ap/galaxies/pc2491webpart4x6.pdf · part 4 :--elliptical galaxies lecture 18 properties of...
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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
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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
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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
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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
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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
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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
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cD galaxies
• Luminosities typically 10x L* (L*=2x1010 Lo)
• Halo extended 50-100kpc
• Origin – mergers of galaxies in cluster core