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Properties of Elliptical Galaxies – I. Stellar Populations and
the Interstellar Medium
•Brightest stars are red giants and
AGB stars w/ spectral type K, M
•Very few stars produced in the last
1 – 2 Gyr
•Stars at the center have ~solar
metallicity (differ from the Milky
Way’s globular clusters but similar
to the bulge star metallicities)
•Color of integrated galaxy light
correlates with galaxy luminosity
Fainter/smaller galaxies are bluer
•either less massive ellipticals are
younger or metal poor
•Galaxies with more recent SF (younger stars) are bluer
•Spectra of model galaxies show “bluer” E’s – so called “E+A galaxies”
•After 10 Gyr, looks like a typical E
Model of galaxy that makes
all stars in 108 yr burst
•strong emission lines and
He absorption (OB stars)
seen after 10 Myr
•After 100 Myr, deep H lines
of A stars are seen (E+A
galaxy)
•Galaxies that are more metal poor are bluer
•Metal absorption lines are strongest in the biggest Ellipticals which are redder
•Also, there is a color gradient in Ellipticals
•Redder toward the center – more metal rich (based on strength of Mg lines)
based on strength of Halpha line and H&K break
Metallicity measured in Z (solar metallicity units) or [Fe/H] = log(NFe/NH)gal – log(NFe/NH)
~90,000 galaxies from SDSS – luminous galaxies richer in heavy elements but currently
have below average star formation rates (SFR).
Why are less massive galaxies metal poor?
 Unable to retain most of the metal-rich gas shed by aging stars
•Ellipticals have lots of globular clusters (about twice that of disk galaxies)
•these fall into two groups based on color
•color determined by metallicity, with more metal-rich GCs (redder) possibly
the result of galaxy mergers
•Ellipticals have much less cool, atomic gas
than spiral galaxies
•< 108 – 109 Msun while an Sc galaxy
contains ~1010Msun
•sometimes (though rare) seen as dust
lanes orbiting E’s - from merger or
capture?
•Ellipticals have hot, ionized gas
•stars lose mass through shedding of stellar envelopes as they age
•this gas is 1 – 3 x 107 K  radiates in X-rays
•luminous, most massive E’s have the hottest gas
•extends to R > 30 kpc with 109 – 1011 Msun (10 – 20% stellar mass)
•smaller E’s have less hot gas – weaker gravity cannot prevent escape
•gas not produced through SNe – low metallicity (gas from stars with large
random motions  kinetic motion heats the gas)
X-ray “surface brightness” is proportional to optical SB in many Ellipticals
jopt ~ jx-ray - surprising!
Because...
jopt ~ n*  stellar density
jx-ray ~ ne2  plasma density
(depends on collisions between e- and ions)
And this means that the gas density falls with
radius more slowly than stellar density to make
SBs so similar.
This happens because plasma T is higher than the stellar T if
n* ~ r-α
ne ~ r-αβ
to fit with observations β = T*/T ~ 0.5
(which is about right)
Tgas = 7x106 K
Tstars (kinetic temp) = 3x106K
X-ray – crosses (Chandra)
optical – line (HST)
normalized at R=10”
(Jeltema et al 2003)
Optical, X-ray, and radio luminosities are correlated  implies
connection between X-ray emitting plasma and radio
continuum emission (Binney 1996)
Properties of Elliptical Galaxies – II. Kinematics
Disordered, random motions are important for Ellipticals
v/σ = ordered motion/disordered motion
v = systematic velocity change across region of galaxy
Vrot or Vr = rotational velocity
σ = velocity dispersion of stars at one position or along line-of-sight (los)
σ = <v2>1/2
Many E’s have v/σ << 1
Spirals generally have v/σ ≥ 1
cD galaxy NGC 1399
notice (Vr-Vsys)/σ << 1
Measuring Stellar Velocities:
The spectrum measured from some point in an external galaxy consists of the
sum of spectra from all unresolved stars along that los. Each star has a
different Vlos, so the composite spectrum will be shifted and broadened.
Define los velocity distribution (LOSVD) as the function F(Vlos) such that the fraction
of stars with velocities between Vlos and Vlos + dVlos is given by F(Vlos)dVlos
mean velocity
dispersion
Vlos = ∫dVlos Vlos F(Vlos)
σ2los = ∫dVlos (Vlos-Vlos)2 F(Vlos)
F(Vlos) can be approximated by a Gaussian distribution, but its true
form is modeled by closely examining line profile shapes (e.g. GaussHermite model – BM 11.1.2 – more on this later…)
For Elliptical galaxies, σlos is determined by the “width” of the absorption features.
Absorption lines are compared with local G & K type stars (templates) to determine
dispersion-related broadening.
K0 Giant star
NGC 2549 S0 galaxy
note Mg b
absorption feature
at 518 nm
• G(λ) = F(Vlos) convolved with S(λ) where F(Vlos) is LOSVD
Correlations among global parameters:
1) σo ∝ color ∝ line strength
higher central velocity dispersion = redder E = stronger metal
absorption lines
Somewhat non-intuitive because optical color comes mainly from light at Re while
Mg strength and σo are based on light primarily from the galaxy center.
 more massive galaxies are more metal rich (stronger Mg2) The reason:
deeper potentials hold ISM longer allowing metals to build up
2) Radius - Surface Brightness Relation
Recall
I(R) = Ie exp{-7.67[(R/Re)1/4-1]}
Then
Ltot = ∫o∞ I(R) 2πR dR = 7.22 π Re2 Ie
Then, mean surface brightness within Re is:
<Ie> = (∫oRe I(R) 2πR dR)/(∫oRe 2πR dR) = (½ Ltot)/π Re2
= (½ (7.22) π Re2 Ie)/(π Re2) = 3.61 Ie = <Ie>
Observations show…
Re ∝ <Ie> -0.83±0.08
Larger galaxies have
fainter effective
Surface Brightness
(Kormendy 1977; Djorgovski & Davis 1987)
Since Le (light interior to Re) = π <Ie> Re2

<Ie> ∝ L -1.5
More luminous Ellipticals have larger Re and fainter mean SB
 larger and more luminous galaxies are fluffier with lower densities
One inference: low-luminosity ellipticals formed with more gaseous
dissipation than giant ellipticals. Consistent with Kormendy 09
interpretation for core ellipticals.
3) σo4 ∝ Le
Faber-Jackson relation
(F&J 1976)
More luminous Ellipticals have higher central velocity dispersions
brightest E’s  σo ~ 500 km/s
faintest E’s  σo ~ 50 km/s
*Can be used as a
distance indicator!!
So, we have correlations between Re and Ie
and between σo and Le. Is there a sensible
way to combine this information?
Before describing the observations, let’s
explore what we might expect from dynamics.
Virial Theorem:
-If Ellipticals are self-gravitating and in dynamical
equilibrium, they should obey the Virial Theorem
2KE + PE = 0
Scalar VT
VT relates average stellar speeds to the depth of the
gravitational potential well in which they move.
Mean velocity squared of all stars in system
KE = ½ M <V2>
PE = -GM2/Rg
In VT, we get
Gravitational radius – similar to “effective
radius” or half-mass r and depends on
detailed mass distribution
M<V2> = GM2/Rg

Expressing VT in terms of mass surface density
Assume 1) <V2> ∝ σ
2) Rg ∝ Re
3) A ∝ Re2
η ∝ σ2/Re
M = <V2>Rg/G
M/A = η = <V2>Rg/(AG)
If an elliptical galaxy obeys VT, then these 3 parameters
contain most of the information about its structure.
All E’s should obey the same relation if E’s are a
homologous family (i.e. E’s have the same SB shape and
velocity dispersion distributions). Then E’s should populate
a plane in η, σ, R space. Since η is not directly observable,
η = M/A = (M/L) <Ie> ∝ (M/L) Ie
(M/L) Ie ∝ σ2 Re-1
What do observations show? Ellipticals do occupy a plane in 3D space of
Ie, σ, Re
The Fundamental Plane
Observations show…
Re ∝ σ1.4 Ie-0.85
(Dressler et al. 87)
Ie ∝ σ1.6 Re-1.2
VT gives
(M/L) Ie ∝ σ2 Re-1
Both are true if
(M/L) ∝ σ0.4 Re0.2
From F-J
From R-SB
σ4 ∝ Le  σ0.4 ∝ Le0.1
Re0.8 ∝ Le  Re0.2 ∝ Le0.25
M/L ∝ L0.35  M/L is higher in more luminous, bigger galaxies
M/L ∝ L0.27+/-0.08 (Pragniel and Simien 1996)
Therefore, results of parameter correlations in ellipticals can be understood if:
1)VT is only strong constraint
2)E’s are a nearly homologous family
3)M/L ∝ L 0.3
How do we interpret this M/L relation?
-Differences in stellar populations (brighter galaxies are also redder)
-Differences in Mdark/Mbaryonic (though Romanowsky 03 show evidence for only small
amounts of DM inside Re)
Trujillo et al. 04 argue FP
tilt due to a systematic
variation of the structural
nonhomology of E’s as a
function of L
•¾ tilt due to structural
nonhomology (more
massive galaxies have
steeper velocity dispersion
profiles (σ1.6 rather than σ2)
& SB with higher n)
•¼ tilt due to stellar pops
Core Fundamental Plane (Faber et al. 97)
•Rb, Ib and σ obey FP relationship also (where “b” refers to the “break” radius)
•VT rules parameters at break radius
•Thicker plane  central M/L ratios may vary
Dn – σ Correlation (Dressler et al. 87)
Dn = diameter within which mean SB is In = 20.75 μB
This essentially replaces Ie and Re with one parameter
Dn/Re is larger for galaxies of high SB than low SB but with same L
Dn ~ σ1.4 Ie0.07
- only weak dependence on Ie
Primarily used as distance indicator (better than L ~ σ because that relation did
not also include SB parameter).
Large Scale Kinematics
•Kinematic parameters of E’s display overall symmetry about the
center of the system (reason to assume equilibrium models explain
current state - VT)
•Vlos changes sign across galaxy center
• Systems display net rotation about minor axis
• System flattened by rotation? though same Hubble types can
have very different net rotation rates…
Observed rotation of E’s is too low to explain observed flattening
To quantify this, define Vmax as maximum Vlos
Where model values are based on a system whose ellipticity is determined only by
rotation (which is ~independent of inclination angle (see BT 4.3))
Thus, (v/σ)* ~ 1 for system flattened by rotation
However, E’s have ratios mostly less than unity
• Intermediate-tolow luminosity
E’s lie closest to
unity
• Brightest (and
very faintest)
have lower
values
BM Fig 11.7
Velocity distribution profile shapes
give a clue…
•Recall broadening of E absorption lines is due
to random velocities of stars along a given line
of sight through the galaxy
•G(λ) = F(Vlos) convolved with S(λ) where
F(Vlos) is LOSVD
• To first order, we assume the
distribution is Gaussian,
though deviations (kurtosis,
skew) have been observed
and show correlations with
the amount of rotational
velocity.
• Use truncated Gauss-Hermite
function to model LOSVD
where skew is 3rd order term,
kurtosis is 4th order term
E’s with highest
Vrot have most
skewed LOSVD
indicating 2
components
•Non-rotating
broad
component
•Fast rotating
narrow
component
Embedded disks
•Recall “disky” isophotes have larger Vrot than “boxy” isophotes
(though photometric modeling is difficult for detecting disks in E’s)
•Vlos profiles provide the best evidence for embedded disk
components (Rix & White 1990; van der Marel et al. 1994)
•Disky E’s have (v/σ)* ~ 1  they are rotationally flattened
•If E’s harbor disks, the relative size of this component dictates
kinematics along major axis
Dynamical models help to explain non-rotationally flattened systems.
Slow rotation in luminous E’s implies that such objects are flattened
by velocity anisotropy rather than rotation. Schwarzchild (1982)
showed that:
•This argues for triaxial objects – many giant E’s have not relaxed
enough to develop an axis of symmetry
•equilibrium triaxial systems could exist with slow rotation about the
minor axis
•Further indication of only partial mixing of stellar orbits – KDC’s
Kinematically Distinct Cores in E’s
•2 kinematic components identified in 25 – 30% of E’s
•In most cases, core rotates differently than outer galaxy
• Rapid rotation in
center, slower
further out
• Rotation direction
different
• Central component
often rotates
around minor axis
(Bender et al 1988)
Formation may be due to
merger (e.g. NGC 5813)
•Core (r < 7”) had distinct
SB, Vrot, σ
•Core is remnant of
dense, low-L E which
may have been captured
by a larger E
•(recall low-L E’s have
brighter Ie, higher Vrot,
lower σ)
Others may be explained by accretion of gas-rich galaxy
which settled to center and formed a disk (many KDCs
appear to have disk-like profiles.
Torques on gas disk by main galaxy cause gas to spin
either parallel or anti-parallel. Star formation eventually
turns gas into stars.
(Efstathiou, Ellis & Carter 1992)