Revealing the X-ray variability of AGN with principal component analysis

25 Pages·2014·4.11 MB·English

MNRAS447,72–96(2015) doi:10.1093/mnras/stu2424
Revealing the X-ray variability of AGN with principal component analysis
M. L. Parker,1‹ A. C. Fabian,1 G. Matt,2 K. I. I. Koljonen,3,4 E. Kara,1 W. Alston,1
D. J. Walton,5 A. Marinucci,2 L. Brenneman6 and G. Risaliti6,7
1InstituteofAstronomy,MadingleyRoad,CambridgeCB30HA,UK
2DipartimentodiMatematicaeFisica,Universita`degliStudiRomaTre,viadellaVascaNavale84,I-00146Roma,Italy
3AaltoUniversityMetsa¨hoviRadioObservatory,Metsa¨hovintie114,FIN-02540Kylma¨la¨,Finland
4NewYorkUniversityAbuDhabi,POBox129188,AbuDhabi,UAE
5CaliforniaInstituteofTechnology,1200EastCaliforniaBoulevard,Pasadena,CA91125,USA
6Harvard–SmithsonianCenterforAstrophysics,60GardenSt,Cambridge,MA02138,USA
7INAF–OsservatorioAstrofisicodiArcetri,LargoEnricoFermi5,I-50125Firenze,Italy
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Accepted2014November13.Received2014November13;inoriginalform2014May30 w
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ABSTRACT fro
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We analyse a sample of 26 active galactic nuclei (AGN) with deep XMM–Newton observa- h
tions, using principal component analysis (PCA) to find model-independent spectra of the ttp
differentvariablecomponents.Intotal,weidentifyatleast12qualitativelydifferentpatterns ://m
n
of spectral variability, involving several different mechanisms, including five sources which ras
showevidenceofvariablerelativisticreflection(MCG–6-30-15,NGC4051,1H0707−495, .ox
fo
NGC3516andMrk766)andthreewhichshowevidenceofvaryingpartialcoveringneutral rd
jo
absorption(NGC4395,NGC1365andNGC4151).Inover halfofthesourcesstudied,the urn
a
variability is dominated by changes in a power-law continuum, both in terms of changes in ls
.o
flux and power-law index, which could be produced by propagating fluctuations within the rg
a/
corona.Simulationsareusedtofinduniquepredictionsfordifferentphysicalmodels,andwe t C
thenattempttoqualitativelymatchtheresultsfromthesimulationstothebehaviourobserved alifo
in the real data. We are able to explain a large proportion of the variability in these sources rn
ia
usingsimplemodelsofspectralvariability,butmorecomplexmodelsmaybeneededforthe In
s
remainder. We have begun the process of building up a library of different principal com- titu
ponents, so that spectral variability in AGN can quickly be matched to physical processes. te o
WeshowthatPCAcanbeanextremelypowerfultoolfordistinguishingdifferentpatternsof f T
e
variability in AGN, and that it can be used effectively on the large amounts of high-quality ch
n
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archivaldataavailablefromthecurrentgenerationofX-raytelescopes.WewillmakeourPCA lo
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codeavailableuponrequesttotheleadauthor. y o
n
A
Keywords: galaxies:active–galaxies:nuclei–galaxies:Seyfert. p
ril 2
, 2
0
1
5
viding acceptable fits to the same data set, meaning that spectral
1 INTRODUCTION
fittingofintegrateddatasetsalonecannotsufficientlydistinguish
Active galactic nuclei (AGN) can be extremely variable in the betweenalternativephysicalmodels.Byinvestigatingtheproperties
X-ray band on time-scales as short as the light traveltime over a ofvariabilityinthesesources,wecanhopetoidentifythephysical
few gravitational radii (R ), which can be from minutes to days, processes driving AGN, probing them at different distances from
G
dependingonthemassoftheblackhole(BH).Examinationofthe theeventhorizonbylookingatdifferenttime-scales.
X-rayspectraofAGNrevealsalargevarietyofdifferentspectral Principalcomponentanalysis(PCA)isamethodofdecomposing
shapes,producedbyvariousdifferentprocesses,mostnotablyab- adatasetintoasetoforthogonaleigenvectors,orprincipalcompo-
sorption by intervening material (see review by Turner & Miller nents(PCs),whichdescribethevariabilityofthedataasefficiently
2009)andreflectionfromtheaccretiondiscandsurroundingma- aspossible(e.g.Kendall1975;Malzacetal.2006).Inpractice,when
terial(seereviewsbyFabian&Ross2010;Reynolds2014).AGN appliedtoasetofspectra,thisproducesasetofvariablespectral
spectracanbeverycomplex,withmultipledifferentmodelspro- componentswhichdescribethevariabilityofthesourcespectrum.
Ifthespectrumismadeupofalinearsumofvariable,uncorrelated
and spectrally distinct physical components, then PCA will, with
(cid:2)
Email:[email protected] sufficient data quality, return an exact description of the physical
(cid:2)C 2014TheAuthors
PublishedbyOxfordUniversityPressonbehalfoftheRoyalAstronomicalSociety
RevealingAGNvariability 73
components.Theadvantageofthismethodisthatitproducesde- beyondthescopeofthispaper.Weselectonlysourceswithmore
tailedspectraofeachvariablecomponent,inamodel-independent thanoneorbitofexposuretime.WeusedScienceAnalysisSoftware
way. Calculating the rms spectrum (e.g. Edelson et al. 2002) can (SAS)version13.0.0foralldatareduction.Thedataarefilteredfor
show the total variability as a function of energy, but cannot be background flares, and we use the EPPROC SAS task to reduce
usedtodeterminehowmanyvariablecomponentscontributetothe the data. We use 40 arcsec circular regions for both source and
variability or to isolate contributions from different mechanisms. backgroundspectraforallsources,selectingthebackgroundregion
Components that are only weakly variable, such as variations in to avoid contaminating sources. Representative spectra for each
absorptionorreflection,willusuallybedrownedoutbyvariations sourcecanbefoundinAppendixA.
intheprimarycontinuum.Detailedspectralmodellingcanbeused ThelistofobservationIDsusedinthisanalysisforeverysource
toovercomethislimitation,bycarefullyfittingthedatafordifferent isshowninTable1(fullversionavailableonline).Forthreesources
intervalsandidentifyingtheoriginofthevariability.However,this (NGC1365,MCG–6-30-15andArk120),wehavemadeuseofdata
isbydefinitionnotmodelindependent,meaningthatverydifferent from joint XMM–Newton and NuSTAR (Harrison et al. 2013) ob-
conclusionscanbedrawnfromthesamedataset(forexample,see servingcampaigns(Risalitietal.2013;Marinuccietal.2014;Matt
the discussion on reflection/absorption models in MCG–6-30-15 etal.2014;Waltonetal.2014).Allotherdataispubliclyavailable,
byMarinuccietal.2014).PCAcombinestheadvantagesofboth andwasdownloadedfromtheXMM–NewtonScienceArchive.To
ofthesemethods,andcanbeusedtocalculatemodel-independent givesomeideaofthenatureofthevariabilityineachsourceand D
o
spectra of multiple variable spectral components. This technique howitchangesbetweenobservationsweshowcount–countplotsin w
n
has many applications both within astronomy and in other fields AppendixA.Inthemajorityofcases,theseplotsareapproximately lo
a
(Kendall1975),andhasbeenusedasapowerfultoolfortheanal- linearwithalargescatter,howeversomesources(e.g.NGC4051, de
d
y20si1s3o)f.X-raybinaryvariability(Malzacetal.2006;Koljonenetal. NUtGtlCey3&51M6)csHhaorwdya(d2o0w03n)t,uarnndatinloswomceoucnatssesas(ed.gis.cRuEsseJ1d0i3n4T+a3y9lo6r), from
h
Early attempts at using PCA to understand spectral variability thesoftandhardbandsseemtobeindependent. ttp
in AGN were hampered by a lack of high-quality data. PCA has In general, we follow the methods discussed in Parker et al. ://m
beenusedinaminorroleforexaminingX-rayspectralvariabilityin (2014a),hereafterP14a.Foreachsource,wecalculatethefractional n
ra
AGNforsometime(e.g.Vaughan&Fabian2004),butfrequently deviationsfromthemeanforasetofspectra(seeexamplespectra s.o
atlowspectralresolutionandwithonlyonecomponentconfidently for NGC 4051 in Appendix A), extracted from 10 ks intervals xfo
identified. The use of singular value decomposition (SVD; Press, (unless otherwise specified). These spectra are arranged into an rd
Flannery&Teukolsky1986)allowsthefullspectralresolutionof n × m matrix M , wheren and m are the number of energy bins jou
rn
theinstrumenttoberetained,producingdetailedcomponentspectra andspectra,respectively.WethenuseSVD(Pressetal.1986)to als
(Milleretal.2007).Morerecentwork(Parkeretal.2014a,b)has findasetofPCs(oreigenvectors)whichdescribethevariabilityof .org
demonstrated that PCA can return multiple components from a thespectrumasefficientlyaspossible.SVDfactorizesthematrix a/
sufficiently large data set, effectively isolating different spectral M, such that M = UAV∗, where U is an n × n matrix, V is an t C
a
components.ThereisnowmorethanadecadeofarchivalXMM– m × m matrix and A is an n × m diagonal matrix. The matrices lifo
Newton EPIC-pn (Stru¨der et al. 2001) data which can be used to UandVtheneachdescribeasetoforthogonaleigenvectorstothe rn
examine the variability of AGN on long time-scales and at high matricesMM∗andM∗M,respectively.Theseeigenvectorsrepresent ia In
s
spectralresolution.Inthiswork,wepresentasystematicanalysis thespectralshapeofthevariablecomponents.Thecorresponding titu
of 207 observations of 26 bright, variable AGN, using PCA to eigenvaluesaregivenbythediagonalvaluesofA,andareequalto te
o
revealhiddenpatternsofvariabilityandtorelatethesepatternsto thesquareofthevariabilityineachcomponent(inarbitraryunits). f T
thephysicalprocessesinAGN.Thepaperisorganizedasfollows. Thefractionalvariabilityineachcomponentcanthenbefoundby ec
h
dividingthesquarerootsoftheeigenvectorsbythesumofallthe n
o
(i) InSection2,we describethedatausedinthisanalysis and squareroots. log
howitwasprocessed,alongwithdetailsoftheanalysisitself.We y
The resulting components show the strength of the correlation o
include a demonstration of the method with a simple toy model, between energy bins, so a flat positive (or negative, the sign of n A
showingthepotentialpowerofPCAasananalytictool. p
PC(Aii)spInecStreac,taionndp3r,ewseentgtihveerdeseutaltislsooffouorusrimmueltahtoiodnosffosrimdiufflaetrienngt twahtheheiyrg-ehaaxseinsaeicrsgoaimerbspiroternaperrnyet)setchnoatmstaipsoppnivoeonstititnisvhgeoewaftfselcothtw.aTtehanlielsrbigsiinecssomvaanprdylicneaeqtgueadatliblvyye, ril 2, 201
physical models of AGN variability. These different spectra then 5
therequirementthattheeigenvectorsareorthogonal,i.e.theirdot-
represent different predictions for the different spectral models,
productmustbezero.Weexaminetheeffectofthisconstrainton
whichwecanusetounderstandtheresultsfromrealdata.
simulatedPCsinSection3.Wenotethatthemethodofpreparingthe
(iii) WepresenttheresultsoftheanalysisinSection4,describ-
spectraissuchthatconstantmultiplicativecomponentswillhaveno
ingandshowingthePCsfoundforeachsource,alongwithsome
effectonthePCAresults,astheywillnotaffectthefractionalresid-
backgroundoneachobject.Wealsogivesomebasicinterpretation
uals. However, a constant spectral component that changes with
ofeachresult,attemptingtomatchthePCspectratothosefound
energywillsuppressthespectralvariabilityofthevariablecompo-
usingsimulations.
nents.Thishasimportantimplicationsfordistinguishingbetween
(iv) Finally,inSections5and6,wediscussoutmainresultsand
absorptionandreflectioninAGNvariability.
summarizeourconclusions.
Thesignificanceofthecomponentsproducedisdeterminedus-
ing the log-eigenvalue (LEV) diagram, an example of which (for
Ark 564) is shown in Fig. 1. This shows the fraction of the to-
2 OBSERVATIONS, DATA REDUCTION AND
talvariabilitywhichcanbeassignedtoeachPC,soforArk564,
ANALYSIS METHOD
∼90percent of the variability is in the first PC and so on. The
WerestrictthisanalysistoXMM–NewtonEPIC-pndataonly.The componentsduetonoiseproducedbythePCAarepredictedtode-
method used is also applicable to other instruments, but that is caygeometrically(seee.g.Jolliffe2002;Koljonenetal.2013),so
MNRAS447,72–96(2015)
74 M.L.Parkeretal.
Table1. Listofobservationsusedinthispaper.Sourcesareorderedbytheirfirstappearanceinthetext.Weshow
0.5–2and2–10keVcountratesforeachobservation,andtheratiobetweenthetwo,sothattheamplitudeofspectral
variabilitycanbeestimated.Notethattheon-sourceexposuretimewillbesmallerthanthetotalduration,andtheactual
usabletimeuseddependsonthesizeoftheintervalsweusetoextractspectra.Fulltableisavailableonline.
Source ObservationID Date Duration 0.5–2keVrate 2–10keVrate Ratio
(s) (s−1) (s−1) 2–10/0.5–2keV
MCG–6-30-15 0111570101 2000-07-11 46453 7.67 2.90 0.38
0111570201 2000-07-11 66197 10.86 4.21 0.39
0029740101 2001-07-31 89432 15.05 4.82 0.32
0029740701 2001-08-01 129367 16.37 5.31 0.32
0029740801 2001-08-05 130487 14.98 4.72 0.32
0693781201 2013-01-31 134214 20.05 6.24 0.31
0693781301 2013-02-02 134214 11.60 3.86 0.33
0693781401 2013-02-03 48918 8.09 3.21 0.40
NGC4051 0157560101 2002-11-22 51866 2.82 0.61 0.22
D
0606320101 2009-05-03 45717 5.56 1.82 0.33 o
w
0606320201 2009-05-05 45645 9.37 2.34 0.25 n
lo
0606320301 2009-05-09 45584 11.40 2.40 0.21 a
d
0606321401 2009-05-11 45447 8.47 1.69 0.20 ed
0606321501 2009-05-19 41843 8.56 2.09 0.24 fro
0606321601 2009-05-21 41936 17.58 3.21 0.18 m
h
0606321701 2009-05-27 44919 3.51 1.30 0.37 ttp
0606321801 2009-05-29 43726 4.72 1.81 0.38 ://m
0606321901 2009-06-02 44891 2.15 0.51 0.24 n
0606322001 2009-06-04 39756 5.25 1.79 0.34 ras
.o
0606322101 2009-06-08 43545 1.69 0.64 0.38 x
0606322201 2009-06-10 44453 4.43 1.46 0.33 ford
0606322301 2009-06-16 42717 6.19 1.37 0.22 jo
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AsimpletestcaseisshowninFig.2.Forthisexample,weadd .org
ytog(xe)th=erstihnr(e2ex)f,uanlcotniognws:ityh1(rxa)nd=om0.n3o+isex./W8;eyc2r(exa)te=50si‘nsp(xec)traan’,d at C/
3 a
oftheformy(xi)=0.6a1y1(xi)+0.2a2y2(xi)+0.1a3y3(xi)+0.1a4, lifo
wherea arerandomvalues,evenlydistributedbetween±0.5and rn
xiarethej200valuesbetween0and6πoverwhichthefunctionsare ia In
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calculated.Intheleft-handpanel,weshowthethreeinputspectra, titu
minusnoise,inthemiddlepanelweshowasampleofthegenerated te
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functionsandintheright-handpanelweshowthefunctionsrecov- f T
eredusingourPCAcode.TheLEVdiagramforthistestisshownin ec
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Fig.3,andclearlyshowsthatthreecomponentsaresignificant,with n
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47percentofthevariabilityinthefirstcomponent,7percentinthe log
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secondand3percentinthethird.Alltheremainderisattributable o
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tonoise.Thesevaluesarefunctionsoftheamplitudeandvariability A
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ofPea1c4haccoamlcuploanteednte,xatnrdemthaelssipgencatrl-atoa-nndoiusseedractioomopfatrhiesodnastat.ospec- ril 2, 2
tralfittingtofindphysicalinterpretationsforthecomponentspro- 01
5
ducedinthatanalysis.However,thisisinefficientforlargesamples
Figure1. LEVdiagramforArk564.Thisshowsthefractionalvariability of objects and could potentially compromise the model indepen-
ineacheigenvectorobtainedfromthePCAofthissource.Theblackline denceoftheresults.Inthiswork,wecreatesimulatedspectra(see
showsthebest-fittinggeometricprogression,fitfromcomponent4to50. Section3)basedonphysicalmodelsthatareallowedtovarywithin
Theremainingthreecomponentsarefoundtobehighlysignificant,asthey
givenparameterranges,thenusePCAtofindthecomponentspectra
deviatefromthislinebymanystandarddeviations.
foreachmodel.ThisproducesapredictedsetofPCspectraforeach
model,whichwecanthenmatchtothePCspectrafoundfromthe
deviation from a geometric progression can be used as a test of dataforeachsource.
the significance of a component. In this case, three components
deviatefromthebest-fittinggeometricprogression,andarehighly
3 SIMULATIONS
significant.Forthesakeofbrevity,weonlyshowanexampleLEV
diagram,ratherthanoneforeverysource.Thestrongeststatement Inthissection,weusesimulationstopredictthePCAspectrapro-
aboutthesignificanceofthecomponentsweinvestigatecomessim- ducedbydifferentmodelsofAGNvariability.Thistechniquefor
plyfromthestrongcorrelationbetweenpointsinadjacentbins.Any analysingPCAspectrawasusedbyKoljonenetal.(2013),andthe
coherentcomponentsproducedareextremelyunlikelytobedueto methodweuseherewasintroducedinParkeretal.(2014b),here-
randomnoise,whichisindependentbetweenbins. afterP14b,whereitisusedtodemonstratethedifferingpredictions
MNRAS447,72–96(2015)
RevealingAGNvariability 75
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Figure2. Left:thethreefunctionsweaddtogether,alongwithnoise,asasimpletestofthePCAmethod.Middle:sampleof10‘spectra’createdbyadding w
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togetherthethreefunctionsontheleftinrandomamountswithadditionalnoise.Right:thePCsreturnedbytheanalysis.Notethatthey-axisisarbitraryand lo
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differentbetweentheleft-andright-handpanels.Errorbarsarenotplottedforclarity. de
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Figure4. Thefirst(top,black)andsecond(bottom,red)PCsobtainedby titu
usingPCAonsimulatedspectraofapowerlawwhichvariesinnormaliza- te
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tionandphotonindex.Thefirstcomponentcorrespondstochangesinthe f T
Figure3. LEVdiagramforthetestcaseshowninFig.2.Inthistest,three normalization,andthesecondtopivotingofthepowerlaw. ec
h
inputfunctionsaresummed,andnoiseisadded.TheLEVdiagramshows n
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thatthreereturnedcomponentsarestatisticallysignificant,theremainder Allofthecomponentsproducedbythesesimulationsareequally lo
g
canbeattributedtonoise.Errorbarsarenotshown,butaresmallerthanthe validwiththey-axisinvertedastheyrepresentdeviationsfromthe y o
pointsforthethreesignificanteigenvectors. mean, ratherthantheminimum,andwillthereforesometimes be n A
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for intrinsic source variability and absorption variability in NGC pthoesictoivmepaonndensotsminettihmeemsannengeartiwveh.icInhgmeankeersalt,hwemeaotstteimntputittiovearsreannsgee. ril 2, 2
WewillinitiallyconsiderthePCsreturnedfromavariablepower 0
1365. 1
law, and then investigate the effect of additional spectral compo- 5
nents. In each case, we will first look at the effect of including
a constant component and varying the power law, then allowing
3.1 Method
thenewcomponenttovary.Finally,wewillexamineaselectfew
In general, we follow the method outlined in P14b and simulate exampleswithmorethanoneadditionalvariablecomponent.
spectrausingtheXSPECcommand‘FAKEIT’,thenanalysetheresults Wherethecomponentsreturnedfromthesimulationcorrespond
usingthesamemethodasweusefortherealdata.Theparameters directlytooneofthemodelcomponents,welabelthefigurewith
ofinterestareselectedrandomlybetweenextremevaluesforeach therelevantsymbols:Npl,Nbb,Nref,NHandfcovcorrespondtopower
spectrum.Forsimplicity,wesimulate10ksEPIC-pnspectra,tobe law,blackbodyandreflectionnormalizations,columndensityand
assimilaraspossibletothosefoundfromrealdata.Wedonotmatch coveringfraction,respectively.
themodelfluxtothedata,insteadexaggeratingthemodelfluxso
thatthefeaturesaremoreprominent.Thisisequivalenttosimulating
3.2 Singleandmultiplepowerlaws
longerexposuresatlowerfluxforthesimplemodelsdiscussedhere,
butlesstimeconsumingtocalculate.Wedonotattempttoexactly Asabaselinemodel,weestablishthecomponentsexpectedfrom
match the PCs produced by the data, instead looking to produce variabilityofapower-lawcontinuum.Fig.4showsthetwocom-
generalpredictionsfordifferentvariabilitymechanisms. ponentsobtainedfromasimulationofasimplevariablepowerlaw,
MNRAS447,72–96(2015)
76 M.L.Parkeretal.
combinationoftwoormoresuchcomponentsthatchangeinrelative
amplituderatherthanindex.
3.3 Blackbody/softexcesscomponents
We now investigate the PCs produced from a constant or weakly
variablesoftexcesscomponent.Foroursimulations,weuseablack-
body for simplicity and brevity, but the resulting components are
equivalent to those that would be produced by any other mod-
els that explain the soft excess in terms of an additional compo-
nentthatonlycontributesatlowenergies(e.g.Comptonizationand
bremsstrahlungmodels).
Initially, we consider the effects of a constant blackbody com-
ponent on the PCs returned from a varying power law. For this
Figure5. Left:thetwosignificantPCsfromasimulationofapowerlaw
simulation,weincludeablackbodywithatemperatureof0.1keV
varyinginnormalizationandphotonindex,inthepresenceofaconstant
hardpowerlaw.Thisspectralcomponentsuppressesthevariabilityofthe and a normalization of 0.1, then vary a power law with a photon Do
indexbetween1.9and2.1,andnormalizationsbetween0.5and1.0. w
PCs at high energies. Right: the two PCs from a simulation where the n
spectralpivotingarisesfromtwopowerlaws,onehard,onesoft,varyingin The effect of such a constant component is to suppress the vari- loa
normalizationbutnotinindex.Thesecomponentsareverysimilartothose abilityseeninthevariablecomponents,pushingthebinswherethe de
d
producedbyapivotingpowerlaw,butwithadditionalcurvature. blackbodyisstrongesttowardszero.Thiscanbeseeninthetoprow fro
ofFig.6,wheretheflatPCsproducedbyavaryingpowerlaware m
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with no other spectral components. The photon index is allowed pushedtowardszeroatlowenergiesbytheblackbody. ttp
to vary between 1.9 and 2.1 randomly, and the normalization is Fixing the photon index and allowing the blackbody to vary ://m
allowedtochangebyafactorof2.Theresultantcomponentsare (betweennormalizationsof0.8and1.2)producesadifferentsecond n
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completelystraight,showingnofeaturesofanykind,althoughthere component,(topmiddlepanelofFig.6)whichhasthesameshape s.o
isaslightincreasewithenergyintheprimarycomponent,duetoa astheblackbodyatlowenergies,thenisnegativebutclosetozeroat xfo
correlationbetweenfluxandphotonindexinthemodel. highenergies.Thenegativevaluesarecausedbytheorthogonality rd
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Foragoodcomparisonwithrealdata,wereferthereaderto3C constraintofPCA,whichrequiresthatthedot-productofanytwo u
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273inSection4.4.Thissourceisdominatedbyapowerlawfrom PCsbezero.Inpractice,thismeansthatiftheprimarycomponentis als
arelativisticjet,andthefirsttwocomponentsfoundfromthedata 100percentpositive,approximately50percentoftheenergybins .org
areanexcellentmatchtothepredictionsforavaryingpowerlaw ofallsubsequentPCsmustbebelowzero. a/
showninFig.4. Amorecomplexcomponentisproducedifwevarythephoton t C
a
Wenextinvestigatetheeffectofaddingasecondpowerlawto index of the power law as well. First, we vary the index weakly lifo
the spectrum. Additional continuum components such as this are (between 1.95 and 2.05), and the results of this are shown in the rn
ia
hard to distinguish spectrally, but have been suggested by some thirdrowofFig.6.Thisproducesaminorchangeinthefirsttwo In
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studies(e.g.Grupeetal.2008;Nodaetal.2013)andareanatural components–theybothshowaninclineathighenergies,ratherthan titu
consequence of multizone Comptonization models. We therefore being completely flat, and produces a third significant PC (right- te
o
include a weaker second power law, with a harder photon index handpanel).Thiscomponentappearstoactasacorrectionfactorto f T
(cid:3)=1andanormalizationof0.1timesthatoftheprimarypower thesecondcomponent,whichnolongerdescribesallofthepivoting ec
h
law.Whenwekeepthissecondcontinuumcomponentconstantand itself.Ifwedoubletherangethatthephotonindexvariesover,we n
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varytheprimarypowerlawasbefore,theeffectissimplytolower seethatthesecondcomponentchangessignificantly(bottomrow). log
y
thefractionalvariabilityoftheprimarycomponentwithincreasing Thiscomponentismostsimilartothepivotingcomponentproduced o
n
energy.ThisisshowninthelefttwopanelsofFig.5. when the blackbody is constant (top row). The third component A
p
inWtheehpahvoetosnoifnadretxreoafteadpsrpiemcatrraylppoivwoetirn-lgawascboenintignuduume.toHcohwaenvgeers, cAhgaanigne,sthoentlhyirvdercyomslipgohntelyn,tahnedreshisowascothrreecstaimonefgaecntoerr,arlastthreurcttuhraen. ril 2, 2
itispossibletogenerateasimilareffectfromtheinterplaybetween a direct match to a single physical component. However, in this 01
5
two(ormore)continuumcomponentswithdifferentphotonindices case the third PC is used to make the second PC appear more
changing in normalization. In the right two panels of Fig. 5 , we liketheblackbodyPCinrows2and3,ratherthantheotherway
showthetwocomponentsproducedfromthesametwopower-law around.InFig.7,weshowtheeffectofaddingthe‘correctionfactor’
model,whenbothpower-lawcomponentschangeinnormalization componentontothesecond-orderblackbodycomponentfromthe
but not index. The primary power law is varied in normalization weaklyvaryingpower-lawindexcase.Thisproducesacomponent
between0.5and2,andthesecondarypowerlawbetween0.08and withthesamespectralshapeasthepivotingterm(topmiddlepanel
0.12.Asexpected,thefirstPCisverysimilarinthiscaseandthat ofFig.6).
withnovariabilityinthesecondpowerlaw,buttherearequalitative The third components produced by these simulations demon-
differencesinthesecondcomponent.Asthisnowcorrespondsto strate a key weakness of this kind of analysis – if two physical
the spectral pivoting caused by changes in the flux of the second components have a similar effect on the spectrum, then they will
continuumcomponent,itisenhancedathighenergies,ratherthan notbeexpressedastwoseparatePCs–rathertherewillbeonePC
damped out as in the previous case. This may be relevant to the describing the average effect, and one describing the differences
objects in Section 4.2, where the second component gets steeper betweenthetwo.Inthiscase,bothanincreaseintheblackbodyflux
withenergy.Fortheremainderofthesesimulations,wewillonly andanincreaseinthephotonindexproduceasteeperspectrum,so
consider the case of a single, pivoting power law, but the reader thesecondcomponentisanaverageofthesetwoeffects.Thiswas
shouldbearinmindthatasimilareffectcouldbeachievedwitha also found to be the case in the absorption simulations shown in
MNRAS447,72–96(2015)
RevealingAGNvariability 77
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Figure6. PCsreturnedfromsimulationsofpowerlawandblackbodyvariability.Thetoprowshowsthecomponentsproducedwhenthepowerlawisallowed ra
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tovaryinnormalizationandphotonindex,whiletheblackbodyiskeptconstant.Thesecondrowshowsthoseforafixedphotonindex,butwheretheblackbody .o
x
fluxisallowedtovary.Thethirdandfourthrowsshowthecomponentsproducedwhenallthreeparametersareallowedtovary,withtheblackbodyvariations fo
rd
beingstrongerinthethirdandthepowerlawpivotingdominatinginthefourth. jo
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binariesthanAGN),itisinstructivetonotethatvariationsinasoft .org
spectral component can result in a PC that shows apparent hard a/
variability.Thismayberelevanttothefourth-orderPCinMCG–6- t C
a
30-15andsimilarobjects(Section4.1). lifo
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In
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3.4 Distantreflection titu
te
o
DistantorneutralreflectionisfoundinmanyAGN(e.g.Riccietal. f T
2014),andoccurswhenX-rayemissionfromthecoronaisscattered ec
h
andreprocessedbycoldmaterial,farfromtheBH.Becauseofthis n
o
muchlargerspatialscale,thevariabilityinthisspectralcomponent log
y
ismuchlowerthanthatfoundincomponentsthatoriginatefromthe o
n
innerdisc,orthoseduetointerveningcloudsorwinds.Itfollows A
p
tvhaartiatbhielitmyaiinnthefefeecnteorgfydbisatnandtsrweflheercetioitniswsitlrlobneg,topadratimcuplaorulyt tthhee ril 2, 2
6.4FeKαline. 01
5
WeshowinFig.8thetwoPCsreturnedfromasimulationofa
Figure 7. The effect of subtracting the ‘correction factor’ PC from the varying power-law continuum and constant distant reflection. We
second-orderblackbodyvariabilitytermforthesimulationsofpowerlawand modelthereflectioncomponentwiththeXILLVERmodel(Garc´ıaetal.
blackbodyvariability.ThePCcorrespondingtotheblackbodyvariationsis 2013),withaninputpower-lawindexof2,anironabundanceof1,
showninreddiamonds,andthethirdPCisshowninbluesquares.Whenone theionizationξ atthelowestallowedvalueof1andaninclination
issubtractedfromtheother,theresultingcomponent(greencrosses)matches
of30degrees.Thefluxofthereflectioncomponentisfixed,andis
thepivotingPCproducedwhenthephotonindexvariationsdominate(see
approximatelyequaltohalftheaveragefluxofthecontinuum.The
thetoprowofFig.6).
primarypowerlawisthenvariedasbefore.WhiletheresultingPCs
doshowslightdifferencesincurvatureoverthewholeenergyrange,
P14b,wherebecausethelow-energyspectrumofNGC1365was these are likely to be undetectable due to noise and the presence
dominatedbydiffusethermalemissiontheabsorptionandintrinsic of other spectral components in the real data. By far the largest
variabilitycomponentswereverysimilar,leadingtoanaveraging differenceisthestrong,narrowironlinevisibleat6.4keV,which
effect.However,thedominantdriverofthespectralvariabilitycan suppresses the variability of the power-law components, pushing
stillbeidentified,asshownhereandinP14b. themtowards0.Wenotethatinthecasewheretheprimarypower
Whilewedonotfindanysourcesthatshowsuchsimpleblack- law is heavily obscured, then it is probable that distant reflection
body variability (which is far more likely to be visible in X-ray willleavemoresignaturesinthePCspectraatlowenergies.
MNRAS447,72–96(2015)
78 M.L.Parkeretal.
asubstantialcontributiontothetotalflux.Thesecondcomponent
is similar, although starting from a diagonal rather than flat line,
itislikewisepushedtowardszerowherethereflectioncomponent
dominates.
Fig. 10 shows the three significant components obtained from
simulationsofamodelwithavaryingpowerlawandvaryingrel-
ativisticreflection,forarangeofionizationparameters.Thefluxes
ofthepower-lawandreflectioncomponentsarekeptapproximately
equal, but the reflection component is only allowed to vary by a
factor of 2, compared to 5 for the power law. The first two PCs
areequivalenttothoseshowninFig.9,andarelargelyduetothe
power-lawvariability.TheadditionalthirdPCrepresentsallofthe
reflectionvariabilitythatcannotbeadequatelydescribedbythefirst
two PCs. This component displays the correlated soft excess and
Figure8. Thefirst(top)andsecond(bottom)PCsfromasimulationof broadironlinetypicalofrelativisticreflection.Unlikethedistant
apower-lawcontinuumvaryinginnormalizationandspectralindexinthe reflection discussed in Section 3.4, relativistic reflection makes a D
presenceofaconstantneutralreflectioncomponent.Themaindifference strong contribution at soft energies, and has a much broader iron ow
causedtotheshapeofthecomponentsreturnedisthestrongnarrowiron line. nlo
linefeatureat6.4keV. These simulations are particularly relevant to the sources dis- ade
d
cussedinSection4.1,fiveofwhichshowboththelow-andhigh- fro
energybreaksinthefirstandsecondcomponentsandahigherorder m
h
PC,verysimilartothosepresentedinFig.10,withacorrelatedsoft ttp
excessandbroadironline. ://m
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ra
s
3.6 Neutralabsorption .o
x
fo
We are also interested in the effects of absorption variability in rd
jo
AGN spectra, although there are problems with using PCA in an u
rn
absorption-dominatedvariabilityregime.Oneofthekeyassump- als
tionsofPCAisthatthedatasetcanbeexpressedasalinearsum .org
of PCs. This assumption is reasonable when applied to additive a/
componentssuchasareflectionspectrum,butisnotvalidwhenwe t C
a
consider variable multiplicative components applied to a variable lifo
spectrum, potentially leading to spurious terms being produced. rn
ia
Constantabsorptionproducesnosuchproblem,asaconstantmul- In
Figure9. Thefirsttwo(topandbottom,respectively)PCsrecoveredfrom s
asimulationofapowerlawvaryinginnormalizationandphotonindex,in tiplicative factor makes no difference to the fractional deviations titu
weusetocalculatethePCs.Nevertheless,asshownbyP14band te
thepresenceofaconstantrelativisticallyblurredreflectioncomponent.The o
effectofthiscomponentistosuppressthespectralvariabilityattheenergies aswedemonstratehere,itispossibletofindphysicallymeaningful f T
oftheironlineandsoftexcess. componentsfromsuchananalysis.Westressthatinallcases,the ec
h
shapeoftheunderlyingspectrumisunimportant,providedthatit n
o
isrelativelyconstantcomparedtotheabsorptionvariability.Again, log
y
thisisduetothePCsbeingcalculatedfromthefractionalresiduals o
3.5 Blurredreflection n
ratherthanthetotalspectrum. A
p
Wsmeenaroewdprereflseecnttiotnhefrroemsultthseoifnsniemrualcactiroentisoinncdliuscd.inPg14reblaptirveissetnictatlhlye parFtiiagl.1c1ovsehroinwgsathbesothrpretieonPCcosmpepcotrnaenptro(dmuocdeedllwedhewniwtheZcPonCsFidAeBrSa ril 2, 2
twocomponentsproducedfromasimulationofavaryingpowerlaw, in XSPEC) applied to a (cid:3) = 2 power law. The covering fraction 01
5
andthethreecomponentsfoundwhenaweaklyvariable(approxi- is allowed to vary randomly between 0 and 1, and the column
mately0.4timesasvariableasthepowerlaw)relativisticreflection density is allowed to vary by a factor of 3. The first component
componentisadded.Wereproduceandexpandupontheseresults correlateswellwiththecoveringfraction;however,theothertwo
here, investigating the effects of a strongly blurred and ionized componentsreturnedbytheanalysisdonotcorresponddirectlyto
reflectioncomponent. a single parameter and represent changes in the column density
In Fig. 9, we show the two components returned from a simu- at different covering fractions. The first component matches well
lationofavaryingpowerlawandconstantreflection.Thereflec- withthefirstcomponentofNGC4395(Section4.3.1),whichshows
tion parameters are the same as those in Section 3.4, except the strongabsorptionvariability(Nardini&Risaliti2011).Indeed,ifwe
normalizationofthereflectioncomponentisincreasedsothatthe simulateasourcewherethevariabilityisdominatedbychangesin
0.3–10keVfluxis approximately equaltothatofthepower law. thecoveringfractionofaneutralabsorber,allowingsomevariability
The reflection spectrum is then convolved with the KDBLUR, with of the underlying power law, we obtain two components which
the inner and outer radii set at 1.235 and 400 gravitational radii, are in excellent agreement to those shown found for NGC 4395.
respectively,andanemissivityindexof3.ThefirstPC,shownin ThissimulationisshowninFig.12,forapartialcoveringabsorber
thetoppanel,canessentiallybethoughtofasaflatlinewiththe that varies in covering fraction from 0.5 to 1, with N fixed at
H
reflectioncomponentsubtracted.Thisthenrepresentsthesuppres- 1022 cm−2, applied to a power law with (cid:3) = 2 that varies by a
sionofvariabilityatenergieswheretherelativisticreflectionmakes factorof∼20percent.
MNRAS447,72–96(2015)
RevealingAGNvariability 79
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Figure10. Thefirst(left,black),second(middle,red)andthird(right,blue)PCsobtainedbyusingPCAonsimulatedspectraofapower-lawplusrelativistic t C
a
reflectionmodel,wherethepower-lawfluxvariesbyafactorof4andthereflectedfluxbyafactorof1.5.Thesecomponentsareshownforfourdifferent lifo
ionizationparameters,andthefractionalvariabilityattributedtoeachcomponentisshownineachplot.Blackdashedlinesindicatezeroonthey-axisforthe rn
secondtwoplots(axislabelsarenotshown,asthescaleisarbitrary). ia In
s
titu
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ril 2
, 2
0
1
5
Figure12. ThetwoPCsfoundfromasimulationofpartialcoveringab-
sorptionandintrinsicvariability.
3.7 Ionizedabsorption
Figure11. ThethreePCsproducedbyasimulationofvaryingabsorption.
In Fig. 13 (reproduced from P14b), we show the PCs produced
Apowerlawisconvolvedwithaneutralpartialcoveringabsorptionmodel,
byvariationsinanionizedpartialcoveringabsorber.Forthissim-
andthecolumndensityandcoveringfractionoftheabsorberareallowedto
change.Thefirsttermshownherecorrespondswelltothecoveringfraction, ulation, we use the ZXIPCF model (Reeves et al. 2008) and allow
andthesecondtwotermsrepresentcorrectionfactorstothis,whichdepend the covering fraction to vary randomly between zero and one for
onthecolumndensity. differentvaluesoftheionizationξ.ThisproducesasinglePCin
allcases,thespectralshapeofwhichdependsstronglyontheion-
The marginally more complex simulations from P14b showed ization. We also investigate allowing the column density to vary,
the effects of diffuse thermal emission on the PCs returned from keeping the covering fraction fixed at 0.5. This produces almost
partialcovering.Thisaddition,whichcharacterizesthePCspectra identicalprimarycomponents,andinthecaseofthelowestioniza-
ofNGC1365,dampsoutthevariabilityatlowenergies. tionsimulationasecondcomponent,similartotheonefoundinthe
MNRAS447,72–96(2015)
80 M.L.Parkeretal.
differentpatternofvariability.Thesesourcesshowsimilarsuppres-
sionoftheprimarypowerlawbyareflectioncomponent,butthe
pivotingtermsteepenssharplywithenergy.
(iii) In Section 4.3, we discuss the three sources (NGC 1365,
NGC 4151 and NGC 4395) that show good evidence of variable
partialcoveringabsorption.Thehigherordertermsdifferbetween
these objects, and may indicate the presence or lack of intrinsic
variability.
(iv) Finally,weincludethePCspectrafortheninesourceswhich
donotappeartofitintothegroupingsdiscussedsofar.Theseobjects
arepresumablyexhibitingdifferentvariabilitymechanisms,andwe
discussthemonanindividualbasis.
4.1 Group1:MCG–6-30-15analogues
Within the sample of objects we have analysed, four additional D
o
NLS1 sources that show the same four variable components as w
n
MCG–06-30-15havebeenidentified.ThesesourcesareNGC4051, lo
1H0707−495, NGC 3516 and Mrk 766. We also found several ade
d
sourceswhichcouldbedisplayingthesamevariabilitypattern,but fro
havelowerdataquality,makingitimpossibletobecertain. m
h
ttp
Figure13. PCsproducedbysimulationsofpartiallycoveringionizedab- 4.1.1 MCG–6-30-15 ://m
n
sorption.Thecoveringfractionisallowedtovaryrandomlybetween0and ra
1,withallotherparametersfixed,producingasinglesignificantcomponent. MCG–6-30-15isverywell-studied,brightandhighlyvariablenar- s.o
x
The four panels correspond to four different ionization parameters. This rowlineSeyfert1(NLS1)galaxy.ItwasthefirstAGNinwhicha fo
figureisreproducedfromP14b. relativisticallybroadenedironlinewasfound(Tanakaetal.1995), rdjo
andalsoshowsthecharacteristicfeaturesofwarmabsorption(Otani urn
neutralcase(Fig.11),isalsoreturned.Wefindthatastheionization etal.1996). als
parameterisincreased,thestrengthofthecomponentreturned(in Fig.14showsthethreePCspectrapresentedbyP14a,alongwith .org
termsofthefractionofthespectralvariabilityattributabletothis theweakfourthcomponentnotdiscussedinthatwork.Thefirstthree a/
component,andnottonoise)lowers.Thisisduetothedecreased t Ca
effect of the absorption, and means that we are most likely to be lifo
abletodetectneutralabsorptionvariabilityusingthismethod. rnia
In
s
titu
4 PCA RESULTS FROM THE DEEP te
XMM–NEWTON SAMPLE of T
e
Inthissection,wepresenttheresultsfromPCAofthe26sources ch
n
in our sample. For each source, we show all the significant PCs olo
returnedandthefractionofthetotalvariabilityattributabletoeach gy
o
component. As in the case of the simulations presented earlier, n
A
the resulting component spectra are equally valid with the y-axis p
inverted.BasedonthePCAresultsobtained,weattempttoarrange ril 2
and categorize the sources analysed in a logical manner, through , 2
0
comparisonwiththesimulationspresentedintheprevioussection, 15
andbreakthesampleintofoursubgroups.
(i) ThefirstsourceanalysedusingthismethodwasMCG–6-30-
15, which was presented in P14a. This was found to have four
significantPCs,althoughthefourthwasweakandwasnotinvesti-
gatedindetail.HavinganalysedoursampleofAGN,wefindfour
moresources(NGC4051,1H0707−495,Mrk766andNGC3516)
whichdisplaythesamepatternofvariabilitywithfourcomponents,
andseveralotherswhicharelimitedbyfluxorlackofvariability,
but which show at least the first two components, with a similar
spectral shape. The key features of this group of objects are the
suppressionofthecontinuumvariabilityaroundtheenergiesofthe
iron line and soft excess and a PC showing a strong correlation
betweentheseenergybands. Figure14. PCspectrafoundinMCG–6-30-15,orderedfromtoptobottom
(ii) Wefindasecondgroupoffourobjects(Ark564,PKS0558- bythefractionofvariabilityineachcomponent,aspresentedinP14a.The
504,Mrk335and1H0419−577)withasimilarbutqualitatively percentageofvariabilityineachcomponentisalsoshown.
MNRAS447,72–96(2015)
RevealingAGNvariability 81
PCsfoundinthisobjectwereanalysedindetailbyP14a,whofound
thattheywerewellexplainedbytheeffectsofapowerlawvarying
innormalizationandphotonindex,anduncorrelatedvariationsina
relativelyconstantreflectionspectrum.Thesefindingsareconsistent
withthelight-bendinginterpretationofthevariabilityinthisAGN,
in which the height of the primary X-ray source above the disc
changes (Martocchia, Karas & Matt 2000; Miniutti et al. 2003;
Miniutti&Fabian2004)leadingtomoreextremevariationsinthe
primaryemissionthaninthereflectedemission.
Thesuppressionoftheprimarycomponentattheenergiesofthe
softexcessandironlineindicatethepresenceofastrong,relatively
constantspectralcomponentattheseenergies.Likewise,thebreaks
inthesecondcomponentcorrespondtothesameenergies,wherethe
primarypowerlaw,andhencevariationsfromthechangesinphoton
index,aresuppressed.Thisisbestexplainedbyastrongrelativis-
tically blurred reflection component, which is relatively constant D
o
whencomparedtothepowerlawduetolightbending.Apartially w
n
coveredpowerlawcanreproducethespectrumofthesource,butnot lo
a
thespectralshapeoftheobservedPCs(P14a,b).InP14b,weshowed de
d
thatthefirstthreecomponentscouldbeproducedbythevariable fro
continuumandreflectionmodel,andthatthepredictionsforeither m
h
ionizedorneutralpartialcoveringabsorptionvariabilityarecom- ttp
pletelydifferentfromthoseduetointrinsicvariability(Figs11and ://m
13) and therefore cannot explain the observed variability without n
ra
extremefine-tuningofmultiplespectralcomponents. s.o
Itisinterestingthatthereflectioncomponentshowsaturnover xfo
below∼0.7keV(thirdpanel),whereasthesuppressionofthecon- rd
jo
tinuumvariability(firstpanel)showsnosuchbreak.Thissuggests u
rn
thatthevariablereflectioncomponentisolatedhereisnotthesole als
origin of the soft excess in this source. The fourth-order compo- .org
nent also appears to contribute to the soft excess, although it is a/
stronglysuppressedbythereflectioncomponent.Theoriginofthis t C
a
ccoomnvpinocnienngtlyrermepariondsuacemiytsutseirnyg, saismwuelathioavnes.so far been unable to Figure15. PCspectrafoundinNGC4051,orderedfromtoptobottomby liforn
thefractionofvariabilityineachcomponent.PCs1,2,3and4correspond ia
to one, two and four and three from MCG–06-30-15, and the additional In
s
component5appearstobeattributabletoavariableabsorptionfeature. titu
te
o
4.1.2 NGC4051 Wenotethatthevariabilityisdominatedbythefirst(power-law) f T
e
component,thespectrumofwhichisqualitativelyverysimilarto ch
NGC 4051 is an NLS1 which is extremely variable on all time- n
the rms spectrum of NGC 4051 presented by Ponti et al. This is o
scales.Pontietal.(2006)showedthatthespectrumofthesource unsurprising,giventhatbothmethodsshouldproduceaspectrum logy
invariousfluxstatescouldbewelldescribedbyapower-lawplus of the relative strength of variability (which is largely due to the on
relativistic reflection model, like that used in MCG–6-30-15. It A
variablepowerlawinbothcases)butitisaninterestingconfirmation p
a&lsUotetlxehyib2i0t1s3s)t,rownhgilcyhflfauvxo-udrepmeonddeelnstintivmoelvilnaggsin(tArilnsstoicn,vaVraiaubgihliatyn ofTouhremmeutchhodh.ighersignaltonoiseinthethirdcomponentrelative ril 2, 2
andrelativisticreflectionoverreprocessingbydistantmaterial. tothefourthcomponentinMCG–06-30-15givesustheopportunity 015
OuranalysisofNGC4051revealsfivesignificantPCs,shownin
toinvestigatethiscomponentinmoredetail,andhopefullytoun-
Fig.15,fourofwhichcorrespondwelltothosefoundinMCG–6-
derstanditsorigin.InSection3,weshowedthatacomponentwith
30-15.PCs1,2and4matchcomponentsone,twoandthreefrom
thisspectralshapecanbeproducedbyaddingasecondreflection
MCG–06-30-15andthesimulationshowninFig.10.Thesecompo-
componenttothespectrum,withahigherionizationparameterand
nentsshowthesamebreaksanddips,anddifferonlyquantitatively.
moreextremerelativisticblurring.
The third PC from NGC 4051 appears to match the weak fourth
componentfoundinMCG–6-30-15.Finally,thefifthcomponent,
which has no analogue in MCG–6-30-15, shows what appears to
4.1.3 1H0707−495,NGC3516andMrk766
beanabsorptionedgeatanenergyof∼1keV,withnootherstrong
features visible in the spectrum. We suggest that this component 1H0707−495,NGC3516andMrk766alldisplaythesamefour
corresponds to a change in the properties of an ionized absorber, variablecomponentsasMCG–06-30-15andNGC4051,againwith
asdescribedin(Ogleetal.2004),howeverthisconclusionisex- the only large difference being the order of the third and fourth
tremelytentativeandmustbetreatedwithcautionbecauseofthe component,whichisreversedwithrespecttoMCG–06-30-15in1H
highorderofthisPC.Weconclude,basedonthealmostidentical 0707−495andMrk766.Thecomponentspectraoftheseobjectsare
components produced, that the variability in this source is driven shown in Fig.16, with the third and fourth components swapped
bythesameprocessesasinMCG–6-30-15. in Mrk 766 and 1H0707−495 for ease of comparison. All four
MNRAS447,72–96(2015)