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A lenticular galaxy is a type of galaxy which is intermediate between an elliptical galaxy and a spiral galaxy in galaxy morphological classification schemes. Lenticular galaxies are disk galaxies (like spiral galaxies) which have used up or lost most of their interstellar matter and therefore have very little ongoing star formation. They may, however, retain significant dust in their disks. As a result, they consist mainly of aging stars (like elliptical galaxies). Because of their ill-defined spiral arms, if they are inclined face-on it is often difficult to distinguish between them and elliptical galaxies. Despite the morphological differences, lenticular and elliptical galaxies share common properties like spectral features, scaling relations and both can be considered as early type galaxies which are passively evolving, at least in the local universe.

Classification
Lenticular galaxies are unique in that they have a visible disk component as well as a prominent bulge component. They have much higher bulge-to-disk ratios than typical spirals and do not have the canonical spiral arm structure of late-type galaxies, yet may exhibit a central bar. This bulge dominance can be seen in the axis ratio (i.e. the ratio between the observed minor and major axial of a disk galaxy) distribution of a lenticular galaxy sample. The distribution for lenticular galaxies rises steadily in the range 0.25 to 0.85 whereas the distribution for spirals is essentially flat in that same range. Larger axial ratios can be explained by observing face-on disk galaxies or by having a sample of spheroidal(bulge)-dominated galaxies. Imagine looking at two disk galaxies edge-on, one with a bulge and one without a bulge. The galaxy with a prominent bulge will have a larger edge-on axial ratio compared to the galaxy without a bulge based on the definition of axial ratio. Thus a sample of disk galaxies with prominent spheroidal components will have more galaxies at larger axial ratios. The fact that the lenticular galaxy distribution rises with increasing observed axial ratio implies that lenticulars are dominated by a central bulge component.

Lenticular galaxies are often considered to be a poorly understood transition state between spiral and elliptical galaxies, which results in their intermediate placement on the Hubble sequence. This results from lenticulars having both prominent disk and bulge components. The disk component is usually featureless, which precludes a classification system similar to spiral galaxies. As the bulge component is usually spherical, elliptical galaxy classifications are also unsuitable. Lenticular galaxies are thus divided into subclasses based upon either the amount of dust present or the prominence of a central bar. The classes of lenticular galaxies are S01, S02, and S03 when based upon the amount of dust absorption in the disk component and SB01, SB02, and SB03 when based upon a central bar.

Sérsic Decomposition


While ellipticals and spirals tend to have somewhat well-defined Sérsic profiles, the surface brightness profiles of lenticular galaxies are often more difficult to quantify. The disk component of lenticular galaxies often has a very flat surface brightness distribution (Sérsic index of n ≈ 1), especially in the outermost regions of the disk. Also, there is typically an observed truncation in the surface brightness of lenticular galaxies at ~ 4 scale radii of the disk. These features are consistent with the general structure of spiral galaxies. However, the bulge component of lenticulars is more closely related to elliptical galaxies in terms of morphological classification. This spheroidal region, which dominates the overall structure of lenticular galaxies, has a much steeper surface brightness profile (Sérsic index of n ≈ 4, or that of a de Vaucouleurs profile) than the disk component. Since the bulge component tends to dominate the galaxy, lenticular galaxy samples are often indistinguishable from elliptical galaxy populations in terms of their overall surface brightness profiles. However, galaxies are often assigned the S0 morphological class when they require multiple Sérsic indices to describe their surface brightness profiles, one to describe the bulge and one to describe the disk. This implies that lenticular galaxies are a distinct morphological subclass of galaxies.

Bars
Like spiral and elliptical galaxies, lenticular galaxies can possess a central bar structure. While the classification system for normal lenticulars depends on dust content, barred lenticular galaxies are classified by the prominence of the central bar. SB01 galaxies have the least defined bar structure and are only classified as having slightly enhanced surface brightness along opposite sides of the central bulge. The prominence of the bar increases with index number, thus SB03 galaxies have very well defined bars that can extend through the transition region between the bulge and disk. Unfortunately, the properties of bars in lenticular galaxies have not been researched in great detail. Understanding these properties, as well as understanding the formation mechanism for bars, would help clarify the formation or evolution history of lenticular galaxies.

Content
In many respects the composition of lenticular galaxies is like that of ellipticals. For example, they both consist of predominately older, hence redder, stars. All of their stars are thought to be older than about a billion years, in agreement with their offset from the Tully-Fisher relation (see below). In addition to these general stellar attributes, globular clusters are found more frequently in lenticular galaxies than in spiral galaxies of similar mass and luminosity. They also have little to no molecular gas (hence the lack of star formation) and no significant Hydrogen α or 21-cm emission. Finally, unlike ellipticals, they may still possess significant dust.

Measurement Difficulties and Techniques
Lenticular galaxies share kinematic properties with both spiral and elliptical galaxies. This is due to the significant bulge and disk nature of lenticulars. The bulge component is similar to elliptical galaxies in that it is pressure supported by a central velocity dispersion. This situation is analogous to a balloon, where the motions of the air particles (stars in a bulge's case) are dominated by random motions. However, the kinematics of lenticular galaxies are dominated by the rotationally supported disk. Rotation support implies the average circular motion of stars in the disk is responsible for the stability of the galaxy. Thus kinematics are often used to distinguish lenticular galaxies from elliptical or spiral galaxies. The distinction between spiral galaxies and lenticular galaxies is often simpler to analyze as the dividing line is often set at a particular bulge-to-disk ratio. Determining the distinction between elliptical galaxies and lenticular galaxies often relies on the measurements of velocity dispersion (σ), rotational velocity (v), and ellipticity (ε). In order to differentiate between lenticulars and ellipticals, one typically looks at the v/σ ratio for a fixed ε. For example, a rough criterion for distinguishing between lenticular and elliptical galaxies is that elliptical galaxies have v/σ < 0.5 for ε = 0.3. The motivation behind this criterion is that lenticular galaxies do have prominent bulge and disk components whereas elliptical galaxies have no disk structure. Thus, lenticulars have much larger v/σ ratios than ellipticals due to their non-negligible rotational velocities (due to the disk component) in addition to not having as prominent of a bulge component compared to elliptical galaxies.

The kinematics of disk galaxies are usually determined by Hα or 21-cm emission lines, which are typically not present in lenticular galaxies due to their general lack of cool gas. Thus kinematic information and rough mass estimates for lenticular galaxies often comes from stellar absorption lines, which are less reliable than emission line measurements. There is also a considerable amount of difficulty in deriving accurate rotational velocities for lenticular galaxies. This is a combined effect from lenticulars having difficult inclination measurements, projection effects in the bulge-disk interface region, and the random motions of stars affecting the true rotational velocities. These effects make kinematic measurements of lenticular galaxies considerably more difficult compared to normal disk galaxies.

Offset Tully-Fisher Relation


The kinematic connection between spiral and lenticular galaxies is most clear when analyzing the Tully-Fisher relation for spiral and lenticular samples. If lenticular galaxies are an evolved stage of spiral galaxies then they should have a similar Tully-Fisher relation with spirals, but with an offset in the luminosity / absolute magnitude axis. This would result from brighter, redder stars dominating the stellar populations of lenticulars. An example of this effect can be seen in the adjacent plot. One can clearly see that the best-fit lines for the spiral galaxy data and the lenticular galaxy have the same slope (and thus follow the same Tully-Fisher relation), but are offset by ΔI ≈ 1.5. This implies that lenticular galaxies were once spiral galaxies but are now dominated by old, red stars.

Formation Theories
The morphology and kinematics of lenticular galaxies each, to a degree, suggest a mode of galaxy formation. Their disk-like, possibly dusty, appearance suggests they come from faded spiral galaxies, whose arm features disappeared. Alternatively, as lenticular galaxies are likely to be more luminous than spiral galaxies, which suggests that they are not merely the faded remnants of spiral galaxies. Rather, lenticular galaxies might result from Galaxy merger, which increase the total stellar mass and give the newly-merged galaxy its disk-like, arm-less appearance.

Faded Spirals
The absence of gas, presence of dust, lack of recent star formation, and rotational support are all attributes one might expect of a spiral galaxy which had used up all of its gas in the formation of stars. This possibility is further enhanced by the existence of gas poor, or "anemic," spiral galaxies. If the spiral pattern then dissipated the resulting galaxy would be similar to many lenticulars. Moore et al. also document that tidal harassment - the gravitational effects from other, near-by galaxies - could aid this process in dense regions. The clearest support for this theory, however, is their adherence to slightly shifted version of Tully-Fisher relation, discussed above.

Mergers
The analyses of Burstein and Sandage showed that lenticular galaxies typically have surface brightness much greater than other spiral classes. It is also thought that lenticular galaxies exhibit a larger bulge-to-disk ratio than spiral galaxies and this may be inconsistent with simple fading from a spiral . If S0s were formed by mergers of other spirals these observations would be fitting and it would also account for the increased frequency of globular clusters. It should be mentioned, however, that advanced models of the central bulge which include both a general Sersic profile and bar indicate a smaller bulge, and thus a lessened inconsistency. Mergers are also unable to account for the offset from the Tully-Fisher relation without assuming the merged galaxies were quite different from those we see today.