Response of the warm absorber cloud to a variable nuclear flux in active galactic nuclei

0.18 MB·English

by  L. Chevallier

Astronomy&Astrophysicsmanuscriptno.chevallier (cid:13)c ESO2008
February5,2008
Response of the warm absorber cloud to a variable nuclear flux in
active galactic nuclei
7
0 L.Chevallier1,2,B.Czerny2,A.Ro´z˙an´ska2,andA.C.Gonc¸alves1,3
0
2
1 ObservatoiredeParis-Meudon,LUTH,Meudon,France

n 2 CopernicusAstronomicalCenter,Bartycka18,00-716Warsaw,Poland
a 3 CentrodeAstronomiaeAstrof´ısicadaUniversidadedeLisboa,Observato´rioAstrono´micodeLisboa,TapadadaAjuda,1349-018Lisboa,
J
Portugal
4

Received22May2006/Accepted20December2006
1
v
2 ABSTRACT
1
1 Recentmodelingofthewarmabsorberinactivegalacticnucleihasprovedtheusefulnessofconstanttotal(gasplusradiation)pressuremodels,
1 whicharehighlystratifiedintemperatureanddensity.Weexploretheconsistencyofthosemodelswhenthetypicalvariationofthefluxfromthe
0 centralsourceistakenintoaccount.Weperformavariabilitystudyofthewarmabsorberresponse,basedontimescalesandourphotoionization
7 codeTITAN.Weshowthattheionizationandrecombinationtimescalesaremuchshorterthanthedynamicaltimescale.Cloudsverycloseto
0
thecentralblackholewillmaintaintheirequilibriumsincethecharacteristicvariabilitytimescalesofthenuclearsourcearelongerthancloud
/
h timescales.For moredistant clouds, thedensitystructurehas notimetovary, inresponse tothevariationsof thetemperatureor ionization
p structure, and such clouds will show the departure from the constant pressure equilibrium. We explore the impact of this departure on the
- observedpropertiesofthetransmittedspectrumandsoftX-rayvariability:(i)nonuniformvelocities,oftheorderofsoundspeed,appeardueto
o
pressuregradients,uptotypicalvaluesof100kms−1.Thesevelocitiesleadtothebroadeningoflines.Thisbroadeningisusuallyobservedand
r
t verydifficulttoexplainotherwise.(ii)Energy-dependentfractionalvariabilityamplitudeinsoftX-rayrangehasabroaderhumparound∼1−2
s
a keV,and(iv)theplotoftheequivalent hydrogencolumndensityvs.ionizationparameterissteeperthanforequilibriumclouds.Theresults
: havethecharacterofapreliminarystudyandshouldbesupplementedinthefuturewithfulltime-dependentradiationtransferanddynamical
v
computations.
i
X
r Keywords.Radiativetransfer;Line:identification;Galaxies:Seyfert;X-rays:galaxies;Galaxies:active
a
1. Introduction a highly clumpy medium with very dense clouds embedded
into low density surrounding plasma. The model of a con-
The environment of radio quiet active galactic nuclei (AGN)
tinuous wind was proposed by Murray & Chiang (1995) and
is still poorly understood.The activity is powered by a black
subsequently studied e.g. by Murray & Chiang (1997, 1998),
holebuttheaccretionflowisaccompaniedbyanoutflowofthe
Proga, Stone & Kallman (2000, 2004), Pietrini & Torricelli-
material. The inflow is in a form of an accretion disk which,
Ciamponi(2000).Ontheotherhand,thestrongX-rayirradia-
furtherout,hasaformofadusty/moleculartorusandtheradial
tionoftheoutflowingmaterialmayleadtothermalinstability
velocitiesoftheinflowarenotmeasureddirectly.Theoutflow
(Kroliketal.1981)thusresultinginclumpinessofapartofthe
takesplaceinalargerangeofanglesaroundthesymmetryaxis
flow. Therefore, clumpy outflow was advocated by a number
but the geometry and the nature of this flow is unclear. The
of authors (e.g. Smith & Raine 1988; Netzer 1993; Krolik &
presence of the outflow manifests best as Broad Absorption
Kriss1995;Netzer1996).Anarrowstreamofclumpyoutflow
Lines (BAL) of optical/UV spectra of some quasars, Narrow
was advocated for by Elvis (2000), while narrow continuous
AbsorptionLines(NAL)inotherquasarsorinSeyfertgalaxies,
streamerswerefavoredbySteenbruggeetal.(2005).Recently,
or as X-ray warm absorbers (WA) in Seyfert galaxies. These
an advanced model of the clumpy outflow was developed by
absorptionfeaturesallowtodeterminetheoutflowvelocityof
Chelouche & Netzer (2005), based on the previous extensive
theplasmaalongthelineofsightbutanyestimatesofthespa-
studiesofthewindaccelerationmechanisms.
tialdistributionofthe plasma,orevenofa representativedis-
Theissuecanbeinprinciplesolveddirectlyontheobserva-
tanceoftheabsorberfromthenucleus,aredifficult.
tionalgrounds.However,X-raydataevenfromgratinginstru-
One of the important questions is whether this outflow is
mentsonboardofChandraorXMM-Newtontelescopescannot
roughly a continuous wind with shallow density gradient or
resolvekinematicalcomponentsnarrowerthan∼ 100kms−1.
Sendoffprintrequeststo:[email protected] HighresolutionUVdatashowthepresenceofabsorptionlines
2 Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN
with the kinematical widths ∼ 100 km s−1 (e.g., NGC 3783, 2. Model
Gabeletal.2003)or50−60∼ 100kms−1 (e.g.,NGC7469,
We study the response of a single warm absorber cloud to a
Scottetal.2005).TheseresultsareconsistentwithX-raydata
change of the incident X-ray radiation flux, F. Using the sta-
but it is still not clear whether we probe the same part of the
tionaryradiativetransfercode,wedeterminethekindsofequi-
flow with X-ray and UV data. Spectral analysis of the X-ray
libriumsolutions:
datasuggeststhatonezonemodeldoesnotwellrepresentthe
observations and at least two photoionization regions are re- – totalpressureandthermalequilibrium,
quiredtoexplainthepresenceoflinesfromthegasindifferent – onlythermalequilibrium.
ionizationstates(NGC4051,Collingeetal.2001;NGC5548,
Kaastra et al. 2002; NGC 3783, Kaspi et al. 2002, Netzer et The first type of solution is the cloud in total pressure equi-
al. 2003and Krongoldet al. 2003;Mkn 304,Piconcelli et al. librium. It correspondsto a cloud which is in complete equi-
2004;H0557-385,Ashtonetal.2006). librium with the incidentflux. The second type of solution is
obtained allowing for a change in the irradiating flux but as-
On the theoretical side, it is not clear whether strong
sumingthatthetimescaleofthischange,t ,isshorterthanthe
X
clumpiness of the medium is possible to achieve and sustain.
timescale needed to restore the pressure equilibrium. In this
Time evolution of the warm absorber medium has not been
caseweperformthecomputationsofthenewthermalandion-
studied in great detail so far. Additionally, AGN are known
ization equilibrium but we retain the original density profile.
fortheirvariabilityintheX-raybandsincetheEXOSATdata.
This second solution will describe the cloud out of pressure
Variable irradiation changes the conditions within the cloud
equilibrium.Theapplicabilityofeitherthefirst,orthesecond
and might even destroy the cloud. Also small compact cloud
solutiondependsonthecloudlocationandthevariabilityprop-
will respondto variable X-ray flux in a different way than an
ertiesofthenucleus.
extendedmedium.
TheradiativetransferusedinbothcasesisthecodeTITAN
(Dumont et al. 2000, 2003). This 1-D code works in plane-
In the presentpaper we concentrateon a single warm ab-
parallel symmetry but uses the Accelerated Lambda Iteration
sorber cloud under constant pressure. We consider a cloud of
(ALI)methodtoprovidefully-consistentmulti-angleradiative
considerably large column density and non-negligible optical
transfercomputationsforbothcontinuumandlines(Rybicki&
depth.Suchacloudisstronglystratifiedsincethedensitypro-
Hummer 1991,and referencestherein).Using an accurate ra-
file is obtained self-consistently from the condition of total
diativetransfermethodisimportantinsuchaproblem,where
pressureequilibrium(seeDumontetal.2002,Chevallieretal.
radiationpressurevariationwithinthecloudplaysanimportant
2006,Ro´z˙an´skaetal.2006),inducingafewsharptemperature
role,especiallyinthedeterminationofthelocationoftempera-
dropsduetothermalinstabilities.Magneticandturbulentpres-
turedropsduetothermalinstabilities.Weconsiderabout1000
sureeffectshavebeenneglectedinthisstudy.Itiswellknown
spectrallines,mainlyintheX-rayrangeofthe10mostabun-
that magnetic pressure may remove the thermal instabilities
dance species in the universe, i.e. H, He, C, N, O, Ne, Mg,
(Bottorff, Korista & Shlosman 2000), but our cloud, if large
Si,SandFe.Throughoutthepaperweusecosmicabundances
enough,willstillremainhighlystratifiedwithashallowertem-
(Allen1973),whichareconstantinthecloud.
peratureanddensitygradientnearthelocationoftheprevious
Thecompleteequilibriumstateischaracterizedbythelocal
thermalinstabilityzone.Itisthesamewithturbulentpressure.
densityattheirradiatedfaceofthecloud,n ,thehydrogencol-
Brightirradiatedsideofthecloudisoflowdensityandhighly o
umndensityofthecloud,N ,andthepropertiesoftheincident
ionizedbutthedensitystronglyincreasesinward(byafewor- H
radiation(apower-lawofindex1from10eVto100keV,and
dersofmagnitude)andthemediumbecomeslessionizedaswe
theionizationparameterξ = L/n R2,whereListhebolometric
approachthedarksideofthe cloud.Suchamediumhasbeen o
luminosityofthesource,Rthedistanceofthemediumfromthe
usedtofittheWAofNGC3783(Gonc¸alvesetal.2006).Here
source).Thedensityprofileisdeterminedconsistentlyfromthe
we study the response of the cloud to the varyingX-ray flux,
conditionofthetotalpressureequilibrium.Theoff-equilibrium
withtheaimtotestthepossibilityofstrongclumpinessinthe
stateischaracterizedbyanewvalueoftheionizationparameter
warmabsorber.Usingthetime-independentcode,weestimate
ξbutthedensityprofileistakenfromthepreviousequilibrium
theevolutionofourcloudatthebasisoftimescales,determined
solution.
separatelyindifferentpartsofourhighlystratifiedcloud.The
We first analyze the timescales for various processes
cloud,initially in total (gaseous+ radiative)pressure equilib-
withinthe cloudin fullequilibrium,in orderto establishself-
rium,isdisturbed;pressureis nolongerconstant,andvarious
consistencyofthecloudresponse.
parts of the cloud expand/contract. We estimate the observa-
Thelighttraveltimeisgivenby
tional consequencesof the cloud departure from equilibrium.
Finallyweshowhowthebehaviorofourcloud,whosedistance H
t = , (1)
fromthecentralsourceisunknown,varywiththisdistance. light
c
In the next section, we recall some generalities about the where H is a geometricalsize of a whole cloud, or of a zone
modelandourphotoionizationcode,andwegiveformulaefor underconsideration.Inourcasethistimescaleisrelevantsince
timescaleswhicharedetailedintheAppendix.Resultsarepre- thecloudisopticallythintothecontinuum.Thislow(butnot
sentedinSect.3.Section4isdedicatedtothediscussionofthe negligible)opticaldepthis causedbysignificantionizationof
physicalandobservationalimplicationsofthesemodels. themediumevenatthedarksideofthecloud.
Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN 3
If the irradiation changes, the whole volume of the cloud
responds to the decrease/increase in photon flux. Therefore, 107
generally we do not have here well defined ionization fronts,
as in the case of an expanding HII region around a star (e.g.
Osterbrock 1974). The relevant description is provided, in-
stead,bytheionizationandrecombinationtimescales.Theion- K] 106
aizaloticoanl tqiounanatnitdyrwecitohminbianactliooundt.reHcotwimeevsecra,lweefocraneaicnhtroiodnucies mperature [
timescales for specific zones, or a whole cloud, by analyzing Te
which ions dominate in the various zones and which transi- 105
tions are close to equilibrium (see the Appendix). We obtain
thefollowingestimates
x4
tion =6×10−3F1−61[s], (2) 104 x3, shifted +1e23 cm-2
0 5e+22 1e+23 1.5e+23 2e+23 2.5e+23 3e+23
Column-density [cm-2]
and
Fig.1. The temperatureprofile of the cloud at the initial state
trec =0.2n−121[s], (3) ξ = 104 erg cm s−1 (red). We also represent the case more
typical of WA: logξ = 3, for which maximalcolumn-density
whereF istheincidentbolometricfluxmeasuredinunitsof
16 is 2×1023 cm−2 (magenta). This curve is shifted in column-
1016ergs−1 cm−2,andn isthecloudhydrogendensityatthe
12 density by a value 1023 cm−2 in order to compare with the
surfaceinunitsof1012cm−3.
logξ =4case.Curvesarenotdistinguishable.
Thelocalthermaltimescaleisdefinedas
kT
t = =12T n−1Λ−1[s], (4) 3. Results
th n Λ 6 12 23
e
3.1.Initialstateofthecloud
wherekistheBoltzmannconstant,Λ isthecoolingfunction
23
in units of 10−23 erg cm3 s−1, T6 is the temperature in units Wemodelfirstthecloudincompletetotalpressureequilibrium.
of 106 K, and the electron density ne ∼ 1.18nH, where nH is Forthisreferencecloud,we chooseξ = 104 ergcms−1, no =
hydrogen density. Isothermal sound speed velocity is locally 107 cm−3.WechoosethelargestN ∼ 3×1023 cm−2 allowed
H
calculatedas for the constantpressure cloud for such an incident spectrum
(Chevallier et al. 2006). This choice of the column-density is
2kT
c = =130T1/2[kms−1], (5) consistent with computationsof the cloud sizes by Torricelli-
s rm 6
H Ciamponi & Courvoisier (1998), which take into account the
where m is the hydrogen atomic mass and the factor 2 ac- thermalconduction.Ifweapplytheirexpressionforthecloud
H
countsformeanmolecularweightinanionizedmedium.Eq.5 corescaling(Eq.5),takingtheirclouddimensionlesssize x =
isrelevantwhentakingintoaccountonlythegaseouspressure 3×107fromtheirFigs.4and5,andtakethecoretemperature
for a perfect gas. With such a stratified cloud, the dynamical 3×104K(i.e.thesmallesttemperatureinourreferencecloud),
timescale (i.e. time forrestorationof pressure equilibrium)of we obtain the expression for the column-densityof the cloud
a cloud zone of a geometrical size ∆z = z − z is obtained N ∼2×1023cm−2,independentfromthecorenumberdensity.
2 1 H
throughintegrationoverz TheinternalkinematicsissetasrandomGaussianmovements
withdispersion100kms−1,whoseonlyeffectistoincreasethe
z2 dz
t = , (6) linewidthbyDopplereffect.
dyn Zz1 cs(z) The temperature profile across the cloud as a function of
Wegeneralizetheresultsforasinglecloudtoawholefam- thehydrogencolumn-densitymeasuredfromthecloudsurface
ily of clouds at various distances from the nucleus. The ini- is shown in Fig. 1. For such abundances, electron density is
tial configuration(i.e. the variation of all quantitiesin optical ne ∼ 1.18 nH and total density is n ∼ 2.265 nH). The cloud
depthscale)practicallydoesnotdependonn (withvaluesbe- developsfourcharacteristiczones:
o
tween105 to1012 cm−3;seeRo´z˙an´skaetal.2006)foragiven
– lowdensityhightemperatureextendedzone(hot),
ξandN .Sinceachangeofthelocaldensityattheilluminated
H – intermediatezone(intermediate),
surface of the cloud is equivalent to a change of distance R
– highdensitylowtemperatureouterzone(outer),
fromthenucleuswecantakeourcloudasrepresentativefora
– thinzoneofhighestdensityandlowesttemperature(end).
wholefamilyofself-similarcloudsatvariousdistances.Soour
modelcan be appliedto severaldistancesR, with appropriate Thelastzoneisgeometricallyverythin,ascanbeseenin
dependenceofn onthe radiusR.We have F(R) ∝ R−2,T as Table1butthehydrogencolumndensityofthiszoneissignif-
o
the function of the hydrogencolumn remains the same, inde- icantbecauseofthehighdensity.Fortheconsideredcloud,the
pendentlyfromthedistance,andnscaleswithn .We request ratio of densities at the cold and hot surfaces is ∼ 103, what-
o
n (R) ∝ R−2,thusH(R) ∝ R2.Consequentlyalltimescalesde- ever the value of density n between 105 and 1012 cm−3. The
o o
finedinthissectionareproportionaltoR2. geometricalsizeofthereferencecloudis5×1015cm,smaller
4 Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN
byafactorof6thanforaconstantdensitycloudwiththesame hot intermediate outer end
columndensityandthesamedensityatthecloudsurface.The ∆z[cm] 3.41015 1.61015 8.41012 9.91011
light travel time across the cloud is 1.7 × 105 s. The typical col.[cm−2] 5.81022 2.31023 1.31022 5.31021
T av.[K] 8.0106 1.3106 1.9105 4.8104
valueofξofwarmabsorbers,estimatedfromtheobservational
n av.[cm−3] 1.7107 1.4108 1.5109 7.2109
data, is rather ∼ 1000 or lower, and such values are met in H
c [kms−1] 370 150 57 28
the interiorof our referencecloud (i.e. intermediatezone, see s
t [s] 1.2105 5.4104 290 34
Table 1) where the density is roughly ten times the density light
t [s] 6103 103 100 30
ion
at the surface of our medium. Figure. 1 confirms that mod- t [s] 2104 2103 100 20
rec
els with logξ = 3 and 4 behave similarly. For our logξ = 3 t [s] 107 2105 103 60
th
model,NH ∼ 2×1023 cm−2,whichisnowthemaximumcol- tdyn[s] 9.3107 1.1108 1.5106 3.5105
umn density. In order to compare these temperature profiles,
Table1.Characteristicsofthefourzonesinthismedium,and
wehaveshiftedthesolutionforlogξ = 3by1023 cm−2 along
all timescales consideredin this study (see the text). t and
light
the column-density axis. Temperature profiles are almost the t = ∆z/c are computedzonebyzone(t = 2×108 sfor
dyn s dyn
same,apartthattheintermediatezoneforthelogξ = 3caseis
thewholecloud).
25%lessthanforthelogξ=4case.
As ionization or recombination timescales are specific of
each ion, we analyzed the ionization structure of a whole
cloud (see the Appendix and Table 3). The longest ioniza- 108
tion timescale is equal to 8×103 s (for ion Fe in the hot 107 Dynamical
zone).Processesrepresentativefortheintermediate,outerand
106
endzonesareconnectedwithS,OandC,respectively.
Therepresentativerecombinationtimescalefora wholecloud 105 Thermal
iaiosnnd2se×fno1dr0tz4hoesner(esacgaoarmeinbSfiionratFi,oeOntimaniendsctCahleehi,nortethszpeoenicnett)ie.vreRmleyep.drieasteen,toautitveer Timescales (s) 110034 Ionization Recombination
The profiles of the timescales calculated locally across 102
the cloud are shown in Fig. 2. We see that photoionization
101
timescaleisroughlyconstantthroughtheslabbuttherecombi-
nationtimescaleismonotonicallydecreasingthroughthecloud 100
since itisinverselyproportionalto the electrondensityne ac- 100-.10 100 5.0 1022 1.0 1023 1.5 1023 2.0 1023 2.5 1023 3.0 1023
cordingto the scaling formula(see Eq. 3). The actual recom- Column-densities (cm-2)
binationtimescalecalculatednumericallyacrossthecloud(see
Fig.2. The dependence of the various local timescales (s)
the Appendix) dependsalso on the temperature (not linearly)
across the cloud (as a function of the column-density): ion-
anddecreasesevenfaster.Therecombinationtimescaleismore
ization timescale, recombination timescale, thermal equilib-
shallowifweconsidervariousionsasrepresentativefordiffer-
riumtimescale,hydrostaticequilibriumtimescale (cumulative
entzones(seeTable1).
through the slab, classical perfect gas). As ionization or re-
Theoverallthermaltimescaledependsbothonthetemper-
combinationtimescalesarespecificofeachion,we chooseto
ature and the density, so it decreases with the distance from representFe, which representthe longest timescale (only
the cloud surface even more rapidly than the recombination in the hot zone for recombination, leaders are Si, O and
timescale (see Table 1), and roughly follows the numerically Cfortheintermediate,outerandendzones,respectively;see
obtained recombination timescale for a single ion. Its maxi-
Tables1and3).
mumvalueof107,atthehotsurface,isveryhigh,muchlonger
thanionizationorrecombinationtimescales.Wehavechecked
thatΛ23 ∼ 1 whateverthe depth forour model, includingthe 3.2.Cloudstatesandconditionsforthe
surfacelayers.Inotherzonesthethermaltimescaleisshorter,
self-consistencyofthecloudresponsedescription
somostionsreachequilibriuminthetimescaleappropriatefor
theintermediatezone(2×105s),andweadoptthisvalueasthe The X-ray flux of AGN nuclei is strongly variable. Since the
longestcharacteristicthermaltimescaleofthecloud.However, timescalescorrespondingto ionization/recombinationequilib-
we must stress that in the case of the hot zone, where highly riumandtothedynamicalequilibriumdifferbyafewordersof
ionizedironspectralfeaturesform,thefullthermalequilibrium magnitude,a cloudis notalwayslikelyto achievea complete
ishardtoachieve.Thetemperaturerises/fallsslowlysinceboth equilibrium.We willnowanalyzethe conditionsofcomplete,
the atomic heating/cooling and the Compton heating/cooling orpartialequilibrium.
are not very efficient. The dynamical timescale of the whole For this purpose, we must compare the cloud internal
cloudobtainedthroughintegrationisequal2×108 s. Bothin timescaleswiththetimescalesoftheintrinsicvariabilityofthe
the hot and in the intermediate zone these timescales, calcu- X-rayincidentflux. AGN do nothave anyspecific timescales
lated separately, are long (see Table 3). In Fig. 2 we plot the butthepowerspectruminSeyfertgalaxiesiswellrepresented
cumulativetimescalesforeachofthezonesseparately,starting by a power law with the two breaks (e.g. Markowitz et al.
fromthebeginningofazone. 2003).Mostofthepowerisbetweenthehighandthelowfre-
Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN 5
quencybreaks, which dependon the central black hole mass. 108
We can consider these frequency breaks of the power spec-
trum in an AGN as a characteristic range of timescales. We
adopt tXshort and tlXong as the shortest and longest timescales 107
of variation, respectively. With a black hole mass of 107M ,
⊙
the appropriate timescales for regular Seyfert 1 galaxies are K]
2tXs0ho0r3t,=Pap6a×da1k0is52s0,0a4n)d, atnlXodngth=e s6ho×rt1t0im7essc(aMleariksobwyitazfeatctaolr. mperature [106
20shorterforNarrowLine Seyfert1 galaxies.Forillustrative Te
purposes,wefurtheradopttshort =105sandtlong =107s.
X X 105
Thefullthermalandpressureequilibriumwithinthecloud
x4
isachievedifthelightcrossingtime,thelongestoftheioniza- x4.5
x5
x6
tion,recombinationorthermaltimescales,thedynamicaltime 104
0 5e+22 1e+23 1.5e+23 2e+23 2.5e+23 3e+23
ofthecloudaremuchshorterthantheshortestX-rayvariability Column-density [cm-2]
timescale,i.e.max(tlight,tth,tion,trecomb,tdyn)≪tX.Ontheother Fig.3. The temperatureprofile of the cloud at the initial state
hand,thethermalequilibriumsolutionwithanunchangedden- ξ = 104 erg cm s−1 and after an increase of the irradiationto
sityprofilesrequiresmax(tlight,tth,tion,trecomb)≪tX ≪tdyn. ξ =3×104,105and106ergcms−1,butbeforeanewpressure
equilibriumisreached.Forallthosecases,we haveneglected
In our reference cloud the second set of conditions is theturbulentpressure.
roughlyfulfilled.Theionizationandrecombinationtimescales
areshortforallimportanttransitions.Thethermaltimescalein
1
theintermediatezoneiscomparabletotshort, onlythethermal
X
0.9
timescaleinthehotzoneissignificantlylongerwhichmayef-
fectthehydrogen-likeironabsorptionfeature.Theshortestdy- 0.8
namicaltimescale in the lastzone is still longerthantshort, so
X 0.7
stlohoyfwestthmeedemobcdalyteoilccuiodstmr,aeippnnpudrttshoi,neplgriokinaueettewethrfooparsrneesdshisoneurnrttedlXtoienzmgqouen=sielcisab1lrbe0iuu7vtmasrr,eaitastahbtihnoileiuintlybgd.aLtcbhkoeensfogiodlelde-r -2Pressure [dyne.cm] 000...456 xx4xx4x4x545445 PPPP PPggrrtaataaooddzztt
densityprofilein thehotandintermediatezone.We postpone
0.3
thecomputationsofsuchhybridmodelsforthefuture.
0.2
Summarizing,our new equilibrium is fully self-consistent 0.1
for an increase in the X-ray flux lasting up to t = 3×105 s
X 0
(i.e.theshortestdynamicaltimescale,seeTable1)ifthedensity 0 5e+22 1e+23 1.5e+23 2e+23 2.5e+23 3e+23
Column-density [cm-2]
profileisleftunchanged.Resultsobtainedforlongertimescales
Fig.4.Variationwiththecolumn-densityofgaseous,radiation
canonlyserveasindicatorsofthetrends.
andtotalpressureforthelogξ =4constanttotalpressurecase,
andunderilluminationlogξ =4.5forafixeddensityprofile.
3.3.Responseofthecloudstructuretothechangeof
irradiationflux 3.4.Responseofthecloudvelocityfieldtothechange
ofirradiationflux
Wethereforecomputeasetofnewcloudequilibriumsolutions After the change in the incident flux, the cloud is not in
byincreasingtheincidentfluxandpreservingthedensitypro- the pressure equilibrium any more. Pressure gradients appear
file fromthepressureequilibriumstate describedin Sect.3.1. whichleadtolocalaccelerationofthegaswithinthecloudand
Figure3showsthetemperatureprofilesofthecloudforwhich subsequent expansion. Figure. 4 shows the gaseous, radiative
theincreaseoffluxisbya factor3,10and100.Naturally,an and total pressure for the initial state logξ = 4 and the final
increasein the X-rayflux resultsin a highersurface tempera- statelogξ = 4.5.Themostprominentfeatureisthehugeposi-
ture. The depth of the first, hottest zone does not change but tivepressuregradientatthetransitionbetweentheintermediate
the temperatureof the intermediatezonerises. An increasein andouterzones.Therefore,ashockmayformatthislocation
X-rayfluxbyafactor100removestheintermediatezonecom- asthematerialstraintorecoverthedynamicalequilibrium.Itis
pletely.Thetwolastcolderzonesalwaysexistalthoughforthe notaclassicalionizationfrontsincethewholecloudisinanew
highestirradiationfluxthetemperatureofthebacksideofthe ionizationequilibriumafterarelativelyshorttimet .Thisisa
ion
cloudrisesupto106 K.However,theriseoftheincidentflux differenttypeofshockwhichformsduetothepresenceofthe
byafactorof3alreadybringsupthetemperatureoftheouter densitygradientintheoriginalmodel,previouslysupportedby
zonealmostclosetothetemperatureoftheintermediatezone. theappropriatetemperaturegradient.Thissupportisremoved
6 Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN
by the sudden rise of the temperature on the cold side. Since 1010
the discontinuityin the total pressure is not verylarge (a fac- 109
tor of 1.25 in case of the flux rise by a factor 3, see Fig. 4) 108
theexpectedMachnumber,M,ofanisothermalshockislow 107 tXlong
(M2 = 1.25), a relatively weak shock forms and propagates
106
wtTShuiitsb∼hszoao7nnsi1pec0,em5eadsoKtwciloaeonhsoseenadtldouyetthhhtaeoevstethhpteeeorelmdaccoaoknlfsiosnidfoseutparnrbetdhislsMeituyhrceizgsboh∼aneles1atn2(tsc0eeemkewmpFeiilrsgla−.at1ul3sir)noe. Timescales (s) 111000345 tXshDoyrntamical Recombination
awpepteDhauurseinetoxoptthheecetrvtpehraayrttdsliinoffefestrhefeonrtcmvloaiunludge.isnotfhtehseevtrealoncsiittiyoinnzoounrecslomuady, 111000012 Thermal IonizaLtiigohnt urrent model
haveaverycomplexprofile:partofthelinemaybenarrow,and 10-1 C
partofthelineprofilemaybebroad.Thepresenceofthesignif- 10-21014 1015 1016 1017 1018 1019 1020
icantvelocitygradientmeansthattheassumptionofaconstant Distance R (cm)
turbulenceacross the cloud may notbe justified but the com- Fig.5.Thedependenceofthemaximumvaluewithinthecloud
putationsoftheradiativetransferwithvariablevelocityfieldis of various timescales as a function of the distance from the
beyondthescopeofthepresentpaper. nucleus for a source with luminosity L = 1045 erg s−1. We
represent the bounds of the characteristic range of variability
of the source, i.e. the the shortest timescale tshort and longest
3.5.Cloudsatvariousdistancesfromthenucleus X
timescaletlong,lighttraveltime,ionizationtimescale,recombi-
X
Thechoiceof n = 107 cm−3 andξ = 104 correspondsto the nation timescale, thermal timescale and dynamical timescale.
o
choice of the distance for a specific choice of the bolometric This value of the thermal timescale excludes the hot zone,
luminosity L of the nuclear source. The domain of observed whereitisupto50timeslonger(seeTable1).Verticallineindi-
luminosities range form 1041 erg s−1 (e.g., NGC 4051) up to catesthecurrentmodelpresentedhere(equivalenttoR = 1017
1047ergs−1(e.g.,quasars).WeadoptL=1045ergs−1cm−2in cm).
thefurthercalculations:the cloudislocatedatthe distanceof
1017 cmfromthenucleus.AllthoseresultsscaleasL/R2,and
tance. The results are shown in Fig. 5, where severalregions,
anyvalueofLcanbechosen.
asafunctionofthedistanceofourcloudfromthenucleus,can
Theresultsobtainedforasinglecloudcanbegeneralizedto bedefined.Ourreferencecloud(i.e.hydrogensurfacedensity
afamilyofcloudslocatedatvariousdistancesfromthenucleus n = 107 cm−3) is marked with the vertical line. Horizontal
o
adopting scaling laws based on the very weak dependence of linesdenotetheboundsofthecharacteristicrangeofvariabil-
theresultsfortheradiativetransferontheadoptedvalueofthe ity timescales of the source, for a given central luminosity,
numberdensityatthecloudsurface,no(seeSect.2). L = 1045 erg s−1. Note that those results depend only on the
Wehavecheckedtheunderlyingassumptionbycalculating valueoftheionizationparameter,ξ,andthecloudcolumnden-
a set of clouds for ξ = 104 erg cm s−1, N = 3×1023 cm−2 sity,N ,andthisfigurecanbescaledwithvariousvaluesofthe
H H
andwithvaluesofn intherangefrom105 to1011 cm−3.The luminosity L. We see fromFig. 5 thatin generalwe can have
o
temperatureprofilesmeasuredasfunctionsoftheopticaldepth fourbasictypesofclouds:
werealmostidentical.Thedensityprofilesasfunctionsofthe
– full(dynamical+thermal)equilibrium,R<3×1016cm
optical depth had very similar shape and differed just in the
– thermalequilibrium,3×1016cm<R<3×1018cm
normalization.Theratioofthedensityattheouteredgeofthe
– noionizationequilibrium,3×1017cm<R<5×1018cm
cloudto n wasalmostconstant,onlyslowlydecreasingfrom
1.5×103too103withtheincreasingdensity. – cloudsatR>5×1018cm
Therefore, at the basis of the numerical results for a sin- The innermost clouds should be described using full equilib-
gle cloud we consider now a family of clouds for ξ = rium computations. The second group of clouds shows the
104 erg cm s−1, NH = 3×1023 cm−2, and the bolometric lu- departure from the dynamical equilibrium, but their ioniza-
minosityofthenucleusL = 1045 ergs−1 cm−2.Thecondition tionequilibriumispreserved.Theirionizationstate shouldbe
ofconstantξinthiscaseimpliesthatthenumberdensityatthe roughlycorrelatedwiththeX-rayfluxmeasuredatagivemo-
cloudilluminatedsurfaceisno(R)/R−172 = 107cm−3,whereR17 ment, and they can be represented as described in Sect. 3.3.
isthedistanceinunitsof1017 cm,anditisbyafactorof103 In particular, a shock forms and propagates at velocity ∼
higher at the dark surface. Other quantities defined in Sect. 2 120kms−1whateverthedistanceR,asthevariabilitytimescale
become H(R)/R217 = 5×1015 cm,tlight(R)/R217 = 1.7×105 s, tX and the extent of the outer zone are both higher than the
tion(R)/R217 = 8.0×103−30cm,trec(R)/R217 = 2×104−20s, time and displacement, respectively, of the matter when the
tth(R)/R217 =2×105−60s,andtdyn(R)/R217 =108−4×105s. sound speed is reached (see Sect. 3.4). Clouds further up are
Using these expressions and a variability timescale of the so extended that separate parts of the cloud responds to dif-
source between 105 s and 107 s, we can estimate the kind of ferent continuum, as their light travel time is comparable to
equilibrium reached by our medium as a function of the dis- the timescales of the X-ray source variability. Only complete
Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN 7
time-dependentcomputationsoftheradiativetransfer,withthe 50
MCG-6-30-15
adopted light-curve, are appropriate to analyze such clouds, x4.1
x4.1 pressure equilibrium
and at present we are unable to perform such computations.
45
For the last group of very distant clouds, the cloud size is so
extended that the assumption of a single cloud breaks down
%] 40
andwedealwithanextendedcontinuouswind. Variability [ 35
4. Discussion Fractional 30
Inthispaperwehaveconsideredthecomplexityoftheresponse
ofthewarmabsorbertothevariableX-rayincidentflux.Inor-
25
der to assess the cloud response we mostly concentrated on
comparisonoftwo states ofasingle warmabsorbercloud:an
initialirradiatedcloudatpressureequilibrium,andacloudsud- 20200 500 1000 2000 5000 10000 15000
denlyirradiatedbyathreetimeshigherfluxi.e.thatcloudcould hnu [eV]
reachnewthermalandionizationequilibriumunderenhanced Fig.6.Thefractionalvariabilityamplitude(herein%,defined
irradiation but the time was too short to reach new pressure as2|F −F |/(F +F ))calculatedusingthelogξ=4spectrum
1 2 1 2
equilibrium.Themodelcanbeusedagainstthepresentlyavail- asareference,fortwomodelsofincreasingfluxtologξ =4.1,
ableandfutureobservationaldata. thefirstoneasdescribedinthisstudyandthesecondoneinto-
Belowwegiveafewexemplaryapplicationsofourrepre- talpressureequilibrium.Thosequantitiesareshownforawide
sentativecloudresults,notyetfocusedatfittingaspecificob- energy range: 200 eV to 15 keV. Some difference is seen in
ject.Moreprecisemodelingshoulduseafamilyofsolutions. thewidthofthehorizontalzonebetween1and2keV,andfor
the featuresaround7keV (iron Kαline region).Spectralres-
olutionis10(Gaussianshape).Theoverallleveloftheampli-
4.1.Observationalapplications
tudereflecttheassumptionabouttheincreaseinthefluxbutthe
4.1.1. SoftX-rayvariability energy-dependentfeaturescan be comparedto the featuresin
the observedfractionalvariability amplitudes.The exemplary
Enhancedirradiationleadstohigherionizationofthecloudand datapointsrepresenta100ksecXMMobservationofMCG-6-
loweropacity,particularlyinthe softX-rayband.Indeed,ob- 30-15(Goosmannetal.2006).
servations based on RXTE monitoring show an enhancement
oftheenergy-dependentfractionalvariabilityamplitudebelow
5keV(Markowitzetal.2003).BeststudiedcaseofaSeyfert1 bandpeakingat1keVshouldbeseenonlyinthesourceswhich
galaxyMCG-6-30-15showsenhancedvariabilityin0.2–4keV show the presence of the warm absorber. Our model shows
bandapproximatelyequalto30%(Fabianetal.2002,Pontiet slightly too much absorption for this data set, and a better fit
al.2004).Thevariabilitybelow0.2keVandabove5keVmust would be reached with a lower column-density, for the same
be intrinsic, as it reflect the changes in the level (and possi- valueofξ. Itisalso interestingtopointoutthatthefractional
blyslope)of thecontinuumbutthe excess0.2–4keV maybe variabilityenhancementobtainedwithoutthepressureequilib-
duetotheopacitychangesinthewarmabsorber(e.g.Sakoet rium extends more into high energies, and seems to fit better
al.2002).Suchaneffectonthisobjecthasbeenstudiedusing thedata.Thiswouldsuggestthewarmabsorberdistancelarger
constantdensityclouds(Gierlinski&Done2006). than 3×1015 cm since the medium had no time to reach the
Usingourdensity-stratifiedclouds,wehavecalculatedthe dynamicalequilibrium(seeSect.3.5).
ratioofthetwospectra(modelswithlogξ =4andlogξ =4.5).
Sincethechangeofthefluxbyafactor3isratherextremeas
4.1.2. Observationaldeterminationofthecolumn
comparedtotheobservedvariabilityinMCG-6-30-15,weonly
density
considerthemodelwithlogξ = 4.1(i.e.increaseof∼ 26%of
the incident flux) without adjustment of the pressure and an- An interesting trend was found of increasing equivalent col-
other one with logξ = 4.1 in constant pressure equilibrium. umndensityoftheabsorberwithanincreaseoftheionization
In Fig. 6 we show the ratios of the two spectra plotted with parameterforthespecies(NGC5548,Steenbruggeetal.2005;
the resolution usually used from the computationof the frac- NGC4051,Ogleetal.2004;NGC7469,Scottetal.2005).Itis
tionalvariabilityamplitude.We also show the fractionalvari- thereforeinterestingtoseewhethersuchatrendisexplainedby
abilityamplitudecalculatedfromoneofthedatasetsobtained our constant pressure clouds. Therefore, we selected the ions
for MCG-6-30-15 (XMM observation in 2000, rev. 303; see studied by Scott et al. (2005) and performed a similar analy-
Goosmannetal.2006).Indeed,thereisastrongenhancement sis,i.e.weusedtheioncolumndensitiesfromoursimulations
ofthevariabilityat1–2keV.Themaximumvalueof50%ofthe (for the initial cloud and the cloud with increase irradiation,
fractionalvariabilityforthelogξ = 4.1caseisclosefromthe out of pressure equilibrium) and inverted them to equivalent
MCG-6-30-15case. Thissuggests thatthe variable ionization hydrogencolumnusingonlyabundancevalues.Theresultsare
of the warm absorber is a promising contributor to the over- shown in Fig. 7. We see thatthe trendseen in the data is in a
allvariability.Ifso,suchenhancedvariabilityinthesoftX-ray natural way explained by our model. The ratio of almost five
8 Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN
24 Wavelength absorption zone model measured
x4
x4.5 Si XIV
A line [km/s] [km/s]
Si XIII
22 O VII Ne IX Mg NXeI X Mg XII 66..6158..... SSii iinntteerrmmeedd 115500 1365200±±960900
O VI O VIII Fe XX 8.42... Mg intermed 150 500±160
Fe XXI
Fe XVII 9.17... Mg intermed/outer 150 680±410
N V
log(N)H20 C IV 1121..1535...... NNee ionutteerrmed/outer 15600 1403200±±257200
12.28... Fe intermed 150 890±570
12.82... Fe intermed 150 1070±340
18 13.45.. Ne outer 60 1050±490
15.01... Fe outer 60 650±320
Table2.KinematicalwidthsoftheX-raylinesestimatedfrom
16 ourcloudmodelincomparisonwiththelinewidthsmeasured
-2 -1 0 1
log(U) byScottetal.(2005).Thirdcolumngivethedominantlocation
Fig.7.Equivalenthydrogencolumn-densityvs. ionizationpa- oftheion(linesidentifiedbyScottetal.2005allcomeeither
rameter for some ions selected in our reference cloud in its fromtheintermediateorfromtheouterzone).
initial state (logξ = 4) and width the increased illumination
(logξ = 4.5). Apparent systematic increase reproduces the
trendseeninthedataofScottetal.(2005). 4.2.Furtherimprovementsinmodeling
Ourapproachtomodelingthetime-dependentresponseofthe
cloudto irradiationwasa first step in thisdirection.Itis well
ordersofmagnitudebetweentheresultsforFe,Mg,Si, known that the problem is complicated, and the best studied
SiandCiswellexplainedbythemodeloutofdynamical classical example is the time-dependent evolution of the ex-
panding H+ region around a newly born star (see Osterbrock
equilibrium.Ontheotherhand,ourcolumndensitiesarelower
1974).Unfortunately,our situation is more complexsince we
thantheseobtainedbyScottetal.(2005).Extensivemodeling
donotdealwithasingleionizationfront,andsimpleanalytical
withtheuseofothercloudparameterswillbenecessarytosee
estimatesdonotapplysoeasily toourcase.However,further
whetherthespecificvaluescharacteristicforNGC7469canbe
improvementofthe descriptionofthe clouddynamicsis nec-
accommodatedwithinourmodel.
essary.
Particularly important and difficult problem appears if
4.1.3. Linewidths clouds are at large distances from the center. Blustin et al.
(2005)arguedthatthewarmabsorberislocatedinmostsources
The predicted line widths dependon the cloud location, for a atdistance∼ 1pc.Ourcloudatsuchadistanceisfarfromra-
fixed nuclear source properties. Cloud located closer in reach
diativeequilibrium.Inthiscasetime-dependentradiationtrans-
equilibrium much faster and the velocity gradient is smaller.
fercomputationsseemtobenecessary.
Cloudslocated much furtheraway will also show smaller ve-
locity gradients since they are too extended to react to the Acknowledgements. Wethank toS.Collin,C.Done, T. Kallman, F.
variableradiationflux.Therefore,themeasurementoftheline NicastroandI.Shlosmanfor helpfuldiscussions. WealsothankA.-
widthwillprovideanindependentlimittothe clouddistance, M.DumontforprovidingussomehelpwiththecodeTITAN.A.C.
andanadditionaltestoftheconstantpressurecloudmodels. Gonc¸alvesacknowledgessupportfromtheFundac¸a˜oparaaCieˆncia
e a Tecnologia, Portugal, under grant no. BPD/11641/2002. Part of
We illustrate this issue in Table 2. We take the measured
this work was supported by grant 1P03D00829 of the Polish State
kinematical width of absorption lines measured in the X-ray
Committee for Scientific Research, and the Laboratoire Europe´en
spectrumofNGC7469byScottetal.(2005)andwecompare Associe´AstrophysiquePologne-France.
themwithourestimatesbasedonthelocationoftheions.
Measured width in the X-ray band are always larger and
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5. Appendix
Inordertoobtaintheionizationtimescalet ofawholecloud
ion
wecalculatethesetimescalesforallionsiseparately,asalocal
quantitieswithinacloud,
+∞ J
(ti )−1 =4π νσi(ν)dν, (7)
ion Zχi/h hν
10 Chevallieretal.:ResponseofthewarmabsorbercloudtovariablenuclearfluxinAGN
property hot intermediate outer end all
Fec 51017 1018 21010 2 21018
Fec 71017 1017 4107 310−4 91017
Fec 61017 51015 3104 210−8 71017
Fer 2104 500 8 0.8 2104
Fer 104 400 7 0.7 104
Sc 81016 21018 1015 21010 21018
Sc 91017 1018 21013 2107 21018
Si 800 103 103 103 103
Sic 81016 31018 21016 21012 31018
Sic 21018 41018 51014 5109 61018
Sir 5104 2103 30 3 5104
Oc 31016 21018 31018 21017 71018
Oc 41019 1020 31018 71015 21020
Oi 40 50 100 200 200
Or 2105 7103 100 10 2105
Cc 21015 1017 31017 61017 1018
Cc 21019 71019 31018 21017 1020
Ci 10 10 10 30 30
Cr 6105 104 200 20 6105
Table3.Tableofthecolumndensities(c,incm−2),ionization
(i)andrecombination(r)timescales(ins)forall4zonesinthe
mediumfortherepresentative,i.ecomparablecolumndensity
forbothionizationstates,ionsofFe,SandSi,O,andCinthe
hot,intermediate,outer,andendzones,respectively.