astr

o-ph

/950

2006

02

Feb

199

5Mon. Not. R. Astron. Soc. 000, 000{000 (0000) Printed 17 January 1995Warm absorbers in active galactic nucleiC. S. Reynolds and A. C. FabianInstitute of Astronomy, Madingley Road, Cambridge CB3 0HAAccepted 1994 November 29. Received 1994 November 1; in original form 1994 July 25ABSTRACTRecent ASCA observations con�rm the presence of X-ray absorption due to partiallyionized gas in many Seyfert 1 galaxies; the so-called warm absorber. Constraints onthe location of the warm material are presented with the conclusion that this materiallies at radii coincident with, or just outside, the broad-line region. The stability ofthis warm material to isobaric perturbations under the assumptions of thermal andphotoionization equilibrium is also studied. It is shown that there is a remarkably smallrange of ionization parameter, �, for which the warm absorber state is stable. Therobustness of this result to changes in the shape of the primary continuum, the assumeddensity and optical depth is investigated. Given the constraints on the location and thestability properties of the material, several models for the environments of Seyfert nucleiare discussed. These attempt to explain the presence of signi�cant amounts of partiallyionized material. In particular, various models of the broad-line region are discussed.The simple two-phase model of the broad-line region proves to be unsatisfactory. Amodel of the broad-line region is presented in which a turbulent, hot intercloud mediumis mechanically heated. Turbulent mixing layers could then give rise to warm absorptionfeatures. Finally, a model is discussed in which the warm absorber is due to a steadystate, radiatively driven out ow.Key words: X-rays: galaxies, Galaxies: active, Galaxies: Seyfert, Atomic processes,Plasmas, Turbulence1 INTRODUCTIONX-ray reprocessing in active galactic nuclei (AGN) signi�-cantly a�ects the observed X-ray spectrum. A study of thisreprocessing is important since it probes the geometry andphysical state of matter in the central regions of AGN. There ection of X-rays from optically thick cold material (e.g.an accretion disc) is invoked to explain the spectra of Seyfert1 galaxies which often display a 6.4-keV uorescent K-line ofcold iron and a broad bump peaking at � 20 keV (Guilbert& Rees 1988; Lightman & White 1988; George & Fabian1991; Matt, Perola & Piro 1991). During the past decade ithas been realized that partially ionized, optically thin gasalong our line of sight to the central X-ray source can alsohave a dramatic e�ect on the soft X-ray spectrum. This par-tially ionized material has become known as the warm ab-sorber. The observational signatures of warm absorbers arediscussed on a theoretical basis by Netzer (1993).The presence of such gas was initially postulated to ex-plain the unusual shape of the absorption needed to �t thesoft and hard X-ray spectrum of the QSO MR 2251�178(Halpern 1984; Pan, Stewart & Pounds 1990) and as a com-ponent in Seyfert 2 galaxies (Krolik & Kallman 1987). Fur-ther evidence came from Ginga which found deeper ironK-edges in some Seyfert 1 galaxies than predicted by the

simple re ection model (Nandra, Pounds & Stewart 1990;Nandra et al. 1991; Nandra & Pounds 1994). ROSAT posi-tion sensitive proportional counter (PSPC) observations ofsome Seyfert 1 galaxies also suggested the presence of ab-sorption K-edges due to Ovii and Oviii (Nandra & Pounds1992; Nandra et al. 1993; Fiore et al. 1993; Turner et al.1993). However, other explanations of the data (such as amultiple-component primary source or partial covering bycold absorbing material) could not �rmly be ruled out bythese data.The superior spectral energy resolution of the ASCAsolid-state imaging spectrometer (SIS) allows, for the �rsttime, X-ray spectral features to be accurately identi�edand measured. This instrument (unlike any previous in-strument) is capable of separating the Ovii and OviiiK-edges (at rest energies of 0.74 keV and 0.87 keV respec-tively). Fabian et al. (1994) have studied the bright Seyfert1 galaxy MCG�6�30�15 (z = 0:008) with ASCA. They�nd clear evidence for Ovii and Oviii edges in the X-rayspectrum, thereby con�rming the presence of a warm ab-sorber. They use the photoionization code cloudy (Ferland1991) to construct a grid of one-zone models in which theprimary continuum photoionizes a geometrically thin shell

2 C. S. Reynolds and A. C. Fabian

Figure 1. Theoretical spectrum produced by the passage of aprimary powerlaw spectrum through a thin shell of warm absorb-ing gas (solid line). The parameters of the model are taken to bethose derived from recent ASCA observations of MCG�6�30�15:i.e. the photon index is � = 1:9, the ionization parameter of thewarm material is � = 35 erg cms�1 and the warm column densityis NW = 1022 cm�2. A radius of 1016 cm is assumed. The e�ectsof emission and re ection from the warm material (assuming unitcovering fraction) as well as absorption are included. The dashedline represents the incident powerlaw spectrum.of gas. These models are characterized by a column density,NW, and an ionization parameter, �, de�ned by� � LnR2 : (1)When such models are �tted to a 30000-s ASCA SIS observa-tion of MCG�6�30�15, the best-�tting model parametersare NW = 1022�0:02 cm�2 and � = 35 � 2 erg cm s�1. Thiscorresponds to gas at 105 K. Fig. 1 shows the theoreticalabsorbed spectrum (from 13.6 eV to 10 keV) for a warm ab-sorber with these parameters. This includes the e�ects ofemission and re ection (assuming a unit covering fraction)as well as absorption. Strong He ii, Ovii and Oviii edgesare seen at 54.4 eV, 0.74 keV and 0.87 keV respectively.Fabian et al. (1994) also �nd variability in the warmabsorber between two ASCA observations separated by 3weeks. During this 3-week period, the ionizing ux decreaseswhile both the ionization parameter and column density in-crease. Section 3 discusses this in more detail.Warm absorption features are common in the X-rayspectra of Seyfert 1 galaxies and narrow emission line galax-ies (NELGs). In the Ginga sample of Nandra & Pounds(1994), 9 out of 20 Seyfert 1 galaxies show evidence forwarm absorbers, as do 3 out of 7 NELGs. Therefore, in thesesources, the warm absorbing material must have a large cov-ering fraction as seen from the central source (perhaps � 50per cent, at least along lines of sight accessible to us). Theabsorption features seen in BL Lac objects (Madejski et al.

1991) may also be due to a warm absorber (possibly en-trained in a jet). However, warm absorbers seem to be ab-sent in other radio-loud quasars and powerful radio-quietquasars. An exception to this is the warm X-ray/UV ab-sorber in 3C351 (Mathur et al. 1994).The present paper discusses the warm absorbing mate-rial in the context of the standard models for Seyfert galaxiesand other AGN. Section 2 discusses the physical state andemission line spectrum of the warm absorbing material. Sec-tion 3 attempts to place constraints on the location of thewarm absorber and concludes that this material exists atradii characteristic of the broad-line region (BLR). Section4 examines the stability of the warm absorber to isobaricperturbations. It is found that the warm absorbing state isonly stable for a remarkably small range of ionization param-eter � unless there is a very soft primary spectrum. Section 5presents possible physical models for the warm absorber. Inparticular, models relating this gas to the BLR are assessed.A new BLR model is presented in which a turbulent hotintercloud medium is mechanically heated by the action ofradiation pressure on the broad-line clouds. Warm absorp-tion features might be expected from the turbulent mixinglayers formed within such a scenario. Section 6 provides asummary of the issues raised.2 PHYSICAL STATE OF THE WARMABSORBERcloudy predicts the detailed physical state of the warm ma-terial, given the assumption of photoionization and thermalequilibrium.We shall take an ionization parameter of � =30 erg cms�1 and a column density of NW = 1022 cm�2(as inferred from ASCA observations of MCG�6�30�15).Given these parameters the temperature of the material is105K. The dominant source of heating is photoelectric ab-sorption by metals (85 per cent of the total heating). Pho-toelectric absorption by helium accounts for much of the re-maining heating (11 per cent of the total heating). Coolingis dominated by the collisionally excited lines of Ovi�1035(30 per cent of the total cooling) and Neviii�774 (20 percent of the total cooling). For unit covering fraction the lu-minosity in these lines can be as much as a few per centof the total ionizing luminosity of the central engine. Othersigni�cant UV/optical lines predicted are Ly�, C iv�1549and Fexiv�5303.Interestingly, IUE observations of MCG�6�30�15show that the high-ionization lines are very weak. Absorp-tion by neutral material has been invoked to explain theweak high-ionization lines. However, X-ray observations sug-gest that no cold absorption (extra to Galactic absorption) ispresent. There are several possible explanations for this ap-parent discrepancy. First, the geometry could be such thatthe material emitting the high-ionization lines is obscuredwhilst the X-ray emitting region is unobscured. The requiredgeometry would be impossible to realize within the standardmodel of Seyfert galaxies. Secondly, a dusty warm absorberor outer BLR could lead to signi�cant optical/UV extinc-tion without a�ecting the X-rays. Such a model predictsnear-infrared thermal emission from the hot dust. Finally,MCG�6�30�15 may have an intrinsically unusual BLR in

Warm absorbers in active galactic nuclei 3which high-ionization lines are not produced by broad-lineclouds and the warm absorber is restricted to our line ofsight. The emission of, say, C iv from the warm absorbermay therefore be much weaker that that predicted assuminga large covering fraction. Such a model is problematic giventhe frequency with which warm absorbers are observed.We note in passing that the high-ionization lines fromthe warm absorber may severely complicate and confuse con-ventional reverberation mapping of the BLR.3 LOCATION OF THE WARM ABSORBERGiven some reasonable assumptions, simple arguments canbe used to constrain the distance of the warm absorb-ing gas from the central engine. In order to derive nu-merical constraints, we shall use parameters appropriate toMCG�6�30�15. Thus, we shall suppose that the warmmaterial has a measured ionization parameter of � =30 erg cms�1 and a column density of N = 1022 cm�2. Weshall take the total ionizing luminosity of the central engine,L, to be 4� 1043 erg s�1.3.1 AssumptionsConsider an idealized geometry for the warm absorbing ma-terial. Suppose the warm material is distributed in a shell(or blob) with an outer radius R from the central engine anda line-of-sight thickness of �R. Assume the material to havea constant density n. Thus, the column density is N = n�R.Furthermore, we assume that the dominant source of ioniz-ing radiation is the central engine of the AGN and that thewarm material is in photoionization equilibrium with thisradiation �eld.Given the highly variable nature of the observed centralionizing ux, the assumption of photoionization equilibriumrequires justi�cation. The recombination time-scales for theions which dominate the cooling of the gas (mainly highlyionized oxygen and neon) are approximatelytrec � 3� 104 Z�2 �T 1=25 n�19 � s (2)where Z is the atomic number of the ion, Te = 105T5K isthe electron temperature and ne = 109n9 cm�3 is the elec-tron density. This uses the approximate form for the recom-bination coe�cients given in Allen (1973), but is in roughagreement with more carefully calculated recombination co-e�cients (Shull & Van Steenberg 1982). For highly ionizedoxygen and neon in the warm state (T5 � 1), this evaluatesto give a recombination time-scale of a few�102n�19 s. Thephotoionization time-scale will be signi�cantly less. Thisis the typical time-scale on which the ionization state ofthe material responds to changes in the ionizing ux. Un-less n9 << 1, this time-scale is shorter than the typicalvariability time-scale of the primary ionizing continuum inSeyfert galaxies. Photoionization equilibrium would then beexpected to apply. However, if n9 << 1 the variability time-scale of the source would become less than the recombina-tion time-scale and photoionization equilibrium would notapply. Under such circumstances the ionization state of thegas would depend on the history of the primary ux varia-tions.

Figure 2. Constraints on the R, �R plane as derived in Sec-tion 3. Disallowed regions are shaded. Line A corresponds to� = 30 erg cms�1 and NW = 1022 cm�2, the approximate param-eters of the warm absorbing gas inferred fromASCA observations.Within the one-zone photoionization model, the warm gas wouldlie on this line. Line B is the geometrical constraint that R > �R.Line C results from imposing that the virial velocity is less than0.03 c (M7 � 1 assumed in the positioning of this line). Line Dgives the constraint that the recombination time-scale is less than3 weeks. Similarly, line E corresponds to the constraint that drift-ing inhomogeneities of size �R produce variability in less than 3weeks.3.2 Basic constraintsGiven the assumptions stated, we will now discuss con-straints on the R, �R plane. Fig. 2 is a graphical repre-sentation of the constraints.The de�nition of � combined with N = n�R leads to�R = NR2�L : (3)Thus, the warm absorber must lie on this curve within theR, �R plane (line A in Fig. 2). Also, purely geometricalconsiderations give R > �R (line B in Fig. 2). Together,these conditions giveR < LN� : (4)Using the measured parameters for MCG�6�30�15, thisevaluates to give R < 1020 cm.The ASCA data require the absorbing material to haveradial velocities less than 0:03 c, where c is the speed of light.If we impose that the virial velocity of the warm absorbinggas is less than 0:01v0:01c, we derive a lower limit to the ra-dius of the warm absorbing material of R > 1016M7v�20:01 cm(line C in Fig. 2), where M = 107M7M� is the mass of thecentral compact body. This limit can be relaxed if materialin the line of sight to the central engine has a radial velocitymuch less than the virial velocity. This would be the casefor material orbiting the central body in near-circular paths.However, material could not remain on such paths withoutencountering the accretion disc which is thought to surroundthe central compact body.

4 C. S. Reynolds and A. C. Fabian3.3 Constraints from variabilityASCA observations of MCG�6�30�15 revealed a signi�-cant change in the warm absorber between two observa-tions which were carried out 3 weeks apart (Fabian etal. 1994). Simple one-zone photoionization models (pro-duced with cloudy) show that the inferred column den-sity increases from 1021:8�0:1 cm�2 to 1022:13�0:02 cm�2. Theinferred ionization parameter also increases slightly from39+7:5�5 erg cms�1 to 44:7� 3 erg cm s�1. This variability canbe used to impose stricter (but model dependent) upper lim-its on R.Suppose the variability is due to warm material re-sponding to changes in the primary ionizing continuum.The inferred recombination time-scale would then have tobe less than (or of the order of) 3 weeks. Such a condi-tion leads to a lower limit on the density of the gas ofn > 2:5 � 106 cm�3. A column density of N = 1022 cm�2would then give �R < 4� 1016 cm (line D in Fig. 2) whichcorresponds to R < 2�1018 cm. However, there is mountingevidence that this simple picture for the variability of thewarm absorber is invalid. First, in MCG�6�30�15 the ion-ization parameter is seen to be higher at a time when theionizing ux is lower (in contrast to the simple photoion-ization model). Unfortunately, the behaviour of the ionizing ux over the whole 3-week period is unknown; the ionizationstate of the warm material may have been responding to anunobserved are between the two ASCA observations. Sec-ondly, ASCA observations of MR2251�178 show it to havea warm absorber with an ionization parameter that remainsessentially constant despite large changes in the 2{10 keVX-ray ux (Kii 1994, private communication). The resolu-tion of this issue will require detailed, time-resolved spectralanalysis of the ASCA data.Tangentially moving inhomogeneities in the warm ab-sorbing material can also lead to observable variability. As-suming the primary source to be a point source, and theinhomogeneities to have a characteristic size � �R and tan-gential drift velocity v, the variability time-scale is given byt � �Rv : (5)The imposition that t be less than 3 weeks and that v is lessthan 0:03c gives �R < 2� 1015 cm (line E in Fig. 2), corre-sponding to R < 5�1017 cm. This constraint is weakened orremoved if the spatial extension of the primary X-ray sourcehas a size comparable to, or greater than, the characteris-tic size scale of the inhomogeneities in the warm absorbingmaterial.Thus we conclude that the warm absorber lies between1015 cm and 1018 cm. This suggests that the warm absorberexists at radii coincident with, or just outside, the BLR. Ourresults are in accord with Mathur et al. (1994) who �nd ab-sorption features within the broad UV lines from materialthat they identify with the warm absorber. Before discussingparticular physical models for the origin of this warm ma-terial (Section 5), we �rst examine the thermal stability ofthis material.

4 STABILITY OF THE WARM ABSORBERMaterial in the environment of the central engine is prone tothermal instabilities if its temperature lies between � 104 Kand the Compton temperature of 107{108 K (McCray 1979;Krolik, McKee & Tarter 1981; Guilbert, Fabian & McCray1983). However, the warm absorber appears to represent asigni�cant amount of material in an intermediately ionizedstate at 105 K. Thus it is interesting to carry out a detailedstudy of its thermal stability.Here we address the stability of the warm material un-der the constraint of isobaric conditions. We use cloudy toexamine the thermal and photoionization equilibrium in ageometrically thick, optically thin spherical shell of materialaround a central point source of ionizing ux (with a �xedionizing luminosity). The shell is constrained to have a con-stant density (�xed to a given value). Such models allow usto determine the temperature, T , as a function of the radiusfrom the ionizing source, r. The ionization parameter, �, canbe trivially calculated from its de�ning equation given thatthe shell is strictly optically thin. Given �(r) and T (r) wecan construct the curve on the T , �=T plane correspondingto thermal equilibrium.The form of this curve gives information on the ther-mal stability of the material. Isobaric perturbations haveconstant �=T and thus correspond to vertical displacementson the T , �=T plane. Consider material in thermal equilib-rium. If an isobaric increase in T leads to cooling dominatingover heating, then the equilibrium will be stable. However,if such a temperature increase leads to heating dominatingover cooling, then runaway heating occurs and the equilib-rium is unstable.Note that the geometrically thick, optically thin shell isnot a physical model; it is merely a construction that provesto be convenient in the analysis of the local thermal stabilityof the material.4.1 ResultsFig. 3 shows such a curve computed for an ionizing contin-uum consisting of a powerlaw with photon index � = 1:8extending from 13.6 eV to 40 keV. The density was �xed at109 cm�3 and solar abundances were assumed. The relativedominances of heating and cooling in various regions of thediagram are indicated. It can be seen from Fig. 3 that partsof the curve that have negative gradient and are associatedwith a multi-valued regime correspond to thermally unstableequilibria.Using the warm absorber parameters obtained from theASCA observations of MCG�6�30�15, it is seen that thewarm absorber appears to exist in a small region of stabilitywithin an otherwise unstable regime. The region of param-eter space for which the warm state is stable is extremelyrestricted (�3:48 < log(�=T ) < �3:43 for the case shownin Fig. 3). However, observed column densities and coveringfractions suggest that a signi�cant amount of material is inthis state. The question arises as to how the material couldget into such a state. These issues are addressed in Section5. In principle, the exact form of the stability curve de-pends on the shape of the primary continuum, the assumeddensity, and the assumed abundances of the material. Thus,

Warm absorbers in active galactic nuclei 5

Figure 3. Equilibrium gas temperature T as a function of �=T .The assumed ionizing continuum consists of a single powerlawwith photon index � = 1:8 extending from 13.6 eV to 40 keV.There are small ranges of �=T for which T is multi-valued, lead-ing to the possibility of multiple phases in pressure balance. Thewarm absorber (T � 105 K) is seen to fall in a small stable regionwithin such a multi-phase regime. Regions of the plane wherecooling exceeds heating and vice versa are indicated.the robustness of the stability curve to various changes wasexamined.4.2 E�ect of ionizing continuum shapeFirst, the e�ect of changing the photon index of the primarysource was investigated. Fig. 4 shows the stability curve for� = 1:3, � = 1:8 and � = 2:5 with �xed low- and high-energycut-o�s at 13.6 eV and 40 keV respectively. For a very atprimary spectrum (� < 1:5) no stable warm state exists. Onthe other hand, steep primary spectra (� > 3) result in alowering of the Compton temperature and a stabilization ofthe material for all �. The e�ect of changing the high-energycut-o� was also investigated. The major e�ect of increasingthe value of the high-energy cut-o� is to increase the Comp-ton temperature of the gas. Such a change has little e�ecton the stability of material at temperatures below � 106K.The e�ect of a soft X-ray excess was examined. Thiswas modelled as a blackbody component with a temperatureof 0.13 keV. Fig. 5 shows the resulting stability curve for� = 1:8 with varying blackbody luminosities. Moderate softexcesses only change the shape of the curve for T < 105K.The trend is for the soft excess to stabilize the cold/warmmaterial. The properties of the hot material (T > 105K) arelittle a�ected by the soft excess unless it is very strong (e.g.see Fabian et al. 1986), in which case the e�ect is to lowerthe Compton temperature.

Figure 4. Equilibrium gas temperature T as a function of �=T forphoton indices of � = 1:3 (dashed curve), � = 1:8 (solid curve)and � = 2:5 (dotted curve). In all cases the powerlaw extendsfrom 13.6 eV to 40 keV.

Figure 5. Equilibrium gas temperature T as a function of �=Tfor a photon index of � = 1:8 and various soft excess luminosities.The soft excesses are modelled by a power-law component with atemperature of 0.13 keV. The solid line is the curve of Fig. 3 withno soft excess. The dashed and dotted lines are the results for asoft excess with 50 per cent and 100 per cent of the power-lawluminosity respectively. In all cases the powerlaw extends from13.6 eV to 40 keV.

6 C. S. Reynolds and A. C. Fabian4.3 Density e�ectsNext the sensitivity to the assumed density was examined.The curve on the T , �=T plane was computed for variousdensities between 0:1 cm�3 and 1013 cm�3. For densities be-tween 10 cm�3 and 1011 cm�3 the form of the curve is veryinsensitive to the assumed density. This is to be expected:consider material with such densities. If it is cold/warm(T < 106 K) the thermal equilibrium is determined by thebalance between photoelectric heating and cooling due toatomic lines (see Netzer 1990 for a discussion of the physi-cal processes). The density will then enter only via the com-bination �. If the material is hot (T > 106K) the thermalequilibrium is determined mainly by the balance of Comptonheating and Compton cooling. Thus it will be independentof density.For densities greater than 1011 cm�3, three-body re-combination becomes important whereas, for densities be-low 10 cm�3, two-body cooling processes become ine�cient.These e�ects produce a more complex dependence on den-sity thereby a�ecting the form of this curve. However, thearguments of Section 3 suggest that these extreme densitiesare not relevant to the observed warm absorbers.4.4 Finite optical depth e�ectsObserved warm absorber column densities are � 1022 cm�2.Thus the optical depths near the dominant absorption edges(i.e. the Ovii and Oviii edges) are not negligible. As theionizing continuum passes through the warm material, theabsorption of ux near the Ovii and Oviii edges could al-ter the shape of the stability curve of material at the outeredge of the shell. To assess the importance of this e�ect,cloudy was used to compute the transmitted spectrumwhich emerges from the warm absorbing material (giventhe parameters obtained for MCG�6�30�15). The stabilitycurve for this spectrum was then computed using the opti-cally thin, geometrically thick shell (as above). It is foundthat warm absorption does little to change the shape of thestability curve.5 PHYSICAL MODELS OF WARMABSORBERSModels for the environment within the nuclei of Seyfertgalaxies must explain the presence of signi�cant quantities ofwarm material. More general AGN models must also explainthe general absence of observed warm absorption features inradio-loud objects and powerful radio-quiet QSOs. The pur-pose of this section is to discuss several models for the originof the warm absorber.The arguments of Section 3 suggest that the warm ma-terial lies between 1015 cm and 1018 cm from the central en-gine (using the parameters for MCG�6�30�15). This placesit roughly coincident with, or just outside, the BLR. There-fore, we shall mainly discuss the warm absorber in relationto various BLR models. Radiatively driven out ows will alsobe discussed as a possible source for the observed warm ab-sorption.

5.1 Pressure-con�ned BLRThe simplest model for the BLR is the two-phase model(McCray 1979; Krolik et al. 1981). If the thermal instabilityof Section 4 can operate over a wide range of �=T , therewill be a range of pressure and mean density in which cold(T � 104 K) clouds exist in pressure equilibrium with a hotphase at the Compton temperature (� 107{108 K). The coldclouds comprise the broad emission line clouds. The coldclouds acquire velocities characteristic of the virial veloc-ity, thereby leading to (Doppler) broadening of the emissionlines as required by observation.Section 4 shows that there is a small range of �=T forwhich a three-phase medium may occur. This would consistof cold (broad-line) clouds in pressure equilibrium with ahot intercloud medium and a warm intermediate phase. Ifthe covering fraction of the cold phase is small, it is plausi-ble that only the warm phase would have su�cient coveringfraction and X-ray opacity to be commonly seen in absorp-tion. As a model of the warm absorber, this su�ers fromproblems. It requires �ne tuning of �=T (and therefore thepressure) to produce the three-phase medium. This modelalso fails to explain the absence of warm absorbers in pow-erful QSOs and radio-loud quasars which seem to displayordinary BLRs.More seriously, even the simple two-phase BLR modelhas serious aws. First, in low-luminosity systems (such asSeyfert galaxies) the cooling time-scale of the intercloudmedium is longer than the dynamical time-scale of the BLR.Thus the assumption of thermal equilibrium need not bevalid. This was noted by Krolik et al. (1981, hereafter KMT).Secondly, the formation of broad-line clouds is not explainedwithin this model. Compton cooling time-scales are too longto allow perturbations of the hot phase to condense intoclouds. Also, self-gravity of the clouds is thought to be neg-ligible, thereby ruling out gravitational instabilities as aformation mechanism. In this sense, the simple two-phasemodel is incomplete. Thirdly, Fabian et al. (1986) showedthat a strong soft X-ray/EUV excess will reduce the Comp-ton temperature to � 106 K and severely restrict the rangeof �=T over which the thermal instability can occur. Thisresult has several consequences.(i) The intercloud medium would have to be opticallythick if it were still to pressure-con�ne the broad-line clouds.An optically thick intercloud medium is inconsistent withthe observed rapid variability of many broad-line AGN.(ii) The ionization parameter of the broad-line cloudscan be determined from the observed line ratios. These ob-served values of � span a larger range than that over whichthe thermal instability operates. Such discrepancies can bereconciled if some physical process (such as cloud evapora-tion or partial magnetic con�nement) increases the pressureof the clouds above that of the intercloud medium (Kallman& Mushotzky 1985).(iii) Broad-line clouds are inferred to have velocities ofup to � 104 kms�1. Such motion through a stationary inter-cloud medium at T � 106 K would lead to rapid fragmenta-tion of the clouds into optically thin �laments, contrary tothe observed line ratios. This di�culty would be alleviatedif the broad-line clouds were advected in some large-scale,high-velocity ow of the intercloud medium.Finally, recent results from reverberation mapping (Pe-

Warm absorbers in active galactic nuclei 7terson 1993) suggest that the BLR is extended with an innerradius at least 10 times smaller than the outer radius. Thetwo-phase model of the BLR would predict a relatively thinshell-like BLR.A full description of the BLR clearly has to be dynamicin nature. We now discuss some dynamic models for theBLR.5.2 Shock-formed BLRPerry & Dyson (1985) have proposed a model in whichthe broad-line clouds are continuously created by radia-tive shocks. A supersonic ow of hot material (e.g. a windfrom the central source) encounters a number of large obsta-cles, such as supernova ejecta or winds from groups of mas-sive stars. The resulting shocks compress and heat the gas,thereby dramatically reducing �=T in the post-shocked gas.Provided the shocks are spatially large, the post-shocked gascan cool isobarically via inverse Compton scattering of theradiation �eld from the central engine. This gas cools to al-most 104K and fragments to form broad-line clouds. Afterthe clouds leave the environment of the shock, they are accel-erated to the local ow speed (thereby giving the broad-linevelocities) and eventually evaporate. No cloud con�nementis necessary due to their continuous production.Within the context of this model, the warm absorbercould be identi�ed with material that has been `boiled' fromthe clouds and is being heated to the Compton temperature.Further investigation is required to examine whether thenecessary column densities, covering fractions and ionizationstates can be achieved. It may, for example, be di�cult toin ate broad-line clouds with a covering fraction of a fewper cent and a column density of � 1022 cm�2 to producea warm absorber covering fraction of � 50 per cent and asimilar column density.A crucial component of this model is the population oflarge obstacles which create the spatially extended shocks inthe hot gas. Reverberation mapping of the BLRs of Seyfertgalaxies suggest it to be surprising small, with spatial ex-tents of only � 20 light days or so. There would have to be alarge number of obstacles within this radius to produce theobserved, fairly regular BLR. This might pose problems forthe model.5.3 Turbulent BLRMechanical heating of the hot intercloud medium has beengiven little attention in recent BLR models. If mechani-cal heating could raise the temperature of the intercloudmedium to � 108K or more, the problems associated witha pressure-con�ned BLR (see Section 5.1) would be allevi-ated. Here we examine turbulent heating of the intercloudmedium.Suppose the hot intercloud medium (HIM) has a tem-perature of T � 108 K and a density of n � 106 cm�3 so thatapproximate pressure balance with the broad-line clouds isachieved. The thermal energy density in the electrons isEHIM = 32nkBT � 10�2 erg cm�3: (6)The Compton cooling time-scale is given by

tComp � mec2R2L�T (7)where me is the rest mass of an electron, �T is the Thom-son cross section and R = 1016R16 cm is the distance fromthe central source which is assumed to have an isotropicluminosity of L = 1043L43 erg s�1. This evaluates to givetComp � 108 R216L�143 s. The Compton cooling rate per unitvolume isWComp � EHIMtComp � 10�10 R�216 L43 erg cm�3 s�1: (8)If additional heat sources can exceed this power per unit vol-ume, they will dominate over Compton cooling and hold theintercloud medium signi�cantly above the Compton temper-ature. We now estimate the turbulent heating and show thatit could dominate Compton cooling in the BLRs of Seyfertgalaxies.Radiation pressure on broad-line clouds will induce mo-tion of the clouds with respect to the intercloud medium.The terminal velocity vt is given by Prad � �v2t where Pradis the radiation pressure on the clouds and � is the mass den-sity of the intercloud medium. The radiation �eld therebydoes work on the broad-line clouds. The rate of doing workon the clouds is � Pradvt per unit illuminated area. There-fore, the rate of doing work per unit volume isW � NAP 3=2radV �1=2 (9)where N = 106N6 is the number of broad-line clouds (withN6 > 1), V is the volume of the broad-line region and A isthe projected area of a single broad-line cloud. If we de�ner = 1012r12 cm to be the typical radius of a broad-line cloud(r12 � 1) and use Prad = L=4�R2c, we deduce thatW � 10�10 N6r212R�616 L3=243 erg cm�3 s�1: (10)Expressed in terms of the covering fraction, fA, of the broad-line clouds, this becomesW � 10�10 fAR�416 L3=243 erg cms�1: (11)It is reasonable to suppose that this energy is transferredinto large-scale turbulent motions within the intercloudmedium. Turbulent cascades would lead to thermalizationof this energy in the intercloud medium. Such a mecha-nism would provide an additional heat source for the in-tercloud medium. The ratio of the turbulent heating rate tothe Compton cooling rate isR = WWComp � N6r212R�416 L1=243 : (12)Turbulent heating will dominate Compton cooling if R > 1.Such a condition may well be satis�ed in Seyfert galaxies.The characteristic size R of the BLR is thought to be propor-tional to L1=2 (i.e. the characteristic BLR ionization param-eter is similar in objects with very di�erent luminosities).Assuming that cloud size, r, is independent of the total lumi-nosity of the object, this gives R / NR�3. Thus, turbulentheating can exceed Compton heating (i.e. R > 1) in moreluminous AGN only if the number of broad-line clouds, N ,increases at least as fast as R3.The radiation pressure on the warm absorbing mate-rial is only a small fraction of the radiation pressure on thebroad-line clouds (of the order of a few per cent). However,

8 C. S. Reynolds and A. C. Fabianthe warm material has a much greater covering fraction.Thus, the action of the radiative forces on the warm ma-terial might also be important for turbulent heating of theintercloud medium.Turbulence in the hot intercloud medium would dis-rupt the surfaces of the broad-line clouds. The cold and hotmaterial would then mix to form a turbulent mixing layer.Begelman & Fabian (1990) use conservation of energy andmomentum to deduce that a steady-state mixing layer ischaracterized by a temperatureTml = �(TcTh)1=2 (13)where Tc and Th are the temperatures of the cold and hotphases respectively and � � 1. For Tc � 104 K and Th �108 K this gives Tml � 106 K. Mixed gas could shear fromthe surfaces of the broad-line clouds to produce opticallythin �laments. Such �laments could be identi�ed with thewarm absorber.Mixing layers will be strong emitters of UV radiation.An estimate for the resultant UV ux can be obtained byconsidering the thermal energy of the intercloud mediumthat is `swept up' by the broad-line clouds each unit of time.If we assume that this energy is completely converted to UV ux, we obtain an approximate upper limit for the total UV ux due to mixing layers. This ux proves to be negligiblecompared with the UV ux of the central engine and has noe�ect on the ionization structure of the broad-line clouds.Mixing layers are complex, non-equilibrium systems andare examined in detail by Slavin, Shull & Begelman (1993)for the case of the interstellar medium. They contain cool-ing components as well as components undergoing heating.Self-photoionization must also be considered. The AGN en-vironment is very di�erent from the interstellar medium: thepressures are much greater, there are high-speed bulk owsand there is a luminous source of hard radiation. Thus, moreinvestigation of mixing layers in AGN is required to assessthe observational consequences.5.4 Out ow modelsRecent ASCA observations of the warm absorber in NGC4051 hint that the absorption edges of Ovii, Oviii, Ne ixand Nex may be blueshifted by � 3 per cent (Mihara et al.1994). If veri�ed, this suggests an out ow of the materialat � 10000 kms�1. Since radiation pressure on the materialcan be comparable with the gravitational attraction of thecentral compact body, the possibility of a radiatively drivenwind arises. Here we sketch some simple ideas relating towarm absorbers as radiatively driven out ows.It is instructive to calculate the critical ionizing lumi-nosity for which the radiative force on the warm absorberbalances the gravitational attraction of the central compactbody. For the purposes of obtaining a crude estimate, sup-pose that all of the oxygen is in the form of Ovii and thatthe dominant opacity of the material is K-shell photoioniza-tion of this ion. Take the source of the ionizing continuum tobe an isotropic emitter of a power-law spectrum with pho-ton index � = 2 between �min and �max. Let this source besituated at R = 0. ThusL(�) = L���1 (14)

where L is the total ionizing luminosity and� = ln��max�min � : (15)The radiative force per Ovii ion is given byFrad = Z 10 L(�)4�cR2 �(�)d� (16)where �(�) is the cross-section for K-shell photoionizationof Ovii. To a fair approximation this can be taken to beproportional to ��3 for � > �th, the threshold frequencywhere � = �th (and zero below �th). Thus we carry out theintegration in the previous expression to giveFrad = L�th12�c�R2 : (17)Now suppose the gravitational potential of the region isdominated by a mass M at R = 0. The gravitational forceon the gas per Ovii ion isFgrav = GMmR2 (18)where m is the mass of gas per Ovii ion. Thus, under thesimplifying assumptions stated, the ratio of radiative force(radially outwards) to gravitational force (radially inwards),�, is given by� = 13� � LLE��mpm ���th�T � (19)where LE is the Eddington luminosity, mp is the protonmass and �T is the Thomson cross-section. Using �th =2:75�10�19 cm2 and approximate solar abundances (so thatm � 103mp), we obtain� � 20� LLE� (20)Thus the critical luminosity for which � = 1 is Lcrit �0:05LE. This is a plausible value for many Seyfert galaxies.So, for L = Lcrit the steady-state radiatively driven windconsists of material in the warm state. Out owing materialthat is fully ionized (with correspondingly lower opacity)would be gravitationally decelerated and thus compresseduntil it recombines to give warm material. Similarly, neutralmaterial (with correspondingly higher opacity) would be ra-diatively accelerated and rare�ed until it partially ionizesto give warm material. Such an argument could explain theunusual ionization state of the warm absorber.Continuing with this simple model, suppose L � Lcritand that this produces a homogeneous out ow of warm ma-terial with constant velocity v beyond some radius rin withina solid angle . Neglecting the region r < rin, the opticaldepth of the ow is given by� (�) � �(�)N(Ovii) (21)where N(Ovii) is the column density of Ovii ions. If the ow becomes optically thick over a signi�cant range of fre-quencies, the radiative force will signi�cantly increase andthe steady state will be broken. Thus, we shall imposethat � (�) < 1 for all �. In particular, � (�th) < 1. Thisyields an upper limit on the column density of Ovii ionsof N(Ovii) < 4�1018 cm�2. This translates into an equiva-lent hydrogen column density of NW < 4�1021 cm�2. Obser-vationally, warm absorbers are seen with NW � 1022 cm�2.

Warm absorbers in active galactic nuclei 9Thus there is crude agreement between the observed columndensity and the maximum column density allowed by thismodel under the constraint of optical thinness. Assuming nomass injection in the region r > rin, conservation of massgives n(r) / r�2. The mass out ow rate (which is given byr2v�) is then_M � 3� 10�4 �rin16NW22 v3� M� yr�1 (22)where rin = 1016rin16 cm, NW = 1022NW22 cm�2 and v =103v3 kms�1 The kinetic luminosity isLK � 1038 �rin16NW22 v33� erg s�1: (23)Thus, even quite high-velocity out ows would not dominatethe energetics of the source.Now suppose L < Lcrit. Our arguments suggest that asteady-state out ow of cold (partly neutral) material mightform. This material would have a su�ciently high opacityfor the radiative force to balance gravitation. Similarly, ifL > Lcrit an out ow of more highly ionized material maybe created. This scenario could account for the observedanticorrelation between the AGN luminosity and intrinsiccolumn density for cold absorption (Reichert et al. 1985;Turner & Pounds 1989). It could also explain the absenceof observed warm absorbers in powerful QSOs (which arethought to be radiating close to the Eddington limit).Clearly, a detailed study of such radiatively drivenwinds would be complicated. Such a treatment would haveto include realistic opacities, the possibility of an inhomo-geneous ow (e.g. break-up of the ow into clouds via thethermal instability of the previous sections), anisotropy ofthe primary ionizing continuum and additional heating andcooling mechanisms (e.g. shocks, turbulence and adiabaticcooling).6 SUMMARYAbsorption features due to partially ionized, warm (�105 K) gas are common in the X-ray spectra of Seyfert 1galaxies and NELGs. The ASCA SIS allows such features tobe accurately identi�ed and measured. The dominant fea-tures in the ASCA energy range are absorption K-edges ofOvii and Oviii. Ne ix and Nex edges are also observablein some sources. One-zone photoionization models allow thecolumn density and ionization parameter � of the warm ma-terial to be estimated (assuming that the material is in pho-toionization equilibrium). The covering fraction of this ma-terial within Seyfert 1 nuclei and NELGs must be large forthis phenomenon to be so commonly observed.Constraints on the location of the warm absorbing gasare derived using the simplifying assumptions that the ma-terial is of uniform density and occupies a region with line-of-sight depth (to the central engine) �R and outer radius Rfrom the central engine. Thermal equilibrium and photoion-ization equilibrium with the radiation �eld from the centralengine are also assumed. We conclude that the warm mate-rial must lie between 1015 cm and 1018 cm from the centralengine. This implies that the warm material is spatially co-incident with, or just outside, the BLR.Intermediately ionized plasma is notoriously unstableto temperature uctuations. Thus, the stability of the warmabsorbing material requires investigation. We have done this

by constructing the equilibrium curve on the T , �=T plane.Parts of this curve that have negative gradient and are asso-ciated with a multi-valued regime correspond to thermallyunstable equilibria. Use of a standard ionizing continuumleads to the conclusion that a stable warm state only existsfor a remarkable small range of �. A steep primary spectrumor a very strong soft excess stabilizes all material cooler than105K. These results are insensitive to reasonable changes inthe assumed density.Given the small range of � for which the warm state isstable, we must explain how such a large amount of mate-rial attains such a state. The absence of observed warm ab-sorbers in most radio-loud objects and powerful radio-quietQSOs must also be explained. In an attempt to address theseissues, several models of the warm absorber are discussed.In particular, possible relationships between the warm ab-sorber and the BLR are examined. Within the context ofthe pressure-con�ned two-phase BLR of KMT, a three-phasemedium may form in which cold broad-line clouds exist inpressure equilibrium with a hot intercloud medium and anintermediate warm phase. It is plausible that only the warmphase would have a su�ciently high covering fraction andX-ray opacity to be seen commonly in absorption. However,the simple two-phase model is incomplete (in the sense thatit neglects dynamical e�ects and does not explain the for-mation of broad-line clouds) and su�ers from inherent dif-�culties such as an optically thick intercloud medium andrapid fragmentation of the broad-line clouds into opticallythin �laments (both of which are contrary to observations).Radiation pressure acting on broad-line clouds can besigni�cant. The work done on the clouds by the radiation�eld can drive turbulent motions in the intercloud medium.This energy undergoes a cascade to smaller and smallerscales until it is thermalized. Such a mechanism providesa mechanical heat source for the hot intercloud medium.We suggest that this can dominate Compton heating of theintercloud medium in the BLRs of Seyfert galaxies. Turbu-lence in the intercloud medium leads to the formation of tur-bulent mixing layers at the surface of the broad-line clouds.Such mixing layers may give rise to optically thin �lamentsof warm material, thereby providing an explanation for theobserved warm absorption features.Finally, a simple model for a steady-state radiativelydriven out ow is examined. It is concluded that, for L �0:05LE, an optically thin out ow of warm material couldform. Lower luminosity objects would have out ows of colder(more recombined) material whereas higher luminosity ob-jects would have out ows of hotter material (more ionized).This explains the apparent anti-correlation of cold absorb-ing column density with luminosity. It also explains the ab-sence of warm absorbers in powerful QSOs (assuming theseobjects to be accreting closer to the Eddington limit thantheir lower luminosity counterparts).In a recent paper by Krolik & Kriss (1994), seen by usafter the submission of this work, it was emphasized that theabsorbing material may not be in thermal equilibrium andthat this may have important implications for the resultantspectrum. Non-equilbrium conditions might be expected tobe relevant to the shock-formed BLR, turbulent BLR andout ow models described above in which mechanical heatingmay be important.The physical state and time variability of this warm ma-

10 C. S. Reynolds and A. C. Fabianterial could be important tools for probing the environmentnear the central engines of Seyfert galaxies. To date, studiesof the BLR have been constrained only by observations ofthe broad lines (and upper limits on quantities such as theoptical depth or X-ray emission of the intercloud medium).If the connection between the warm absorber and BLR isvalid, the properties of this warm material could be an im-portant diagnostic of the BLR. Furthermore, the presence orabsence of warm absorbers in the various classes of objectcan be used to assess uni�ed AGN models.ACKNOWLEDGMENTSWe wish to thank Niel Brandt, Alastair Edge, RoderickJohnstone, Tsuneo Kii, Paul Nandra and Martin Rees foruseful discussions throughout the course of this work. Wealso wish to thank Gary Ferland for his valuable help inthe operation of cloudy. ACF thanks the Royal Society forsupport. CSR thanks PPARC for support.REFERENCESAllen C.W., 1973, Astrophysical Quantities. Athlone Press, Lon-donBegelman M.C., Fabian A.C., 1990, MNRAS, 244, 26PFabian A.C. et al., 1994, PASJ, 46, L59Fabian A.C., Guilbert P.W., Arnaud K.A., Shafer R.A., TennantA.F., Ward M.J., 1986, MNRAS, 218, 457Ferland G.L., 1991, Ohio State University, Astronomy Depart-ment Internal Report 91-01Fiore F., Elvis M., Mathur S., Wilkes B.J., McDowell J.C., 1993,ApJ, 415, 129George I.M., Fabian A.C., 1991, MNRAS, 249, 352Guilbert P.W., Rees M.J., 1988, MNRAS, 233, 475Guilbert P.W., Fabian A.C., McCray R., 1983, ApJ, 266, 466Halpern J.P., 1984, ApJ, 281, 90Kallman T., Mushotzky R.F., 1985, ApJ, 292, 49Krolik J.H., Kallman G.A., 1987, ApJ, 320, L5Krolik J.H., Kriss G.A., 1995, preprintKrolik J.H., McKee C.F., Tarter C.B., 1981, ApJ, 249, 422 (KMT)Lightman A.P., White T.R., 1988, ApJ, 335, 57Madejski G.M., Mushotzky R.F., Weaver K.A., Arnaud K.A.,Urry C.M., 1991, ApJ, 370, 198Mathur S., Wilkes B., Elvis M., Fiore F., 1994, ApJ, 434, 493Matt G., Perola G.C., Piro L., 1991, A&A, 245, 63McCray R.A., 1979, in Hazard C.R., Mitton S., eds, Active Galac-tic Nuclei. Cambridge Univ. Press, Cambridge, p. 227Mihara T., Matsuoka M., Mushotzky R.F., Kunieda H., Otani C.,Miyamoto S., Yamauchi M., 1994, PASJ, 46, L147Nandra K., Pounds K.A., 1992, Nat, 359, 215Nandra K., Pounds K.A., 1994, MNRAS, 268, 405Nandra K., Pounds K.A., Stewart G.C., 1990, MNRAS, 242, 660Nandra K., Pounds K.A., Stewart G.C., George I.M., HayashidaK., Makino F., Ohasi T., 1991, MNRAS, 248, 760Nandra K. et al., 1993, MNRAS, 260, 504Netzer H., 1990, in Courvoiser T.J.-L., Mayor M., eds, ActiveGalactic Nuclei, Saas Fee Advanced course 20. Springer-Verlag, Berlin, p. 57Netzer H., 1993, ApJ, 411, 594Pan H.-C., Stewart G.C., Pounds K.A., 1990, MNRAS, 242, 177Perry J.J., Dyson J.E., 1985, MNRAS, 213, 665Peterson B.M., 1993, PASP, 105, 247Reichert G.A., Mushotzky R.F., Petre R., Holt S.S., 1985, ApJ,296, 69

Shull J.M., Van Steenberg M., 1982, ApJS, 48, 95Slavin J.D., Shull J.M., Begelman M.C., 1993, ApJ, 407, 83Turner T.J., Pounds K.A., 1989, MNRAS, 240, 833Turner T.J., Nandra K., George I.M., Fabian A.C., Pounds K.A.,1993, ApJ, 419, 127