The Emission Lines of Quasars and Similar Objects

The erI-iission lines of quasars and siva-filar objects Kris Davidson"

Astronomy Department, Uniuersity of Minnesota, Minneapolis, MN 55455 Hagai Netzert Department of Astronomy, University of Texas, Austin, TX 78712

Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So fax, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements —carbon, nitrogen, and oxygen in particular —are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV—which are not directly observable —may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables.

CONTENTS 715 VII. Some Additional Possibilities A. Concerning the absence of broad forbidden lines 752 I. Introduction 715 B. Can densities be surprisingly high~ 753 A. Some historical remarks 715 C. Additional heating processes 753 B. Quasars, as observed optically 717 D. Nonthermal emission lines ~ 754 C. Topics not included in this review 718 E. Emission-line variability 755 D. Topics included in this review 722 VIII. Gas Motions and Dynamics; Line Profiles 756 II. Photoionized Nebulae —A Brief Overview 722 A. Gener alities 756 A. The photoionization equilibr ium: Counting B. Acceleration of gas —mainly by radiation the photons 722 pressure 757 B. Thermal equilibrium: Counting the ergs 724 C. Emission line profiles 758 C. The emergent spectrum 726 D. More remarks about certain parameters 760 D. Where to find ionic data 727 Acknowledgments 761 III. Conventional, Dustless Photoionization Models References 761 for Quasars' Spectra 728 A. Historical and pr eliminary 728 B. A specific photoionization calculation 731 C. Varying the assumed parameters 733 IV. Line Transfer 736 A. General considerations 736 I. INTRODUCTION B. Possible suppression of resonance emission A. Some historical remarks lines 738 C. The hydrogen line spectrum 739 Like other modern astronomical subjects, the study of D. The helium line spectrum 741 quasars has been greatly affected by fashion and by E. Fluor es cent process es 742 chance; Weedman (1976a) has reasonably argued that V. Dust and Quasars 743 these influences have sometimes led to misplaced at- 743 A. Correlation of visual and ultraviolet data tention and unnecessary debates. B. Dust in our Galaxy 745 C. Intergalactic dust ~ 745 The first quasars to be noticed were some radio D. Dust in quasars' galaxies 746 sources that were identified, during the early 1960s, E. Dust in quasars 746 with optically observable "stars" (see Schmidt, 1963; F. What is the intrinsic spectrum of a quasar'P 747 Oke, 1963; Greenstein and Mathews, 1963; and Bur- G. Comparing lines with continua 748 bidge and Burbidge, 1967). When it was recognized that VI. Some Additional Spectral Features 750 these were really not stars in our Galaxy, they became A. Forbidden lines 750 known as "quasistellar objects" or "QSO's" —or today, B. FeII lines 751 quasars. Their near-ultraviolet, visual, and near-in- C. The "3000 A. bump" 752 frared spectra were found to be continua plus a few emission lines, red-shifted like the spectra of very *Alfred P. Sloan Foundation Besearch Fellow, 1975-1979. distant galaxies; if the quasars' red shifts, like those ++On leave from the Dept. of Physics and Astronomy, Tel of galaxies, indicated cosmological distances, then Aviv University. their intrinsic luminosities must considerably exceed

Reviews of Modern Physics, Vol. 51, No. 4, October 1979 Copyright 1979 American Physical Society Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects those of galaxies. However, some quasars were seen easily, because they are close enough to be recogniz- to fluctuate in br ightness within a few years or less; able as galaxies. But only a small fraction of galaxies this meant, according to arguments involving light- are Seyferts, and as with quasars, spectra are re- travel times, that the luminous souces must be smaller quired for identification. than a few light-years across, tiny compared with any The distances of the nearest quasars, estimated from galaxy and far too small to be resolved optically. This their red shifts, are of the order of 10' light-years; inspired a lengthy dispute about whether quasars' red while the distances of the farthest ones are comparable shifts are really cosmological (see Field, Arp, and to the size of the observable universe. Considering Bahcall, 1973). light-trave1. times, this means that we see the more But long before any quasars had been noticed, a few distant objects as they were moderately early in the galaxies, called "Seyfert galaxies, " were known to have history of the universe, not long after the first galaxies luminous, compact nuclei, with emission lines in their formed. Although we do not know much about quasars' spectra. Often mentioned in connection with quasars lifetimes, it is probable that the early ones are now ex- during the 1960s, Seyfert galaxies assumed new im- tinct. Quasars span such a wide range of intrinsic portance when some of their central brightnesses were luminosities that some of the more distant ones appear seen to fluctuate like quasars (see references cited by as bright as some of the nearest. The nuclei of Seyfert Weedman, 1976a, 1977). Today it seems probable that galaxies are intrinsically less luminous than most quasars are like a certain class of Seyfert nuclei, but quasars but more luminous than most ordinary more luminous; they are probably at the centers of galaxies. galaxies (which are detectable in some cases —see Many theorists have "explained" the radio, infrared, Morton, Williams, and Green, 1978; Wehinger and Wy- visual, ultraviolet, x-ray, and y-ray continua of quas- ckoff, 1978; Hawkins, 1978; and earlier references ars by invoking nonthermal processes such as synchro- cited by these authors, as well as comments by Bahcall, tron radiation (magnetobremsstrahlung) and the inverse 1971), a,nd their emission-line red shifts do indeed in- Compton effect, while the basic energy sources are dicate cosmological distances. suspected to be gravitational fields of black holes (see Although it was their radio emission that drew atten- Sec. I.C below). But the details of these explanations tion to the first-known quasars, today we know that are unsatisfying, because many parameters are both most quasars are not prominent radio sources (Sandage important and unobservable. There must be supplies and Luyten, 1969; Lynds and Wills, 1972; Osmer and of energetic electrons, accelerated by mechanisms that Smith, 1977a; Murdoch and Crawford, 1977; Sramek are imperfectly understood (!), in magnetic fields whose and Weedman, 1978). Of the nearly 1000 presently geometries are model dependent; one must guess known quasars, several hundred were first noticed as whether the electron-energy spectra are correlated with radio objects, but only a minority of these are strong magnetic field strengths, and how the electrons' veloci- radio sources. Among those which were first noticed ties might be correlated in direction with magnetic at optical wavelengths, only a small fraction —10% to field lines; the relativistic electrons may lose most of 30/~ —can be detected with present-day radio telescopes. their energies to radiation, or they may escape; ener- Even in a "radio-bright'* quasar, the visual-wavelength getic protons and other massive particles or i.ons may radiation usually carries significantly more energy than or may not contain as much total energy as the elec- the radio emission. But this is not to say that these trons; magnetic fields may be quasistatic, or there objects are predominantly visual-wavelength emitters; may be strong low-frequency electromagnetic waves; their infrared, ultraviolet, x-ray, and perhaps even and so on. Even though the theoretical situation is so y-ray fluxes are also important. complex, it produces few observable quantities: usually At visual wavelengths the most conspicuous quasar only a total Qux, a few tentative statements about the is a "12th magnitude" object, i.e., it seems about shape of the emitted continuum, and perhaps statements 1/300th as bright as a faint naked-eye star; most of about linear or circular polarization; and these results the other known quasars are of the 15th to 20th mag- may not follow uniquely from a.ny one particular model. nitude, 10 to 1000 times fainter. Being so faint, quas- Thus, being dissatisfied with a largely theoretical ars that fail to draw attention as radio emitters are nonthermal continuum approach, we think that emission difficult to identify, because on most photographs they lines are presently more useful for learning about look just like the equally faint foreground stars, which quasars. The emission-line spectra have several good are multitudinous. Sometimes colors have been useful attributes. First, there are a number of individual (most quasars are "bluer, " i.e., tend to emit at shorter lines whose relative intensities can be measured, giv- wavelengths, than most stars), but generally the emis- ing a fair number of well-defined observables. The line sion lines are necessary for identification; it has be- profiles, although more difficult to measure, may also come possible to use special photographs on which each be useful. Second, the physical mechanisms involved image is actually a small spectrum, so thai quasars in producing the lines are fairly well understood, and can be picked out because of their emission lines (see geometrical assumptions, while significant, are not references cited by Smith, 1978). Even with this tech- quite as crucial as in models for nonthermal continua. nique only a small fraction of the sky has been exam- Third, the emission-line spectra of most quasars are ined, and it appears likely that the total number of surprisingly alike, with a few interesting exceptions. quasars down to 20th magnitude is of the order of 10' There are other motives for investigating the emission or 10'. lines. In Sec. V we shall express a suspicion that the Most known Seyfert galaxies have been found more true continua cannot be known until the lines are under-

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and simiIar objects 717 stood. The line-emitting regions may be related to the ("rest") wavelength A., is observed at wavelength "fuel" A, = & mysterious supplies of (gravitationally accreted .»....& (1+z)X„where z 0 because of the expansion material) which are required in most theoretical pic- of the universe. The object's distance is proportional tures of quasars. And it is from the emission lines that to z for z «1 and in general depends upon cosmological we learn of the occurrence of postprimordial nucleo- parameters. The nearest quasars have z somewhat synthesis even in the earliest, highest-red-shift ob- less than 0.1 (which corresponds toadistance of roughly jects yet seen: they are (or were) rich in elements 1.5X 10' light-years), while z exceeds 3 for the most heavier than helium. For all of these reasons, we think distant examples. Because of the Earth's atmosphere that the emission lines deserve a high priority in the and instrumental detection efficiencies, ground-based study of quasars. observations of emission lines have mostly been re- Unfortunately, analyses of these emission-line spec- stricted to the apparent wavelength range 3000-9000 A, tra are complicated, have been considered in realistic corresponding, for example, to rest wavelengths detail by only a few people, and have not been given 1000-3000 A. in a case where z = 2. Thus, until recently, adequate attention in any published review; hence the quasars' spectra at visual rest wavelengths were known following review. This account will be concerned largely only for low-red-shift objects while the intrinsic ultra- with models of line-emitting regions, and how such violet spectra were known only for high-red-shift ob- modeI. s can be used to extract information from the ob- jects. This was potentially dangerous, because the dis- served spectra; many observational details will be tant, high-red-shift quasars, occurring relatively early omitted. Even so, the topic is lengthy. in the history of the universe, might have been quite different from nearby, low-red-shift, present-day ob- jects. Fortunately, ultraviolet spectra, obtained with satellite- or rocket-borne instruments, and also some infrared data have begun to appear since 1976, and so B. Quasars, as observed optically far there is no evidence that high- and low-red-shift quasars' spectra are very different. We shall not be very careful here about what we call Estimating a quasar's distance from its red shift, a quasar. Without arguing the point, we suppose that and combining this with its apparent brightness in some the nuclei of "Type 1" Seyfert galaxies —those with observable wavelength range, we can find the intrinsic broad emission lines —are modest quasars; but if this luminosity (radiated power) in that range. As an order assumption is wrong, only a few details of our dis- of-magnitude approximation, at least some quasars' cussion will be invalid as a consequence. The Seyferts luminosities are evenly distributed among the near- are spiral galaxies with prominent, compact nuclei; infrared (1-5 pm), visual (3000-9000 A), ultraviolet for descriptions of them and their resemblances to (500-2500 A), and x-ray (1-10 keV) ranges. (We do quasars, see Weedman (1977) and references therein. not know whether something profound or simple is be- There are other luminous objects, called "N-type hind this remarkable fact. ) Total luminosities are often galaxies" and'"broad-line radio galaxies, " which share between 10 ' and 10" erg s ', although Seyfert galaxies many of the characteristics of Seyferts and quasars may be less luminous and a few very luminous high- (in fact, some quasars are probably in N-type galax- red-shift quasars at least temporarily exceed 10" ies); for details, see references cited by Osterbrock ergs '. For comparison, the luminosity of the Sun is and Grandi (1979). "BL Lacertae objects" are almost 10 ' erg s ' and a fairly respectable galaxy may pro- (if not precisely) quasars without prominent emission duce 10" or 104' ergs ~. lines; see Stein, O'Dell, and Strittmatter (1976), As mentioned above, although they are far more Miller (1979), and the Proceedings of the 1978 Pitts- luminous than galaxies, quasars are much smaller than burgh conference on BL Lac objects (edited by A. galaxies and may exist within galaxies. Some (though ' Wolfe). Rowan-Robinson (1976, 1977) has discussed not all) quasars' continua have varied within a few years some speculative generalizations about these various (e.g., see Neugebauer et a/. , 1979; Scott et a/. , 1976; classes, which together are often called "active galactic Heckmann, 1976; McGimsey et aI, 1975; Liller and nuclei. " Liller, 1975; Grandi and Tifft, 1974; Angione, 1973; For interesting reviews of observational data on quas- and other references to be cited later in this review). ars, see Smith (1978) and Weedman (1976); older, more In an extreme case, a quasar can vary in brightness by traditional reviews are those by Burbidge and Burbidge a factor of more than 10 in less (sometimes much less) (1967) and Schmidt (1969). Regarding observations of than a year. However, these fluctuations generally in- emission lines in particular, see Baldwin (1978), Neuge- volve only the continuum; the emission lines remain bauer et a/. (1979), and Strittmatter and Williams fairly steady except in some Seyfert nuclei with rela- (1976). For a list of several hundred quasars, with tively modest luminosities. We also note that ~ost some data and many references, see Burbidge, Crowne, quasars (especially the "radio-quiet" ones) may be and Smith (1977). Quasars have beencataloguedin many fairly steady over time scales up to at least 50 years. ways, so that different objects often have dissimilar- It is conceivable that the very far ultraviolet and soft- looking identification numbers such as 3Q 273, 4+05.34, x-ray continua may be steady even where the visual, PHL938, PKS0237-23, etc.; these individual tags wil1 moderate ultraviolet, and moderately hard-x-ray fluxes not matter here. vary (this may be relevant to some of our discussion in The foremost observational parameter of a quasar is Sec. V). its emission-line red shift z: a line with laboratory Let E(s)ds denote an energy flux in photon-energy in-

Rev. Mod. Phys. , Vot. 51, No. 4, October 1979 718 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects tervaldc. ' It has been customary to represent a typical lies, and continuum luminosities of quasars. Many quasar's infrared-ultraviolet continuum as a power law, rough theoretical ideas about quasars are plausible, F(s)-s ', with s close to unity. However, Fig. 1, but the more detailed scenarios are quite speculative which is taken from Neugebauer, Oke, Becklin, and and do not appear particularly susceptible to direct Mathews (1979), shows that this is usually an over- observational tests. Several descriptions of the topic, simplification. Quasars' continua are often "bumpy" from what is lately a conventional point of view, have and curved on a log&(s) —logs plot. These continua are been given by Bees (1977a, b; 1978a, b) Many galaxies probably nonthermal in origin, i.e., due to processes have central nuclei —massive, dense star clusters, very like synchrotron radiation and inverse Compton scatter- much more compact than the galaxies —and most theo- ing; but there may be thermal exceptions in the in- ries of quasars have involved such galactic nuclei. If frared, far ultraviolet, and soft-x-ray regions of the a galactic nucleus is dense enough, considerable amounts spectrum. of gas must be released, in supernova explosions, stellar Modern observations of quasars' emission lines have collisions, and other catastrophic events in the nucleus. been described by Baldwin (1975, 1978), Osmer and If this gas does not escape, it may form new stars, or, Smith (1976, 1977a), Baldwin and Netzer (1978), and more likely, will tend to collect at the center of the others; similar observations of Seyfert galaxies and galactic nucleus, presumably in some sort of disklike related objects have been described by Adams and configuration (because its angular momentum is signifi- Weedman (1975), Osterbrock (1977), Grandi and Oster- cant). Perhaps a central, massive black hole will form, brock (1978), and Phillips (1978a). Figure 2 shows, surrounded by a rotating disk of gas which spirals into for example, a spectrum of a low-red-shift quasar with the black hole because of viscous effects (probably in- z = 0.206. The emission lines in this spectrum are volving turbulence). This leads to a model proposed by familiar to astronomers, because many gaseous nebulae Lynden-Bell (1969) which has become rather standard in our Galaxy show the same lines. However, unlike an (although its truth has not been proven). [See also Lyn- ordinary nebular spectrum, some of the quasar's lines den-Bell (1978).] The total gravitational energy con- are quite broad. These are the "permitted" lines, in- verted into luminosity is probably of the order of O. lc' cluding the Balmer series of hydrogen. The linewidths per unit mass which falls into the black hole; this are probably due to differential Doppler shifts, involv- means that an accretion rate of 10"g s ', about 10 ing large-scale velocity dispersions in the line-emitting solar masses per year, can provide a quasarlike material. Some other lines —"forbidden lines" —are luminosity of the order of 10" ergs '. However, the relatively narrow (narrower, in fact, than Fig. 2 shows, details of the conversion to a continuum spectrum are since instrumental broadening is present); we shall not at all obvious. Events in the surrounding explain the likely reasons for this difference later. region —the dense star cluster' —must supply the ac- Figure 3 shows the spectrum of a Seyfert galaxy, which creted mass; stellar collisions and near-collisions, in this particular case differs from the quasar's spec- supernova explosions, and tidal disruptions of stars trum in two qualitative respects: the Balmer lines have passing close to the black hole may be important. One asymmetric shapes, and there are strong features in- can argue that the most important problems regarding volving many lines of singly ionized iron. Figure 4 quasars, their origins and sustenance, involve the sur- shows the ultraviolet spectra of several high-red-shift rounding regions rather than the hypothetical central quasars. Most of the ultraviolet emission lines can be black holes. The line-emitting gas, to be discussed in identified with little difficulty; the most prominent this review, occurs in or near these regions. lines involve hydrogen, C", C", and Mg' ions. There It appears that a quasar can best be represented by a are no narrow ultraviolet forbidden lines, and the dif- "kitchen sink" model, with a drainpipe (the black hole) ferent quasars' spectra in Fig. 4 resemble each other. and many interesting items piled up above the drain- Much of this review will be a discussion of how we pipe (stars, pulsars, small black holes, gas clouds, can derive physical information —gas and energy densi- electromagnetic fields); but there are many ways to ties, chemical compositions, sizes of emitting reg- choose and arrange the piled-up items. Plasma-phys- ions —from the relative intensities of spectral lines ics effects (e.g., see Lovelace, 1976) and explosive shown in Figs. 2, 3, and 4. Although the results will events (e.g., see Blandford and McKee, 197V) may oc- be imprecise, we think that there is more derivable cur in the accretion vortex. For a variety of compli- information in the emission lines than in the perhaps cated ideas about this complicated subject, see I ynden- featureless, perhaps "bumpy" continua. Bell and Rees (1971), Arons, Kulsrud, and Ostriker (19V5), von Hoerner and Saslaw (1976), Ginzburg and C. Topics not included in this review Ozernoi (1977), Young, Shields, and Wheeler (197V), We shall not discuss in detail the many theories that Bailey and Clube (1978), Hills (19V8), Keenan (1978), have been invented to explain the origins, energy supp- Rowan-Robinson (1977), and Begelman and Rees (1978). Another topic that we shall avoid is the study of quas- ~We shall usually discuss photon energies c and wavelengths ars at radio wavelengths. In some cases, activity in A, although some astronomers refer to frequencies v even in , quasars can be resolved by radio techniques (whose the optical range. For convenience, note that a photon energy 6=10 eV, near the important I,yman-alpha emission line, cor- angular resolution is now better, in some cases, than O 5 responds to A. =1240 A and &=10 Hz. In this review, 8 and that of optical astronomy), and some information fol- ~ will usually be "rest" values, i.e., as measured in the ref- lows from the radio continua. However, the energy erence frame of the quasar. fluxes involved are only small fractions of quasars'

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

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I I — —1.0 -25 13.5 14.0 14.5 15.0 14.0 14.5 15.0 15.5 Iog ~0(Hz) log vp(Hz) FIG. 1. Log f„-log v plots of the infrared-to-ultraviolet continuum spectra of several quasars, according to Neugebauer, Oke, Becklin, andMathems (1979). Emission lines are mostly not included. Frequencies &0 are in the quasars' "rest" (intrinsic) frames. (Note that v=10~5 Hz corresponds to 8=4 lev or X.=3000 A=0.3 pm. ) Copyright The AstrophysicaL JournaL. total outputs, the precise implications of the radio ob- 1 GeV) observations and theory. Some quasars have servations are model dependent, and most quasars are appreciable fractions of their luminosities in this difficult to detect at radio wavelengths. See Kellerman range; see Culhane (1978), Elvis et al. (1978), Giacconi (1974, 1978), Burbidge, Jones, and O'Dell (1974), (1978), Marshall et al. (1978), Sta'rk, Burnell, and Jones, O'Dell, and Stein (1974), and Miley and Miller Culhane (1978), Swanenberg et al. (1978), Barr et al. (1979). (1977), DiCocco et al. (1977), and Gursky and Schwartz We shall not discuss x-ray and y-ray (s- 1 keV to (1977). In general, we shall not discuss the origins

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 f20 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

l72l+ 34

I.' + FIG. 2. The visual-wavelength spectrum of a typical low-red- F shift quasar withe =0.2, ob- tained by D. Wills and B.Wills FO at MacDonald Observatory. C -88 O 0 Z C7 (Note that the abscissas here 03 are apparent wavelengths, rathe r than "rest" wavelengths. The absorption feature near O 76OQ A is due to the terres- trial atmosphere. )

i 4000 6000 7000 8000 Observed wavelength of nonthermal continua in any wavelength range. are less than the quasar's emission red shift z, ; some A typical high-red-shift quasar's spectrum has many are close to z, but others are not. For example, in a naxrozo abso~tion Eines, especially including the Ly- spectrum with z, = 2.00, one "absorption system" man-alpha line of atomic hydrogen, with many different might have z„=1.95 (which may correspond to a dif- red shifts z,~. Almost all of the absorption red shifts ference of several thousand km s ' between the line-of-

HP [0IKj Akn 120 486I 4959, 5007 I I I

FIG. 3. The visual-wave- length spectrum of a "Type 1" Seyfert galaxy with strong Fe ii 0.0 I I 4000 5000 emission, from. Osterbrock REsT M/AVELENGTH {5) and Phillips (1977). Courtesy I.Q of the Publications of the I I Astronomical Society of the

Pacific ~

I I I 5000 6000 REST WuVE LENG TH (A)

Rev. Mod. Phys. , Vol. 5'1, No. 4, October 1 979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

I l I I [ I l t l I I l l [ t' t Lya TON 490

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Cl ATM 4C 29.50 FIG. 4. Ultraviolet spectra ~0.~ 8 of several high-red-shift qua- 0 sars, from Baldwin and Net- zer (1978). (Note that the or- 0.4 dinates are fluxes per unit frequency, rather than Quxes per unit wavelength. Thus the I I J .& I I I I I I I I l, I I ! I I emission features toward the left edge are underemphasized ATM ATM here. ) Copyright The Astro- physica/ Journal. 8

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sight velocities of the emitting region and the interven- been reviewed more than the emission lines. See Perry, ing absorbing gas) while another might be at z, ~ =0.80 Burbidge, and Burbidge (1978) and many references (in which case the indicated velocity difference would be therein, as well as Bahcall (1978). comparable to the speed of light). There is a tendency A few peculiar quasars have broad absorption fea- for absorption systems to be concentrated near z, . Be- tures that probably are related to their emission fea- cause the absorption lines are so narrow, some of them tures; expanding shells or envelopes, with characteris- have easily observable fine structure (e.g., the C 1V tic speeds exceeding 10' kms ', seem to be involved. doublet whose rest wavelengths are 1548, 1551 A), which See Lynds (1967), Burbidge (1970), Boksenberg, Cars- sometimes leads to information about the gas and radia- well, Smith, and Whelan (1978), and Weedman, Lewis, tion densities in the absorbing gas clouds. Thus it is and MacAlpine (1979). thought that these clouds are not dense enough or close Observational techniques and uncertainties, and enough to the quasars to be identified with the emission- methods used to find quasars, will also be neglected line regions that we discuss in this review. There has here. Some of these topics are discussed by Smith been a long dispute, not yet settled, about whether the (1978). Another topic of interest is the distribution of absorbing clouds have been ejected from the quasars quasars in red shift z; the large number of luminous or whether they are completely unrelated to the quas- high-red-shift quasars implies that such objects were ars. Assigning some clouds to each point of view may far more common 10 or 15 billion years ago than they be possible. Here, we shall not discuss the narrow are today. If one could take samples of the past uni- absorption lines, especially since in the pa, st they have verse as a function of red shift z, the number of quas-

Rev. IVlod. Phys. , VoI. 51, No. 4, October 1979 722 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects ars per unit mass would increase somewhat like and subject to a sort of "entropy, " in practice one may (I+a)', or perhaps like an exponential function of the as well use simplified models for many purposes any- "look-back time" to z. It also seems likely that quasars how! (But some experience is required in order to know were typically more luminous in the past. See Schmidt how much simplification is allowable; for example, it is (1970, 1972), Sramek and Weedman (1978), Turner usually wrong to assume any particular uniform tem- (1979), and references cited therein. perature. ) (iii) A specific explanation of just one or two spectral D. Topics included in this review features —without considering the other features —is In Sec. II, we shall review some of the physical pro- usually wor thless. cesses and circumstances that are relevant to astro- nomical emission-line spectra; photoionization equili- II. PHOTOIONIZED NEBULAE —A BRIEF OVERVIEW bria are particularly important. Section II is intended mainly for the reader who is unfamiliar with traditional A. The photoionization equilibrium: counting the photons nebular astrophysics, but we note also that there are important differences between classical nebular analy- Throughout our own Ga.laxy, hot, luminous sta, rs ses and analyses of quasars' spectra. radiate enough ultraviolet energy to photoionize their In Sec. III, we describe the "photoionization models" surrounding interstellar gas clouds —which then become that were developed, mostly between 1969 and 1976, "emission nebulae" or "H II regions. " Physical con- to explain quasars' ultraviolet emission lines. These ditions in these nebulae have become fairly well known models give us some ideas of the relative elemental since the work of Zanstra, Bowen, Stromgren, Menzel, abundances in the emission regions —in particular, Aller, and others, beginning before 1930. The pro- carbon, nitrogen, and oxygen appear to be about as cesses involved in ordinary galactic nebulae have been abundant, relative to hydrogen, as in some nearby ga- reviewed by Aller (1956), Seaton (1960, 1972), Hummer lactic nuclei. The photoionization models also indicate and Seaton (1963, 1964), Spitzer (1968, 1978), Oster- approximate values of the radiation-to-gas density ratio brock (1974), and in a, collection of papers edited by in the line- emitting r egions, while giving rough li mits Menzel (1962). Here we shall present a sketch of these on the gas density. processes, with a different emphasis appropriate to a Section IV is a discussion of certain emission lines different type of photoionized nebula. Our idealized for which the emitting regions are optically thick, and nebula will be associated with a quasarlike object rather the associated radiative-transfer problems. From the than with a hot star; gas and radiation densities are observed relative intensities of these lines, it is possi- higher than in a galactic nebula, while the energy dis- ble to guess characteristic radiation densities in the tribution of the ionizing photons is quite different. For emission regions, and, therefore, the distances of convenience, we shall first ignore some processes, these regions from the quasars' centers. and then acknowledge them later in the discussion. We In Sec. V, we discuss how the likely existence of in- shall not specify accurate values for most parameters tervening solid "dust" grains can modify the preceding of interest, because there are so many of them; ref- arguments. We favor models in which dust is signifi- erences to such values will be cited in Sec. II.D. cant, but in some of these models the quasars' lumi- Consider first an "optically thin" or transparent nosities are even more grandiose than previously sug- cloud of pure hydrogen gas, with density n„of hydrogen gested. The evidence is not yet conclusive. atoms and ions, exposed to a monodirectional flux of Section VI is about some spectral features, not dis- ionizing photons. Molecular hydrogen is extremely cussed in the preceding sections, which may convey scarce in the cloud because of the ultraviolet flux, so useful information. Unfortunately, these features are the ionization equilibrium involves only H and H' ions, poorly understood at present. with densities n(H') and n(H'). Let &(s) ds be the inci- In Sec. VII we mention several ways in which the rest dent energy flux in photon energy interval dc, approxi- of our discussion may be wrong: these involve pro- mated for our purposes by cesses that we believe to be almost negligible, but it is &(c) = (s/IH) 'e ' 'oI'H. (2 1) possible to imagine loopholes in our reasoning. Any radically different, alternative type of model will Here IH = 13.6 eV, corresponding to a wavelength of probably have to be more complicated than our pre- 912 A, is the ionization threshold of a ground-level hy- ferred models in order to achieve equal success in ac- drogen atom, often called the "Lyman limit" by as- counting for the observed line intensities. tronomers. The flux parameter I"H, the spectral index Finally, Sec. VIII i. s a rather sketchy attempt to de- s, and the cutoff energy co are constant parameters. scribe the ideas of many authors about gas dynamics We shall suppose that cp ++IH and adopt s = 1 as an ex- and movements in the line-emitting regions. The pro- emplary value, which gives a flux &H of ionizing photons files of emission lines are significant in this regard. (s &IH). The corresponding energy flux depends lo- There are many pitfalls in this subject, whose nature garithmically upon c„but since x-ray photons with is typified in three basic rules: c & 1 keV do not interact strongly with the gas, we can (i) Simplified models of quasars' emission regions temporarily suppose that c, is indefinitely large. are usually wrong, in the sense that many complicated Most hydrogen atoms are in the ground level, so the effects can be shown to modify the physical parameters only photoionization cross section that we need now is of the situation. for the ground level of H'; call this o H(c). It can be (ii) However, because observational data are limited calculated almost exactly, neglecting relativistic ef-

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects fects (Bethe and Salpeter, 195I), and a good practical the local photon flux is reduced to E(s)e "('~, and the approximation is local ionization ratio n(H')/n(H') is decreased accord- At some depth x =xH, there is an "ionization (6.3x10 "cm')(c/IH) ingly. gH(s)= ", front" or transition zone where n(H') becomes larger I„&c ~ 100 eV. (2.2) than n(H'). One can integrate numerically to find n(H'), n(H'), and v(s) as functions of but without actually The rate of photoionization events per unit volume is x; doing this, we can easily guess the approximate ionized evidently thickness xH, as follows. For reasonably large UH, E(c) 10 n(H')/n(H')»1 throughout most of the ionized region, e(H') oH(s) dh = EHn(H') . c 22.88+ s &I so n, =n(H')=nH there. The total column rate of re- combinations per unit illuminated area i.s thus The inverse process is radiative recombination, whose (' x H rate per unit volume is o(Hn, n(H'), where o.H is a total AHlzHB(H ) cfx o(HBHxH ~ "recombination coefficient" for hydrogen and the elec- "p tron density n, is equal to n(H') if the gas is pure hy- This must the total flux of absorbed ionizing pho- drogen. This rate includes recombinations to all levels, equal tons, which is of the order of I'H,' therefore quickly followed by cascading radiative decays to the x„ = EH/o. HnH. The material thickness of the ionized region ground level. The effective value of AH depends some- is proportional to UH. what upon the distribution of free-electron energies; as we shall explain later, in cases of interest a typical n„xH= n,xH= U„/nH= (10"cm '-)UH/c . (2.5) free electron has a kinetic energy of the order of 2 eV (If the gas were initially un-ionized and the flux EH (corresponding to a. kinetic temperature near 15000 K), started instantaneously, then the time required to es- so that o. is of the order of 10 "' cm's ' (Seaton, H tablish the equilibrium ionized region would be several 1959, 1960). The characteristic time to approach ioniza- times the recombination time =xH/UH. Hence tion equilibrium, will usually be quick enough (nHnH) (nHn, ), be interpreted as a "speed of adjustment" to for the H'/H' ratio to be practically in equilibrium. UH may flux variations. %e also note that scattering of photons Then, by free electrons may be neglected if n,x„«10' cm ', n(H') 10 "cm 's EH i.e., if UH «3x 10" cm s '.) (2.3a) n(H') 2.8+ s n, Let ~„denote the thickness of the ionization front, say, the distance between points where the gas is &80/() It will be convenient to adopt an "ionization parameter" ionized and &20% ionized. Then ~xH= K/o„nH, where with velocitylike dimensions, U„=EH/n„ then, for o. is the threshold cross section and K is of the order s= j. „ , of 20 for realistic cases (wherein high-energy photons are absorbed ions other than hydrogen) and larger n(H ) U„ by c(H') 10"cmc ') (2.3b) for the pure-hydrogen case. Using the smaller value of K, In typical photoionized nebulae, and probably in the gas 10' cms ' associated with quasars, UH generally happens to be (2 6) larger than the speed of sound (which is slightly above xH UH 10' cm s ') but less than the speed of light. ' Then, ac- This means that the ionization front is well defined for cording to Eq. (2.3b), the gas is mostly ionized if the U„+&10' cms ' and becomes relatively narrower and gas cloud is "optically thin" or transparent to the ioniz- more distinct as UH is increased. ing radiation. A real cloud of gas will contain other elements be- Now consider what happens if the cloud of gas is thick sides hydrogen. In most of our galaxy, the helium- enough to absorb most of the ionizing phoions. Suppose hydrogen ratio is about n„ /nH = 0.1, while heavier that the illuminated edge of the cloud is planar and that ions —chiefly carbon, nitrogen, oxygen, and neon —have the ionizing photon flux is normally incident upon it. abundances n~/nH &10; a major aim in the analysis of Suppose that the density nH =n(H')+n(H') is uniform quasars' spectra is to determine whether the material within the cloud. At linear depth x into a pure hydrogen associated with quasars has a similar composition. cloud, the photon-energy-dependent "optical depth" is Photoionization equilibr ia for these elements —e.g., n( eH'+)/n( eH')/n( eH) —can be estimated by a nearly T(s) = vH(s) n(H') dx', (2.4) straightforward extension of the method used for hydro- ~c)p gen. Multiply charged ions have higher ionization thresholds, smaller threshold photoionization cross sections, and larger recombination coefficients than 2Various parameters which are equivalent to UH appear in hydrogen; so for a given value of UH, their successive papers on ionization near quasars. U&, as used by Davidson ionization ratios are smaller than that given for hydro- (1972, 1973, 1977a, b), Baldwin and Netzer (1978), and others, gen by Eq. (2.3b). For example, with spectral index is practically the same as UH. The parameter Uz used by s= 1, Shields (1976), and I' used by Mathews (1975) are essentially UH/c. Other authors have used more complicated parameters, n(He") U„ (2. sometimes denoted &, g, or y. The effective pressures or c(Hc') 10 cmc ') 3c) kinetic energy densities of ioni'zing radiation and of gas are roughly equal, for s~1, if UH=0. le=109 cms~. In an optically thick cloud with a "conventional" com-

Rev. Mod. Phys. , Vol. 51, No. 4, October 'f979 724 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects position, most of the ionizing photons are absorbed by ing photon is reabsorbed "on the spot, " so that, in ef- hydrogen and helium, while the scarcer, heavier ions fect, the recombination event never occurred. Thus, have much less effect on the positional dependence of instead of using the total recombination coefficient, in the ultraviolet flux. Three important ionization fronts the "on the spot approximation" one allows recombina- occur, involving He''/He', He'/He', and H'/H', with tions only to the excited levels of hydrogen, which pro- relevant ionization thresholds 54.4, 24.6, and 13.6 eV, duce only nonionizing photons. This reduces the effec- respectively. Most analyses related to quasars find tive value of nH by as much as 40%. Similar approxima- three important ionization zones, as follows: tions can be used for some helium recombinations but (a.) Near the illuminated boundary of the gas cloud, are usually unnecessary for heavier elements. Where photons of all energies are found. If UH is large enough, more precise calculations are desired, it is necessary helium is mostly He" and hydrogen is mostly H'. to solve the photon-energy-dependent radiative transfer Most of the photons with c, & 54.4 eV are absorbed in problem by an iterative method. However, such a ma, inta. ining the He''/He' equilibrium in this zone. The pr oper solution is geometr y dependent. relative thickness of the He''/He' ionization front is For large values of U„and photons in the x-ray ener- larger than that given by Eq. (2.6). gy x ange, ions heavier than helium axe impor tant for (b) Beyond the He" /He' ionization front lies a zone determining the radia. tive transfer, even if they are where most of the photons (except perhaps some highly much less abundant than helium; but the relevant ioniz- penetrating x-ray photons) have energies below 54.4 ing fluxes for E» 100 eV are quite uncertain in any eV, and where He' and H' predominate. In principle, case. this zone can be bounded by either the H'/H' or the Collisional ionization by free electrons is usually of He'/He' ionization front, depending upon the incident secondary importance in photoionized regions. How- ionizing spectrum and the helium/hydrogen abundance ever, under conditions discussed in Sec. IV.C below, ratio. But for likely ranges of parameters, the posi- collisional ionization from the n = 2 level of hydrogen tions of these two ionization fronts are interdependent becomes important near the. H'/H ionization front. and tend to occur almost together. ' The inverse process, three-body nonradiative recom- (c) The third zone contains mostly H' and He', with bination, is negligible if n, «10 cm ~. photon energies mostly below 13.6 eV. However, x-ray Dielectronic recombination, wherein the recombining photons, with c & 200 eV, may penetrate into this zone electron disposes of its initial energy by raising a bound to cause some ionization. electron to an excited level, is important for some ions, In such a neatly stratified arrangement of zones, the and is rather sensitive to the initial electron energy. heavier elements are ionized according to their ioniza- Various charge-exchange reactions are also impor- tion thresholds. Carbon is a good example. The tant. A notable example is C" +H —C' +H', which is thresholds of O', C', O'+, C", C", and C" are 11.3, important in models with UH ~ 10' cm s '. (The inverse 24.4, 47.9, 64.5, 392, and 490 eV. The last two thres- process is negligible, because of Coulomb repulsion holds are so high that the C"/C"/C" equilibrium de- between C' ' and H' ions. ) pends upon whether there is an x-ray "cutoff" in the Photoionization cross sections are not easy to calcu- power law spectrum; and also, large values of U„would late for multielectron ions; and unlike the case for be required to make C" or C" predominate. There- most galactic nebulae, photoionization from inner fore in the highly ionized zone (a), if UH is moderately shells of electrons must be taken into account if the large, carbon may be either C", C", or C' . In the ionizing spectrum is qua, sarlike. When an inner-shell He' zone (b), carbon would be mostly C'" (because electron has been removed, the resulting ion is in an photons to ionize further are lacking there), and in excited state. If it decays radiatively, a secondary zone (c), carbon would be O'. However, if U~ ~ 10' ionizing photon may be produced. In the case of a re- cm s, it is found that significant equilibrium concen- moved K-shell electron, ionic readjustment often in- trations of C" and C" also occur in zone (a) while a volves the Auger effect, wherein one or more additional significant amount of C'' occurs in zone (b). electrons are ejected. Moreover, electrons which have We shall now mention some complications, which in been freed by x-ray photons may be so energetic that most cases do not lead to qualitative changes. First, they cause secondary ionizations and excitations before it is evident that some diffuse secondary ionizing radia- being "thermalized" as discussed in the next section. tion must be produced within the ionized gas. For ex- Quantitative details about most of these processes may ample, when a typical 2-eV free electron radiatively be found in the references cited in Sec. II.D below. recombines with a proton in such a way that a ground- level H' atom results directly, then a 15.6-eV ionizing B. Thermal equilibrium: counting the ergs photon is emitted. Unless the gas cloud is optically thin, this photon is likely to be reabsorbed to cause Having described the equilibrium between ionization another ionization. In some cases, one can crudely and recombination events, we now consider the equili- allow for this by pretending that such a secondary i.oniz- brium between energy gains and losses in the ionized gas. A very convenient and accurate approximation can be introduced immediately: In most cases, the dis- 3In many galactic nebulae, the central stars have ionizing spectra which decrease steeply above 8=13.6 eV; such nebulae tributions of kinetic energies of ions and free electrons have sizable regions where H+ and He predominate together. are practically Maxwellian, with just one kinetic tem- But this is not the case for most photoionization models related perature T applying to all ions and electrons. This is to quasars. true because of the effectiveness of elastic collisions

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 725 between charged particles in redistributing kinetic en- from the gas with little difficulty; but as mentioned in ergies; see Spitzer (1962). We must emphasize, very the preceding section, some ionizing photons are also strongly, that the temperature T characterizes only the produced, whose subsequent transfer must be consid- kinetic energies; the radiation field, the ionization ered in any elaborate calculation. ratios, and the populations of ionic internal energy Another cooling process, in a pure-hydrogen nebula, levels are often very different from ordinary thermal involves inelastic collisions of free electrons with hy- distributions. 4 drogen atoms. Such collisions convert kinetic energy Consider some locale within a pure-hydrogen photo- into excitation energy, usually transfering atoms from ionized region. When a photon of energy c is absorbed the n= 1 ground level to the n=2 or n=3 levels; the in a photoionization event, the initial kinetic energy of atoms then decay radiatively back to n = 1, so that the the freed electron is nearly (c —IH). Elastic collisions net result is conversion of kinetic energy to photons. very quickly spread this energy among the ions and As mentioned earlier, typical electron energies 3kT/2 electrons, the net result being a kinetic energy "heat- will turn out to be around 2 eV in a real nebula, while ing" contribution of (c —IH). The total local heating rate excitation energies of ions are usually much larger can obviously be calculated from the local values of (e.g. , 10 eV from n=1 to n=2 in H'). Therefore only n(H') and &(c): the electrons in the high-energy "tail" of the Max- wellian distribution can cause excitations. Neverthe- (heating per unit volume) = less, the excitation process inherently has such large +(s) cross sections that its overall rate per unit volume can n(I-I') (s —IH)o H(c) ds . (2.V) exceed the recombination and bremsstrahlung cooling rates Be.cause a factor — is involved, with For the moment, we shall neglect other heating pro- exp( E„/kT) & 2kT, the collisional-excitation cooling rate is very cesses: adiabatic compr ession by shock waves, in- E;& sensitive to and a verse-bremsstrahlung absorption of radio-frequency temperature therefore is fairly good ther mostat. waves, excitation by energetic charged particles, vis- The above cooling processes all involve electron —ion cous dissipation of turbulent motions, conduction of interactions. Ion —ion interactions (meaning H' —H' or heat from adjoining hotter gas, magnetic field line re- Ho —H' for hydrogen) are negligible for optical and connection, etc. Most of these are probably unimpor- ultraviolet transitions, because the collision times ex- tant in a quasar's emission-line regions. ceed the ions' internal natural periods Elec- Several types of "cooling" processes remove kinetic 5/E, ~. tron-electron collisions are very elastic because they energy from the gas by converting it to photons. Most involve no dipole moments. obviously, radiative recombination removes electrons electric Having assembled the cooling and heating rates as with various energies. Integrating the product of the functions of temperature in our fictitious pure-hydrogen energy-dependent recombination rate with the Max- nebula, we can find the equilibrium temperature where wellian distribution, one finds that the average recom- heating is balanced cooling. The ionization and bining electron has an initial kinetic energy close to by thermal equilibria are interdependent, because the ef- kT. This energy, plus some binding energy, becomes fective recombination rate is temperature dependent a photon. Bather crudely, aH while the heating and cooling rates depend upon n(H')/ (recombination cooling per unit volume)= n(H'). Therefore an iterative procedure must be used to find a self-consistent solution; but this does not cause (2.8) much difficulty in practice. If the cooling is mainly due where the recombination coefficient n„ is itself a func- to recombination and bremsstrahlung (as in pure hydro- tion of T. (In fact, o.~- T o' for temperatures of in- gen gas with large UH), then the equilibrium value of terest. ) More precise values of this cooling rate have kT is roughly the same as the average value of (s —IH) been calculated by Seaton (1959, 1960). The brems- for the absorbed photons. But if collisional excitation strahlung process causes additional cooling, wherein dominates the cooling rate (as in a low-UH hydrogen electron-ion Coulomb collisions convert some kinetic case, or in the realistic case mentioned below), then energy into radiation. This is very closely related to the temperature is lower. radiative recombination; recombinations are "free- What if the gas has a realistic composition, rather bound" transitions and bremsstrahlung events are than being pure hydrogen? The primary changes in the "free-free" transitions by the electrons. Consequently, heating rate are obvious: photoionization of each ion the bremsstrahlung cooling rate is comparable to the species must be taken into account, including inner recombination cooling rate. Equation (2.8) would shells. Recombination and bremsstrahlung cooling crudely represent the total of recombination and brems- rates are also augmented slightly. In some cases, most strahlung cooling if SkT/2 were used instead of kT. For of the heating as well as the recombination and brems- temperatures of interest, most bremsstrahlung and re- strahlung cooling involve just hydrogen and helium. combination photons have c &IH and hence can escape The less abundant heavier ions are very important, though, because some of them are efficient collisional- excitation coolants. imagine a rather 4Yhe thermal distribution of electrons actually extends down- For example, ward into the closely spaced uppermost bound states of ions, typical ionized region, where the most abundant ele- e.g., levels n &10 for hydrogen; the free electrons' zero-en- ments are largely in the forms of O', C",0'+, etc. ergy level is not perfectly straightforward to define. But for Consider collisional excitations of the various ion most nebular purposes, this fact is of minor importance. species. Hydrogen is the most abundant element, but

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 726 Kris Davidson and Hagai Netzer: Emission lines of quasars and sirniiar objects only a tiny fraction if it is excitable H . As for helium, for most ions of interest in photoionized regions be- neither He+ nor He' can be excited with an energy of cause usually E„&2 or 3 eV and kT= 2 eV. In a low- less than 21 eV; this is so high as to be negligible if density, "radiatively deexcited" case where A&& +& C, ;, kT &4 eV. But C" has an excited level at 8 eV, and n, /n«becomes very small. As a first approximation, because of' the ionization, n(C'+) may be comparable to therefore, we can neglect excited ions when we calcu- n(H'). The ion 0" and other multielectron ions also late photoionization rates; we can similarly neglect have excited levels of interest. Therefore collisional cooling due to the further excitation of excited ions (i.e., excitation of certain heavy ions may easily dominate the collisional excitation from level j to a higher level). cooling. This is the main reason why rather "low" tem- A proper calculation is often more complicated than peratures, of the order of T= 15000 K or AT= 1.3 eV, the two-level approximation described above, but the are found in photoionization calculations with roughly qualitative result remains valid. Sometimes level j "conventional" heavy-element abundances —even if may decay to an intermediate third level; or different most photoionization events give initial kinetic energies states in level j may have very different radiative decay of 10 eV or more to the freed electrons. It is worth rates. Then two or more equilibrium equations must remarking that a real photoionized gas is almost always be solved simultaneously to find the level populations. thermally stable —the cooling/heating ratio rises quick- Excited levels may be populated by recombination ly with temperature. events as well as collisional excitations. Another com- We shall now be more specific about collisional ex- plication arises if the emitted photons of energy E;; citation rates. Let Z'+ denote an ion species, two of are reabsorbed by ions in level i. Then such photons whose energy levels are i and j. Suppose that j is above may escape from the gas only after many resonance i, the energy difference being F.;, The levels' statis- "scattering" (actually absorption and reemission) tical weights (numbers of states) are «d,. and &u, . If an events, and collisional deexcitation becomes more im- ion is in level i, then inelastic collisions by free elec- portant than the ratio C, ,/A, «might suggest. The.ef- trons will cause transitions to level j, at rate C;&. It fects of resonance scattering are discussed in Sec. IV has become customary to employ a dimensionless below. "collision strength" 0;& to specify the rate as a function C. The emergent spectrum of temperature: Nebular emission with a continuous spectrum, re- X/2 2aog 7t I„Q&; sulting from recombination and bremsstrahlung, is tJ observationally difficult to separate from the basic

10'K '" n. 1' continuous spectrum of the quasar itself; so we are (10 7'06 cm3 s «) sj -Egq /& (2.9a) T more interested in nebular spectral lines, which are easier to observe. The most important elements for The inverse rate for an ion in level j to be collisionally producing these lines are hydrogen, helium, carbon, deexcited to level i, causing a free electron to g&&n nitrogen, oxygen, magnesium, and perhaps silicon and energy, is iron. Observable emission lines in the spectrum of a nebula 10 K 0;. C =(10 '"cm's ') "n (2.9b) result, of course, from radiative decays of ions in T 8 various excited levels. Some excited levels are popu- The effective collision strength 0;,. is really an integral lated by recombination events; the resulting emission involving cross sections, electron velocities, and the intensities convey information about total recombina- Maxwellian distribution; it has the virtue of being ap- tion rates. Other levels are populated chiefly by col- proximately independent of temperature for most transi- lisional excitation; the resulting emission lines give tions and temperatures of interest. Furthermore, information about cooling rates. In ordinary nebulae, 0,.&/a, and 0;&/&u«are often of the order of unity for hydrogen and helium produce mainly recombination optical and ultraviolet energy transitions. For a better lines while heavier ions produce collisionally excited definition of 0;&, see Seaton (1958, 1960) or Osterbrock lines. (One intense exception is the Lyman-alpha line (1974); but note that our 0;& is assumed to be averaged of hydrogen, for which collisional excitation can be appropr iately over electron velocities. comparable to recombination. ) Two differences be- Radiative transitions between levels i and j can-also tween recombination lines and collisionally excited occur. In the present context, incident photon fluxes lines should be borne in mind: (1) the emissivity per I will usually be low enough so that radiative excitation unit volume for a recombination line of ion Z'+ is pro- and stimulated emission rates are much less than C;& portional to n(Z""), while a collisionally excited and C&;, therefore, consider only spontaneous radiative emissivity is proportional to n(Z*'); and (2) the intensi- decay from j to i, with rate A;;. Let i be the ground ties of recombination lines are not strongly sensitive level of ion Z". For simplicity we shall pretend that i to the ratios E«&/kT, while factors e «&~ are involved and j are the only levels of interest. The equilibrium in coQisional excitation. ratio of densities of ions in the two levels is evidently Several classes of transitions may be distinguished. = n&/n« C«&/(A&, +C««), a. n. d the effective cooling rate, in- Permitted transitions satisfy the electric-dipole radia- volving emission of photons, is F&&A&,nz. In a high- tive selection rules. Two important examples are H density, "collisionally deexcited" case, where C, ; 1s—2P(E„.= 10.2 e&) and C" 2s —2P(8.0 eV). The former »A««, the population ratio n;/n« is close to the simple is the Lyman-alpha, ("I ««") line at a wavelength of 1215 = thermal ratio C«&/C&; (~,/cu«)e «&~, which is small A, or "H I A, l.215"; the latter we shall call "CIv A. 1549."

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 727

(Strictly speaking, A. 1549 is a doublet, 3%1548, 1551.) in each spectral line of the Lyman series (whose lower Permitted optical or UV transitions typically have A,, ; level is the n = 1 ground level); but since relatively few —10' s ' and (0;,/u~)- 1, so that C, , =A&; at densities of the hydrogen atoms are in the n ~ 2 levels, it is pos- of the order of n, - 10"cm '. However, because per- sible for a nebula to be transparent to any of the Bal- mitted photons may undergo many resonance scattering mer, Paschen, etc., lines. Suppose, for example, that events before escaping from the gas, and each such a recombination event has just produced a hydrogen event gives another chance for collisional deexcitation, atom in the n = 3 level. It can decay either through n collisional deexcitation can be important at densities =2, emitting a Balmer-alpha ("Ho.") and then a Lyman- as low as 10" or even 10" cm ' (see Sec. IV below). alpha ("Lu") photon, or directly to n = 1, emitting a. Intercombination or semiforbidden transitions involve Lyman-beta ("IP") photon. In the former case, the Ha C"'2s' 'S — 'P' spin changes. An example is 2s2p (E,& photon may escape easily and the La photon emerges =6.5 eV), which gives rise to the CIIIj X1909 line. (The after many resonance scattering events; bui in the lat- single square right-hand bracket indicates an inter- ter case, the LP photon will almost certainly be reab- combination line. ) For these transitions, A;; can be sorbed, exciting another hydrogen atom to the n = 3 of the order of 100 s ' while (Il,&/~, ) is almost as large level and giving another chance for decay by either as for permitted transitions. Therefore collisional de- route. Obviously, II a and Ln emission are enhanced excitation becomes important at densities of the order whileI, P is suppressed in this situation. It is sometimes of n, = 10 or 10' cm '. legitimate to suppose that all Lyman-series emission Eoxbidden transitions are electric quadrupole or mag- is thus degraded into La plus Balmer, Paschen, etc. , netic dipole transitions, sometimes with spin changes. lines (this is referred to intheliteratureas the" Case B" For example, nebular astronomers often study the approximation). More complicated cases will be men- 'H-'D transition (E;, = 2.5 eV) in the ground (2P') con- tioned below in Sec. IV; we shall also see in Sec. V how figuration of 0+'; the resulting emission lines are the presence of continuum-absorbing material, such as [OIII] AA5007, 4959, where the square brackets indicate dust grains, can modify an emergent nebular spectrum. forbiddenness. Forbidden lines are very important in D. Nlhere to find ionic data ordinary galactic nebulae because of their modest ex- citation energies, but collisional deexcitation makes In this section we merely cite references where quan- them less important in quasars. For example, titative values are given for the ionic processes men- ' [OIII] A. 5007 has A&;= 0.02 s and (0&;/~&) = 0.5, so tioned above. For the ions of interest, most available collisional deexcitation of this transition sets in between parameters have been calculated rather than measured; n, = 10' and 10' cm '. (Most galactic nebulae have den- some reviews of the methods have been given by Seaton sities n, «10' cm '; quasars have denser gas. ) (1958), Moiseiwitsch and Smith (1968), Bely and Van Many forbidden lines have wavelengths between 3000 Regemorter (1970), Burke (1972), and others. Oster- and 7000 A, which can penetrate the Earth's atmos- brock (1974) has provided many very handy tables of phere. Most important permitted and semiforbidden useful quantities; but serious typographical errors oc- lines (excepting hydrogen and helium recombination cur in some of these tables, so cross-checking is al- lines) are between 1000 and 3000 A and can be observed ways advisable. from the Earth's surface only in the highly red-shifted Karzas and Latter (1961) calculated many values as- spectra of distant quasars. This is one reason for the sociated with radiative transitions by an electron in a great difference between classical nebular analysis and Coulomb field. These data are relevant to bremsstrah- the study of quasars' spectra. Astronomers have only lung, radiative recombination, and photoionization in- recently begun to use instruments above the terrestrial volving hydr ogenic ions. atmosphere to observe the ultraviolet spectra of ordi- The photoionization cross section of atomic hydrogen nary nebulae. has been described by Menzel and Pekeris (1935), Eine-structure transitions, usually at infrared ener- Bethe and Salpeter (1957), and Burgess (1964). This gies for ions like carbon or oxygen, can be excited or can be modified to apply to other hydrogenic (i.e., one- deexcited by ion-ion as well as electron-ion collisions. electron) ions. For the photoionization cross section Typical fine-structure excitations are collisionally de- of He', see Bell and Kingston (1967), Brown (1971), excited at lower densities than the visual-wavelength and Marr and West (1976). Note that many of the cross forbidden lines. sections and interaction coefficients of interest here One should be aware of the possibility of duo-Photon have complicated resonance features, which are usually radiative processes. The most important example oc- blurred or averaged out for practical applications. curs in hydrogen at low densities. There, a hydrogen Cross sections for photoionization of outer shells of atom in the 2s level may decay, via a virtual inter- ions of C, N, O, and Ne are given by Henry (1970), mediate state, to the 1s level, emitting two photons Hidalgo (1968), and Sakhibullin and Willis (1978); mis- whose total energy is 10.2 eV; the rate is 8 s ' and the cellaneous heavier ions have been similarly treated by emitted spectrum is continuous. If n, » 10' cm, this Conneely et al. (1970), Chapman and Henry (1971,1972), process is negligible because collisionally induced Black et al. (1972), Shevelko (1974), Daum and Kelly 2s -2p transitions are then faster. (1976), Combet Farnoux and Lamoureux (1976), and Finally, we note that optical depth effects can alter others. Regarding photoionization of inner electron the relative emergent intensities of some emission shells, see Daltabuit and Cox (1972), Weisheit (1974), lines. The best-known example is the case of hydrogen. and Weisheit and Collins (1976). The "Stobbe formulae" Almost any photoionized nebula is optically very thick are useful for these (Bearden, 1966). Victor and Con-

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 728 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects stantinides (1979) have discussed "double photoioniza- Nussbaumer (1972), Jackson (1973), Flower and Nuss- tion, " in particular 0'-0' +2e, which has not been baumer (1975), Malinovsky (1975), and Berrington et al. included in quasar-rela. ted calculations. The Auger ef- (197V). Forbidden lines are of less interest in quasars; fect is discussed by MacAlpine (1974), by Bergeron and their collision strengths or emissivities have been cal- Collin-Souffrin (1974), and by Weisheit (1974). Dalgarno culated or listed by Czyzak et al. (1968), Czyzak et al. and McCray (1972) and Shull (1979) have discussed x- (1970), Saraph and Seaton (19VO), Seaton (1975), Prad- ray heating in general. han (1974, 1976, 1978), and Garstang, Robb, and Roun- Radiative recombination coefficients for hydrogen (and tree (1978). (In some of these papers the symbol Y by extension, other hydrogenic ions), a,s functions of has been used for the velocity-averaged value of Q.) temperature, have been calculated by Seaton (1959), A large compilation of radiative transition rates A, & Bates and Dalgarno (1962), Boardman (1964), Glasco for permitted and forbidden (but not semiforbidden) and Zirin (1964), and Burgess (1964). Similar values lines is available in Wiese, Smith, and Glennon (1966); for helium have been given by Burgess and Seaton (1960) energy levels and ionization thresholds are also con- and by Robbins (1968, 1970). For discussions of hydro- veniently listed there. More recent references for per- gen and helium emission lines and level populations re- mitted'~, 's include Heroux (196V, 1969), Nussbaumer sulting from recombinations in ordinary nebulae, see (1972), Flower and Nussbaumer (1975), Morton and Brocklehurst (1970, 1971, 1972), Giles (1977), and Seaton Smith (1973), Zeippen et al. (1977), Phillips (1979), and (1978). Radiative recombination coefficients for more Czyzak and Krueger (1979). A few semiforbidden A;, 's complex ions have been estimated by Gould (1978),' Tar- have been estimated or quoted by Nussbaumer (1972), ter (1971, errata corrected 1973), and Aldrovandi and Nussbaumer and Storey (1978), Loulergue and Nuss- Pequignot (1973, errata corrected 1976). baumer (1976), Flower and Nussbaumer (1975), and A useful semiempirical formula for dielectronic re- Malinovsky (1975); see also Baldwin and Netzer (1978) combination coefficients has been given by Burgess for a short compilation. Forbidden A, &'s have been {1965); Aldrovandi and Pecquignot (1973) have listed lited by Ga, rstang (1968), Nussbaumer (1971), and Nuss- appr oxlmate parameters for cl udely estlmatlng IQany baumer and Rusca, (1979). di.electronic recombination rates at low densities. How- Collisional ionization by free electrons is difficult to ever, this process is partially suppressed if either the calculate; see Bely and Van Regemorter (1970), electron density or the infrared radiation density is McWhirter (1975), and references therein. Collisional high; suppression factors for several ions of interest ionization of hydrogen is discussed by Geltman and were estimated by Davidson (1975). Rudge (1963), Rudge (1963), Rau (1971), and Krolik a.nd Very few cross sections for charge exchange (charge McKee (1978), and references therein. For other ions, transfer) have been calcula. ted; Dalgarno a.nd Butler see Canto and Daltabuit (1974), Burgess e& al. (1977), (1978) and Dalgarno (1978) have reviewed this situation. Franco and Daltabuit (1978), Khare and Padalia (1970), Charge-exchange processes of relevance to quasars' Moores and Nussbaumer (1970), and references there- spectra have been calculated by Blint et al. (1976), in. The inverse process, three-body recombination, Christensen et al. (1977), and Butler et al. (1977); was mentioned by Bates et al. (1962a, b) and by Bates other possibly important reactions have been suggested a,nd Dalgarno (1962). by Steigman (1975).. See also Chamberlain (1956), Field The two-photon decay process in hydrogenic ions, and and Steigman (1971), Brown (1972), and Tarter et al. certain related collisional transitions, were discussed (1979). by Breit and Teller (1940), Spitzer and Greenstein (1951), Regarding excitation of H' by electron collisions, Purcell (1952), Seaton (1955), Bethe and Salpeter (1957), Krolik and McKee (1978) and Crandall et al. (1974) have and Shapiro and Breit (1959). For an indirectly related compiled some likely rate coefficients; see also Gelt- situation involving He', see Drake et al. (1969), Burke man and Burke (1970), Felden and Felden (1972), Kunc et al. (1969), Griem (1969), and Drake (1971). and Zgorzelski (1975), and references 'cited by Krolik Krolik and McKee (1978) have discussed various radia- and McKee. Collisional excitation of He' has been tive processes involving the low-energy {infrared, treated by Flannery and McCann (1978). millimeter-wave) continuum a, nd its effects on some An extremely useful table of collision strengths for transitions. Raymond and Smith (19VV) have listed pa- several important permitted and semipermitted transi- rameters for many. x-ray lines. tions, involving carbon and heavier ions, has been as- sembled by Osterbrock and Wallace (1977). Calcula- II I. CONVENTIONAL, DUSTLESS PHOTOIONIZATION tions of collision strengths for permitted transitions of MODELS FOR QUASARS' SPECTRA such ions are described by Bely et al. (1963), Bely (1966), Burke and Moores (1968), Blaha (1969, 1972), A. Historical and preliminary Roberts {1970), Mewe (1972), Davis (1974), and Flower Most quasars have the same emission lines that we and Nussbaumer (1975). (In some cases, beware of a would expect to see in a photoionized nebula; therefore factor of 2 in the definition of 0;;.) Among semifor- it has seemed na, tural, since ihe mid-i960s, to think bidden transitions, the most notable in quasars is that quasars' line-emitting regions are photoionized. Clll]11909, whose collision strength or emissivity has Although this surmise cannot be verified rigorously, been discussed by Osterbrock (19VOa, b), Nussbaumer we shall later mention several pieces of observational (1972), Flower and Launay (1972, 1973), Loulergue and evidence that photoionization is more important than Nussbaumer (19V6), and Berrington et al. (1977). Other other ionizing and heating mechanisms in the line- semiforbidden collision strengths are mentioned by emitting gas.

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

In one of the first papers on the subject, Greenstein numerous cloudlets, filaments, or sheets, with a small and Schmidt (1964) compared spectra of the low-red- overall "filling factor" (fraction of volume actually oc- shift quasars 3C48 and 3C273 with spectra of ordinary cupied). A thin spherical shell can serve as an idea- nebulae within our Galaxy. Noting that forbidden lines lized approximation for some purposes. Shklovsky in 3C273 are relatively weak, and therefore (presum- (1965) pointed this out, and observations by Sandage, ably) collisionally deexcited, Greenstein and Schmidt Westphal, and Strittmatter (1966), of variations of con- proposed an electron density of the order of 3x 10' cm ' tinuum flux concurrent with nonvariations in line in- for this object. Higher densities have since become tensities in the quasar 3C 446, also suggested that the more fashionable, for the following reason. Forbidden line-emitting gas is not distributed compactly. [Shields, lines in quasars' and some active galaxies' spectra are Oke, and Sargent (1972) later gave the same argument narrower than the permitted and semipermitted lines for the active galactic nucleus 3C120.] Shklovsky (see, e.g. , Baldwin, 1975; Osterbrock, 1977); after (1965) and Burbidge, Burbidge, Hoyle, and I.ynds some controversy (see Sec. VIII below), the linewidths (1966) qualitatively discussed the stratification of are now thought to represent velocity dispersions of the photoionized regions in quasars —although the latter emitting regions; therefore the observed forbidden authors supposed that the linewidths were due to elec- lines probably arise in distinct, Less-dense regions tron scattering rather than velocity dispersions. that have smaller velocity dispersions than the gas A few more arguments were adduced in favor of where the broad lines originate. In other words, since photoionization in the nuclei of Seyfert galaxies as well we can't even detect broad forbidden lines, the broad- as quasars. Searle and Sargent (1968) noticed that the line gas must be quite dense: n, »10' cm '. (In Sec. ratio of the HP recombination line intensity to the under- VII we shall mention one or two conceivable though lying continuum brightness is roughly constant in the unlikely ways to avoid this conclusion. ) The broad-line spectra of many Seyferts and quasars, over a wide regions are of more interest here because they are range of absolute Luminosities. Because a recombina- more iritimately associated with the quasars' centers tion line from a photoionized gas indirectly measures of activity. the number of absorbed ionizing continuum photons, Before the discovery of strongly red-shifted quasars, this is suggestive of photoionization, and the numerical the Earth's atmosphere had prevented astronomers values are consistent with a moderate power-Law con- from observing ultraviolet nebular lines. By the mid- tinuum spectrum. Oke, Neugebauer, and Becklin (1970) 1960s, several quasars' spectra had become available, similarly noted that the extrapolated power-law con- and Osterbrock and Parker (1966) made some calcula- tinua of quasars seem to contain enough ionizing flux to tions to assess the idea that the observed emission account for the emission lines. Souffrin (1969a, b) re- lines were produced under fairly straightforward, though marked that the absence of certain visual-wavelength dense, nebular conditions. They found that quasarlike emission lines, arising from highly excited levels, is relative line intensities would result, from conventional evidence against the high temperatures that would ionic abundances, rather like those in some galactic probably result from strong nonphotoionization heating nebulae, at temperatures around 15000 K. This did not mechanisms. It should also be mentioned that a few constitute a derivation of chemical composition, be- early arguments aga~ns& photoionization (e.g., see cause alternative sets of elemental abundances and ioni- Osterbrock and Parker, 1965; Oke and Sargent, 1968) zation ratios would also have produced satisfactory did not take the properties of power-law and soft-x-ray spectra, , at slightly different temperatures. Bather, continua fully into account. the significance of Osterbrock and Parker's paper was The earliest period of quasar-spectrum analysis that the order of magnitude of the proposed temperature ended when Bahcall and Kozlovsky (1969a, b) produced lent plausibility to the idea of photoionization. If T models that can be regarded as Logical and major ex- ~ 10' K had been found to give the best results, then tensions of the Osterbrock and Parker (1966) approach. other heating mechanisms would have been indicated; Like Osterbrock and Parker, Bahcall and Kozlovsky but only photoionization produces doubly and triply specified particular temperatures; but instead of guess- ionized species at equilibrium temperatures below ing the ionization ratios for each element, they calcu- 30000 K lated position-dependent photoionization equilibria in Photoionization posed a geometrical question. Given modified spherical configurations with particular gas the electron density, one can estimate the volume of densities and with power-law ionizing spectra emanating emitting gas required to produce the observed emis- from a central source. Chan and Burbidge (1975) de- si.on-line luminosities. If, as supposed in many early scribed later calculations of the same type. papers, this gas were concentrated in a single cloud The next, very important step was to calculate equili- around a compact continuum source, then for reasonable brium temperatures as well as ionization ratios. In densities the cloud would be considerably Less than a classical nebular analysis, applicable at low electron light-year across and would be optically thick to elec- densities where collisional deexcitation is not too im- tron scattering. The radiation/gas density ratio UH portant, temperatures can sometimes be deduced from would be much higher than the values required in the observed intensity ratios of forbidden lines involving photoionization models discussed below. However, as different excited levels of the same ion species. Using Schmidt (1964) remarked, line-emitting gas may be such temperatures, one can calculate relative emissivi- distributed less simply. By analogy with galactic nebu- ties for other observed lines, and thus find the relative lae and supernova remnants, which are very inhomo- ionic abundances required to produce the lines. But no geneous, we may expect the gas to be in the form of direct temperature indicators are available in quasars'

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 730 Kris Oavidson and Hagai Netzer: Emission tines o7 quasars and similar objects

spectra (aside from one or two crude limits). Instead, containing the quasars. (Today, [0II] X3727 is known one can only hope that requiring self-consistency of to be a narrow line. ) ionization and thermal structures —modeling the flow (2) Even without data on linewidths, there was rea- of energy through the system —will provide additional son to suspect that the ultraviolet lines originated in information by eliminating almost all of parameter denser gas than the forbidden lines. Densities of 10' space, " where the parameters include elemental abun- cm ' or more were most suitable for the "dense com- dances. We shall describe how this might work in Sec. ponent. " III.C; meanwhile, we emphasize that the thermal equili- (3) The most straightforward models involved ioniza- brium is just as important as the ionization equili- tion parameters UH just above 10' cms ' in the denser brium! (It is relevant to note that in certain parts of gas. Such values entailed ionizing radiation pressures the models by Bahcall and Kozlovsky, the assumed which were smaller than the gas pressures (though not temperatures made collisional ionization locally more enormously smaller); this must have dynamical im- important than photoionization; in effect, some arbitrary plications. extra heating was introduced into the system when (4) With relative elemental abundances resembling thermal equilibria were not calculated. ) In the follow- those in our own Galaxy, successful models were easy ing, the term "photoionization calculation" will be to construct. But if heavy elements were assumed to be meant to include thermal as well as ionization equilibria very "overabundant" or "underabundant" relative to as functions -of position. hydrogen, then some rather intricate difficulties were Photoionization calculations, intended to apply to as- encountered. However, no proof was given that uncon- tronomical x-ray sources, were described by Williams ventional abundances could not be made to work. (1967), Tarter, Tucker, and Salpeter (1969), and Tar- Shortly thereafter, MacAlpine (1972) produced photo- ter and Salpeter (1969)'; except for deficiencies in ionization models at about the same level of calculative some ionic parameters, these were essentially suitable sophistication. He explored the consequences of vary- for application to quasars. They were in fact applied ing several parameters, and emphasized that heavy to Seyfert galaxies (Williams and Weyman, 1968; Tucker ions can play a non-negligible role in absorbing x-ray and Tarter, 1968), mainly to reproduce the observed energy. [Some of the early calculations appear to have visual-wavelength lines (ultraviolet lines in Seyferts' neglected inner -electron-shell photoionization. This is spectra could not be observed at that time). However, not true of the Davidson (1972) or of course the MacAl- one can argue that the most appropriate use for photo- pine (1972) discussions. ] In many of MacAlpine's mod- ionization calculations is to analyze the ultraviolet els, the assumed helium/hydrogen abundance ratio was permitted and semiforbidden lines, rather than the very low, as suggested by Bahcall and xozlovsky (1969a) visual-wavelength forbidden lines, because (1) in many and Osterbrock and Parker (1966) on the basis of the objects the ultraviolet lines are more representative observed weakness of the He IIA4686 and X1640 lines, of the denser, inner regions, (2) the ultraviolet lines especially in the quasar 3C273. However, as noted by account for most. of the cooling at densities above 106-' Williams (1971), these are recombination lines, whose cm ', and therefore are essential in a photoionization weakness may indicate a shortage of He'-ionizing calculation, and (3) the forbidden lines are too density photons (s & 54.4 eV) rather than a shortage of helium. dependent to be reliably modeled for Seyfert nuclei and Subsequent observations of various quasars (e.g., see quasars. Until adequate ultraviolet spectra of low-red- Baldwin, 1975) have revealed He I lines whose intensi- shift objects have become available, high-red-shift ties are not easy to analyze (see Sec. IV.D below) but quasars are the most natural subjects for photoioniza- which appear consistent with a "normal" helium abun- tion analyses. dance, n„,/nH= 0.1. Tarter and Salpeter (1969) made some comments re- Later photoionization calculations have been applied garding quasars, but the first detailed application of to quasars by Scargle, Caroff, and Tarter (1974), self-consistent photoionization calculations to quasar s Davidson (1973, 1977b), Shields (1976), Netzer (1976, was described by Davidson (1972). In order to include 1977, 1978), Baldwin and Netzer (1978), Daltabuit, both ultraviolet and visual-wavelength lines (which MacAlpine, and Cox (1978), Ferland and Netzer (1979), were not all observable for any one object), a "com- and Shuder and MacAlpine (1979); some of their im- posite" spectrum was used for comparison. The con- plications will be discussed below. Applications to clusions were as follows: Seyfert and similar galactic nuclei have been made by (1) To the extent that they were known at the time, Yankulova (1974), Shields (1974), Shields and Oke (1975), quasars' spectra could be reproduced by photoionized and others; discussions by Bergeron and Souffrin (1971, models. The only line which seemed difficult to explain 1974) are also relevant. was [0 II] A. 3727, which is collisionally deexcited at In Sec. III.B we shall give a specific example of a rather low densities. But this line was very faint in the photoionization model for a particular quasar, and in observed spectra and could probably be due to gas at Sec. III.C we describe the effects of varying the assumed distances of hundreds or thousands of light-years from parameters. But first, a few general remarks are each quasar —perhaps interstellar material in galaxies necessary. To begin with, there are some practically unanswer- able questions about the geometrical arrangement of 5Hjellming (1966), Goodson (1967), Harrington (1968), Rubin gas associated with a quasar. As mentioned above, (1968), and Flower (1969) applied similar calnQations to ordi- plausible homogeneous-density models are difficult to nary galactic nebulae illuminated by hot stars. construct. We suppose instead that a quasar has num-

Rev. Mod. Phys. , Vol. 5'l, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 731

I erous clouds, filaments, or sheets of gas, perhaps im- X1909 is about 10"cm ' (note that many pre-1977 ref- mersed in a transparent lower-density medium; a thin erences quote an erroneously higher value). Therefore shell is conceivable either as an approximate represen- we probably require average electron densities of less tation or as an alternative configuration, while disklike than about 10' cm ', although specially adjusted mod- configurations have also been suggested, e.g., by els with unusually high carbon abundances and low UH Shields (1977). We shall see that the whole assembly, values can be made to work at densities up to 10' ' or excepting the forbidden-line emission regions, is likely 10"-' cm '. Considerations outlined in Secs. IV.C and to be 1 to 1000 light-years across, which, at large IV.D below make us suspect that the actual densities cosmological distances, will probably not be resolvable are somewhat above 10' cm '. at visual wavelengths in the near future. There are The C IIIj A1909 line also provides a useful tempera- reasons (to be mentioned later) for thinking that each ture limit, because it is observed to be brighter than individual cloud is optically thick to most ionizing pho- the permitted C III A977 line (Bahcall and Oke, 1971; tons (13.6 eV&z 1 keV), so ionizing radiative transfer Baldwin and Netzer, 1978). At relevant densities, must be considered. In many calculations, the surface these two lines should have an energy-emissivity ratio of an individual cloud, filament, or sheet is approxi- f(~977) n, mated by a plane-parallel geometry. Proper treatment I(A. 1909) of convex surfaces would be much more difficult, and n, in almost any case we would not know how to select the where 'E, =71900 K and n, = 10"cm '. Although A.977 right shape and size. Fortunately, because the secon- is in an observationally unfavorable part of the spec- dary ionizing radiation is less important than the inci- trum —shortward of I , where many absorption lines dent radiation, geometrical details do not seem crucial occur in high-red-shift spectra —it is thought to be to the results; in fact, modified "on-the-spot" approxi- typically less than half as bright as A. 1909; therefore ma.tions (see Sec. II.A) are sometimes good enough to the appropriate average C" temperature cannot exceed be useful. For these reasons, in this review we do not 25000 K. This is fairly good evidence in favor of discuss the details of the iterative diffusionlike radia- photoionization and against strong additional heating tive transfer treatments, which are not particularly mechanisms. sophisticated in most calculations anyway. "Shadow- (It is true that the C IV A. 1549 and C III X977 lines, ing", and the effects. of clouds' secondary radiation mentioned in the preceding arguments, are potentially upon each other, have not received much attention; nor subject to resonance-scattering difficulties as discussed have possible internal pressure and density nonuni- in Sec. IV below. Except for possible absorption by formities in the clouds. dust grains, however, these difficulties are estimated A quasar's photoionized gas must have some distribu- to be harmless for n, ~ 10" cm '. One might also try tion of densities and values of the ionization parameter to reduce the implications of CIII] &1909 by supposing UH. In practice, the best representation that we can that it is produced by a different component of gas than use in a model is to include one, two, or three distinct C IV A. 1549 and other lines; but then upon calculation it "components" having particular values of n, and U„; turns out that the Ciil ] component must be comparable there are not enough observational data to support any- in overall importance to the C IV component, so the thing more complex. Some published models have con- estimated limits remain significant. ) tinuous distributions of UH (although the authors usually Finally, we note that the models discussed in Secs. do not specify them in these terms), but the particular III.B and III.C are mainly concerned with ultraviolet distributions chosen are rather arbitrary. (Example: lines, whose photons are assumed to escape from the one can suppose that gaseous clouds, all of one size and ionized regions, without much absorption by dust internal density, are spread uniformly throughout a grains, for example. During the past two or three spherical volume centered on a small ionizing source. years, very serious discrepancies between calculated This gives a particular distribution of UH values. ) and observed spectra have appeared, cohen the entitle There are some probable limits on gas densities and rest-wavelength range of 1000-7000 A is included. This temperatures in quasars' broad-line emission regions. problem will be discussed separately in Sec. V below; The most nearly straightforward lower limits on density it appears that wavelength-dependent extinction by dust are provided by the absence of broad [OIPj A4363 and grains is indeed important. Therefore the immediately X5007 emission (see Baldwin, 1975), which would origi- following discussion represents on)y a first approxima- nate in the same ionized zones as the prominent C ~ tion to a truly complex situation. X1549 line. If the carbon joxygen abundance ratio is not A photoionization calcoiation far from "normal, " and if the forbidden lines' absence B. specific is due to collisional deexcitation, then electron densi- We shall now describe a concrete example of a photo- ties in the broad-line gas must exceed 10' cm ', prob- ionization model; more general discussions will then be ably by a considerable factor. Upper limits on densi- given by Secs. III.C and V. Our example is a model de- ties are suggested by the presence of semiforbidden scribed by Baldwin and Netzer (1978), with the unim- lines, especially C III] A. 1909, whose importance in this portant addition of some effects involving scatteririg and regard was noted by Osterbrock (1970). The observed slight collisional deexciiation of permitted lines. It intensity of X1909, relative to Crv X1549, is large was intended to produce ultraviolet line intensities which enough to require some care to reproduce in photo- resemble the observed spectrum of PHL 938, a fairly ionization models, even if collisional deexcitation is typical quasar. PHL 938 has a red shift z = 1.95, so that unimportant. The critical deexcitation density for its ultraviolet spectrum (1000-3000 A) appears to us at

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 732 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects ground-based observable wavelengths 3000—9000 A. The assumed geometry of the gas is semi-infinite, with an ionizing continuum perpendicularly incident O. I— upon the plane boundary. This is the most convenient approximation to an illuminated surface of a represen- .OI— tative cloud of filament or sheet, which is optically thick to the ionizing photons that are produced else- where in the quasar. A finite spread in these photons' angles of incidence would not be terribly important, if O. I U„ is considered in terms of radiation density rather r X .OI — -- &+ than radiation flux. The incident ionizing continuum -- Lr-- which can be joined smoothly to the observed slope of .OOI— CARBON 1 — 'e "'o, the continuum of PHL 938, has the form F(c) c I l with s = 0.8, co = 0.7 keV (the chosen value of co is rather I 2 arbitrary). At the illuminated surface, U„= 10'0 cm s ' (IO cm) ' and n, = 10 cm . The gas pressure is constrained to FIG. 6. Equilibrium ionization fractions for helium and carbon, be uniform. The relative elemental abundances are as functions of position in the same photoionized region shown nz/n„= (100, 1.4, 1.1, 2.6, 0.4, 0.12, 0.12, 0.06, and in Fig. 5. 0.1) x 10 ' for Z=He, C, N, 0, Ne, Mg, Si, S, and Fe. (Except for helium, these values are unusually large by a large initial energy. [Even before they can be ther- astrophysical standards; but there is no need to discuss malized by elastic collisions, such energetic electrons this point yet. See the next section. ) cause excitations of atoms, especially H . See Shull With these input parameters, some details of the (1979).] Temperatures of several thousand kelvins per- calculated photoionization equilibrium, as functions of sist far beyond x = 10x„. position x in the gas, are shown in Figs. 5 and 6. Examination of the carbon ionization fractions (Fig. 7) Throughout most of the ionized zones, T is between reveals other nontrivia, l effects. Carbon is largely C ' = 0 13 000 and 16 000 K. The ionized thickness is xH 10"' in the H zone because carbon cross sections at x-ray cm, which is somewhat larger than that predicted by energies are larger than those of hydrogen and helium. Eq. (2.5), partly because of secondary ionizing photons. Some charge-exchange reactions are important where- Note in Fig. 6 that the optical depth 7„ for photon ener- ever n(H')In, or n(He )In, exceeds 0.01; for carbon, gies just above the hydrogen threshold I„=13.6 eV is of only C '+H -C"+H' was included in this calculation, the order of 50 at the ionization front where n(H ) = n(H'). but higher-ionization reactions are probably important Immediately beyond the ionization front, the tempera- too, so the C + and C" fractions have most likely been ture remains above 10000 K, because some ionization overestimated. is caused there by penetrating soft-x-ray photons Even if some aspects of the calculation are unreliablia e (c&200 eV). Helium atoms absorb many of these pho- in the H 0 zone, the calculated emission spectrum will tons; although the rates are too small to produce a not be correspondingly bad —because most of thee energyener large equilibrium He'/He' ratio, the resultant heating absorbed in this zone goes into collisionally excited hydro- is very effective because each freed electron is given gen emission, almost regardless of details. However ) most of the Mg II & 2798 emission comes from this same

I zone and may be affected by such details. The observed T —I5000 prominence of this line is evidence that at least some gas is optically thick to ionizing photons. n 4— T „, n, : (K) Calculated relative intensities of some ultraviolet IOOOO lines are shown in Table I, along with observed values (IO'cm') for PHL 938. The I-n. , CIV, C III], and Mgt; intensi- 0 ties are fairly successful, and with further "tuning" a / plausible model can be constructed. Note that the high- IO— H excitation N V A. 1240 line, and part of He II X 1640, pro- bably require a "second component" of gas, which may r / be optically thin and which either has a, relativelive y hiigh O. I— U„or else is ionized by some additional process. See .OI— Baldwin and Netzer (1978) for details. Some of the .OOI— geometrical parameters are interestinlng . First,0 it~ turns out that the observed line intensities I measured relative to the underlying continuum bright- 0 I 2 I'HL X (lO cm) ness of 938, can be explained by supposing that the gaseous regions (clouds, filaments, or whatever) FIG. 5. Various quantities as functions of position, in a par- intercept only few of the quasar's ticular photoionization model with 11~i&orm gas pressure. T is a percent ionizinnizing photons. kinetic temperature, ne is electron density, and n H is hydrogen density (including ions as well as atoms). In the lower part of Second, with the assumed values of U„and n,et the en- th e figure, the threshold hydrogen photoionizatkon optical depth ergy density of ionizing radiation in the gas is about 7H is shown along with the equilibrium fractions of H+ and H . 1/15 as large as the thermal kinetic energy density in

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 733

TABLE I. Relative line intensities (energy fluxes) from a pho- depend, are imperfectly known. Many have uncertain- toionization calculation, compared with the spectrum of the ties of 10% or 20%; some, especially those involving quasar PHL 938. faint emission lines, are worse. To that the photoionizing continuum Line C alculation PHL 938 begin, suppose is adequately parameterized by E(c}-c'e '~" in the & C r&r ~977 2.7 relevant range 13.6 eV& c 1 keV. Unfortunately, we 0vr &1034 1.1 can only guess the values of s and co, by extrapolating I~ (Hl ~1215) 100 (by def. ) 100 (by def. ) the observed 1 eV& c & 15 eV continua and by watching Nv &1240 5.8 36+ 16 for inconsistencies in the calculated emission spectra, Sl I V ~1397 1.2 and, perhaps, in x-ray observations. Suppose that O tvj ~1402 1 2. electron densities are in the previously suggested Q tvj &1486 4.0 4~ 1.6 10~ cm ' 4 10"cm '. Suppose also that the Q Iv &1549 45 45+ 10 range, &n, helium/hydrogen abundance ratio about "normal, " He ~i A. 1640 3.0 6+ 2 is O»r] ~1663 3.6 3 + 1.5 n„,/nH =0.1. In many ordinary galactic nebulae, n„,/n„ N &II] &1750 4.4 1 + 0.5? can be measured by comparing visual-wavelength re- C ir&] &1909 22 19+ 4 combination lines of both He I and HeII with those of Mg ir ~2798 28 18+ 6 hydrogen; this works well because He and He" together fill nearly the same regions as H in those nebulae, and 34/o of I.+ is due to recombination; 66% is due to collisional because recombination lines' ratios are insensitive to excitation of H . temperatures and densities there. Quasars' recombi- nation lines are trickier (see Sec. IV.D regarding the the gas and amounts to roughly 10 ' erg cm '. (This He I lines, which are most important), but the "de- is about 20 times the energy density of sunlight on the rived" helium/hydrogen ratio still seems to be close to Earth. ) PHL 938 produces an ionizing luminosity of thai quoted above —presumably because most of the perhaps 10~7' erg s ' (about 10" 7 times the total lumi- helium was synthesized in the primordial universe be- nosity of the sun), so the characteristic distance of the fore stars or quasars existed. The remaining parame- photoionized regions from the central object —if there is ters are a characteristic value (or values) of U„and the one —would be of the order of 10"' cm or 20-30 light- abundances of heavy elements, chiefly carbon, nitrogen, years. and oxygen. Carbon is especially important, because But the characteristic thickness of each photoionized C IV X1549 is a major coolant while the ratio of the region is only x„=10"'cm! Either the gas clouds (or CIII j X1909 and C Ivh 1549 lines is an indicator of U„. filaments, or whatever) are exceedingly small compared As is usually the case in nebular astrophysics, we must with the overall configuration, or only a tiny fraction assume that the relative abundances are fairly uniform of each cloud is ionized, or both. Moreover, the char- throughout the line-emitting regions of a quasar, for acteristic dynamical and ionization time scales in the otherwise the situation becomes hopelessly complicated. ionized gas, x„/w and x„/U„(where gv = isothermal Regarding the internal structures of the ionized clouds— speed of sound = 15 km s '), are around 2 days and ~ h, constant pressure, or constant density, or whatever- respectively. Evidently, the photoionized gas, overall, see the references cited. is in some sort of quasisteady state. Changing the Figure 7 schematically shows U„dependences of parameters U„and n„within plausible limits, does not qualitatively alter this remarkable situation. Incidentally, if we speculate that the photoionized re- l I gions have the same prI.'ssure as some thinner medium "THICK" 'THIN' (hotter gas, electromagnetic fields, or high-energy l034 particles) which fills the spaces between, then the en- ergy density of this medium is just above 10~ erg cm with the parameters used in the model. The energy con- tained in the region 50 light-years across wouldbe of the order of 10' erg, equivalent to less than 100 years of LLJ luminous output by the quasar.

C. Varying the assumed parameters ~~ O. l CL A model like the one sketched above, by itself, is only speculatively useful, because other models may give similar spectra. We must consider the effects I I I I I I I of the various input parameters, to see how much the IO IO lO lO IO IO IO

model could have been changed without seriously af- UH (cm s') fecting the emitted spectrum. We should also be pre- FIG. Relative line intensities produced in photoionized pared to deal with other spectra, which may differ from 7. regions with a particular ionizing-continuum shape and par- that of PHL in manner 938. Investigations this have ticular elemental abundances, as functions of the ionization been sketched Davidson 197 and Shields by (1973,1975, 7b) parameter UH. "Thick" models have &H &100; ''thin" models (1976}. Throughout the following discussion, remember have TH&1. In this figure, the intensities have been normalized that most atomic and ionic parameters, upon which we so that the recombination part of L a is equal to unity.

Rev. Mod. Phys. , Vol. 5'I, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

most of the brightest emission-line intensities (remem- self so that carbon lines, plus other heavy-ion lines, ber, w'e are always referring to the broad-line rather provide adequate cooling. C IV X 1549 is observably the than the forbidden-line regions): OVIX1034, Ln X1215, most important of these lines, while C III] A. 1909 is also NVX1240, Civ&1549, HeII X1640, and CIII]A. 1909. quite prominent. The C IV/Ln intensity ratio would These account for most of the cooling. The figure, therefore depend almost entirely upon the ratio of re- which is slightly modified from those used by David- quired cooling rate to hydrogen recombination rate; son (1977b), applies to the case of a power-law spec- this ratio is essentially the heating rate per photoioniza- trum (s = 1, co-~) with rather conventional abundances tion event, which is a measure of the average photon — nz/nH - O. l, 0.0004, 0.0002, 0.0008 for Z = He, C, N, O. energy and has little to do with the carbon abundance. These CNO abundances are smaller than those in the But in reality, for low or moderate values of U„, enough model described in Sec. III.B. Figure 7 is nearly valid H atoms are mixed in with the H' to allow collisionally for 10 cm &n, & 10' cm ', above 109 cm 3, the excited I n to assume a significant and abundance-de- C III ] X1909 intensity gradually diminishes in propor- pendent share of the cooling burden, making the observed tion to n,/(n, + n, ) with n, = 109' cm 3, while the other line ratios dependent upon the carbon abundance. Un- intensities are valid up to about 10' cm '. The MgII ~2798 fortunately, this dependence is not as strong as we and Balmer lines have not been i'ncluded, but may be would like (cf. the proportionality relations —Davidson, considered, in effect, to be a part of the calculated 1973), because of the limited extent of the zone where L n intensity. The left half of the diagram shows the C IV A. 1549 production and collisional H' excitation occur spectra of gas clouds which are optically thick to ioniz- together. Much of the collisionally excited I n origi- ing photons, while the right half refers to optically nates in the H'/H' transition zone, where it dominates thin, homogeneous clouds. Equilibrium temperatures, the cooling; much of the C IV emission originates in a among different ionization zones and values of U„, vary more thoroughly ionized zone, where it dominates the from 10000 to 50000 K in the models represented by the cooling; and only an intermediate zone gives a strongly figure. abundance-dependent contribution to the spectrum. CIII] X1909 is generally observed to be less intense Moreover, the actual amount of necessary cooling de- than C IVX. 1549 in quasars, typically by a factor of 2 or pends upon the ionizing continuum. In the exemplary 3. In Fig. 7, this occurs at U„slightly above 10' cm s ' model described in Sec. III.B, nc/n„was more than 3 for a thick cloud, or slightly below 10' cms ' for a thin times the value used in Fig. 7. Aside from minor cal- one. Many calculations have shown that this result is in- culative differences, this apparent discrepancy arises sensitive to the carbon abundance, being essentially a because (1) the ionizing spectrum with s =0.8, c,=0.7 measure of the C"/C" ionization ratio; and regarding keV has more photons around 100 eV than the s = 1 different ionizing spectra, we note that the C"/C" ra- power law, and such photons cause effective heating; tio depends upon photons just above the C" threshold (2) C III ] X1909 is reduced by about 40/0 by collisional of 48 eV. If n, &10' cm ' so that C III] X1909 is colli- deexcitation at the density adopted by Baldwin and Net- sionally deexcited, then U„must be decreased (but not zer for PHL 938, and this leads to a reduced value of very much). The suggested order of magnitude of U„ is U„, which in turn reduces the fraction of carbon which consistent with the observed brightness of Mg II X2798, is CIV; and (3) both the Lo./X1549 and the X1549/X 1909 which depends upon U„as well as other parameters. intensity ratios are close to 2 in PHL 938, rather than At the indicated value of U„on the left side of Fig. 2.5 or 3. To further emphasize the difficulties of the 7, I n is 2 or 3 times as bright as C IV A. 1549. Since this situation, we note that some early estimates (Davidson, matches the observed quasarian ratios, we deduce that 1973) made nc/n„surprisingly small, partly because the assumed carbon/hydrogen abundance ratio may be of calculative simplifications but mainly because the about right (even though it differs from the model in adopted ionizing continuum had a rather low cutoff para- Sec. III.B; we' ll explain this discrepancy later). If we meter so=0.2 keV (which may or may not be realistic), mere using the thin version, where the CIV line in Fig. while the Ln/X1549 and X1549/X1909 line ratios were 7 is unacceptably bright relative to L n, we mould read- then thought to be 3 or 4 rather than 2 or 3. just the carbon abundance downward. Some crude pro- Returning our attention to Fig. 7, we see that for portionality relations given by Davidson (1973) are use- UH =10 cms, OVI 11034 3nd NV & 1240 are much ful for estimating the dependences of CIII]/Civ/Lo. in- weaker than observed. If the adopted continuum is not tensities upon nc/n„. far wrong, these high-ionization lines must originate We must now digress on a matter of nebular principle, in another component of gas, which either has higher concerning the above "derivation" of nc/n„. The C IV/Ln values of U„, or else is ionized and heated by some intensity ratio depends significantly upon nc/n„only be- additional mechanism. In order to make NV 11240 about cause part of the L n emission is due to collisional ex- as bright as OVI X1034, while both are comparable to citation of H atoms. If I n were purely a recombination I-a in the second component, it is probably necessary to line (intensity= 1 in Fig. 7), then it would represent increase the nitrogen/oxygen abundance ratio [Osmer merely the number of recombination events, which for and Smith (1976) noted this point]. The high-excitation T«10~ K play only a minor role in cooling the gas (see component of gas may be optically thin, except perhaps Sec. II). The temperature would necessarily adjust it- to He+-ionizing photons just above 54.4 eV and to radio- frequency waves (see Sec. VII.C below). As remarked by Davidson (1973), an optically thin secondary com- Modified to take into account charge exchange, and partial ponent is also useful for providing HeII A. 1640 emission. collisional deexcitation of C &&&I &1909 at ne =10 cm Note: we do not insist that the two components are well

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 735 defined and distinct, but rather, that "two components" roughly the same ionization zones, and all have roughly merely provide the simplest representation of what may similar temperature dependences; so in some ways be a disagreeably complex situation, involving some their implications are not strongly model dependent. continuous distribution of values of U„and n, . However, the weak lines are too faint to have been re- By going into the numerical details of a two-compo- liably measured yet, and some of them may be colli- nent model (e.g. , see Davidson, 197Vb, or Baldwin and sionally deexcited to an uncertain degree (see Baldwin Netzer, 1978), one finds that the major, low-U„com- and Netzer, 19V8). The most useful weak line is per- ponent may have U„around 10' cms ' or possibly less, haps NIV] A. 1486, whose ratio with CIV 11549 is quite while the required carbon/hydrogen abundance ratio is a good relative-abundance indicator, and whose critical larger than it was in a single-component model which deexcitation density is several times higher than that of sought to explain only the CIII]/CIV/I o. ratios. This is C Ill]X1909. At present there is a suspicion, fore- the main reason why, for example, a model discussed shadowed by Shields' discussion and exemplified in the by Scargle, Caroff, and Tarter (1974) was able to have PHL 938 model described in Sec. III.B, that the nitro- a carbon abundance significantly larger than the rather gen/carbon ratio is larger than "normal. " VPnere nitro- low single-component values mentioned by Davidson gen is similarly overabundant in some objects in our (1973). Scargle, Caroff, and Tarter postulated a par- own Galaxy, it is thought to be due to secondary nucleo- ticular, widespread spherical distribution of values of synthesis, involving nuclear processing in stellar ma- U„. Netzer (1976) later described a somewhat more terial which has already been provided with appreciable sophisticated spherical model; while MacAlpine's concentrations of heavy elements. In miscellaneous (1972) earlier calculations had also been spherical. At samples of galactic material, n„/(nc+ no) is often cor- the level of approximation allowed by available data, related with (no + no)/n„, in a way that has a qualitative these spherical models were practically equivalent to explanation involving star formation and nucleosynthesis two-component models, with high U„ in the inner re- rates (see Peimbert, 1975; Pagel, 1976; Searle, 1976; gions and low U„near the outer edges. It has some- Pagel et al. , 1978; Shields and Searle, 1978; and refer- times been said that a two-component model is unde- ences therein). Thus we surmise that an unusually large sirable because it involves more parameters than, say, nitrogen/carbon ratio implies unusually large heavy- a spherical-distribution model; but this is not true, element abundances in quasars. But this is only a suspi- because the latter type of model must have at least one cion, without firm observational or theoretical bases. or two parameters which specify the radial dependence . What about the form of the ionizing continuum? As of the gas distribution. (These parameters have often explained by Davidson (1977b), if 5'(c) decreases less been made implicit and therefore inconspicuous, by steeply than c ', then a larger carbon abundance and a arbitrarily supposing the gas to have uniform density, in smaller value of U„are indicated for the major com- some sense which may involve a constant" filling factor. ") ponent of gas. A flatter spectrum, with a high-energy Incidentally, the three sets of spherical models that cutoff somewhere beyond 200 eV, has some appeal be- we have just mentioned exemplify three alternative cause it makes the high-excitation OVI, Nv, and HeII choices regarding optical depths. Scargle, Caroff, and lines easier to explain; in an extreme case, a single- Tarter (1974) assumed the gas to be optically thin. component model might suffice. It is slightly disturbing This simplifies the calculations, but is implausible be- that there is rio evidence for a correlation between ob- cause of the observed MgII emission mentioned earlier, served continuum slopes and line intensities (see Fig. because of the lack of observed Lyman continuum emis- 3 of Baldwin and Netzer, 1978), and in Sec. V we shall sion from the ionized gas (Davidson, 1976), and be- worry about whether the observed continua as well as cause of some photon-counting arguments to be cited the line intensities may be affected by wavelength-de- in Sec. V. MacAlpine (1972) supposed that the gas is pendent extinction along the line of sight to each quasar. optically thick to ionizing photons, but (mainly for cal- Occasionally there has been speculation that much of culative convenience) he assumed that each of the nu- the ionizing radiation in quasars is emitted by some merous clouds is individually thin. We are not enthu- very hot thermal gas (T& 10' K). This would be dis- siastic about this picture either —partly because Lyman comfiting, because such gas might produce strong continuum absorption is usually not observed (Oke, 1974; ionizing lines as well as a continuum. For the moment, Osmer and Smith, 197V), partly because the individual we shrink from numerical consideration of this pos- clouds would have to be amazingly thin in the geometri- sibility —but see Daltabuit, MacAlpine, and Cox (1978). cal sense (see remarks near the end of Sec. III.B above), In summary, the preceding arguments are relevant and partly because we require large optical depths in and necessary, but dissatisfying: the winds of argument the Balmer lines (see Sec. IV.C below). The spherical blow through too many loopholes, and the field is posted configuration adopted by Netzer (1976)consisted of many with too many caveats. We can assign limits to the im- clouds which were each optically thick to ionizing pho- portant parameters, but these limits are partly subjec- tons; the "covering factor" may be small so that we tive, in the sense that they recede somewhat if one is can see between clouds into the center of activity where willing to postulate special circumstances. the continuum originates. &oze scarce can the heavy elements be? In an early Next, as discussed by Shields (1976), one can try to discussion (Davidson, 1973), nc/n„ in quasars was pro- estimate the oxygen/nitrogen/carbon abundance ratios posed to be smaller than the solar value by a factor of by comparing certain faint ultraviolet NIII], N IV], the order of 6. But this suggestion followed from "ob- OIII ], and OIV] lines with the C III ] and C IV emission. served" CIII]/CIV and CIV/Ln intensity ratios which Shields pointed out that these lines all originate in were smaller than more recent values, from the use

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 736 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects of an ionizing continuum which was steeper than cur- thermal motions of atoms and perhaps subsonic tur- rently fashionable continua, from a neglect of colli- bulence. In hydrogen gas, the relative linewidth &X~/ 4 sional deexcitation of C III ] A. 1909, and from the use of X~ is then of the order of zv/c-10 (where ge is the a one-component model, which seemed acceptable be- speed of sound). Since the oscillator strength for I.o. cause the OVI and NV lines were not, at that time, is about the same as the integrated oscillator strength generally known to be intense. Today, the observa- for the Lyman continuum, the ratio of I n optical depth tional data make it difficult to allow a carbon abundance to photoionization optical depth is very roughly &~/w„ smaller than perhaps half the solar value. A smaller /&Az -104. Figure 5 shows that w„= 50 is easily value would not permit the carbon lines to assume their possible in a photoionized region, giving 7 ~ -10 . Dif- observed share of the cooling. fusion of resonance photons through such optical depths IIom overabundant might the heavy elements be? Per- is a nontrivial problem. haps several times more abundant than in the Sun, as in The first realistic approaches to this problem, so far as the model described in Sec. III.B; but this limit is even we know, were those by Holstein (1S47), by Zanstra and by more difficult to establish than the lower limit. Imagine, Sobolev (see Zanstra, 1949, 1951).Their results, and the for example, that electron densities are actually as high work of Koelblad (1S56), Osterbrock (1962), and Capriotti as 10'o cm ', or even a bit higher; then C III ] X1909 (1965, 1966), justify a very simple example, which gives a emission would suffer appreciable collisional deexcita- surprisingly correct impression of the general results. tion, requiring a larger carbon abundance to provide the Imagine a simple resonance emission line in a spheri- observed intensities. We suspect that one cannot push cal gas cloud. The line opacity is uniform throughout this speculation very far, because the dependences are the cloud; the cloud's geometrical radius r corresponds such that it would become very difficult to explain why to a line-center optical depth &0» 1. The linewidth is the relative intensities of C III X 977, C &II] X1909, due to thermal motions, so that if we measure the photon CIV A. 1549, and Ln do not vary more from quasar to wavelength displacement q (q= 0 at line center) in ap- quasar. It is difficult to make such an argument defi- propriate units, then the optical depth profile is simply nite —but given the observed presence of semiforbidden "' lines in quasars' spectra, and supposing that "God is &(n) = 7.e . (4.1) not malicious, " we are prejudiced against special mo- Suppose that every resonance absorption event is fol- dels, in which these lines are severely affected by col- lowed reemission, so that we have pure resonance lisional deexcitation but nevertheless remain prominent by "scattering. " Henyey (1940) pointed out that absorption because the elemental abundances are carefully adjusted at leads to reemission at g' with probability given by to give compensating effects. p a calculable "redistribution function" R(}7,q'}. In the We remark, in passing, that one of the most interest- thermal-width case, it turns out that we obtain prac- ing facts in astronomy is the prevalence of heavy-ele- tically correct results pretending that q' is uncor- ment abundances which are either like those in the Sun, by related with —the "complete redistribution approxima- or scarcer. However, some galactic nuclei may have g tion. " The probability of reemission in interval dq' then larger concentrations of heavy elements (see Shields becomes and Searle, 1978), This seems consistent with recent ' modeling tendencies regarding quasars. y(q')d}7'=7} e dq', Concerning the ionization parameter U~: Most of the L a emission probably originates in the low-U„com- regardless of q. We can also pretend that the scattering ponent of gas. There, U„ is of the order of 10' cms '. is isotropic. Imagine now that a resonance photon is This means that the thermal energy density of the initially created at the center of the spherical cloud. ionized gas is between 10 and 100 times the ionizing After almost every scattering event, the photon's ~q~ radiation energy density. This may have some gas- will be small enough so that its mean free path to the dynamical implications, but also, it is something to next scattering event is not larger than several times wonder about: is there a reason for such a factor to x/7'o« x. Diffusion in space will re(luire very many occur? scattering events before the photon has traveled appre- Finally, we close this section with avery large caveat: ciably far from the center of the sphere; and before in Sec. V, we shall explain why much of the above dis- this has happened (as explained by Osterbrock, 1962), cussion, and some of the observational data, should be there occurs a single scattering event, involving an ion taken with a grain of salt, or more likely, with many in the "tail" of the Maxwellian velocity distribution, fine absorbing grains of dust. which causes ~q~ to suddenly become large enough so that &(q) & 1, allowing the photon to escape "in one IV. LINE TRANSFER jurnp. " Essentially, we can neglect excursions in space (except of course the last one) and consider only excur- A. General considerations sions in wavelength, each of which is negligibly corre- Until now we have supposed that nonionizing photons lated with previous events. The probability of escape, always escape from nebulae. But this is not necessarily per scattering event, is approximately true for "resonance lines" (permitted transitions whose lower levels are ground levels}, which can have very @(n}e ~'dn=w"* exp( n* ~,e-*}an- large optical depths in a photoionized cloud. Consider, J for example, the special case of L n. -Suppose thai its v2 1 (4.3} local linewidth is due to the Doppler effect, involving e~ln7'0 To 1+9llnro ro

Rev. Mod. Phys. , Vot. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 737

Most escape events occur near q =+Vln~o. The average and by Adams (1971, 19V2, 1975a,b), Harrington (1973), number of scattering events before escape is therefore and Hummer and Kunasz (19V9), who used different methods. Their results show, fortuitously bui conven- Q +1 (4.4) op iently, that Eqs. (4.4) and (4.5), with moderate values where K, =1.9V'ln&, is close to 6 for a wide range of &,. of K, and K» are indeed realistic for 10 & so~ 107. (Note that when escape occurs after Q scatterings, K, and K, vary only through factors of the order of 3 diffusion in space has typically removed the photon from over this range in &o. Adams (1975b) found that K, be- ihe center of the sphere by a relatively small distance, comes proportional to &0 ' as 70 increases beyond 10'. only several times &0'~2r ). If &0 and ~ in Eqs. (4.4) and (4.5) represent the half- The average distance between scattering events being thickness through the appropriate gaseous region, K, =3 somewhat larger than y/7'o, the totalpathlengthtraveled and K, = 6 are useful volume-averaged estimates for by the photon before escape is many practical cases. We suspect that the Doppler width of a line partly =K y, (4.5) l, involves local subsonic turbulence; this can appreciably where K, is moderately larger than K„and of course widen a line of a heavy ion species, supplementing the the flight time to escape is I„,/c. ions' thermal speeds by bulk motions with a fair. frac- If resonance line photons are created throughout the tion of the larger sound speed zv. It is usual to suppose sphere, we find that the appropriate volume-averaged that a turbulent velocity dispersion mimics a Maxwellian K, and K, are somewhat less than the central values; distribution (Gaussian in each direction); but there is and we can use the same equations, crudely, for a plane no assurance that this is correct at the edges of the dis- or cylindrical geometry if vo and r are half-thicknesses. tribution in g. In some early discussions, velocity dis- These results have several implications: persions for line scattering near quasars were taken to (1) Density of trapped resonance line pho-tons: If be very large because the observed emission lines are resonance scattering did not occur, the average escape so broad; but for various reasons, including analogies time would be about y/c; with scattering, this is multi- with more familiar galactic objects, we now prefer to plied by K,. So the equilibrium density of resonance think that each localized cloud of gas has a relatively photons is enhanced by a rather modest factor of the small internal velocity dispersion, while an observed order of K,. Therefore, despite the terrific optical linewidth corresponds to relative velocities of thousands depth for I n in a photoionized region, the radiation of kms ' between many different clouds. pressure of trapped L n photons is not enormously Ferland and Netzer (1979) have combined a Monte greater than that of the ionizing continuum and may even Carlo resonance scattering program with photoioniza- be smaller. tion calculations and have remarked that it is necessary (2) Continuum absorption of resonance photons: Sup- to be careful with L n and with other resonance lines pose that resonance photons can be destroyed by some that partly originate in gas where n(H ')/n(H ') is not very continuum absorption process (e.g., photoionization; large. For each resonance line they defined a "generat- or absorption by dust grains) with optical depth &,« ~o. ing function" G(70), proportional to the rate of creation In the path length l „the effective absorption optical of resonance photons per unit of optical depth. Some depth is K,&,. examples of G(&0), for CIVX1549 and Ln in typical (3) Branching alternatives oy collisional deexcitation, . plane-parallel photoionized regions, are shown in Fig. After an ion has been excited by resonance absorption, 8. The generating functions for C &VX. 1549 are fairly it will probably decay by reemitting a resonance photon. well behaved, so one can easily obtain valid results for But there may be some small probability of alternative this line by using average escape probabilities Q, esti- decay to an intermediate level, or of ionization of the mated from published scattering calculations or guessed excited ion, or of collisional deexcitation. Then the from Eq. (4.4). Because there is a limit to the column resonance scattering process gives Q chances for the density of C" in a particular model, the 11549 photons alternative process to occur. For example, if the can escape through the maximum-&0 side as well as the critical electron density for collisional deexcitation of the resonance excited level, neglecting scattering, is I I I I (typically 10" or 10'6 cm '), then the criti- n, effective 5 cal density is "'=n,/Q. n, &a L&, In principle, these agreeably simple results may seem 4— C ZZ dangerously oversimplified. The actual redistribution 0 ) I54e function R(rt, 7l') does in fact cause q' to be somewhat 2— correlated with q (Unno, 1952). Worse, for largish ~'ill I I I I I (typically ~q~ R 3, important for &o & 10 ), the line' s wings have a Lorentzian natural profile rather than a 10 IO IO lO IO IO IO IO IO IO lO ~0 Gaussian Doppler profile, so that 7(ri) becomes pro- portional to g rather than e +, and g' becomes FIG. 8. Generating functions for the Ia and C &v A1549 reso- strongly correlated with g. Then it turns out that ex- nance lines in thick photoionized regions, according to Ferland and Netzer (1.979). These functions describe the production of cursions in space as well as in q are important. This resonance-line photons per unit optical depth To at line center. problem has been solved numerically by Avery and House Note that the C && A1549 production region is distinctly limited (1968), Auer (19'68), Panagia and Ranieri (1973), and in 70, but collisional excitation in the H zone produces some Bonilha et al. (19V9), who used Monte Carlo methods, La emission even for 70 &105.

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

&p 0 boundary. The cases of 0 VI p 1034 and N V A 1240 although we may have overlooked some possibilities. should be similar. Next, we mention collisional deexcitation. C IV X 1549 The La line is different. Throughout most of the H' is a convenient and important example. The rate for region, for 7'o~ 10~ in Fig. 8, Ln photons result from deexcitation of the excited 2P level by thermal electrons recombination and G(ro) is automatically rather uniform is (10 7 cm3s ')n, at temperatures near 15000 K. If the But near and beyond the ionization front, where L e radiative decay rate is A, ,, but Q scattering events must emission is caused by collisional excitation of H atoms, occur before a resonance photon escapes, then the ef G(r,) is sensitive to U„and to the slope of the ionizing fective radiative rate is A, ,/Q =(10"s ')Q '. The effec- continuum. Comparable numbers of L a photons can be tive collisional and radiative deexcitation rates are created in the two regimes. Ferland and Netzer found equal at an electron density n,"'=(10"' cm ')Q '. To that the recombination La photons cannot penetrate the guess Q, we need 7, Fine structure in the upper level thick partial-H' zone, but are reflected back to escape splits the A. 1549 line into two components, and for sim- through the 70= 0 boundary. The eollisionally excited plicity we shall use the optical depth inthe brighter com- I n photons also tend to escape in the same direction. ponent. Adopting a thermal linewidth, we find a half- A proper representation of G(ro) for. La is important, thickness &0 = 10 in the carbon-rich, U„=10' cm s ' because two of the processes discussed below (Balmer model described in Sec. IH.B; Z, =3 then gives Q = 10~' line emission, and collisional deexcitation of Ln) de- and ~',"=10" cm-' for CEV A. 1549. This value would be pend upon it. decreased for larger U„. Minor details: LQ. connects only the 2p and 1s levels. Shuder and MacAlpine (19V9) and Ferland and Netzer Collisions with electrons, ions, and atoms cause transi- (1979), considering possible deexcitation of CEV1549 in tions back and forth between 2p and 2s (Seaton, 1955). more detail, have found that the A. 1549 intensity is un- Below, when we cite approximate arguments regarding likely to be reduced very much except perhaps in ex- Ln scattering, we shall usually ignore the existence treme, unconventional photoionization models. Ferland of ihe 2s level, and no serious error will result; but it and Netzer have argued that the emergent intensity is is understood that the 2s level is included in most au- not strongly reduced even at high densities approaching thors' detailed calculations. A few other processes, z,"', because this line is the primary coolant in regions such as induced emission, are similarly glossed over where C" is abundant. If collisional deexcitation of in this discussion, because they are inessential for our CIV X1549 reduces the cooling efficiency, then the local purposes. equilibrium temperature must be increased so that the A. 1549 B. Possible suppression of resonance emission lines resulting intensity is scarcely affected after all. This example shows the danger of adopting any fixed Now we shall be slightly more specific about some temperature when thinking about this subject. (The re- possibilities mentioned above. First, there is the pos- sult for A 1549 becomes more complicated in models sibility that resonance photons may be absorbed by con- with "flat" ionizing continua, where OVI X 1034 and tinuum processes. Absorption by solid grains is poten- NVX1240 can assume much of the cooling burden. ) tially so important that we discuss it separately in See. Krolik and McKee (1978)and Zirin (1978)suggested that V. This leaves ionization of excited ions by the reso- quasars' hydrogen lines are largely "thermalized, "by nance photons. As discussed in See. IV.C, thepopulation which they meant that collisional excitations and deexeita- of H atoms in the n=2 level is enhanced by I e scatter- tions from the n= 2 level are very important. Colli- ing, and such atoms can be ionized by UV photons with sional excitations to n= 3 are most important, were A &3645 A. MgII X2798 is the resonance line which is discussed by Shields (1974) and Netzer (1977a), and will most likely to be destroyed in this way, because the be mentioned in Sec. IV.C below; but here, let us con- relevant photoionization cross section is largest close sider collisionaldeexcitations from the n= 2 level be- to the 3645 A limit, and also because the excited H cause these might reduce the L n intensity. The critical atoms are most numerous in the H'/H transition re- electron density, at which collisional deexcitations oc- gion where the Mg&I emission originates. Accordjng cur as fast as escaping L n photons, is to Ferland and Netzer (1979), in some extreme models yg«f -(10&6.9 cm-3)Q-~ =(]0~6 4 cm 3)7 (4.8) there can be enough excited H atomstogiveacontinuum optical thickness of the order of 0.1 near 2798 A. The where &~ is the total line-center optical depth mea- effective thickness for resonance-scattered photons is sured from the illuminated boundary (we have assumed enhanced by a factor of the order of K,/2, or perhaps thai Ln photons cannot escape in the direction toward K2 if escape toward the large-7'o direction is impossible; large rz ). In a photoionization model, most of the re- so it is conceivable that 30%or more of the Mgo X2798 comMnation Le emission comes from zones where emission might thus disappear. 7~ &10 and therefore is not strongly reduced by eol- Another possibility concerns He atoms in the meta- lisional deexcitation unless n, exceeds 10" cm '. 3S stable 2 level (see Sec. IV.D), which can be photoion- Coll isional 1y excited Ln is produced near the ioniza- ized by CIV 11549 and L e photons. Davidson, Fastie, tion front and beyond, where 7 ~ becomes very large and Hartig (19VV) suggested that Ln is reduced this but where n, is probably smaller than in the H zones. way. But likely column densities of He 2'S atoms, as %here it is produced, collisionally excited Ln accounts estimated by Feldman and MacAlpine (19V8) and Netzer for most of the cooling, so we have the same effect as (1978), seem too small to destroy much of the C Iv or for C&VA. 1549: any reduction in cooling efficiency sim- L n emission —as noted by Krolik and McKee (19V8). ply causes the temperature to rise until the required Other excited ions are probably even less important, cooling rate is obtained. The temperature rise in this

Rev. Mod. Phys. , Vol. 61, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 739 case is only slight; for example, a rise from T= 10000 ordinary nebular values: I(Hn)/I(HP) is often far too K to T = 12 500 K would increase the basic H excitation large while I(HP)/I(Hy) is slightly too large (Baldwin, rate by a factor of. 10. If n, Z (10'5' cm 3)w~~, colli 1975; Weedman, 197V, and references therein; Oster- sional excitation from the n= 2 level to higher levels be- brock, 197V). Possible explanations have been dis- comes fast enough so that Balmer lines account for a cussed by many authors, including Osterbrock and noticeable fraction of the local cooling; in effect, some Parker (1965), Oke and Sargent (1968), Anderson energy flux is then diverted from La to the IIa line. (19V0), Wampler (1971), Adams and Petrosian (1974), A photoionization calculation which ignores this effect and others cited below. Wavelength-dependent extinc- will nevertheless give almost the correct total for ihe tion by interstellar dust is an obvious possibility —but hydrogen line intensities, provided that the density is a reasonable wavelength dependence cannot explain both not extremely high. the Hn/HP and the HP/Hy ratios simultaneously. Col- Ferland and Netzer (1979) and Shuder and MacAlpine lisional excitation from the ground level (see Parker, (1979) have verified some of the above points by includ- 1964) is also inadequate, even in combination with ing collisional deexcitation in phoioionization calcula- extinction. Two more promising ideas are that col- tions. The La output cannot be reduced by more than lisional excitation from the n = 2 level (mentioned near 30'%%up or 40% if n, ~ 10'P cm ~, and the actual effect is the end of Sec. IV.B) is moderately important, and/or probably smaller. Mgii, Fell, and C III] emissions that the emission regions are optically thick in the Bal- may be enhanced by the possible rise in temperature. in mer lines. These effects may happen if the density of the H zone —unless they also are collisionally deexcited. H' atoms in the n =2 level is greatly enhancedby trapped These effects were included in the calculation discussed L n photons. in Sec. III.B, bui do not amount to much more than the We can guess whether a plane-parallel photoionized uncertainties in ionic parameters. Often, aphotoioniza- region like that described in Sec. III.B is optically thick tion calculation which does not include collisional de- to Balmer-line photons, as follows. First, let the excitation of resonance lines mill give fairly correct columnar Ln creation rate in the photoionized region- results for the bright ultraviolet line intensities, even i.e., Ln photons created per unit area of illuminated if collisional deexcitation does in fact play a moderate surface —be PE„, where E„=n, U„as previously defined role (this is an example of rules (i) and (ii), cited in and g is of the order of unity. (Realistic models, with Sec. I.D). The fainter lines may be affected, though. L n produced by collisional excitation as well as re- Resonance-excited ions might be photoionized by the combination, usually have /=1 to 5.) l, et Q~ denote incident continuum. For example, if the Balmer con- the average number of scattering events undergone by tinuum (c & 3.4 eV, X &3645 A) is intense enough to ionize a Ln photon before escape; during each of these "scat- a hydrogen atom in the a=2 level in less time than tering" events, a hydrogen atom lingers in the 2P level Q/A, ,, this would reduce the Ln intensity and there for a time A~' =1.6 x10 's. The column density of ex- mould be other effects also. It is easy to show that this cited atoms is therefore process is less important than collisional deexcitation N(H 2P) = A~' (4.7) if U„ is less than about 10"cms '. However, the ef- fE„Q~ fect may provide a small amount of extra heating en- According to Eq. (4.4), Q~ =K,7'~„, where 7~ is the ergy, from the Balmer continuum, in the less-ionized total line-center optical thickness of the H' region be- zones. cause we suppose that Ln photons can escape only through the illuminated boundary. For a thermal line- C. The hydrogen line spectrum width at T =15000K, the line-center cross section for In ordinary galactic nebulae, hydrogen emission lines Ha absorption is 0~ =10 " cm'. Thus of the visual-wavelength Balmer series (Ho.'&6563, HP X4861, ... ) and the infrared Paschen series &H~ =Or~&i~ &EH~i &ie (Po. AI8751, PP A. 12818, ... ) are by-products of re- combination events. These lines' intensity ratios can 10'o 6 cm 2s ' 7 be predicted from relative rates of recombination to the various levels, branching ratios of decays toward (F 1024 4 cm-2 s-1 H ' (4.8) the ground level, and less important parameters (Sea- ton, 1959; Brocklehurst, 1971). Radiative transfer (Here 7„ is the photoionization optical depth as pre- does not present much difficulty for ordinary nebulae, viously used. ) For a photoionized region like that dis- which are optically thin in the Balmer and higher series cussed in Sec. III.B, with U„=10' cm s ' and n, = 10 ' of lines but so thick in the I.yman lines that LP, Ly, cm ', this gives &„=0.002 7~ =20&„. The appropriate etc., are mostly degraded to Ln plus other lines (this value of v„ to limit the region of interest, although is called "case B"; see remarks near the end of Sec. indefinite, will exceed unity and may be considerably ILC). The calculated intensity ratios I(Hn)/I(HP) and larger (see Fig. 5); so it is evident that Balmer-line I(HP)/I(Hy) are rather insensitive to densities and tem- optical thicknesses in quasars' photoionized regions perature, and generally match observed nebular spec- are probably large. tra quite well if certain mell-understood observational The parameters v„and f are mildly dependent upon corrections are made. U„and upon the shape of the ionizing continuum, and However, when broad Balmer lines are observed in also, if each linewidth && is increased, then ~~ is pro- the spectra of low-red-shift quasars and Seyfert gal- portional to 4X '. Aside from these dependences, &0 axies, their intensity ratios do not always match the is basically a measure of the local photon flux E„, which

Rev. Mod. Phys. , Vol. 5't, No. 4, October 1979 740 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects probably varies as R ' where R is distance from the hypothetical central source. Since we can roughly es- timate a quasar's luminosity, a characteristic value l.5 of P„gives us a characteristic radius for the arrange- ment of Balmer line-emitting regions. This adds in- l.o terest to an actual estimate of vH derived from line ratios. Capriotti (1964a, b; 1966) investigated the ratios of 0.5 optically thick Balmer lines mhich might occur in low- density nebulae (n, ~ 10' cm '); he found that I(Ho. )/ I(Hp) rose with increasing v~, but I(Hp)/I(Hy) de- l GOO creased. Cox and Mathews (1969) later studied cases with some leakage of Lyman lines. In all of these cal- FIG. 9. Schematic dependences of the Ha, HP, Hy, and E'n culations, absorption processes from levels n ~ 3 (i.e., recombination line intensities upon TH~, the optical depth in Paschen and higher series) were neglected. This was the IIo. line. Each ordinate is roughly a line intensity relative justifiable at low densities, but as the populations of to the traditional nebular "Case B"value. Possible contribu- excited levels increase with density, Paschen line ab- tions due to collisional excitation of A are not included here. sorption can become important near quasars. Netzer (1975, 1977a) calculated ratios of hydrogen ionization front. More generally important at high den- lines at quasarlike gas densities, including absorp- sities and moderate temperatures are excitations from tions and collisional transitions from many levels; the n = 2 level, as mentioned by Shields (1974), Netzer Krolik and McKee (1978), adding some elaborations and (1977), Krolik and McKee (1978), and Ferland and considering more extreme cases, later found essen- Netzer (1979). Such excitations are important if the tially similar results. These calculations were based electron density exceeds 10' cm '. However, the pro- upon "mean escape probabilities" for each line, derived cess cannot be calculated very reliably, because it from average numbers of scattering events undergone depends upon the n =2 population. According to Ferland by photons before escape from uniform, plane-parallel and Netzer, hydrogen lines tend to result from recom- slabs (Capriotti, 1965). For recombination lines, Fer- bination where H+ predominates, and from collisional land and Netzer (1979) have estimated that the most ap- excitation where H predominates; to some extent the propriate "average" value of 7H, for use in an equa- two regions may be considered separately. A homo- tion like (4.4), corresponds roughly to the middle of the geneous, uniform-temperature model is generally not photoionized region and is smaller than the total Hn a valid approximation to this type of situation. optical thickness by a factor of 10-30. The effective The collisional excitations mentioned above are caused value of 7H for use in conventional quasar-related by thermal electrons. But in a case where soft-x-ray models is therefore between 50 and 500, accompanied photons are numerous enough, and in a region where by a v~ of the order of 104''. Of course, 7Hp 0 27' n, «n(H'), additional effects may be caused by non- T~ =0.067„, etc. thermal electrons with energies of the order of 100 ev. In a gas which is optically thick in the Balmer lines, Such electrons are produced by soft-x-ray photoion- an obvious effect is the conversion of HP to Pn and Hn, izations (especially of helium atoms), and may lose because after every HP absorption event, the hydrogen appreciable fractions of their initial energies by ion- atom which is left in the n = 4 level has a. 52% prob- izmg and excxtxng H' and He' (Spitzer and Tomasko, ability of decaying to n =3 (emitting a Pn photon) rather 1968; Spitzer and Scott, 1969; Dalgarno and Me&ray, than to n =2 (HP). This increases I(Hn)/I(HP), and 1972; Shull, 1979). This effect is an exception to the since TH„& r„, I(Hp)/I(Hy) is decreased. But as Netzer rule that elastic collisions usually cause effectively (1975) pointed out, the Paschen optical depth r~ may instantaneous thermalization of most superthermal par- become significant if 7„ is sufficiently large, because ticles in nebular situations. Direct excitation of lines trapped Hn photons increase the n = 3 population. If Pn in this manner has not been included in most photoion- photons cannot escape freely, the emergent HP inten- ization calculations. sity is increased at the expense of Pa and Hn. Figure In summary, the observed intensity ratios of the 9 shows typical behavior of emergent Ha, HP, Hy, and Balmer and Paschen lines in quasars' spectra seem to Pa intensities in cases where these lines result almost be quite reasonable for photoionized regions with den- entirely from recombination; if the effective value of sities n, ~ 10 cm ', but theoretical complexities pres- is of the order of 100—as indeed it should be, in ently deter us from making very specific additional photoionization models with 10 &n, &10' cm '—then statements. There are observational difficulties, too, the effective value of 7'~ is of the order of 2 and I(Hn)/ including the possibility that wavelength-dependent ex- I(HP)/I(Hy)-5/1/0. 35. These line ratios are just like tinction may occur outside the emission regions (see those observed in typical quasars and Seyfert galaxies. Sec. V). Some of the Balmer and Paschen emission may result The various Balmer and Paschen line profiles may be from thermal collisional excitations of H' atoms. Such different, if each line preferentially originates in a dif- excitations directly from the ground level are negligible ferent part of the gas because of the interplay of all the with ionizing continua like 5'(c)-z ' (Netzer, 1977a), but effects described above. Such differences in line shapes may be important for "flatter" or "harder" continua, would not be large and have not yet been established. whose soft x rays cause more heating beyond the H'/H In objects whose lines vary in time, one can look for

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 741 changes in the intensity ratios in order -to check their or 8, with only slight dependence on temperature or consistency with possible changes in T„„(seeBoksen- density; this fact should be useful inassessing thewave- berg and Netzer, 1977; Tohline and Osterbrock, 1976; length-dependent influence of intervening material upon Phillips, 1978a). quasars' spectra. In some low-red-shift quasars, the It is essential to remember that each detailed cal- 14686 line is surprisingly faint (Bahcall and Oke, 1971; culation, such as we have been mentioning, refers only Baldwin, 1975; Chan and Burbidge, 1975). to a small region (cloud?) of gas, while a real quasar's The HeI lines are perhaps more interesting, because spectrum must be the total of many such localized spec- they represent a larger fraction of the helium and also tra. 'The distributions of the gas, in density as well as because they are subject to complicated transfer ef- location, are indeterminate. This fact helps to cause fects. Two types of helium recombination lines are "observational entropy, " which leads to the second rule observed in ordinary nebulae: those resulting from tran- cited in Sec. I.D. sitions between singlet levels, and those involving trip- Finally, we should mention the LP line, which for let levels. %e shall'not discuss the singlet lines, be- reasons mentioned above must be faint. The presence cause they are relatively faint and should behave qual- or absence of LP ~1026 in a quasar's spectrum is very itatively like hydrogen lines. The triplet lines are dif- difficult to establish; because of the usual presence of ferent, because the lowest triplet level (1s2s 'S or 2'8) OVI A1034 emission. Bahcall (1966) discussed the pos- is metastable; forbidden decay from there to the ground sible escape of LP emission from quasars' clouds; level (1 'S) usually requires a long time, about 8000 s Adams (1975a) and Netzer (1976) later considered the (Griem, 1969; Drake and Dalgarno, 1969; Drake, 1971). problem with some refinements and similar results. It At large densities (n, ~ 10' cm '), 2'S is depopulated appears that 7~ ~ 10 would be required in order to per- mainly by collisionally induced transitions to 2 'S and mit I(LP)/I(Ln) ~0.1. Such a small optical depth is pos- 2 'P. 'The equilibrium population of the metastable level sible only if the local velocity dispersion (i.e., in each can be large enough to cause optical depth effects. small fraction of each ionized zone) is very large (thou- Figure 10 shows the lowest He' triplet levels. Some sands of kms '). As remarked by Netzer (1976), the galactic nebulae are optically thick in the &3889 line, Ly line would then be almost half as bright as LP; and so that decays from 3'P to 3'S convert some trapped Ly has not been observed. Netzer also discussed the &3889 photons to ~~43 o00, 7065, 10830 emission. Ob- possibility that LP can be enhanced in clouds with more served relative intensities of ~3889, ~7065, and other conventional internal velocity dispersions, if T~ is 1ines then provide enough information to estimate large; but even in the most favorable cases I(LP)/I(Lo.') &(13889) and to make appropriate allowances when de- ~ 0.05. Because the 0 VI ~1034 line is brighter, and be- ducing the helium abundance; see Bobbins (1968, 1970), cause rest wavelengths shortward of L~ are obser- Bobbins and Robinson (1971), and Brocklehurst (1972). vationally difficult, the LP line is of little use at the Such nebulae are also thick in the ~10830 line. present time. However —as the reader will probably not be sur- prised to learn —additional complications occur near D. The helium line spectrum quasars. Many quasars' and Seyfert galaxies' HeI ~5876 intensities, when compared with Hn or HP, imp1y Several helium lines —He I A~4471, 5876, 7065, larger-than-"normal" helium abundances /n„~ 0.2) 4686 have been observed in quasars' (n„, HeG &&1640, — if ordinary nebular assumptions are made (Baldwin, and be used to estimate the helium abun- spectra may 1975; Osterbrock, 1977). If some of the hydrogen emis- there. The He lines may also provide infor- dances sion is collisionally excited, as discussed in Sec. IV.C, mation about possible, avelength-dependent extinction, the results become more extreme. Today it is believed while the He I line ratios give us some hints about radia- that the helium is not greatly overabundant, but rather tion densities in the line-emitting regions. that a quasar's ~5876 emission is enhanced by process- The He Q lines are mainly due to recombination and es that are negligible in lower-density nebulae. should not be significantly affected by self-absorption; Shields, Oke, and Sargent (1972) and Shields (1974) their standard "case 8" emissivities, as used for pointed out that soft-x-ray photoionization is more ef- galactic nebulae (Seaton, 1959; Brocklehurst, 1971) but fective for helium than for hydrogen, so that helium/ extended to higher densities, are probably adequate. ' These lines provide an indication of the number of He+- ionizing photons (c &54.4 e&) which are absorbed in the emission regions (Williams, 1971). Moreover, the intrinsic ratio I(&1640)/I(&4686) should be close to 7

~Chan and Burbidge (1975) suggested that L e A1215 depopu- lates the n =4 level of He+ by causing stimulated emission. FIG. 10. The lowest triplet This would reduce the He&& &4686 intensity. However, as re- levels of Heo. marked by Davidson (1977), even if the wavelength coincidence were perfect, the necessary I cz density would require unlikely gas densities (e~ &10~~ cm ); and Krolik and McKee (1978) have doubted that the effect would work even at high densities. Moreover, the relevant wavelengths (hydrogen la, and the HP analog of He+) differ by 0.5 A, which is equivalent to a ve- locity difference of more than 100 km s ~.

Rev. Mod. Phys. , Vol. 51, No. 4, October 'f 979 742 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects hydrogen recombination line ratios can be misleadingly Feldman (1978) has show'n that if U„~ 10' cms ', then large in H regions excited by soft x rays. But this the He 2'S and 2'P levels are noticeably depopulated process would enhance most of the helium lines togeth- by photoionization. This tends to reduce ~(A.10830). er, and in particular, the Helg4471 line (2'R 4'D) The HeI &5876 line is broader than Bp in some spec- should have almost 40%%u~ as large an intensity as &5876 tra (see references cited by Netzer, 1978). Netzer if both are straightforwardly due to recombinations. has argued that the ~5876 emissioncomespreferentially Although the ~4471 line is too faint to observe accu- from regions with larger I'„, i.e., from regions closer rately in most quasars, it appears that I(&4471)/ to the center, as discussed above; so thatthedifference I(A5876) &0.3 in some cases (Baldwin, 1975). Therefore in linewidths means that velocity dispersions increase selective enhancement of X5876 seems to be required. inward. This would occur in some types of gravita- MacAlpine (1976) proposed collisional excitation as a tionally bound systems. suitable mechanism for enhancing &5876. Collisional E. Fluorescent processes excitation of ground-level helium atoms by thermal electrons is almost certainly negligible, while col- Suppose that an ion species Z has a resonance line lisional excitation from the metastable 2'S level to 3'D whose wavelength nearly coincides with a strong emis- (see Fig. 10) is expected to have a small rate coeffi- sion line produced by some other ion species, so that cient. Therefore MacAlpine suggested that the exci- Z" ions are radiatively excited by the emission line. tations are based on the 2 'P level. If there are enough Suppose that the Z'+ ions also have intermediatelevels, metastable He' 2'S atoms, the gas is optically thick which provide alternative routes for radiative decay in the ~10830 line; trapped &10830photons then enhance from the radiatively excited level. Then resonance the 2'P population and the rate for 2 'P-3'D excitation fluorescence occurs: the strong emission line is partly by electron collisions is appreciable. In order to ob- converted to longer-wavelength lines of Z". tain the desired enhancement of ~5876, MacAlpine in- The classic nebular example involves some OIII lines voked a trapping factor (number of scatterings before emitted in transitions between several 2P3d, 2P3P, and escape) Q(&10830) —300, optical depth ~(X10830)-100, 2P3s levels, which are about 41, 37, and 33 eV above and electron density n, -10"cm '. He remarked that the 2p' 'P ground level of 0++. These spectra1. lines the enhancement factor can give information about the have wavelengths between 2800 and 3800 A. In nebulae, gas distribution, because it depends upon the local flux they should not be significantly produced either by col- parameter E„=n, U„. Feldman and MacAlpine (1978) lisional excitation (the excitation energies are too high) have made detailed calculations involving 11 levels of or by recombination (oxygen is much scarcer than hy- He, with particular reference, to the spectra of certain drogen and helium); nevertheless, the lines are ob- Seyfert galaxies, and have essentially verified 1VIac- served in many nebular spectra. This was explained Alpine's earlier estimates. Netzer (1978) incorporated long ago by Bowen (1934, 1935), as follows: The He' multilevel helium into specific photoionization calcu- analog of Ia(&= 30.379A), which is producedstrongly lations. by recombination, can excite 0" from its 2P' 'P, near- The enhancement of He I~5876 is more complicated ground level to 2P3d 'P, (A.=303.80 A). From this excited than that of Be, but has similar results: The enhance- level, an 0'+ ion can decay through the other levels ment factor depends upon the thickness of the He' zone mentioned above, producing the observed lines. The in such a way as to be dependent upon E„and less sen- Bowen process is numerically complicated, because sitive to n, . One can use photoionization models to the HeII &304 recombination photons must coexist with guess UH and therefore to assign a characteristic value 0 ions, and these resonance photons can also cause of n, to any particular I'„. The slope of the ionizing photoionization of H', He, and other species. A sec- continuum is important; for a given value of I'„, ~5876 ondary process is also possible: 0 III~374 photons, is enhanced more strongly if there are relatively more emitted in transitions downward from the 2P3s 'P higher-energy photons. level, may be absorbed by N+ to give additional flu- In order to enhance HeI &5876 by a factor of 2, which orescent lines including N DI X4640. would roughly match observations, E„must be almost Weymann and Williams (1969) calculated relevant 10" cm 's '. Vfith reasonable values for U» this im- conversion efficiencies and escape probabilities for plies n, —several times 10 cm '. These values are like Hei' I n in regions ionized by moderate power-law the photoionization model in Sec. III.B and are also continua like E(s) —s '. Their calculations, although consistent with the Balmer line ratios as discussed in intended to represent forbidden-line gas in Seyfert gal- Sec. IV.C; the results of Feldman and MacAlpine (1978) axies, are probably relevant to higher-density gas. and Netzer (1978) seem reasonably consistent. The assuming thermal linewidths, they found large effi- proposed value of I'H would occur about 10 or 20 light- ciencies (20%%uq —45/o) for Bowen conversion of HeH I.n years from the center of a luminous quasar, or less to OUI emission; but they also pointed out that velocity than 1 light-year from the center of a rather modest gradients can be important. At present, the Bowen Seyfert nucleus. The helium abundance is probably OM emission must be regarded as only a possible in- close to "normal, *' i.e., n„,jns =0.1, not far above the dicator of internal motions in quasars' clouds; obser- value produced in the primordial fireball. But this vational data are too limited for any significant con- statement is not very certain, and we should acknow- clusions. ledge that some of the above-cited numerical results Perhaps more useful are the 0&A.X1304, 8446 lines. are not valid in a speculative model that we discuss in In many Seyfert galaxies and quasars, I(X8446) Sec. V. F below. -0.05I(Ho. ) (Oke and Shields, 1976; Netzerand Penston,

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission tines of quasars and similar objects 743

1976; Phillips, 1978); and in the spectra of some high- NV &1240, or both. There are serious difficulties with red-shift quasars, I(&1304)-0.05 I(Ln) (Osmer and LP fluorescence: it should entail other emission lines Smith, 1976, 1977; Baldwin and Netzer, 1978). These which are not seen, the observed ratio I(MgIIA2934)/ lines cannot result from collisional excitation or from I(OIA8446) would require an implausibly large mag- recombination, bec ause the exc itation ene rgies are nesium/oxygen. abundance ratio, and (because the rel- high, because oxygen is expected to be too scarce, and evant wavelength coincidence is imperfect) implausibly because certain other 0& lines are not seen. The most large local turbulent velocities of 100 kms ' would be likely excitation mechanism is that described by Bowen required. Since the wavelength coincidence involving (1947), who noted a near-coincidence between LP, at NV &1240 is even less perfect, velocity differences of &=1025.72 A, and the 1025.77 A transition between several hundred kms ' would be required for exci- atomic oxygen levels 2P' 'F, (practically ground level) tation by &1240; but Grandi and Phillips suggest that and 2p' 3d 'D'. If an oxygen atom is radiative1. y excited in this case, the velocity differences need notbe local- by Lp, it can decay to 2p' 3p 'P (A =11290A), then to the Np emission may be emitted and absorbed in dif- 2P' 3s 'S' (8446 A), then to the ground level (1304 A). ferent clouds of gas. The line near 2950 A has roughly This process is not very effective in ordinary galactic a fourth the intensity of MgIz&2798, and merits further nebulae, where LP photons are too easily destroyed by investigation; i.ts wavelength does not straightforwardly conversion to Hn and La. But Shields (1974) pointed match &2934. out Chat a large optical thickness &~, as discussed above for quasars and Seyfert galaxies, can increase V. DUST AND QUASARS the LP density so that resonance excitation of oxygen Correlation visual and ultraviolet data becomes more effective. Oke and Shields (1976) sug- A. of gested that the OI &8446 emission in Seyferts may in- In 1976 or 1977, it became evident that something volve either this process, or else radiative excitation important was missing from previous analyses of qua- by the continuum, which occurs in galactic nebu1, ae sars' spectra. Ultraviolet lines with rest wavelengths (Grandi, 1975). However, the latter process should also &2000 A had been measured only ln high-red-shift spec- form 0I &7990 emission, which is not observed inqua- tra, while visual and infrared lines with ~ & 3000A had sars and Seyferts (but see Christensen, 1979). The been measured only for low-red-shift objects. In most QIX&1304, 8446 lines probably confirm that Balmer- attempts to specify composite sets of line intensities, line optical depths are large as discussed in Sec. IV.C. the visual and ultraviolet spectra had been joined by Netzer and Penston (1976) estimated the OI &8446pro- supposing that I(Ln)/I(HP) was of the order of 40 as in duction efficiency, using mean escape probabilities with the simplest photoionization models. However, Baldwin uniform distributions of atomic oxygen and T~; they (1977a) showed evidence for a much smaller Lo.'/AP found that ratio. Assuming that low- and high-red-shift quasars are basically alike, he constructed a composite spec- I(X8446) &o 0 (4.9) trum in which the connection near 2500A was made I(H~) ""n„' by referring to the continuum brightness and to the where Q„ is a mean escape probability. Q„ is pro- MglI&2798 line. This led to I(Lo.)/I(HP) =3, which has portional to T„, and, according to Sec. IV.C above, is since been confirmed —except perhaps for an ines- probably of the order of 10' in quasars' broad-line sential factor of 2 or so—by ultraviolet and infrared emission regions. This gives I(A8446)-0. 02I(Hn) if the observations. Wu(1977), Davidsen, Hartig, and Fastie oxygen abundance is conventional (solar); but heavy (1977), Boksenberg et al. (1978), and others have used elements like oxygen may be "overabundant" near qua- rocket- and satellite-borne instruments to observe sars (see Sec. III). Hence the observed &8446 inten- ultraviolet spectra of objects whose visual-wavelength sities are explainable without much difficulty. The main spectra are known from ground-based observations. limitation of the calculations is the assumption of uni- Hyland, Becklin, and Neugebauer (1978), Soifer et al. formity, but the orders of magnitude are probably cor- (1979), and Puetter, Smith and Willner (1979) have ob- rect. 'The 0I lines provide gratifying confirmation of served visual-rest-wavelength lines shifted into the Secs. III.Cand III.D; it now seems probable that relevant infrared in high-red-shift spectra. In each case, I(Ln)/ electron densities are mostly close to 10"cm ', U„ I(HP) is not far from 5 or 6 while I(I a')/I(Hn) is less. is around 10 cms ', the gas is optically thick in many than 2. Thus we have the so-called "Lu/HP (or La/Ha) hydrogen and helium lines, etc. problem": the observed ratios are an order of magni- We shall mention 0& X~1304, 8446 again in Sec. Q, tude smaller than the expected values. because these lines may be useful indicators of "red- In Sec. IV we have already mentioned one possible dening" or wavelength-dependent extinction by inter- explanation, proposed by Krolik and McKee (1978) and stellar dust grains. The emission of an 0I &8446 photon by Zirin (1978), wherein collisional excitations and de- ls almost inevitably followed by emission of a, +1304 excitations from e =2 enhance the Balmer lines while photon, giving an intrinsic ratio I(&1304)/(&8446) = 6.5. reducing L6. But if the observed Ln/Hn/HP ratios If the observed ratio is smaller, then there must be are to be explained entirely in this way, the electron preferential extinction of the &1304 line. densities must be above 10' cm ', making the observed Mg D &2798 is prominent in quasars' spectra. Grandi Clif] X1909 emission an embarrassment. and Phillips (1978) have proposed that a feature near Moreover, other ultraviolet/visual line ratios also 2950 A is Mg G ~2934, and that both this and at least show discrepancies. 'The HeG X1640 and X4686 re- part of &2798 are fluorescence lines excited by LP, combination lines are analogous to the Hn and Pn lines

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

3500 2000 l500 l000

PHL 957 FIG. 11. Quasars' ultraviolet F„cc u (reddened) ~ 2256+ OI T continua as reddened power ~ OH 47I laws. The crosses, circles, I.O— and dots show the apparent continua of three high-red- shift quasars, at ultraviolet 0.8— rest wavelengths. The curves

Cll show two hypothetical continua C= o 6— which initially were power 0. laws (Cat or rising), but which have suffered rather ordinary 4 0.4— amounts of inter stellar redden- ~o ing by dust grains without a 2200 A feature. The point of 0.2— this figure is that the log-log curvatures of the reddened power laws resemble the curvatures of the observed continua.

LOg

of hydrogen, but require far higher densities than the frared/visual line ratios (see Wampler, 1968, 1971; hydrogen lines in order to be affected by self-absorp- Bees et.al. , 1969; Osterbrock, 1978). Ifquasars' emis- tion and collisional excitations; I(&1640)/I(X4686) should sion-line spectra are reddened by intervening dust, be close to 7 under plausible conditions. But it appears their continua are probably also affected. Continuum that I(X1640)/I(L o.) = 0.05 in typical high-red-shift quas- reddening and line reddening can be different, ' but for ars while I(A4686)/I(HP) =0.15 in low-red-shift quasars simplicity we shall assume that they are the same. One (e.g. , see Baldwin, 1975; Baldwin and Netzer, 1978), argument against reddening of quasars, based on as- giving [I(X1640)/I(X4786)],~~„,„, =2 if the apparent Lo./ sumed power-law spectra (McKee and Petrosian, 1974), Hp ratio is 6. (Cf. Netzer and Davidson, 1979; Shuder is not very strong because the observed continua are and MacAlpine, 1979). Observations by Osterbrock and not smooth power laws (see Fig. 1). Abroad absorption Koski (1976) and Boksenberg et al. (1978), when com- feature near 2200 A, often associated with interstellar bined, give the same result for the particular Seyfert. reddening in our Galaxy, is not prominent in quasars; galaxy NGC 4151. Another pair of useful lines is but this does not disprove reddening there, because the OIX1304 and %8446, mentioned in Sec. IV.E, whose physical basis of this feature is not well understood, and intrinsic ratio should be I(&1304)/I(&8446) = 6.5.' Again besides, a somewhat mysterious "bump" around 3000A making a composite estimate, using references cited makes the 2000-4000 A continua uncertain for many in Sec. IV.E, we find that [I(X1304)/I(X8446)], „,„, is quasars. If we don't worry about these features, we closer to unity than to 6.5. For the quasar 3C 273 this can fit the observed shapes of typical high-red-shift ratio may be less than unity, although the X1304 inten- continua by smoothly reddened power laws —with the sity is very uncertain (Oke and Shields, 1976; Boksen- important detail that the intrinsic continua F(c)-s ' may berg et al. , 1978). Therefore, although the HeII and have spectral indices s which are zero or negative 0 I lines are faint and difficult to measure, we think (Fig. 11). that they provide evidence for an overall ultraviolet/ Pn emission has been measured in at least two quas- visual discrepancy, a factor of the order of 4 which ars' spectra (Grasdalen, 1976; Puetter et al. , 1978). probably also accounts for much of the Lcr/HP discrep- Since this line has the same upper level as HP, it has ancy. been suggested that the apparent Pn/HP intensity ratio This ultraviolet/visual deficiency, if real, is evidence can be used to measure reddening. The indicated amount that many small solid grains exist somewhere along the of reddening is less than we have suggested in the case line of sight to each quasar. Interstellar dust grains of 3C 273, but larger in the case of another quasar. in our Galaxy are known to "redden" the light of distant However, as explained in Sec. IV.C, the Balmer and stars, i.e., they absorb and scatter more at shorter Paschen lines of quasars are probably affected by self- wavelengths. Similar reddening has long been suspected absorption effects, and also, an infrared/visual red- for Seyfert galaxies, partly because of certain [SII] in-

sror example, suppose that redde~I~g occurs near a quasar; 0 I ~1304 is a resonance line, but resonance scattering and imagine a model wherein the line-emitting regions are distri- collisional deexcitation should affect it less than in the case of buted in a doughnut-shaped volume largely surrourided by dust, L 0. , because oxygen is far less abundant than hydrogen and but with less dust covering the "hole of the doughnut" where therefore has smaller optical depths. the compact continuum source is.

Rev. Mod. Phys. , Vol. 61, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 745

dening deduction, e.g., from PcI/Hp, must be extra- uniform, so that a hydrogen column density N„gives an polated to give the much stronger ultraviolet effect. extinction optical depth at wavelength X = 5000 A, Therefore we shall not weight the Pn/HP results very 7'~(&5000) = (10 "' cm') 1) highly in this discussion. X„. (5. There are several possible locales for thehypothetical On the average, n„-1 cm ' in our part of the galactic dust grains. We shall now discuss these locales sep- disk, with a half-thickness of about 300 light-years; arately. this would imply v, (X5000) a 0.2 toward extragalactic objects, except that the actual extinction is patchy be- B. Dust in our Galaxy cause n„ is very nonuniform. Some astronomers have Dust grains (solid particles with sizes & 1 p. m; found practically no extinction in directions perpen- "smoke" might have been a better term) are associated dicular to the galactic disk (e.g. , Sandage, 1973; with interstellar gas almost everywhere in our Galaxy. Feltz, 1972), but others have suggested minimum values The investigation of such dust has become a sizable of ~„(X5000) between 0.04 and 0.2, with 0.1 a likely com- topic: see the review articles by Wiekramasinghe and promise value (see Holmberg, 1974; Appenzeller, 1975; Nandy (1972), Aannestad and Purcell (1973), Salpeter Knude, 1977; Bursteinand Heiles, 1978 a, b, and refer- (1977), and Ney (1977), and references therein, as well ences, therein). Values toward most quasars must be as parts of a book by Spitzer (1978). somewhat larger because their directions are not perpen- Some of the properties of interstellar dust can be dicular to the galactic Qisk. Ultraviolet extinction is studied by comparing the spectra of selected nearby — roughly 3 times as strongas at 5000A (Fig. 12). Therefore stars with those of more distant stars of the same types. we expect that extinction within our galaxy reduces For most eases, the wavelength-dependent extinction most low-red-shift quasars' apparent LoI/Hp ratios by per unit column density is close to a standard function, 10% to 60%, perhaps 30% is typical. The effect is much shown in Fig. 12. This must be due to dust because less for a high-red-shift quasar, because differential the interstellar gas is very transparent at most non- extinction is smaller for the longer red-shifted w3ve- ionizing wavelengths. The extinction curve is almost lengths. proportional to A. ' for visual wavelengths. There is a It is possible to imagine a larger effect, which is not strong broad feature near A-2200 &, and there are excluded by presently available data. Suppose that there also infrared features not shown in the figure. Different is a component of relatively small grains, which cause types of grains are important at different wavelengths. extinction mainly at ultraviolet wavelengths, extending At some wavelengths, extinction is due to scattering to distances well beyond 300 light-years from the and to absorption in roughly equal amounts, but the galactic plane. We would have no good way of knowing infrared and the 2200 A features are mostly absorption. about such dust from pre-1978 observations, but there Absorbed radiation. usually heats a grain and is ther- could be a significant effect on apparent ultraviolet/ mally reemitted at infrared wavelengths; some grains, visual intensity ratios for extragalactic objects. made of silicates, metals, or graphite, can survive at C. intergalactic dust? temperatures up to 1000 K or more. Because grain temperatures are not necessarily related to gas tem- We should not exclude the possibility that dust may peratures, dust ean exist in photoionized gas. be found anywhere along the line of sight to a quasar. 'The galactic dust-to-gas ratio is said to be rather Some absorption lines in quasars' spectra may be due

I NTERSTELLAR EXTINCTIQN CUR&E

IO— ~ ~) ORL klo55 FIG. 12. Interstellar extinc- I tion in our Galaxy, as a func- I ~ / ~ tion of wavelength. The data 8- ~ ~ ~ ~ ~ EQ u 0/ t are taken from Schild (1977) 0/ Cm] XI909 CK LI549 and reference s therein. The . CP 6- extinction optical depth is CL normalized arbitrarily. CI hlgII X2798

I I 0 6 I/X (p, '}

Rev. Mod. Phys. , VoI. 51, No. 4, October 1979 746 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects to intervening galaxies or intergalactic gas clouds; dust The maximum temperatures at which dust. can survive, grains may also be present there. The resulting extin- T„=1000—1500 K, occur at x'- 1-100 light-years, close ction effects would tend to be greater for high-red-shift to the locations of the dense emission-line regions. quasars, and this would oppose the red shift depen- Most of the grains' infrared radiation would be at dence of reddening in our Galaxy. The 2200 A feature, rest wavelengths near (30 p.m) (T„/100 K) '. (Note, if present, would be smeared out by differential red however, that T~ may span a considerable range in any shifts (as noted by Shuder and MacAlpine, 1979). There one object. ) Some quasars' spectra have "bumps" near might also be tenuous dusty material filling clusters X- 3 p, m, and emission around 10 p, m may alsobe present, of galaxies around the quasars. See Schmidt (1976). but the important wavelengths between 20 p, m and 100 p.m arepracticallyunexplored Neuge- D. Dust in quasars' galaxies (see Neugebauer, 1978; bauer et a/. , 1979; Rieke, 1978). We must admit, how- Although the evidence is incomplete, we suppose that ever, that data on 3C 273 do not suggest the presence of quasars occur in galaxies, probably in galactic nuclei. a very large far-infrared flux (Hildebrand et a/. , 1977; he analogy with Seyfert galaxies makes it plausible Elias et a/. , 1978). Much of a quasar's intrinsic en- that spiral galaxies, containing dusty gas, are in- ergy output may be in the soft-x-ray range (see below), ' volved. The observed narrow forbidden lines may where grains' absorption efficiencies are low; so we come from such gas, and a few quasars have observable should not expect the total infrared flux to approach the emission-line "haloes" with large galaxy-sized radii total luminosity. If quasars vary over timescales of (Kristian, 1973; Wampler et a/. , 1975; Stockton, 1976; hundreds or thousands of years, their apparent in- Richstone and Qke, 1SVV; Green, Williams, and Mor- frared fluxes may be reduced by light-travel-time ef- ton, 1978; Bergeron, 1976). Interstellar dust may fects. therefore be present at distances between 100 and 10' Polarization studies may be relevant. Dust grains light-years from a quasar. 'To cause extinction by a cause polarization in two ways: polarization-deper. — factor approaching 10 at ultraviolet wavelengths, with dent extinction occurs if elongated grains are statis- a dust-to-gas ratio like that in our Galaxy, the gas tically aligned (see Chap. 8 of Spitzer, 1978), while column 10" ' density' pf„would be of the order of cm polarization-dependent reflection is possible even if the -10' cm light-years. This is not a terribly large val- grains are spherical. Nonthermal (e.g. , synchrotron) ue. Incidentally, the gas is likely to be ionized by the processes can also produce polarized continua, but if quasar; this is one reason why we should not expect the emission lines are polarized like the continuum, we the dust to be exactly like that in our Galaxy. may conclude that scattering and/or extinction have Some relevant points are: (i) Such extinction would occurred. 'This appears to be the case for some Seyfert occur in the same wavelength reference system as the galaxies (Angel et a/. , 1S76; Stockman, Angel, and emission spectrum. Resonance scattering can there- Beaver, 1S76), but most quasars are only weakly po- fore increase the extinction of the central parts of the larized, and at least parts of their polarizations are Ln and CIV X1549 lines. (ii) Because most observations not due to dust grains (Stockman and Angel, 1978; of quasars include galaxy-sized regions, se~tfexinI. by Stockman, Angel, and Miley, 1979). Polarization, dust is only indirectly important and the effective ex- unfortunately, can only be a positive indicator of ex- tinction is mostly due to absorPtion (iii) Th. e apparent tinction or scattering; extinction can occur without po- continua probably show that the 2200 4 absorption fea- larization. ture cannot be as strong as it is in our Galaxy, although this feature is perceptible in the spectrum of PHL S38 E. Dust in quasars (Baldwin, 1977a; Drew, 1978). As implied above, some dust grains might exist, at We can roughly estimate the equilibrium grain tem- temperatures of the order of 1000 K, within a quasar's peratures that result from ultraviolet absorption and line-emitting regions. This possibility was acknowl- infrared reemission. For simplicity, suppose that the edged by Baldwin (1977a), Davidson (197Vb), Davidsen, absorption-emission efficiency of a roughly spherical Hartig, and Fastie (1977), and Hyland, Becklin, and grain is proportional to X '. Suppose that the quasar's Neugebauer (1978), and has been considered in some radiation is equivalent in grain-heating effect to an detail by Baldwin and Netzer (1S78), London (1979), ultraviolet luminosity L (-104' 104' erg s ') concentrated Shuder and MacAlpine (1979), and Ferland and Netzer at a wavelength of 100o A. Then the equilibrium dust (1979). grain temperature at distance x from the quasar is Dust within a photoionized region can very effectively (10001ighk-year, s)"' absorb the Ln and other resonance lines. As explained +( I)'' in Sec. Vf.A, resonance scattering increases the aver- age escape path length by a factor K, -6. This means that an ultraviolet resonance line can be strongly ab- sorbed while nonresonance ultraviolet lines are only Some radio sources with emission lines are at the centers slightly affected and nonresonance visual-wavelength of elliptical or giant elliptical which are galaxies, traditionally lines are practically unaffected. Since is roughly less dusty than spirals. If quasars are really in such galaxies, K, the same for all resonance the amount of de- as suggested by Sandage (1972), Silk, Spinrad, and Field(1973), lines, Hawkins (1978), Wehinger and Wyckoff (1978), and others, our struction of such a line depends mainly upon the size discussion is weakened but not invalidated —the emission lines of that line's creation zone. If the Ln photon density obviously show that some diffuse matter is present. See also is decreased by absorption, the population of the n =2 Rowan-Robinson (1977). level of hydrogen is also decreased, and this would

Rev. Mod. Phys. , VoI. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 747 change the situation discussed in Sec. IV.C. Baldwin TABLE II. A possible "corrected" quasar's line spectrum. — and Netzer (1978), Shuder and MacAlpine (1979), and [Intensities relative to E(l.a) = 100]. Ferland and Netzer (1979) have concluded that such res- onance-line absorption may be non-negligible in quasars Apparent Corrected C alculated Line intensity for reddening in model but cannot account for factors exceeding 2 or 3 in ratios like I(La)/I(HP). If Ln and other resonance lines were 0vr ~1034 20 31 38 more strongly reduced by absorption, then the apparent IA .&1215 100 100 100 weaknesses of HeQ X1640 and some other ultraviolet Nv &1240 25 24 27 lines as well as the continuum, relative to La, would 0 rv] &1402 10 7 2 be difficult to understand. The suggested internal dust- N rv] &1486 3 2 3 to-gas ratio, to give a moderate effect as discussed by Crv ~1549 40 23 30 He rr &1640 5 2.6 5 the above-cited authors, is small —about 10% of the 3. Q rrr] &1663 3 1.5 1 ratio in our Galaxy. C rrr] &1909 18 7 5 Internal dust can also absorb some of the ionizing Mg rr ~2798 23 5 radiation and thus modify the line generating functions. He rr &4686 2.5 0.37 0.44 Unfortunately, it is difficult to know how the absorp- HP &4861 17 2.5 1.7 tion efficiency varies with photon energy; one cannot Her &5876 0.5 0.1 safely extrapolate the curve shown in Fig. 12. A cor- Hn &6563 77 9.6 7.7 relation between He'/H' ratios and infrared emission P(x &18 751 6 0.5 0.4 from dust, in some emission regions in our has Galaxy, 22% of I-o. is due to recombination; 78Vo is due to collisional been interpreted as an effect of differential extinction excitation of H . of H -ionizing photons (c & 13.6 eV, X &912 A) and Heo- ionizing photons (c &24.6 eV, X&504 A); this has led to suggestions that v~ continues to rise with photon en- the quasar. If we make plausible corrections for red- ergy at ionizing energies (Mezger, Smith, and Church- dening, the intrinsic continuum and relative line inten- well, 1974; Panagia and Smith, 1978). On the other sities are changed from those which were used in Sec. hand, theoretical considerations suggest that dust III; so photoionization analyses must be reconsidered. grains' absorption efficiencies should not increase Here we shall describe just one suitably modified photo- steeply at ionizing photon energies (Huffman, 1976, ionization model. 197V; Jones et a/. , 197V). Very small grains (sizes Table II shows a typical, composite spectrum of line & 0.02 p.m) cause increased extinction somewhat beyond intensities, obtained by averaging many observed spec- c-10 eV, but for c» 10 eV, the photon energies and tra. We have listed observed values as the "apparent" frequencies must exceed characteristic solid-material spectrum; then we have corrected these relative inten- energies and frequencies so much that grains become sities for reddening, using an idealized extinction law transparent except for internal photoionization. Baldwin vgX) =(3100 A/A). This is very crude —no discrimina- and Netzer (1978) described photoionization calculations tion has been made between absorption and scattering with dust such that 7„-~ ' and also ~~-X '; Shuder and by dust, nor has resonance scattering of L+ been con- MacAlpine (1979) considered the case r~- cosnt. (These sidered to affect the extinction —for our intent is mere- are really just absorption efficiencies; scattering by ly to give a fair impression of how the situation is dust was assumed to be mostly forward. -directed and changed from Sec. III. therefore unimportant for this problem). The former To be consistent, we should also correct the observed cases have the most drastic effects, cutting off the quasars' continuum shapes E(c) for reddening. If this ionizing continua at high photon energies. Then, be- is done using the idealized extinction law, then the re- cause the H+/H transition zone is less strongly heated sulting intrinsic visual-wavelength continua decrease by soft x rays, collisionally excited Ln and MgIIX2798 only gradually toward the ultraviolet, while the cor- are severely weakened. However, as noted above, real rected ultraviolet continua (c &5 eV, X &2500 A) actually dust grains are probably not so effective for absorbing increase toward higher photon energies; two different soft-x- ray photons. continuum emission processes may be indicated. But Beyond the ionization front of a photoionized region, it is difficult to be more specific, because the true ex- the H region may be extensive and may contain dust. tinction law is probably more complicated than v. ~-A. ' In such a case, ultraviolet emission lines and perhaps and this affects the curvature of the continuum on a even visual-wavelength lines can escape only through logE(c)-loge plot. Moreover, the observed continua the illuminated (inner?) boundary of each cloud or fila- are not all alike. We suspect that quasars' intrinsic ment Ferland. and Netzer (1979) tried to take this into continua in the c -10 eV region may resemble E(c) account, but the uncertainties in dust properties (es- - const or E(c) -c"; even steeper spectra are possible. pecially scattering details) are important. Most of the energy is presumably concentrated near a high-energy cutoff. A typical cutoff energy cannot be F. What is the intrinsic spectrum of a quasar? above 1 keV; otherwise, more quasars would be known According to the preceding discussion, extinction by sources in the several-keV x-ray region. dust within a quasar's emission regions may be non- In the particular photoionization model described here negligible but the He II and 0 I lines suggest that "ex- '(see Netzer and Davidson, 1979), the assumed contin- ternal" reddening is probably more important. This is uum shape is E(c)-c+'~3e ' 'o, with co= 200 eV, U„ most likely to occur in or near a galaxy surrounding =10"cms ', and q, -l0' cm '. (The exponent+1/3

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and=Hagai Netzer: Emission lines of quasars and similar objects

would match either thermal radiation from the most though such a model may need two components to ac- simplified, idealized sort of "accretion disk" or else a count for the 0 V& and N V emission. ) With special ge- limiting case involving synchrotron radiation, but there ometries and dust arrangements, and modified extinc- is obviously no need to take this particular number very tion curves, it is possible for the reddening to be dif- seriously. The specified value of c, was chosen to give ferent for continuum, nonresonance lines, and reso- a satisfactory set of emission line intensities; if ther- nance lines. Many improved observations and argu- mal, it would correspond to a maximum temperature ments will be necessary before we can be confident just above 10' K.) The calculated pla. ne-parallel, con- about any particular model. stant-gas-pressure photoionized region is optically One can speculate that the hypothetical soft-x-ray thick to ionizing photons, with C, N, 0, and Mg about flux may be thermal rather than nonthermal. Soft-x- 80%%uo as abundant as in the model described in Sec. III. B. ray thermal emission from shock-heated gas can occur The intense soft-x-ray flux around c-200 eV has the in a central-accretion situation, or in collisions be- following effects: (i) The most highly ionized zones, tween gas clouds at relative speeds of several hundred near the illuminated boundary, are fairly hot (T-25000 km s '. The latter possibility has been mentioned or K) despite moderately large heavy-element abundances. discussed by many authors, including Nussbaumer and C)VI X1034 and N V A1240 emission are therefore so Osterbrock (1970), Davidson (1972, 1973, 1977b), Dalt- bright that a "second component" invoked in Sec. III is abuit and Cox (1972), and especially Daltabuit, Cox, unnecessary. (ii) The H'/H transition zone is fairly and MacAlpine (1978). The hypothetica. l thermal con- hot (T-12000 K), so that most hydrogen lines are tinuum (most prominent at extreme ultraviolet and soft- strongly enhanced by collisional excitation. (iii) The x-ray wavelengths) may fluctuate less dramatically than total luminosity is much larger than the observable the nonthermal emission which comes from a compact visual-ultraviolet continuum luminosity. This means source. Correlations between red shift and apparent- that the observed emission line-to-conti. nuum ratios visual-wavelength variability may be relevant to this point; can be explained if the line-emitting regions' "cover- see Uomote, Wills, and Wills (1976)and Wills (1976).

ing factors" are very small —i.e. , even if less than I%%uz Arguments &g&i&st the type of model outlined above of the central luminosity is intercepted by photoionized are provided by one particular quasar, 3C 2'V3. We regions. (iv) Although U„ is about the same as in Sec. have mentioned at the end of Sec. V. B that the apparent III, the total pressure of ionizing radiation in each Pn/H|3 intensity ratio for 3C 273, if interpreted in the photoionized region is comparable to the gas pressure, simplest way, suggests only slight reddening; we have rather than a factor of 10 smaller as in Sec. III. noted in Sec. V. D that this object does not show a very There are only two nontrivial discrepancies in Table large peak in iis spectrum at infrared wavelengths; and II. The calculated 0 IV]X1402 intensity is deficient by in addition, the He II X4686 recombination line is very a factor of 3, but this is only mildly objectionable: the weak in 3C 2'73, which seems inconsistent with a model relevant collision strength is uncertain, the ionization that includes many He'-ionizing photons. However, fraction of 0" may be less certain than those of some this quasar is generally thought to be atypical (partly other ion species, and Si IV emission may also be pres- because of the lack of He II X4686), and may be extreme ent. It i.s more disturbing that the calculated HeI A. 58'76 in some ways. A very la,rge value of T~ may explain intensity is too small by a factor of 5. However, this the Pn/HP ratio even if there is some reddening. If U„ line is difficult to calculate reliably (see Sec. IV. D), is rather low, and the hydrogen lines are collisionally and direct excitation of He bound levels by secondary excited, the relative He II weakness may be accounted electrons was not included here. Such fast electrons, for; maybe the average electron density is unusually freed in soft-x-ray photoionization events, are impor- high. Much of the 2-20 pm infrared radiation may in- tant in the low-ionization zones, causing ionization deed be emitted by dust grains, and for the sake of (which was included in the calculation) and excitation completeness, the 40-p, m-wavelength region should be (which was not). So it is possible that the calculated observed. Besides, if 3C 273 fluctuates in luminosity He I X5876 intensity is indeed an underestimate. with a timescale of 1000 years or so, and is now seen Aside from these two discrepancies, the strong soft- in an unusually bright state, then the dispersion in x-ray model is remarkably successful in accounting for light-travel-times would reduce the observable infrared the observed emission lines; O VI A. 1034 and N V X1240 flux) Therefore we need more data on 3C 273, but also, in particular are more simply explained than in the we need to understand how it is like and unlike other traditional models discussed in Sec. III. The required quasars. The same statement obviously applies to elemental abundances and characteristic value of U„ Seyfert galaxies. are not very different from those in the earlier models. G. Comparing lines with continua Models with dominant soft x rays were discussed, from different viewpoints, by Tarter and Salpeter (1969), As mentioned in Sec. III.A, one reason for the popu- Bergeron and Salpeter (1973), Bergeron and Collin- larity of photoionization models is the fact that most Souffrin (1974), and Shields (1974). This type of model quasars' spectra have roughly similar emission-line- is very flexible, which may be considered either an ad- to-continuum intensity ratios. Although such a result is vantage or a disadvantage. We can vary U„, pz„and the not assured, a correlation between continuum bright- elemental abundances (see Sec. III. C), as well as the ness and ionized gas is suggestive of photoionizaiion. power-law spectral index and cutoff energy of the ion- The detailed interpretatio~ of this correlation is af- izing continuum. (In particular, the total luminosity is fected if there is reddening by dust. reduced if the cutoff s, is actually less than 200 eV —al- For clarity, imagine an oversimplified pure photo-

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects ionization picture with no dust. Suppose that the hydro- obscured by a dense emission-line region would not be gen lines are entirely due to recombination; the con- recognizable. Imagine, for example, that the dense gas tinuum has the shape E(c) c ', the absorption of each is dusty and arranged in a disk; such a configuration ionizing photon eventually leads to the emission of one might be inconspicuous when viewed edge-on. The idea recombination Lu photon; and the Lu/HP intensity ra- of a disklike or toroidal arrangement of gas has been tio has a standard recombination value. Under these discussed by various authors, including Shields (1977) conditions, a measurement of either the Lu or the HP and Osterbrock (1978c). Incidentally, in this discussion line, relative to the continuum, would clearly indicate we do not consider certain peculiar objects like PHL the fraction of ionizing photons which are absorbed in 5200, whose spectra have broad absorption lines on the photoionization events. Various complications must oc- short-wavelength sides of ultraviolet emission lines. cur in practice —for example, part of each line may be Such objects are probably surrounded by envelopes of due to collisional excitation of H —but estimates of this ejected gas (which need not be dense), and the "emis- type have been attempted for quasars by many authors, sion lines'* may really be due to scattering —their in- including Shklovsky (1965), Searle and Sargent (1968), tensities resemble the intensities which have been re- Oke, Neugebauer, and Becklin (1970), Oke (1974), Bald- moved from the continuum in the adjoining absorption win (1975,1977a), Osmer and Smith (1976), Baldwin and features. [See Iynds (1967), Scargle, Caroff, and Netzer (1978), and Neugebauer et al. (19V9). The Balm- Noerdlinger (1970), Hewitt and Noerdlinger (1974), Marti er lines in low-red-shift spectra have seemed to imply and Noerdlinger (1977), Weedman et al. (1979), and ref- that most of the ionizing continuum is usually absorbed, rences cited by Perry, Burbidge, and Burbidge (1978).j but the I a emission in high-red-shift spectra has ap- If covering factors are small, why do the Balmer peared to require only a fraction (-10O/o'p) of the ion- lines seem to indicate covering factors near unity? izing photons; this discrepancy is of course a manifes- Two obvious answers are (1) the Balmer lines may be tation of the "Lu/HP problem. " enhanced by collisional excitation, and/or (2) the naive The photoionized regions are probably optically thick power-law extrapolations of visual continua may be in- to most iomzing photons (see arguments cited in Sec. valid. Boih of these explanations are correct in a mod- III; Davidson, 1976; and other aspects mentioned be- el. like that outlined in Sec. V. F. Moreover, because so low). Therefore the fraction of ionizing photons which much far-UV and soft-x-ray luminosity is available in are absorbed can be interpreted as a "covering factor, " such a model, the covering factor can be far less than 0.1. i.e., the fraction of sky which is covered by the photo- %hat happens to most of the ionizing photons? If ionized regions as seen from a hypothetical central . there is extinction by dust, outside the dense emission- source. (We assume that the ionizing radiation is not line regions but still within the quasar's galaxy, then "beamed" in particular directions. ) Another way to gas must also be present along with the dust; perhaps guess the covering factor is to observe the continuum this gas can be identified with the narrow-line-emitting near the Lyman edge (the H' ionization threshold: rest regions. But since we do not observe sA on@ emission wavelength 912 A). If, for example, the average qua- lines from such gas, or strong Lyman-continuum ab- sar's covering factor is 0.2, then one might naively ex- sorption, it must not absorb most of the ionizing pho- pect 20%%up of the quasars' spectra to show absorption tons. Without going into deta1.ls~ we note thRt this discontinuities near the Lyman edge, due to the Lyman places a lower limit on U„ in the hypothetical extinc- continuum and perhaps the highest-order Lyman lines tion-causing material: if U„- 10' cms ', most of the [see Bahcall and Sargent (1967) for an early view of this ionizing photons can be absorbed by the dust rather than ideaj. In fact, some high-red-shift quasars have no by the gas. For several quasars, there is evidence that Lyman discontinuities in their spectra, while others . only small fractions of their ionizing luminosities are have discontinuities at absorption-system red shifts being Rbsorbed 1D photolonlzRtlon events wlthlD 10 which are probably unrelated to the dense line-emitting light-years of the sources (Davidson, 19VVa, 1978; Sar- regions; but discontinuities of the naively expected type gent and Boroson, 1979)—although we do not wish to in- are quite rare (see Oke, 1974; Beaver et a/. , 1976; sist here that a quasar's luminosity remains steady as Baldwin et al. , 1976; Osmer and Smith, 1977b; Osmer, long as 10' years i See also Arons and Wingert (1972) 1978; Wright et al. , 1978). The average geometrical and Osmer (1978). (Strong continuum fluctuations in covering factor seems to be less than 0.2. Independent about 1000 years, as mentioned above in connection evidence that covering factors are less than unity, at with the infrared, might explain the absence of strong least in a few cases, is provided by the fact that some forbidden lines in another way —involving light-travel- quasars are compact radio sources. Dense ionized re- times. This explanation would require quasars to be gions of the types discussed in Sec. III are quite opaque "turned off" most of the time. ) at wavelengths much greater than 1 mm. These cover- A related problem concerns correlations between ing-factor arguments may be taken as evidence zgzi&st luminosities and emiss ion-line -to-continuum ratios. photoionization models in which resonance lines are Baldwin (19VVb) suggested that quasars' Lu and/or C IV suppressed by internal dust absorption or by collisional A.1549 intensities, measured relative to the underlying deexcitation. If, for instance, the apparent I n inten- continua, tend to be smaller for move luminous qua- sity has been reduced by such effects, but the apparent sars; this statement appears to have been confirmed continuum has not, then a large covering factor is re- for the C IV line, but is not really settled yet (Osmer, quired —which may be inconsistent with the facts that 197V; Baldwin et al. , 1978; Smith, 19V8). It is easy to we have just mentioned. invent speculative explanations of such correlations It may be that a quasar whose continuum source is (whether or not the correlations are real! ), but it is

Rev. Mod. Phys. , Voa. 51, No. 4, October 1979 750 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects difficult to decide which explanations are correct. The quasars are known to have galaxy -sized forbidden-line suspected correlations cannot continue down to the low- "haloes" (Wampler et a/. , 1975; Stockton, 1976; Rich- er luminosities of Seyfert galaxies, if photoionization stone and Oke, 1977; Bergeron, 1976). Furthermore, models are valid, because then the line-to-continuum some Seyfert galaxies' forbidden lines remain constant ratios would require covering factors larger than unity. while their broad lines vary; this probably means that The idea of significant extinction by dust, which has the forbidden-line regions are much larger than the been favored in this section, may require quasars to broad-line regions. Dynamical arguments, involving produce embarrassingly monstrous luminosities. Many the velocity dispersions implied by the linewidths, lead of them appear to have ultraviolet luminosities cI, to similar conclusions. Like the denser broad-line ga.s, = &L~-10 ' erg s ', and a few extraordinary objects the forbidden-line regions probably do not fill the avail- sometimes approach 10 ' erg s ' (Eachus and Liller, able volumes and may consist of many clouds, fila- 19'l5; Ulrich, 1976; Osmer and Smith, 19l'la, b; Wright ments, or sheets. and Kleinmann, 1978; Gottlieb and Liller, 1978). The The forbidden lines are not as bright as the broad proposed corrections for extinction would raise these lines, either because the narrow-line regions have a ultraviolet values to several times 10"erg s ', and smaller overall covering factor than the broad-line re- may lead to soft-x-ray luminosities of the order of 10'o gions, or because the forbidden-line gas is optically erg s '! By adjusting our models (e.g. , by moving the thin to ionizing radiation, or because of dust, or be- intrinsic peak to E-20 eV rather than 200 eV), we can cause of fairly long-timescale continuum variability. probably reduce the maximum luminosity to about 10~' Nevertheless, considering the density dependences of erg s ', but in any case these values are too large for emissivities, the amount of gas representedby forbidden comfort. The required compact objects would probably lines must greatly exceed that which produces the broad have the masses of galaxies, with "fuel" consumption lines. A quasar's dense regions, discussed in Secs. III. rates up to 1000 solar masses per year. The overall and IV, may contain only 100 or 1000 solar masses of sizes of the emission-line regions would be larger than diffuse photoionized material (of course, there may also those suggested in Sec. III. B. Nevertheless, we do not be some related nonionized gas); the forbidden-line re- think that these numbers are quite large enough to gions may be 1.0' to 10' times more massive. The in- amount to a proof of impossibility. tensity ratios of certain forbidden lines, particularly [Om ] X5007/X4363 and [S n] A. 6731/X6717, give infor- Vl. SOME ADDITIONAL SPECTRAL FEATURES mation about temperatures and densities (see references cited above); T-10 to 3 x 10 K, -l0' to 10' cm ' A. Forbidden lines n, are typical guesses, which allow photoionization as a We shall not discuss quasars' narrow forbidden lines possible dominant heating mechanism. Heating by shock in much detail, for several reasons: they are not as- fronts may also be important. Photoionization models, sociated with the mysterious centers of activity as adjusted to produce the high-ionization forbidden lines, closely as the broad lines are; they do not carry as generally do not produce adequate [0 u] and [S n] emis- much energy as the permitted l.ines; they are very den- sion. Some possible ways of enhancing the low-excita- sity dependent; and most of their implications can be tion lines through geometrical or time-dependence as- derived by the traditional methods of nebular analysis sumptions have been described by Shields and Oke which have been extensively reviewed in the astronom- (1975); but it should be noted that low-ionization line ica,l literature. We have already cited some of these intensities are difficult to explain even in ordinary reviews in Sec. II.A; for applications to Seyfert galax- nebulae in our Galaxy. Phi. llips (1978a) has remarked ies and quasars, see Osterbrock (1978b) and references that high-ionization forbidden lines ( [0III] in particular) therein. Some relevant photoionization calculations are in some cases slightly blue-shifted relative to low- have been described by Williams and Weymann (1968), er -ionization forbidden lines. This presumably indi- Tucker and Tarter (1968), Yankulova (1974), Shields cates that the lines preferentially originate in different (1974), Shields and Oke (1975), and Boksenberg and zones. (If the relative shift is always in the same Netzer (1977). sense, this also leads us to suspect that a typical con- Quasars' forbidden lines must originate in rela- figuration is symmetric, with some dust to obscure tively low-density gas (n, & 10' cm~) and are nar- emission in particular places and/or directions. ) It rower than the permitted lines (widths correspond has been generally difficult or impossible to deduce to several hundred km s ' vs several thousand km s '). elemental abundances from quasars' and Seyferts' for- In some spectra. , narrow Balmer lines, evidently pro- bidden lines. duced in the forbidden-line gas, can be seen superim- If the Fe" and Fe~o' ions (required to give observed posed on the broad Balmer lines. The forbidden lines [Fex] and [Fe XI] lines) are photoionized, then there represent a wide variety of stages of ionization, in- must be significant soft-x-ray fluxes- at photon energies cluding [Oz], [Sar], [Nlx], [Ozl], [Olla], [Nelly], near 250 eV. Alternatively, as Oke and Sargent (1968) [Ne v], [Fevol], [Fe x], and [Fe xr]. As one ~ight ex- suggested, there may be enough hot (T-10 K), low- pect, the forbidden-line regions are not very close to density (n, -100 cm '), collisionally ionized gas to pro- the centers of activity. In some nearby Seyfert galax- duce such lines. It is interesting that the [Fe XI] X7892 ies (e.g. , NGC 7469; see Ulrich, 1972), the forbidden- line is broader than the other forbidden lines in some line zones can be partly resolved and are several hun- spectra (Grandi, 1978). The critical density for colli- dred light-years across; these dimensions should prob- sional deexcitati. on of this line is of the order of 10' ably be scaled up for more luminous quasars. Some cm ', so it may originate in at least the lower-density

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects parts of the broad-line regions. By comparison with MgII X2'798, Phillips stated that Incidentally, one should be skeptical of any photoiori- an implausibly large Fe'/Mg' abundance ratio would be ization calculations of iron lines. There are too many required to produce the observed intensities by colli- stages of ionization of iron, each very poorly known sional excitation. Also, with collisional excitation, the regarding ionization and excitation cross sections, re- observed relative intensities of various FeII features combination rates, charge-exchange reactions, etc. , are difficult to explain and the ultraviolet 1-3 lines for this element to be treated decently. should appear in emission. Nevertheless, this mecha- nism should not yet be excluded as a possibility (see B. Fe ii lines Boksenberg and Netzer, 1977). Collin-Souffrin et ~l. Wampler and Oke (1967) identified some broad emis- (1979) have proposed collisional excitation in a rather sion features in the spectrum of the quasar 3C 273 as hot, nonphotoionized gas. blends of several permitted Fe II multiplets. The FeII fluorescence was proposed by Wampler and Oke strongest blends are around A. -4570, 5190, and 5320 A. (1967}and further discussed by Bahcall and Kozlovsky Sargent (1968) identified similar features in the spec- (1969a), Osterbrock (1976), Oke and Shields (1976), trum of a Seyferi galaxy, and Fe II emission has since and others. The idea is that some of a quasar's con- been observed in many quasars' and Seyferts' spectra tinuum photons can be absorbed in FeII 1-3 quasireso- (see Fig. 3). Extensive observational work on this sub- nance lines. Most of the resulting level 3 Fe' ions will ject has been reported by Osterbrock (1977) and Phil- decay directly to levels 1, but if resonance scattering lips (1978a); it appears that perceptible Fe LL emission operates in a favorable manner, the indirect decay is produced by most "Type 1"Seyfert nuclei but is less routes 3-2-1 may be important. The desired emission common in quasars. The lines are broad and therefore results from 3-2 decays while the 2-1 transitions are probably originate in the dense central regions. In mostly collisional rather than radiative if z, &10' cm 3. some cases, the total of the Fe II intensities exceeds In order to get the observed intensities, each 1-3 line the HP intensity. must remove part of the total continuum equivalent to Some nebulae and peculiar stars in our Galaxy have at least bA &1A or be (Doppler broadening) &100 km s '. permitted FeLL as well as forbidden [Fe LL] emission in Adams (1975a) described some 3-level simplified their spectra (e.g. , see Thackeray, 1967; Viotti, 1976). models for this process, and Phillips (1978b) and Col- We generally do not understand such features in quan- lin-Souffrin et al. (1979) have constructed more elabo- titative detail, because Fe' is such a complicated ion rate multilevel models. The FeII -emission zones in that many of its relevant parameters are only vaguely these models are essential. ly uniform in temperature known. The near-ground levels of Fe' have even parity; and density, although the regions of interest are prob- we sha1.1 call them "levels 1." About 3 eV above them ably H+/Ho transition zones. Collin-Souffrin et ~/. re- are some more even-parity levels 2, and about 5 eV marked that Fe'+ should be more common than Fe', above the ground level are some odd-parity levels 3. even in a H+/H' transition zone, because of photoioniza- There are many permitted transitions 1-3 (X-2300- tion from excited levels; but perhaps charge exchange 2800 A) and 2-3 (mostly 4000-6000 A), and forbidden is important. transitions 1-2 (mostly 3500-5500 A). The lines ob- The picture which seems most favorable for FelI served in quasars' and Seyferts' spectra correspond to fluorescence, while being consistent with most of our the 2-3 transitions; 1-2 and 1-3 transitions are not discussion in. preceding sections, has the following fea- represented. The absence of the forbidden 1-2 lines tures: (i) I,oc~f velocity dispersions (within individual probably indicates high densities, z, &10' cm '. How- clouds, filaments, or sheets} are small, of the order of ever, the absence of permitted 1-3 lines is not quite 10 km s ', and each local region is optically thick in as easy to explain, considering that they have larger each FeLL 1-3 line. (ii) There are larger-scale velocity transition rates than the observed lines. Presumably, dispersions considerably greater than 100 km s"' in resonance scattering plays a role here; we can also some radial'directions, so thai enough continuum ra- imagine observational complications involving redden- diation can be absorbed. Phillips mentions hydrogen ing, the "3000 A bump" (see Sec. VL C), and perhaps column densities N„-10~ to 10"cm"'. (iii) The over- evqn the 2200 A dust feature. It should be noted that all velocity dispersion is several thousand km s ', in Fe', like Mg+, is easily ionized and therefore should order to give the observed overall linewidths. (iv) be scarce in a photoionized H' region (unless UH is very Covering factors are much less than unity (at least in low). Most of the Fe' ions should be found in the H'/H' the guasars, if not the Seyferts), so that we do not ob- transition zones and in H' regions. serve the FeII 1-3 lines in absorption. Such a model What is the excitation mechanism? Ordinary recom- may just barely be able to account for ihe observed bination is almost certainly inadequate; the observed Fe II intensities. FeII intensities would require such a large iron abun- According to Phillips (1978b), a further difficulty with dance that other iron-ion features would appear, al- fluorescence as the dominant mechanism for Fe II emis- though some sort of charge-exchange reaction might sion is the absence of some Si II lines that should be conceivably have the same effect as very efficient re- produced in the same way. A.t this time, it is difficult combination. The most likely mechanisms are co1.li- to wholeheartedly accept or exclude either fluorescence sional excitation, and fluorescence in which continuum or collisional excitation of the FeII emission. photons are absorbed in the 1-3 quasiresonarice lines. Surprisingly, there are no definite, confirmed corre- Phillips (1978b) and Collin-Souffrin et al. (1979) have lations between observed FeII emission and other spec- discussed these processes. tral features; but at least two possibilities have been

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 752 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

suggested. (i) Fen emission may be anticorrelated sity ratios such as I([OnI] X5007)/I(C iv x1549), as with radio emission (Osterbrock, 1977; Grandi and mentioned by Davidson (1972), are (i) the carbon/oxy- Osterbrock, 1978); and (ii) Allen (1976) has proposed gen abundance ratio may be large, and/or (ii) the tem- a correlation between Fels emission and infrared emis- perature may be high so that the lower excitation ener- sion in Seyfert galaxies, more or less by analogy with a gy of X5007 becomes less advantageous, relative to similar correlation among objects in our Galaxy. The X1549. Possibility (i) is unlikely in view of the promi- latter suggestion, if correct, may imply that Seyferis nence of 0 VI X1034, and possibility (ii) appears incon- are dustier than quasars. sistent with the absence of C II& X977 (see Sec. III.A), In the spectrum of the Seyfert galaxy NGC 4151, there not to mention other implausibility factors. Scargle, are forbidden [Fe il] lines, originating in the less dense Caroff, and Tarter (19'l4) constructed a low-density narrow-line regions (Boksenberg et ~l. , 1975; Netzer, model whose forbidden lines were not very prominent; 1974}. This interesting object is peculiar in several but they did not clearly distinguish between broad and ways, which we shall not discuss here. narrow lines, and their calculated forbidden-line in- tensities were larger than in observed bxo~d-fj~e "3000 bump" spec- C. The A tra. Many quasars' and Seyfert galaxies' spectra have Some interesting mechanisms, particularly relevant broad "bumps" in the wavelength range 3000—4000 A; to [0?It] emission, were proposed by Burbidge et ~l. see Oke, Neugebauer, and Becklin (19"l0), Shields, Oke, (1966), Burgess (1967), and Pfleiderer and Grewing and Sargent (1972), Baldwin (1975), Phillips (1978a), (1967), and have been rediscussed by Shull and McGray and Neugebauer et al. (19'l9). In some cases this may (1978). Essentially, the idea is that radiation densities be the Balmer continuum in emission (Xc 3645 A), but may be so large and forbidden transition rates so slow in other cases the intensity is too large and the peak that an excited 0"ion is usually photoionized or photo- wavelength is too small. Among additional suggested excited before it creates a forbidden-line photon. If this contributors to the feature are Fe II emission, and ha, ppens, the forbidden lines may be weak even at low "two-photon" emission produced by 2s-1s decays of gas densities; and the relative intensities of forbidden hydrogen. The latter seems implausible because colli- lines, e.g. , [0 III] X4363/X5007, may be altered. How- sional 2s-2p transitions should be faster than two-pho- ever, for these processes to be more effective than ton decays at reasonable densities yz, »10' cm ', but collisional deexcitation in suppressing [0 Ill] X5007 it may occur in H zones, where decay from 2p is in emission, the radiation-to-gas ratio U„must be very effect suppressed by enormous L,& optical depths. large, U„&10"cms '. Such values of U„would entail This somewhat mysterious spectral feature may be radiation pressures which greatly exceed gas pres- relevant to the possibility of extinction by dust grains sures, and would be very difficult to reconcile with ex- (Sec. V above). At visual rest wavelengths (A. &4000 A), isting photoionization results. extinction is expected to be small or moderate, while Although the radiative processes cited above do not the ultraviolet (X &2000 A) extinction is uncertain but invalidate the usual lower limits on gas densities, they may be large. Because intermediate wavelengths in- do affect the 0"/0" ionization ratios in dense regions clude the Balmer continuum, possible extra emission, and should be included in photoionization calculations. and a possible 2200 A extinction feature, it is difficult As explained in Sec. II.A, because the ionization to join the visual and ultraviolet continua smoothly. The threshold of He' is 54.4 eV, a typical photoionized re- 3000 A bump may disguise the presence of a 2200 A gion has a zone of H+ and He' where the local ionizing feature or may even fill it in to some extent. One can continuum has a cutoff at s= 54.4 eV (although there may even speculate that the 3000 A feature is partly due to be some penetrating photons above 100 eV). This is the dust. Energy deposited in a dust grain is normally as- zone where 0'+ traditionally occurs, because 54.9 eV is sumed to be quickly thermalized and then reemitted at required to ionize ground-level 0+'. But only 52.4 eV infrared wavelengths, but perhaps this is not always is required to ionize 0"from its lowest metastable correct. Perhaps some effects (photoionization and (forbidden-line) level; and in a quasar-related model, recombination'? disruption by fast charged particles'? precisely because densities are high, almost 10% of perhaps secondary electrons?) produce more direct the 0"ions are in this excited level. Therefore it is radiation —scintillation —from electronic transitions in possible for continuum photons between 52.4 and 54.4 grains. The photon energies around 3000 A seem noi eV to change some of the 0++ to O'+. This effect is quite unreasonable, and transitions in a grain produce dif- important for conventional power-law spectra with UH fuse spectral features rather than sharp lines. ~ 10"eius ' and can affect the intensities of 0 HI] X1663 and 0 tv) X1402 (cf. Appendix B of Baldwin and Vll. SOME ADDITIONAL POSSIBILITIES Netzer, 1979). Davidson (1972) hoped for the sake of simplicity that absorption of high-order Hell "Lyman A. Concerning the absence of broad forbidden lines series" lines would eliminate this effect, but the re- Forbidden lines are not very intense in a typical qua- quired local linewidths are probably excessive. sar's spectrum, and b&o&d forbidden lines are very An argument against low densities, independent of faint. Therefore most authors suppose that the broad- forbidden lines, is provided if broad-line intensities line emission regions are so dense (n, &10' or 10' cm '} are seen to vary with time scales of 'a few years. If that forbidden lines are suppressed by collisional de- suspected values of UH are realistic, then dense emis- excitation. But this has occasionally been doubted. sion-line gas must be distributed over regions several Two obvious alternative ways to explain reduced inten- light-years across, or less-dense gas must be distri-

Rev. IVlod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 753 buted over much larger regions. Considering travel other processes will probably affect the heating more times for light, we are not very surprised if dense-re- than they affect the ionization. There are two likely ef- gion line intensities vary in a few years, but no line fects: (i) photoionized regions, basically like those dis- variations should appear if densities are low'. cussed in preceding sections, may be slightly hotter than in the standard calculations, B. Can densities be surprisingly high'F and/or (ii) there may be adjoining regions of lower density, which are very We think that the observed semiforbidden lines, es- hot because their heating is dominated by processes pecially C &&& J X 1909, show that typical electron densi- other than photoionization. Low -density, high-temper- ties in the broad-line regions do not greatly exceed 10" ature gas is likely to be very transparent and ean ser- cm . However, we cannot absolutely prove this upper iously affect, at most, only the high-ionization emission limit, and the "Lu/HP problem" has led to suspicions lines; but it may be dynamically important —it can re- thai higher densities may be important. No self-con- strain or confine the photoionized regions if instabilities sistent photoionization models (or, indeed, self-consis- are not too serious. tent alternative models) are available for such high den- Energetic, nonthermal charged particles can heat gas sities, because serious complications occur for yg, by causing excitations and ioniza, tions, and by Coulomb ~ 10" cm '. permitted transitions become collisionally scattering; such heating has been discussed by Oster- deexcited in a radiative-transfer-dependent manner, brock and Parker (1965), Eilik and Caroff (1976), and highly excited levels and also the bremsstrahlung con- others. The least energetic particles are most effec- tinuum become more important as resonance lines are tive for heating purposes. Protons or electrons with saturated, three-body recombination (e.g. , 2e + H' energies below 1 MeV lose energy so quickly that they —H'+ e ) becomes important, etc. We can imagine cannot penetrate far into "thick" photoionized regions some likely difficulties in a very high-density model: with U„& 10'; such particles, if present in large num- (i) Somehow, the observed C HlJ X1909/Ln intensity ra- bers, may create thin, extremely hot edges or "coro- tio must be obtained even though X1909 is far more se- nae" around our hypothetical photoionized clouds or verely reduced by eollisional deexcitation than Ln is, filaments. Charged particles far above 10 or 100 MeV and this must be done without introducing much C III do noi lose energy to the gas very quickly, so a very X977 emission. If strong nonphotoionization heating is large energy density of such particles —implying a invoked, the resulting high temperatures may violate pressure greater than that of the gas —would be re- the X977 limit. The only obvious way of getting adequate quired to cause significant extra heating of the photo- C III J emission is to suppose that carbon is surprisingly ionized regions. Regarding particles of several MeV, abundant, nc/n„a 10 ". Other semiforbidden lines, we note that a magnetic field of only 10 ' 6 would make including N mj xl750 and N lvj A1486, must also ap- their Larmor orbits much smaller than the thicknesses pear. (ii) The hydrogen lines must have satisfactory of the photoionized zones; and actual ambient fields are ratios. Extreme "thermalization", as proposed by probably much stronger, because the energy density as- Zirin (1978), might result in LP/Lu and HP/Haratios, sociated with 10 ' G is 10 orders of magnitude smaller which do not resemble the observations. (iii) The He I than the likely thermal energy densities in the line- lines must have satisfactory ratios even though they ap- emitting gas. Therefore effective charged particles can pear to indicate lower electron densities (see Sec. IV. enter the photoionized zones only along magnetic field D). (iv) Aside from fluorescence, there must be no lines. The magnetic field configuration (which we do not perceptible visual-wavelength emission lines from high- know) must affect the results of any calculation; so we ly excited levels of carbon, nitrogen, and oxygen ions. feel uneasy about any calculated model of heating by Such lines appear in the spectra of some stars with hot charged particles. Since large energy densities of sev- gaseous envelopes (see Underhill, 1966). (v) The par- eral MeV particles would be necessary to obtain strong tial suppression of major emission lines must not cause effects, and considering that there is-no evident reason bremsstrahlung and radiative recombination to assume w'hy any hypothetical particle ftuxes should be concen- too much of the cooling burden, because then the total trated in this energy range, we suspect that this form energy-supply problem would become difficult. These of heating is unimportant in a quasar's line-emitting points, taken together, show why we are unenthusiastic gas. about the very-high-density possibility. From astro- Next, there is compressive heating by shock waves. nomical e'zperience, we know that the spectra of ordi- Direct heating of the line-emitting regions by shocks is nary low-density nebulae are recognizably different unattractive. To obtain significant extra heating in from the spectra of higher-density hot stellar enve- photoionized gas, but not so much heating that the emis- lopes; and except for the easily understandable lack of sion spectrum becomes unsatisfactory (i.e., to obtain forbidden lines, quasars' line spectra look pgebular and localized temperature enhancements between 1000 and not stellar. 30000 K), the speed of a shock front must be of the or- der of k- 30 km s ', which is rather low in the sense C. Additional heating processes z,h, that each shock carries only a miniscule amount of en- Because so many far-ultraviolet continuum photons ergy by quasarian standards. To produce a significant are obviously present, photoionization is virtually cer- average luminosity effect AL - 10 ' erg s ', the shocks tain to be important in a quasar's line-emitting regions; would have to sweep through material ai a rate of the but some additional heating may result from other order of AL/v2h„k-10" gs '-10' solar masses per processes. Purely photoionized regions are year; each cloud or filament would have to experience remarkably cool for their levels of ionization, so these repeated shocks with recurrence times not much great-

R ev. IVlod. Phys. , Vol. 51, No. 4, October 754 Kris Davidson and Hagai Netzer: Emission lines of qoasars and similar objects er than the characteristic gas cooling time, which is resentation of a complex gas-dynamical situation, with less than an hour for n, -10' to 10 ' cm '. It is not ob- turbulent Inotions and numerous shock fronts. Some of vious how this could be made to work. the highest-ionization emission lines, particularly [Fe Shock waves are more interesting in a different way, x] X6374 and [Fe XI] X7892 (Grandi, 1978) may arise as sources of ionizing radiation. Nussbaumer and in shock-heated gas. Osterbrock (1970) mentioned that ionizing radiation is Krolik, McKee, and Tarter (1978) have pointed out emitted in collisions between fast-moving gas clouds, that radio-frequency waves can heat the gas. In photo- and Davidson (1972) proposed the compressed parts of ionized regions, the most important radio absorption colliding clouds as suitable locales for a quasar's dense process is free-free (bremsstrahlung) absorption, line-emitting regions. Daltabuit and Cox (1972), com- whose relevant coefficient per unit volume is propor- bining these aspects, proposed that colliding clouds tional to yg,'A. '. A photoionized region like those dis- contain both the sources of ionizing radiation and the cussed in Sec. III is practically transparent at short photoionized regions. Consider an idealized picture, in wavelengths Ac 0.01 cm, absorbs much of the radiation which two identical cl.ouds collide head-on at relative at X -0.1 cm, and is quite opaque for A. ~ 1 cm. This speed V which may be of the order of 1000 kms '. The means that radiation in the wavelength range A. -0.1 to ions and electrons of the two separate clouds cannot 1 cm heats the photoionized r egions. Even quasars interpenetrate because there are small. magnetic fields which are "strong" radio sources have only small frac- imbedded within the clouds. Therefore, as the colli- tions of their luminosities in this range (e.g. , see Elias sion proceeds, a shock front moves into each cloud, et g/. , 1978; and Fig. 10 of Oke, Neugebauer, and creating a highly compressed region near the plane of Becklin, 1970), and most quasars have relatively mod- symmetry. Gas crosses each shock front. at a speed est radio luminosities; so this is not likely to be a very slightly less than V/2 and is adiabatically heated to a important effect. However, the radiation at longer temperature such that its isothermal sound speed is wavelengths, A. ~ 1 cm, is absorbed in such a small roughly ~=0.2V, i.e. , to a temperature T=(10"K) amount of gas that it may lead to the formation of a hot, (V/1000 kms ')'. As the shock moves away from it, lower-density "corona" adjoining each dense photoion- this hot gas cools by emitting (mostly) ionizing photons, ized region. It is therefore conceivable that [Fe XI], while remaining almost at constant pressure. The ion- [Fe x ], 0 vl, and N v emission may be enhanced by izing photons create two photoionized regions: a region radio-frequency heating. If the "coronal" temperature in the dense cooled material near the collision plane, rises too high, thermal instability occurs and the gas and a less dense region in gas which has not yet passed may become very hot indeed. Then other low-frequency through the shock. DaItabuit, MacAlpine, and Cox processes also become important, for example, the (1978) have made specific calculations of situations like induced Compton effect (I evich and Sunyaev, 1970). A this. They enumerate five distinct zones, beginning in hot, rarefied, transparent medium, roughly in pressure the undisturbed parts of a cloud and moving toward the equilibrium with photoionized clouds, may result. Kro- collision plane of symmetry: A, undisturbed material lik, McKee, and Tarter have suggested that "BI. which may be un-ionized; B, the photoionized region Lacertae objects" lack dense gas clouds because of very approaching the shock; C, the hot shocked gas; D, the strong radio-frequency heating. dense postshock photoionized region; and E, a very Collin-Souffrin et ~l. (1979) have proposed that the dense H region near the plane of symmetry. Suppose Fe II lines originate in dense gas which is beyond the that we very crudely represent the shape of the ionizing reach of most ionizing photons, but which is heated by spectrum of zone C as E(c)-exp(-s/kTc), where Tc is some unspecified process. This hypothetical. gas is hot perhaps half the maximum temperature behind the (T-20000 K?) but is so dense that it is not thoroughly shock. Then it is easy to estimate that U„-(10' cm s ') ionized —perhaps the atmosphere of an accretion (V/1000 kms ') in zone B, and U„-(10' cms ') (V/ disk is involved. The main objection to this idea, 1000 kms ') ' in zone D, except that the last value perhaps, is that it is a special explanation for just the must be increased if magnetic fields limit the compres- FeII emission and does not help to explain other spec- sion of gas in zone D. If we want U„-10' cms ' and ~, tral. features. -10"cm ' as in the simpler photoionized models, D. Nonthermal emission lines? then we might consider either zones B in collisions of dense clouds at V-1000 km s ~, or zones D in collisions An unusual model was proposed by Ptak and Stoner of larger, less-dense. clouds at lower speeds. The (1973a,b), who considered streams of "suprathermal" former possibility gives higher maximum tempera- ions (e.g. , 100 keV protons) moving through ambient tures, T-10"K. The real spectrum of a hot shocked gas which is mostly H'. Charge exchange and other zone C is not a simple continuum, but also includes interactions occur, and the radially streaming ions are ionizing emission lines and "edges"; see Cox and Dalt- said to produce broad emission lines like those of a abuit (1971), Raymond and Smith (1977), Daltabuit, quasar or Seyfert nucl. eus. Several. solar masses per Cox, and MacAlpine (1978), and Shull and McKee (1979). year must flow outward in the streams, but the ratio of Note, by the way, that the energy source is largely streaming particles to ambient gas must be small shifted to cloud motions in this type of model, and rapid enough to avoid ionizing and blowing away the latter. ultraviolet variations are not to be expected —because Stoner, Ptak, and Ellis (1974) calculated some asym- many small clouds are presumably colliding at any metric line profiles in this model, which matched cer- time, and also because of light-travel-time arguments. tain observed profiles; other aspects or modifications The idea of "cloud collisions" may be an idealized rep- were discussed by MacAlpine (1974), Ptak and Stoner

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

(1975, 1977), Mergenthaler (1975), and Kimmer (1976). 10' s; unless the actual densities are many orders of Katz (1975) criticized this model on several grounds: magnitude smaller than we have supposed, each small emission by the ambient gas should produce intense cloud or filament of gas can adjust its ionization struc- narrow cores in at least some of the lines, some ob- ture quickly enough, compared with continuum varia- served spectra have asymmetric line profiles which do tions, to be practically in ionization and thermal equi- not match those calculated by Stoner, Ptak, and Ellis librium at all times. See Bahcall, Kozlovsky, and Sal- (cf. Boksenberg et a/. , 1975; Osterbrock and Koski, peter (1972), Shields and Oke'(19V5), and Boksenberg 19V6), and the required geometry seems rather special and Netzer (1977)." and therefore implausible. Stoner and Ptak (1977) have If we could see an individual photoionized cloud near replied that the narrow emission line "cores" may be a quasar, its appearance at any time would depend upon trapped in the neutral ambient gas, and that modifica- the ionizing luminosity of the hypothetical central ob- tions to the model can cure other difficulties. Ptak and ject at a somewhat earlier time; an obviously relevant Stoner (1976) predicted that the Fe?I lines, being pro- parameter is the total light-travel time from the cen- duced in the ambient gas, should be narrower than the tral source to the cloud and then to us. The ensemble hydrogen lines; but according to Phillips (1978a), this of dense photoionized regions associated with a quasar is not so. Strittmatter and Williams (1976) argued must have an overall size scale and therefore a mini- against the Ptak and Stoner models on the basis of ob- mum possible time scale for variability. As suggested served Mg II A. 2798 widths and remarked that these mod- in preceding sections, the likely size scales, derived els represent attempts to explain line profiles quantita- from preferred values of U~, pg„and ionizing lumin= tively and line intensities qualitatively, even though line osities, range from a light-year (for a rather modest intensities are better known than profiles and are per- Seyfert nucleus) to hundreds of light-years (for a very haps less influenced by geometrical details. luminous quasar) Th.ese estimates are not seriously The suprathermal ion streaming models are unattrac- inconsistent with any reliable observations that we tive because they invoke several arbitrary, and in some know of. (Cf. Bahcall et a/. , 1972.) respects implausible assumptions, without achieving a Early in the history of observations of quasars, MgII correspondingly detailed success in explaining observa- emission was thought to have varied in the spectrum of tions. Ionizing photons, which we know to be present, one quasar (Burbidge and Burbidge, 1966; Dibai and are not really included; the streams of suprathermal Esipov, 1967; Wampler, 1967), but this is now thought ions are postulated arbitrarily; even if such streams to have been an error, perhaps related to continuum exist, it is very surprising if they move through neutral variations (cf. Pfleiderer and Grewing, 196V). General- gas in an orderly manner (presumably along magnetic ly, when a quasar's continuum varies within a few field lines) without dramatically heating and ionizing the years, its emission-line intensities remain fairly gas; some special geometrical assumptions are re- steady; this was suspected at an early date (see San- quired in order to obtain the calculated line profiles; dage et a/. , 1966; Kinman et a/. , 1966; Oke, 1967) and and the relative line intensities are not explained in de- has since been noted occasionally (e.g. , see Shields, tail. Oke, and Sargent, 1972; Osmer and Smith, 19VVb) al- though systematj. c data are scarce. For the moment, Emission-line variability E. at least, we are observationally justified in believing Many quasars' ultraviolet continua are known to fluc- that a luminous quasar's line-emitting clouds are tuate markedly, over irregular time scales of several spread over a region which is considerably more than years or sometimes one year or less. %e'should there- a light-year across. fore consider time-dependent effects in the line-emit- On the other hand, emission lines have been observed ting regions. to change, sometimes in time scales of much less than Jura (1973) proposed to explain the weakness of the a year, in the spectra of a few Seyfert nuclei: see HeII X4686 lines in 3C 273 as a time-dependent effect. Andrillat and Souffrin (196V), Pastoriza and Gerola Suppose that a nebula is ionized impulsively, perhaps (1970), Andrillat (1971), Tohline and Osterbrock (1976), by a sudden, temporary gust of ionizing radiation. Boksenberg and Netzer (197V), and Phillips (1978a). After the ionizing process recedes, the gas begins to The most disturbingly rapid changes —over times of recombine and to cool. Because recombination is faster the order of 10 days —have been reported by Lyutyi for doubly ionized helium than for hydrogen, after a (1977) but have not been completely confirmed. Col- certain time there are few He" ions left while the gas lin-Souffrin (1978) has asserted that these fluctuations is still mostly H+ and He', then the He II 'X4686 recom- bination line becomes weak compared with HP. There are several good arguments against this scenario. ~~The idea of nonequilibrium ionization suggests a modified First, it would almost preclude the existence of enough type of photoionization model. Imagine a cloud being "evap- 0'+ C", I ', and ions to explain the observed C IV, N V orated" by ionizing photons; i.e., a steady flow of gas becomes and 0 VI emission, during the time when He II A.4686 is ionized and heated as it passes through the ionization front, and weak. Low temperatures would also be entailed (be- thereafter expands and dissipates while being illuminated by cause cooling is initially faster than hydrogen recom- ionizing radiation. This can in principle be a nearly steady- state situation, wherein the ionization and thermal structures bination), making it even more difficult to high- explain are locally out of equilibrium because the gas is not stationary. excitation lines. And ihe time scales do not make In practical cases, however, the departures from local equi- sense. In a gas with ~, =10"cm"', for example, the librium are likely to be small, being measured by the small characteristic recombination time for hydrogen is only ratio se/UH (where zo is the speed of sound).

Rev. IVlod. Phys. , Vol. 5'l, No. 4, October 1979 756 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects constitute evidence against photoionization models, but mentioned in Sec. I, bX/A. -2v/c. " A few relevant com- this is not very clear. The Seyfert nuclei in question ments, about the gas pressures, a likely confining are less luminous than quasars, so with our standard "intercloud medi. um, "and the total implied energies, assumptions, their emission regions should have over- have al.ready been made ai the end of Sec. III. B. These all size scales of the order of one light-year; it would comments need only slight revision if dust is important be easy to imagine asymmetric distributions of gas as discussed in Sec. V. Now some remarks about the which would permit variations in much less than a year. velocity dispersion v are in order. It seems likely— Also, we have no assurance that these particular ob- though not yet provable —that z is related to gravita- jects are exactly like quasars —for example, the rele- tional (orbital or escape) speeds in the emission re- vant electron densities may be larger than those in qua- gions. This is obvious if the emission regions are or- sars, allowing more compact arrangements w'ith small- biting or falling into a central mass; it is also worth er light-travel times. An interesting aspect of the ob- considering if the line-emitting gas has been ejected servations is a tendency for the Hn/HP intensity ratio from a central loca, lity. If M is the mass within radius to become larger as the HP intensity decreases; in ~, and M~ denotes one solar mass, the escape speed at other words, Ha seems to vary less dramatically than radius & is HP. (Does this mean, according to the discussion in M/10'M g Sec. IV. C and especially Fig. 9, that rH &100'?) =(1700 km s ') v„, 1 light-yea. r If a quasar's photoionized line-emitting regions are r dispersed in space so that there is a considerable dis- If we adopt characteristic values UH-10" cm s" and persion in light-travel times, then the observed line n, -10"cm ', as discussed previously, and if L, de- spectrum is related to some appropriate average lum- notes the total luminosity of a qua. sar, then {very inosity of the continuum source. Recalling comments crudely) r-(3 light-years) (L/10 ' erg s ')' ' for the made in Sec. V. G about correlations between observed broad-line-emitting regions; so luminosities and emission-line-to-continuum ratios, suppose that we were to plot these characteristics for (1.0' kms') v„, 108~s 10" . (8.2) a large ensemble of quasars, in the manner of Baldwin (, ~o„,erg s (1977b). There would be a statistical tendency for the Masses of 10' to 10" M~ seem consistent with the ob- instantaneously highest-luminosity objects to be above served linevyidths. their average luminosities, and this would help to ex- There is another relation involving M and L, , known plain the observed effect. It is also possible to invent as the "Eddington limit. " Make the fashionable suppo- other ways in which continuum fluctuations, over time sition that much of the luminosity of a quasar derives scales of many years, would induce this type of corre- from gravitational accretion onto one or more compact lation, especially if some of the line-emitting gas is objects (most likely a centra, l massive black hole). optically thick and some is optically thin to ionizing Some outward momentum is transferred from escaping photons. radiation to the infalling material. If the luminosity is sufficiently large relative to the central mass, this ra- VIII. GAS MOTIONS AND DYNAMICS; LINE PROF ILES diation pressure strongly impedes the accretion. But A. Generalities A truly "self-consistent" phoioionization model would include some sort of dynamical equilibrium within each ~2Shklovsky (1965) proposed that quasars' linewidths are ionized zone, as well as thermal and ionization equilib- actually due to scattering by free electrons, so that v is re- ria. There should be an explanation for the character- lated to elect~on velocities in a hot, quiescent medium; istic gas pressures and values of U„which have been Burbidge et aL. (1966) even suggested that this would explain observed differences between permitted and forbidden line- mentioned in Secs. III, IV, and V. . And there should also widths. Weymann (1970), Mathis (1970), and Auer and Van be explanations of the characteristic emission line- Blerkom (1972) calculated some related line profiles. Today, widths and profiles which are observed. Unfortunately, we do not believe that scattering by free electrons is generally relations between these matters and available observa- important; this is mainly because photoionization analyses lead tional data are so indirect that unique conclusions can- to models which are optically thin to such scattering [UH not be drawn from the data —this situation is even «10~~ cm s~; see comment following Eq. (2.5)], and partly murkier than the ionization problems discussed earlier. because the idea of electron scattering provides no advantage Papers on quasar-related dynamical problems tend to in explaining the observed line profiles as we know them today. Moreover, one can show that a simple model, with a single be quite detailed, specific —and idealized. central source surrounded by a hot gas, cannot meet all of the At a very simple, order-of-magnitude level, we can following conditions which must obtain before electron scatter- guess several interesting parameters for a quasar's ing can become important: the gas must be optically thick to broad-line emission regions: the photoionized gas scattering, but it cannot absorb radio waves too strongly, and pressure (P„, 10 ' dyncm '); either the total radiation the overall dimension must be small enough to allow scattered pressure or the ionizing radiation pressure (P„„-10' continuuum radiation to vary within a year or so. Note, also, or 10 ' dyncm '); the local velocity dispersion within that are cannot use resonance scattering to weaken the first condition, because the observed semiforbidden lines are as each photoionized region, including thermal motions broad as the resonance lines. With the possible exceptions of and subsonic turbulence (w 15 or 20 kms '); and the peculiar high-excitation lines from nonphotoion'ized gas in a overall velocity dispersion (v 10' to 104 km s '). This few special objects (C &v in NGC 4151~), electron scattering is last parameter is indicated by the observed linewidths likely to be important regarding the prominent linewidths.

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects 757 the luminosity depends upon the accretion rate; so diation pressure. This fact inspired Mushotzky, Solo- there is a limit to the luminosity-to-mass ratio L/M. mon, and Strittmatter (1972) to suggest that radiatively This limit depends upon the opacity of the infalling gas, driven winds also occur around quasars; Tarter and and for ionized gas is highest if the gas is hot and rare- McKee (1973) then derived better estimates of the rates fied so that scattering by free electrons is the dominant of momentum transfer. Many papers on this subject process. (Obviously, the dense line-emitting regions have appeared subsequently. Mathews (1974) and Kip- do not contain. such gas. ) Then the "Eddington limit" is penhahn, Perry, and R5ser (1974) calculated the ac- celerations of optical. ly thin, photoionized clouds (see L ~ (10"' erg s-')(M/1. 0'M, ) . (8.3) also Opher, 1974a). Blumenthal and Mathews (19V5) (Many subtleties can occur here, especially if there are employed a few simple assumptions to show that an en- optically thick blobs or special geometrical arrange- semble of such clouds, constantly replenished near the ments. We feel obliged to mention the Eddington limit center of activity, might produce emission-line pro- because it is so often invoked, but the interested reader files which resemble those of quasars. may invent ways of evading it. ) If (8.3) is valid, then However, Williams (1972) pointed out that isolated, comparison with (8.2) gives photoionized clouds must be disrupted by internal pres- 1/4 sures (including trapped resonance photons) before kms ') u.,„-(800 10 ' ergs ' (8.4) large velocities can be attained; see also Weymann ( (1973), Noerdlinger and Rybicki (1974), and McKee and It is both easy and consistent to imagine that a quasar Tarter (1975). Because of the nature of the ionization and its line-emitting regions have these characteris- equilibrium, the radiative momentum absorbed per unit tics: (i) The luminosity is not very far below the volume is proportional to ~,', so the acceleration is Eddington limit. (ii) The central mass is 10'-10"Mz, proportional to pg, . High densities are required for rea- roughly proportional to the luminosity. (iii) The ob- sonable accelerations, but isolated, compact, high-den- served velocity dispersion ~ is comparable to z„, for sity clouds, expanding at roughly their internal sound the l.ine-emitting regions. speeds, dissipate very quickly. A conceivable escape Most imagined pictures of quasars include several from this difficulty —if instabilities are not too bad —is components: A massive central object, a dense gase- to suppose that each gas cloud is confined by a sur- ous disk, a dense cluster of stars and related ojects, rounding medium; Blumenthal and Mathews (1975) in- a rarefied medium (either hot thermal gas or nonther- voked such a medium in their line-profile calculations. mal particles and fields), and dense clouds of line- Mathews (1976), Mathews and Blumenthal (1977), and emitting gas. Some of these components may not be Krolik (1979) have discussed some relevant gas-dynam- easily distinguishable, and some may be unnecessary. ical instabilities. Suppose that a photoionized cloud is Gas may be liberated when stars are disrupted, either radiatively accelerated through a low-density medium tidal. ly by the black hole, or in stellar collisions, or in whose pressure is sufficient to confine the cloud (ex- supernova explosions; or gas may be falling in from a cept for instabilities). If the cloud is optically thin, a surrounding galaxy. Some gas may fall into the disk Rayleigh-Taylor-like instability develops at the leading and spiral into the black hole; some may be confined in edge. However, accor'ding to Mathews and Blumenthal, clouds at the emission-line-region densities, yg, -10" there are mitigating effects, so that as the instability cm ', some may become part of a low-density hot grows to a nonlinear stage, its growth rate may slow medium. The low-density gas may be blown outward down; the practical result is left in doubt. A cloud with in a "wind, "by radiation pressure or by relativistic an appreciable but moderate optical depth to ionizing particles and field, or by its own pressure; this wind photons (v'„-20?) can be stable. A thick cloud, which may carry line-emitting clouds along with it, or may contains an H'/H' ionization front. (TH& 50), is quite condense into clouds or sheets or filaments because of unstable at the ionization front. A cloud which is ac- instabilities. The hypothetical disk may contain the celerated by surface forces (i.e., by the confining me- emission-Line gas or may be its source. Shock waves, dium) is also very unstable. Mathews and Blumenthal and sources of energetic particles and electromagnetic suggest that flat ("pancake-shaped") photoionized clouds fields, can occur in many places among the various with moderate optical depths may produce Inost of the components. Many authors have rung the changes in important emission lines. This seems inconsistent this bewildering belfry since the mid-l960s. with some of our comments in Secs. IG-V, where we Because the observational data are obviously inade- suggested thai large optical depths, v'„&50, are nec- quate to give us much more than we have already dis- essary for several. reasons. However, the dynamically cussed in Secs. III-V, one is tempted to try to choose critical thickness depends upon a radiation pressure among the various schemes by looking for theoretical gradient, and if x-rays are more important than Math- inconsistencies or instabilities. Occasionally an author ews and Blumenthal supposed, the discrepancy may be claims that some intricate scenario is inevitable, but reduced. assertions of this type have often turned out to be wrong. Kippenhahn, Mestel, and Perry (1975) developed We shall restrict our attention to a few' aspects of the solutions for a continuous "quasar wind, "driven by problem. radiation pressure but influenced by internal gas pres- sure. The hypothetical wind is mostly rarefied, op- B. Acceleration of gas —mainly by radiation pressure tically thin, and practically invisible, but according to Some hot stars are known to eject material in contin- Mestel, Moore, and Perry (1976) and Kippenhahn uous "stellar winds" which are driven largely by ra- (197V), an ionization instability may cause density

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 758 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

waves to form, leading to shock fronts and perhaps Lyon + N V L'l240 —C Pl k1549 Synthptic; blend -- C 16] M909 condensations. These authors intended to explain ab- I I sorption lines in quasars' spectra, and it is not clear TON 4 how their results may be related to the emission-line regions or to the results of Mathews and Blumenthal. See also Kippenhahn (1978). Burbidge and Perry (1976) attempted to derive quasars' masses from ideas about 4C 29.50

radiation-driven wiods; considering that some of their e I ~ v ~ assumptions and parameters can easily be modified, l their results are consistent with conventionally sus- pected values, 10' to 10" solar masses. This does not ~ '~ prove that the winds exist, of course. Radiation-driven clouds and winds have been popular 331+170 largely because they are susceptible to idealized, z ,~pqV ~ ~ ~ ~ - ' ~ r ~ v e y i ' v ' -~ r v ~ ~ mathematically well-def ined treatment. We suspect, r g v by analogy with supernova remnants and diffuse nebulae z in our Galaxy, that nonradiative pressures —the "con- PKS 0424-1 fining medium, " in fact —may dominate the dynamics of quasars' emission regions. Eilik and Caroff (1976) and Rowe, Stoner, and Ptak (1978), have considered +31 the possible "volume forces" (rather than surface pres- sure) that would result from nonthermal particles streaming through the gas, but little attention has been 25.05 given to the possible role of magnetic or electromag- netic fields (see Arons, Kulsrud, and Ostriker, 1975, F ~ for possible inspiration or discouragement). Marscher VELOCITY ( 2000 KM/SK(: INTE&&AL&l . (1978) has discussed acceleration of clouds by repeated explos ion waves. FIG. 13. The profiles of several lines in high-red-shift qua- sars' spectra. See Baldwin and Netzer (1978) for details; the C. Emission-line profiles point is that the I e, C &v and C»& lines all seem to have the same intrinsic profile, if one allows for absorption on the A. few years ago, it was hoped that quasars' line pro- short-wavelength side of Le. Note, however, that the particu- files would provide decisive information about the emis- lar luminous quasar B 1225 +31.7 is an exception. sion regions. Unfortunately, various contradictory ex- planations of the observed profiles have a,ll been partly successful. There are four basic facts to be explained: file is symmetric and rather triangular, with slightly (i) In a typical quasar's spectrum, the broad lines all concave sides ("wings"). A good example, despite many have practically the same shape and relative width. superimposed absorption lines, is shown in Fig. 14, For example, the profiles of C Iv X1549 and C III] X1909 taken from data obtained by Boksenberg et &E. See also can usually be superimposed (see Fig. 13, taken from Osmer and Smith (1977a), Baldwin and Netzer (1978), Baldwin and Netzer, 1978). The t.u profile is trickier Osterbrock (1977), and Fig. 13. The peak of each line because it usually has absorption lines on its short- probably includes emission from the narrow-line re- wavelength side and N V A, 1240 emission on its long- gions. wavelength side; but the data are usually consistent (iv) But in some objects' spectra, the profiles are with the idea that intrinsic Ln and N V A.1240 profiles asymmetric. The quasar PHL 1093 is one good ex- are like that of C IV 11549. The broad Balmer and ample (Baldwin, 1975); see also Ulrieh (1972b), Disney helium lines are probably similar in most cases. [See (19V3), Osmer, Smith, and Weedman (1974), and Miley Baldwin (1975,1978), Osterbroek (1977), and Osmer and Miller (1979). Many Seyferts also have asymme- and Smith (1976, 19VVa). ] Most guasars' broad line- tries (Osterbrock, 1977). In most such cases, the line widths cb A/X (where b X = "FWHM, " "full width at half- profiles resemble triangles with unequal sides, in such maximum") are between 10' and 10 kms ', 5000 kms ' a way that the lines' "centers of gravity" are at longer is a good typical value. wavelengths than their peaks. Where perceptible nar- (ii) However, some objects produce broad lines which row lines are superimposed, they usually appear near are not all alike. In two very luminous quasars, PHL the peaks of the asymmetric broad lines. 957 and B 1225+ 31.7, the C IV line is narrower than the Shields (1978) has discussed some of the questions C III ] and I ck lines (Coleman et a/. , 1976; Baldwin and raised by these facts. If the emitting regions are sim- Netzer, 1978). In several objects, including the pe- ply rotating in a disk or falling inward, then their char- culiar Seyfert galaxy NGC 4151, the He I X5876 line is acteristic velocities should depend upon radial position, known to be wider than Hp (Boksenberg et aL, 1975; v -y"' ', the broad wings of each line should be formed Osterbrock and Koski, 1976). MgII A. 2798 may occa- in the innermost parts of the configuration. But the line sionally be wider than HP (Grandi and Phillips, 1978). ratios produced at any radius depend upon U» there- Ha and HP have different widths in some cases (Oster- fore, in order for I u, C IV X1549, and C III] X1909 to brock, 19VV). have similar profiles, U„must be nearly independent (iii) In most quasars' spectra, each broad-bne pro- of radius. Shields suggests that this is additional evi-

Rev. Mod. Phys. , Vot. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects

2126 -158 300-

200- COUNTS

h i

f

(( 100—

I 500 1000 1500 CHANNEL NUMBER FIG. 14. The profile of a particular quasar's I-n line, obtained with high spectral resolution by Boksenberg's group. The hori- zontal width of the figure corresponds to a rest-wavelength interval of about 150 A. This spectrum has many narrow I n absorp- tion lines, probably not directly related to the broad emission line; note that they tend to fall along the short-wavelength side of the emission line. dence for something that we must already suspect: However, this model is unappealing because each of there is a physical connection between the gas and ra- its clouds is optically thin. The information conveyed diation densities which causes them to have a particular by a standard symmetric line profile is like that given ratio. However, as Shields also notes, in this picture by the standard set of line intensities: some finite re- the gas densities that produce the line wings should be gion in parameter space" is allowable. For the line very much greater than those which give the centers of profiles, if we assume spherical or axial symmetry, the lines; this makes it difficult to explain how C&» ] the important parameters are the distributions of ~„ X1909 can have broad wings while narrower [0 «, ] X5007 Us, r„, and covering factors, as functions of velocity emission is rveak. The relation v-~ ' ' is probably dispersion v. Radial position y-, although important, oversimplified; but the idea that velocity dispersion is affects observable quantities only indirectly. correlated with radial position may be useful in par- Asymmetric profiles have been interpreted by Cap- tially explaining fact (ii) above. As we mentioned in riotti, Foltz, and Byard (1979) and Ferland, Netzer, Sec. IV. D, He& F5876 is enhanced more strongly if I'„ and Shields (1979) as evidence that tbe line-emitting is larger, presumably at smaller values of y; so it is gas is moving outward. These authors discuss en- qualitatively reasonable for He I A58V6 to be wider than sembles of thick clouds, moving radially outward. Be- HP in some gravitationally bound cases (Netzer, 1978). cause of resonance and Balmer-line scattering an /1ro Most writers on the subject have agreed with Shields internal dust, emission from the photoionized part of (1978) in preferring models wherein the gas flows out- each cloud tends to escape through the illuminated gv~rd. The role of gravity in such a model is not com- inner edge of the cloud. Looking at an expanding array pletely obvious. Since it is difficult to believe that the of clouds from a distance, we therefore see the clouds central mass of a quasar can be very much less than on the far side best; since those clouds are moving the values mentioned earlier, it appears that the hy- away from us, the observed asymmetric line profiles pothetical outflow velocities are not very much greater can be explained —qualitatively, at least, and perhaps than zr.„at the source of the outflow. (This is remini- also quantitatively. But if this is true, why do most scent of stellar winds. ) Blumenthal and Mathews (1975) quasars have symmetric emission lines? Perhaps most showed that a particular model with radiatively acceler- quasars' emission regions are not very thick (Mathews ated clouds would produce symmetric line profiles and Blumenthal might prefer this view); or perhaps the much like those which are observed in most cases. velocity dispersions in most guasars have substantial

Rev. Mod. Phys. , Vol. 51, No. 4, October 1979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects nonradial components. Note, also, that much depends volving envelopes around many stars, especially red upon the viewing angle if the configuration is not spher- giant stars. The situation need not be hydrostatic; ically symmetric. For example, gravitational and there may be steady flows, or locally unsteady flows transverse Doppler red shifts can modify the l.ine pro- whose average properties are represented by the whole files for a disklike configuration seen "face-on" (Net- conf iguration. zer, 1977b). Another interesting speculation concerns radiation As mentioned in Sec. VII. D, Stoner, Ptak, and Ellis densities arid dust grains. As discussed in Sec. IV, (1974) proposed a quite different explanation for some radiation densities seem to be roughly ihe same in most asymmetric line profiles. quasars' broad-line-emitting regions; and as discussed in Sec. V, these radiation densities are just adequate to D. More remarks about certain parameters heat solid grains gimost to their evaporation tempera- tures. According to Shields (1978), perhaps this is Unless we have been misled in Secs. III, IV, and V, more than a coincidence. Perhaps there is some in- many quasars, spanning a wide range in luminosity, stability that causes dense line-emitting clouds to form all seem to have line-emitting regions with similar val- as soon as dust grains have condensed in an outflowing ues of U„and is probably just above 10' cm s ', n,. U„ "wind, "or where grains are destroyed in infalling gas. while is probably just below 10"cm '. The corre- z, One could extend this speculation by wondering whether sponding thermal energy density (or pressure) in the each photoionized region has a moderate but not exces- photoionized gas is just above 0.01 erg cm ', and ihe sive optical thickness for ultraviolet absorption dust; total radiation energy density is not much less. Com- by this might set UH. We shouM also remember that most parabl. e energy densities have sometimes been men- published radiaiive-accel. eration models have not in- tioned for relativistic particles and electromagnetic cluded dust. fields which produce nonthermal emission in some qua- Maybe there are some clues, which we do not quite sars see Jones et (1974) and Burbidge et al. [e.g. , al. understand, in the surprising geometrical parameters. (1974), as well as references cited by Burbidge and The thickness g „of each dense photoionized region is Burbidge (1967)]. Furthermore, one can imagine a probably only 10~' or 10~' cm, so that the associated thermal "iniercloud medium" with the same energy time scales ~H/U„and ~H/w are only about 10' and 10' and whose of sound com- density (pressure) speed is s. The total cross-section area of all of the photoion- parable to the observed velocity dispersions. " These ized regions, required to give the necessary "covering order-of-magnitude numbers are vaguely in satisfying, factor, "must be 10 to 10"cm' for a respectable qua- a speculative but we should to explain them. way, try sar. U each ionized region resembled a spherical In particular: why are the gas and radiation pressures cloud, more than 10' such clouds would be requiredt comparable in the line-emitting regions, and what is This is why sheeilike photoionized regions are appeal- special about the value 0.01 erg cm '? The idea of ing. Three obvious types of sheets may occur (i) near radiation pressure balancing gas pressure, while ob- shock fronts, (ii) on the surfaces of large, very dense vious, is made difficult by instabilities —see the ref- H clouds, or (iii) on the surface of a hypothetical gas- erences cited in Sec. VIII. B. eous disk. The latter two possibilities are not entirely Shields (1978) has mentioned some of the many possi- distinct, because a disk is likely to be inhomogeneous. ble starting points for answers to these questions. For The idea of an assembly of clouds may be topologically example, suppose that ionizing radiation illuminates a wrong; shock fronts and very hot or nonthermal gas gravitationally bound atmosphere from above. If the may from "bubbles" or "tunnels" in a cooler gaseous radiation pressure forces exceed gravity forces in the medium, and the photoionized gas may form the sur- photoionized layers, then these layers are compressed face of these bubbles or tunnels. radiation so that radiation and gas pressures are by Throughout this whole problem runs the difficulty that comparable there, while gravity serves to stabilize the we do not really understand the dynamical behavior of situation. If the ionizing continuum is a power law like interstellar cl.ouds, nebulae, and supernova remnants E(c) -s ', then the expected value of U„ is of the order in our own Galaxy. Many "theoretical" papers about of 10' rather than 10' cm s '; but if the ionizing spec- quasars have been based on elaborate scenarios. Ge- trum is "harder" or "flatter" as discussed in.Sec. V. F, ometrically detailed models, invented in the same this discrepancy is less serious. ShieMs speculates way but applied to resolvable objects in our Galaxy, have that the hypothetical atmosphere is on the surface of an often (usually? ) been overthrown as soon as adequate accretion disk, but one might also consider a model. in- observations have become possible. There is no rea- son to think that similarly detailed models of quasars would fare any better if observers could resolve qua- ~3The required temperature would be almost 109 K, so that sars' structures. kT is almost 100 keV, and the density n, would be almost 105 %e believe that attention should be concentrated on cm ~. In the usual case, such a thermal medium cannot fill parameters whose values (or orders of magnitude, at the entire region of interest, because it would be optically least) are known without much recourse to geometrical thick to scattering by free electrons. As noted by Davidson suppositions. These parameters are their a variation of this idea is to that there are E„agd ~„ (1972), suppose ratio their large, not-so-hot clouds, withn8 -10~ cm ~, whose random UH, associated energy density or pres- velocities provide the overall energy density or pressure- sure, and their implied size scales; the characteristic i.e., when such clouds collide they form the dense regions velocity dispersion; perhaps the "covering factor"; the whose emission lines we observe. total luminosity; the relative abundances of hydrogen,

Rev. Mod. Phys. , Vol. 61, No. 4, October 'l979 Kris Davidson and Hagai Netzer: Emission lines of quasars and similar objects helium, and heavier elements, and the existence or Bahcall, J. N. , 1966, Astrophys. J. 145, 684. nonexistence of associated dust; and the continuum Bahcall, J. N. , 1971, Astron. . J. 76, 283. spectrum shape, and its fluctuations in time. Except Bahcall, J. N. , 1978, Phys. Scr. 1V, 229. and -Z. the last these cannot be de- Bahcall, J. N. , B. Kozlovsky, 1969a, Astrophys. J. for very item, parameters 155, 1077. rived without knowing about the emission lines; even Bahcall, J. N. , and B.-Z. Kozlovsky, 1969b, Astrophys. J. the shape of the continuum spectrum may be modified 158, 529. by intervening dust, whose presence is detectable Bahcall, J. N. , B.-Z. Kozlovsky, and E. E. Salpeter, 1972, through its effect on emission lines. One might object Astrophys. J. 171, 467. that most of the parameters that we have mentioned are Bahcall, J. N. , and J. B.Oke, 1971, Astrophys. J. 163, 235. not directly related to the hypothetical energy source— Bahcall, J. N. , and W. L. W. Sargent, 1967, Astrophys. J. Lett. L65. which may or may not be a massive black hole —but we 148, Bailey, M. E., and S. V. M. Clube, 1978, Nature (Lond. ) 275, reply that (i) if a "central object" does not provide us 278. with useful, specific observable quantities, then spec- Baldwin, J. A. , 1975, Astrophys. J. 201, 26. ulations about its related small-scale details are un- Baldwin, J. A. , 1977a, Mon. Not. R. Astron. Soc. 178, 67P. satisfactory because they cannot be verified or over- Baldwin, J. A. , 1977b, Astrophys. J. 214, 679. thrown by observations; and (ii) perhaps the most im- Baldwin, J. A. , 1978, in Pxoceedhngs of the 2977 NATO Cam- portant questions about a quasar involve its formation bridge Surnme~ Conference on Quasars (in press). Baldwin, A. W. L. Burke, C. M. Gaskell, and E. Wamp- and its persistent supply of "fuel"—both of which in- J. , J. ler, 1978, Nature (Lond. ) 273, 431. volve diffuse matter that is probably related to the Baldwin, J. A. , and H. Netzer, 1978, Astrophys. J. 226, 1. emission regions. Baldwin, J. A. , H. E. Smith, E. M. Burbidge, C. Hazard, H. S. Murdoch, and D. L. Jauncey, 1976, Astrophys. J. Lett. 206, ACK NOW LE DGIVIE NTS L83. Barr, P., N. E. White, P. W. Sanford, and J. C. Ives, 1977, We began the preparation of this review at the 1978 Mon. Not. R. Astron. Soc. 181, 43P. Santa Cruz "Summer Workshop" on Quasars and Active Bates, D. B., and A. Dalgarno, 1962, in Atomic and Molecular Galactic Nuclei, and wish to thank the organizers and Processes, edited by D. R. Bates (Academic, New York), p. participants of that meeting for much inspiration, pro- 249. vocation, and advice. Vfe are grateful to J. A. Bald- Bates, D. R., A. E. Kingston, and R. W. P. McWhirter, win, J. B. Oke, D. E. Osterbrock, add D. and B. Wil1.s 1962a, Proc. R. 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