Systematic comparison of photoionised plasma codes with application to spectroscopic studies of ...

15 Pages·2016·0.89 MB·English

A&A596,A65(2016) Astronomy
DOI:10.1051/0004-6361/201628721
&
(cid:13)c ESO2016 Astrophysics
Systematic comparison of photoionised plasma codes
with application to spectroscopic studies of AGN in X-rays
M.Mehdipour1,J.S.Kaastra1,2,3,andT.Kallman4
1 SRONNetherlandsInstituteforSpaceResearch,Sorbonnelaan2,3584CAUtrecht,TheNetherlands
e-mail:[email protected]
2 DepartmentofPhysicsandAstronomy,UniversiteitUtrecht,POBox80000,3508TAUtrecht,TheNetherlands
3 LeidenObservatory,LeidenUniversity,POBox9513,2300RALeiden,TheNetherlands
4 NASAGoddardSpaceFlightCenter,Code662,Greenbelt,MD20771,USA
Received15April2016/Accepted7October2016
ABSTRACT
Atomic data and plasma models play a crucial role in the diagnosis and interpretation of astrophysical spectra, thus influencing
ourunderstandingoftheUniverse.Inthisinvestigationwepresentasystematiccomparisonoftheleadingphotoionisationcodesto
determine how much their intrinsic differences impact X-ray spectroscopic studies of hot plasmas in photoionisation equilibrium.
WecarryoutourcomputationsusingtheCloudy,SPEX,andXSTARphotoionisationcodes,andcomparetheirderivedthermaland
ionisationstatesforvariousionisingspectralenergydistributions.Weexaminetheresultingabsorption-linespectrafromthesecodes
forthecaseofionisedoutflowsinactivegalacticnuclei.Bycomparingtheionicabundancesasafunctionofionisationparameterξ,
we find that on average there is about 30% deviation between the codes in ξ where ionic abundances peak. For H-like to B-like
sequence ions alone, this deviation in ξ is smaller at about 10% on average. The comparison of the absorption-line spectra in the
X-ray band shows that there is on average about 30% deviation between the codes in the optical depth of the lines produced at
logξ∼1to2,reducingtoabout20%deviationatlogξ∼3.Wealsosimulatespectraoftheionisedoutflowswiththecurrentand
upcominghigh-resolutionX-rayspectrometers,onboardXMM-Newton,Chandra,Hitomi,andAthena.Fromthesesimulationswe
obtainthedeviationonthebest-fitmodelparameters,arisingfromtheuseofdifferentphotoionisationcodes,whichisabout10to
40%. We compare the modelling uncertainties with the observational uncertainties from the simulations. The results highlight the
importance of continuous development and enhancement of photoionisation codes for the upcoming era of X-ray astronomy with
Athena.
Keywords. plasmas–atomicprocesses–atomicdata–techniques:spectroscopic–X-rays:general
1. Introduction hydrogendensityincm−3,andrthedistancebetweentheplasma
andionisingsourceincm.
An astrophysical object with an intense continuum radiation
Given the definition of ξ, a self-consistent solution to the
stronglyinfluencestheionisationandthermalstateofitsnearby
ionisation and energy balance equations yields the temperature
gas. For example, this is the case in active galactic nuclei
and ionic abundances of a PIE plasma as a function ξ. The
(AGN), where accretion of matter onto a supermassive black
photoionisation codes, namely Cloudy1 (Ferlandetal. 2013),
hole (SMBH) releases a huge amount of radiation, leading to
SPEX2 (Kaastraetal. 1996), and XSTAR3 (Kallman&Bautista
the photoionisation of the surrounding gas outflows. Such a
2001;Bautista&Kallman2001),computethisthermalandioni-
medium is generally treated as in photoionisation equilibrium
sationbalancebasedonthespectralenergydistribution(SED)of
(PIE), and thus the ionisation state of the plasma is primarily
theionisingsourceandtheelementalabundancesoftheionised
regulated by the balance between photoionisation and recom-
plasma.Thecodestakethevastdatabaseofatomicdataintoac-
bination. Photoionised plasmas are however complex environ-
count to derive the solution between various heating and cool-
mentstomodelbecauseofvariousprocessesthatplayarolein
ingmechanisms,suchasphotoionisation,recombination,Auger
reaching photoionisation equilibrium. The equilibrium electron
ionisation,collisionalionisation,bremsstrahlung,andCompton
temperatureT ofaPIEplasmaisdeterminedbythesolutionto
scattering. For a classical paper describing a PIE plasma and
the energy balance equation, where the rate of energy injection
modellingitsrelevantprocesses,seeKallman&McCray(1982).
into the plasma (e.g. photoelectrons) is set equal to the rate of
Forareviewofatomicdatausedinthemodellingofhotplasmas,
energy loss from the plasma (e.g. radiation by radiative recom-
seeKallman&Palmeri(2007).
bination).
The ionisation parameter ξ (Tarteretal. 1969; Kroliketal. In this investigation we used Cloudy version 13.01, SPEX
1981) conveniently quantifies the ionisation state of a PIE version3.02.00,andXSTARversion2.3tocarryoutasystematic
plasmawithasingleparameter,whichisdefinedas comparison of the results from these photoionisation codes. In
Sect.2wedescribethePIEcalculationsviathethreecodesfor
L
ξ ≡ , (1)
n r2
H 1 http://www.nublado.org
where L is the luminosity of the ionising source over the 2 http://www.sron.nl/spex
1−1000 Ryd (13.6 eV to 13.6 keV) band in erg s−1, n the 3 http://heasarc.gsfc.nasa.gov/xstar/xstar.html
H
ArticlepublishedbyEDPSciences A65,page1of15
A&A596,A65(2016)
Table1.Absoluteabundancesofchemicalelementsthatweusedinour
1013
computations of the photoionisation equilibrium and the transmission
BB
spectrum.
AGN1
Element Abundance Element Abundance
Hz) 1012 H 1 S 1.622×10−5
Jy PL He 9.705×10−2 Cl 1.991×10−7
F (ν AGN2 Li 2.143×10−9 Ar 3.573×10−6
ν
Be 2.360×10−11 K 1.449×10−7
1011 B 7.244×10−10 Ca 2.328×10−6
C 2.773×10−4 Sc 1.327×10−9
N 8.166×10−5 Ti 9.528×10−8
10−4 10−2 100 102 O 6.053×10−4 V 1.102×10−8
Photon energy (keV)
F 3.097×10−8 Cr 5.047×10−7
Fig. 1. Four different SEDs that we used for our photoionisation bal- Ne 1.268×10−4 Mn 3.556×10−7
ancecalculationsinCloudy,SPEX,andXSTAR.TheAGN1andAGN2 Na 2.223×10−6 Fe 3.266×10−5
SEDs are the normal and obscured SED versions of a typical Seyfert Mg 3.972×10−5 Co 9.057×10−8
AGN (NGC 5548), taken from Mehdipouretal. (2015). The PL SED
isapower-lawcontinuumwithΓ=2,andtheBBSEDisablackbody Al 3.258×10−6 Ni 1.888×10−6
withT =50eV. Si 3.855×10−5 Cu 2.084×10−8
P 3.199×10−7 Zn 5.012×10−8
differentSEDs.InSect.3wedeterminethethermalstateofPIE Notes. The values are from proto-solar abundances of Loddersetal.
plasmasusingeachcodeandpresenttheirthermalstabilityanal- (2009).
ysis. In Sect. 4 we study how different processes contribute to
the cooling and heating of a PIE plasma, and how they change
for different SED cases. In Sect. 5 we compare the ionisation us to investigate the effects of the ionising SED on the derived
state of PIE plasmas computed by the three codes. We analyse resultsfromeachcode.
thecorrespondingtransmissionspectrainSect.6,anddetermine The first SED, labelled AGN1, corresponds to that of
thespectral-linedifferencesfoundbythethreecodes.InSect.7, Seyfert1galaxyNGC5548,derivedinMehdipouretal.(2015)
for the study of ionised outflows in AGN, we compare the un- frommodellingextensivemultiwavelengthcampaigndataofthis
certaintiesarisingfrommodellingwithdifferentphotoionisation object.TheAGN1SEDrepresentsthebroadbandcontinuumof
codes with the statistical uncertainties from observations with astandardunobscuredAGN.ThesecondSED,labelledAGN2,
high-resolutionX-rayspectrometers.Wediscussallourfindings is the obscured version of AGN1. This SED is also taken from
inSect.8andgiveconcludingremarksinSect.9.InAppendixA Mehdipouretal. (2015) and represents the broadband contin-
weprovideatable,comparingtheionicabundancesfoundbythe uumafterabsorptionbycoldgasatthecoreofthisAGN.Theex-
threecodes. tremeultraviolet(EUV)andsoftX-raypartsofthisSEDaresup-
pressedasshowninFig.1.ThisobscuredSED(AGN2)ionises
thoseoutflows,whicharelocatedfurtheroutfromthenucleus.
2. Photoionisationequilibriumcalculations ThethirdSED,labelledPL,correspondstoasimplepower-
law continuum with Γ=2, spanning from 0.1 eV to 1 MeV. A
We computed the ionisation balance in Cloudy, SPEX, and
power-law SED is sometimes used as an approximation for the
XSTAR using the four SEDs described in Sect. 2.1 and the el-
SED of those objects, which their broadband continuum model
emental abundances described in Sect. 2.2. In SPEX, we used
isnotestablished.ThefourthSED,labelledBB,correspondsto
the new pion model for photoionisation calculations, which
the spectrum of a simple blackbody emitter with a temperature
is introduced in Sect. 2.3. In our ionisation balance calcula- of T =50 eV. This SED is chosen to be in contrast with other
tions with each code, we adopt an optically thin photoionised
SEDstorepresentaverysoftspectrum.
plasmainequilibriumwithaslabgeometry.Thehydrogenden-
sitywassetton =1×108cm−3,withatotalcolumndensityof
H
NH =1×1016cm−2.LaterinSects.6and7,wherewecalculate 2.2. Elementalabundances
the absorption-line spectra of photoionised plasma, the column
densityissettoN =1×1022cm−2. FortheelementalabundancesofthePIEplasma,theproto-solar
H
Wenotethatuptoandincludingversion13.03ofCloudy,L valuesofLoddersetal.(2009)wereadopted.Theabsoluteabun-
inthedefinitionofξwastakentobethetotalionisingluminosity dances used in our calculations with each code are given in
as first defined by Tarteretal. (1969). However, from version Table1.
13.04ofCloudy,thedefault Lischangedtobeconsistentwith
the commonly used definition, where it ranges between 1 and
2.3. ThenewpionmodelinSPEX
1000 Ryd. In this paper, L is always over 1–1000 Ryd in our
calculationswitheachcode. HereweintroducethenewpionmodelinSPEX,whichisaself-
consistent photoionisation model that calculates both the ioni-
sation balance and the spectrum. Previously, we used the xabs
2.1. Spectralenergydistributions
modelinSPEX,whichcalculatedthetransmissionthroughaslab
Inthispaper,weusedfourdifferentSEDsforourionisationbal- of photoionised plasma with all ionic abundances linked in a
ance calculations, which are displayed in Fig. 1. This enables physicallyconsistentfashionthroughprecalculatedrunswithex-
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M.Mehdipouretal.:Systematiccomparisonofphotoionisationcodes
Table2.ComparisonoftheComptontemperature(T )valuesobtained
C
101 Cloudy bythethreecodesforthefourSEDcasesshowninFig.1.
SPEX
XSTAR
100 AGN2 AGN1 Cloudy SPEX XSTAR
SED T (keV) T (keV) T (keV)
V) C C C
ke 10−1 AGN1 8.7 9.4 8.7
T ( AGN2 13.1 14.1 13.1
PL 4.6 4.8 4.5
10−2
BB 0.043 0.049 0.048
10−3
andXSTARforthetemperatureandionisationofthePIEplasma.
10−2 100 102 104 106
InFig.2weshowtheelectrontemperatureT oftheplasmaasa
ξ
functionofξfoundbythecodesforeachofthefourSEDs.
Figure 2 demonstrates the different impact of each SED on
101 Cloudy the ionisation balance of the plasma, and hence T(ξ). The re-
SPEX
XSTAR sultsshowthatthereisreasonableagreementbetweenT(ξ)from
100 PL thecodesforeachSEDcase.Wecomparedthetemperaturesat
logξof1.0,2.0,and3.0,whichcoversarangecommonlyfound
V)
ke 10−1 in AGN ionised outflows from X-ray spectroscopy. Over this ξ
T ( range,fortheAGN1SEDthereisbetween25%and29%devia-
tionbetweenthemaximumandminimumT valuesfoundbythe
10−2 BB codes. FortheAGN2 SED,thedifferenceis greateratbetween
37%to45%,whileforthePLSED,itisbetween27%and36%.
10−3 FortheBBSED,thereistheleastamountofT differenceat17%
10−2 100 102 104 106 to19%.
ξ ThereisareasonablygoodagreementbetweentheCompton
temperaturesT foundbythecodesforallfourSEDcases.The
Fig.2.ElectrontemperatureT ofaPIEplasmaasafunctionofioni- C
sationparameterξ.ThecurvesarecalculatedusingtheCloudy,SPEX, obtainedTC valuesaregiveninTable2.Thedeviationbetween
and XSTAR photoionisation codes, shown in blue, red, and green, re- thecodesfromthemeanTCisabout4%.TheTCvalueishighest
spectively.ThecalculationsarecarriedoutforthefourdifferentSEDs fortheAGN2SEDcaseandlowestfortheBBcase.
ofFig.1:AGN1(toppanelinsolidline),AGN2(toppanelindashed AnionisingSEDdeterminestheionisationbalanceandther-
line),PL(bottompanelinsolidline),andBB(bottompanelindashed mal stability of photoionised plasmas, such as the ionised out-
line). flows in AGN. A photoionised plasma can be thermally unsta-
ble in certain regions of the ionisation parameter space. This
ternalcodes(CloudyorXSTAR).However,thenewpionmodel can be investigated by means of producing the thermal stabil-
isdevelopedtocalculateallthestepsinSPEX. ity curves (also called S-curves or cooling curves), which is a
The pion model uses the ionising radiation from the con- plot of the electron temperature T as a function of the pressure
tinuum components set by the user in SPEX. So during spectral form of the ionisation parameter, Ξ, introduced by Kroliketal.
fitting, as the continuum varies, the ionisation balance and the (1981).TheionisationparameterΞ,isdefinedasΞ≡ F/n ckT,
H
spectrumofthePIEplasmaarerecalculatedateachstage.This where F isthefluxoftheionisingsourcebetween1–1000Ryd
meanswhileusingrealisticbroadbandcontinuumcomponentsto (in erg cm−2 s−1), k is the Boltzmann constant, T is the elec-
fitthedata(e.g.ComptonisationandreflectionmodelsforAGN), trontemperature,andn isthehydrogendensityincm−3.Taking
H
thephotoionisationbalanceandthespectrumarecalculatedac- F = L/4πr2andusingξ ≡ L/n r2,Ξcanbeexpressedas
H
cordingly by the pion model. Thus, the variable nature of the
L ξ ξ
source continuum can also be taken into account in ionisation Ξ= = ≈19222 · (2)
balancecalculations.SoratherthanassuminganSEDshapefor 4πr2n ckT 4πckT T
H
ionisationbalancecalculations,thepionmodelprovidesamore
OntheScurveitself,theheatingrateisequaltothecoolingrate,
accurate approach for determining the intrinsic continuum and
sothegasisinthermalbalance.Totheleftofthecurve,cooling
the ionisation balance. For example, Chakravortyetal. (2012)
dominatesoverheating,whiletotherightofthecurve,heating
have shown that just the temperature of the accretion disk and
dominatesovercooling.OnthebranchesoftheScurvethathave
the strength of the soft X-ray excess component in AGN (e.g.
apositivegradient,thephotoionisedgasisthermallystable.This
Mehdipouretal. 2011) can significantly influence the structure
means small perturbations upwards in temperature increase the
and stability of the ionised outflows in AGN. The pion model
cooling,whilesmallperturbationsdownwardsintemperaturein-
wasfirstusedinarecentpaperbyMilleretal.(2015)tomodel
creasetheheating.However,onbrancheswithnegativegradient,
thecomplexabsorptionspectrumofionisedflowscausedbythe
thephotoionisedgasisthermallyunstable.Inthiscase,asmall
tidaldisruptionofastarbyamassiveblackhole.Foradescrip-
perturbation upwards in temperature increases the heating rel-
tionoftheatomicdatabaseusedinthepionmodel,seetheSPEX
ative to the cooling, causing further temperature rise, whereas
manual.
a small perturbation downwards in temperature leads to further
cooling.
InFig.3weshowthecomputedcoolingcurves,correspond-
3. Thermalstateofphotoionisedplasmas
ingtothefourSEDcasesofFig.1.Wenotethatthedisplayed
Following the ionisation balance calculations described in Ξ range in Fig. 3 corresponds to the same ξ and T range used
Sect.2,herewepresentthesolutionsobtainedbyCloudy,SPEX, in Fig. 2. Comparing the results for AGN1 and AGN2 SEDs,
A65,page3of15
A&A596,A65(2016)
!!""##$$%%&&''(())**++,,--))..//0011%%22))11%%&&""//33))44))**++,,55))..22##//66""22))11%%&&""//33
101 Cloudy --77(cid:239)(cid:239)88
SPEX BB00$$##11))!!""##$$%%&&''
XSTAR --77(cid:239)(cid:239)== !!""##$$%%&&''))CCDD))EE6600$$00(cid:239)(cid:239)""11""??$$>>00&&//
100 --/3/3(cid:239)(cid:239) !!!!""""####$$$$%%%%&&&&''''))))CCCCDDDD))))F*F*GG00''@@""EE>>$$))00""&&11""))??//$$??>>##00$$&&$$""//>>%%&&''
V) AGN2 AGN1 AA?@)?@)(cid:239)(cid:239) --77(cid:239)(cid:239)99 !!""##$$%%&&''))CCDD))FF00@@EE$$00&&))%%00&&%%//##$$%%00&&
T (ke 10−1 #$").">')#$").">') ----7777(cid:239)(cid:239)(cid:239)(cid:239);<;<
10−2 ')>')>
#$%&#$%& --77(cid:239)(cid:239)::
""
10−3 !! --77(cid:239)(cid:239)--77
10−1 100 101 --77(cid:239)(cid:239)----
Ξ --77(cid:239)(cid:239)55 --7777 --7755 --7788 --7799
(cid:106)(cid:106)
101 Cloudy !!""##$$%%&&''(())**++)),,--..//%%00))//%%&&""--11))22))3333)),,00##--44""00))//%%&&""--11
SPEX 5566(cid:239)(cid:239)88
XSTAR BB..$$##//))!!""##$$%%&&''
100 PL 5566(cid:239)(cid:239)== !!""##$$%%&&''))CCDD))EE44..$$..(cid:239)(cid:239)""//""??$$>>..&&--
T (keV) 10−1 A5A5')?@)-1')?@)-1(cid:239)(cid:239)(cid:239)(cid:239) 55556666(cid:239)(cid:239)(cid:239)(cid:239)<9<9 !!!!!!""""""######$$$$$$%%%%%%&&&&&&''''''))))))CCCCCCDDDDDD))))))FGFFGFHH....''@@@@""EEEE>>$$$$))....""&&&&//""))))??-%-%..$$??>>&&##..%%$-$-&&$$##""--$$>>%%%%..&&&&''
">">
10−2 #$"),#$"), 5566(cid:239)(cid:239);;
')>')>
10−3 BB #$%&#$%& 5566(cid:239)(cid:239)::
""
10−1 100 101 !! 5566(cid:239)(cid:239)5566
Ξ
5566(cid:239)(cid:239)5555
Fig. 3. Electron temperature T of a PIE plasma as a function of the 5566(cid:239)(cid:239)77 556666 556677 556688 556699
pressureformoftheionisationparameterΞ.Thecurvesarecalculated (cid:106)(cid:106)
using the Cloudy, SPEX, and XSTAR photoionisation codes, shown in
Fig.4.HeatingrateinaPIEplasmaasafunctionofionisationparameter
blue,red,andgreen,respectively.Thecalculationsarecarriedoutfor
thefourdifferentSEDsofFig.1:AGN1(toppanelinsolidline),AGN2 ξfortheAGN1andAGN2SEDs(toppanel),andthePLandBBSEDs
(bottompanel).ThecurvescorrespondingtoAGN1andPLareshown
(toppanelindashedline),PL(bottompanelinsolidline),andBB(bot-
insolidlines,andthosecorrespondingtoAGN2andBBareindicated
tompanelindashedline).
withdashedlines.Foreachcase,thetotalheatingrateisshowninblack,
andthecontributionsfromindividualprocessesareshowninthesame
it is clear that the EUV/soft X-ray obscuration has a signifi- coloursastheircorrespondinglabels.
cant impact on the ionisation balance and thermal stability of
theplasma,andproducesamoreextendedunstablebranch.For
each SED case, the predicted unstable branches from Cloudy,
the total heating rate is 72.1%, 17.7%, 10.2%, and 0.05%, re-
SPEX,andXSTARaresimilar.
spectively. For the AGN2 SED, although the order is the same,
thevaluesaredifferent.Inthiscase,heatingbyphoto-electrons
islowerat49.7%,whileheatingbyComptonscatteringishigher
4. Physicalprocessesinphotoionisedplasmas
at38.9%.ForAGN2,heatingbyAugerelectronsandCompton
Figures 4 and 5 show how different heating and cooling pro- ionisationareonlyslightlyhigherthaninAGN1withvaluesof
cessescontributetothetotalheatingandcoolinginaPIEplasma. 11.3%and0.09%,respectively.Thesedifferencesarisefromthe
They are derived from our computations using the SPEX pion significant suppression of EUV/soft X-ray part of the SED in
modelforeachSEDcase.Theyallowustounderstandhoweach AGN2relativetoAGN1(seeFig.1).
processactsunderdifferentionisingSEDs,whichleadstoadif-
ForthePLSED,thestrengthoftheprocessesaresimilarto
ferentionisationbalancesolution.Thepercentagesreportedbe-
those of AGN1: 79.1% for photo-electrons, 9.5% for Compton
lowinourexaminationoftheresults,correspondtothefractional
scattering, 11.4% for Auger electrons, and 0.02% for Compton
contributionbyeachprocesstothetotalheatingorcoolingrate
ionisation.FortheBBSED,theheatingratesoftheprocessesare
overthespecifiedξrange.
rather different. Heating by photo-electrons strongly dominates
at 99.8%, while strengths of the other processes are very small
4.1. Heatingprocesses at0.1%forAugerelectrons,0.05%forComptonscattering,and
almostzeroforComptonionisation.
FromtheresultsofFig.4wecalculatedtheaverageheatingrate
for each process between 1.0≤logξ ≤3.0, which is the most Apartfromtheaforementionedheatingprocesses,theSPEX
relevant ionisation range. We find for all four SED cases, the pion model also takes heating by free-free absorption into ac-
heating by photo-electrons is the most dominant heating pro- count. However, the contribution of this process to the total
cess. For both AGN1 and AGN2 SEDs, the heating processes heating rate is minute and below the displayed range of Fig. 4.
fromstrongesttoweakestare:(1)photo-electrons;(2)Compton For 1.0≤logξ ≤3.0, the average heating rate by free-free
scattering;(3)Augerelectrons;and(4)Comptonionisation.For absorption is 9.5×10−9% at its lowest point for the BB SED
theAGN1SED,thefractionalcontributionoftheseprocessesto and6.5×10−4%atitshighestpointforthePLSED.
A65,page4of15
M.Mehdipouretal.:Systematiccomparisonofphotoionisationcodes
!!""""##$$%%&&''(())**++,,((--..""##$$//((##$$%%00..11((22(())**++33((--//44..5500//((##$$%%00..11 inverseComptonisationarelowerthanthoseoftheotherSEDs
,,66(cid:239)(cid:239)77 at7.9%and0.01%,respectively.
BB"">>44##((??""""##$$%%&&
,,66(cid:239)(cid:239)<< !!""""##$$%%&&((CCDD((??""####$$..$$""%%44##((00EE??$$>>44>>$$""%%
,,.1.1(cid:239)(cid:239) !!!!""""""""####$$$$%%%%&&&&((((CCCCDDDD((((=$=$%%00FF??00""==@@..00CC(($$!!%%44"">>@@$$""GG%%>>""%%((..??44>>>>00==$$%%&&
AA@(@((cid:239)(cid:239) ,,66(cid:239)(cid:239)88 !!!!""""""""####$$$$%%%%&&&&((((CCCCDDDD((((H0H0==##000000??(cid:239)(cid:239)>>==HH""==00%%00(($$((""00%%@@$$..$$44....>>$$$$""""%%%% 5. Ionisationstateofphotoionisedplasmas
??
&(&( ,,66(cid:239)(cid:239);;
0=0= Here we present the ionisation state of PIE plasmas from com-
4>0(-4>0(- ,,66(cid:239)(cid:239):: putationsbyCloudy,SPEX,andXSTAR.WeusetheAGN1SED
&(=&(= (seeFig.1)forthesecalculations,whichrepresentsthemostre-
"#$%"#$% ,,66(cid:239)(cid:239)99 alisticionisingSEDforatypicalAGN.Wederivethevariation
""
!! ,,66(cid:239)(cid:239),,66 of ionic abundances with ξ, and compare the temperature Tpeak
andionisationparameterξ atwhichionicabundancespeak.
,,66(cid:239)(cid:239),,,, peak
In Fig. 6 we show the ionic fractions of the most relevant
,,66(cid:239)(cid:239)33 ,,6666 ,,6633 ,,6677 ,,6688
(cid:106)(cid:106) ions as a function of ξ in a PIE plasma, calculated by Cloudy,
SPEX, and XSTAR. To examine the results in Fig. 6, we intro-
!!""""##$$%%&&''(())**((++,,""##$$--((##$$%%..,,//((00((1111((++--22,,33..--((##$$%%..,,// duce ∆logξ and ∆f , which are defined as the difference
4455(cid:239)(cid:239)77 peak peak
BB"">>22##((??""""##$$%%&& betweenthelowestandhighestvaluesoflogξpeak and fpeak,re-
4455(cid:239)(cid:239)<< !!""""##$$%%&&((CCDD((??""####$$,,$$""%%22##((..EE??$$>>22>>$$""%% spectively,asfoundbythecodesforeachion.Forexample,we
44,/,/(cid:239)(cid:239) !!!!""""""""####$$$$%%%%&&&&((((CCCCDDDD((((=$=$%%..FF??..""==@@,,..CC(($$!!%%22"">>@@$$""GG%%>>""%%((,,??22>>>>..==$$%%&& can see in Fig. 6 that there is a good agreement between the
AA@(@((cid:239)(cid:239) 4455(cid:239)(cid:239)88 !!!!""""""""####$$$$%%%%&&&&((((CCCCDDDD((((H.H.==##......??(cid:239)(cid:239)>>==HH""==..%%..(($$((""..%%@@$$,,$$22,,,,>>$$$$""""%%%% codesforOviiandOviiiions.Foreachoftheseions,ξpeak and
??
2>.(+.=&(2>.(+.=&( 44445555(cid:239)(cid:239)(cid:239)(cid:239):;:; i∆fopenloaiksgavξtaipoelaunkess(cid:46)tac0ga.el1cs0uolaaftnOedd,∆tfhroefpmedaikffth(cid:46)eer0ecn.0oc5de.etseHnaordwesectvoloebrs,eecttooowmeaearcdlahsrgoleothrw.eeArr:
"#$%&(="#$%&(= 4455(cid:239)(cid:239)99 sbiemtwileaerntrethnedicsoadlessoffoorunhdigfho-rioFnei,swathioerneitohnesrethisabneltotewr-aigorneiesamtieonnt
""
!! 4455(cid:239)(cid:239)4455 ions. We find that from Fexviii to Fexxvi, ∆logξ (cid:46)0.1.
FromFeixtoFexvii,∆logξ (cid:46)0.2.However,towaperadkslower
4455(cid:239)(cid:239)4444 peak
4455(cid:239)(cid:239)66 445555 445566 445577 445588 ionisedions, thedifferencebecomes increasinglygreater,rang-
(cid:106)(cid:106) ing from 0.3 at Feviii to 4 at Feii. The ∆f is (cid:46)0.05 for all
ix xxvi peak xvii
ionsbetweenFe andFe ,withtheexceptionof Fe ,
Fig.5.CoolingrateinaPIEplasmaasafunctionofionisationparam- whichishigherat0.2.ForionsbetweenFeiiandFeviii,∆f
eterξfortheAGN1andAGN2SEDs(toppanel),andthePLandBB peak
rangesbetween0.05and0.5.
SEDs(bottompanel).ThecurvescorrespondingtoAGN1andPLare
showninsolidlines,andthosecorrespondingtoAGN2andBBarein- Thecomparisonforpartiallyionisedionsofthemostabun-
dicatedwithdashedlines.Foreachcase,thetotalcoolingrateisshown dantelementsareprovidedinTableA.1.Inthistablewelistthe
inblack,andthecontributionsfromindividualprocessesareshownin temperature T and ionisation parameter ξ for each par-
peak peak
thesamecoloursastheircorrespondinglabels. tially ionised ion. The ionic fraction value at its peak for each
ionisgivenby f inthetable.Wecomputedthesevaluesfor
peak
the AGN1 SED using Cloudy, SPEX and XSTAR. Taking into
accountallthe177ionsreportedinTableA.1,themeanandme-
4.2. Coolingprocesses dian ∆logξ are 0.44 and 0.16, respectively. The mean and
peak
median ∆f are 0.11 and 0.05, respectively. The median val-
FromtheresultsofFig.5weobtainedtheaveragecoolingrate peak
uesprovideabetterrepresentationbecauseofthefewoutliersin
foreachprocessbetween1.0≤logξ ≤3.0.Wefindthatforall
thelist.InSect.8,wediscussthedeviationsbetweentheresults
four SED cases, cooling by collisional excitation is the most
ofthethreecodes,giveninTableA.1.
dominant cooling process. For both AGN1 and PL SEDs, the
coolingprocessesorderedfromstrongesttoweakestareasfol-
lows: (1) collisional excitation; (2) free-free emission; (3) re-
6. TransmissionofphotoionisedplasmasinX-rays
combination;(4)electronionisation;and(5)inverseComptoni-
sation. For the AGN1 SED, the fractional contribution of these
FollowingthecomputationofionicabundancesforPIEplasmas,
processestothetotalcoolingrateis66.8%,17.4%,14.9%,0.6%
we calculated the corresponding X-ray absorption spectra with
and0.3%,respectively.ForthePLSED,theyare67.3%,15.9%,
eachcode.TheabsorptionspectrawerecalculatedfortheAGN1
15.7%, 1.0% and 0.1%. However, the order and strength of the
SED. In our calculations, the column density for a slab of PIE
processes are different for the AGN2 SED. In this case, the plasma was set to N =1×1022cm−2, with a turbulent veloc-
H
contributions from collisional excitation and recombination are ityofσ =200kms−1.Thesearetypicalvaluesobservedinthe
v
lower at 57.6% and 9.2%, respectively. On the other hand, the
AGNionisedoutflows.Herewepresenttheresultsoverthemost
contributions from free-free emission, inverse Comptonisation,
relevantrangeofionisationparameters,inwhichprominentlines
andelectronionisationarehigherat27.4%,5.0%,and0.8%,re-
areproducedintheX-rayband.Figure7showsthemodelX-ray
spectively.
spectracalculatedbyCloudy,SPEX,andXSTARforlogξof1.0,
For the BB SED, cooling by collisional excitation is higher 2.0, and 3.0. The spectra are shown in the rest frame with zero
thanthoseoftheotherSEDsat72.7%ofthetotalcoolingrate. outflowvelocity.
UnliketheotherSEDs,coolingbyrecombinationisthesecond To compare the end results of our photoionisation calcula-
strongestprocessfortheBBSEDat14.9%.Furthermore,cool- tions, we obtained the optical depth of the strongest X-ray ab-
ingbyelectronionisationishigherthanthoseoftheotherSEDs sorption lines. This is useful because the line optical-depth de-
at 4.4%. On the other hand, cooling by free-free emission and terminesthestrengthoftheabsorptionlineinthespectrum.The
A65,page5of15
A&A596,A65(2016)
1.0 1.0 1.0
n
o He II C III C IV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o C V C VI N III
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o N IV N V N VI
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o N VII O III O IV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o O V O VI O VII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o O VIII Ne III Ne IV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Ne V Ne VI Ne VII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Ne VIII Ne IX Ne X
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Mg III Mg IV Mg V
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
10−1 100 101 102 103 104 10−1 100 101 102 103 104 10−1 100 101 102 103 104
ξ ξ ξ
Fig.6.IonicabundancesinaPIEplasmaasafunctionofionisationparameterξ,whichiscalculatedusingCloudy(showninblue),SPEX(shown
inred),andXSTAR(showningreen)fortheAGN1SEDasdescribedinSect.5.
opticaldepthatthelinecentreisgivenby AGN1 SED, with N =1×1022cm−2 and σ = 200 kms−1.
H v
√
Thepanelsshowtheresultsforthefollowingthreeionisationpa-
τ =αhλ f N /2 2πm σ (3)
0 c osc ion e v rameters:logξof1.0,2.0,and3.0.Thefewmissingdatapoints
where α is the fine structure constant, h the Planck constant, in Fig. 8 occur when lines are not found in all the codes. We
λc thewavelengthatthelinecentre, fosc theoscillatorstrength, discussthecomparisonresultsofFig.8inSect.8.
N the column density of the absorbing ion, m the electron
ion e
mass, and σ the velocity dispersion. Thus, by comparing τ
v 0
of each line from the codes, we are essentially comparing the 7. StudyofionisedoutflowsinAGNwith
product of fosc and Nion, provided λc and σv are the same. In high-resolutionX-rayspectrometersusing
Fig. 8 we present a comparison of the optical depth τ of the
0 differentphotoionisationcodes
strongestX-rayabsorptionlinesatwavelengthsbelow40Å(en-
ergies above 0.3 keV) from Cloudy, SPEX, and XSTAR calcu- Here we investigate the impact of using different photoionisa-
lations. They were calculated for a PIE plasma, ionised by the tion codes on the derived parameters from X-ray observations
A65,page6of15
M.Mehdipouretal.:Systematiccomparisonofphotoionisationcodes
1.0 1.0 1.0
n
o Mg VI Mg VII Mg VIII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Mg IX Mg X Mg XI
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Mg XII Si III Si IV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Si V Si VI Si VII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Si VIII Si IX Si X
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Si XI Si XII Si XIII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Si XIV S III S IV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o S V S VI S VII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o S VIII S IX S X
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
10−1 100 101 102 103 104 10−1 100 101 102 103 104 10−1 100 101 102 103 104
ξ ξ ξ
Fig.6.continued.
of PIE plasmas. We simulated spectra of PIE plasmas in AGN componentwithN =1×1020cm−2(atypicallowGalacticN ,
H H
withthecurrentandfuturehigh-resolutionX-rayspectrometers, such as seen in our line of sight towards NGC 5548), absorb-
andobtainedthedeviationonthemodelparametersarisingfrom ing the AGN1 SED. We used the hot model in SPEX for mod-
theuseofthethreephotoionisationcodes.Thesimulationswere ellingtheGalacticX-rayabsorptioncomponent,asdescribedin
carriedoutforaPIEplasmaionisedbytheAGN1SED(i.e.the Mehdipouretal.(2015)forNGC5548.
NGC 5548 unobscured SED). The column density and turbu- For each calculation by the three codes, we convolved
lent velocity of the plasma were fixed to NH =1×1022cm−2 the corresponding spectrum with the response matrix of
and σv = 200 kms−1. We carried out the photoionisation cal- each of the high-resolution X-ray spectrometers. We used
culationsandspectralsimulationsforarangeofionisationval- XMM-Newton RGS (denHerderetal. 2001), Chandra LETGS
ues, in which logξ ranged between 1.0 and 3.0 with an incre- (Brinkmanetal. 2000), and HETGS (Canizaresetal. 2005),
ment of 0.5. This is a typical range of ξ values seen in X-ray Hitomi(Astro-H)SXS(Mitsudaetal.2014),andAthenaX-IFU
observations of AGN ionised outflows, such as in NGC 5548 (Barretetal. 2016) for our simulations. For RGS, LETGS, and
and NGC 3783. For our spectral simulations with the spec- HETGS, instrumental response matrices from the last observa-
trometers, we also included a foreground Galactic interstellar tions of NGC 5548 were used, while for SXS and X-IFU we
A65,page7of15
A&A596,A65(2016)
1.0 1.0 1.0
n
o S XI S XII S XIII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o S XIV S XV S XVI
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe III Fe IV Fe V
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe VI Fe VII Fe VIII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe IX Fe X Fe XI
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe XII Fe XIII Fe XIV
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe XV Fe XVI Fe XVII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe XVIII Fe XIX Fe XX
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe XXI Fe XXII Fe XXIII
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
1.0 1.0 1.0
n
o Fe XXIV Fe XXV Fe XXVI
cti
a 0.1 Cloudy 0.1 Cloudy 0.1 Cloudy
n fr SPEX SPEX SPEX
o XSTAR XSTAR XSTAR
I
10−1 100 101 102 103 104 10−1 100 101 102 103 104 10−1 100 101 102 103 104
ξ ξ ξ
Fig.6.continued.
usedthelatestpubliclyavailableresponsematricesasofSeptem- statistical errors of the fitted parameters at 1σ confidence level
ber 2016. Each simulated spectrum by a code was fitted with forminimumandmaximumexposuretimesof100ksand1Ms.
the other two codes to obtain its best-fit ξ and N parameters. The modelling and observational uncertainties are presented in
H
Thus,anydifferenceinthederivedmodelparametersforagiven Fig. 9. We discuss the deviation in the model parameters ob-
spectrumwouldbeduetointrinsicdifferencesbetweenthethree tainedbythecodesinSect.8.
photoionisation codes. The standard deviation of the fitting re- InFig.9,themodellinguncertaintiescanbecomparedwith
sultswerecalculatedtorepresentameasureofthemodellingun- theobservationaluncertainties.Thesimulatedobservationalun-
certainty in ξ and NH parameters. For each instrument, we also certaintiesforeachinstrumentcorrespondtotheobservedX-ray
calculated the observational uncertainties corresponding to the fluxlevelofAGN1SED(NGC5548),whichisabrightSeyfert1
A65,page8of15
M.Mehdipouretal.:Systematiccomparisonofphotoionisationcodes
log ξ = 1.0 AGN in X-rays with F = 3.1×10−11 ergcm−2 s−1 and
0.3−2keV
1.0 F = 3.5×10−11 ergcm−2 s−1.WecanseeinFig.9that
e 2−10keV
nc 0.8 themodellinguncertaintiesaregenerallylargerthantheobserva-
mitta 0.6 tionaluncertainties.However,atlogξ =3,themodellinguncer-
s 0.4 taintiesareatthesamelevelorsmallerthantheobservationalun-
n
Tra 0.2 SPEX certainties,exceptforX-IFU,wheretheobservationaluncertain-
0.0
ties are tiny owing to its exceptional sensitivity. The upcoming
1.0
nce 0.8 Athena X-IFU microcalorimeter will provide us with unprece-
smitta 00..46 dAeGnNte.dIndeptaaritliscouflatrh,eitpahllyoswicsaulssttoruacctucureraotefltyhdeeoteurtmfloinweinthgegparsopin-
Tran 00..02 XSTAR ethrtrioeusgohftthheehdiegthe-citoionnisaotfioFnecxoxmivpo,nFeenxtx(lvo,gaξn=d F3)eoxfxthveioliunteflsoiwn
e 1.0 the6keVbandwithanenergyresolutionof2.5eV.Inthecaseof
anc 0.8 AGN1SED,wefindthatfora100ksX-IFUobservation,thesta-
smitt 00..46 tisticalerrorsintheξ and NH parametersofthehigh-ionisation
n componentaresmallerthanthemodellinguncertaintiesbyfac-
Tra 0.2 Cloudy torsof30and10,respectively.
0.0
1 10
Energy (keV)
8. Discussion
log ξ = 2.0
1.0 The deviation in the ionisation state results, derived by the
e
nc 0.8 three codes, is presented visually in Fig. 6 and numerically in
a
mitt 0.6 Table A.1 for the most relevant ions. Consequently, any devia-
s 0.4 tion between the codes in ionisation state results in some dif-
n
Tra 0.2 SPEX ferencesinthestrengthoftheX-rayabsorptionlines,whichare
0.0 shown in Figs. 7 and 8. The effects on the derived plasma pa-
1.0
e rameters, from modelling observational X-ray spectra of AGN
nc 0.8
a ionisedoutflows,arepresentedinFig.9.
mitt 0.6 In general, the observed differences between the results of
s 0.4
Tran 00..02 XSTAR mthoedceolldiensgaoref athmeahneiafetisntagt/icoonoloinfgallprthoecelsisttelse daniffdertehneciresaisnsotchie-
e 1.0 ated atomic data. Figure 6 shows that there is some discrep-
nc 0.8 ancybetweenthecodesforthelow-ionisationstagesofFe(i.e.
a
mitt 0.6 Fei-vii). This most likely originates from differences in the
ns 0.4 low-temperature dielectronic recombination (DR) calculations
Tra 0.2 Cloudy by the codes. In SPEX, the ionisation balance calculations of
0.0
Bryansetal. (2009) are adopted. The DR and radiative recom-
1 10
Energy (keV) bination (RR) rate coefficients used in Bryansetal. (2009) are
the same as in Bryansetal. (2006), but these data are updated
log ξ = 3.0 to include corrections to some of the rate coefficients, as well
1.0
e as updated DR data for Mg-like ions of H through Zn, and for
anc 0.8 Al-like to Ar-like ions of Fe, taken from Badnell (2006a,b),
mitt 0.6 Altunetal. (2007). The DR and RR data for all other ions, in-
ns 0.4 cludingFei-vii,arefromMazzottaetal.(1998).Theratesfrom
Tra 00..02 SPEX Mazzottaetal. (1998) do not include the low-temperature DR
1.0 for Fei-vii. However, in Cloudy, the low-temperature DR for
nce 0.8 Fei-v is estimated using the mean of all the existing DR rates
mitta 0.6 for each ionisation stage, while for Fevi-vii, the DR rates cal-
s 0.4 culatedbyM.F.Guareused(priv.comm.).Ontheotherhand,in
n
Tra 0.2 XSTAR XSTAR, the low-temperature DR for Fei-viii is estimated from
0.0 ix
nce 01..80 tXhSeTlAoRwu-tseemtpheerDatRurerapteasrtooffBthaednFeell(2D0R06raa)tef.oBroFtehixCltoouFdeyxainiid,
smitta 00..46 ahsigwheerllioansistahteioDnRstargaetessopfrFoev.ided online4 by N.R. Badnell for
n
Tra 0.2 Cloudy Thereisabouta4%deviationinthevalueofComptontem-
0.0 peratures obtained by the three codes. Some of this deviation
1 10 isattributedtotherelativisticcorrectionsusedbythecodesfor
Energy (keV)
the energy exchange by relativistic electrons in Compton scat-
tering. Cloudy uses numerical fits to the results of Winslow
Fig. 7. Model transmission X-ray spectra of a PIE plasma with
N =1×1022cm−2andσ =200kms−1,producedbyCloudy,SPEX, (1975),asusedinKroliketal.(1981),whichwereprovidedby
H v C. B. Tarter (priv. comm.). The treatment of Compton heating
andXSTARatlogξof1.0,2.0,and3.0.Themodelspectraarecalculated
fortheAGN1SEDasdescribedinSect.6. andcoolinginXSTARversionspriorto2.3werenotaccuratefor
4 http://amdpp.phys.strath.ac.uk/tamoc/DR/
A65,page9of15
A&A596,A65(2016)
log ξ = 1.0 log ξ = 2.0 log ξ = 3.0
Fe IX 16.789AÅ Fe XVIII 14.204ÅA Ni XXVII 1.589ÅA
Fe IX 16.539AÅ Fe XVII 15.261ÅA Fe XXVI 1.784ÅA
Fe VIII 16.973AÅ Fe XVII 15.014ÅA Fe XXVI 1.778ÅA
Fe VIII 16.972AÅ Fe XV 15.359ÅA Fe XXV 1.850ÅA
Fe VIII 16.929AÅ Fe XIII 15.890ÅA Fe XXV 1.573ÅA
Fe VIII 16.907AÅ Fe XIII 15.849ÅA Fe XXV 1.495ÅA
Fe VIII 16.803AÅ Fe XII 16.025ÅA Fe XXIV 10.663ÅA
Fe VIII 16.709AÅ Fe XI 16.179ÅA Fe XXIV 10.620ÅA
Fe VIII 16.678AÅ Fe XI 16.176ÅA Fe XXIV 7.996ÅA
Fe VIII 16.656AÅ Fe X 16.366ÅA Fe XXIV 7.986ÅA
Ca XI 30.447AÅ Fe X 16.358ÅA Fe XXIV 1.864ÅA
Mg IX 9.378AÅ Fe IX 16.539ÅA Fe XXIV 1.861ÅA
Ne IX 13.447AÅ Ar XIII 29.320ÅA Fe XXIV 1.857ÅA
Ne IX 11.547AÅ Ar XII 31.389ÅA Fe XXIII 11.020ÅA
Ne VIII 13.655AÅ S XIII 32.238ÅA Fe XXIII 10.981ÅA
Ne VIII 13.653AÅ S XII 36.398ÅA Fe XXIII 8.305ÅA
Ne VII 13.814AÅ S XII 34.533ÅA Fe XXIII 7.473ÅA
Ne VII 12.175AÅ S XII 28.222ÅA Fe XXIII 1.870ÅA
Ne VI 14.047AÅ S XI 39.240ÅA Fe XXII 11.706ÅA
Ne VI 14.020AÅ Si XIII 6.648ÅA Fe XXII 11.459ÅA
O VIII 18.972AÅ Si XI 33.513ÅA Fe XXII 11.421ÅA
O VIII 18.967AÅ Si XI 6.778ÅA Fe XXII 8.935ÅA
O VIII 16.006AÅ Si X 39.443ÅA Fe XXI 12.284ÅA
O VII 21.602AÅ Mg XI 9.169ÅA Ca XX 3.019ÅA
O VII 18.628AÅ Mg XI 7.851ÅA Ca XIX 3.177ÅA
O VII 17.768AÅ Ne X 12.137ÅA Ar XVIII 3.737ÅA
O VII 17.396AÅ Ne X 12.132ÅA Ar XVIII 3.731ÅA
O VII 17.200AÅ Ne X 10.238ÅA Ar XVII 3.949ÅA
O VII 17.086AÅ Ne IX 13.447ÅA S XVI 4.733ÅA
O VII 17.009AÅ Ne IX 11.547ÅA S XVI 4.727ÅA
O VI 22.021AÅ Ne IX 11.000ÅA S XVI 3.991ÅA
O VI 22.019AÅ O VIII 18.972ÅA S XV 5.039ÅA
O VI 21.788AÅ O VIII 18.967ÅA Si XIV 6.186ÅA
O VI 19.379AÅ O VIII 16.007ÅA Si XIV 6.180ÅA
O VI 19.379AÅ O VIII 16.006ÅA Si XIV 5.218ÅA
O V 22.370AÅ O VIII 15.177ÅA Si XIV 5.217ÅA
N VII 24.785AÅ O VIII 15.176ÅA Si XIII 6.648ÅA
N VII 24.779AÅ O VIII 14.821ÅA Mg XII 8.425ÅA
N VI 28.788AÅ O VII 21.602ÅA Mg XII 8.419ÅA
N VI 24.900AÅ O VII 18.628ÅA Mg XII 7.106ÅA
N VI 23.771AÅ O VII 17.768ÅA Ne X 12.137ÅA
C VI 33.740AÅ O VII 17.396ÅA Ne X 12.132ÅA
C VI 33.734AÅ N VII 24.785ÅA Ne X 10.240ÅA
C VI 28.466AÅ N VII 24.779ÅA Ne X 10.238ÅA
C VI 28.465AÅ N VII 20.910ÅA O VIII 18.972ÅA
C VI 26.990AÅ N VI 28.788ÅA O VIII 18.967ÅA
C VI 26.990AÅ C VI 33.740ÅA O VIII 16.006ÅA
C V 34.973AÅ C VI 33.734ÅA N VII 24.779ÅA
C V 33.426AÅ C VI 28.466ÅA C VI 33.740ÅA
C V 32.754AÅ C VI 28.465ÅA C VI 33.734ÅA
0.1 1.0 10.0 0.1 1.0 10.0 0.1 1.0 10.0
τ ratio τ ratio τ ratio
0 0 0
Fig.8.Comparisonoftheopticaldepthτ ofthestrongestX-rayabsorptionlinesatwavelengthsbelow40Å(energiesabove0.3keV),from
0
Cloudy,SPEX,andXSTARcalculationsforaPIEplasma,ionisedbytheAGN1SED,withN =1×1022cm−2andσ =200kms−1.Thedisplayed
H v
datagivetheratioofτ fromeachcoderelativetothemeanτ foundbythecodes.Theτ ratioisshowninbluecirclesforCloudy,reddiamonds
0 0 0
forSPEX,andgreensquaresforXSTAR.Thelistedlinescorrespondtothe50lineswiththehighestτ valuesatlogξof1.0(leftpanel),2.0(middle
0
panel),and3.0(rightpanel).Thedottedverticallineatτ ratioof1indicateswheretheresultsfromthecodeswouldbeidentical.
0
hardspectrawithsignificantfluxabove100keV.However,this Fromanalysisoftheionicfractionsofpartiallyionisedions
hasbeenupdatedinversion2.3andthispaper,usingratesfrom inTableA.1,wefindthatforH-likeandHe-likesequenceions
I.Khabibullin(priv.comm.),basedontheexpressionsgivenby there is on average about a 7% deviation between the codes
Shestakovetal.(1988).Theenergyshiftperscatteringiscalcu- in ξ , at which ionic fractions peak. This deviation between
peak
latedbyinterpolatinginatable.InSPEX,theheating/coolingby the codes rises slightly to 9% for Li-like ions, 11% for Be-like
Compton scattering is calculated using the formulae provided ions, and 13% for B-like ions. The deviation becomes greater
by Ferland&Rees (1988; originally from Winslow 1975) and for higher isoelectronic sequence ions: 39% on average for the
Levich&Sunyaev(1970). C-likethroughFe-likeionslistedinTableA.1.Ifoneconsiders
A65,page10of15