The compelling dynamical evidence for massive dark objects in galactic nuclei does not uniquely imply massive black holes (BHs). To argue convincingly that these objects are BHs we must rule out alternatives to a BH, and the alternative to a point mass is a cluster of some sort of nonluminous objects, such as a cluster of brown dwarfs or stellar remnants.We use simple physical considerations to derive the maximum possible lifetime of a dark cluster which may consist of any plausible form of non-luminous gravitating objects -from brown dwarfs and very low-mass objects of cosmic composition, to white dwarfs, neutron stars, and black holes. The lower this limit relative to the galaxy age, the more implausible is the cluster hypothesis, thus arguing for a point mass. A cluster with a lifetime much shorter than 10 Gyr is unacceptable, since observing it at the present epoch would be highly improbable.Since the goal is to rule out a dark cluster by showing that its lifetime must be very short, we make the most generous assumptions possible under the observational constraints to allow for its survival. We find that the lifetime of such an hypothetical cluster must be much shorter than the galaxy age only in the cases of NGC 4258 and our Galaxy, thus strongly arguing for a point mass. In all other galaxies, the case of a massive BH, although compelling, is not yet watertight. We also note that there are two exotic alternatives to a massive BH that cannot be ruled out even in the cases of NGC 4258 and the Galaxy: clusters of elementary particles (e.g. bosons), and clusters of very low-mass ( ∼ < 0.04 M ⊙ ) BHs. We point out, however, serious difficulties with these alternatives, and argue that they are highly implausible.

Two experiments qualify the previously observed finding that a moderately incongruent brand extension is evaluated more favorably than a congruent or extremely incongruent brand extension and reconcile this finding with other outcomes that have been reported in the brand extension literature. A congruent brand extension is judged more favorably than either a moderately incongruent extension or an extremely incongruent extension when involvement in the task is low. Apparently, incongruity per se does not always prompt the elaboration required to reconcile a moderately incongruent extension with the parent brand and, thereby, enhance evaluation of the moderately incongruent extension. Further, when involvement is high, a moderately incongruent brand extension may only be judged more favorably than a congruent one if the extension is undifferentiated. If the extension is differentiated, the differentiation may provide a basis for favorable evaluation irrespective of the level of congruity with the brand. Recall of information about the performance of the extension relative to competitive brands and measures of attitude toward the parent brand, fit between the extension and the parent brand, and task satisfaction provide insight into the processes that underlie these effects.In the past decade, a popular marketing strategy has been to introduce new products using an established brand name. Although many of these so-called brand extensions have involved product categories that readily "fit" with common associations to the parent brand name, a number of recent brand extensions have been into product categories that seem incongruent because they lack an obvious connection with the brand (Liesse, 1993). For example, BIC (pens, lighters, and razors) launched a line of perfumes, Uncle Ben's (rice) introduced pasta sauces, Bill Blass (fashion designer) offered gourmet chocolates, Starbucks (coffee) expanded into ice cream, and Jack Daniels (whiskey) marketed charcoal. The observation that some of these extensions have been successful (Starbucks ice cream), whereas others have been quickly withdrawn from the markets (BIC perfume), raises an important question:What is the relationship between the congruity of an extension with the parent brand and consumers' response to the extension?An investigation reported by Meyers-Levy, Louie, and Curren (1994) offers some evidence relevant to this question. Research participants were asked to evaluate brand extensions that were chosen to be congruent (Kellogg peanut butter flavored cereal), moderately incongruent (Kellogg corn chips), or extremely incongruent (Kellogg peanut butter covered crackers) with the parent brand. Their findings revealed that a moderate level of incongruity between the extension and the parent brand resulted in more favorable evaluations than either a high level of congruity or incongruity.The authors explain the inverted U pattern that they observe by drawing on theorizing regarding how schema congruity affects cognitive elaboration (see Mandler, 1982). Accordi...

Observations of line emission from water masers near the center of the galaxy NGC 4258 have recently provided compelling evidence for the presence of a rotating disk of gas, viewed nearly edge-on, surrounding a massive black hole. We show that this disk is very likely to be only marginally stable to radial perturbations-a stability regime where weak, nonaxisymmetric disturbances grow via the ''swing amplification'' effect, leading to the formation of a ragged, multiarmed spiral pattern similar to that observed in Sc galaxies. This suggests a natural explanation for the apparent clustering of the high-velocity emission sources into several distinct clumps and for the observed regularity in the distance intervals between them. The clumps of maser sources appear at the intersections of the spiral arms and the radial lines of longest coherent gain path (the diameter through the disk perpendicular to the line of sight) and are thus spaced apart at the characteristic crest-to-crest radial distance between the arms.This interpretation implies a disk thickness of 10.003(Q/1.6) pc at a radius of 10.2 pc, where the local value of the stability parameter is 1.2 = Q = 2. The H 2 density is 11.8 ϫ 10 10 (Q/1.6) Ϫ1 cm Ϫ3 , assuming that H 2 dominates the mass density in that region. The disk mass is =10 6 M J , which is consistent with the accuracy of the Keplerian fit to the rotation curve of the maser emission sources. These results closely concur with previous estimates based on independent considerations.

The rapidly rotating, masing circumnuclear disk in the central subparsec region of the galaxy NGC 4258 is remarkably circular and Keplerian, yet a striking asymmetry appears in the maser spectrum : the redshifted, high-velocity sources are much more numerous and signiÐcantly more intense than the blueshifted ones. A similar strong asymmetry also appears in the recently discovered, masing, circumnuclear disks in NGC 1068 and NGC 4945, thus suggesting it may be a general phenomenon.We show that the observed Doppler shift asymmetry can naturally arise due to spiral shocks in circumnuclear disks. We argue that population inversion can largely be quenched in these systems because of IR photon trapping, and that the high-velocity maser emission originates within thin slabs of postshock gas, where the physical conditions are conducive to maser action. The high-velocity masers with the longest gain paths appear where the line of sight is tangent to shock fronts. Since the spirals have a trailing geometry due to the action of di †erential rotation, the locations of the masers make the blueshifted radiation travel through a column of noninverted gas that maintains close velocity coherence with the maser source, where absorption occurs. The resulting asymmetry in the high-velocity maser spectrum, where the redshifted emission appears systematically stronger, is independent of the existence of a warp in the disk or the azimuthal direction to the observer, and is insensitive to small distortions in the velocity Ðeld in the disk.The high velocities of these features reÑect the rotational velocities in the disk and have nothing to do with the shock speed. The low-velocity emission arises within a narrow annulus near the inner edge of the disk, where direct irradiation by a central source may provide the energy that ultimately powers these masers. In NGC 4258Ècurrently the most well-deÐned masing diskÈthe proposed scenario can also account for the intriguing clustering of the high-velocity maser spots in distinct clumps, the restricted radial distribution of the low-velocity sources, and the dip in the maser spectrum at the systemic velocity of the disk. In this case, we infer a molecular density of D109 cm~3, a disk mass of D104 and a mass accretion rate of order D7 ] 10~3 yr~1, which is consistent with an advection-M _ , M _ dominated accretion Ñow. These results di †er signiÐcantly from those of the Neufeld and Maloney model (^107.5 cm~3, D100and D7 ] 10~5a yr~1, respectively). M _ , M _ The predicted maser luminosities of the blueshifted and redshifted, high-velocity features in NGC 4258 are consistent with the observations, both in the case of C-type (MHD) shocks and dissociative J-type shocks, where the shock speed is about 20 km s~1. The high-velocity features arise nearly along a diameter through the disk that makes an angle of about 2¡ with the midline. It does not introduce any noticeable deviation from a Keplerian rotation curve (the velocity gradient across the shock is always perpendicular to the line of si...