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3-1-1999 Megamaser Disks in Active Galactic Nuclei John F. Kartje University of Chicago

Arieh Königl University of Chicago

Moshe Elitzur University of Kentucky, [email protected] Right click to open a feedback form in a new tab to let us know how this document benefits oy u.

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Notes/Citation Information Published in The Astrophysical Journal, v. 513, no. 1, p. 180-196.

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This article is available at UKnowledge: https://uknowledge.uky.edu/physastron_facpub/218 THE ASTROPHYSICAL JOURNAL, 513:180È196, 1999 March 1 ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI JOHN F. KARTJE AND ARIEH KOŽ NIGL Department of Astronomy and Astrophysics and Enrico Fermi Institute, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637; kartje=jets.uchicago.edu, arieh=jets.uchicago.edu AND MOSHE ELITZUR Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506; moshe=pa.uky.edu Received 1997 October 8; accepted 1998 October 13 ABSTRACT Recent spectroscopic and VLBI-imaging observations of bright extragalacticH2O maser sources have revealed that the megamaser emission often originates in thin circumnuclear disks near the centers of active galactic nuclei (AGNs). Using general radiative and kinematic considerations and taking account of the observed Ñux variability, we argue that the maser emission regions are clumpy, a conclusion that is independent of the detailed mechanism (X-ray heating, shocks, etc.) driving the collisionally pumped masers. We examine scenarios in which the clumps represent discrete gas condensations (i.e., clouds) and do not merely correspond to velocity irregularities in the disk. We show that even two clouds that overlap within the velocity-coherence length along the line of sight could account (through self- ampliÐcation) for the entire maser Ñux of a high-velocity ““ satellite ÏÏ feature in sources like NGC 4258 and NGC 1068, and we suggest that cloud self-ampliÐcation likely contributes also to the Ñux of the background-amplifying ““ systemic ÏÏ features in these objects. Analogous interpretations have previously been proposed for water maser sources in Galactic star-forming regions. We argue that this picture pro- vides a natural explanation of the time-variability characteristics of extragalactic megamaser sources and of their apparent association with Seyfert 2Èlike galaxies. We also show that the requisite cloud space densities and internal densities are consistent with the typical values of nuclear (broad emission line region type) clouds. We examine two scenarios of clumpy disks in which the maser emission is excited by a central contin- uum source. This excitation mechanism was Ðrst considered in the context of megamaser disks by Neufeld & Maloney, but our proposed models are clearly distinct from their warped, homogeneous disk interpretation. In our Ðrst scenario we consider an annular disk (or ““ ring ÏÏ) whose inner edge corre- sponds to the innermost radius of the observed maser distribution and whose mass is dominated by the clumped, high-density gas component. The shielding of the high-energy continuum, which is required in order that the gas remain molecular, can be provided in this case by the dusty clouds themselves. We show that even the simplest version of this model, in which the disk is Ñat and the continuum radiation reaches the masing clouds through the plane of the disk, can account for the maser observations in NGC 1068. We point out the striking similarities between the maser ring properties as interpreted with this model and the inferred characteristics of the circumnuclear disk in the Galactic center, and we brieÑy discuss the implications of such rings for the AGN accretion disk paradigm. Our second scenario is motivated by the apparent warps observed in some of the imaged megamaser disks and by our Ðnding that the Ñat-disk version of the irradiated ring scenario could apply to a source like NGC 4258 only if the water abundance in the masing clouds were higher than the value implied by equilibrium photoionization-driven chemistry. This scenario is based on the disk-driven hydromagnetic wind model originally proposed to account for the molecular ““ tori ÏÏ in Seyfert 2Èlike galaxies and for several other observed phenomena in AGNs. In this picture, the wind uplifts (by its ram pressure) and conÐnes (by its magnetic pressure) dense clouds fragmented from the disk, which mase after they become exposed to the central radiation Ðeld. Much of the requisite continuum shielding can be provided in this case by the dusty portions of the wind. We show that comparatively massive clouds that move in low- altitude, nearly circular orbits could be shielded in this way, and we suggest that an apparent warp in the maser distribution might arise under these circumstances from an observational selection e†ect induced by the strong vertical density stratiÐcation that characterizes a centrifugally driven wind. We construct a self-contained illustrative model where the wind transports the bulk of the disk angular momentum, and we show that it is consistent with the data for NGC 4258 as well as with the advection- dominated accretion Ñow interpretation of the spectrum in this source. Subject headings: galaxies: individual (NGC 1068, NGC 4258) È galaxies: nuclei È galaxies: Seyfert È masers INTRODUCTION 1. 2 and LINER galaxies whose nuclei are hidden by a fairly Strong 22 GHz water maser emission has now been large column of optically obscuring and X-rayÈabsorbing detected toward the nuclei of some 20 active galaxies. These gas (Braatz, Wilson, & Henkel 1996, 1997). There is mount- ““ megamaser ÏÏ sources are generally associated with Seyfert ing evidence, from spectral measurements and VLBI 180 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 181 imaging, that in many (if not all) of these objects at least of the mass distribution in the centers of active galactic part of the emission originates in a rotating circumnuclear nuclei (AGNs). In particular, the high mass concentrations disk on scales of D0.1È1 pc. The best examples to date are inferred in sources like NGC 4258 currently provide provided by NGC 4258 (e.g., Miyoshi et al. 1995; Greenhill perhaps the strongest argument for the presence of massive et al. 1995b) and NGC 1068 (e.g., Greenhill et al. 1996; black holes in galactic nuclei (e.g., Maoz 1995, 1998; Rees Greenhill & Gwinn 1997), where the imaged maser spots 1998). By combining centripetal-acceleration and proper- are arranged in a thin and apparently slightly warped disk. motion measurements of the systemic maser spots, one can, In both sources one detects features that are located on the in principle, also derive distance ladder-independent values near side of the disk at the vicinity of its apparent inner edge for the distances of these sources (Herrnstein et al. 1997b). and have line-of-sight velocities that are close to the sys- But the maser observations also constitute a powerful tool temic velocity of the galaxy, as well as high-velocity for probing the nature of circumnuclear disks in AGNs. In ““ satellite ÏÏ features that are strung out along the projected fact, since the bolometric luminosity in these sources most major axis (the midline) of the disk on either side of the likely derives from accretion, and since nuclear jets have nucleus (where they give rise to red- and blueshifted emis- been detected in many of these objects, the inferred physical sion, respectively). In NGC 4258 the systemic maser com- conditions in the maser emission regions may have direct \ ponents lie nearrin B 0.13 pc (assuming a distance D 6.4 implications for the study of accretion and outÑow pro- Mpc) and the high-velocity features lie between D0.16 and cesses in AGNs. D0.26 pc; in NGC 1068 the inner edge is atrin B 0.65 pc There have been two distinct interpretations of the origin (for D \ 15 Mpc) and the radii of the high-velocity com- of AGN megamaser disks, based on two alternative excita- ponents span the range D0.65È1.1 pc. In the case of NGC tion mechanisms. Although there is general agreement that 4258 the emission is dominated by the low-velocity features, the masers are pumped collisionally, in one picture the which are clustered near the line of sight to the center (the maser emission arises from the irradiation of the disk by the center line); in NGC 1068, the redshifted high-velocity fea- central continuum source (e.g., Neufeld, Maloney, & tures dominate the measured Ñux and the emission from the Conger 1994), whereas in the alternative interpretation the inner edge is not conÐned to the vicinity of the center line masers originate in shock waves that propagate through the (in fact, a full quarter of the inner edge of the disk appears to disk (e.g., Maoz & McKee 1998, hereafter MM98). In the be masing in this source, exhibiting a linear increase of the disk-irradiation scenario it has been suggested that the disk line-of-sight velocityvlos with projected distance from the becomes exposed to the central radiation Ðeld because of center). The variation of the line-of-sight velocity of the warping, so that the innermost radiusrin from which maser high-velocity features in NGC 4258 with projected distance emission is observed e†ectively coincides with the onset from the center indicates a Keplerian disk around a central radius of the warp (Neufeld & Maloney 1995). The location ] 7 mass of D3.5 10 M_ ; the rotating disk interpretation in of the latter is, in principle, determined by the physical this source is further supported by measurements of the mechanism that triggers the warping (e.g., radiation apparent centripetal acceleration of the systemic masers pressure-induced warping instabilityÈMaloney, Begelman, (Haschick, Baan, & Peng 1994; Greenhill et al. 1995a). In & Pringle 1996aÈor an orbiting massive objectÈ NGC 1068 thevlos curve of the high-velocity features Papaloizou, Terquem, & Lin 1998). In the shock scenario, exhibits a sub-Keplerian drop with distance, and the the high-velocity emission has been attributed to spiral 7 inferred central mass is Z10 M_. shocks arising from the steepening of self-sustaining waves Similar results have been obtained in several other that, in the case of a nonÈself-gravitating, nearly Keplerian sources, although the data have often been more sketchy. In disk, are triggered by external forcing (MM98). The trailing the case of NGC 4945 (Greenhill, Moran, & Herrnstein spiral shocks envisioned in this model provide a natural 1997b), red- and blueshifted maser features, symmetrically explanation of both the quasi-regular spacing of the high- positioned with respect to the systemic feature (at projected velocity features in sources like NGC 4258 and NGC 1068 distancesZ0.2 pc) have been imaged and a central mass and the tendency of the redshifted features to dominate the 6 Z10 M_ has been inferred. A possible maser disk has also blueshifted maser emission in most of the objects observed been found in NGC 3079 (Trotter et al. 1998); in this case to date. only high-velocity (blue- and redshifted) features, distrib- In the models considered so far in the literature the disk uted over D1.7 pc, have been identiÐed and their motions was taken to be essentially homogeneous, and this assump- are consistent with rotation around a binding mass of D106 tion was used in estimating the mass accretion rate through M_.HOther likely candidates for an association of 2O the maser emission region. In the case of NGC 4258, megamaser emission with a rotating disk include NGC Neufeld & Maloney (1995) considered an irradiated, viscous 2639 (Wilson, Braatz, & Henkel 1995), the Circinus galaxy accretion disk and concluded that a rest mass conversion (Greenhill et al. 1997a), and NGC 5793 (Hagiwara et al. efficiency of D0.25/a (where a ¹ 1 is the Shakura & 1997). A noteworthy aspect of some of these apparent disks Sunyaev 1973 viscosity parameter) was needed to account 42 ~1 is that they are misaligned with the local symmetry axis. for the bolometric luminosityL bol B 10 ergs s of the This is particularly pronounced in the case of NGC 1068, central source (Wilkes et al. 1995; Chary & Becklin 1997). where the projected maser disk axis is tilted at an angle of This efficiency is a factor D250 higher than the value D35¡ with respect to the inner radio jet, which in turn is inferred in this object from an advection-dominated accre- nearly perpendicular to the plane of the circumnuclear gas tion Ñow (ADAF) interpretation of its observed spectrum distribution (see Gallimore, Baum, & OÏDea 1996a, 1997; (Lasota et al. 1996; Chary & Becklin 1997; Herrnstein et al. Tacconi et al. 1997). A similar situation is indicated in NGC 1998a). Although the latter estimate applies to disk regions 3079, where the apparent maser disk is tilted by D45¡ with that are signiÐcantly smaller than the maser emission zone, respect to the nuclear radio jet. the two values are mutually inconsistent if the disk has been The imagedH2O maser systems are a unique diagnostic accreting in a steady manner over the last few million years 182 KARTJE, KO NIGL, & ELITZUR Vol. 513

(Neufeld & Maloney 1995). The ADAF-implied value also speciÐcally applies to a clumped mass distribution, we appears to be incompatible with the radiation-induced present in ° 5 an interpretation of the high-velocity features warping instability model for this galaxy (Maloney et al. in terms of clouds that are uplifted from the surface of a 1996a). The spiral shock model, on the other hand, is evi- magnetized accretion disk by a centrifugally driven wind. dently consistent with the steady state accretion rate Such winds have previously been invoked to explain the ] ~2 ~1 (D2 10 a M_ yr ; see Herrnstein et al. 1998a) implied origin of the molecular ““ tori ÏÏ in Seyfert 2Èlike galaxies and by the ADAF interpretation (MM98). other AGNs(KoŽ nigl & Kartje 1994, hereafter KK94), and In this paper we take a closer look at the constraints their interaction with embedded clouds may have addi- imposed by the observed maser emission on AGN disk tional important ramiÐcations for active galaxies (Kartje & models. In ° 2 we argue, based on general radiative and KoŽ nigl 1997, 1999). Using a self-contained set of assump- kinematic considerations, as well as on the observed Ñux tions to represent a ““ generic ÏÏ model of this type, we show variability characteristics, that the maser emission regions that this scenario is consistent with the maser observations are clumpy. The likelihood of clumping, which is also indi- in a source like NGC 4258. We also demonstrate that the cated by the spectroscopic and imaging data, has already previously noted discrepancies between the irradiated acc- been recognized before (e.g., MM98) and could be associ- retion disk model for NGC 4258 and the ADAF interpreta- ated with either velocity irregularities or density inhomoge- tion of its spectrum can, in principle, be resolved if a neities. The implications of a turbulent velocity Ðeld to the centrifugally driven wind carries away a signiÐcant fraction observed maser spectra have been considered by Wallin, of the disk angular momentum in the maser emission Watson, & Wyld (1998, 1999). Here we focus on the possi- region. In ° 6 we summarize our results and discuss their bility that distinct gas condensations (clouds) are a major implications for the origin of maser emission and the nature (or even dominant) component of the disk and discuss the of accretion disks in AGNs. expected properties of the resulting maser emission. The motivation for this study is strengthened by our Ðnding that 2. MASER FLUXES FROM AGN DISKS the cloud parameters implied by the maser observations are 2.1. Flux Constraints consistent with those deduced by independent means but on roughly similar scales for optical/UV-emitting clouds in Even with high-resolution VLBI imaging, the beam size Seyfert galaxies (the so-called broad emission line region is much larger than the typical maser emission region in an [BELR] clouds). AGN. The Ñux measured from any small source is given by In ° 3 we discuss the conditions for efficient water maser F \ I), where I is the intensity and ) is the solid angle emission, starting with the general case of a collisionally subtended by the source at the observing position. If A is pumped gas and then specializing to irradiated clouds in an the observed area of the source and D its distance, then AGN environment. Although the masing clumps could, in 2kT A principle, be excited in shocks as in the MM98 model, we \ b F 2 2 , (1) concentrate in this paper on scenarios that are based on the j D alternative possibility of radiative excitation. We construct whereTb is the source brightness temperature and j is the two such models of irradiated clumpy disks that are qualit- wavelength (B1.35 cm for the water maser transition). We atively di†erent from the homogeneous disk model of now specialize to maser features (of arbitrary shape) that lie Neufeld & Maloney (1995). In the Ðrst such model (° 4) we in a disk whose plane is aligned with the observer. We consider a ““ minimalist ÏÏ scenario in which the central con- denote the half-length of the maser emission region along tinuum radiation reaches the clouds through the plane of the line of sight by l and deÐne the e†ective aspect ratio a the disk: in this case there is, in principle, no need to appeal by to warping as in the homogeneous irradiated disk model. In this picture the megamaser disk has a physical inner edge at l a \ . (2) rin and is therefore better described as a ““ ring ÏÏ (or JA/n ““ annulus ÏÏ).1 Furthermore, because of the small cloud volume Ðlling factor, the estimated disk mass is much lower For a larger than a few the maser is saturated and its bright- than that deduced from a homogeneous disk model. Focus- ness temperature can be expressed asT B 1012a3 K, \ b 10 ing on the case of NGC 1068, we discuss the striking simi- wherea10 a/10 (e.g., Elitzur, McKee, & Hollenbach 1991, larity between the maser ring as interpreted in this picture hereafter EMH91). The observed maser Ñux is then and the circumnuclear dust ring (the so-called circumnu- l 2 clear disk, or CND) observed in the center of our own F \ 4.7 ] 1017a A B Jy . (3) galaxy (e.g., Genzel, Hollenbach, & Townes 1994). 10 D In applying the minimalist scenario considered in ° 4to For a maser feature at a distance r from the galactic center, the megamaser disk in NGC 4258, we Ðnd that a strictly corresponding to an angular distance (in milliarcseconds) Ñat-disk model is untenable unless the water abundance is # \ 2.1 ] 108(r/D), this can be rewritten in the form signiÐcantly higher than that implied by local mas photoionization-driven chemistry. Since the disk in this l 2 F \ 11 #2 a A B Jy . (4) source appears to be warped (e.g., Herrnstein, Greenhill, & mas 10 r Moran 1996a), it is natural to consider a scenario in which the maser distribution is not coplanar. As an alternative to Equations (3) and (4) are quite general, the only assumption the warped disk model of Neufeld & Maloney (1995) that being that the pumping conditions are optimal. The pumping, however, may be driven by any mechanism 1 A similar disk geometry has been adopted also in the Maoz & McKee (shocks, X-ray heating, etc.), and the geometry in the plane (1998) interpretation of NGC 4258. can be arbitrary. Equation (4) has the added convenience No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 183 that, in VLBI-imaged sources,#mas is a measurable quan- NGC 4258 does not make up the entire velocity-coherent tity. region. From equation (3) it is seen thatF P a l2. Taking P 10 One can derive an upper bound on the ratio l/r in equa- a10 lcoh/wcoh, using equations (6) and (7), and noting that, tion (4) by using the velocity-coherence requirement for the for a Keplerian velocity Ðeld,r P v~2, one obtains F P ~4.5 los maser emission region. We assume Keplerian rotation and vlos . If, instead, one assumes thata10 is more or less focus attention on parcels of gas that give rise to a high- uniform throughout the emission region (as would be the velocity maser feature. If one such parcel is located on the case, for example, for a collection of similar X-rayÈ disk midline at a distancer \ 0.1r pc from the center and irradiated clouds), then an even steeper dependence, F P 0.1 ~5 has a line-of-sight velocityvlos, then another parcel that lies vlos , is obtained. Now, in the Ðrst interferometric mapping at a radius r ] dr and is displaced from the midline a dis- on 1994 April 26, the emission from the high-velocity fea- tance y will satisfy the coherence requirement *vlos [ *v/2 tures in NGC 4258 did exhibit a trend of F decreasing with (where *v is the width of the maser line) so long as vlos (see Fig. 1 of Miyoshi et al. 1995), but the decline was much milder thanv~4.5 (see also Fig. 11 of Nakai et al. dr ~1@2 y2 ~3@4 *v los KA ] B C ] D [ K 1995). In mappings performed on 1995 January 8 and 1995 1 1 ] 2 1 [ . (5) r (r dr) 2vlos May 28 the highest velocity peaks rose sharply, so the Ñux This result implies that the emission region for any given near the high end of the spectrum was actually increasing maser feature is conÐned to a velocity-coherence ““ box ÏÏ of withvlos (Herrnstein et al. 1996b), the opposite of the trend half-width (along the midline) predicted by velocity coherence. Hence, independent of the normalization of the pump estimates, one concludes that A*vB ] 14 A *v B the line-of-sight maser sizes do not sample the source veloc- wcoh B r B 3.1 10 r0.1 ~3 cm (6) vlos 10 vlos ity Ðeld and therefore are not directly determined by the and half-length (along the line of sight) disk dimensions. The inference that the size of the emission region in 2 *v 1@2 *v 1@2 objects like NGC 1068 and NGC 4258 is independent of B A B r B 8.0 ] 1015r A B cm (7) lcoh 0.1 ~3 that of the velocity-coherence box is consistent with the 3vlos 10 vlos MM98 model, in which the dimensions of the masing region (cf. MM98).2 Equations (5)È(7) again have a rather general are determined by the spiral shock characteristics. One can, validity and, in fact, apply to any masing gas that is distrib- however, argue, based on measurements of Ñux variability, uted in a Keplerian disk. that the emission must arise in distinct clumps (representing Equations (4) and (7) can be combined to give velocity or density irregularities within the disk) even if the *v large-scale structure of the masing region is deÐned by F [ 0.7a #2 A B Jy , (8) 10 10 10~3v shocks. In the case of NGC 4258, VLBA observations los reported by Herrnstein et al. (1996b) have revealed strong \ where#10 #mas/10. The maximum Ñux from a maser (up to a factor of D3) variations in the Ñux measured from feature would be produced if the emission came from the some of the high-velocity features on timescales of *tvar [ entire velocity-coherence box. Adopting a slablike geometry 8 *t months. A similar behavior was also noted in spectro- 2 8 for this box, the observed maser emission area is A B 2wcoh scopic observations of NGC 1068 (Nakai et al. 1995) and (Elitzur, Hollenbach, & McKee 1992, hereafter EHM92), NGC 5793 (Hagiwara et al. 1997). Such variability (which is and hencea B 0.125l /w . Substituting from equa- manifested both by increases and decreases in the maser 10 coh coh ~3 ~1@2 tions (6) and (7), one getsa10 B 3.2(*v/10 vlos) , so Ñux) is not expected in a uniform emission region, but it can equation (8) becomes be readily interpreted in terms of a relative drift (at a trans- ~1 ~1 A *v B1@2 verse speedZRc/*tvar B 5Rc13 *t8 km s ) of distinct F B 2.4#2 Jy . (9) masing clumps of projected sizeR \ 1013R cm that max 10 10~3v c c13 los move into (or out of) alignment with each other along the Specializing to NGC 1068, for which we adopt as Ðducial line of sight to the observer (see ° 2.2). In order for this ] ~3 mean parameters#mas B 10.9 and (*v/vlos) B 3.5 10 , behavior to be observed, the clump overlap probability we infer from equation (9) thatFmax B 5.3 Jy. This is about must be high (see eq. [17] below), which is equivalent to the an order of magnitude larger than the maximum Ñux (D0.4 cloud covering factor in the emission region being large. Jy) reported for the high-velocity features in this object (e.g., This, in turn, explains why the Ñux from a given feature can Greenhill et al. 1996). The implication of this result is that occasionally decline without the entire maser emission only a fraction of the potentially observable volume in this region fading away: when one pair of clouds drifts out of source actually contributes to the maser emission. In the alignment, another pair is likely to drift into alignment on a case of NGC 4258 the measured maximum Ñux in the high- similar timescale. velocity features (e.g., Moran et al. 1995) sometimes The presence of clumps has also been deduced in sources approaches the estimated value ofF [D1.1 Jy, using like NGC 4258 from spectral and imaging observations of ~3 max #mas B 6.7and (*v/vlos) B 10 ]; however, in this case, too, the systemic masers (e.g., Haschick et al. 1994; Greenhill et most of the high-velocity features typically have lower al. 1995a, 1995b; Herrnstein et al. 1997b). It is interesting to Ñuxes. There is, in fact, an independent piece of evidence note in this connection that the latter features also exhibit that indicates that the high-velocity maser emission zone in strong variability (including a factor of D10 Ñares lasting on the order of 1 month; Greenhill et al. 1997c) that could 2 The height of the velocity-coherence box is determined by such factors potentially arise from similar clump alignment e†ects (see as the vertical acceleration of the emitting gas, the thickness of the layer in which optimal masing conditions prevail, and the telescope beamwidth. In ° 2.2), although variability in the central radio continuum the models discussed in this paper, the relevant factor typically turns out to source may also be relevant in this case (e.g., Herrnstein et be the beamwidth([0.5 mas). al. 1997a). 184 KARTJE, KO NIGL, & ELITZUR Vol. 513

2.2. Flux from Masing Clouds For self-consistency,smin is required to be\2lcoh (eq. We now consider the maser emission from individual [7]). This condition appears to be satisÐed in NGC 4258, clouds that have a Keplerian disklike distribution. We start where (usingD B 0.64, a B 1, andF B 10 in eq. [14] 10 \10 0.1 with the case of saturated masers and then address the and evaluating eq. [7] at r 0.21 pc),smin/lcoh B 1.4, as well unsaturated ones at the end of this subsection. As discussed, as in NGC 1068, where (with D B 1.5, a B 1, F B 4, \ 10 10 0.1 for example, by EHM92, strongly ampliÐed masers have a and r 0.88 pc)smin/lcoh B 0.27. The fact that the estimated high degree of beaming and therefore have a Ðlamentary value ofsmin turns out not to be much smaller than the appearance. This is true even for spherical masers, whose maximum value oflcoh suggests that there is a strong obser- observed transverse sizes are signiÐcantly smaller than their vational bias for detecting high-velocity megamaser features radii on account of ampliÐcation-bounded beaming. Cylin- in Seyfert 2Èlike galaxies. In these AGNs the disk rotation drical masers, on the other hand, are matter bounded, so axis is nearly perpendicular to the line of sight and the their observed radii are the same as their projected physical corresponding value oflcoh is large: by contrast, AGNs sizes. For the sake of simplicity we consider in what follows with disks that are viewed at smaller angles to the axis have \ a comparatively low probability of overlap for masing cylindrical masers of radiusRc and half-length lc aRc, although it should be borne in mind that the actual physical clouds that satisfy the velocity-coherence constraints. Note dimensions of the masing clouds could be characterized by that, if cloud ““ stretching ÏÏ is tied to the velocity shear in the smaller aspect ratios. Real clouds in a di†erentially rotating disk, then a large inclination angle would also be favored by disk would probably be elongated at least to some degree in the dependence of the Ñux on the Ðlament aspect ratio a. the azimuthal direction and hence may be better represent- One can show that masing clouds with typical param- ed by cylinders than by spheres. eters that are even moderately elongated are likely to be Focusing on the high-velocity maser features, which we saturated. The saturation condition for a cylindrical maser represent as Ðlaments viewed end-on, the Ñux from an indi- can be written as vidual cloud is given by exp [ai0 Rc] F B 5.0 ] 10~6D~2 R2 a3 Jy (10) \ 4Jc , (15) c 10 c13 10 a \ (see eq. [3]), where we setD10 (D/10 Mpc). This value is much smaller than the Ñux(F Z 0.1 Jy) typically measured wherei0 is the unsaturated line center absorption coeffi- from the bright high-velocity maser features in AGNs. cient (EMH91). When all parameters except for a are Ðxed, However, if two cloud emission regions that lie within the this relation determinesasat, the minimum aspect ratio for velocity-coherence box overlap along the line of sight, the saturation. As an illustration, when the masing gas is char- Ñux from the background cloud can be strongly ampliÐed acterized by a hydrogen number density of 109 cm~3,tem- by the foreground emission region (Deguchi & Watson perature of 400 K, maser line width of 1 km s~1, and 1989; EMH91). The e†ective brightness temperature T fractional water abundance of 10~5, then i R \ b,eff \ 0 c for two overlapping masers that are separated by a distance 0.8, 1.2, 2.7, and 3.7 forRc13 0.5, 1, 5, and 10, respectively. The solutions of equation (15) are then a B 12.9,8.0,3.0, s, each characterized by a brightness temperatureTb and sat aspect ratio a,is and 2.2, respectively, where we setc \ 1. The correspond- 5 ~4 2 2 ~1 ing values for a fractional water abundance of 10 are 16 A s B C ] A s B D i R \ 2.7,3.7,6.1, and 7.2 anda B 3.0,2.2,1.2, and 1.0, Tb,eff B 1 Tb , (11) 0 c sat 11 aRc di respectively. (Note that, in order to be considered Ðlamen- where tary, the maser must satisfya ? max M1, i0 Rc/4N; EMH91.) For comparison, a spherical maser of radiusR saturates d \ 1018a2 c1@2R cm (12) \ c i 10 5 c13 wheni0 Rc B 7.5 (assuming againc5 1), at which point it is the interaction distance, expressed in terms of the ratio appears as a cylinder with an e†ective aspect ratio of D2.9 \ 5 (see EHM92). These results indicate that masing clouds that c 10 c5 of the maser saturation intensity to the unsatu- rated source function (EMH91; see also Elitzur 1992). The are at least somewhat elongated and havei0 Rc-values of corresponding Ñux is given by the order of a few would be saturated. In a source like NGC 4258 one can use information on ] ~2 ~2 2 ] ~4 2 ~2 ~1 F B 7.3 10 a10 D10 s16(1 10 s16 di18) Jy , (13) the systemic masers to help assess whether the saturation \ 16 \ 18 condition on the high-velocity features is satisÐed. Based on where we puts16 (s/10 cm) anddi18 (di/10 cm). the location of the systemic masers relative to the nuclear Note the interesting result that, in the limits > di, the self- ampliÐed Ñux is independent of the cloud size (depending radio jet and on the apparent correlation between the jet on the cloud dimensions only through the aspect ratio a) continuum and maser Ñux densities, it has been inferred and is determined primarily by the line-of-sight separation that the systemic maser features in this object act as ampli- between the clouds (F P s2). It is seen that even two such Ðers of the background radio continuum (e.g., Herrnstein et clouds could, in principle, account for the entire measured al. 1997a). On the assumption that each such feature is \ produced by the same type of Ðlamentary clouds that give ÑuxF 0.1F0.1 Jy of a maser feature if they were separated by a distance greater than rise to the high-velocity emission (except that they are now viewed at a right angle to their axes), the brightness tem- s B 1.2 ] 1016F1@2 D a~1@2 cm (14) min 0.1 10 10 perature of the systemic masers is found to be Tb,sys B 2.6 along the line of sight (expression valid fors > d ). The ] 1015(F/2Jy)(a/2)~1(R /5 ] 1013 cm)~2 K. Setting min i \ c 8 value ofsmin would be larger if the cloud emission regions Tb,sys exp (qsys,tot)Tb,cont, whereTb,cont ([10 K; Greenhill overlapped only partially. On the other hand, the value of et al. 1995b; Herrnstein et al. 1998a) is the brightness tem- smin could be smaller if more than one interacting pair of perature of the ampliÐed background continuum, we masing clouds contributed to the observed Ñux. deduce that the total optical depthqsys,tot of the systemic No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 185 masers is D17.1. If the maximum systemic maser Ñux is maser emission might too. The motion of individual clouds produced by two fully overlapping clouds then it follows into or out of alignment along the line of sight (see ° 2.1) thati0 Rc Bqsys,tot/4 B 4.27. Now, the total optical depth could then also explain some of the strong Ñux variability q for the high-velocity masers is given in terms of the exhibited by the systemic masers (e.g., Greenhill et al. hi,tot ] 15 maser brightness temperature Tb,hiB 1.6 10 (F/0.5 1997c). We address additional aspects of the systemic Jy)(R /5 ] 1013 cm)~2 K and the excitation temperature masers in ° 4. c 2 Tx B 10 K (e.g., Elitzur 1992) by qhi,tot B ln (Tb,hi/Tx). MASING CONDITIONS Attributing the high-velocity emission to two overlapping 3. Ðlaments viewed end-on, we obtain for the above Ðducial Optimal emission in the616 È523 22 GHz maser tran- valuesai R B 7.6, which, when combined with the sys- sition from collisionally pumped water molecules is 0 c 8 9 temic masers result, implies a B 1.78. This value is just shy achieved for hydrogen nuclei densities of nH D 10 È10 of the saturation aspect ratioa B 1.81 obtained from cm~3, temperatures ofT Z 250 K, and fractional water \ sat ~5 ~4 equation (15) for i0 Rc 4.27. abundancesx(H2 O) 4 n(H2 O)/nH D 10 È10 (e.g., From the above estimate we conclude that the saturation Elitzur 1992). We note in passing that the required densities assumption for the high-velocity masers in a source like fall within the inferred characteristic range in BELR clouds NGC 4258 is probably valid, although it might be only (e.g., Baldwin et al. 1995). Neufeld et al. (1994) showed that marginally so in clouds with large values ofRc. (Recall in these conditions are attained in a dusty gas of density nH Z this connection that an upper bound onR is provided by 108 cm~3 that is irradiated by a typical AGN X-ray spec- c 23 ~2 the half-widthwcoh of the velocity-coherence box, given by trum if the column densityNH exceeds D10 cm (see eq. [6].) Our interpretation of the high-velocity features in also Pier & Voit 1995; Wallin & Watson 1997). The thermal terms of two overlapping Ðlaments would not fundamen- structure of a photoionized, optically thin medium is in tally change even if the Ðlaments were unsaturated. In that general determined by the ionization parameter $ 4 \ case the brightness temperature of each individual Ðlament Fion/pc, whereFion is the local ionizing Ñux and p nH kT 12 3 2 would drop fromD10 a10 K toD10 exp (2ai0 Rc) K, (with k being BoltzmannÏs constant) is the gas thermal pres- but the self-ampliÐcation factor would increase from the sure (modulo a molecular weight factor). In the case of a value given by equation (11) toDexp (2ai0 Rc), resulting in dusty, molecular gas, which absorbs the low-energy ionizing the same Ðnal brightness temperatureTb,hi. [Note that the photons up to an energy that depends on the magnitude of two masers would remain unsaturated only if the condition the column density, one can construct an e†ective ioniza- 2 2 (nRc/4ns ) exp (2ai0 Rc) [ 1 is satisÐed, which would be tion parameter that explicitly accounts for the attenuation the case only if the cloud separation s is not too large.] Even of the incident ionizing ÑuxFion,0 and that can be approx- though the ampliÐcation factor in the unsaturated case no imated by$eff B Fion,0/NH pc (Maloney, Hollenbach, & longer depends on s (in contrast with eq. [11]), the argu- Tielens 1996b). Neufeld et al. (1994) identiÐed the maximum ment that high-velocity maser features should be seen only value of$eff where a stable molecular phase Ðrst appears, at large inclination angles to the disk rotation axis still and Neufeld & Maloney (1995), in turn, used this value to applies since a comparatively large value oflcoh is still obtain the minimum pressure that is required (given Fion,0 required to attain a measurable probability of cloud andNH) for the gas in an irradiated disk to be molecular. In overlap. the models considered in this paper it is more convenient to If the systemic maser emission in a source like NGC 4258 inquire about the minimum shielding column,Nmin, that arises in two or more overlapping clumps that amplify the must be present for given irradiating Ñux and gas pressure background continuum, then their detection probability in order for the gas to be molecular. To derive the gas would also be maximized at large inclination angles. The thermal properties in our particular applications we employ coherence half-length near the center line of a Keplerian the photoionization code CLOUDY (Ferland 1996) and disk viewed along its plane can exceed the midline value (eq. compute the run of temperature and water abundance as a [7]) if the emission originates sufficiently close to the center function of depth into a slab of given (uniform) density that line. Exactly along the center line all points have the same is irradiated by an external continuum Ñux and is shielded \ line-of-sight speed(vlos 0), whereas for a masing parcel at by a dusty gas of column densityNshield. The grain and a radius r where*v [ vlos [ vK/2 (withvK denoting the elemental abundances are taken to be those of the local Keplerian rotation speed) the coherence half-length is ISM. Figure 1 shows the run ofNmin obtained in this way as D(*v/3vlos)r (which di†ers slightly from the expression in a function of p/k for clouds (of hydrogen nuclei density nc MM98); these values may be reduced if the disk plane is and temperatureTc)H that are located in the2O maser tilted with respect to the line of sight. Since the coherence emission regions in NGC 1068 and NGC 4258. For NGC length is maximized along the center line, one would expect 1068 we adopt the spectrum given by Pier et al. (1994) with ] 44 ~1 \ the systemic maser emission to peak there; in fact, the maser L bol B 4 10 ergs s and set r 1 pc, whereas for NGC spectrum in NGC 4258 exhibits a dip atv \ 0, which is 4258 we use the spectral information from Wilkes et al. los 42 most naturally attributed to absorption outside the emis- (1995) and Chary & Becklin (1997) and setL bol B 10 ergs sion region (Watson & Wallin 1994; MM98; see ° 4). The s~1 and r \ 0.25 pc. Approximate polynomial Ðts to the systemic maser emission is thus maximized on either side of functionNmin(p) for these two cases are given in the caption the center line, where the velocity-coherence length along to Figure 1. SinceTc is determined by the value of the the line of sight from the emission point does not reach all ionization parameter,Nmin can be regarded as being just a the way into the absorption region. For these features the function of nc. line-of-sight coherence length may still be comparable to, or Molecular gas in an AGN can remain dusty beyond the even exceed, the value associated with the high-velocity dust sublimation radiusrsub, deÐned as the distance interior masers. Hence, if the high-velocity maser emission orig- to which dust grains exposed to the ambient radiation Ðeld inates in overlapping clouds, at least part of the systemic are evaporated. The primary signiÐcance of dust to AGN 186 KARTJE, KO NIGL, & ELITZUR Vol. 513

perature remains below 250 K and the water level popu- lation inversion required for maser emission does not occur. We propose that, in the context of clumpy disk models, this condition (rather than the transition from molecular to atomic gas invoked in the homogeneous disk model of Neufeld & Maloney 1995) determines the outermost radius rout of the maser emission region. SpeciÐcally, for a given incident continuum spectrum, the condition T B 250Kat the upstream edge of a cloud determines the magnitude of the intervening column density, which we denote by Nmax. For a given gas distribution, this value, in turn, Ðxes rout. Since the temperature is tied to the value of the e†ective ionization parameter$eff, which depends on the gas density,N is a function ofn (and, likeN , scales max~1 c min roughly as nc ). Clouds located at radiir \ rout have temperatures T [ 250 K, so their water molecules are collisionally FIG. 1.ÈMinimum shielding column density of dusty gas that is pumped. Adopting again the Ðlamentary geometry intro- required for photoionized clouds to be molecular, as a function of the duced in ° 2.1, the maser efficiency in these clouds can be \ reduced pressurep/k nH T of the irradiated clouds. The two curves corre- parameterized in terms of the e†ective emission measure spond to clouds that are located at a distance of 1 and 0.25 pc from the ] 44 ~1 central continuum source in NGC 1068(L bol B 4 10 ergs s ) and m \ 0.2x (H O)n2 R /*v , (16) NGC 4258(L B 1042 ergs s~1), respectively. Fitting these curves by an ~5 2 c9 c13 5 bol \ ] ] 2 \ \ ~5 \ 9 ~3 expression of the formlog Nmin c1 c2 x c3 x , where x log (p/k), wherex~5(H2O) x(H2O)/10 , nc9 (nc/10 cm ), and \ [ [ \ 5 ~1 one Ðnds Mc1, c2, c3N M47.10, 3.29, 0.10N and M14.46, 1.99, 0.12N for *v5 (*v/10 cm s ) (Elitzur, Hollenbach, & McKee NGC 1068 and NGC 4258, respectively. 1989, hereafter EHM89). Optimal masing conditions obtain for1 [ m [ 100. Form Z 100, the (dusty) cloud column maser emission is that, by absorbing UV and soft X-ray densityD1023m*v /(x n ) cm~2 becomes too large for T photons from the central continuum, it lowers the ioniza- 5 ~5 c9 to remain above D250 K.4 tion state and hence the temperature of the gas so that water molecules can survive (or form) at distances from the 4. MASING RINGS center where the gas would otherwise be hot and atomic. In In this section we incorporate the masing conditions the presence of a sufficiently large shielding column the derived in ° 3 into a set of self-consistency constraints for a temperature drops below T B 1500 K and the gas remains minimalist model of an irradiated disk, and we demonstrate (or becomes) molecular (see, e.g., Fig. 1 in Neufeld et al. that this model can account for theH O maser obser- 1994). At this temperatureH is efficiently produced by the 2 ~] ] ] 2 vations in a source like NGC 1068. A schematic illustration reactionH H H2 e, which permits water formation of the envisioned scenario is given in Figure 2. We consider via the reaction networkO ] H ] OH ] H; OH ] ] ] 2 a planar ring of inner radiusrin that surrounds the central H2 H2O H. Therefore, even if the water abundance continuum source. The ring is composed of dusty molecular in the disk were initially low, it could become comparatively ~5 clumps and possibly also of a dusty interclump medium, but high[x(H2O) Z 10 ] after it gets exposed to the (shielded) the total column density through the disk is assumed to be central continuum. The magnitude of the sublimation sufficiently low that the ionizing radiation can reach the radius depends on the detailed spectral energy distribution 1@2 masing clouds through the plane of the ring. For simplicity, and scales with the source bolometric luminosity asL bol . Its we consider a collection of identical cylindrical clouds of precise value also depends on the grain composition and densitync, radiusRc, and aspect ratio a B 10, whose axes size distribution (e.g., Laor & Draine 1993). Using the same are roughly perpendicular to the radius vectors from the prescription as in KK94 (see their Appendix B), we infer 5 ] 44 ~1 1@2 center. We further assume that the clouds are distributed rsub B 0.23(L bol/4 10 ergs s ) pc in NGC 1068 and uniformly throughout the disk. Focusing attention on the r B 0.015(L /1042 ergs s~1)1@2 pc in NGC 4258. In a sub bol 44 ~1 1@2 high-velocity features, which we interpret in terms of over- similar manner we deducersub B 0.15(L bol/10 ergs s ) lapping clouds (see ° 2), we derive an approximate estimate pc in NGC 4945 (using the spectral information in Iwasawa ] 44 ~1 1@2 of the minimum number density of cloudsNc,min that is et al. 1993) andrsub B 0.25(L bol/3 10 ergs s ) pc in NGC 3079 (using the scaled nuclear bolometric luminosity 4 In the case of a dust-free gas, a similar upper limit on the optical depth from Hawarden et al. 1995 together with the inferred spec- is commonly attributed to the fact that, form Z 100, the maser quenches tral shape of NGC 4258). If the maser emission is excited by because of infrared photon trapping that tends to thermalize the level populations (EHM89). However, in the case of a dusty gas, Collison & continuum irradiation thenrsub should not exceed the inner radiusr of the maser emission region: the observed values Watson (1995; see also Wallin & Watson 1997) have shown that, if the in grain and gas temperatures di†er by more than D10 K, the pumping is no ofrin (see ° 1) evidently satisfy this inequality for the above longer quenched but instead remains constant with increasing optical sources.3 depth. Although this condition is generally satisÐed for the clouds that we When the column density of dusty gas that shields the model in this paper, mB100 is still the relevant upper limit because of the continuum source becomes large enough, the cloud tem- temperature constraint mentioned in the text. In any case, the clouds in the scenarios that we explore are sufficiently small that their individual column densities do not even approach this upper limit. 3 The possible relevance of the dust sublimation radius to the location 5 A more physical characterization of the clouds would have been in of the inner boundary of the maser emission region was already pointed terms of their pressure p rather thannc (see Neufeld et al. 1994), but for the out by Greenhill et al. (1996) in their discussion of the NGC 1068 VLBI narrow range in temperatures that is of interest to us the distinction is not imaging data. signiÐcant. No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 187

FIG. 2.ÈSchematic diagram of a clumped ring that orbits a black hole in an AGN. In an attempt to mimic the inferred conditions in NGC 1068, the ring plane is shown tilted at an angle of 45¡ with respect to the equatorial plane, whereas the radio jet axis is depicted as being normal to that plane. For a similar reason, the ratio of the disk width to its inner radius was taken as*r/rin B 0.6. The ring rotation axis is shown at an inclination of 80¡ with respect to the line of sight. The gas in the ring is assumed to be dusty (consistent with the fact that the dust sublimation radius lies interior torin) and to be composed of cold, dense clumps and possibly also a warm, more tenuous interclump medium. In the case of NGC 1068 there is evidence for ionized gas that produces free-free radio emission withinrin. This emission (which may in part originate in the inner rim of the ring) could be ampliÐed into maser radiation by clumps located nearrin. High-velocity maser features may be associated with self-amplifying clumps situated along the ring midline. required for our line of sight through the disk plane to nateRc from this expression by Ðxing the e†ective maser intercept, on the average, two overlapping clouds within a emission measure (eq. [16]) at mB1, the minimum value for 2 velocity-coherence length, by setting Nc,min B 1/nRc lcoh. efficient masing (EHM89). Then Substituting from equation (7), we obtain \ ~2 Rc13 5m*v5 x~5(H2 O)nc9 , (19) N B 1.2 ] 1013(*v/10~3v )~1@2R~2 r~1 pc~3 . (17) c,min los c13 0.1 \ 7 and, for a ring around a black hole of mass Mbh 10 M7 It is noteworthy that this Ðducial value of the cloud space M_, density, which is applicable to any scenario that interprets ] 23 1@4 ~1@4 1@2 the high-velocity maser features in terms of overlapping Ncent B 1.6 10 mM7 r0.1 *v5 clumps, is consistent with independent estimates for BELR ] (*r/0.5r)x~1(H O)n~1 a~1 cm~2 . (20) clouds in typical AGNs (e.g., Arav et al. 1997, 1998). ~5 2 c9 10 The minimum cloud space density given by equation (17) We now combine the constraints given by the values of corresponds to a cloud volume Ðlling factor Nmin, Nmax, andNcent. Using the parameters of NGC 1068 as an example, we choose a radius nearr (r \ 1 pc) and f B (2R /al ) out V,min c coh plot these three column densities in anNshield versus x(H2O) ] ~4 ~3 ~1@2 ~1 ~1 diagram (Fig. 3). The curves are labeled by the chosen cloud B 2.5 10 (*v/10 vlos) a10 r0.1 Rc13 (18) densities. For any particular value ofnc, we focus on the and a cloud contribution to the mean gas density in the disk portion of the oblique(Ncent) line that lies between the cor- ofSncTBfV,min nc. Since the radial extent of the masing ring responding horizontal(Nmin andNmax) lines. This segment is typically?lcoh, one expects the clumped disk component of theNcent(nc) curve corresponds to a certain range of water to provide a nonnegligible shielding column in the direction abundancesx(H O). Over that range, dusty clouds located 2 \ of the central continuum. For a cloud located at a distance betweenrin B 0.65 pc and r 1 pc can provide sufficient \ [ *r r rin from the ringÏs inner edge, the shielding shielding of the central continuum to render the cloud at column of intervening clumps can be approximated by r \ 1 pc molecular, but not so much shielding that the 1@2 Ncent BSncT*r B (6vlos/*v) (*r/r)nc Rc/a. We can elimi- cloudÏs temperature drops below D250 K. Since we chose a 188 KARTJE, KO NIGL, & ELITZUR Vol. 513

FIG. 3.ÈPhase-space diagram in the shielding column vs. fractional H2O abundance plane of the minimalist irradiated ring model for NGC 1068. The dusty gas column densitiesNmin, Nmax, andNcent correspond, respectively, to the minimum shielding that is required for a cloud to be molecular (see Fig. 1), the maximum shielding that allows the temperature of a cloud to exceed D250 K so that collisional pumping can operate (which, in turn, determines the outer maser radiusrout), and the shielding of the central continuum by intervening clouds (see eq. [20]). All these columns depend on the cloud densitync and were calculated for a cloud located at r \ 1 pc. In order for the model to be self-consistent, the water abundance must be such thatNcent for the given cloud density lies between the corresponding values ofNmin andNmax. To guarantee that the ring is not dispersed by radiation pressure on the dusty gas,Nmax should not be much smaller thanNrad (eq. [21]).

FIG. 4.ÈFractional water abundance (top panel) and gas temperature radius nearr , we expect the cloud temperature to be \ 14 max (bottom panel) as a function of distanced 10 d14 cm into a dusty, close to 250 K; the total shielding column must therefore be uniform-density slab that is irradiated by the nuclear continuum of NGC close toN , but ifN is lower thanN one can attrib- 1068 (assumed to be unattenuated before it reaches the slab) at a distance max cent max of 1 pc from the center. The curves are labeled by the value of the slab ute the di†erence to the presence of an intercloud medium. \ 9 ~3 densitynH 10 n9 cm and terminate at the point where the tem- Since the requirement of a sufficiently high maser efficiency perature declines to 250 K. has already been incorporated into the expression for Ncent, the indicated range would represent a self-consistent masing ring model if the required water abundance could be dusty gas that would prevent the ring from being dispersed attained. by the radiation pressure force exerted by the central con- Figure 4 shows the water abundance and temperature as tinuum. Since the e†ective Eddington luminosity for dust a function of the distance d from the irradiated surface of a opacity isL B 1042 M ergs s~1 (e.g., KK94), and since dusty slab that is placed at the adopted Ðducial distance crit 7 the bulk of the continuum radiation is absorbed within a (r \ 1 pc) from the center of NGC 1068.6 This Ðgure dusty column of D1021 cm~2, we estimate demonstrates that abundances as high asx~5(H2O) B 1 are 23 44 ~1 ~1 ~2 attained in the irradiated clouds (consistent with the values Nrad B 10 (L bol/10 ergs s )M7 cm . (21) shown in Fig. 1 of Neufeld et al. 1994; note that Fig. 2 in that paper indicates signiÐcantly higher abundances, which The value ofNrad for NGC 1068 is indicated in Figure 3 by we, however, were unable to reproduce). In conjunction the heavy dashed line. If the typical cloud densities are with Figure 3, these results imply that essentially any cloud nc9 [ 0.5, thenNmax Z Nrad and the gas in the maser emis- density that lies in the optimal masing range could be sion region can withstand ejection by the radiation pressure accommodated by a ring model that satisÐes the indicated force. We note from equations (6) and (19) that the condi- tionR \ w implies, forx (H O) [ 1 andm Z 1, that a constraints. In particular, the requirement Ncent[nc, c \coh ~5 2 x(H O)] \ N (n ) is evidently satisÐed for x (H O) B 1 cloud at r 1 pc in this source must have nc9 [ 0.07. 2 max c ~5 2 Clouds withn B 0.5 would haveR B 2 ] 1014 cm and, irrespective of the value ofnc. (The insensitivity to the cloud c9 c \ density can be understood from the fact thatN and N even with a B 10, would still satisfy lc aRc > lcoh max cent (B2 ] 1017 cm). In any case, we expect the disk to also have a similar dependence on nc.) With all other parameters being equal, lower density contain nonmasing gas and therefore to have an even greater inertia against radiative acceleration. One indica- clouds give rise to a higher shielding columnNcent to the center. In a high-luminosity source like NGC 1068, a rele- tion of the presence of nonmasing gas in masing AGN disks vant additional constraint is the minimum columnN of is provided by the appearance of an absorption trough at rad the systemic velocity in the maser spectra of sources like NGC 4258 (see ° 2.2). In the current model, this absorption 6 Note that dust-reprocessed radiation emitted within the slab is can arise in irradiated gas beyondr , whose temperature included in the calculation of the gas thermal structure. The contribution out of this component is, however, expected to be reduced in a realistic clumpy lies in the range D100È250 K. In the case of NGC 1068 it disk. The opposite limit, in which the dust-reprocessed radiation is appears, making a rough extrapolation of the curves in neglected altogether, was adopted in the derivation ofNmax in ° 3. Figure 4, that an absorbing columnZNrad could be main- No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 189 tained at such temperatures even if the typical cloud den- between NGC 1068 and the Milky Way is that the former sities are such that the total columnNmax(nc) in the masing appears to have a large reservoir of gas (which could be the region remains smaller thanNrad. The absorption optical source of fuel to the central engine) in the inner spiral arms, depth is maximized at T B 200 K, and, for that temperature whereas in our own galaxy there is a relative paucity of gas and*v5 B 1, it is given by on similar scales. The origin of the Galactic CND is still an open question, q B ] ~25x N absorb 5.9 10 ~5(H2O) absorb , (22) and if similar structures indeed manifest themselves as whereN is the absorbing hydrogen nuclei column (e.g., extragalactic megamaser disks, then its resolution could absorb ] 23 ~2 MM98). By settingNabsorb Z Nrad (B2.4 10 cm for provide important clues to the nature of accretion in AGNs NGC 1068) and adoptingx~5(H2O) B 1, we infer from (see ° 6). One of the key issues is the presence of a well- equation (22) a systemic velocity Ñux reduction factor Z1.2, deÐned inner edge at such a comparatively large distance which seems to be consistent with the data (see, e.g., Fig. 1 from the center; interestingly, the existence of such an edge in Greenhill et al. 1996). Note, however, that the extent to has been indicated also in theH2O maser distributions of which the observerÏs line of sight to the center intersects the NGC 1068 and NGC 4258. If the inÑowing gas in the disk is r Z rmax absorbing region in any given source depends on broken up into distinct clumps as it approachesrin, then the the disk geometry and the viewing angle. accretion efficiency could conceivably decrease at lower The properties of the masing ring in NGC 1068 that are radii, providing at least a partial explanation for the implied by this interpretation bear a remarkable resem- occurrence of an ““ edge ÏÏ at that location. However, it blance to the inferred characteristics of the CND in the appears that mass leaves the inner edge of the CND in the Galactic center. In NGC 1068, adoptingn B 0.5 as a form of ““ streamers ÏÏ at about the same rate as it is inferred c9] ~4 typical cloud density, we deducefV,min B 3 10 (eq. to Ñow through the disk (Jackson et al. 1993). It has been [18]) and a lower limit on the mass (considering only the suggested that the presence of clumps and the large mea- masing gas betweenr andr and adopting a disk half- sured velocity dispersion in the CND can be attributed to in ]out 3 thickness of D0.1r)ofD4 10 M_. Just like the NGC tidal disruption (e.g., Genzel et al. 1994). The Roche critical 1068 maser emission region, the Galactic CND has the density, given (for an assumed molecular weight of 2.33) by appearance of a ring with a sharp inner edge (located at a ] 11 ~3 ~3 nH,crit B 3.5 10 M7 r0.1 cm , (23) comparable distance from the center,rin B 1.5 pc; the outer radius of the CND has been inferred to beZ7 pc): it is is D2 ] 109 cm~3 at the inner edge of the maser ring in inclined with respect to the galactic plane (by D20¡È25¡) NGC 1068. Ifnc exceeds this value then the masing clouds and is slightly warped (tilt angle varying in the range D10¡È in this object could withstand tidal disruption and might 25¡;GuŽ sten et al. 1987), and it exhibits a dominant circular therefore be relatively long lived. motion (which in the case of the CND corresponds to a The maser features that delineate the inner edge of the nearly uniform rotational speed of D110 km s~1) but with a disk in NGC 1068 likely amplify a background radio con- nonnegligible velocity dispersion. It also has a similar tinuum source, as has been inferred to be the case for the 4 inferred mass (D10 M_ within 4 pc) and an indicated systemic masers in NGC 4258 (see ° 2.2). In fact, Gallimore central black hole of comparable mass (within a factor of et al. (1997) obtained radio images of a parsec-scale disk in D6; see Genzel et al. 1997). It is particularly noteworthy NGC 1068 that they interpreted in terms of a hot, ionized that the CND appears to be highly clumped: HCN obser- gas at the inner edge of the nuclear disk. It is therefore vations (e.g., Jackson et al. 1993) have revealed that the bulk possible that the ring inner edge itself is the source of the of the material is characterized by hydrogen nuclei densities background radiation. It is interesting to note in this con- in the range D106È108 cm~3 and volume Ðlling factors nection that the Galactic CND also exhibits an ionized, D10~3È10~2, corresponding to mean densities in the range radio-emitting inner rim (e.g., Genzel et al. 1994). In fact, D104È105 cm~3, and by an area covering factor D0.1. In only part of the CNDÏs inner circumference (notably, the fact, there is no observational evidence for the presence of a so-called Western Arc) is manifested in this fashion, which substantial component of a low-density interclump medium has been attributed to absorption of the central ionizing in the CND. Also, in both cases, there is evidence of mass radiation in certain directions by infalling matter within the inÑow into the ring, which on larger (D102È103 pc) scales is central cavity (Jackson et al. 1993). A similar explanation associated with bar streaming (e.g., Helfer & Blitz 1995). In may perhaps be relevant to the fact that only one quadrant fact, as was Ðrst noticed by Greenhill & Gwinn (1997), the of the inner rim of the NGC 1068 ring has a measurable position angles of the maser ring axis and the nuclear CO maser Ñux. The conÐnement of the maser emission to the bar in NGC 1068 di†er by only D20¡. On the basis of these vicinity of the disk inner edge could reÑect the fact that the similarities one can surmise that the Galactic CND would background radiation is intercepted and absorbed within a appear as a water maser ring akin to that in NGC 1068 if it narrow radial range nearrin. It is nevertheless puzzling why had a comparably bright high-energy central continuum.7 one does not observe enhanced maser emission near the The high-luminosity nonthermal emission in NGC 1068, center line. In the case of a planar disk and a 90¡ viewing which is a signature of the currently active phase of its angle, both background and self-ampliÐcation by clouds are nucleus, is evidently powered by accretion into the center. expected to contribute to the Ñux near the systemic velocity As was pointed out by Helfer & Blitz (1995), the main di†er- on account of the comparatively large velocity-coherence ence in the circumnuclear molecular gas distribution length near the center line. (As noted above, the emission originating right along and in the immediate vicinity of the 7 center line would be subject to absorption by the non- Although oneH2O maser was detected near the inner edge of the CND (Levine et al. 1995), it appears to coincide with a luminous, reddened masing gas atr [ rout.) The absence of a Ñux peak near the star and is therefore likely to have a di†erent origin than the NGC 1068 systemic velocity may be due to the diskÏs departure from megamasers. planarity or velocity coherence or to the viewing angle 190 KARTJE, KO NIGL, & ELITZUR Vol. 513 being sufficiently smaller than 90¡. It is, however, also con- that in this case we use the inferred spectrum of NGC 4258 \ ceivable that the total shielding column through the disk is and set r 0.25 pc (which is close torout in this source). We large enough for all the ionizing continuum radiation to be do not plot the value ofNrad (eq. [21]) since radiation pres- absorbed nearr (see MM98). In that case a continuum- sure acceleration is not an issue in this low-luminosity in 42 ~1 irradiation excitation of the high-velocity features would (L bol B 10 ergs s ) object. We Ðnd that, as before, the require raising the masing gas above the midplane as orig- photoionization-induced water abundance does not rise inally envisioned by Neufeld & Maloney (1995). abovex~5(H2O) B 1 and that, for this value,Ncent(nc) is Before concluding our discussion of this scenario it is of signiÐcantly larger thanNmax(nc). In other words, for the interest to inquire whether the minimalist model that we minimum cloud space density (eq. [17]) required to explain considered for NGC 1068 could also be applied to NGC the high-velocity features in terms of overlapping maser 4258. Figures 5 and 6 are the analogs of Figures 3 and 4, clumps, the implied cloud self-shielding of the central con- respectively, and are based on the same assumptions, except tinuum is too high to allow the masing region to extend as far as it is observed to do. A possible resolution of the above difficulty is that ~5 x(H2 O) is, in fact, greater than D10 . One potential source of water in dusty clouds is the evaporation of icy mantles of grains that become exposed to the central radi- ation Ðeld and are heated to a temperature ofZ100 K. Ice could form on the surfaces of grains that are embedded in a cold, molecular disk through the hydrogenation of oxygen (Brown, Charnley, & Millar 1988). Infrared observations of star-forming regions in dense molecular clouds have revealed that D10% of the elemental oxygen is in water ice: ] ~5 in that casex(H2O) could be D6 10 (Ceccarelli, Hol- lenbach, & Tielens 1996). Brown et al. (1988) originally hypothesized that this mechanism could yield water abun- ] ~4 dances as high as D5 10 . Forx~5(H2O) B 6, Figure 5 indicates that a planar disk model could be self-consistent only fornc9 [ 1. For cloud densities of that order one can FIG. 5.ÈSame as Fig. 3, but for the continuum source parameters of infer from Figure 6 that the column of absorbing gas at \ NGC 4258 and r 0.25 pc. Because of the comparatively low luminosity r [ r would be[1024 cm~2, which, by equation (22) of this source, the shielding columnNrad (eq. [21]) is not a relevant con- max straint in this case. withx~5(H2 O) B 6, would yield a Ñux reduction factor D30. This is consistent with the systemic velocity value of D10 measured in this source. For mB1, x~5(H2O) B 6, andnc9 Z 1, the characteristic cloud radius would be rc13 [ 1 (eq. [19]). We conclude that if ice evaporation as invoked in collapsing protostellar envelope calculations is also a viable mechanism in molecular accretion Ñows in AGNs, then the minimalist planar ring model could, in principle, also apply to a source like NGC 4258. If the mantle evaporation mechanism is for some reason inappli- cable, then NGC 4258 might still represent a clumpy ring, but in order for the maser emission to be excited by contin- uum irradiation the maser clouds could not all lie in the same plane. 5. CLOUDS UPLIFTED BY A DISK-DRIVEN WIND In ° 4 we discussed irradiated clumpy rings and showed that, while they may adequately explain the maser distribu- tions in objects like NGC 1068 and perhaps even NGC 4258, certain aspects of the observations may be easier to interpret if the masing clouds are not strictly coplanar. Since the maser disks in both of these sources in fact appear to be slightly warped (a feature that they share also with the Galactic circumnuclear ring), one is led to examine plausible physical mechanisms that could give rise to a non- coplanar distribution of masing clouds. As we noted in ° 1, previously proposed warping scenarios were constructed for homogeneous disk models. Although these mechanisms would presumably remain applicable if the disk contained a turbulent velocity Ðeld, it is less clear how efficiently they would operate in a highly inhomogeneous disk with a dis- FIG. 6.ÈSame as Fig. 4, but for the continuum source parameters of tinct, lowÈÐlling-factor cloud component. In this section we NGC 4258 and r \ 0.25 pc. address the issue of a noncoplanar cloud distribution and No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 191 propose an alternative to the warped disk interpretation of KoŽ nigl 1997, 1999). A nominal estimate of the maximum continuum-irradiated megamaser sources. We suggest that cloud mass that can be ejected from the disk at a radius r the maser features represent diamagnetic molecular clouds may be obtained by balancing the wind ram pressure and that are uplifted from the surface of a circumnuclear accre- tidal gravitational forces (see eq. 25]). This gives tion disk by a dusty hydromagnetic wind. In this picture the 2 1@2 wind is driven centrifugally along rotating magnetic Ðeld Mc,max BnM0 w Rc/(GMbh r) lines that are anchored in the disk (Blandford & Payne \ 9.8 ] 1023M0 R2 M~1@2 r~1@2 g , (24) 1982). Dust from the outer, molecular regions of the disk is w,~3 c13 7 0.1 \ ~3 ~1 carried out with the gas and survives destruction by the whereM0 w 10 M0 w,~3 M_ yr is the mass outÑow rate intense central continuum along wind streamlines whose in the wind. The clouds can be assumed to be pressure footpoints in the disk lie beyond the dust sublimation conÐned by the wind magnetic Ðeld. The approximate cloud radiusrsub. KK94 showed that such a wind could produce trajectories under the joint action of the wind-cloud drag the obscuration of the central continuum source that has force and the gravitational Ðeld of the central mass can be been attributed to the phenomenological molecular obtained by solving the equation ““ torus ÏÏ that is inferred to surround the BELR of Seyfert 2 ¿ 2 galaxies (e.g., Antonucci 1993). The incorporation of clouds d c [GM ] nRc ow ¿ [¿ ¿ [¿ B 2 rü o w c o ( w c) , (25) into such a wind has previously been considered in the dt r Mc context of models of BELR clouds in Seyfert galaxies and ¿ ¿ QSOs (Emmering, Blandford, & Shlosman 1992; Bottor† et wherec, Mc, w, andow are the cloud velocity, cloud mass, al. 1997), EUV and X-ray absorption-line clouds in BL wind velocity, and wind mass density, respectively. We assume that the cloud density is determined by the local Lacertae objects(KoŽ nigl et al. 1995; Kartje et al. 1997), and P 2 broad absorption line QSOs (de Kool & Begelman 1995; wind magnetic Ðeld strengthBw (nc Bw for T nearly Kartje &KoŽ nigl 1997, 1999). Although in this paper we do constant). We further assume that the mass of each cloud does not change and that the clouds maintain a roughly not speciÐcally address the origin of the clouds, the internal P ~2@3 densities and space densities of the masing clumps that we spherical shape (i.e., Rc Bw ). model are consistent with the parameters inferred for BELR In view of the minimum shielding required for keeping clouds (e.g., Baldwin et al. 1995; Arav et al. 1997, 1998). the clouds molecular (see Fig. 1), the masing clumps must be located atr [ r behind a sufficiently large column of In applying the uplifted-cloud scenario toH2O mega- sub maser sources we show that the necessary shielding from dusty wind and uplifted clouds. The precise geometry and the high-energy central continuum photons can be provid- kinematic properties of the maser emission region depend ed for comparatively massive clouds that initially move on both on the cloud characteristics (sizes, masses, and ejection nearly circular trajectories close to the disk surface. Since radii) and on the dynamical properties of the wind. In par- the velocity Ðeld of these clouds is well approximated by the ticular, the wind mass outÑow rateM0 w is a key parameter. rotation law of the underlying disk, it follows from the con- In sources with a high value ofM0 w the dust shielding might siderations of ° 2 that this scenario can account for the be e†ective up to comparatively high latitudes and the pro- jected locus of efficient maser emission within the wind detection ofH2O maser features in Seyfert galaxies that are viewed at large angles to their symmetry axes. In this would take the form of a narrow strip (whose width picture the apparent warp in the maser distribution may increases with height above the disk) that extends along the result from an observational selection e†ect: a cloud uplift- innermost dusty streamline (see Fig. 7a). In this case the ed at a given radius would attain optimal masing conditions line-of-sight velocities of high-latitude maser features would at a height large enough that shielding by the dust in the be expected to drop with distance from the rotation axis in intervening wind and clouds is not too high, but not so a sub-Keplerian fashion even if the equatorial disk were large that the shielding column or the cloud density become Keplerian (see Fig. 7b). By contrast, in winds with a lower too low for efficient masing. Both the shielding column to mass outÑow rate, which are less e†ective at shielding the the center and the cloud density (which is determined by the central continuum, the projected locus of efficient masing conÐning ambient pressure) drop rapidly with height in cen- would be a narrow strip extending along (and right on top trifugally driven outÑows of the type that we envision. of) the disk surface (Fig. 7a). To ensure that their trajectories Therefore, for typical wind mass outÑow rates, the maser lie within the most highly shielded wind region close to the emission region would be conÐned to the immediate vicin- disk surface, the masing clouds in this case would need to be ity of the disk surface. Since the maser-shielding column in fairly heavy(Mc [ Mc,max ; see eq. [24]). The motions of this interpretation is directly related to the equivalent X- such relatively massive clouds would closely mirror the rayÈabsorbing hydrogen column density, both being associ- ambient velocity Ðeld near the disk surface, and hence, in the case of a Keplerian disk, their line-of-sight velocities ated with the disk-driven wind (see KK94), this model also P ~1@2 readily accounts for the inferred correlation between the would satisfyvlos r (Fig. 7b). The latter alternative is evidently the one that best describes the basic morphology probability of detectingH2O maser emission in a Seyfert galaxy and the magnitude of its X-rayÈabsorbing column and kinematics of theH2O masers in a source like NGC (Braatz et al. 1997). 4258. In light of the arguments presented in ° 2, wind- uplifted clouds that overlap along the line of sight could, in 5.1. Cloud Dynamics principle, account for the observed Ñux level and variability In our proposed picture, dense clouds fragmented from of the maser features in this source. the disk are uplifted by the wind ram pressure and trans- ported along the streamlines (with radiation pressure poss- 5.2. A Clumpy Disk-driven W ind Model ibly contributing to the acceleration once the clouds get To Ñesh out the above scenario we now incorporate the exposed to the central continuum source; see Kartje & dynamical constraints on the uplifted maser clouds into a 192 KARTJE, KO NIGL, & ELITZUR Vol. 513

(where the factor 0.6 accounts for the assumed composition). To make the model self-contained, we assume that the wind extracts most of the angular momentum of the accret- ed matter. This allows us to relate the magnetic Ðeld strength in the wind to the mass accretion rate M0 acc through the disk. Using the angular momentum conserva- 2 tion relation for a thin, equatorial disk, M0 acc vK/8nr B Bz o BÕ,s o /4n, (whereBz andBÕ,s are, respectively, the verti- cal component and the azimuthal surface component of the disk magnetic Ðeld), we obtain B2 M0 v w \ acc K , (27) 8n 16nbr2 \ 2 where the parameterb Bz o BÕ,s o /Bw depends on the detailed magnetic Ðeld conÐguration near the disk surface. In the cold, radially self-similar wind model of Blandford & Payne (1982), which has been employed in several of the applications cited at the beginning of this section, one can express b in terms of the self-similarity variables i (the normalized mass-to-Ñux ratio), j (the normalized total spe- ciÐc angular momentum), andm0@ (the radial-to-vertical Ðeld component ratio at the disk surface) as b \ i(j [ 1)/[i2(j [ 2] ] 2 1) (1 m0@ )]. This yields bB0.32 for the wind solu- tion used in Figure 7 (see Table 1 in KK94). We thus \ parameterize b 0.3b0.3. To complete the speciÐcation of the model we need to FIG. 7.È(a) Schematic diagram illustrating the expected regions of effi- relate the wind mass outÑow rate (which appears in eq. [24] cient maser emission from clouds embedded in accretion diskÈdriven forMc,max) to the disk mass accretion rate (which appears in hydromagnetic winds that are viewed orthogonally to the rotation axis. eq. [27]). We parameterizeM0 \ dM0 and choose d \ The light dashed curve indicates the dust sublimation surface in the wind, w acc 0.1 while the shading demarcates the masing zones: along the sublimation d/10 as a representative normalization factor. Using the surface for high-density winds and along the disk surface for lower density adopted Ðducial values of b, g, and d, and parameterizing \ winds. The heavy dashed curves show poloidal projections of representa- the temperature in the masing clouds byTc500 (Tc/500 K), tive cloud trajectories. Lighter clouds (of massMc [ Mc,max ; see eq. [24]) we can combine the above expressions to get tend to move along wind streamlines and rise to high altitudes, whereas heavier clouds(M Z M ) tend to move across wind streamlines and 2 c c,max 36nbg dkTc r remain close to the disk surface. The maser features in a source like NGC Rc B 4258 are evidently best modeled by a comparatively low density wind that 7GMbh mH gives rise to a narrow efficient masing strip near the disk surface. (b) Line- ] 13 2 ~1 of-sight velocity as a function of (cylindrical) radius for clouds moving in a B 1.4 10 b0.3 g10 d0.1 Tc500 r0.1 M7 cm . (28) disk-driven wind. The wind is assumed to be radially self-similar and is described by model A1 in KK94 (with a total mass outÑow rate of 0.03 M It is remarkable that the typical cloud radius obtained in ~1 \ ] 7 _ yr and a central massMbh 3.5 10 M_). The solid and dashed this fashion for a source like NGC 4258 agrees with the curves represent clouds with massesMc B 0.5Mc,max and Mc B 11Mc,max, value inferred from the requirements of efficient maser respectively. The latter curve adequately describes the nearly Keplerian pumping (see eq. [19]). If we explicitly impose the condition velocity Ðeld of the maser features in a source like NGC 4258. that the maser efficiency factor m (eq. [16]) beZ1, we can directly estimate the characteristic mass accretion rate through the disk, ] ~2 1@2 ~1@2 ~1@2 1@2 ““ generic ÏÏ model of a disk-driven hydromagnetic wind. As M0 acc B 2.7 10 b0.3 g10 d0.1 m we discussed in 5.1, the maser observations in an object ° ] *v1@2 x (H O)~1@2T 1@2 r3@2 M yr~1 . (29) like NGC 4258 are best described in the context of this 5 ~5 2 c500 0.1 _ \ picture in terms of clouds of masses Mc Interestingly, this value is compatible with the ADAF inter- 3 8 (4n/3)(1.4mH)Rc nc Z 10Mc,max (where the factor 1.4 pretation of the NGC 4258 spectrum (see ° 1). In conjunc- accounts for the assumed composition of molecular hydro- tion with equation (27) we then deduce gen with a 20% helium abundance). We thus parameterize \ \ B B 4.4 ] 10~2b~1@4 g~1@4 d~1@4 m1@4 Mc gMc,max, withg 10g10. Another relation between w 0.3 10 0.1 ] 1@4 ~1@4 1@4 1@4 ~1@2 the cloud and wind properties is provided by the pressure *v5 x~5(H2 O) T c500 M7 r0.1 G . (30) conÐnement condition. We assume that the clouds are dia- magnetic (i.e., that they are not penetrated by the ambient The toroidal Ðeld componento BÕ,s o would be smaller than magnetic Ðeld) and impose a balance between their internal this value; using again the Blandford & Payne (1982) (mostly thermal) pressure and the wind (mostly magnetic) pressure. This can be written as 8 As we show in Appendix A, if a centrifugally driven wind carries away B2 much of the disk angular momentum, then the ADAF interpretation can w B 0.6n kT , (26) also be compatible with the radiation-induced warping instability model 8n c c for this source. No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 193 similarity variables, we deduce o B o /B \ i(j [ 1)/[i2(j show that even two overlapping Ðlamentary clumps near [ 2] ] 2 1@2 Õ,s w 1) (1 m0@ )] , which for the wind solution used in the midline of a Keplerian disk that are separated from each Figure 7 is D0.55. Hence, at a distancer0.1 B 2 in NGC other (along the line of sight) by less than the velocity- 4258 (whereM7 B 3.5), a line-of-sight Ðeld component of coherence length can account, through self-ampliÐcation, D2 ] 10~2 G is predicted in the wind. This is lower than for the entire Ñux of a maser feature in sources like NGC the upper limit of 0.3 G inferred from circular polarization 1068 and NGC 4258. The observed Ñux variability can then measurements in the maser feature at that location be attributed to relative motions that bring the clumps into (Herrnstein et al. 1998b), although we note that, under our or out of alignment with each other along the line of sight. assumption of diamagnetic clouds, the magnetic Ðeld ampli- The clump overlap probability is maximized for edge-on tude in the masing clumps might in fact be lower than the viewing of the disk, especially in the case of saturated emis- estimate (eq. [30]) for the homogeneous outÑow com- sion (for which the minimum cloud separation that is ponent. required to account for the observed high-velocity maser As a self-consistency check, we evaluate the shielding Ñuxes can approach the coherence length); we point out column associated with the dusty wind itself. Assuming that that this could explain the strong observational bias in \ the wind is atomic and has a vertical speed vw,z sC(Tw), favor of detectingH2O maser emission in galaxies that are wheres \ 3s andC(T ) is the isothermal speed of sound observed at a large angle to the disk rotation axis. 3 w 4 corresponding to the wind temperatureTw B 10 K, and The interpretation ofH2O maser features in terms of approximatingM0 w B 2nr(1.4mH)vw,z NH,w, we infer a shield- aligned dense clumps has previously been proposed for ing column Galactic sources (Deguchi & Watson 1989; EMH91). One example is provided by W49N, the most luminous Galactic N B ] 22b1@2 g~1@2 d1@2 s~1m1@2 H,w 1.5 10 0.3 10 0.1 3 water maser source, whose brightest features have Ñuxes of ] 1@2 ~1@2 1@2 ~1@2 ~2 4 *v5 x~5(H2 O) r0.1(Tw/20Tc) cm . (31) a few times 10 Jy (e.g., Gwinn 1994). Interestingly, these Ñuxes are within about an order of magnitude of the peak Forr [ rout this value should not exceed the maximum Ñuxes of the high-velocity maser features in sources like shielding columnNmax for collisional pumping (see ° 3). By NGC 4258 and NGC 1068 when the distance is scaled from substituting the observed value ofrout in NGC 4258 and D11 kpc to D6 and D15 Mpc, respectively. Furthermore, using the Ðducial values of all the other parameters in equa- ] 22 ~2 the bright outbursts in W49N have been commonly attrib- tion (31), we obtainNH,w B 2.5 10 cm , which is uted to chance alignments of individual maser features (e.g., approximately equal to the value ofNmax shown in Figure 5 EMH91), and it has even been argued that they involve for the corresponding cloud density(nc9 B 2), assuming distinct clouds (Boboltz et al. 1998). All in all, NGC 4258 x~5(H2O) B 1 (see Fig. 6). This suggests that in this case the resembles maser outbursts in W49N both in terms of the interclump medium (i.e., the dusty wind) may provide most Ñux level and variability. Another example is provided by of the requisite shielding of the masing gas from the incident theH2O maser source in Orion, where polarization mea- high-energy radiation, whereas the clumped component surements of a strong Ñare have been interpreted in terms of (i.e., the uplifted clouds) mainly contributes the high-density aligned clumps in a rotating disk that is viewed edge-on gas that is needed for the collisional pumping of the masers. (e.g., Matveenko, Graham, & Diamond 1988; Abraham & All in all, even though a comprehensive dynamical calcu- Vilas Boas 1994). A similar disk interpretation has also been lation of a clumpy wind is evidently required to fully estab- proposed for other water maser sources associated with lish the applicability of this model, the results of our simple young stellar objects (e.g., Fiebig et al. 1996; Torrelles et al. analysis indicate that this is likely to be a viable explanation 1998). These examples suggest that the basic properties of of the maser distribution in a source like NGC 4258. extragalactic water megamaser sources may be quite similar SUMMARY AND DISCUSSION to those of their bright Galactic counterparts even if the 6. circumstances under which they arise are unique to the Water megamaser emission in AGNs is typically detected AGN environment. in Seyfert 2Èlike galaxies that are viewed at a large angle to In this paper we focus attention on a class of models that the symmetry axis. Recent VLBI-imaging observations of attributes the maser emission to heating by the central con- several of these sources reveal that the masers generally tinuum source. In order for water molecules to survive the appear as discrete features that lie in a thin disk of radius intense irradiation at the observed positions of the masers, r D 0.1È1 pc and radial extent*r [ r. Spectroscopic data shielding by a dusty medium of column density Nshield Z indicate that the masers rotate with a nearly Keplerian 1022È1023 cm~2 is required. Gas densities in the range velocity distribution, with high-velocity red- and blueshifted D108È1010 cm~3, with a temperatureZ250 K and a frac- satellite features appearing on either side of the projected tional water abundance D10~5È10~4, are also needed for disk diameter (the midline). The masers are believed to be optimal masing. In our interpretation of the megamaser pumped collisionally. disks we identify the outer radiusrout of the maser emission By comparing the maser-emitting volume that produces region with the shielding columnNmax above which the the satellite features in a source like NGC 1068 with the temperature drops below D250 K and collisional pumping maximum volume permitted by velocity-coherence con- of water molecules ceases. We incorporate the above con- siderations, and on the basis of the spectral and temporal straints into a minimalist scenario for AGN maser disks, in behavior of the maser Ñux in a source like NGC 4258, we which the disk represents a low-mass ring that consists of a argue that, independent of the exact maser excitation dominant cloud component and possibly also of a more mechanism, the emitting gas is likely clumped. The clumps tenuous intercloud medium. In the simplest representation could correspond to velocity irregularities in a turbulent of this model the radiation reaches the clouds through the medium, but in our speciÐc models we assume that the plane of the ring; we Ðnd that such a Ñat-disk model is maser features in fact represent distinct dense clouds. We consistent with the observations in NGC 1068 and may also 194 KARTJE, KO NIGL, & ELITZUR Vol. 513 be applicable to NGC 4258 if the water abundance exceeds providing much of the requisite shielding. The apparent (e.g., because of the evaporation of icy grain mantles) the warp may then represent an observational selection e†ect value determined by equilibrium photoionizationÈdriven induced by the strong vertical density stratiÐcation that chemistry. The required gas densities and space densities of characterizes centrifugally driven winds. We analyze the the clumps in this scenario are consistent with the values ingredients of a self-contained ““ generic ÏÏ model of a clumpy inferred for BELR-type clouds in AGNs. wind that transports the bulk of the angular momentum of We note the striking similarity between the ring proper- the underlying accretion disk. Using representative param- ties implied by this interpretation of the tilted maser ring in eters, we show that this model can yield optimal masing NGC 1068 and those attributed to the circumnuclear disk conditions in a source like NGC 4258. We also demonstrate (CND) in the Galactic center. Various suggestions have that the mass accretion rate implied by a hydromagnetic been considered for the origin of the CND and of its well- wind-driving disk model of this type is consistent with the deÐned inner edge (e.g., Jackson et al. 1993), and the study ADAF interpretation of the spectrum of this source (Lasota of analogous structures in AGN megamaser disks might et al. 1996). help resolve these issues. In the case of the CND there is The spiral shock model of Maoz & McKee (1998) pro- evidence for ongoing accretion through the disk at a rate of vides an alternative to the continuum-irradiation picture of ] ~2 ~1 D3 10 M_ yr , which is similar to the values megamaser disks. The shock scenario does not conÑict with inferred in some of the megamaser disks. Furthermore, in the discrete clumps interpretation presented in this paper the Galactic case it has been argued on the basis of several since the maser emission in the clumps could, in principle, dynamical considerations that the ring is a short-lived be excited by shocks. In fact, the relative motion of distinct (\105 yr) structure (e.g., Genzel et al. 1994). If a similar clumps is still the most natural explanation of the strong conclusion applies to the extragalactic megamaser rings Ñux variability exhibited by a source like NGC 4258. One then this could have important implications to our picture attractive feature of the spiral shock model is that it readily of how mass accumulates in the centers of AGNs. In partic- accounts for the apparent tendency of the redshifted high- ular, could it be that, on the scales of the maser emission velocity maser features in the existing sample of megamaser regions, most of the mass Ñows to the center through short- sources to dominate over the blueshifted ones. There are, lived, comparatively low-mass disks whose axes may be however, reported cases where the blueshifted features signiÐcantly tilted with respect to the local symmetry axis dominate (e.g., NGC 3079; Trotter et al. 1998), including a (as determined, for example, by the nuclear jet)? If most of case (NGC 5793) where the Ñux of a redshifted feature the mass in such disks is in the clumped component, as decreased from being twice as large as the blueshifted maser inferred in the CND and consistent with the above interpre- Ñux to below the detection threshold on a timescale of D1 tation of the megamaser disk in NGC 1068, how exactly is month (Hagiwara et al. 1997). In these instances it is likely the angular momentum of the inÑowing gas transported that the e†ects of cloud self-ampliÐcation, rather than the away? In a source like NGC 1068, does there also exist a geometry of any shocks that might be present, control the massive circumnuclear disk that is roughly perpendicular to appearance of the source. This conclusion is supported, in the inner radio jet axis, as has been inferred from various the case of NGC 3079, by the apparent fading and lighting other observations (e.g., Antonucci 1993; Gallimore et al. up of certain maser features between consecutive obser- 1996a, 1997; Tacconi et al. 1997)? If a distinct massive disk vations, and it remains valid even if the maser emission in indeed exists in this archetypal object, does it interact this source is excited by some other mechanical means (e.g., dynamically with the maser ring? Could the simultaneous by the impact of a misaligned jet on the disk, as proposed by presence of edge-on disks and tilted rings in Seyfert 2Èlike Trotter et al. 1998) rather than by spiral shocks. Further galaxies be relevant to the puzzling Ðnding of reprocessed insights into the excitation mechanism of theH2O mega- Ka lines in Seyfert 2 and narrow emission line galaxies masers might be provided by studies of other masing mol- (Turner et al. 1998)? Should the ring picture be found to ecules, such as OH. In fact, it is now becoming clear that at adequately describe the maser observations, then these and least some of the OH maser emission detected in extra- other related questions would need to be critically galactic sources is associated with the nuclei of active gal- addressed. axies (e.g., Trotter et al. 1997; Lonsdale et al. 1998), and in We also consider the case in which the disk is too massive some cases (e.g., NGC 1068; Gallimore et al. 1996b) it even to permit the central continuum radiation to reach the appears to originate in the same material that produces the masing clumps through its plane. The apparent warp seen water maser radiation. These studies may be expected to in the maser distributions of both NGC 4258 and NGC lead to a comprehensive model of the megamaser emission 1068 provides observational support for the notion that the in AGNs and could shed new light on the nature of the masing gas intercepts the incident radiation above the mid- associated disks. plane. We present a scenario that, unlike the homogeneous disk model of Neufeld & Maloney (1995), does not require the disk to be physically warped. Our proposed model is We thank G. Ferland for assistance with the use based on the hydromagnetic disk-driven wind scenario we of CLOUDY, R. Antonucci, R. Barvainis, G. Ciolek, had previously applied to the interpretation of the molecu- C. Gwinn, D. Hollenbach, J. Moran, T. Oka, and W. lar ““ tori ÏÏ in Seyfert 2Èlike galaxies and to other pheno- Watson for valuable conversations and correspondence, mena in AGNs (e.g., KK94; Kartje &KoŽ nigl 1997). In this and the anonymous referee for insightful comments. A. K. picture, the wind uplifts (by its ram pressure) and conÐnes also thanks T. Mazeh and H. Netzer for helpful discussions (by its magnetic pressure) dense, diamagnetic clouds that and hospitality at Tel Aviv University during part of this form near the disk surface. The maser emission originates in work. This research was supported in part by NASA grants the dense clouds once they become exposed to the central NAG5-2766 and NAG5-3687 (University of Chicago) and continuum radiation, with the dusty regions of the wind NAG5-3010 and NAG5-7031 (University of Kentucky). No. 1, 1999 MEGAMASER DISKS IN ACTIVE GALACTIC NUCLEI 195

APPENDIX A RADIATION-INDUCED WARPING INSTABILITY IN A HYDROMAGNETIC WIND-DRIVING ACCRETION DISK

In ° 5 we discuss a clumpy, accretion diskÈdriven hydromagnetic wind model for water megamaser sources. We show that, under the assumption that a signiÐcant fraction of the disk angular momentum is carried away by the wind, the implied mass accretion rate is consistent with that inferred from the ADAF interpretation of the spectrum in NGC 4258 (Lasota et al. 1996). In contrast, the irradiated viscous disk scenario considered by Neufeld & Maloney (1995) implies an accretion rate that is signiÐcantly smaller than the ADAF value. In this Appendix we point out that a similar wind-driving accretion disk model can also resolve the discrepancy between the ADAF interpretation and the radiation-induced warping instability scenario for the origin of the apparent warp in this source.9 One should, however, bear in mind that the warping instability model for homogeneous disks is clearly distinct from the uplifted-cloud interpretation of the apparent warp outlined in ° 5. In the radiative instability mechanism, Ðrst studied by Petterson (1977) and more recently elaborated on by Pringle (1996) and Maloney et al. (1996a), a disk illuminated by a central radiation source becomes unstable to warping if it is optically thick to both absorption and emission. The origin of the warp is the torque exerted locally on the disk by the reemitted radiation, which is directed normal to the disk surface (in contrast to the absorbed Ñux, which, being radial, produces no torque).10 The net torque on any given annulus of the disk is nonzero if the annulus is warped, and this would generally occur if there is a radial gradient in either the tilt angle or the angle of the line of nodes of the disk. Pringle (1996), using a local stability analysis, showed that the instability in a steadily accreting source is expected to arise at radii greater than \ 2 rwarp,min f(t/v) RS , (A1) \ \ 2 \ 2 wheret l2/l1 is the ratio of the e†ective (r, z) and (r, /) viscosities,v L bol/M0 acc c is the radiative efficiency, RS 2GM/c is the Schwarzschild radius, and the constant f is D8n2. Maloney et al. (1996a) applied the radiation-induced warping instability to the interpretation of the apparent warp in NGC 4258 (e.g., Herrnstein et al. 1996a). They noted, however, that this interpretation is inconsistent with the advection-dominated accretion model for this source. The origin of the difficulty can be seen by estimating the radiative efficiency in equation (A1) on the assumption of advection-dominated accretion. TakingL B 1042 ergs s~1 and adopting a viscosity parameterZ0.1, one getsv [ 2 ] 10~2. Using this estimate and the bol ] 5 2 ] 4 Ðducial value of f yieldsrwarp,min Z 2 10 t RS, which exceedsrmin B 4 10 RS for tB1. However, as was already emphasized by Pringle (1992),l1 andl2 are physically distinct quantities, so t in general may well di†er from 1. This parameter may, in fact, be expected to be less than 1 in a disk where a centrifugally driven outÑow is the dominant angular momentum transport mechanism. In particular, if one uses the ““ a prescription ÏÏ to represent the two e†ective viscosities, then, whilea2 (which likely corresponds to a real viscous stress) is[1, a1 B ( o vr o /C)(r/h) [where h is the disk scale height,vr is the radial inÑow velocity, C is the speed of sound, anda1 now describes the e†ective (z, /) viscosity] could potentially be ?1 (sinceo vr o [ C in such a disk and r/h ? 1; see, e.g., Wardle &KoŽ nigl 1993). If the disk in NGC 4258 drives a hydromagnetic wind, it may thus, in principle, be both advection dominated and warped by a radiation-induced instability. Another potentially relevant aspect of a disk-driven hydromagnetic wind is related to the results of the global stability analysis carried out by Maloney et al. (1996a), who generalized the local treatment of Pringle (1996). They showed that radiation-induced warping instabilities in AGNs would be dominated by modes that peak near the outer radius of the disk, identiÐed as either the physical edge of the disk or the radius where the disk becomes optically thin to the bulk of the incident or reemitted Ñux. Since a hydromagnetic disk outÑow is expected to be dusty beyond the sublimation radius (see KK94), the radial Ñux component at the disk surface (which enters into the calculation of the torque on the disk) would be attenuated by passage through the wind as a result of dust scattering and absorption (as well as of electron scattering). This would tend to shift the e†ective outer radius of the disk inward, with the exact location determined by the density proÐle and total mass outÑow rate in the wind. To summarize the discussion in this Appendix, a disk-driven hydromagnetic wind may reconcile the radiation-induced warping interpretation and the advection-dominated accretion model in a source like NGC 4258. It may also be expected to a†ect the location of a warp arising from this instability. A physical warp is a necessary ingredient of the irradiated homogeneous disk model of Neufeld & Maloney (1995), but, as discussed in °° 4 and 5, one could, in principle, account for the megamaser emission from AGN disks even if they were not warped. It is also worth reiterating our conclusion in ° 2.1 that a radiatively heated maser disk in a source like NGC 4258 is likely clumped even if warping (rather than, say, wind ram pressure on clouds) is responsible for exposing the masing gas to the central continuum.

9 It is worth noting that the apparent warps that have so far been observed in megamaser disks (as well as in the Galactic CND) are comparatively mild and do not directly support the proposition that the radiation-induced warping instability could account for the collimated ““ ionization cones ÏÏ found in Seyfert 2 galaxies (see Pringle 1997). 10 An analogous mechanism, involving the torque exerted by a wind evaporated from the irradiated disk surface, was proposed by Schandl & Meyer (1994).

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