1 : Preliminaries   6 :   Dynamics I 11 : Star Formation  16 : Cosmology
2 : Morphology   7 :   Ellipticals 12 : Interactions 17 : Structure Growth 
3 : Surveys 8 :   Dynamics II 13 : Groups & Clusters  18 : Galaxy Formation 
4 : Lum. Functions  9 :   Gas & Dust   14 : Nuclei & BHs 19 : Reionization & IGM  
5 : Spirals 10 : Populations    15 : AGNs & Quasars 20 : Dark Matter





(1) Introduction

(a) The Myths

Our view of Elliptical galaxies has changed greatly : [image]
In the 1970s, Ellipticals were thought to be : To a large extent, all of the above are now thought to be wrong.

(b) Subdividing the Elliptical Class

In what follows, it will be useful to consider three classes of Ellipticals : Luminous and midsize have somewhat different properties, but form a single sequence in mass.
Diffuse dwarf Es & dwarf spheroidals are significantly different.

(c) Parameters

Here are a few recurring parameters we need to be familiar with : Also important, are properties of the core : Remember : I(R) is independent of distance ! (for small redshifts).

(d) Deprojection

Note that all the above quantities are projected onto the sky.
Ultimately we want true 3D spatial information. I.e. we want to derive : In general, with z2 = r2 - R2 and dz = r dr / (r2 - R2)1/2, we have [image]


This is an Abel Integral equation, with solution


Note : if the image is elliptical, a unique inversion is only possible for an axisymmetric figues viewed from the equatorial plane.

Just to orient ourselves, consider a single power law of index (typically, 0.5 < < 1.5)

(e) Observational Concerns

There are a number of practical difficulties facing accurate surface photometry


(2) Radial Light Profiles: Outside The Core

Elliptical galaxy light profiles are relatively similar with important differences: [image]

There is a long history of trying to fit these brightness profiles.
Reynolds (1913) and Hubble (1930) used: I(R) = I(0) / (1 + R/R0)2

A modified form has the benefit of having an analytic deprojected density:
I(R) = I(0) / [1 + (R/r0)2]   with   j(r) = I(0) / 2r0[1 + (r/r0)2]3/2

Today's preferred fitting functions are a little different.

(a) Fitting Functions

(b) Resulting Fits

For many years, the deVaucouleurs R1/4 was the primary fitting function
It now seems there are systematic variation that require the other 3-parameter functions
The nuclear regions are in any case poorly fit, and are discussed separately below.
A recent and very thorough study is that of Kormendy et al (2009


(3) Nuclear Regions

It transpires that the nuclear regions are very important:
    they give insight into the galaxy's formation history
    they can be influenced significantly by a central black hole

Early (pre-1975) work suggested that I(R) turned over in a flat core of constant density
This was naturally understood in terms of isothermal and King models (see below)
However, the serious influence of seeing, especially in photographic work, had not been appreciated.
The existence of flat cores was shown to be incorrect with CCD images (eg Kormendy 1977)
Significant progress was only possible using HST.

In general, the above functions fail to match the nuclear regions very well.
Within a "break radius" there can be deviations both below and above the best fit to the outer parts.

(a) Fitting Functions

(b) Results: Two Types, Cores & Power-laws

(c) Summary: Three Kinds of Ellipticals


(4) Scaling Relations

There are many correlations between the various properties of Ellipticals.
The tightness of some are quite remarkable, and point to an underlying homogeneity of this class of galaxy.

(a) Early 2-Parameter Correlations

(b) The 3-Parameter Fundamental Plane

The above 2-parameter correlations have considerable real scatter ([image], B&M 4.43)
Furthermore, the residuals in one plot correlate with those in another.
This suggests we look for a tighter correlation among three parameters: The choice of the 3 parameters is not unique
Three choices have been studied --- they are essentially equivalent.


(5) The Shape of Elliptical Galaxies

To first order, isophotes are concentric, aligned, ellipses: [image]
Ellipticity = 1 - b/a, eccentricity e = 1 - (b/a)2   [e = (2 - ); = 1 - (1 - e)½ ]
Recall, ellipticals are classified En where n = 10

The apparent ellipticity combines the true shape and projection effects
Hence, unlike other morphological designations, n (in En) is not intrinsic

(a) 3-D Shapes

(b) Isophote Shapes: Boxy & Disky

The a4 parameters are very important since they correlate with many other variables (see below, § 8)


(6) Kinematics of Elliptical Galaxies

(a) Methods of Analysis

(b) Amount of Rotation

(c) Axis of Rotation

(d) Kinematically Distinct Cores and Dust Lanes


(7) Mass to Light Ratios

In principle : In practice, not so straightforward:

(a)   Inner Parts

(b)   Outer Parts & Halo


(8) Two Kinds of Ellipticals : Boxy and Disky

Summary of properties which differ for boxy (a4 < 0) and disky (a4 > 0) ellipticals and bulges :

Property Boxy (a4 < 0) Disky (a4 > 0)
Luminosity high : MB < -22 low : MB > -18
Rotation Rate slow/zero : (Vr / )* < 1 faster : (Vr / )* ~ 1
Flattening velocity anisotropy rotational
Rotation Axis anywhere photometric minor axis
Velocity Field anisotropic nearly isotropic
Shape moderately triaxial almost oblate
Core Profile cuspy core steep power law
Core Density low high
Radio Luminosity radio loud and quiet
1020 - 1025 W/Hz
radio quiet
< 1021 W/Hz
X-ray Luminosity high low

Some of these are shown here:   [image]
Note that to first order : Boxy and Disky galaxies have the same :

It is still unclear quite how to interpret this dichotomy :
The two types may be closely related, or may have quite different histories

Semi-empirically, Kormendy and Bender suggest a modified Hubble diagram   [image]

This all has important implications for Elliptical Formation


(9) Formation of Ellipticals

(Note Mergers and Galaxy Formation discussed more in Topics 12 & 19)

Still unclear -- but we have made progress

(a) Two scenarios discussed

(b) Relevant Issues & Problems

(c) Hybrid : Merger Induced Dissipational Collapse