Improved observational techniques reveal features which challenge the very definition of elliptical galaxies. Many ellipticals contain disks or rings of stars, dust, or gas; others show signs of recent accretions in the form of shells of luminosity.
High-resolution surface photometry shows some elliptical galaxies have breaks (once known as `cores') where their luminosity profile slopes change decrease markedly, while other ellipticals show a constant or only gradually changing slope to the innermost point measured. Direct imaging (Kormendy et al. 1994) and nonparametric deprojection of luminosity profiles (Gebhardt et al. 1996) both dramatize the difference between resolved breaks and power-law profiles. But parameter correlations offer some support to the possibility that many power-law profiles actually break at projected radii smaller than 0.1 arc-sec.
Perhaps most basic is the roughly linear correlation between absolute spheroid luminosity and physical break radius (Kormendy et al. 1994 , Faber et al. 1997). Most of the power-law profiles belong to galaxies with M_V > -21; these galaxies could well have breaks at radii R_b < 10 pc and may follow the correlation found for the well-resolved galaxies. Luminosity also correlates with central velocity dispersion sigma_0 and with surface brightness I_b at radius R_b.
These parameters obey a `fundamental plane' relationship (Faber et al. 1997), analogous to the one already found for the global parameters R_e, sigma, and I_e. The existence of such a plane implies that the virial theorem rules the parameters at the break radius; however the central plane seems thicker than the global plane, perhaps implying that central M/L ratios vary from galaxy to galaxy.
High signal-to-noise CCD images of elliptical galaxies show that some have non-elliptical isophotes (Carter 1979, 1987, Lauer 1985a, Jedrzejewski 1987, Bender, Dobereiner, & Mollenhoff 1988, KD89). Departures from a perfectly elliptical form typically have amplitudes of a few percent, and most galaxies are either boxy or pointed. Two equivalent methods are used to measure isophote shapes:
Isophote fitting (Carter 1979). As a function of the azimuthal angle measured with respect to the major axis, a chosen isophote is fit to
-- \ (1) R(theta) = a_0 + | a_i cos(i theta) + b_i sin(i theta) . / -- i = 1Here a_0 gives the isophote's mean radius, the i = 1 coefficients contain information about its center, and the i = 2 coefficients contain information about its ellipticity and position angle.
Surface-brightness fitting (Lauer 1985b). To detect non-elliptical distortions, the surface brightness along a trial ellipse is fit to
-- \ (2) I(theta) = A_0 + | A_i cos(i theta) + B_i sin(i theta) . / -- i = 1Here A_0 is the mean surface brightness along the ellipse, which is adjusted until the i = 1 and i = 2 coefficients vanish.
Results obtained using these two methods are related by
a_i A_i b_i B_i (3) --- = --------- , --- = --------- a_0 A_0 gamma a_0 A_0 gammawhere gamma is the logarithmic slope of the brightness profile.
In most elliptical galaxies the most significant non-elliptical term is the a_4 coefficient, which is typically in the range -0.02 < a_4/a_0 < 0.04. Galaxies with a_4 < 0 are termed `boxy' since their isophotes are somewhat rectangular, while those with a_4 > 0 are accurately described as `pointed', though the term `disky' is widely used since such galaxies appear to contain disks. Kormendy & Bender (1996) have proposed that boxyness or diskyness be adopted as the primary classification criterion for elliptical galaxies. Isophotal shape correlates with several other important parameters, including optical luminosity, X-ray luminosity, and degree of rotational support (Bender et al. 1989, KD89, Fig. 3). But some galaxies appear both disky and boxy, depending on the surface brightness examined, somewhat blurring this classification scheme.
In a sample of 42 early-type galaxies, 10% had a_4/a_0 > 0.02 and appear to be likely candidates for systems with embedded disks (Lauer 1985a). However, the actual percentage of ellipticals with embedded disks could be much larger. Photometric models combining a spheroidal r^1/4 bulge and an exponential disk indicate that embedded disks must be either very substantial or nearly edge-on to be readily detected. Detection statistics are consistent with the hypothesis that all ellipticals with a_4 > 0 contain disks contributing 20% of the total light (Rix & White 1990).
Photometric modeling is unreliable in recovering disk parameters by decomposing the observed images. The practice of finding the best-fit ellipse and attributing only the residuals to the disk systematically and drastically underestimates the luminosity contributed by the latter (Rix & White 1990).
Surface-brightness data cannot unambiguously diagnose the presence of a disk since some ellipticals may have intrinsically pointy isophotes for unrelated reasons. Line-of-sight velocity profiles provide a more definitive diagnosis (Rix & White 1990).
To measure velocity profiles, galactic absorption-line spectra are compared with the spectra of template stars. Such comparison may be performed in several different ways (Rix & White 1992):
Fourier transform methods invoke the convolution theorem; the transform of the observed spectrum is (approximately) equal to the transform of the velocity profile times the transform of the template spectrum (Sargent et al. 1977, Franx, Illingworth, & Heckman 1989).
Cross-correlation methods measure the correlation between the observed and template spectra as a function of the relative shift in wavelength (Tonry & Davis 1979, Bender 1990).
Direct methods synthesize the observed spectrum by adding up shifted versions of the template spectrum. This is somewhat expensive computationally but avoids the `belling' needed to produce well-behaved transforms of finite spectral intervals, allows masking of discrepant features to reduce mismatch between template and galactic spectra, and permits a straightforward error analysis (Rix & White 1992).
Non-Gaussian line profiles may be characterized using the Gauss-Hermite series (van der Marel & Franx 1993):
-- alpha(w) \ v - V (4) LP(v) = Gamma -------- | h_j H_j(w) , w = ----- , sigma / sigma -- j = 0where Gamma is the line strength, sigma is the Gaussian velocity dispersion, V is the system velocity, and
-1/2 2 (5) alpha(x) = (2 pi) exp(- x / 2)is a normalized Gaussian with unit dispersion. The set of functions H_j(x) are Hermite polynomials of degree j; these are orthogonal with respect to the weight function alpha(x)^2:
1/2 / 2 (6) 2 pi | dx H_j(x) H_k(x) alpha(x) = delta_jk . /
In applying Eq. 4, the parameters Gamma, sigma, and V are chosen by requiring that h_0 = 1 and h_1 = h_2 = 0; non-Gaussian line profiles yield nonzero h_j for j > 2. In particular, h_3 parametrizes the skewness of the line profile, while h_4 measures whether the profile is more or less peaked than a Gaussian.
Application of these techniques has revealed line profiles characteristic of embedded stellar disks in many ellipticals (Franx & Illingworth 1988, Bender 1990, Rix & White 1992, van der Marel & Franx 1993, van der Marel et al. 1994). Embedded disks yield h_3 values with opposite signs on opposite sides of the galaxy's center, implying the presence of a rapidly rotating component. The characteristics of these embedded disks show considerable variation: NGC 5322 has a relatively `warm' disk, with v/sigma = 1.4, while the disk in NGC 3610 is quite `cold', with v/sigma = 4.5 (Rix & White 1992).
Isophote shape is known to be correlated with rotation velocity: Elliptical galaxies with a_4 > 0 tend to be rapid rotators (KD89). Kinematically cold disks may be partly responsible for this correlation, since at some radii such disks may make very substantial contributions to the light and will tend to dominate line-of-sight velocity measurements parametrized by simple Gaussians (Rix & White 1990). For example, purely Gaussian fits to composite line profiles may overestimate rotation curve amplitudes by > 30% (van der Marel & Franx 1993).
Many elliptical galaxies have dust lanes produced by cold interstellar material distributed in disks or rings (e.g. van Gorkom 1992). Velocity measurements show that in many cases this cold gas counter-rotates or is otherwise kinematically distinct from the underlying stellar component; a likely interpretation is that this material has been accreted since the galaxy formed.
Unlike stars, the gas can only settle down on closed (and stable) orbits. In theory this might allow determination of the principal planes of a galaxy's potential, but in practice settling times are long enough that this is questionable (KD89).
One galaxy in which a gas ring does define the principal plane is IC 2006 (Schweizer 1987, Franx, van Gorkom, & de Zeeuw 1994). This galaxy has an external ring containing some young stars. Neutral hydrogen observations show that the velocity varies along the ring in a perfectly sinusoidal manner, indicating that the ring - and the potential it moves in - is exactly circular. The inclination angle of the ring is 37 deg.
X-ray observations indicate that many ellipticals contain 10^9 to 10^10 solar masses of gas at temperatures of 10^7 K (Forman et al. 1979, Trinchiere & Fabbiano 1985, Schweizer 1987). This is comparable to the mass of cold and warm gas present in typical spiral galaxies; thus it seems fair to say that ellipticals are not, in fact, gas poor compared to disk galaxies. The hot gas typically forms a pressure-supported `atmosphere' around the galaxy.
The surface brightness of E galaxies doesn't always decline smoothly and monotonically with radius. When a smooth luminosity profile is subtracted from the actual surface brightness, `shells' or `ripples', centered on the galaxy, are seen (Malin & Carter 1980, Prieur 1990). At least 17% of field E galaxies have shell-like features, and the true fraction may be more than 44% (KD89).
Shells have spectral energy distributions characteristic of starlight. In many cases the shells are somewhat more blue than the galaxies they occupy (KD89). Shell systems have a variety of morphologies; some galaxies have shells transverse to the major axis and interleaved on opposite sides of the center of the galaxy, while other galaxies have shells distributed at all position angles (Prieur 1990). Both the colors and the varied morphologies of shells can be explained by accretion events in which a large elliptical galaxy captures and tidally disrupts a smaller companion.
Profile subtraction sometimes reveals other kinds of structures in E galaxies, including plumes, linear features or `jets' (not the jets seen in AGNs!), `X-structures', etc. (Schweizer & Seitzer 1992).
Due date: 1/28/97
4. How could you use the correlation between effective surface brightness I_e and effective radius R_e (see Eq. 3 of Lecture 2) to measure distances? What kind of accuracy could you achieve, assuming all the scatter shown in Fig. 2 of KD89 is intrinsic to the galaxies?
Last modified: January 22, 1997