MAXI observations of long-term variations of Cygnus X-1 in the low/hard and the high/soft states

2.4 MB·

by  Juri Sugimoto

PASJ:Publ.Astron.Soc.Japan,1–??,hpublicationdatei
c 2016.AstronomicalSocietyofJapan.
(cid:13)
MAXI observations of long-term variations of Cygnus X-1 in the low/hard and the
high/soft states
JuriSugimoto1,2,TatehiroMihara1,ShunjiKitamoto2,5,MasaruMatsuoka1,MutsumiSugizaki1,
HitoshiNegoro3,SatoshiNakahira4andKazuoMakishima1
∗
1MAXIteam,InstituteofPhysicalandChemicalResearch(RIKEN),2-1Hirosawa,Wako,Saitama351-0198,Japan
2DepartmentofPhysics,RikkyoUniversity,3-34-1Nishi-Ikebukuro,Toshima,Tokyo171-8501,Japan
6 3DepartmentofPhysics,NihonUniversity,1-8-14,Kanda-Surugadai,Chiyoda-ku,Tokyo101-8308
1 4ISSScienceProjectOffice,InstituteofSpaceandAstronauticalScience(ISAS),
0 JapanAerospaceExplorationAgency(JAXA),2-1-1Sengen,Tsukuba,Ibaraki305-8505,Japan
2 5ResearchCenterforMeasurementinAdvancedScience,

n RikkyoUniversity,3-34-1Nishi-Ikebukuro,Toshima,Tokyo171-8501,Japan
a [email protected]
J

2 (Receivedhreceptiondatei;accepted2016January11)
1
Abstract

]
E Long-termX-ray variability of the black hole binary, Cygnus X-1, was studied with five years of MAXI data
H from2009to 2014,which includesubstantialperiodsof the high/softstate, as wellas the low/hardstate. In each
state, NormalizedPowerSpectrumdensities(NPSDs)werecalculatedinthreeenergybandsof2-4keV,4-10keV
.
h and10-20keV.TheNPSDsinafrequencyfrom10 7Hzto10 4Hzareallapproximatedbyapower-lawfunction
− −
p withanindex 1.35 1.29. ThefractionalRMSvariationη,calculatedintheabovefrequencyrange,wasfound
- − ∼−
o to show the following three properties; (1) η slightly decreases with energy in the low/hard state; (2) η increases
r towardshigherenergiesin the high/softstate; and (3)in the 10–20keV band, η is 3 times higherin the high/soft
t
s state than in the low/hard state. These properties were confirmed through studies of intensity-correlated changes
a oftheMAXIspectra. Ofthesethreefindings,thefirstoneisconsistentwiththatseenintheshort-termvariability
[
duringtheLHS.Thelattertwocanbeunderstoodasaresultofhighvariabilityofthehard-tailcomponentseeninthe

1 high/softstatewiththeaboveverylowfrequencyrange,althoughtheoriginofthevariabilityremainsinconclusive.
v Keywords:blackholephysics—accretion,accretiondisks—X-ray:general—stars: individual:CygnusX-1
0
4
7 1. Introduction plasma.TheoriginofhardtailintheHSSisdifferentfromthat
2 intheLHS,andisstillunknown.
0
Black-hole (BH) X-ray binaries emit X-rays through the TimevariationsoftheX-rayintensityareanotherimportant
.
1 massaccretionfromtheircompanionstars. Thematteraccretes aspectofBHX-raybinaries.EspeciallyCygnusX-1(hereafter
0 ontotheBHforminganaccretiondisk,whichisconsideredto Cyg X-1), the leading galactic BH binary with an orbital pe-
6 work as an efficient energy-releaseengine. The propertiesof riodof5.6d, hasprovidedrichinformationonthe short-term
1
accretion disks have been studied by both theoreticaland ob- variabilityin bothstates (e.g. Churazovetal. 2001;Grinberg
:
v servational approaches. From the theoretical studies, a disk etal.2014).Thepowerspectrumdensity(PSD)intheLHShas
i is considered to evolve from the RIAF (Radiative Inefficient apower-lawshapewithanindexofabout 1inthefrequency
X
Accretion Flow ; Ichimaru 1977; Narayan & Yi 1994) state, rangefrom10 4to10 2Hz. Between10−2Hzand10 1Hz,
r − − − −
a throughthestandard-diskstate(Shakura&Sunyaev1973),up thePSDisconstantasawhitenoise. Above10−1 Hz, thein-
to the slim-disk state (Abramowiczet al. 1988), as the accre- dex returns to about 1. There is a break again at around 1
−
tionrateincreases. Observationally,galacticBHbinariesshow Hz, above which the index becomes steeper (e.g., Belloni &
two spectral states, the low/hard state (hereafter LHS) which Hasinger1990;Nowak2000;Negoroetal.2001;Pottschmidt
is dominated by a power-law spectrum, possibly correspond- et al. 2003). These time scales are thought to reflect the dy-
ingtotheRIAF,andthehigh/softstate(hereafterHSS)which namics of accretion flows, and the process of energydissipa-
is dominated by an optically-thick thermal emission from an tionorparticleaccelerationinavicinityoftheBH.Thebreak
accretion disk, i.e. the standard-disk (Tanaka & Shibazaki at1HzintheLHScanbeinterpretedasadecaytimescaleof
1996; Remillard & McClintock 2006; Done et al. 2007). In individualshots, which appear in a light curve (Negoro et al.
theHSS,ahardtailcomponentisseenintheenergyspectrum, 2001). In the HSS, the PSD is approximatedby a power-law
whichoftenextendsfrom10keVtoseveralMeVbyapower- alsowithanindexof 1,butthisformcontinues,withoutflat-
law (Gierlin´ski et al. 1999). In the LHS, there is also hard tening,from10 4 Hz−upto20Hz, beyondwhichitsteepens.
−
tailextending 100keVwithaclearcut-off,whoseoriginis ThePSDextendingwithaconstantindex 1suggeststhatthe
∼ −
consideredthatthermalComptonizationofdiskphotonsbyhot accretion flows in the HSS have no characteristic time scales
overthe10 4–20Hzrange.Churazovetal.(2001)explained
∗ Lastupdate:Jan9,2016 −
the overallshape ofthe PSD in the LHSandthe HSS ofCyg
2 AstronomicalSocietyofJapan [Vol.,
X-1 with a phenomenological model that the optically-thick Cyg X-1 was in the LHS for about ten months. At around
diskissandwichedbyoptically-thinaccretionflowsextending MJD=55378,thesourcemadeatransitiontotheHSS,where
up to a largedistance fromthe BH. Inthe LHSthe optically- it stayed for another ten months. After several times of state
thick disk is truncated at some distances from the BH, turn- transitions,ithasbeenmainlyintheHSSsinceMJD=56078.
ingintooptically-thinandgeometricallythickaccretionflows
(Makishimaetal.2008). 3. Analysisandresults
On frequencies lower than 10 4 Hz (time scales of 0.1
∼ − 3.1. Definitionofspectralstates
d), thevariabilityof Cyg X-1hasbeen studiedmainlyby ap-
plying PSD analyses to the data obtained with RXTE obser- AsshownintheHRhistoriesinfigure1,CygX-1exhibited
vations. Reig etal.(2002)calculatedPSDs ofCygX-1using distinct LHS and HSS. Since the two HR histories have the
morethanelevenyearsofdataobtainedwiththeRXTE/ASM. same trend, we hereafteruse the I(4–10keV)/I(2–4keV) ra-
TheyshowedthatPSDs inthe10 7 to10 5 Hzrangecanbe tio,whichhasbetterstatistics. Thetoppaneloffigure2shows
− −
expressed by a power-law with an index of 1, and that the a hardness-intensitydiagram. Thus the two states are clearly
−
PSDs dependontheenergy(over1.3– 12.2keV) bya factor separated. The bottom panel in figure 2 shows a histogram
of3 5.Thelong-termvariabilityofhardX-raysfromCygX- of the HR, which exhibits two clear peaks corresponding to
1wa∼sstudiedbyVikhlininetal.(1994),downto4 10 4Hz, theHSSandtheLHS.Wefitthehistogramwithtwogaussian
−
×
using the GRANAT/SIGMA data. They detected a very low functionsanddeterminedtheirmeanvaluesandstandarddevi-
frequencyQPO(Quasi-PeriodicOscillation)around0.04–0.07 ations.Thenwedefinedtheboundariesofeachstateas3σfrom
Hz. However,onfrequenciesof<10 4Hz,ourunderstanding the gaussiancenter, i.e. HR<0.43forthe HSS and 0.48<HR
−
ofCygX-1variabilityhasremain∼edmuchpoorer,especiallyin fortheLHS.
the HSS, than the rich informationaccumulatedon the short- Fromfigure1andfigure2,theperiodsofthetwostateshave
termvariability. beenobtainedaslistedintable1.
The Monitor of All-sky X-ray Image (MAXI) obtained a
long-termlightcurveofCygX-1formorethanfiveyears.The 10
object had been in the LHS until 2010 June, and after that it
stayedmainlyin theHSS(Negoroetal. 2010). By analyzing
)
PSDsandenergyspectrafromthisuniquedataset,weinvesti- -2 m
gatedthecharacteristicsoflong-termvariationsofCygX-1in c
bothstates. -1s
s
n
o
2. Observation ot
h
P
(
The data of Cyg X-1 to be analyzed here were obtained V
e
with MAXI (Matsuoka et al. 2009), which is attached to the 0 k
InternationalSpaceStation. AstheInternationalSpaceStation 1
-
2
orbits the earth in every 92 min, MAXI scans over nearly y
the entire sky with two kinds of X-ray cameras: the Gas Slit sit 1
n
Camera(GSC:Miharaetal.2011)coveringtheenergybandof nte
2–20keV,andtheSolid-stateSlitCamera(SSC:Tomidaetal. I
2011)covering0.7–7keV.
FromtheMAXIhomepage1, wedownloadedone-daybin
and 90-minute bin archival data of Cyg X-1. These archival 40
data were selected on the conditionthat X-ray incident angle m
a 30
to a camera is smaller than 38 andscan times of the source gr
◦ o
andthebackgroundarebothlongerthan15s. Energyspectra st 20
Hi
oftheGSCandSSCwereprocessedbytheMAXIon-demand
10
datawebpage2 (Nakahiraetal.2013). Weselected2 .0fora
◦
sourceregionand3 .0forabackgroundregion. 0
◦ 10-1 1
Figure 1 shows one-day bin light curves of Cyg X-1 ob-
tainedwiththeGSCfrom2009August15(MJD =55058)to Hardness Ratio (4-10 keV / 2-4 keV)
2014November9(MJD=56970),inthreeenergybands(2–4
keV, 4–10 keV and 10–20 keV). Time histories of two kinds
Fig.2. Thehardness-intensitydiagram(toppanel)andthehistogram
ofhardnessratios(HR),I(4–10keV)/I(2–4keV)andI(10–20 ofthe4–10keVvs. 2–4keVHR(bottompanel). Blueandreddata
keV)/I(4–10keV),arealsoplotted. ThestateofCygX-1can pointsspecifytheLHSandtheHSS,respectively, whileblackpoints
berecognizedbythevaluesoftheHR. weretakenduringtransitions.
Since the start of the MAXI observation in 2009 August,
1 http://maxi.riken.jp/top/index.php?cid=1&jname=
J1958+352
2 http://maxi.riken.jp/mxondem/
No.] Usageofpasj00.cls 3
( a )
LHS 1 H S S 2 3 4 5 6 7 8 9 10 11 12
4
V
e
k 2
4
2- -2 m) 0
V c
e 1 2
k -s
10 ns 1
4- oto 0
h
V p 0.4
e (
k
0 0.2
2
-
0 0
1
V V
s Ratio 4 - 10 ke 2 - 4 ke 01
s
ne V V0.8
Hard 10 - 20 ke 4 - 10 ke0.40 55500 56000 56500 MJD
(2010) (2011) (2012) (2013) (2014) (year)
( b ) 10−20 keV light curve in log scale ( c ) 10−20 keV light curve in linear scale
LHS (No.1−all) 0.3 LHS (No.1−all)
0.2
0.1 0.2
0.05
-2 m) 0.02 -2 cm) 0.1
-1otons s c 00.0.21 HSS (No.8−all) -1hotons s 0.03 HSS (No.8−all)
( ph 00.0.15 ( p 0.2
0.1
0.02
0.01 0
0 100 200 300 400 0 100 200 300 400
days from start MJD days from start MJD
Fig.1.(a)One-daybinlightcurvesandHRhistoriesofCygX-1obtainedwiththeMAXI/GSC.Fromthetoptobottompanels,the2–4keV,4–10keV
and10–20keVintensities, andtheI(4–10keV)/I(2–4keV)andI(10–20keV)/I(4–10keV)ratiosareplotted. Theblackandgrayregionsatthetop
indicatetheLHSandtheHSSperiods,respectively.Datapointswithlargeerrorbars,duetohighbackgroundcounts,wereomitted.(b)Expanded10–20
keVlightcurves(three-daybin)ofDataNo.1-allandNo.8-all,representingtheLHSandtheHSS,respectively. Ordinatesarelogarithmic.(c)Thesame
aspanel(b),butwithlinearscales.DataNo.1-allanddataNo.8-allareshownLHSandHSS,respectively.ThedataNo.isindicatedintoppanel,andthe
correspondingMJDsarelistedintable2andtable3.
4 AstronomicalSocietyofJapan [Vol.,
Table1.Spectral states of Cyg X-1 during the MAXI observation. MAXIlightcurvesaregenerallysensitivetosourcevariations
Datanumbersareindicatedinfigure1. notonlyontimescalelongerthan5400s, butalsotothesein
between40 70sand 5400s.
data spectrum start end duration ∼ ∼
InordertocorrectthePSDsfortheeffectsofgaps(hereafter
No. state MJD MJD day
gapeffects),andthoseoftheshortexposurewithlong-interval
1 hard 55058 55376 318
sampling (hereafter sampling effects), we simulated MAXI
2 soft 55378 55673 295
data of a variable source with specified variability. Since the
3 hard 55680 55788 108
PSDofCygX-1canbeapproximatedbyapower-lawwithan
4 soft 55789 55887 98
5 hard 55912 55941 29 indexof 1(Reigetal.2002;Churazovetal.2001),thisform
−
6 soft 55943 56068 125 ofPSDwasemployedastheinputvariability. Furtherassum-
7 hard 56069 56076 7 ingthatthephasesoftheFouriercomponentsarerandom,we
8 soft 56078 56733 655 produceda hundredfake lightcurves, eachofwhichhas54s
9 hard 56735 56741 6 time bin and covers the same time span as figure 1. Details
10 soft 56742 56757 15 of the PSD simulation are given in Appendix A. Then, for
11 hard 56781 56824 43
each simulation run, we picked up one data pointfrom every
12 soft 56854 56970∼ 116∼
100bins(=5400s=oneorbit)anddiscardedthe99pointsto
simulatethesamplingeffects,andappliedthesameobserving
windowas forCyg X-1in orderto reproducethe gapeffects.
3.2. Powerspectra
Interpolatingthegapsinthesamewayasfortheactualdata,a
3.2.1. DefinitionofPSDs PSD wascalculatedfroma fakelightcurve. Finally, we took
TheX-raylightcurvewith90-minutebinwasconvertedto anaverageofthe100simulatedPSDs,andnormalizedittothe
thePSDbythediscreteFouriertransformationas assumedinputPSD,toobtainthetransferfunction(inFourier
space;figure9inAppendixA)ofthepresentMAXIobserva-
N
2
F (f)= y cos(2πf∆t j) tionofCygX-1.Below,PSDsobtainedfromtheobserveddata
c j
N × are dividedby the transferfunctionthus obtained, in orderto
j=1
X correct for the gap effects and the sampling effects. Prior to
N
2 thisdivision,wesubtractthePoissonnoise,whichisestimated
F (f)= y sin(2πf∆t j) (1)
s N j × byanumericalsimulation(AppendixB).
j=1
X 3.2.3. Results(1):usingthelongestdatalength
whereyiistheintensity(photonss−1cm−2)atthei-thbin,N ForboththeLHSandHSS,wecalculatedNPSDsfromthe
is the number of data after filling the gaps as described later, lightcurvesinthethreeenergybands,2–4keV,4–10keVand
and∆tisa timeintervalof5400s, whichisthe regularsam- 10–20keV.Incalculation,thelongestspanofdatawasusedfor
plingtimeoftheMAXIpublicdata,f isthefrequencywhich eachstate,i.e.318daysfortheLHSand477daysfortheHSS.
isanintegermultipleof∆f=1,andT isthetotaltimespanof These data segments are shown in table 2 (as No. 1-all) and
T
theobservation. Thefactorof2/N isemployedsothatFc(f) table3(asNo. 8-all),respectively,togetherwithothershorter
andFs(f)representtheamplitudeofthecosineandsinecom- segmentsavailable.OnlytheGSCdatawereused,becausethe
ponents,respectively,regardlessofN. ThePSDisthesumof SSCdataaremuchmoresparsethanthoseoftheGSC.Inthe
squaresofF andF as, HSS, the selected span is shorter than Data No. 8 in table 1
c s
becauseshortdatabunchesatthebeginningandtheendofthe
T
P(f)= F2(f)+F2(f) . (2) span were removed. After subtracting the Poisson noise and
2 c s
correctingforthegapandthesamplingeffects(section3.2.2),
Bymultiplyin(cid:8)gwithafactorof(cid:9)T/2,thederivedPSDbecomes we obtained NPSDs down to 3 10 8 Hz as shown in figure
−
independent of T, and has a unit of (RMS2/Hz). The PSD 3. The error of each data point×was obtained by propagating
isnormalizedbythesquareoftheaverageintensityfollowing
errorsoftheobservedlightcurve. TheNPSDsextendroughly
Miyamotoetal.(1994).ItiscallednormalizedPSD(NPSD). witha power-lawshapedownto3 10 8 Hz, buttheyscatter
−
3.2.2. Correctionsforsamplingandgapeffects largelyinthelowfrequency( 3 ×10 7Hz)region.
−
The MAXI data are not completely regular-sampled. ≤ ×
3.2.4. Results(2):usingshorterdatalengths
Sometimes data gaps are caused by sun avoidance, high par-
By shorteningthedatalengthtobeusedinaFouriertrans-
ticlebackgroundregions,smalldeadregionsatthescanpoles
form by equation (1), we can produce a larger number of
which move with the precession period of the orbit of the
NPSDs,andtaketheiraverage.TheNPSDobtainedinthisway
InternationalSpace Station, and other effects. Therefore, we
isexpectedtosuffersmallerstatisticalerrors,althoughitlacks
interpolated each gap with a linear line, which connects the
theinformationinthelowestfrequencies. Thus,thedataspan
pre-gap intensity (averaged over 5 data points) and the post-
wasrestrictedto40and43daysfortheLHSandtheHSS,re-
gap value (also averaged over 5 data points) (Sugimoto et al. spectively,tocoverafrequencyrangedownto 3 10 7Hzat
−
2014).Furthermore,thederivedPSDsarestronglyaffectedby thesacrificeofthe3 10 8 3 10 7Hzran∼ge.×Bydoingso,
− −
aliasing effects, because MAXI measures the intensity of an × − ×
thefractionofdatagapswasreducedfrom 50%to 10%.
X-raysourceonlyfor40 70s,every5400speriod. Thatis, As listed in table 2, six data segments wer∼e extracted∼for the
∼
each data point is a very short snapshot, with a long interval
LHS,andeightdatasegmentsintable3fortheHSS.Then,we
to thenext(orfromthe preceding)sampling. Asa result, the
converted these data segments individually into NPSDs, and
No.] Usageofpasj00.cls 5
Table2.DatasegmentsusedincalculatingNPSDintheLHSs. of 0.3(intheLHS)and 0.2(intheHSS).
∼ ∼
Figure4revealstwomoreimportantproperties. Oneisthat
data start end
the NPSD normalizationsin the HSS are significantly energy
No.∗ MJD MJD
dependent,increasingtowardshigherenergies, whereasthose
1-all 55058 55376
intheLHSshowamuchweakerandoppositetrend.Theother
1-1 55060 55100
is that Cyg X-1 is much more variable, at least above 4 keV,
1-2 55138 55178
on the relevant time scales while it is in the HSS than in the
1-3 55209 55249
1-4 55277 55317 LHS. To quantify these properties, we integratedthe 6 (3 en-
3-1 55700 55740 ergybandstimestwo states) ensemble-averagedNPSDsfrom
11-1 56781 56821 10 6to9.2 10 5Hz,andderivedindividuallythefractional
− −
×
RMSvariationηas
*:“I-J”denotestheJ-thsegmentintheI-thdata. “I-all”meansas ☎☎ NF
thesegmentsintheI-thdatanumber. η= 2∆f NPSD(f ) (3)
i
s
i=1
X
Table3.Thesameastable2butfortheHSS. where N is the number of data points in each NPSD. The
F
data start end results, given in table 4, indeed confirm the above inferences
No. MJD MJD : the fractional RMS variation in 10–20 keV in the HSS
8-all 56130 56607 (η = 0.70) is larger than that in the LHS (η = 0.21). This
2-1 55487 55530 property can be read directly from the light curve in a loga-
2-2 55623 55666 rithmic scale presented in figure 1b. Meanwhile, when plot-
8-1 56201 56244 ted in a linear scale (figure 1c), the absolute amplitude of
8-2 56273 56316
variability is similar between the LHS and HSS. These two
8-3 56418 56461
propertiescan beexplainedasfollows. The 10–20keV value
8-4 56564 56607
of η is 0.70/0.21 3.3 times higher in the HSS than in the
8-5 56637 56680 ∼
LHS, while the average 10–20 keV intensities (as read from
12-1 56926 56969
figure 1c) in the HSS is 0.089/0.19 0.47 times that in the
∼
LHS.ThereforetheabsoluteamplitudeofvariationsintheHSS
tooktheiraverages,separatelyovertheLHSandHSS.Theob- shouldbe3.3 0.47=1.55timesthatintheLHS.Thisisclose
×
tainedensemble-averagedNPSDsareshowninfigure4,where tounity,thoughnotexactlythesame.
theverticalerrorbarsrepresenttheNPSDscatter(standardde- In the LHS, a peak corresponding to the orbital period of
viation) within each ensemble. In figure 4, ordinate employs 5.60 d is clearly seen in the low energy band (2–4 keV) at
powertimesfrequency,insteadofpoweritself. 2.06 10−6 Hz. However, it is not clear in the other two en-
×
As expected, the NPSDs in figure 4 are less scattered even ergybandsintheLHS,inagreementwiththeGinga/ASMre-
in the low frequencyrangebelow10 6 Hz, and show similar sultsbyKitamotoetal.(2000). IntheHSS,theorbitalperiod
−
structuresinalltheenergybands,althoughtheycouldstillbe isnotclearlyseeninanyenergyband.
subject to some structures including shallow dips around3 Figure5showsour4–10keVNPSDsinbothstates,incom-
10 6Hz,andtheweaktendencyofflatteningbelow3 10×7 parisonwithpreviousworksbyCuietal.(1997),Pottschmidt
− −
Hz. As shown by a simulation in Appendix A, the p×ossible et al. (2003), and Reig et al. (2002). In both states, our re-
flattening is unlikely to be caused by the data gaps. Instead, sultsat10−4HzlocateonsimpleextrapolationsoftheNPSDs
it could be within the scatter of NPSDs, considering that the obtainedpreviouslybytheRXTE/PCAinthefrequencyregion
effectisseenin onlythelowest-frequencydatapointsinboth above10−3Hz.Thefigurereconfirmsandvisualizesthehigher
states. We also note that the energy dependence in figure 3 variabilityintheHSS,alreadypresentedintable4.TheNPSD
andfigure4isslightlydifferent. Especially,thenormalization in Reig et al. (2002) is located between the two states of the
of the 4–10 keV NPSD in the HSS in figure 3 is higher than presentwork.Thisdifferenceispresumablybecausetheirdata
thatinfigure4.Consideringtheensemble-averagingprocedure include some of the HSS and the transition periods, although
involved in the NPSDs in figure 4, we regard them as better themainpartisintheLHS.
representingtheCygX-1variabilitythanthoseinfigure3.
3.3. EnergySpectra
As seen in figure 4, the NPSD slope does not appear to
depend significantly either on the spectral state or the energy In order to investigate the spectral componentsthat are re-
band. To confirm this suggestion, we fitted the individual sponsible for the observed long-term variations, we analyzed
NPDSswithapower-law,overafrequencyrangeof10 6 and energyspectraofCygX-1obtainedwiththeMAXI/GSCand
−
9.2 10 5 Hz. Then, the 18 NPSDs before taking ensemble theSSC.WeusedthesameperiodsasinthePSDanalysis,i.e.
−
aver×ages(6segmentstimes3energybands)intheLHSgavean from MJD = 55058 to MJD = 55376 for the LHS, and from
averageslopeandtheassociatedRMSscatteras 1.35 0.29, MJD = 56130 to MJD = 56607 for the HSS. The SSC data,
whereas the 24 HSS ones (8 segments times 3 e−nergy±bands) availableonlyforaboutonethirdofthetime,werealsoincor-
gave 1.29 0.23. Therefore, the NPSD slope is consistent porated.
with b−eing in±dependentof the state. In addition, slope differ- Insection3.2,wefoundthatthelong-termvariabilityofCyg
encesamongthe3energybandsareatmostwithinthescatter X-1,particularlyintheHSS,issignificantlyenergydependent.
6 AstronomicalSocietyofJapan [Vol.,
106 Porb=5.6 d LHS 106 Porb=5.6 d HSS
)
) 2
2 n
an 105 ea 105
e m
m
-1Hz/ 104 -1Hz/ 104
2S 2S
M 103 M 103
R R
SD ( 102 2−4 keV SD ( 102 2−4 keV
NP 101 140−−1200 k keeVV NP 101 140−−1200 k keeVV
10-8 10-7 10-6 10-5 10-4 10-8 10-7 10-6 10-5 10-4
frequency (Hz) frequency (Hz)
Fig.3.NPSDsofCygX-1intheLHS(left)andintheHSS(right),eachcalculatedusingthelongestdataspan(No. 1-allintable2andNo. 8-allin
table3).Theblue,blackandredpointsrepresentNPSDsinthe2–4keV,4–10keVand10–20keVband,respectively. Theverticallineat2×10−6Hz
indicatesthe5.6-dayorbitalperiod.
0.1 0.1
LHS HSS
D D
S 0.01 S 0.01
P P
N N
* *
y y
c c
n n
e e
equ 10-3 P =5.6 d equ 10-3 P =5.6 d
fr orb fr orb
2−4 keV 2−4 keV
4−10 keV 4−10 keV
10−20 keV 10−20 keV
10-4 10-4
10-7 10-6 10-5 10-4 10-7 10-6 10-5 10-4
frequency (Hz) frequency (Hz)
Fig.4. TheNPSDscalculatedovershorterdatasegments(40d×6fortheLHSand43d×8fortheHSS),andaveraged. Here,theNPSDsareshown
aftermultiplyingwiththefrequency.
Table4.ThefractionalRMSηofNPSDsfrom10−6to9.2×10−5Hz.
Spectralstate LHS HSS
Energyband(keV) 2-4 4-10 10-20 2-4 4-10 10-20
η 0.31±0.09 0.24±0.05 0.21±0.04 0.31±0.09 0.53±0.12 0.70±0.29
No.] Usageofpasj00.cls 7
Reig+2002
105
HSS
103
LHS
D
S 101
P Cui+1997
N
10-1
Pottschmidt+2003
10-3
10-8 10-6 10-4 10-2 100 102
frequency (Hz)
Fig.5.AcomparisonoftheMAXI4–10keVNPSDsintheLHS(blue)andtheHSS(red),withthepreviousworks. Thedashedlineisthe2–13keV
NPSDintheLHSbyPottschmidtetal.(2003),thedottedlineisthatintheHSSin2–13keVbyCuietal.(1997),andthedot-dashedlineisthatbyReig
etal.(2002)wherethemostdataareintheLHS.
To reconfirm the implied spectral variation in this frequency whereaisanappropriatenumericalfactoroforderunity,which
range, we divided the observed data into bright and faint pe- canbeapproximatedasenergyindependent. Thisawasintro-
riodsbycomparingthe individualone-dayGSC intensitiesin ducedbecausethe variationη of equation(3)calculatedfrom
2–20 keV with their 15-day running averages. Since the 15- NPSDcanbedifferent,byaconstantfactor,fromthatderived
daytimescalecorrespondstoafrequencyof8 10 7Hz,this by equation (5). The derived values of η are also shown in
− ′
×
procedure means an extraction of time variations longer than table 5, were a =2.9 has been adopted. Thus, the values of
8 10 7 Hz. Then, eightspectra in totalwere produced;the η agree,withinerrors,withη intable4whichisbasedonthe
− ′
×
GSC and SSC data in the bright and faint periods, from the PSDanalysis.
LHSandHSS.Thebackground-subtractedeightMAXIspectra To understand the physical origin of the behavior seen in
obtainedinthiswayareshowninfigure6. Thus,asexpected, figure 7, as well as in table 4 and table 5, we proceeded to
theHSSspectraaremuchsofterthanthoseoftheLHS,ingood simultaneous model fitting to the 2–20 keV GSC spectrum
agreementwiththegeneralunderstandingofthespectralstates. and the 0.7–7 keV SSC spectrum. The 1.5–2 keV range of
Forreference, these spectraincludeperiodsofincreasedlow- the SSC was excluded to avoid the known systematic uncer-
energy absorption (seen as dips in the 2–4 keV light curves), tainty in the effective area (Tomida et al. 2011). First, we
whichoftenappearfor 15%oftheorbitalphase. employed a model composed of a multi-color disk (diskbb)
∼
To bettervisualizetheintensity-correlatedspectralchanges model (Shakura & Sunyaev 1973; Mitsuda et al. 1984) for
infigure6,wepresent,infigure7,theratiosoftheGSCspec- the low-energy part, and a power-law (powerlaw) as a hard
trum in the brightperiodto that in the faintperiod. The SSC tail. This model has often been used in the previous stud-
data are not shown here, because the errors are large. In the ies of BH X-ray binaries including Cyg X-1 (e.g. Dotani
LHS,theratiodecreasesslightlywithenergy,whereastheHSS et al. 1997). The photo-electric absorption model (phabs)
ratioincreasessignificantlytowardshigherenergies. Toquan- with abundances by Anders & Ebihara (1982) and the Fe-
tify these spectral results and examine their consistency with K emission line model (gaussian) were incorporated. The
table 4, we calculated the ratio R of the photon flux in the modelthenbecomesphabs (diskbb+powerlaw+gaussian)in
×
bright period F to that in the faint period F , and show the the Xspec (Arnaud 1996) terminology; hereafter, we call it
b f
resultsintable5. WemayexpressRas diskbb+powerlawmodel.Theinnermostradiusofdiskbbisde-
rivedasr =D N /cosi,whereN isthenormal-
R=F /F =(F +∆F)/(F ∆F), (4) in diskbb diskbb
b f − izationofthediskbbmodel.ThedistanceDfromtheearthand
where F Fb+Ff is the average photon flux in the specified theinclinationanpgleifromourlineofsightwereadoptedtobe
≡ 2
ethniesrfgoyrmbaanlidsman,tdhe∆fFrac≡tioFnba−2lFRfMdSenvoatreiastitohnecvaanribaeblgeivpeanrta.sIn 1g.e8n6ckoplucmanndde2n7s◦i,tyreNspHecatnivdetlhye(Ogaruosssziaentapla.r2a0m1e1t)e.rsTwheerheycdorno--
strainedtobecommonbetweenthefaintandthebrightspectra
η a∆F/F =a(R 1)/(R+1) (5)
′ ineachstate,butwereallowedtodifferbetweenthetwostates.
≡ −
8 AstronomicalSocietyofJapan [Vol.,
LHS HSS
10 10
) )
−1 −1
V V
e e
k k
−1 −1
s s
−2 −2
m m
s c 1 s c 1
n n
o o
ot ot
h h
P P
( (
V 2 V 2
e e
k k
0.1 0.1
2 2
χ 0 χ 0
−2 −2
1 2 5 10 20 1 2 5 10 20
Energy (keV) Energy (keV)
Fig.6.Background-subtractedunfoldedMAXIspectraintheLHS(left),andtheHSS(right).Redandblackindicatethebright-perioddataoftheSSCand
GSCrespectively,whileblueandgreenindicatethefaintperiodsoftheSSCandGSC,respectively. Themodelisphabs*(diskbb+nthComp+gaussian),
withtheparameterslistedintable7.The1.5–2keVenergyrangeisignoredinthefitting.Thedottedlinesrepresentcontributionsofthethreecomponents.
Thebottompanelsareresidualsfromthemodel.
LHS HSS
2 2
o
i
t
a
R
1 1
2 5 10 20 2 5 10 20
Energy (keV) Energy (keV)
Fig.7.RatiosoftheGSCspectrainthebrightperiodtothatinthefaintperiod,intheLHS(leftpanel),andintheHSS(rightpanel).
No.] Usageofpasj00.cls 9
The fit has been approximatelysuccessful, and yielded the ThederivedvaluesofR ,shownintable7,areindeedlarger
in
best-fit parameters as summarized in table 6. Thus, in both thanr intable6(althoughwedonotdiscussabsolutevalues
in
states, the diskbb parameters are the same, within errors, be- of R ). The LHS is characterized by about twice larger R
in in
tween the brightand faintspectra. In the LHS, the powerlaw thantheHSS,implyingadisktruncationintheLHSasnoted
index is steeper in the bright spectrum than in the faint one, before(Makishimaetal.2008;Yamadaetal.2013a). Finally,
whiletheoppositetrendisfoundintheHSS.Theseareconsis- in eitherstate, thedisk parameters(T andR ) are foundto
in in
tentwiththespectralratioshowninfigure7. Ther valuefor beapparentlyconstantasthesourcevaries.
in
theLHSisconsistentwiththatfromapreviouswork(Yamada
et al. 2013a). On the other hand, that for the HSS is smaller 4. Discussion
thanthatreported,e.g.,inDotanietal.(1997)(evenaftercor-
4.1. Summaryofdataanalysis
rectionsforthedistanceandthemass),presumablybecausethe
luminosityinthepresentresultisroughlyhalfthoseintypical Using5yearsarchivaldataobtainedwithMAXI,wederived
HSSobservationsmadepreviously(Zhangetal.1997). the NPSDsofCyg X-1in itsLHSandHSSfrom10 7 Hz to
−
Referringtoequation(5),wecalculatedη alsoforthepow- 10 4 Hz in the three energy bands. It is of particular impor-
′ −
erlawcomponentonly,andshowtheresultsintable5. Acom- tancethatthelong-termvariationsinthetwostateswerestud-
parison of the two values of η , one from the entire photon iedinaunifiedwayusingthesameinstrument,withthesame
′
countswhiletheotherfromthepowerlawcontribution,reveals analysismethod,andundersimilardatastatistics. Inaddition,
that the overall source variability in > 4 keV is determined thelong-termNPSDintheHSSwasobtainedforthefirsttime
solelybythepowerlawvariation,inagreementwiththespec- thanks to a fortunate opportunity that Cyg X-1 stayed in the
traldecompositioninfigure6(right). Inthe2–4keVband,in HSSinmostofthetimesince2010June. Theseresultsonthe
contrast, the overallη is reduced to 60% of the powerlaw HSS are expected to providesome clues to the still unknown
′
∼
variability; this effect is readily attributed to the presence of originof thehard-tailcomponent,whichis nearlyalwaysob-
the stable disk component. In addition, table 5 reveals slight servedinthisspectralstate.
increaseofη (bothtotalandpowerlaw)fromthe10-20keVto In the LHS, the NPSD down to 10 7 Hz obeys a power-
′ −
4–10 keV bands. The behavior of η agrees with that of η in law,andisapproximatelyexpressedasanextrapolationofthe
′
table4andmeansthatthepowerlawslopeslightlyhardensas NPSD above 0.01 Hz (Pottschmidt et al. 2003; Nowak et al.
itgetsstronger,asvisualizedinfigure7(right)andquantified 1999). We foundthattheNPSD inthe low (2–4keV)energy
in the fittingresults intable 6. Thisfindingis notnecessarily band is slightly larger than those in the 4–10 and 10–20 keV
consistent, however, with previousreports on Cyg X-1 in the bands(figure3left,figure4left,andtable4).
HSS (e.g., Jourdain et al. 2014) and other HSS sources (e.g., The newly obtained 10 7 10 4 Hz NPSD in the HSS
− −
−
Koyamaetal.2015),thatthehard-tailslopeisrelativelyinde- is also approximated by a power-law, and on an extrapola-
pendentof the source intensity. It is possible that the present tion of the NPSD previously obtained in frequencies above
HSSwassomewhatatypical,becausethevaluesofΓ 2.9we 10 4 Hz (Churazovet al. 2001;Cui et al. 1997). The NPSD
−
measured is steeper than those ( Γ 2.4; Dotani et∼al. 1997) (RMS2/mean2 Hz 1) in the HSS is about one order of mag-
−
∼
observedfromtheseBHBsintheirtypicalHSS. nitude larger than that in the LHS in 10–20 keV. This differs
Forafurtheranalysis,wereplacedthepowerlawwithamore from the case of other BH binaries reported by Miyamoto et
realistic modelnthComp(Zdziarskietal. 1996),whichrepre- al.(1993),althoughtheirdatawerelimitedtohigherfrequency
sentsComptonscatteringofsomesoftphotonsbyhotelectrons range above 0.01 Hz. In the HSS, the NPSD from 10 7 Hz
−
(diskbb+nthCompmodel). Theseedphotonsourcewassetto to 10 4 Hz has an energy dependence in such a way that it
−
bethediskbbcomponentrepresentingthediskemission.Since is 5 6 times higher in the 10–20 keV band than that in the
∼
the electron temperature T of the nthComp modelcannot be lowenergyband(2–4keV).Thisfindingextendstheresultsof
e
determinedwithourdata,wefixedittoatypicalvalueof100 energydependencein 0.2–200Hz reportedby Grinbergetal.
keVSunyaev&Tru¨mper(1979);Makishimaetal.(2008).The (2014). These energydependencesof the long-termvariation
best-fit parameters are summarized in table 7 and the best-fit intheHSSwerereconfirmedviathespectralanalysisinsection
modelsareshowninfigure6. Thefitsarenotyetformallyac- 3.3.
ceptable,butthemodel,asshowninfigure6,reasonablyrepro- In the presentpaper, we used onlythe MAXI data because
ducesthespectrafrom0.7keVto20keV.Inthismodeling,the theenergybandissuitableforsimultaneousanalyzingthevari-
diskphotonsarepartiallyfedintonthComp,sothattheparam- ationsofthediskcomponentandthepower-lawcomponent.In
eterr inthediskbbmodelissmallerthanthetrueinnerradius order to further study the hard tail variability, the Swift/BAT
in
whichisdenotedR hereafter. ThisR wascalculatedfrom data with good statistic above 20 keV should be utilized: we
in in
thesumof0.01–100keVphotonfluxofthediskbbcomponent, considerthatthisisourfuturetask.
Fdisk,andthatofnthCompcomponent,Fnth,utilizingthein-
ph ph 4.2. Comparisonwithshort-termvariability
nermosttemperatureT ofdiskbbandtheequationbyKubota
in
&Makishima(2004)as SincethefirstdiscoverybyOdaetal.(1971),theaperiodic
fastX-rayvariationofCygX-1hasbeeninvestigatedbyanum-
Fdisk+Fnth
ph ph berofauthors(e.g.,Negoroetal.1994,Churazovetal.2001),
R2 cosi T 3 mainlyintheLHSandtypicallyover10−3 102Hzfrequency
=0.0165 in in phs−1cm−2. (6) range. Similarstudieshavebeenperforme−donotherBHBsas
(D/10kpc)2 1keV
" # ! well, including in particular GX 339-4 (Maejima et al. 1984;
10 AstronomicalSocietyofJapan [Vol.,
Table5.ThefluxratioRofequation(4),andtheRMSvariationη′ofequation(5).
Spectralstate LHS HSS
Energyband(keV) 2-4 4-10 10-20 2-4 4-10 10-20
Total
R 1.25±0.11 1.19±0.07 1.16±0.08 1.17±0.20 1.43±0.24 1.64±0.31
η′ 0.32±0.10 0.25±0.06 0.21±0.08 0.23±0.19 0.52±0.20 0.70±0.23
Powerlaw
R 1.29±0.12 1.19±0.07 1.16±0.08 1.33±0.16 1.47±0.22 1.64±0.31
η′ 0.37±0.11 0.25±0.06 0.21±0.08 0.41±0.14 0.55±0.18 0.70±0.23
Table6.Thebest-fitparametersoftheabsorbeddiskbbpluspowerlawmodel.
Model=phabs*(diskbb+powerlaw+gaussian)
Component Parameter LHS/bright LHS/faint HSS/bright HSS/faint
phabs N∗ 5.8±0.6 4.92±0.12
H
diskbb Tin(keV) 0.24±0.02 0.21±0.02 0.50±0.01 0.49±0.01
r† (km) 84+34 99+49 33+1 36+1
in −22 −26 −5 −5
powerlaw Index 1.66±0.01 1.62±0.01 2.85±0.03 2.98±0.03
Norm‡ 2.09±0.04 1.65+0.04 19.5+1.0 16.7±1.0
−0.03 −1.0
gaussian LineE(keV) 6.66+0.17 6.62±0.07
−0.16
Sigma(keV) 0.7(fixed) 0.70+0.09
−0.08
Norm§ 7.2±1.6 28.3+3.7
−3.2
fitgoodness χ2ν(ν) 1.38(420) 1.31(356)
*:Inaunitof1021cm−2.
†:Thedistanceisassumedtobe1.86kpcandtheinclinationangleisassumedtobe27◦(Oroszetal.2011).
‡:Inaunitofphotonscm−2s−1keV−1at1keV.
§:Inaunitof10−3photonscm−2s−1.
Table7.Thebest-fitparametersofthemodelconsistingofadiskbbandnthComptakingaccountofthephoto-electricabsorption.
Model=phabs*(diskbb+nthComp+gaussian)
Component Parameter LHS/bright LHS/faint HSS/bright HSS/faint
phabs N∗ 6.1±0.6 3.6±0.1
H
diskbb Tin(keV) 0.23±0.02 0.20±0.02 0.48±0.01 0.47±0.01
Fdisk† 47.0 43.2 69.6 72.5
ph
nthComp‡ Gamma 1.68±0.01 1.65±0.01 2.81±0.03 2.91±0.04
Fnth† 12.9 10.9 36.3 27.4
ph
gaussian LineE(keV) 6.65±0.16 6.64±0.07
Sigma(keV) 0.7(fixed) 0.64+0.09
−0.08
Norm§ 7.6+1.6 24.5+3.1
−1.5 −2.8
innerradius Rl (km) 116±15 127±21 54±2 53±2
in
Luminosity# 1.76±0.04 1.50±0.03 2.71±0.02 2.35±0.02
Comptonfraction∗∗ 0.87 0.89 0.51 0.41
fitgoodness χ2ν(ν) 1.37(420) 1.38(370)
∗:Inaunitof1021cm−2.
†:Photonfluxinaunitofphotonscm−2s−1intheenergyrangeof0.01-100keV.
‡:TheelectrontemperatureTeisfixedat100keV.ThespectrumoftheseedphotonisdiskbbandthetemperatureTbbisfixedatTin.
§:Inaunitof10−3photonscm−2s−1.
l:Thedistanceisassumedtobe1.86kpcandtheinclinationangleisassumedtobe27◦(Oroszetal.2011).
#:Inaunitof1037ergs−1andintheenergyrangeof0.5-100keV.
∗∗:ThefractionalluminosityinnthComp,whichiscalculatedfromthediskluminosityLdiskandtheComptonluminosityLnthas LdisLkn+thLnth.