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Galaxies
• Introduction
• Elliptical galaxies
• Spiral galaxies
• Scaling relations
• Central black holes
• Luminosity functions
• Spectra
Introduction
Classification: the Hubble sequence
spirals
ellipticals
lenticulars
barred spirals
Introduction - 2
• The Hubble classification is morphological and influenced by
projection effects (2D view, not 3D)
• Elliptical galaxies belong to classes En (n = 0,…,7)
b

where n  101  
 a
b
a
• Ellipticity is not necessarily an intrinsic property of the galaxy (a
cigar or a disk could be classified E0, depending on the viewing angle)
Introduction - 3
• Spiral galaxies are classified Sa, Sb, Sc, Sd depending on the
importance of the bulge with respect to the disk and the characteristics
of the arms
• Intermediate classes
(Sab, Sbc, Scd) are
also introduced
• Barred spirals have
a similar classification:
SBa, SBab, SBb,…
• Galaxies not fitting
in that scheme are
classified irregulars
Introduction - 4
Mass / luminosity ratio (ϒ or Y)
Y M L
• Generally given in solar units → Y = 1 for the Sun
• Depends on the spectral band (ex: YV = M/LV)
• Extrapolated to bolometric luminosity using spectral models
• Applies to stars, star clusters, galaxies, galaxy clusters
• Ex:
massive stars: Y < 1
gas-rich spiral galaxies: Y ~ 1 – 10
elliptical galaxies: Y ~ 10 – 100
galaxy clusters: Y ~ 300
Why Y > 1 in
most galaxies ?
Introduction - 5
• Most massive stars (→ most luminous) evolve faster (M ≈ ct but L
decreases)
→ Y increases when galaxy ages
(and mostly when star formation slows down)
• Hot stars ionize gas around them (HII regions, high L for very low M)
→ reinforce the variation of Y with age
• Stellar remnants have a very high Y
• and dark matter an infinite Y…
Introduction - 6
Color
• The color of an object is measured by a color index
(ex: B–R = mB – mR)
• After correction for dust reddining (if necessary), it is an intrinsic
property of the object
B
• An object with a large
color index is called red,
an object with a low (or
negative) color index,
blue
red object
blue objects
R
Introduction - 7
Metallicity
• Content in elements from carbon and heavier
• Iron is often considered representative
Fe/H  log N Fe
N H *  log N Fe N H O
• Applies to stars, interstellar matter, galaxies
• Depends on the chemical history of matter (previous stellar
generations) → generally not homogeneous in a galaxy
• Higher metallicity → redder object (since more absorption lines in
the blue)
Introduction - 8
Magnitudes
• For a point-like object:
m  2.5 log F  c t
• For an extended object:
t
– either one measures the integrated magnitude m  2.5 log Ftot  c
– either one measure the magnitude per unit of solid angle
  2.5 log I surf  ct
where Isurf is the flux received per unit solid angle
(μ in mag/arcsec2)
Introduction - 9
Virial theorem
• For an isolated system in dynamical equilibrium:
2 EK + EP = 0
(in absolute value, kinetic energy = ½ potential energy)
• Estimate of the mass of a cluster (of galaxies):
R = mean distance between 2 galaxies → EP ~ −GM2/2R (*)
V = mean velocity of galaxies → EK ~ ½ MV2
(* /2 in order not to count twice the energy associated to a pair of galaxies)
2 RV 2
M ~
G
Elliptical galaxies
(early-type galaxies)
Sub-types
– gE (giant elliptical)
– E (elliptical)
ESO 325−G004
(gE)
– cE (compact elliptical)
– dE (dwarf elliptical)
(surface brightness of dE
lower than cE)
M 32 (cE)
NGC 205 (dE)
Elliptical galaxies - 2
– cD galaxies: supergiant ellipticals (c) with extended halo
→ appear diffuse (D)
located at the center of some
rich clusters
Image: NGC 3311 (cD)
and NGC 3309 (gE) at the
center of Hydra I cluster
Note the presence of
thousands of globular
clusters around these
galaxies
Elliptical galaxies - 3
– S0 galaxies: lenticulars (intermediate between spirals and ellipticals)
≈ spirals without spiral arms
Image: NGC 2784
Elliptical galaxies - 4
– dSph galaxies: dwarf spheroidals, very low surface brightness
→ observable only in the local group
(maybe the most
frequent galaxies,
but very hard to
observe)
Image: NGC 147
Elliptical galaxies - 5
Luminosity profile
• The surface brightness decreases from the center to the outskirts
according to a simple empirical law (de Vaucouleurs law):


I surf R   I e exp  7.669 R Re 
or:
 R 1/ 4 
  e  8.33   1
 Re 

Re = effective radius (contains half
the emitted light)
Ie = surface brightness at the
effective radius
1/ 4

1
(r1/4 law)
Elliptical galaxies - 6
• For cD galaxies, there is an excess brightness at large radii compared
to the r1/4 profile
→ cD ≈ gE + extended luminous halo
• The extended halos of the cD
galaxies could be the remains
of many small galaxies
`swallowed´ by the giant
elliptical
• The de Vaucouleurs law can
be generalized to elliptical
isophotes
R  ab
e
e e
where ae and be are the major
and minor semi axes
Elliptical galaxies - 7
Composition
• old stars, little gas
→ no more star formation
• sometimes dust bands (remains
from absorbed spirals?)
Centaurus A
NGC 7049
Elliptical galaxies - 8
Ellipticity
• Why have ellptical galaxies kept their shape and did not all become
spherical?
• Rotation as in spirals?
• Rotation flattening significant if vrot ~ σv
where  v2  vi2  v
2
However, vrot << σv
+ triaxial galaxies
→ rotation can not explain the
observed ellipticity
→ shape is a testimony of history
The center of the Virgo cluster
Elliptical galaxies - 9
Stability of the ellipsoidal shape
• Collisions between stars tend to increase the symmetry of the system
• The time needed for this `relaxation´ can be estimated by:
trelax  tcross N ln N
trelax = characteristic time for direction change due to collisions
tcross = crossing time of the system
N = number of stars in the system
• With tcross ~ 108 years and N ~ 1012
→ trelax ~ 1018 years >> age of the Universe
→ ellipsoid is stable
Elliptical galaxies - 10
Departures from ellipsoidal shape
• Generally: isophotes ≈ concentric ellipses
• But:
− ellipticity ε not always constant with radius
− major axis orientation may vary: isophote twisting
• Twisting can be a
projection effect if ε varies
(apparent direction of major axis
seems to vary more if ε → 0)
Elliptical galaxies - 11
Shells and waves
• Complex structures sometimes visible at low surface brightness
• Signs of complex
evolution, probably
linked to merging of
galaxies
Image: NGC 474
Spiral galaxies
(late-type galaxies)
Sub-types
– spirals: Sa, Sb, Sc, Sd (+ intermediates Sab, Sbc, Scd)
– barred spirals: SBa, SBb… (+ intermediates SBab, SBbc…)
M74
NGC1365
Spiral galaxies - 2
• Sub-classes a, b, c correspond to differences in:
Sa
Sb
Sc
large (~0.3)
medium (~0.13)
small (~0.05)
winded up (~6°)
(~12°)
open (~18°)
smooth
intermediate
granular
color (B−V)
red (~0.75)
(~0.64)
blue (~0.52)
gas fraction (Mgaz/Mtot)
low (~0.04)
average (~0.08)
high (~0.16)
importance of bulge (Lbulbe/Ltot)
opening of arms (θ)
structure of arms
bulge
θ
arm
• Barred spirals (± as numerous as spirals) have a similar classification
Spiral galaxies - 3
Sa
M 104 « Sombrero »
Spiral galaxies - 4
Sab
Sb
M 81
M 63
Spiral galaxies - 5
Sbc
Sc / Sd
NGC 3184
NGC 300
Spiral galaxies - 6
SBb
SBb
M91
M 95
Spiral galaxies - 7
SBbc
SBc
NGC 1300
M 109
Spiral galaxies - 8
`intermediate´ (embryo of a bar)
M 83
Spiral galaxies - 9
Luminosity profile
• The (mean) surface brightness of the disk decreases with distance
from the center according to an exponential law:
I surf R   I 0 exp R / Rd 
or:
  0  1.086R Rd 
• μ0 not directly measurable (center inside the bulge)
→ extrapolation
• μ0 nearly constant in `normal´ galaxies:
0  21.5  0.4 Bmag / arc sec 2 Sa  Sc 
(Freeman law)
• The surface brightness of the bulge follows the same law as
elliptical galaxies
Spiral galaxies - 10
Rotation curves
• If the galaxy is not seen face-on:
vR   vrad R  sin i
where i = inclination (angle between the galactic plane and the plane of
the sky)
- vrad measured by spectroscopy (Doppler effect)
- i determined by assuming that the disk is
circular
(apart from spiral arms…)
Spiral galaxies - 11
• The rotation velocity in the outer parts is too high for the estimated
mass (stars + interstellar matter)
→ one postulates the existence
of a dark matter halo
Spiral galaxies - 12
• Modelling: one assumes circular orbits in the disk (+ spherical halo)
m v 2 G m M ( R)


R
R2
v2 R
 M ( R) 
G
where M(R) = mass included inside the radius R
One estimates the amount of `normal´ (luminous) matter Mlum from
L(R) and an estimated M/L ratio
GM lum
vlum ( R) 
→ gives a predicted rotation curve
R
→ the amount of dark matter Mdark is what we need to add to explain
the rotation curve:
R 2
2
M dark ( R)  v ( R)  vlum
( R)
G
Spiral galaxies - 13
• The different components are modelled separately (disk, bulge, halo,
central black hole)
R
z
r
GM
  F ( R)
The gravitational potential F(R) is defined by v( R) 
R
Fdisk ( R)  
r
r 2GM disk
2
 (a  z )

2 3/ 2
(Kuzmin potential)
4πG 0R03  R
R

Fdark ( R)  
 arctan  (isotherma l sphere)

R
R0 
 R0
Parameters Mdisk, a, ρ0, R0… are adjusted to fit the observations
Spiral galaxies - 14
Composition
1. Stars:
Later type → more young stars
→ more massive stars
→ bluer color
M 81
(In agreement with the
reduced importance of
the bulge, redder and
containing older stars)
NGC 300
Spiral galaxies - 15
2. Gas:
Later type → larger proportion of gas (necessary for star formation)
3. Dust:
Mass of dust ~1% mass of gas
If dust heated by hot stars → emission in far IR (FIR) → mainly in
late-type spirals
M104 in false colors:
blue = visible (HST)
red = FIR (Spitzer)
Spiral galaxies - 16
Structure
1. Spiral arms:
Higher contrast in blue but arms also seen in red
→ imply all components of disk but excess of young stars
Density waves (amplitude ~10 – 20%) that propagate at a speed
different from that of matter
Perturbation amplified by dynamic evolution
Various theories to explain their appearance: chaotic phenomenon,
tidal effect from a companion, triggering of star formation by
differential rotation…
Spiral galaxies - 17
2. Bar:
Stable over several
rotation periods
Triggered by instability in
the disk
NGC 6050 and IC 1179
Scaling relations
Scaling relation =
• relation between several characteristic properties of a class of objects
• determined empirically in the nearby Universe
• that can be applied to remote objects for which the determination of
one of these properties would necessitate the knowledge of distance
Ex:
δv
independent of d
L
depends on d
→ allows to estimate the distance of these remote objects
Scaling relations - 2
Tully – Fisher relation (spiral galaxies)

L  vmax
vmax = maximum rotation velocity (in the `plateau´ – measured e.g. by
the 21cm H line)
L = integrated luminosity
α = exponent varying with wavelength (α increases with λ)
• nearby galaxies: spatially resolved spectrum
• remote galaxies: integrated spectum
W  2
0
c
vmax sin i
W
Scaling relations - 3
Interpretation:
I surf ~
L
4πR 2
 L ~ 4πR 2 I surf
(1)
2
vmax
R
GM GL  M 
M
 R 2  2  
G
vmax vmax  L 
(2)  (1) : L ~ 4π I surf
if one assumes
G L M 
 
4
vmax  L 
2 2
2
 L~
I surf  c t ( Freeman law)
and M L  c t (including dark matter)
4
 L  vmax
(2)
4π I surf
1
4
v
2 max
2
G M L 
Scaling relations - 4
Interpretation (2):
Since L is roughly proportional to M*, Tully-Fisher links M* and v4
However, in some galaxies (less massive ones, which have the lowest
star formation rate), Mgas should be taken into account
One gets indeed a better correlation
between log vmax and log(Mdisk =
M*+Mgas) than with M* alone
→ suggests that the M/L ratio (and
thus the fraction of dark matter) is
± constant in a large range of
galactic masses (disk-halo
conspiracy)
M*
Mdisk
Scaling relations - 5
Faber – Jackson relation (elliptical galaxies)
L   04 or log  0  0.1M B  c t
σ0 = velocity dispersion in the center of the galaxy
L = integrated luminosity
Dispersion around the relation larger
than for Tully-Fisher
→ suggests that (at least) another
parameter plays a role
Scaling relations - 6
Fundamental plane (elliptical galaxies)
• One seeks a relation between 3 parameters in order to reduce the
dispersion
• It is empirically found that Re ~ I e

where Re = effective radius (contains half of the luminous flux)
and I e = mean flux inside Re
→ suggests to seek a relation between I e , Re et σ0
Re  
1.4
0

0.85
e
or log Re  0.34  e  1.4 log  0  c t
Scaling relations - 7
I
Central black holes
Black hole = solution of the general relativity equations for a `point
mass´
• escape speed vesc:
1 2
Mm
mvesc  G
2
R
 vesc
2GM

R
• Schwarzschild radius: RS = R for vesc = c
2GM
RS  2  3M
c
(in km if M in M O )
• black hole = object for which R < RS
• all sufficiently massive galaxies seem to contain a central
supermassive black hole (SMBH, M ~ 105 – 109 MO)
Central black holes - 2
Detection in inactive galaxies
• Dynamical effect can be measured in a region where black hole (BH)
potential dominates
GM BH
GM BH
vKepler 
 0
 R0 
R
 02
R0 = radius of the sphere in which the black hole potential dominates
σ0 = velocity dispersion at the center of the (elliptical) galaxy or of the
bulge (in a spiral)
• Angular resolution needed:
  RD  0.1M BH 106 MO   0 100km/s 2 D 1Mpc 1
0
→ possible in nearby galaxies with the best instruments
Central black holes - 3
• Increase of velocity dispersion σ or of the rotation velocity vrot in the
central region (R < R0)
• No direct proof that it is due to a black hole but no alternative
solution (huge mass in a limited volume)
image
of the
galactic
center
spectrum
x
spectrograph
slit
λ
Central black holes - 4
Correlations
• Estimates of the SMBH mass in a sample of galaxies
→ study of correlations with galactic properties
→ one observes a correlation
between the mass of the black
hole and the mass of the bulge:
MSMBH / Mbulge ~ 0.002
→ joint evolution?
or result of galactic mergers?
Central black holes - 5
Sagittarius A*
• At the center of our Galaxy: compact star cluster centered on the
radio source SgrA*
• The proper motions and radial velocities of ~1000 stars in that
cluster could be measured (inside 10 arcseconds around SgrA*)
→ imply the presence of a
mass
M = (3.6±0.4) 106 MO
in R < 0.01 pc (2000 AU)
centered on SgrA*
Luminosity function
Luminosity function = number of objects as a function of their
luminosity
• Φ(L) dL = number of galaxies per unit volume, whose luminosity is
between L and L+dL

• Total density:
   Φ ( L)dL
0
• There is a similar function in (absolute) magnitude:

Φ( M ) :
   Φ( M )dM

• One can define a luminosity function for each class of galaxies (or
for any object); it can also vary with time
Luminosity function - 2
• Difficulties:
– measurement of L depends on distance (often estimated from the
redshift z)
– need for representative samples → large volume (but not too large
as the function evolves with time…)
– L depends on the chosen filter and shift with z (k-correction)
– Malmquist bias → difficulty to determine Φ at low L
→ need to build a volume-limited sample and not a magnitudelimited one
Luminosity function - 3
Schechter luminosity function:

L
Φ ( L)  Φ*   e  L / L*
 L* 
L* = characteritic luminosity
(exponential decrease for L > L*, power law for L < L*)
Φ* = normalisation factor
(Φ*, L*, α depend on filter)
→ good empirical approx. of the
global luminosity function
L* ~ 1010 h–2 LO
Φ* ~ 10–2 h3 Mpc–3
α ~ –1
Luminosity function - 4
• Each class of galaxies has its own luminosity function:
– spirals on narrow L domains
– ellipticals dominate at high L
– low L dominated by Irr and dE
• Different distributions in the field
and in clusters:
Ex: – Irr / dE ratio at low L
– (Sa+Sb) / (SO+E) at high L
Luminosity function - 5
Color-magnitude diagrams
• Simpler classification (does not need morphological studies)
→ bimodal distribution:
a `luminous and red´ peak; another `fainter and bluer´ peak
• Φ different for `red´ and
`blue´galaxies
→ Schechter ≈ coïncidence
• at a given L, always 2
peaks in the color
distribution
Luminosity function - 6
• The central color (the mode) of each peak shifts towards the red when
luminosity increases
• The M/L ratio is larger for the red population (fewer young, very
luminous stars)
• Above ~ 2 – 3 × 1010 MO,
`red´ galaxies dominate
• Below, `blue´ galaxies
dominate
Galactic spectra
• In UV, visible, near IR: the spectrum of galaxies is dominated by
emission from stars (+ gas emission lines)
→ spectrum of a galaxy = superposition of stellar spectra (with
Doppler effects → shift + broadening of lines)
Fλ
λ(Å)
Spectrum of an elliptical galaxy
Galactic spectra - 2
• Stellar evolution rather well understood
• Stellar spectra computed from stellar model atmospheres
→ the galactic spectrum can be computed if one knows the number of
stars as a function of their mass, chemical composition, evolution stage
• these parameters
can be computed
from the initial
mass function
(IMF) and the star
formation rate
(SFR)
NGC 1672
Galactic spectra - 3
Initial mass function
• IMF
φ(m)dm = fraction of stars having, at birth, a mass between m and
m+dm
ms
Normalisation:
with mi ≈ 0.08 MO
 m (m)dm  1 M
mi
ms ≈ 100 MO
Reference IMF (Salpeter):
φ(m) ~ m–2.35
(overestimates very low masses)
O
Galactic spectra - 4
Star formation rate
• SFR
ψ(t) = rate of star formation (in MO/year):
 (t )  
dmgas
ψ(t) depends of the history of the galaxy considered
dt
Metallicity
• Z(t) = proportion (in mass) of chemical elements from carbon and
over (thus synthesized in stars)
• The initial Z of a star is that of the interstellar medium in which it
forms (enriched by previous stellar generations)
• Z gives a 1st approximation to the chemical composition
Galactic spectra - 5
Spectral energy distribution
• SED
Sλ,Z (t) = energy emitted by a sample of stars with metallicity Z and
age t, per unit wavelength and time
Stellar populations synthesis
t
• Flux emitted by a galaxy:
F (t )   (t  t ) S  ,Z ( t t) (t ) dt 
0
Integration goes back in time from t΄ = 0 (present time) to t (birth of
the galaxy)
Galactic spectra - 6
Sλ,Z (t–t΄)(t) = spectrum emitted at time t, taking into account the
chemical evolution of the galaxy and the stage of evolution of the stars
→ computed from stellar evolution and atmospheres models
On the basis of the adopted IMF, one
computes the population density
along the isochrones
→ Sλ,Z (t–t΄)(t) = sum of all spectra on
an isochrone
Galactic spectra - 7
• Spectra of a stellar population born in a single event t billion years
ago (t = 0.001 → 13)
106 years: dominated by massive stars (UV)
107 years: fast decrease of UV light and
increase NIR (red supergiants)
108 years: UV nearly disappears and NIR
stable (red giants)
109 years: dominated by red giants
4–13×109 years: very slow evolution
13×109 years: slight increase UV (post-AGB
stars and very hot white dwarfs)
4000 Å break: after 107 years, opacity H ↔ H–, useful to determine redshift and
galaxy type
Galactic spectra - 8
• Detailed spectra not always available
→ color indices (shorter observing time, many simultaneous
observations…)
• Integrate spectra in the filter passbands
→ theoretical color indices
– fast reddening for young populations
– M/L increases with age since M constant
and L decreases (much stronger effect in
visible compared to near-IR)
→ LK ± good indicator of mass
Galactic spectra - 9
• Influence of the star formation rate
Single age populations may be well suited for stellar clusters but not
for most galaxies
→ take the SFR evolution into account
`Classical´model:
1 t t f  
 (t )   e
H t  t f 
tf = time of startup
τ = characteristic time for star formation
H(t) = 0 if t < 0, = 1 if t > 0 (Heaviside function)
→ sudden start followed by exponential decrease caused by
progressive gas exhaustion
Galactic spectra - 10
• The predicted color strongly depends on the characteristic time for
star formation τ
If τ is very long, the reddening with
time is lower since new, blue,
massive stars continue to form
To explain the colors of E/SO
galaxies, one needs τ < 4×109 years
→ basically no more star formation
for the last 4 to 5 billion years
(but this does not take galactic
collisions into account)
Galactic spectra - 11
• Contributions of the different components:
– stars: continuum + absorption lines
– gas: emission lines
– dust: extinction + reddening (light absorbed more strongly in the
blue and UV and re-emitted in IR)
Galactic spectra - 12
• Evolution along the Hubble sequence (from ellipticals to late-type
spirals):
– SED bluer for later types
– 4000 Å break gets weaker
– strength of absorption lines
decreases
– emission lines increase (HII
regions around young stars)
– spectra of E and SO nearly
identical (old stars)
Galactic spectra - 13
• Modelling:
– adjust composite stellar populations via
SSP models (Single Stellar Population) of
given Z and t
Galactic spectra - 14
• Main absorption lines in the visible:
atm.
Fe (5270)
break à
4000 Å
NaI D (5895)
MgI b (5174)
Hβ (4861)
bande G (4300)
CaII H et K (3934-3969)
Hα (6563)
Galactic spectra - 15
• Main emission lines in the visible:
Hα (6563)
[OII] (3727)
Hβ (4861)
[OIII] (4959-5007)
[NII] (6548-6583)
[SII] (6717-6734)
Galactic spectra - 16
Study of the gas content
• Reddening
Dust absorbs radiation → heats up → emits in FIR
F  I  10  c. f (  )
or
log F  log I   c. f ( )
where Iλ = intrinsic flux
Fλ = observed flux
f(λ) = reddening curve
c measures the importance
of reddening
f(λ) depends on the types of dust
grains
f(λ)
Galactic spectra - 17
• Balmer decrement
Depending on the emission mechanism, the theoretical intensity ratios
for some lines can be computed (in particular for the Balmer series of
hydrogen)
One often uses the Hα to Hβ intensity ratio (Balmer decrement)
E
n=5
n=4
The theoretical intensity ratio varies
from 2.85 (HII region) to 3.1 (AGN)
Comparison of observed and
theoretical ratios → estimate of
reddening


F
I
Hα
Hα

c  3.1 log
 log

F
I
Hβ
Hβ


Hα
Hβ
Hγ
n=3
n=2
n=1
Galactic spectra - 18
• Ionization source
The comparison of some emission line intensities allows to distinguish
between the different excitation and ionization sources
Intensity ratios of neighboring lines are particularly interesting as they
are nearly independent of reddening
Ex: [OIII]/Hβ, [NII]/Hα
Galactic spectra - 19
• Estimate of the SFR
Many indicators in different spectral ranges, calibrated from stellar
population models
– UV flux ↔ massive and very young population, but very sensitive to
reddening
– visible and NIR: intensity of some emission lines ↔ ionizing flux ↔
hot stars
– FIR: thermal emission from dust heated by massive hot stars
– radio: emission from supernova remnants
All these indicators being indirect, one tries to combine several of them
to reduce the uncertainties
Galactic spectra - 20
Examples of SFR indicators:
SFR(M O yr 1 )  7.91042 L(Hα)(erg s 1 )
SFR(M O yr 1 )  (1.4  0.4)1041 L(OII)(erg s 1 )
SFR(M O yr 1 )  1.711010 L(8  1000μm)LO 
Birthrate parameter b 
SFR
= present SFR / average past SFR
R
Measures the present rate of activity
compared to past one
`starburst´ galaxy: b > 2 – 3