Download The “Tuning Fork” Diagram Galaxy Properties 1 “Early”

The “Tuning Fork” Diagram
“Early”
“Late”
Galaxy Properties
From M. Longair “Galaxy Formation”
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Trends in spiral galaxies
(see CO Tables 25.1/25.2)
CO Fig 25.12
…
{,∆
z
„
dE
E
S
Irr
• Mass/Light ratios
E, dE
• Sa Î Sc : M/LB = 6.2 Î2.6
but Longair’s plot Î constant
• Sc’s dominated by younger, hotter, more
massive stars.
• Colors
Red
Blue
• Sa Î Sc : B-V = 0.75 Î0.52
• Bluer colors Î Sc’s dominated by younger,
hotter stars.
• Mgas/Mtotal
S, Irr
Low L
High L
• Sa Î Sd: Mgas/Mtotal = 0.04 Î 0.25
• Molecular/atomic hydrogen
• Sa Î Sd: MH2/MHI = 2.2 Î 0.3
• Metallicity
• Depends on absolute magnitude
• No. of Globular Clusters/Total Luminosity
CO Fig 25.16
H I Spectra of Spiral Galaxies
Vmax
Vsys
2
Tully-Fisher Relation
Rotation Curves
• Maximum rotation velocity-Luminosity
relation [FIG 25.10]
• Tully-Fisher relation
• MB = -9.95 log10VMax + 3.15
• MB = -10.2 log10VMax + 2.71
• MB = -11.0 log10VMax + 3.31
Semi-derivation of
Tully-Fisher Relation:
MB = -9.95 log10Vmax + 3.15
MB = -10.2 log10Vmax + 2.71
MB = -11.0 log10Vmax + 3.31
(Sa)
(Sb)
(Sc)
(Sa)
(Sb)
(Sc)
• Mass interior to outermost R where rotation curve can be measured:
Mass =
• Assume
2
Vmax
R
G
L = Mass / const.
• “Freeman Law” (observed fact ---maybe):
L
= const.
Surf .Bright. =
4πR 2
4
L = const × Vmax
Important as a
DISTANCE
calibrator!
• Convert to Absolute B-band magnitudes:
 L 
 = −10 log10 Vmax + const.
M B = M sun − 2.5 log10 
 Lsun 
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Dwarf
spheroidal
(Leo I)
Ellipticals
Huge mass range:
•
•
•
•
•
Dwarf spheroidals: 107-108 M
Blue compact dwarfs: ~109 M
Dwarf ellipticals: 107-109 M
Normal (giant) ellipticals: 108-1013 M
cD galaxies in cluster centers: 1013-1014 M
Dwarf ellipticals M32, NGC 205
Giant E
(NGC 1407)
cD (NGC 3311)
Ellipticals
cD
Be
s
t
r1/4
•
R1/4 law usually fits radial surface brightness distribution
od
Go
Be
tte
r
•
•
I ( R ) = I e10
Also Hubble’s law
I ( R) =
Io

R
1 + 
Ro 

2
Modified Hubble’s law
I ( R) =
•
+ others
HST
images
  R 1 / 4 
 −1
−3.33  
  Re 



Diverges, but at least is projection
of simple 3D distribution:
Io
1 +  R 
 Ro 
2
I ( R) =
Io
  R 2 
1 +  Ro  
 
 
3/ 2
4
The Virial Theorem [CO 2.4]
• For gravitationally bound systems in equilibrium
• Total energy = ½ time-averaged potential energy.
E = total energy
U = potential energy.
K = kinetic energy.
E=K+U
• Can show from Newton’s 3 laws + law of gravity:
where I = Σmiri2 = moment of inertia.
• ½ (d2I/dt2 ) -2K = U
• Time average < d2I/dt2 > = 0, or at least ~ 0.
• Virial theorem Î -2<K> = <U>
<K> = - ½ <U>
<E> = <K> + <U> Î
<E> = ½ <U>
2K = -U
<v2> = 3 <vr2>
Î σ2r = GM/(5R)
U =−
3 GM 2
5 R
• See pp. 959-962, + Sect. 2.4
• Applied to nuclei of spirals Î
presence of massive black holes
• Also often applied to
Rot. Velocity
• Virial Theorem
Vel. Disp
Mass determinations from
absorption line widths
• E galaxies
• Galaxy clusters
Nuclear bulge of M31
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Mass determinations from
absorption line widths
Observed Spectrum
• Virial Theorem
U =−
• 2K = -U
• <v2> = 3 <vr2>
• Î σ2r = GM/(5R)
K star
3 GM 2
5 R
E galaxy = K star
convolved with
Gaussian velocity
distribution of
stars.
• See pp. 959-962, + Sect. 2.4
• Applied to nuclei of spirals Î
presence of massive black holes
Fourier Transforms
Star
• Also often applied to
Galaxy
• E galaxies
• Galaxy clusters
Ratio
Gaussian fit:
• Convolution turns into multiplication in F.T. space.
• F.T. of a Gaussian is a Gaussian.
Faber-Jackson relation: Le ~ σ04
(Absolute magnitude)
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Homework Assignment 5
Due Monday Oct. 1
• CO 2nd edition problems 25.13, 25.14, 25.16
• Same as 1st edition problems 23.11, 23.12, 23.14
• There may be one addition derivation-type problem having
to do with the stellar velocities found in E galaxies. It
depends on whether I cover that in class with enough lead
time.
Do CO problem 25.20 ( = problem 23.18 in 1st edition)
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