale forthesystemandthence
t a107M blackhole.Inorderforthelinenottobesignificantly
s amassfortheblackhole(Reynoldsetal.1999).Thisrequires, ⊙
a however,thatthe variouscomponentsof theline bespectrally moresmearedbytheorbitalmotion,Iwasawaetal.(1999)es-
: timateablackholemassof∼2×108M . Alternatively,they
v resolvedontimescalesshorterthantheintrinsicresponsetime ⊙
suggestthatamuchlowermassispossibleifallthelineemis-
i scaleoftheline-emittingmaterial.
X sionarisesfromr<5GM/c2.
Atpresent,ASCA,BeppoSAX,andChandraaretheonlyX-
r raytelescopeswiththespectralresolutiontomeasurefluxesin A major complication that a high-mass model faces is the
a large amplitude and rapid X-ray variability of MCG- 6-30-15
different line components separately. Unfortunately, the inte-
(Fig. 1). In particular, during the performance verification
gration times (∼>10ks) required to obtain this resolution are
phase of ASCA, Reynolds et al. (1995) noted that the 0.5–
longer than the light travel time across the inner edge of an
10keV flux increased by a factor 1.5 over 100s, i.e., the dy-
accretiondiskarounda108M Schwarzschildblackhole.Fur-
⊙ namical time scale at the inner disk edge surroundinga max-
thermore, the fits to the iron line appear to require a Kerr ge-
imal Kerr, 2×106M black hole. Typically one expects the
ometry(althoughseeReynolds&Begelman1997)inorderto ⊙
bulkoftheX-rayvariabilitytooccurondynamicaltimescales
explain the broad red wing of the line and the lack of signif-
orlonger.Itisclearlyimportanttodeterminewhetherthisvari-
icant emission blueward of 6.4keV, thus making the relevant
abilityrepresentedarare,rapideventorifsuchtimescalesare
timescalesevenshorter. Nonetheless,overlongertimescales,
trulycharacteristicofthebehaviorofMCG- 6-30-15.
ASCA has measured significant variability in the shape of the
MCG- 6-30-15FeKαline(Iwasawaetal.1996). Onemightexpectthatcharacteristictimescalesshouldscale
with the mass of the central object (see, e.g., the discussions
Time-resolved spectral investigations (Iwasawa et al. 1996;
of McHardy1988and Edelson & Nandra1999); therefore, in
Iwasawa et al. 1999) suggest that the broad and narrow com-
thisworkwe try to gaugethe size ofthe system andthe mass
ponentsoftheironlinearecorrelateddifferentlywiththeflux
of the black hole in MCG- 6-30-15 by studying its character-
statedependingonthetimescaleinvestigated.Forintegrations
istic X-ray variability propertiesin comparison to other black
∼>104s,thenarrowcomponentvarieswiththecontinuumflux
hole systems such as Cyg X-1 and NGC 5548. For the high-
whilst the broad component appears to be anti-correlated. In
frequencyvariabilityanalysis,weusethe1997Augustsimulta-
contrast,onshortertimescalesthebroadcomponentresponds
neousASCA/RossiX-rayTimingExplorer(RXTE)observation
immediately to flux changes whilst the narrow componentre-
discussed by Iwasawa et al. (1999)(see also Lee et al. 1998).
1JILA,UniversityofColorado,CampusBox440,Boulder,CO80309-0440,USA;[email protected],[email protected]
1
2 ImplicationsoftheX-rayVariabilityfortheMassofMCG- 6-30-15
3.5
s)
cp 3.0
V (
e 4.0
k
5
1 3.0
8-
2.0
3.0
s) 2.5
p
c
V ( 2.0
e
2 k 1.5
5-
0. 1.0
0.5
5 5 5
0 2•10 4•10 6•10
Time (sec)
FIG.1.—TheRXTE8–15 keVband(top)andtheASCA0.5–2keVband(bottom)lightcurves,in4096stimebins.Thesedatahavebeenobtained
fromthearchival1997AugustsimultaneousASCA/RXTEobservation(Leeetal.1998).
InouranalysiswescreentheASCAdataasoutlinedbyBrandt PSD have comparable shapes, i.e., flat from ≈10- 6–10- 5Hz
et al. (1996), exceptthat we use the more stringentcriteria of andslightlysteeperthan f- 1athigherfrequencies.
7 GeV/c for the rigidity and an elevation angle of 10◦. Data We have fit a broken power law to the data, assuming er-
frombothSISdetectorsarecombinedintoasinglelightcurve. rorbarsequalto theaveragePSD valuedividedbythe square
FortheRXTEdata,weusescreeningcriteriaandanalysistech- rootofthenumberoffrequencybinsaveragedover. Although
niquesappropriateforfaintsources,aswehavepreviouslydis- such error estimates are only valid for averages made from
cussed in Chiang et al. (2000). Specifically, we only analyze independent frequency bins (which is not strictly true for the
toplayerdatafromproportionalcounterunits0,1,and2. Lomb-Scargleperiodogram;Scargle1982),thisshouldprovide
aroughestimate,especiallyasthelightcurvesarenearlyevenly
2. POWERSPECTRA sampled. The best fit PSD slopes are - 1.3±0.2 for the PCA
MCG- 6-30-15 is detected by the All Sky Monitor (ASM; and - 1.6±0.3 for ASCA (errors are ∆χ2 = 2.7). The break
Levineetal.1996)onRXTEwithameancountrateof0.44cps frequenciesarefoundtobe(8±3)×10- 6HzforthePCA,and
in the 1.3–12.2keV band. Currently, there is a 0.1 cps uncer- (1.5±0.5)×10- 5Hz for ASCA. These break frequencies are
tainty in the zero level offset, as well as comparable magni- consistentwiththevaluefoundbyMcHardy,Papadakis&Utt-
tude systematic time-dependent variations due to, for exam- ley(1998).
ple, the solar angular position relative to the source (Remil- At frequencies >5×10- 4Hz there are enough contiguous
lard 1999, priv. comm.). Assessing the very low frequency data segments to be able to calculate the PSDs using stan-
(f <∼10- 6Hz) X-ray variability of MCG- 6-30-15is therefore dard FFT methods (Nowak et al. 1999, and extensive refer-
problematic. Efforts are currently underway, however, to re- ences therein). In Fig. 2 we show the calculated, background
visetheASMdatareductionprocessinordertominimizesuch and noise-subtracted, PSD for the 1.8–3.6keV and 8–15keV
systematiceffects(Remillard1999,priv.comm.);therefore,an RXTE bands. Below ≈ 2×10- 3Hz, where signal to noise
ultra-lowfrequencyvariabilitystudyofMCG- 6-30-15inprin- is greatest, both PSDs are consistent with being ∝ f- 2±0.3
ciplewillbefeasibleinthenearfuture. and having 6% rms variability. From the generated back-
We are able, however, to investigate the high-frequency ground lightcurves, we estimate that background fluctuations
power spectral density (PSD) of MCG- 6-30-15 by using the contribute at most 1.5% and 2% rms variability, respectively,
RXTE 8–15keV and the ASCA 0.5–2keV lightcurves binned to these PSDs at < 2×10- 3Hz. As the PSDs of the back-
on 4096sec time scales. Both lightcurves contain data gaps, ground lightcurves tend to be slightly steeper than f- 2, there
especially on the orbital time scale of ≈5ks due to blockage maybe some trendfor backgroundfluctuationsto steepen the
bytheEarthandpassagethroughtheSouthAtlanticAnomaly. observed high-frequency PSDs, and, in fact, Yaqoob (1997)
We therefore use the techniques of Lomb (1976) and Scargle findaslightlyflatter(∝ f- 1.4)high-frequencyPSDforMCG- 6-
(1982) to calculate the PSD, and we only consider frequen- 30-15.
cies f <∼10- 4Hz(evenlysampledinintervalsoftheinverseof
3. TIMEDELAYS
the observation duration). Higher time resolution lightcurves
showedexcesspoweronthe≈5ksorbitaltimescale. There- In order to examine time delays between the low energy
sults,binnedoverthegreateroffourcontiguousfrequencybins ASCA lightcurve and the high energy RXTE lightcurve, we
or logarithmically over f →1.15 f, are presented in Fig. 2. use the Z-transformed Discrete Cross-Correlation Function
Hereweuseaone-sidednormalizationwhereintegratingover (ZDCF) of Alexander (1997), which is based upon the DCF
positivefrequenciesyieldsthetotalmeansquarevariabilityrel- methodofEdelson&Krolik(1988).Auto-correlationfunctions
ative to the squared mean for the particular lightcurve being canalsobecomputedbythisprocedure,andwenotethatPSD
analyzed. The ASCA lightcurve shows 28% rms variability, derived from autocorrelations calculated via the ZDCF yield
whereastheRXTElightcurveshows16%rmsvariability. Both identicalresultstothosepresentedinFig.2. WeusetheMonte
Nowak&Chiang 3
1 0 4
ASCA
1 0 3
RXTE-PCA
z1 0 2
H
2S/
M
R
1 0
RXTE-PCA
1
0 . 1
1 0-6 1 0-5 1 0-4 1 0-3
Frequency (Hz)
FIG. 2.—PSDconstructedfromASCA0.5–2keV(filleddiamonds),RXTE1.8–3.6keV(opendiamonds), andRXTE8–15keV(opensquares)
lightcurves.Dashedlinesshowthebrokenpowerlawfitsdiscussedinthetextandan f- 2powerlaw.Backgroundandnoisehavebeensubtracted
fromthehigh-frequency1.8–3.6keVand8–15keVRXTEPSD,withtheresidualnoiselevelsshownasadottedandsolidline,respectively.
CarlomethodsdescribedbyPetersonetal.(1998)toassessthe 10- 3Hz. This is to be compared to the Cyg X-1 PSD which
significanceofanyuncertaintiesduetofluxmeasurementerrors has a comparable rms amplitude and shape, and has a set of
aswellasunevenorincompletesampling. PSD breaks at frequencies between 0.03–0.3Hz and 1–10Hz
We have previously applied these methods to a simultane- (Nowak et al. 1999, and references therein). The black hole
ous Extreme Ultraviolet Explorer(EUVE)/ASCA/RXTEobser- mass in Cyg X-1 is estimated to be 10M (Herrero et al.
⊙
vationofNGC5548(Chiangetal.2000),wherewefoundev- 1995); therefore, if these break frequencies scale with mass,
idenceforthe lowenergyASCAbandleadingthe highenergy then the central black hole mass of MCG- 6-30-15 could be
RXTEbandby5ks. TheresultsfortheMCG- 6-30-15dataare as low as 106M . NGC 5548, which is believed to have a
⊙
shown in Fig. 3, for which we have used lightcurves binned centralblackholemassof108M (Done&Krolik1996;Chi-
⊙
at 512s resolution. A positive delay indicates that the RXTE ang&Murray1996;Peterson&Wandel1999),showsasimi-
light curvelagsthe ASCA lightcurve. Due to the ambiguities lar PSD with breakfrequenciesat≈6×10- 8Hz and between
associated with interpreting cross-correlation results, particu- 3×10- 7–3×10- 6Hz(Chiangetal.2000). Again,ifthebreak
larlyforsuchsmalldelays,weconsideredthreedifferentmea- frequenciesscale with mass, then the central black hole mass
suresofthe“lag”. ForeachMonteCarlotrial,weestimatethe forMCG- 6-30-15couldbeseveralordersofmagnitudelower
characteristic lag by (1)fitting a parabolato the ZDCF values thanthatforNGC5548.
to find the locationof the peak, (2) computingthe centroidof Todate,themostcarefullystudiedX-rayPSDforanyAGN
theZDCFoverpositivevaluesbracketingthemaximumvalue, is that for NGC 3516 (Edelson & Nandra 1999). (See also
and(3)usingthelocationoftheactualmaximumvalueofthe McHardy, Papadakis & Uttley 1998 who present preliminary
ZDCF. In all three cases, our simulations yield evidencefor a results for a number of AGN, including MCG- 6-30-15.) For
positivelagatvariousdegreesofsignificance:τ =0.9±0.7ks, NGC 3516 the PSD was seen to break from nearly flat at
fit
τ =0.9±1.3ks,τ =0.4+1.9 (90%C.L.). Althoughthe <∼3×10- 7Hz,andthengraduallysteepenintoan f- 1.74 power
fictetnetdroidpeak estimate is cmoanxsistent- 1w.2ith a positive lag, both the law up to frequencies as high as ≈ 10- 3Hz. NGC 3516 is
centroid and ZDCF-maximum estimates are formally consis- seen to be intermediate between NGC 5548 and MCG- 6-30-
tentwithzerogivinganupperlimitofτ <∼2ks. 15. Based upon these measurements (and upon other factors,
At high Fourier frequency, we have used the 1.8–3.6keV suchasthesourceluminosity),Edelson&Nandra(1999)argue
and8–15keV RXTElightcurvesdiscussedabovetosearchfor forablackholemassintherangeof107–108M ,i.e.,interme-
⊙
frequency-dependenttimelagsusingstandardFFTtechniques. diatetothemassesofNGC5548andMCG- 6-30-15discussed
(Acompletediscussionofsuchmethods,includingcalculation above.
oferrorbars,ispresentedinNowaketal.1999andreferences The RXTE/ASCA lag upper limit for MCG- 6-30-15 is also
therein). No significant time delays were found, and the 1-σ intermediate between the observed X-ray lags for Cyg X-1
upperlimitswere50–100sinthe5×10- 4–2×10- 3Hz range. (Miyamoto et al. 1988; Nowak et al. 1999) and NGC 5548
Note that there were an insufficient number of uninterrupted, (Chiangetal.2000). ThetimelagobservedinNGC5548,ef-
strictlysimultaneousASCA/RXTElightcurvestoallowcalcula- fectivelymeasuredonthe f- 2 portionofitsPSD,is5ks. Time
tionoftheirrelativetimedelaysviadirectFFTmethods. lagsontheflatportionoftheNGC5548PSDcouldbeconsider-
ablylonger(Chiangetal.2000). NearthePSDbreakfromflat
to f- 1,theX-raytimelagsinCygX-1are≈0.1s,whilstonthe
4. DISCUSSION f- 2portionofthePSDtheX-raytimelagsare10- 3–10- 2s. The
TheMCG- 6-30-15PSDbreakstobeing∝ f- 1at≈10- 5Hz, MCG- 6-30-15 time lags may cover a similar dynamic range
and then breaks to being approximately∝ f- 2 between 10- 4–
4 ImplicationsoftheX-rayVariabilityfortheMassofMCG- 6-30-15
FIG. 3.—Z-transformeddiscretecorrelationfunction(ZDCF)oftheSIS,0.5-2keVlightcurverelativetothe8–15keVRXTE-PCAlightcurve
(512stimebins).ThesolidlineisaparabolafittotheZDCFvalues.MonteCarlosimulationsofthesedatayieldanupper-limitontheRXTEtime
lagof2.2ks(90%ConfidenceLevel).
from<2ks(overalllag)to<100s(highfrequencylag2). where ultra-low frequency noise is typically associated with
If the characteristic variability and lag times are indicative dippingactivityduetoobscurationbytheaccretionstream(An-
of mass, then a mass as low as 106M may be required for gelini, White & Stella 1994). Previous models, for example,
⊙
thecentralblackholeofMCG- 6-30-15.Assumingabolomet- haveassociated‘veryhighstate’low-frequencyvariabilitywith
ric luminosityof 4×1043 ergss- 1 (Reynoldset al. 1997),this fluctuationsof a viscously unstable α-disk (Nowak 1994, and
would implythatMCG- 6-30-15is emitting at30%of its Ed- referencestherein).
dingtonrate,whichislargebutstillplausible. Arelativelylow Thishighlightsthemajorcaveatthatneedstobementioned;
centralblackholemasswouldmakethelargeamplitude,rapid we do notknowthe averagePSD shapenorthe scaling of the
variabilityreportedbyReynoldsetal.(1995)mucheasiertoun- break frequencies as a function of fractional Eddington lumi-
derstand,whereasamassaslargeasthe2×108M ,theupper nosity in either galactic black hole candidates or AGN. This
⊙
end discussed by Iwasawa et al. (1999), seems very unlikely. is an especially importantconsiderationas the mass estimates
The<∼100slagsseenathighfrequencythenlikelyprovidean discussed above imply a large range of Eddington luminosity
upperlimittotheComptondiffusiontimescale(seethediscus- ratios. Considering all the evidence for rapid variability and
sionofNowaketal.1999). Thesetimescalesareproblematic extremely short time lags in MCG- 6-30-15 discussed above,
forfuturehopesofsimultaneouslytemporallyandspectrallyre- however,alowmassforMCG- 6-30-15seemstousverycom-
solvingtheironKαlineinthissystemwithConstellation-Xas pelling. With the adventofthe X-ray Multiple Mirror (XMM)
itwillrequire≈1ksintegrationtimestostudythelineprofile mission, which has large effective area and is capable of ex-
ofMCG- 6-30-15(Young&Reynolds2000). tremely long, uninterrupted observations, these analyses will
A 30%Eddingtonluminosityindicatesthatitisworthwhile becomemoredetailedforNGC5548andMCG- 6-30-15,and
to search for ultra-low frequency (f <∼10- 6Hz) variability in willallowonetodevelopastatisticalsampleofnumerousother
excessof≈3%rms, thatis, abovean extrapolationofthe flat AGN.
partoftheASCAandRXTE-PCAPSDs. ‘Veryhighstate’,i.e.,
>∼O(30%L ),galacticblackholecandidatescanshowPSDs
Edd
that are flat below ≈10- 2Hz, are approximatelyproportional We thankR.RemillardforgeneratinganASMlightcurveof
to f- 2 PSD between ≈ 10- 2–10- 1Hz, are flat again between MCG- 6-30-15,andO.Blaes, K.Pottschmidt, N.Murray,and
≈ 10- 1–1Hz, and then break into an f- 2 PSD at higher fre- J.Wilmsforusefulconversations.Thisworkhasbeenfinanced
quencies. (Specifically, see Fig. 4b of Miyamoto et al. 1991, byNASA GrantsNAG5-4731,NAG5-7723,and NAG5-6337.
which shows a ‘very high state’ PSD of GX339- 4.) The low ThisresearchhasmadeuseofdataobtainedthroughtheHigh
frequency portion of the ‘very high state’ PSD has no simple EnergyAstrophysicsScienceArchiveResearchCenterOnline
analogy in the (usually observed) low/hard state of Cyg X-1, Service,providedbytheNASA/GoddardSpaceFlightCenter.
2AlthoughthelowenergybandheredifferedfromtheASCAband,ifthetimelagsscalelogarithmicallywithenergy(Nowaketal.1999andreferencestherein)
wewouldhaveexpectedthelagwithrespecttotheASCAbandtobeapproximatelyafactorof2greater.
Nowak&Chiang 5
REFERENCES
Alexander, T., 1997, in Astronomical Time Series, ed. D. Maoz, et al., McHardy,I.M.,Papadakis,I.E.,&Uttley,P.,1998,inTheActiveX-RaySky:
(Netherlands:KluwerAcademicPress),163 ResultsfromBeppo-SAXandRXTE,ed.L.Scarsi,H.Bradt,P.Giommi,F.
Angelini, L., White, N. E., & Stella, L., 1994, in New Horizon of X-Ray Fiore,(Amsterdam:Elsevier),509,inpress
Astronomy,ed.F.Makino,T.Ohashi,(Tokyo:UniversalAcademyPress), Miyamoto,S.,Kimura,K.,Kitamoto,S.,Dotani,T.,&Ebisawa,K.,1991,ApJ,
429 383,784
Brandt,W.N.,Fabian,A.C.,Dotani,T.,Nagase,F.,Inoue,H.,Kotani,T.,& Miyamoto,S.,Kitamoto,S.,Mitsuda,K.,&Dotani,T.,1988,Nature,336,450
Segawa,Y.,1996,MNRAS,283,1071 Nowak,M.A.,1994,ApJ,422,688
Chiang,J.,&Murray,N.,1996,ApJ,466,704 Nowak,M.A.,Vaughan,B.A.,Wilms,J.,Dove,J.,&Begelman,M.C.,1999,
Chiang,J.,Reynolds,C.S.,Blaes,O.,Nowak,M.A.,Murray,N.,Madejski, ApJ,510,874
G.,&Marshall,H.,2000,ApJ,inpress(astro-ph/9907114) Peterson,B.M.,&Wandel,A.,1999,ApJ,521,L95
Done,C.,&Krolik,J.H.,1996,ApJ,463,144 Peterson,B.M.,Wanders,I.,Horne,K.,Collier,S.,Alexander,T.,Kaspi,S.,&
Edelson,R.A.,&Krolik,J.H.,1988,ApJ,333,646 Maoz,D.,1998,PASP,110,660
Edelson,R.A.,&Nandra,K.,1999,ApJ,514,682 Reynolds,C.S.,&Begelman,M.C.,1997,ApJ,488,109
Herrero,A.,Kudritzki, R.P.,Gabler,R.,Vilchez,J.M.,&Gabler,A.,1995, Reynolds,C.S.,Fabian,A.C.,Nandra,K.,Inoue,H.,H.Kunieda&K.Iwasawa
A&A,297,556 1995,MNRAS,277,901
Iwasawa,K.,etal.,1996,MNRAS,282,1038 Reynolds,C.S.,Ward,M.J.,Fabian,A.C.,&Celotti,A.,1997,MNRAS,291,
Iwasawa,K.,Fabian,A.C.,Young,A.J.,Inoue,H.,&Matsumoto,C.,1999, 403
MNRAS,submitted(astro-ph/9904078) Reynolds,C.S.,Young,A.J.,Begelman,M.C.,&Fabian,A.C.,1999,ApJ,
Lee,J.C.,Fabian,A.C.,Reynolds,C.S.,Iwasawa,K.,&Brandt,W.N.,1998, 514,164
MNRAS,300,583 Scargle,J.D.,1982,ApJ,263,835
Levine,A.M.,Bradt,H.,Cui,W.,Jernigan,J.G.,Morgan,E.H.,Remillard, Tanaka,Y.,etal.,1995,Nature,375
R.,Shirey,R.E.,&Smith,D.A.,1996,ApJ,469,L33 Yaqoob,T.,1997,ApJ,479,184
Lomb,N.R.,1976,Ap&SS,39,447 Young,A.J.,&Reynolds,C.S.,2000,ApJ,inpress(astro-ph/9910168)
McHardy,I.M.,1988.MemoriedellaSocietaAstronomicaItaliana,59,239.ed.
Pallavicini,R.andWhite,N.E.