Properties of Ellipticals
• Classification
– E0-E5 3-D shapes
Part 4 :--Elliptical Galaxies
• Surface brightness profiles
• Observations
– Dynamics
• Luminosity-Dispersion Relation
Lecture 18
– Fundamental plane
• King Curves
• Mass of ellipticals
– Central black holes
• X-ray emission
Ellipticals
Basic observed properties
• No disk, or spiral structure
• No evidence for young stars
Starformation history cartoon
• Ellipticals had large Star formation rate
(SFR) in early universe
– no HII regions
• Red colours – dominated by red giants
– >5Gyrs old
• The ISM is hot (106-7K gas)
– observable in X-rays
– (no neutral hydrogen at ~100K)
• High average metal abundance
Classification
• Ellipticals E0E7
Ellipticals
• The E0-E7 classification is not intrinsic
– eg an E7 viewed face-on may appear as E0
– E0
• En where
n = 10
•
E3
E6
(a − b )
a
NB not intrinsic E6 E0 end on
• 3D structure (cf disks ~2D)
1
Axial ratios
3-D shapes
• Statistically apparent axial ratio (En) can be converted to
true axial ratio
• Isophotes are ~elliptical
• 3-D shapes can be
– Oblate a=b>c eg diskus
3D
– Prolate a=b <c eg cigar
~2D
– Triaxial a ≠b ≠c
Surface Brightness Profile
Surface Brightness Profile
• Surface brightness I(r)∝ r1/4
• Measured in annuli

  r 1/ 4  
I (r ) = I e exp − 7.67   − 1 

  Re 




• Re = radius which contains ½ light
• Ie = surface brightness at Re
• Surface brightness in Lo pc-2
• Centrally peaked cf Disk gal
• Follows r1/4 Law
spiral
I(r)∝ r1/4
Surface Brightness Profile
• R1/4 Law compared with disk exponential law

 r 
I (r ) = I e exp − 7.67  

  Re 


1/ 4

− 1 


I (r ) = I o e
r
−
ro
Surface Brightness Profile
• Integrating r1/4 law (non trivial)
∞
L = ∫ I (r )2πrdr ≈ 7.22πRe2 I e
0
– R1/4 Law
• = deVaucouleurs Law
– Compare with exponential (easy)
r
−


∞
ro
L
=
I
e
2πrdr = 2πI o ro2 
 tot ∫0 o


2
Measuring Elliptical galaxy
dynamics
Surface Brightness Profile
• Often plot log (I) vs log r
• Not easy!
– No Neutral Hydrogen
– No O & B stars
• No HII regions No Hα etc
– Ellipticals are 3D – not 2D
• Need to observe stellar absorption spectra
–
–
–
–
Elliptical galaxy dynamics
Stars old, low mass low luminosity
Lines weak Ca, Mg, Na etc
Lines often blended together
Lines sampling 3-D field
Edge-on spiral
Line profiles along line of sight blended
• Ellipticals are 3-D objects
• Spectra will be blended along lines of sight
– More complex than disk galaxies which are usually
2-D
– Eg spirals ‘edge-on’
Cannot use Vr = Vcirc (r )sin i cos θ
for Ellipticals
Elliptical galaxy dynamics
• Typical Spectrum
Absorption spectra
• Average Spectrum of many stars
• We can measure
– rotation (v): the net rotational velocity of a
group of stars
– dispersion (σ
σ): the characteristic random
velocity of stars
• Linewidth ∆λ is measure of stellar dispersion σ
3
Elliptical galaxy dynamics
• Eg NGC4365 (Virgo Cluster)
Elliptical galaxy dynamics
• Massive ellipticals show
– Low rotation velocities ~ 50100 km/s
– High dispersion velocities ~2-300 km/s
• Flattened Ellipticals may NOT be
supported by rotation
Elliptical galaxy dynamics
•
Velocity/ dispersion
– Ellipticals
• v/σ typically 01
Elliptical galaxy dynamics
• Low luminosity oblate ellipticals may be
supported by rotation
– Milky way disk
• V=220km/s σ=~30 km/s
• v/σ
σ ∼7
•
To be supported by rotation
– It can be shown
1
V
σ
•
 ε 2
≈

1− ε 
b

ε = 1 − 
a

• Similar to disks
More luminous ellipticals show V/σ < predicted
–
ie less rotation
Elliptical galaxy dynamics
• Lower luminosity ellipticals have higher v/σ
– ∴may be rotationally supported.
• Higher luminosity ellipticals have lower v/σ
– ∴dispersion supported NOT rotation
– 3-D shape maintained by anisotropic
stellar dispersion velocity σ1 σ2 σ3
• Implies Triaxial shape
Luminosity-Dispersion Relation
• An empirical relation between
– Luminosity L and the Stellar dispersion σ of
elliptical galaxies
4
Luminosity-Dispersion Relation
• Luminosity is proportional to (Dispersion)4
L ∝ σ4
Why large scatter in L-σ relation?
• Note that in Tully-Fisher relation if we did not
correct for galaxy inclination– this would
introduce large scatter
• known as the Faber-Jackson relation
– Analogous to Tully-Fisher relation for spirals
– But dispersion is not rotational velocity
– & there is scatter of +/- 2 magnitudes
• ( compared with +/- 0.2 for Tully-Fisher)
• ie ∆v depends on i
• As well as L, ∆v
– i is another parameter
– +would introduce scatter
Luminosity-Dispersion Relation
• Much of the scatter in the L-σ relation is intrinsic
– Not due to measurement errors
• The dispersion σ is also a function of
– Re -the half-light radius of the elliptical galaxy
– & Σ e average surface brightness within Re
Part 4 :--Elliptical Galaxies
• (note Ie = surface brightness at Re)
Lecture 19

  r 1/ 4  
I (r ) = I e exp − 7.67   − 1 

  Re 




Properties of Ellipticals
• Classification
– E0-E5 3-D shapes
• Surface brightness profiles
• Observations
Luminosity-Dispersion Relation
• plot σ vs other parameters
– eg dispersion (σ) vs half light radius (Re)
– Dynamics
• Luminosity-Dispersion Relation – Fundamental plane
• King Curves
• Mass of ellipticals
– Virial Theorem
• Central black holes
• Active galactic nuclei
• X-ray emission
5
‘Fundamental plane’
• The 3 parameters Re, Σe and σο are related by
Re ∝ σ Σ
1 .4
o
Fundamental plane
• Hence plotting Re vs σ1.4 Σ-0.9
– we get small scatter
−0.85
e
• ie a 3-D surface ‘The Fundamental Plane’
• Re is the half light radius
• Σe is the mean surface brightness within Re
–
∑e =
•
•
L/2
πRe2
σo is the central velocity dispersion
Fundamental plane
– ∴Can be used for distance estimates like
Tully-Fisher
Fundamental plane
• Origin of relationship
• 3-D Plot of
– Luminosity(L)
– dispersion (σ)
– half light radius (Re)
• Galaxies lie on a
‘Fundamental Plane’
– Average surface brightness
Σe =
L/2
πRe2
– Potential energy ~ kinetic energy
GM
= kσ 02
Re
– k is the ‘structure parameter’ containing information
on the elliptical galaxy
Fundamental plane
• Hence
−1
Re =
k  M  2 −1
  σ o Σe
2πG  L 
• Compared with
• Implies
Surface Density Profiles
• Elliptical galaxies & globular clusters have
similar surface density profiles
– M15 (GC) ~106 Mo
M89 (E0) ~1011 Mo
Re ∝ σ o1.4 Σ e−0.85
M 
k −1   ∝ L0.25 (see examples 2)
 L
6
King Curves
King Curves
(King 1966 -Astron J. 71 64)
• Initially devised for globular clusters
– Star
density=~103 pc-3
8
3
velocity =10 km /s
(
10 v km s
n( pc −3 )
Relaxation Time tc ≈
−1
)
– Isothermal distribution
f (E ) ∝ e − βE
• King’s Models assume ‘core’ radius rc
years
• (<< galactic ~1013 years)
• Relaxation times< age of clusters
– Stars interact
• ∴assume the energies of stars in Globular Clusters
follow Maxwell- Boltzmann function
f (E ) ∝ e − βE
King Curves
King defined concentration parameter
& produced family of curves
– where density is half central density ρo
ρ (rc ) =
– Relaxation times ~ 108 – 109 years
•
•
• Similar to gas at temperature T
r 
 tidal radius 
c = log t  = log

 core radius 
 rc 
– eg Surface brightness Σ vs radius
King Curves
• Implies that stars in elliptical galaxies also
follow Maxwell-Boltzmann distribution.
• BUT
– Relaxation times in ellipticals are ~1013 years!
– Longer than Hubble time
– Hence the Maxwell-Boltzmann distribution is
imprinted at birth.
ρo
2

3σ 
⇒ rc =

4πGρ o 

– And a ‘tidal radius’ rt at which ρ0
– Globular clusters tidally disrupted for r>rt due to effect of
Milky Way
King Curves
• Hence plotting Log Surface brightness vs log radius
– If c=0.751.5 Globular clusters
– If c=2.2 Elliptical galaxies
– (if c=0.5 Dwarf Ellipticals)
Mass from Virial Theorem
• For the Virial theorem to be valid
• (i) the stellar motions must be invariant with
time and
• (ii) stellar interactions are neglible
• Then it can be shown that
2T + Ω = 0
• T= kinetic energy of system
• Ω= gravitational potential energy of system
7
Mass from Virial Theorem
• Kinetic energy of stars mass mi , velocity vi
T=
1
2
∑m v
i
2
i
i
= 12 M v
2
• M is total mass & <v2> is mean value of vi2
Mass from Virial Theorem
• Potential energy
Ω = −∑∑
i
j ≠i
Gmi m j
rij
= −α
GM 2
Re
– Where α is factor of order unity
• Hence combining equations using virial equation
• Potential energy of i stars separated by rij
Ω = −∑∑
i
j ≠i
Gmi m j
rij
Mass from Virial Theorem
M≈
– Re ~ 10 kpc
G
α ≈1
Application to Galaxy clusters
– <v2>1/2 ~ 200 km/s
Re v 2
αG
• Same principle applies
• Example
M≈
Re v 2
=
(α~1)
10000 × 3 × 1016 × 2000002
= 1.7 × 1041 kg
6.67 ×10 −11
• M ~ 9X1011 Mo
M≈
R v2
G
• For the Virial theorem to be valid
– (i) the galaxy motions must be invariant with time
– (ii) galaxy-galaxy interactions can be neglected
Central Black Holes
• Many ellipticals & bulges of spirals (spheroids)- host
‘super’ massive Black Holes (SMBH > 106Mo)
• The Black Hole mass appears to be correlated with
spheroid luminosity (not total luminosity)
Central Black Holes
• Even better correlation between Black Hole
mass and spheroid velocity dispersion
8
Central Black Holes
Central Black Holes
• Accretion of gas onto Central black holes
• Note ‘size’ of Black Hole (Schwartzschild radius)
rsch
 M 
2GM
= 2 ≈ 10−5  8
 pc
c
 10 M o 
•
Whereas Bulge/ elliptical is kpc100s of kpc
•
Not Fully Understood
• Implying velocities 103 104 km/s
• & High UV + X-Ray flux
Central Black Holes
• Collimated outflows radio jets
– Shocks in outflows relativistic electrons
– Synchrotron emission
Radio jets & lobes
• Fornax A
– Active Galactic Nucleus (AGN)
– Bright,variable star-like nucleus
– Broad High excitation emission lines
Centaurus A
Central Black Holes
• Radio jets & lobes
• M87
3C296
X-Ray emission
• NGC 6482
9
X-Ray emission
• Massive elliptical galaxies often
surrounded by X-Ray emitting halo
X-ray emission
• Continuum emission is via free-free mechanism
– Temperature T~ 107K
– Electron density ne ~ 10-1 10-4 cm-3
– Mass Mgas~ 108 1010 Mo
– X-ray Luminosity ~ 1033 1035 Watts
• Also highly ionised metals (eg Fe, Mg) emit lines
– FeXXVII, FeXIV, OVIII
M87
X-Ray emission
• X-ray emitting haloes common around Elliptical galaxies
• Virgo A
Cooling times
• Cooling time of ionised gas
−1
e
tcool ∝ n T
1
2
cD galaxies
• Giant ellipticals at centres of clusters
• Large stellar halo
– ie hotter gas takes longer to cool
• Gas with ne ~ 0.1 cm-3 and T ~107K
• Cooling time is ~109 years
10
cD galaxies
• Luminosities typically 10x L* (L*=2x1010 Lo)
• Halo extended 50-100kpc
• Origin – mergers of galaxies in cluster
core
11