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General GeoAstro II: Astronomy

The name of the game:

slides will NOT be put on the web
attend the lectures, take notes !

suggested reading: “Universe” (Kaufmann & Freedman)

no laptops, no mobiles during class

classes are not complicated, but please repeat them regularly

only few formulae, but you have to know them
General GeoAstro II: Astronomy

Stars
-
Nature of stars
- Milky Way
- Cosm. Expansion
Birth of stars
- Other galaxies - Big Bang
Stellar evolution
- Supermassive - Tests of our
Endpoints:
black holes
theories
White Dwarfs
- New
Neutron Stars
Black Holes
developments
-

Galaxies

Cosmology
Distance to the stars
From brightness? No!
 Parallax-experiment …
 Stellar parallax …

d= 1/p
Distance to the stars

Define: “star has a distance of 1 parsec (pc) if its
parallax is one arcsecond”

1 pc = 3.26 light years

Brightest stars on the night sky: too far to measure
parallax

Blurring of atmosphere: parallaxes < 0.01 arcsec
extremely hard to measure
reliable out to d= 1/p = 100 pc
Distance to the stars

Hipparcos: High Precision Parallax
Collecting Satellite (Hipparchus: greek astronomer)

Parallaxes still important to gauge other
distance indicators

Stellar motions ….
Brightness and Distance
(“Inverse square law”)

Distance and brightness
luminosity

Stars have different masses
different luminosities

“luminosity= energy/time” [J/s]

“brightness= energy/(time surface area)” [J/s m2]
Brightness and distance
• brightness ….
•b= L/(4 p d2)
•“double the distance
brightness reduced by a factor 4”
luminosities

huge variety of stellar luminosities:
Lmax =1010 Lmin
(1010 = number of all people that ever lived on earth)
The Magnitude system



System to classify stellar brightness
Very old: Hipparchus (200 B.C.):
“ brightest stars:
first magnitude
half as bright:
second magnitude
……
sixth magnitude”
“apparent magnitudes”
Attention: “scale backwards”
Magnitude system

19th century astronomers: “first magnitude stars
shall be 100 times brighter than sixth magnitude
stars”

difference of 5 mag corresponds to a
factor of 100 in brightness,
i.e. x5 = 100
x= 2.52
“half as bright
1/2.52
as bright”
Magnitude system
Scales backwards: “the brighter the more
negative”
 Examples:
 Venus:
m= - 4
 Full moon: m= - 13
 Our sun:
m= - 26.8
 Relation brightness – magnitudes...

m2-m1= 2.5 log(b1/b2)
Absolute magnitudes

Definition: ”absolute mag.= relative mag. as seen
from a distance of 10 pc”

Distance modulus (m-M)…

m - M= 5 log(dpc) – 5
dpc: distance in pc
m : apparent magnitude
M : absolute magnitude
Stellar colours

Stellar colours depend
on the surface temperature !

Wien’s law: lmax T = const …
Spectra of stars

How do we know the same laws of physics hold in
the observable universe?

Sun: absorption line spectrum (=continuum + dark lines)

Spectral classification: O B A F G K M
“Oh be a fine girl/guy kiss me…”
“hot”
Tsurf ~ 25 000 K
Sun
“cool”
Tsurf ~ 3000 K
Spectra of Stars

Advent of quantum mechanics:
Interpretation of absorption lines in terms of atomic energy levels
Stellar sizes
impossible to measure with telescopes
 measure
i) brightness
luminosity
ii) distance (parallax)
iii) surface temperature (spectral type)
.

Stefan Boltzmann law
.
Radius
Hertzsprung-Russel diagram

Idea: plot luminosity vs. temperature
(spectral type)
information about radius
classification of stars
Hertzpsrung-Russel diagram
not random, just a few classes
 most stars on “Main Sequence” (hydrogen burning)
 White dwarfs: same temperature, but lower
luminosity
small radius

RWD ~ 10 000 km ~ Rearth

Giants:
same temperature, but higher
luminosity
large radius
Rgiant = 10 - 100 Rsun
Tsurf = 3000 – 6000 K

Supergiants:
up to 1000 Rsun
Stellar Masses



need binary stars ! (~50% of all stars in binaries)
“double stars” either i) “optical double stars”
ii) true binary star
How to get masses???
Kepler III:
w2= G (M1+M2)/a3
M1: mass star 1
M2: mass star 2
a : separation between stars
G : gravitational constant
w= 2 p/T, T: orbital period
measure a and T
total system mass
Stellar masses

individual masses?
i) find center of mass (CM)
ii) distances from CM to stars, a1 & a2
a1= (M2/Mtot) a
a2= (M1/Mtot) a
Mass-luminosity relation

Observation:
L  M3.5 …..
“proportional

Stellar lifetime t :
to”
t  M-2.5
“fat blokes die young”
The Birth of Stars

“We see a region of space extending from
the centre of the sun to unknown distances
contained between two planes not far from
each other…” (Immanuel Kant: “Allgemeine Naturgeschichte und
Theorie des Himmels”)

Nuclear burning in the sun (“hydrogen to helium”):
consumes 6 1011 kg/s of hydrogen
no infinite fuel resources: finite life time
stellar evolution (“birth, evolution, death”)
Birth of Stars

“snapshot problematic”
stellar >> human lifetime

Derive evolutionary sequence from a set of
“snapshots”
Stellar Birth

Stars are born in the
gravitational collapse of
giant molecular clouds
Stellar Birth

computer-simulation of
the collapse of a giant
molecular cloud by
Mathew Bate




very dynamic process
stars form in groups
many binary/multiple
star systems form
observation:
~ 50% of stars are in
binary systems
Stellar birth

Where does star formation take place?
…in the spiral arms of galaxies…
Interstellar Medium (ISM)

ISM provides matter of which stars are
made

ISM consists of a combination of gas and
dust

Interstellar clouds are (for historical
reasons) called nebulae
Interstellar medium

Three kinds of nebulae:
Emission N.
Reflection N.
Dark N.
Interstellar medium

Emission nebulae:
 temperatures: ~ 10 000 K
 masses:
~ 10 – 10 000 Msolar
 density:
n ~ few 1000 atoms/cm3
(compare with: “air” ~ 1019 atoms/cm3
ISM ~

1 atom/cm3)
found near hot, young stars (O and B
stars with Tsurf > 10 000K)
Interstellar medium: emission nebulae

Interstellar hydrogen found in two forms”
 “HI-region”: neutral hydrogen
 “HII-region”: ionized hydrogen (i.e. protons
and electrons)
Interstellar medium: emission nebulae

Emission mechanism HII-region:
recombination
(proton captures electron, emits light
as it cascades down)

most important transition
from n=3 to n=2
(“Ha-photons”)
reddish colour
•Reflection nebulae

Lots of fine-grained dust, low density
reflects short-wavelengths more
efficiently than long ones
blue colour
•Dark Nebulae
High density of dust grains
block view to the stars
 Temperature: 10 – 100 K


Density:
hydrogen
molecules
n ~ 104 – 109 atoms/cm3
Stellar Evolution

Protostars:
 Gravity has to overcome gas pressure
dense & cold regions preferred
dark nebulae (“stellar nurseries”)

“standard cosmic abundances”:
 75 % Hydrogen
 24 % Helium
 1 % heavier elements
Protostars

young protostars more luminous than later on the
main sequence (gravitational energy)

Decrease of luminosity at almost constant surface
temperature,
but central temperature
rises

Evolutionary path in
HR-diagram…
Protostars

At Tcentral ~ 106 K: thermonuclear reactions
(H
He) set in
produce energy/pressure
stop contraction
hydrostatic equilibrium+nuclear burning
= Main sequence (MS) reached

Exact position on MS determined by stellar
mass…
Main sequence masses

Extreme cases:
 Mass too small (<0.08 Msol)
no ignition of hydrogen, no main sequence stage
Brown Dwarf
 Mass too big (>100 Msol)
violent winds
disruption of the star
Main sequence: 0.08 < MMS < 100 Msol
Young stellar objects (YSOs):
…youngsters in revolution…

Accretion disks:

Jets:
Young stellar objects

examples of accretion disk – jet connection

interaction of these outflows with surrounding
matter: Herbig-Haro objects

Jets are usually short-lived: 104 years,
but can eject large masses (~1 Msol) during this
time

many young stars lose mass via strong winds:
mass loss 10-7 Msol/year
(our sun: 10-14 Msol/year)
Young stellar objects

Young stars like to hang around in groups
(see previous movie)
“open clusters”

fastest stars may leave
“evaporation” of open clusters
Stellar evolution: overview

once formed, evolution of stars depends on
their masses:

M < 0.08 Msol:

0.08 < M < 8 Msol:
no nuclear fusion
“Brown dwarfs”
i) Main sequence
ii) Giant phase
iii) White Dwarf +
planetary nebula
Stellar evolution: overview


8 < M < 25 Msol:
i) Main Sequence
ii) Giant phase
iii) supernova
explosion
neutron star
M > 25 Msol:
i) Main Sequence
ii) Giant phase
iii) supernova
explosion
black hole
Evolution of a M < 8 Msol star

“our sun”:
- MS-star, H-burning in core
- Red Giant: H in core
exhausted, H-burning in
shell
- Red Giant:He ignites in
stellar core, radius ~ 1 AU
earth swallowed
(~ 5 109 years from now)
- final
stages: hot, cooling
Carbon-Oxygen core,
eject envelope
White dwarf + “planetary nebula”
8 Msol -star

Planetary nebulae:
8 Msol -star

Evolution in the HR-diagram:
Testing stellar evolution:globular clusters

Globular clusters

~105 stars

in halo of galaxy

Old: about same age as
galaxy
Globular clusters and HR-diagrams

Basic idea:
- heaviest stars have already evolved away from
main sequence
- lightest stars still on main sequence
age of cluster
Evolution for M > 8 Msol

Stages:
• Main sequence
• Giant stage
• Final stage:
Evolution for M > 8 Msol

No more nuclear fuel (beyond iron)
“core”-collapse
supernova explosion (type II)
Evolution for M > 8 Msol

Supernova explosion results in
either
i) a neutron star (M < 25 Msol)
or
ii) a black hole (M > 25 Msol)
End stages of stellar evolution:

White dwarfs:

Left behind in center of planetary nebula

No more nuclear burning
away
just cools until it fades
Masses: 0.2 – 1.4 Msol
above 1.4 Msol
collapse to neutron star

Densities: ~ 106 – 108 g/cm3
(earth: ~ 5 g/cm3)

Equilibrium between gravity and degeneracy pressure

White dwarfs

Degeneracy pressure:

purely quantum mechanical effect:

Electrons are “Fermions” (spin= ½)
don’t want to be in the same state
(Pauli-exclusion principle)
resist compression even at zero temperature
• all
mass from neutrons and protons
•all pressure from electrons
white dwarfs

Mass-Radius relationship:
“More massive WDs are smaller”
R

M -1/3
:
Neutron Stars
End Stages of stellar evolution

Masses:
~1.4 Msol

Radius:
~10 - 15 km

Density: few 1014 g/cm3
observed neutron star mass
distribution

Magnetic field: 1012 - 1015 G
(earth: ~ 0.5 G)
Neutron stars

hard to detect:

new-born neutron
star in Supernova
remnant
Neutron Stars

Internal structure:

mostly neutrons
(~90% neutrons, ~10% protons)


crust: iron-like
nuclei
center: “exotic”
particles?
End Stages of stellar evolution:
Black holes

neutron star has limiting mass, above that
mass: collapse to a black hole

not even light can escape from a black
hole…
How can a black hole be detected?
Black holes

Black hole “accretes” mass from
companion star
x-ray binary
Galaxies:
Our Galaxy: the Milky Way
The Structure of the Milky Way
Galactic Plane
Galactic Center
The actual structure of our Milky Way is
very hard to determine because:
1) We are
. inside
2) Distance measurements are difficult
3) Our view towards the center is
obscured by gas and dust
Structure of the Milky Way (MW)

So what can we do to explore the MW ??
a) space craft?
No
b) select bright objects that can be seen
throughout the MW
c) observe in different wavelengths
d) trace velocities of all visible objects
Structure of Milky Way: a) space craft

a) How long would it take to get good
“outside view” of our Galaxy
(travel at speed of light)?
i) 2 months
ii) 1 year
iii) 500 years
iv) 30 000 years
v) 5 million years ??
Answer:
iv) 30,000 years
The Sun is about
Sun
8.5 kpc = 8,500 pc
≈ 30,000 light years
from the Galactic
center.
Galactic Center
=> No spacecraft
will ever travel a
significant distance
through or even out
of the Milky Way
Structure of Milky Way: b) bright objects
b) What are bright objects?

A type stars ?

Brown dwarfs ?

White dwarfs ?

O type stars ?
Structure of Milky Way: b) bright objects

Answer: O- and B-stars !
Remember: O and B stars
are the most massive, most
luminous stars
Look for very young
clusters or associations:
O/B- Associations !
Structure of Milky Way: b) bright objects
optically bright objects
O/B Associations
Sun
O/B Associations trace out
3 spiral arms near the Sun.
Distances to O/B Associations
determined using Cepheid Variables
Structure of Milky Way: b) bright objects
Globular Clusters
Globular Cluster
M80
• Dense clusters of 50,000 – a million stars
• Old (11 billion years), lower-main-sequence stars
• Approx. 200 globular clusters in our Milky Way
Structure of Milky Way: b) bright objects

Globular cluster distribution:
we are not in the centre of our Galaxy
Structure of Milky Way: c) different wavelengths

Galaxy (optical):
absorption by gas and dust

Galaxy (near-infrared):
emission from warm dust
Structure of Milky Way: c) different wavelengths

Galaxy more transparent at longer (than optical)
wavelengths….

most transitions in hydrogen atom at “short”
wavelengths, but …

coupling magnetic moments electron and
proton in neutral hydrogen hydrogen:
21cm radio emission
Structure of the Milky Way

Neutral hydrogen creates
radio emission (l= 21cm):
coupling between magnetic
moments of proton and electron…
“21-cm radiation” can be
used to trace the
distribution of neutral
hydrogen in the Galaxy
Structure of the Milky Way
75,000 light years
Disk
Nuclear Bulge
Sun
Halo
Open Clusters,
O/B Associations
Globular Clusters
Animation
Structure of Milky Way

Stellar Populations:
…heavier elements are formed in various
burning stages of stars…

Question: how does the metal content of young
and old stars differ?
1) Old stars should be more metal-rich…
2) Young stars should be more metal-rich…
3) They should be the same…
Structure of Milky Way

Of course: young stars are “metal”-rich

Stellar Populations
Population I: Young stars:
metal rich; located in spiral
arms and disk
Population II: Old stars: metal
poor; located in the halo
(globular clusters) and
nuclear bulge
Dynamics in the Milky Way (I)
Population I
(disk stars)
Population II
(halo stars)
Dynamics in the Milky Way (II)
Differential Rotation
Sun orbits around
Galactic center
with 220 km/s
1 orbit takes approx.
240 million years.
Dynamics in the Milky Way

Question: What determines the velocity with which the
sun is moving around the Galactic centre?

Mass of the sun?

Rotational period of the spiral arm pattern?

Mass inside the orbit of the sun ?

Angular momentum of the Milky Way ?
Dynamics in the Milky Way

Answer:
Newton’s Laws tell us that it is the mass inside the radius
of the sun that determines its velocity
The more mass there is inside
the orbit, the faster the sun has to
orbit around the Galactic center
(argument similar to Kepler’s III.
law)…
V= 220 km/s
Minside ~ 1011Msol
R= 8.5 kpc
Dynamics in the Milky Way

Forms of rotation

rigid rotation

differential
rotation…
Dynamics of the Milky Way

21-cm-radiation of neutral hydrogen to
determine the rotation curve (“velocity as a function of radius”)
of our Galaxy
Use the
observed
expected (if
mass concentrated
in centre)
Dynamics in the Milky Way
explanation for the observed rotation curve:
There must be more mass than is visible !!!

“ DARK MATTER “ (DM)
- 90 % of the matter in the
Galaxy is “invisible”
- only 10 % in stars
Dynamics in the Galaxy

What could dark matter be made of?
i) dim stars, massive planets, black holes?
(= massive compact halo objects= MACHOS)
experiments: only small fraction of
DM are MACHOS
ii) A new kind of particle ?
(=weakly interacting massive particle= WIMP)
maybe, but none such particle has
been detected yet…
The centre of our Galaxy
Our view (in visible light) towards the Galactic center (GC)
is heavily obscured by gas and dust:
Only 1 out of 1012 optical photons makes its way
from the GC towards Earth!
Galactic center
Wide-angle optical view of the GC region
Radio View of the Galactic Center
Many supernova remnants;
shells and filaments
Arc
Sgr A
Sgr A
Sgr A*: The Center of our Galaxy
Galactic Center contains a supermassive
black hole of approx. 2.6 million solar masses.
Centre of our Galaxy

motion of stars close to Galactic centre
(observed !)
everything consistent with a black
hole of 2.6 million solar masses
Other Galaxies

types galaxies
 spiral galaxies

barred spiral
galaxies
Other Galaxies

elliptical
galaxies

irregular
galaxies
Other galaxies

...some more beautiful galaxies…
Sombrero galaxy
Blackeye galaxy
Andromeda galaxy
Other galaxies

Stars do not collide !

But galaxies do…
(observations !)
Other Galaxies

galaxy mergers
(computer simulation !)
Other galaxies

Do other galaxies also contain supermassive
black holes ?
YES !
Similar to accretion
disk-jet connection in
young stellar objects
Cosmology
 Ancient
Mythology and Modern
Cosmology:
Is there a Difference ?
Creation Stories I:
The Christian/Jewish View
Genesis: In the beginning God created the heavens
and the earth. And the earth was waste and void;
and darkness was upon the face of the deep: …
Creation Stories II:
Greco-Roman Mythology
Hesiod: In the beginning there was only “chaos” [the infinite
emptiness]. Then out of the void appeared Erebus, the
unknowable place where death dwells, and Night. All else
was empty, silent, endless, darkness. Then somehow Love
was born bringing a start of order. From Love came Light
and Day. Once there was Light and Day, Gaea, the earth
appeared.
Then Erebus slept with Night, who gave birth to Ether, the
heavenly light, ...
Common Themes and Concepts:







Anthropomorphism
Action of a supreme craftsman
Generation from a seedling/egg
Imposition of order over “chaos”
Life cycle dominates over eternal/unchanging:
there is a beginning
Hybrid schemes: act of creation, but supreme
being/chaos existed forever
Anthropocentrism
Scientific “Creation” Story 2005:
In the beginning there was neither space nor time
aswe know them, but a shifting foam of strings
and loops, as small as anything can be. Within the
foam, all of space, time and energy mingled in a
grand unification. But the foam expanded and
cooled. And then there was gravity, and space and
time, and a universe formed. …
 Is there a difference ?
The Scientific Method
general principle
induction
deduction
observations
prediction
revision
specific instances
individual events
History:


Mythology vs the scientific method
Cosmos = Earth  solar system  Milky Way 
Hubble sphere
Edwin Hubble
(1889-1953)
Four major accomplishments
in extragalactic astronomy
 The establishment of the
Hubble classification
scheme of galaxies
 The convincing proof that galaxies are island
“universes”
 The distribution of galaxies in space
 The discovery that the universe is expanding
Doppler effect (for light)
The light of an approaching source is shifted to the
blue, the light of a receding source is shifted to the
red
Doppler effect
The light of an approaching source is shifted to the blue,
the light of a receding source is shifted to the red.
blue shift
red shift
Doppler effect
redshift:
1 v / c
1 z =
1- v / c
z=0: not moving
z=2: v=0.8c
z=: v=c
The redshift-distance relation
Key results
Most galaxies are moving away from us
 The recession speed v is larger for more
distant galaxies. The relation between recess
velocity v and distance d fulfills a linear
relation:
v = H0  d
 Hubble’s measurement of the constant H0:
H0 = 500 km/s/Mpc
 today’s best fit value of the constant:
H0 = 71 km/s/Mpc (WMAP)

Question:
If all galaxies are moving away from us,
does this imply that we are at the center?
Answer:
Not necessarily, it also can indicate that the
universe is expanding and that we are at no
special place.
Einstein’s General Relativity +
observation of expanding Universe:
Universe started from a point:
“Big Bang Model”
Example: static universe
R(t)
t
Example: expanding at a constant rate
R(t)
t
i
s
s
l
Example: expansion slowing down
t
x
p
a
n
s
i
o
n
R(t)
t
l
e
:
R(t)
e
x
p
a
n
s
i
Example: expansion accelerating
Example: Collapsing Universe
R(t)
t
Cosmological redshift
While a photon travels from a distance
source to an observer on Earth, the Universe
expands in size from Rthen to Rnow.
 Not only the Universe itself expands, but
also the wavelength of the photon l.

lreceived
Rnow
=
lemitted
Rthen
Cosmological redshift

General definition of redshift:
lreceived - lemitted
z=
lemitted
 for cosmological redshift:
1 z =
lreceived
lemitted
Rnow
=
Rthen
A large redshift z implies ...
The spectrum is strongly shifted toward red
or even infrared colors
 The object is very far away
 We see the object at an epoch when the
universe was much younger than the present
day universe
 most distant astrophysical object discovered
so far: z=5.8
 z>5.8: “dark ages”

k>0
k=0
k<0
Are there any indications that this
picture is correct?

Yes !

Primordial Nucleosynthesis

Cosmic Microwave background
Primordial Nucleosynthesis
Georgy Gamov (1904-1968)



If the universe is expanding, then
there has been a big bang
Therefore, the early universe must
have been very dense and hot
Optimum environment to breed the elements by
nuclear fusion (Alpher, Bethe & Gamow, 1948)
 success: predicted that helium abundance is 25%
 failure: could not reproduce elements more massive
than lithium and beryllium ( formed in stars)
The Cosmic Microwave
Background (CMB)
Last scattering surface
transparent
opaque
Penzias and Wilson 1965
Working at Bell labs
 Used a satellite dish to measure radio
emission of the Milky Way
 They found some extra noise in the receiver,
but couldn’t explain it
 discovery of the background radiation
 Most significant cosmological observation
since Hubble
 Nobel prize for physics 1978

More results from the CMB

The Earth is moving
with respect to the
CMB  Doppler shift

The emission of the
Galaxy

Fluctuations in the
CMB
•Fluctuations in CMB responsible for
structure formation in the universe