1

Part 4 :--Elliptical Galaxies

Lecture 18

Properties of Ellipticals

• Classification– E0-E5 3-D shapes

• Surface brightness profiles • Observations

– Dynamics • Luminosity-Dispersion Relation

– Fundamental plane• King Curves• Mass of ellipticals

– Central black holes• X-ray emission

EllipticalsBasic observed properties

• No disk, or spiral structure• No evidence for young stars

– 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

Starformation history cartoon• Ellipticals had large Star formation rate

(SFR) in early universe

Classification

• Ellipticals E0E7

• En where

• NB not intrinsic E6 E0 end on

( )a

ban

−=10

Ellipticals

• The E0-E7 classification is not intrinsic– eg an E7 viewed face-on may appear as E0

– E0 E3 E6

• 3D structure (cf disks ~2D)

2

Axial ratios

• Statistically apparent axial ratio (En) can be converted to true axial ratio

3D

~2D

3-D shapes • Isophotes are ~elliptical• 3-D shapes can be

– Oblate a=b>c eg diskus

– Prolate a=b <c eg cigar

– Triaxial a ≠b ≠c

Surface Brightness Profile

• Measured in annuli

• Surface brightness in Lo pc-2

• Centrally peaked cf Disk gal• Follows r1/4 Law

I(r)∝ r1/4

spiral

Surface Brightness Profile

• Surface brightness I(r)∝ r1/4

• Re = radius which contains ½ light• Ie = surface brightness at Re

( )

−

−= 167.7exp

4/1

ee R

rIrI

Surface Brightness Profile

• R1/4 Law compared with disk exponential law

– R1/4 Law • = deVaucouleurs Law

( ) or

r

oeIrI−

=( )

−

−= 167.7exp

4/1

ee R

rIrI

Surface Brightness Profile

• Integrating r1/4 law (non trivial)

– Compare with exponential (easy)

( ) ee IRrdrrIL ∫∞

≈=0

222.72 ππ

== ∫∞ −

2

022 oo

r

r

otot rIrdreIL o ππ

3

Surface Brightness Profile

• Often plot log (I) vs log r

Measuring Elliptical galaxy dynamics

• 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– Stars old, low mass low luminosity– Lines weak Ca, Mg, Na etc– Lines often blended together– Lines sampling 3-D field

Elliptical galaxy dynamics

• 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’

( )sEllipticalfor

cossinuseCannot θirVV circr =

Edge-on spiralLine profiles along line of sight blended

Elliptical galaxy dynamics

• Typical Spectrum

• We can measure– rotation (v): the net rotational velocity of a

group of stars – dispersion (σσσσ): the characteristic random

velocity of stars

Absorption spectra

• Average Spectrum of many stars

• Linewidth ∆λ is measure of stellar dispersion σ

4

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

– Milky way disk• V=220km/s σ=~30 km/s

• v/σσσσ ∼ 7∼ 7∼ 7∼ 7

• To be supported by rotation – It can be shown

• More luminous ellipticals show V/σ < predicted– ie less rotation

−=

−≈

a

bV1

1

21

εε

εσ

Elliptical galaxy dynamics

• Low luminosity oblate ellipticals may be supported by rotation

• Similar to disks

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

5

Luminosity-Dispersion Relation

• Luminosity is proportional to (Dispersion)4

• 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)

4σ∝L

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

• 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

– & Σe average surface brightness within Re

• (note Ie = surface brightness at Re)

( )

−

−= 167.7exp

4/1

ee R

rIrI

Part 4 :--Elliptical Galaxies

Lecture 19

Properties of Ellipticals

• Classification– E0-E5 3-D shapes

• Surface brightness profiles • Observations

– Dynamics • Luminosity-Dispersion Relation

– Fundamental plane• King Curves• Mass of ellipticals

– Virial Theorem• Central black holes

• Active galactic nuclei

• X-ray emission

Luminosity-Dispersion Relation

• plot σ vs other parameters – eg dispersion (σ) vs half light radius (Re)

6

‘Fundamental plane’

• The 3 parameters Re, Σe and σο are related by

• ie a 3-D surface ‘The Fundamental Plane’• Re is the half light radius• Σe is the mean surface brightness within Re

–

•• σo is the central velocity dispersion

85.04.1 −Σ∝ eoeR σ

2

2/

ee R

L

π=∑

Fundamental plane• Hence plotting Re vs σ1.4 Σ-0.9

– we get small scatter

– ∴Can be used for distance estimates like Tully-Fisher

Fundamental plane

• 3-D Plot of– Luminosity(L)

– dispersion (σ) – half light radius (Re)

• Galaxies lie on a ‘Fundamental Plane’

Fundamental plane

• Origin of relationship– Average surface brightness

– Potential energy ~ kinetic energy

– k is the ‘structure parameter’ containing information on the elliptical galaxy

2

2/

ee R

L

π=Σ

20σk

R

GM

e

=

Fundamental plane

• Hence

• Compared with

• Implies (see examples 2)

121

2−

−

Σ

= eoe L

M

G

kR σ

π85.04.1 −Σ∝ eoeR σ

25.01 LL

Mk ∝

−

Surface Density Profiles

• Elliptical galaxies & globular clusters have similar surface density profiles– M15 (GC) ~106 Mo M89 (E0) ~1011 Mo

7

King Curves (King 1966 -Astron J. 7164)

• Initially devised for globular clusters– Star density=~103 pc-3 velocity =10 km /s

– Relaxation times ~ 108 – 109 years• (<< galactic ~1013 years)

• Relaxation times< age of clusters– Stars interact

• ∴assume the energies of stars in Globular Clusters follow Maxwell- Boltzmann function

( ) EeEf β−∝

( )years

)(

v10Time Relaxation

3

138

−

−

≈pcn

skmtc

King Curves

• Similar to gas at temperature T– Isothermal distribution

• King’s Models assume ‘core’ radius rc

– where density is half central density ρo

– And a ‘tidal radius’ rt at which ρ0

– Globular clusters tidally disrupted for r>rt due to effect of Milky Way

=⇒

o

cG

rρπ

σ4

3( )2

ocr

ρρ =

( ) EeEf β−∝

King Curves• King defined concentration parameter

• & produced family of curves – eg Surface brightness Σ vs radius

=

=

radius core

radius tidalloglog

c

t

r

rc

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)

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.

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

• T= kinetic energy of system• Ω= gravitational potential energy of system

02 =Ω+T

8

Mass from Virial Theorem

• Kinetic energy of stars mass mi, velocity vi

• M is total mass & <v2> is mean value of vi2

• Potential energy of i stars separated by rij

∑=i

imT 2i2

1 v 221 vM=

∑∑≠

−=Ωi ij ij

ji

r

mGm

Mass from Virial Theorem

• Potential energy

– Where α is factor of order unity

• Hence combining equations using virial equation

ei ij ij

ji

R

GM

r

mGm 2

α−=−=Ω ∑∑≠

1v2

≈≈ ααG

RM

e

Mass from Virial Theorem

• Example

– <v2>1/2 ~ 200 km/s

– Re ~ 10 kpc (α~1)

• M ~ 9X1011 Mo

kgG

RM

e 4111

2162

107.11067.6

20000010310000v×=

××××=≈ −

Application to Galaxy clusters

• Same principle applies

• For the Virial theorem to be valid – (i) the galaxy motions must be invariant with time – (ii) galaxy-galaxy interactions can be neglected

G

RM

2v≈

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

9

Central Black Holes

• Note ‘size’ of Black Hole (Schwartzschild radius)

• Whereas Bulge/ elliptical is kpc100s of kpc

• Not Fully Understood

pcM

M

c

GMr

osch

≈= −

85

2 1010

2

Central Black Holes• Accretion of gas onto Central black holes

– Active Galactic Nucleus (AGN)– Bright,variable star-like nucleus– Broad High excitation emission lines

• 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

Central Black Holes

• Radio jets & lobes • M87 3C296

Radio jets & lobes

• Fornax A Centaurus A

X-Ray emission

• NGC 6482

10

X-Ray emission

• Massive elliptical galaxies often surrounded by X-Ray emitting halo– Temperature T~ 107K– Electron density ne ~ 10-1 10-4 cm-3

– Mass Mgas~ 108 1010 Mo

– X-ray Luminosity ~ 1033 1035 Watts

X-ray emission

• Continuum emission is via free-free mechanism

• Also highly ionised metals (eg Fe, Mg) emit lines– FeXXVII, FeXIV, OVIII

M87

• Virgo A

X-Ray emission• X-ray emitting haloes common around Elliptical galaxies

Cooling times

• Cooling time of ionised gas

– ie hotter gas takes longer to cool

• Gas with ne ~ 0.1 cm-3 and T ~107K• Cooling time is ~109 years

211Tnt ecool

−∝

cD galaxies

• Giant ellipticals at centres of clusters• Large stellar halo

11

cD galaxies

• Luminosities typically 10x L* (L*=2x1010 Lo)

• Halo extended 50-100kpc

• Origin – mergers of galaxies in cluster core