6. EXCITATION MECHANISMS

6.1. Nonstellar Photoionization

The origin and excitation of the ionized gas in the central regions of nearby galaxies has been a longstanding problem (Minkowski & Osterbrock 1959; Osterbrock 1960). Ever since the early suggestion of Ferland & Netzer (1983) and Halpern & Steiner (1983), photoionization by a central AGN has surfaced as the leading candidate for the excitation mechanism of LINERs. Given the success with which more luminous sources have been explained within this framework, and the growing realization that BHs are commonplace, extending photoionization models to LINERs is both natural and appealing. The requisite relative strengths of the low-ionization lines in LINERs can be achieved by lowering the ionization parameter, commonly defined as U = Q_ion / 4 r² c n, where Q_ion is the number of photons s^-1 capable of ionizing hydrogen, r is the distance of the inner face of the cloud from the central continuum, n the hydrogen density, and c the speed of light. While Seyfert line ratios can be matched with logU -2 ± 0.5 (e.g., Ferland & Netzer 1983; Stasinska 1984; Ho, Shields & Filippenko 1993), LINERs require logU -3.5 ± 0.5 (Ferland & Netzer 1983; Halpern & Steiner 1983; Péquignot 1984; Binette 1985; Ho, Filippenko & Sargent 1993; Groves, Dopita & Sutherland 2004).

An issue that has not been properly addressed is which of the primary variables - Q_ion, r, or n - conspire to reduce U in LINERs to the degree required by the models. The answer seems to be all three. The dominant factor comes from the luminosity, as LINERs emit an order of magnitude less ionizing luminosity than do Seyferts: < L_H > = 3 × 10³⁹ ergs s^-1 versus 29 × 10³⁹ ergs s^-1 (Ho, Filippenko & Sargent 2003). Given the gas-poor environments of LINERs (see Section 5.6), we can now say with some certainty that the reduction in ionizing luminosity is intrinsic and not due to obscuration (as proposed by Halpern & Steiner 1983). But this is unlikely to be the end of the story. The electron density of LINERs (< n_e > 280 cm^-3), at least as probed by the relatively low-density tracer [S II] 6716, 6731, is ~ 50% lower than in Seyferts (< n_e > 470 cm^-3). Very little is known about the detailed morphology and spatial distribution of the NLR in LINERs, or for that matter in low-luminosity Seyferts. Whereas the NLR in luminous Seyferts span ~ 50-1000 pc in radius, scaling roughly as L^0.5 (Bennert et al. 2006), LINERs seem to be significantly more compact. This is perhaps not surprising, if the NLR size-luminosity relation extends to LLAGNs. At typical ground-based resolution, narrow-band imaging studies find that the ionized gas in LINERs tends to be quite centrally peaked, with typical dimensions of r 50-100 pc (Keel 1983a; Pogge 1989). In the instances where narrow-band images or slit spatial profiles are available from HST (Bower et al. 2000; Pogge et al. 2000; Cappellari et al. 2001; Verdoes Kleijn et al. 2002; González Delgado et al. 2004; Walsh et al. 2008), the line-emitting gas appears even more concentrated still, with scales tens pc, although some of it clearly extends to scales of at least ~ 200 pc (Shields et al. 2007). The covering factor is high, on average ~ 0.3 for the LINER nuclei of the radio galaxies studied by Capetti, Verdoes Kleijn & Chiaberge (2005). With very few exceptions (e.g., NGC 1052; Pogge et al. 2000), extended, elongated structures analogous to classical ionization cones in Seyferts do not exist in LINERs. Interestingly, both of these trends (smaller n_e and r) would naively drive U in the opposite direction needed to explain LINERs. On the other hand, we know that the NLRs of AGNs in general, and perhaps of LINERs especially, contain a wide range of densities not probed by [S II] and that this material is highly stratified radially (Wilson 1979; Pelat, Alloin & Fosbury 1981; Carswell et al. 1984; Filippenko & Halpern 1984; Péquignot 1984; Binette 1985; Filippenko 1985; Ho, Filippenko & Sargent 1993, 1996; Barth et al. 2001b; Laor 2003; Shields et al. 2007; Walsh et al. 2008). The effective ionization parameter, therefore, depends on the detailed spatial distribution of the gas.

Whereas basic single-zone photoionization models can match many of the strong lines, it is well-known that more complex, multi-component models, especially ones that incorporate a range of densities, are required to achieve a satisfactory fit (Binette 1985; Gabel et al. 2000; Sabra et al. 2003). A notorious deficiency of single-zone models has been their inability to reproduce the high values of the temperature-sensitive ratio [O III] 4363 / [O III] 5007. However, because of the different critical densities of these two transitions, they need not originate cospatially, making [O III] 4363 / [O III] 5007 no longer a valid thermometer. The discovery that these two lines indeed have different line widths removed one of the principal objections to photoionization models (Filippenko & Halpern 1984; Filippenko 1985).

The observed weakness of He II 4686 / H (see also Section 5.8) has also been a thorny problem. Péquignot (1984) achieved a consistent fit to the spectrum of NGC 1052 by invoking a modified ionizing spectrum consisting of an 80,000 K blackbody coupled with an X-ray tail extending to higher energies. The main difficulty with this proposal is that the observed SEDs of LINERs do not have a blackbody component peaked in the UV, nor is Péquignot's specific model unique because Gabel et al. (2000) achieved an equally good - if not better - fit using a simple power-law continuum with = -1.2. Since we now have ample evidence that the SEDs of LINERs are not the same as those of more luminous AGNs, future photoionization calculations should adopt empirically motivated input spectra. Important steps in these directions have been taken (e.g., Nicholson et al. 1998; Gabel et al. 2000; Nagao et al. 2002; Lewis, Eracleous & Sambruna 2003), but much more can be done. One fruitful avenue to pursue is to incorporate the full observed SED, which is noteworthy not only because of its hard ionizing spectrum but, due to its radio-loudness, also because it presents a copious supply of relativistic, synchrotron-emitting particles, which can dramatically alter the excitation of the NLR (Aldrovandi & Péquignot 1973; Ferland & Mushotzky 1984; Gruenwald & Viegas-Aldrovandi 1987). "Cosmic ray heating" boosts the strengths of low-ionization lines such as [N II] 6548, 6583 and [S II] 6716, 6731 (Viegas-Aldrovandi & Gruenwald 1990), which are normally underpredicted (e.g., Ho, Filippenko & Sargent 1993; Lewis, Eracleous & Sambruna 2003), and thereby help to constrain alternative solutions that invoke selective abundance enhancement of N and S (Storchi-Bergmann & Pastoriza 1990) or dust grain depletion (Gabel et al. 2000).

6.2. Contribution from Fast Shocks

Despite the natural appeal of AGN photoionization, alternative excitation mechanisms for LINERs have been advanced. Collisional ionization by shocks has been a popular contender from the outset (Burbidge, Gould & Pottasch 1963; Osterbrock 1971; Osterbrock & Dufour 1973; Koski & Osterbrock 1976; Danziger, Fosbury & Penston 1977; Fosbury et al. 1978; Ford & Butcher 1979; Heckman 1980b; Baldwin, Phillips & Terlevich 1981). Shocks continue to be invoked (Bonatto, Bica & Alloin 1989; Dopita & Sutherland 1995; Alonso-Herrero et al. 2000; Sugai & Malkan 2000) even after concerns over the [O III] 4363 temperature problem had been dispelled as a result of either revised measurements (Keel & Miller 1983; Rose & Tripicco 1984) or complications arising from density stratification (Filippenko & Halpern 1984). Dopita & Sutherland (1995) showed that the diffuse radiation field generated by fast ( 150-500 km s^-1) shocks can reproduce the optical narrow emission lines seen in both LINERs and Seyferts. In their models, LINER-like spectra are realized under conditions in which the precursor H II region of the shock is absent, as might be the case in gas-poor environments. The postshock cooling zone attains a much higher equilibrium electron temperature than a photoionized plasma; consequently, a robust prediction of shock models is that shocked gas should produce a higher excitation spectrum, most readily discernible in the UV, than photoionized gas. In all the cases studied so far, however, the UV spectra are inconsistent with the fast-shock scenario because the observed intensities of high-excitation lines such as C IV 1549 and He II 1640 are much weaker than predicted (Barth et al. 1996, 1997; Maoz et al. 1998; Nicholson et al. 1998; Gabel et al. 2000). Dopita et al. (1997) used the spectrum of the circumnuclear disk of M87 to advance the view that LINERs are shock-excited. This argument is misleading because their analysis deliberately avoids the nucleus. Sabra et al. (2003) demonstrate that the UV-optical spectrum of the nucleus of M87 is best explained by a multi-component photoionization model.

Analysis of the emission-line profiles of the Palomar nuclei further casts doubt on the viability of the fast-shock scenario (Ho, Filippenko & Sargent 2003). The velocity dispersions of the nuclear gas generally fall short of the values required for fast-shock excitation to be important. Furthermore, the close similarity between the velocity field of LINERs and Seyferts as deduced from their line profiles contradicts the basic premise that shocks are primarily responsible for the spectral differences between the two classes of objects. For a given bulge potential, LINERs, if anything, have smaller, not larger, gas velocity dispersions than Seyferts (L.C. Ho, in preparation). And as discussed in Section 5.2, the incidence of extended radio jets, the most likely source of kinetic energy injection into the NLR, is actually lower in LINERs than in Seyferts, again contrary to naive expectations.

Notwithstanding these complications, it is inconceivable that mechanical heating, especially by lower velocity (~ 50-100 km s^-1) shocks, does not play some role in the overall excitation budget of LINERs. The velocities of the line-emitting gas are, after all, highly supersonic, turbulent, and most likely pressure-dominated (L.C. Ho, in preparation). The trick is to figure out what is the balance between shocks and photoionization, and what physical insights can be gained from knowing the answer. It would be worthwhile to revisit composite shock plus photoionization models, such as those developed by Viegas-Aldrovandi & Gruenwald (1990) and Contini (1997) with the latter component maximally constrained by observations so that robust, quantitative estimates can be placed on the former. Such an approach might yield meaningful measurements of the amount of mechanical energy deposited into the host galaxy by AGN feedback.

6.3. Contribution from Stellar Photoionization

Another widely discussed class of models invokes hot stars formed in a short-duration burst of star formation to supply the primary ionizing photons. Ordinary O-type stars with effective temperatures typical of those found in giant H II regions in galactic disks do not produce sufficiently strong low-ionization lines to account for the spectra of LINERs. The physical conditions in the centers of galaxies, on the other hand, may be more favorable for generating LINER-like spectra. For example, Terlevich & Melnick (1985) postulate that the high-metallicity environment of galactic nuclei may be particularly conducive to forming very hot, T (1 - 2) × 10⁵ K, luminous Wolf-Rayet stars whose ionizing spectrum would effectively mimic the power-law continuum of an AGN. The models of Filippenko & Terlevich (1992) and Shields (1992) appeal to less extreme conditions. These authors show that photoionization by ordinary O stars, albeit of somewhat higher effective temperature than normal (but see Schulz & Fritsch 1994), embedded in an environment with high density and low ionization parameter can explain the spectral properties of transition objects. Barth & Shields (2000) extended this work by modeling the ionizing source not as single O-type stars but as a more realistic evolving young star cluster. They confirm that young, massive stars can indeed generate optical emission-line spectra that match those of transition objects, and, under some plausible conditions, even those of bona fide LINERs. But there is an important caveat: the star cluster must be formed in an instantaneous burst, and its age must coincide with the brief phase (~ 3-5 Myr after the burst) during which sufficient Wolf-Rayet stars are present to supply the extreme-UV photons necessary to boost the low-ionization lines. The necessity of a sizable population of Wolf-Rayet stars is also emphasized in the study by Gabel & Bruhweiler (2002). As discussed in Ho, Filippenko & Sargent (2003), the main difficulty with this scenario, and indeed with all models that appeal to young or intermediate-age stars (e.g., Engelbracht et al. 1998; Alonso-Herrero et al. 2000; Taniguchi, Shioya & Murayama 2000), is that the nuclear stellar population of the host galaxies of the majority of nearby AGNs, irrespective of spectral class, is demonstrably old (Section 4.2). Stellar absorption indices indicative of young or intermediate-age stars are seldom seen, and the telltale emission features of Wolf-Rayet stars are notably absent, both in ground-based and HST spectra. Sarzi et al. (2005) find that young stars can account for at most a few percent of the blue light within the central few parsecs of nearby LLAGNs, in most cases incapable of providing enough ionizing photons to account for the observed H emission. Post-starburst scenarios face another serious dilemma: if most LLAGNs, which constitute the majority of nearby AGNs and a large percentage of all galaxies, are described by this scenario, then where are their precursors? They do not exist. These empirical facts seriously undermine the viability of starburst or post-starburst models for LLAGNs.

Evolved, low-mass stars, on the other hand, probably contribute at some level to the ionization. This idea was advocated by Binette et al. (1994), who proposed that post-asymptotic giant branch (post-AGB) stars, which can attain effective temperatures as high as ~ 10⁵ K, might be responsible for photoionizing the extended ionized gas often observed in elliptical galaxies. The emission-line spectrum of these nebulae, in fact, tend to be of relatively low ionization (Demoulin-Ulrich, Butcher & Boksenberg 1984; Phillips et al. 1986). Invoking evolved stars has the obvious appeal of not violating the stellar population constraints discussed above. This mechanism, however, cannot be the dominant contributor to compact LINERs. The line emission tends to be very centrally concentrated (Section 6.1), much more so than the underlying stellar density profile. Moreover, the line strengths in most LLAGNs are simply too high. The calculations of Binette et al. predict H equivalent widths of EW 1 Å, whereas the LINERs and transition objects in the Palomar survey have an average EW 3-4 times higher (Ho, Filippenko & Sargent 2003), with over 70% of the sample having EW > 1 Å.

To obtain a quantitative estimate of the contribution of post-AGB stars to the ionization budget of the weaker emission-line nuclei, I convert the nuclear stellar magnitudes (m₄₄) given in Ho, Filippenko & Sargent (1997a) to stellar masses assuming a mass-to-light ratio of M / L_B = 8(M / L_B) and that post-AGB stars have a specific ionization rate of Q_ion = 7.3 × 10⁴⁰ (M / M) s^-1 (Binette et al. 1994). Within the 100 × 200 pc aperture of the Palomar spectra, the integrated stellar mass is ~ 10⁷ to 10¹⁰ M, with a median value of 2 × 10⁹ M, which corresponds to an ionizing photon rate of Q_ion = 1.5 × 10⁵⁰ s^-1. These estimates depend on the choice of the stellar initial mass function, and, most importantly, on detailed processes during the late stages of stellar evolution that are still not fully understood (see, e.g., O'Connell 1999). Nevertheless, taking the fiducial estimates as a rough guide, the predicted values of Q_ion can be compared to the actually observed, extinction-corrected H luminosity. Assuming complete reprocessing of the ionizing continuum and that on average it takes 2.2 Lyman continuum photons to produce one H photon, I estimate that the nebular line emission in roughly one-third of the Palomar sources can be powered by photoionization from post-AGB stars. The fraction is higher for LINERs (39%) than Seyferts (16%), being most prevalent for LINER 2s (44%) and transition objects (33%). Eracleous, Hwang & Flohic (2008b) performed a similar analysis for a handful of LINERs with central stellar luminosity profiles available from HST, concluding also that post-AGB stars can alleviate the ionizing photon deficit in some objects.

6.4. Energy Budget

In luminous AGNs, important confirmation of the basic photoionization paradigm comes from the strong empirical scaling and correlated variability between line flux and the strength of the ionizing continuum. Although very little information exists in terms of line-continuum variability for LLAGNs, enough X-ray observations have now been amassed to examine the correlation between optical line luminosity and X-ray luminosity. The X-ray band is only indirectly coupled to the bulk of the Lyman continuum, but in LLAGNs, it offers the most reliable probe of the high-energy spectrum. Studies in the soft X-ray band suggest that LLAGNs roughly follow the extrapolation of the L_H - L_X correlation established for higher luminosity sources (Koratkar et al. 1995; Roberts & Warwick 2000; Halderson et al. 2001). Intriguingly, no clear differences could be discerned between LINERs and Seyferts, confirming preliminary evidence presented in Halpern & Steiner (1983). A more complex picture, however, emerges at higher energies (2-10 keV). Terashima, Ho & Ptak (2000) and Terashima et al. (2000) note that LINER 2s, unlike LINER 1s, suffer from a deficit of ionizing photons: the X-ray emission of the nucleus, when extrapolated to the UV, underpredicts the observed H luminosity by a factor of ~ 10-100. This trend persists in more recent Chandra observations (Terashima & Wilson 2003b; Flohic et al. 2006; Eracleous, Hwang & Flohic 2008b), one that seems to be especially endemic to transition objects (Ho et al. 2001; Filho et al. 2004).

Figure 10a shows an update of the L_H - L_X relation for all Palomar sources with high-resolution ( 5") X-ray measurements. For comparison, I also include z < 0.5 Palomar-Green (PG; Schmidt & Green 1983) quasars and luminous Seyfert 1s with well-determined SEDs (Figure 7; L.C. Ho, in preparation). All broad-line sources follow an approximately linear relation over nearly 7 orders of magnitude in luminosity. In detail, L_H L_X^1.1, such that quasars and luminous Seyferts have a median ratio L_X / L_H 2, to be compared with L_X / L_H 7 for Palomar Seyfert 1s. Ignoring the possible effect of a luminosity-dependent covering factor, this can be interpreted as the consequence of a decrease in the ratio of UV radiation to X-rays with decreasing luminosity, reflecting a pattern familiar from samples of bright AGNs (e.g., Strateva et al. 2005), now extended down to lower luminosities by ~ 3 orders of magnitude. Since LINER 1s are weaker than Seyfert 1s and their SEDs lack a UV bump, it is surprising that they actually have a somewhat lower L_X / L_H ratio (~ 5) than Seyfert 1s. This suggests that at least some of the H emission in LINER 1s, presumably in the narrow component, is not powered by AGN photoionization. In fact, this turns out to be a property symptomatic of all type 2 LLAGNs (Table 1). The most extreme manifestation can be seen among transition objects, with L_X / L_H 0.4, but both LINER 2s and Seyfert 2s also exhibit an ionizing photon deficit. For conditions typical of LLAGNs, Eracleous, Hwang & Flohic (2008b) use photoionization calculations to infer L_ion = 18 L_H f_c^-1, where L_ion is the ionizing luminosity between 1 Ryd and 10 keV and f_c is the covering factor of the line-emitting gas. Since L_ion 3 L_X for a power-law spectrum with = -0.1 to -0.9, L_X / L_H 6 f_c^-1. It is clear that most narrow-line LLAGNs violate this energy balance condition, even for the optimistic assumption of f_c = 1.

Figure 10. (a) Correlation between (total) H luminosity and X-ray (2-10 keV) luminosity. The dotted lines mark LX / LH = 1, 5, and 25. (b) Distribution of radio-loudless parameter versus Eddington ratio, with the bolometric luminosity estimated assuming Lbol = 16 LX.

There are several possible solutions to the ionization deficit problem. (1) The X-rays could be highly obscured, perhaps even Compton-thick. In light of the evidence given in Sections 5.3, 5.6, I consider this solution to be untenable for LINER 2s; highly absorbed sources do exist (e.g., NGC 4261; Zezas et al. 2005), but they are in the minority. Moreover, many of the X-ray measurements have already been corrected for absorption. The situation is more complex for Seyfert 2s. Some of the sources with low L_X / L_H indeed show direct evidence for Compton thickness from their X-ray spectra (Cappi et al. 2006). Others, however, are too faint for spectral analysis, and for these, their status as Compton-thick sources was based on the observed ratio of 2-10 keV flux to [O III] 5007 flux (Bassani et al. 1999; Panessa & Bassani 2002). Applying an average correction factor of 60 to the X-ray luminosity would bring the Seyfert 2s into agreement with the Seyfert 1s on the L_H - L_X relation (Panessa et al. 2006). But this procedure assumes that the low values of L_X / L_H are due to a reduction of the X-rays by absorption rather than an enhancement of H (see below). (2) The SED could be drastically different, specifically in having a much more prominent UV component. This proposition can be promptly dismissed because the SEDs of LLAGNs generically lack a UV bump. There is certainly no indication that type 2 sources are preferentially brighter in the UV; in the case of LINERs, type 2 sources, if anything, tend to be redder than type 1 sources (Maoz et al. 2005). (3) Lastly, and most plausibly, a significant fraction of the ionization for the narrow-line gas comes from nonnuclear sources. As discussed in connection with the preceding two subsections, young, massive stars and fast shocks are generally not viable options. There are a number of candidate sources of "extra" ionization, including hot, evolved stars, turbulent mixing layers, diffuse X-ray emitting plasma, low-mass XRBs, cosmic ray heating, and mechanical heating from radio jets. As all of these sources probably contribute at some level, efforts to single out any dominant mechanism may be hopelessly challenging. Nevertheless, as discussed in Section 6.3, post-AGB stars appear especially promising. Taking the calculations of Binette et al. (1994) as a guide, the stellar mass within the central 100-200 pc region generates sufficient Lyman continuum photons to account for the H emission in ~ 30%-40% of the LINER 2s and transition objects. This estimate is crude and admittedly optimistic, as it assumes a covering factor of unity for the NLR, but it serves as a useful illustration of the types of effects that should be included in any complete treatment of the energy budget problem in LLAGNs.

6.5. The Nature of Transition Objects and a Unified View of LLAGNs

The physical origin of transition nuclei continues to be a thorny, unresolved problem. In standard line-ratio diagrams (Figure 3), transition nuclei are empirically defined to be those sources that lie sandwiched between the loci of "normal" H II regions and LINERs. This motivated Ho, Filippenko & Sargent (1993) to propose that transition objects may be composite systems consisting of a LINER nucleus plus an H II region component. The latter could arise from neighboring circumnuclear H II regions or from H II regions randomly projected along the line of sight. A similar argument, based on decomposition of line profiles, was made by Véron, Gonçalves & Véron-Cetty (1997). If transition objects truly are LINERs sprinkled with a frosting of star formation, one would expect that their host galaxies should be similar to those of LINERs, modulo minor differences due to extra contaminating star formation. The study of Ho, Filippenko & Sargent (2003) tentatively supports this picture. The host galaxies of transition nuclei exhibit systematically higher levels of recent star formation, as indicated by their far-IR emission and broad-band optical colors, compared to LINERs of matched morphological types. Moreover, the hosts of transition nuclei tend to be slightly more inclined than LINERs. Thus, all else being equal, transition-type spectra seem to be found precisely in those galaxies whose nuclei have a higher probability of being contaminated by extra-nuclear emission from star-forming regions.

This story, however, has some holes. If spatial blending of circumnuclear H II regions is sufficient to transform a regular LINER into a transition object, the LINER nucleus should reveal itself unambiguously in spectra taken with angular resolution sufficiently high to isolate it. This test was performed by Barth, Ho & Filippenko (2003), who obtained HST/STIS spectra, taken with a 0.2"-wide slit, of a well-defined subsample of 15 transition objects selected from the Palomar catalog. To their surprise, the small-aperture spectra of the nuclei, for the most part, look very similar to the ground-based spectra; they are not more LINER-like. Shields et al. (2007) reached the same conclusion from their STIS study of Palomar nuclei, which included six transition objects, showing that even at HST resolution these objects do not reveal the expected excitation gradients.

The "masqueraded-LINER" hypothesis can be further tested by searching for compact radio and X-ray cores using high-resolution images. Recall that this is a highly effective method to filter out weak AGNs (Sections 5.2, 5.3). Filho, Barthel & Ho (2000, 2002a; Filho et al. 2004) have systematically surveyed the full sample of Palomar transition objects using the VLA at 8.4 GHz. They find that ~ 25% of the population contains arcsecond-scale radio cores. These cores appear to be largely nonstellar in nature. The brighter subset of these sources that are amenable to follow-up Very Long Baseline Interferometry (VLBI) observations (Filho et al. 2004) all reveal more compact (milliarcsecond-scale) cores with flat radio spectra and high brightness temperatures ( 10⁷ K). These radio statistics are hard to interpret, however, in the absence of a control sample of other LLAGNs surveyed to the same depth, resolution, and wavelength. The Nagar, Falcke & Wilson (2005) 15 GHz survey satisfies these criteria. As Table 1 shows, the frequency of radio cores in transition objects is roughly half of that in Seyfert 2s and LINER 2s. On the other hand, the detection rate of X-ray cores is actually remarkably high - 74% - identical to that of LINER 2s and similar to that of Seyfert 2s. This observation strongly suggests that the majority of transition objects indeed do harbor AGNs.

In light of these recent developments, the basic picture for the physical nature of transition objects needs to be revised. Inspection of the statistical properties in Table 1 offers the following clues, which help not only to explain transition objects but provide a unified view to relate the different classes of LLAGNs.

1. Seyferts, LINERs, and transition objects define a sequence of decreasing accretion rate. This is most evident from L_X and L_bol / L_Edd, but it is also seen in L_H and P_rad.

2. As noted in Section 5.10, type 1 sources have significantly higher luminosities and Eddington ratios than type 2 systems. The basic premise of the conventional orientation-based unification scenario does not hold for LLAGNs. The systematic reduction in accretion rate along the sequence S L T also provides a viable explanation for the systematic decrease in the detection rate of broad H emission, especially the precipitous drop among transition sources (f_b in Table 1).

3. Transition objects appear to be anomalously strong in their H emission. In light of the HST evidence for a distributed source of ionization, I suspect that a significant fraction of the H emission in these objects in fact is not photoionized by the central AGN. This leads to misleading values of L_X / L_H and R_o (which is based on L_H). For this class either the X-ray or radio core provides a cleaner measure of the AGN power.

4. The loose inverse correlation between radio-loudness and accretion rate, best seen by comparing R_X versus either L_X or L_X / L_Edd, mirrors the trends found by Ho (2002a) and Terashima & Wilson (2003b).

5. Focusing on the type 2 sources, note that LINER 2s are very similar to Seyfert 2s, the former being ~ 1/3-1/2 as strong as the latter in terms of H luminosity and radio power. The two groups have almost identical L_X and L_X / L_Edd, although this may be an artifact of incomplete absorption correction for Seyfert 2s, some of which are highly absorbed (Panessa et al. 2006). In the same vein, I propose that transition objects represent the next step in the luminosity sequence. Judging by their X-ray luminosity, radio power, L_X / L_Edd, and radio detection fraction, the AGN component in transition objects is ~1/4 to 1/2 as strong as that in LINER 2s.

According to the picture just outlined, most, if not all, type 2 sources are genuinely accretion powered. Using the accretion rate as the metric for the level of AGN activity, Seyfert 1s rank at the top of the scale, followed by Seyfert 2s, LINER 1s, LINER 2s, and finally ending with transition objects. This scenario, which in broad-brush terms explains a wide range of data summarized in Table 1, has the virtue of simplicity. It is also physically appealing, given the broad spectrum of accretion rates anticipated in nearby galaxies.

There is, however, one loose end that needs to be tied. What powers the spatially extended, "excess" optical line emission in transition objects? For the reasons explained before, the source of the ionization is unlikely to be shock heating or photoionization by hot, massive stars, notwithstanding the success with which such models have been applied to some individual objects (Engelbracht et al. 1998; Barth & Shields 2000; Gabel & Bruhweiler 2002). Shields et al. (2007) suggest two candidates for a spatially extended source of ionization: hot, evolved stars and turbulent mixing layers in the interstellar medium (Begelman & Fabian 1990). In Section 6.3, I showed that the stellar mass in the central 100-200 pc indeed seems to provide enough post-AGB stars to account for the correct level of H emission in a significant fraction of the transition objects. I would like to suggest two other sources, ones that have the advantage of being empirically well motivated by recent observations. These processes probably operate in all nuclear environments all the time, maintaining a "baseline" level of weak optical line emission that is only noticeable after the AGN has subsided to a very low level.

As discussed in Sections 5.3, 5.4, the X-ray morphology of the central few hundred parsecs of galaxies can be quite complex. The nucleus, if present, is often encircled by other point sources, mostly XRBs (Fabbiano 2006). With X-ray luminosities ranging from ~ 10³⁷ to 10³⁹ ergs s^-1 (Flohic et al. 2006), XRBs individually or collectively can outshine the nucleus itself (Ho et al. 2001; Eracleous et al. 2002; Ho, Terashima & Ulvestad 2003; see Figure 5). The discrete sources themselves are embedded in extended emission, consisting of an optically thin thermal plasma with kT 0.5 keV and a spectrally harder diffuse component, which contributes a luminosity of ~ (5 - 9) × 10³⁸ ergs s^-1 in the 0.5-10 keV band (Flohic et al. 2006). The hard diffuse component most likely represents the cumulative emission from faint, unresolved low-mass XRBs, although this interpretation seems somewhat at odds with the spectrum derived by Flohic et al. (power law with = -0.3 to -0.5). Low-mass XRBs typically can be fit by a thermal bremsstrahlung model with kT = 5-10 keV or a power law with = -0.6 to -0.9 (e.g., Makishima et al. 1989). High-mass XRBs would provide a better match to the observed spectrum, but in view of what we know about the stellar populations (Section 4.2), they are probably untenable. A possible solution is to invoke a multi-temperature plasma (M. Eracleous, private communications); a hotter component (kT few keV), when added to the cooler kT = 0.5 keV component, would presumably permit a significant contribution from low-mass XRBs without violating the spectral constraints. We can estimate the expected X-ray output from low-mass XRBs from the correlation between optical and X-ray luminosity established for normal galaxies (Fabbiano & Trinchieri 1985). Using again the nuclear stellar magnitudes from the Palomar survey, I obtain a median L_X(2-10 keV) = (3 ± 1) × 10³⁸ ergs s^-1 within the central 2" × 4" aperture, which falls within the ballpark of the value measured by Flohic et al. (2006). The combination of hot gas and XRB emission, therefore, supplies ~10³⁹ ergs s^-1 in X-rays, comparable to the amount coming from the nucleus alone for Seyfert 2s and LINER 2s, and double the amount from transition nuclei (Table 1). Voit & Donahue (1997) suggest that hot plasma additionally may transfer heat conductively to the line-emitting gas in LINERs, in a manner analogous to the situation in cooling flow filaments in galaxy clusters.

Lastly, cosmic ray heating (Section 6.1) by the central radio core will further enhance the optical line luminosity (Ferland & Mushotzky 1984). The very source of the fast particles, namely compact radio jets, itself probably injects an additional source of mechanical heating, although this is more difficult to model concretely. Both processes - photoionization by off-nuclear X-rays and cosmic ray heating - have a convenient virtue: they will tend to produce low-ionization spectra and therefore provide a natural match to the spectral characteristics of nearby LLAGNs.