The following pages contain lecturing material selected for advanced
higher students at secondary schools in Scotland. The material was
collected for and presented at the INSET-meeting at
Kirkcaldy High School, November 13, 2015. Credits to Dr Aleks Scholz
(lecturer AS1001), Dr Anne-Marie Weijmans (lecturer AS1101)
and Prof Moira Jardine for providing material from their university courses.
Download here as .odp
(OpenOffice powerpoint) or here as
(the files contain movies which appear as big grey boxes marked by
"?" and will not work, unfortunately)
(however, you can click on links
provided below to download those movies)
The presentation contains some questions
marked in blue
which you might want to ask and answer
yourself, or to discuss with your students. You can find my
We start our journey from stars to the cosmic cycle
of matter with the star we know the best - our sun. The optical
image (lower right) shows the appearance of the sun's photosphere,
from which the majority of radiative energy is released into
space, with the typical limb-darkening and a few sun spots. At
shorter wavelengths (far UV, extreme UV, soft X-ray), we mostly
see the outermost hot layers surrounding the sun, the chromosphere
and the corona, where temperatures are as high as a few millions
of Kelvin. At the shortest wavelengths, the photosphere is too cold
to produce any significant emission.
Sketch of the mean temperature as function of height
above the convective layer which forms the footpoint of the solar
photosphere. Note that the photosphere is characterised by a
negative temperature gradient, before there is an inversion in the
chromosphere, followed by a quite sudden transition into the much
hotter and thinner corona.
Image Credit: Adapted by M.B. Larson
from Sun, Earth, Sky by Kenneth Lang.
the dynamic sun
The picture shows that magnetic field lines emerge
preferentially from sun spots, forming "coronal loops" in the corona
where hot and highly ionised gas is trapped in the magnetic field,
emitting hard UV photons and X-rays. The movie furthermore shows the
rotation of the sun, and shows that the corona is far
from being a stationary phenomenon. Compare the radial extension of
this figure (the solar radius is Rsun
~ 700 000 km.)
with the radial extension of the temperature structure shown in the above
figure (~ 3000 km), showing that the photosphere of the sun is indeed
Solar Dynamics Observatory, NASA,
download movie here
solar flares and coronal mass ejections
Spectacular mass ejection events observed by the
Solar Dynamics Observatory. Coronal Mass Ejections (CMEs) typically
last a few hours and produce solar storms with velocities of up to a
couple of 1000 km/s. The physical mechanisms leading to these events
are not exactly known, but seem related to instabilities in the
magnetic field, causing sudden re-connections of the twisted field
lines. The sudden changes of the magnetic field induce strong electric
fields, along which the ionised plasma is accelerated.
the Solar Dynamics Observatory, NASA,
, download the
A solar prominence with Jupiter and Earth to
size. Image Credits: Wikipedia.
Image Credits: NASA.
The opacity κλ
[1/m] describes the opaqueness of a medium;
is the mean free path of photons of wavelength
λ in that medium. The integral over the opacity along a
photon path is called the optical depth τλ
Photons emitted from radius r have probability
(r)) to escape the star when emitted
radially. Taking into account that photons can also exit the star at
slanted angles (not necessarily radially), the layer at
= 2/3 is found to contribute most to the
emerging flux (Eddington-Barbier approximation). Therefore,
) = 2/3 is the proper
definition of the stellar radius.
The effective temperature of
the star Teff is defined via the total radiative flux
that emerges from the stellar atmosphere per unit area. Considering an analog
black body sphere of radius Rstar, whose total radiative
flux is given by the Stefan-Boltzmann law as F=σT4,
we define Teff as the temperature of an analog black body
which would produce the same total flux.
Using the definition of
the luminosity as integral of the total flux over the stellar surface
results in the Stefan-Boltzmann law in the form
Lstar = 4π Rstar2
The brightness of stars are measured in
magnitudes, and depends on wavelength. Concerning the wavelengths,
broad standard photometric filters are applied, for example
"ultra-violet" U (λ~365 nm),
"blue" B (λ~445 nm),
"visual" V (λ~550 nm),
"red" R (λ~660 nm),
"infra-red" I (λ~805 nm).
The unit magnitude is derived from a system first used
by the Greek astronomer Hipparcos (2nd century BC). In his catalogue
of stars, 1st magnitude are the brightest stars, 6th magnitude are
the stars just visible for the human eye. The relation to the
physical flux Fλ
was established later by
realising that the human eye has a logarithmic sensitivity, and the
factor 2.5 was adjusted to get similar results as Hipparcos.
practise, magnitudes are not measured in an absolute way, but
relative to standard stars, that's why there are two
objects A and B in the above equation. A could
be the standard star (with known mλ), and B
could be the star which magnitude we want to measure.
absolute magnitude Mλ is obtained by moving the
star to a standard distance of 10 pc, use Fλ ~
1/d2 to derive the second from the first equation.
One parsec is the parallax of one arc-second, a distance unit used
in astronomy, i.e. the distance by which objects appear to wobble on
the sky due to the orbital motion of the Earth
around the sun. The absolute brightness Mλ is
important to compare the physical properties of stars situated at
different distances, for example in the Hertzsprung-Russel (H-R) diagram,
see below. For main sequence stars,
Mλ is directly related to the stellar luminosity
Lstar as introduced above.
This sketch shows the basic stellar atmosphere
problem. Energy is flowing in from below by convection and photons
from the hot dense interior of the star. This energy flux is
converted into other photons which leave the star in a transition
layer known as the "photosphere". In order to understand and predict
the optical appearance of stars, we need to precisely infer the physical
structure of the photosphere, i.e. its pressure and temperature
structure, and we need to know the element composition.
This sketch explains schematically how stellar
atmosphere models work. Based on the assumed temperature/pressure
structure, the abundance of all electrons, atoms, ions and molecules
are computed, along with the populational numbers of their excited
states. This information is then used to obtain the continuum and
line opacities, including scattering. Based on the opacity structure,
the equation of radiative transfer (ERT) is solved
numerically to obtain a formal solution of the radiation field at
all positions in the stellar atmosphere, including the observable
radiative flux leaving the atmosphere at the top. We can now check
energy conservation by comparing the total radiative (plus
convective) flux through all layers. In radiative equilibrium,
this flux must be constant in plane-parallel geometry
Frad + Fconv =
σTeff4 = const ("radiative equilibrium").
If it isn't, we need to modify the assumed temperature/pressure
structure in the stellar atmosphere and start all over again.
The red boxes highlight the physical assumptions
and principles used in simple stellar atmosphere models.
Joseph Fraunhofer (6 March 1787 – 7 June 1826) was a
skillful and passionate manufacturer of optical instruments, such as
lenses, prisms, and microscopes. He invented the spectrograph and
discovered hundreds of dark lines in the solar spectrum, which were
later identified to be atomic absorption lines by Kirchhoff and
Bunsen. These lines are still called Fraunhofer lines in his
honour. In the chemistry lab, it is easy to let the students see
atomic emission lines by sprinkling different salts (containing
different elements) over a bunsen burner and watching the emitted
light through some refractory instrument like a hand spectrograph or
a CD. It is less easy to demonstrate that the same lines appear in
absorption if observed against a bright continuum source. The
latter experiment is very close to the situation in stellar
If we observe the narrow spectrum of a star around a
single spectral line, the opacity in the stellar atmosphere is much
larger at line centre as compared to the neighbouring
continuum. Therefore, the layer which emits most of the spectral flux
(τλ(r) = 2/3) is situated high
in the photosphere at line centre, and deep in the continuum. One
could say that the star appears to be a bit bigger at line
centre. Since there is a negative temperature gradient in the
photosphere, we probe cold gas at line centre, but hot gas in the
continuum. Therefore, we see an absorption line. The fact that stars
do exhibit absorption lines provides direct evidence for negative
temperature gradients in stellar photosphere. If stars possessed the
opposite, a radially increasing temperature structure, they would
exhibit emission lines.
The figure summarises some stellar properties
according to the Harvard spectral classification, found by
observations and stellar atmosphere models. Note that the stellar
mass is only valid on the main sequence (MS), whereas the
associated effective temperatures and appearance of lines is also
valid for giants and super-giants. There are additional letters
used for carbon stars (C), white dwarfs (D), as well as brown dwarfs
(L, T and Y).
Credits: St Andrews University, AS1101.
The spectra of main sequence stars
Sequence of spectra of main sequence stars from L to
B-type, compiled from different tables of stellar atmosphere models
(Drift/Phoenix, Phoenix, and Kurucz), which come with different
spectral resolution. The x-axis is the wavelength [nm], the y-axis
is the wavelength times the spectral flux
] at the
stellar radius, the "surface flux". Note the Balmer jump at 365 nm
and the series of Balmer lines Hα, Hβ, Hγ,
etc. occurring in particular in A-type stars.
the movie here
Understanding the inner structure and evolution of
stars is based on similar assumptions and physical principles as
explained earlier for stellar atmospheres. We assume again
hydrostatic equilibrium and use similar descriptions for the
radiative and convective energy transport.
However, we must
consider a much more sophisticated equation of state, which remains
valid even under the extreme pressure/temperature conditions in the
interior of stars, and we must include one new physical phenomenon,
namely the energy production via nuclear reactions. To do this,
networks of nuclear reactions have been developed (the rate
coefficients can be measured in particle accelerators) which predict
the total local energy production rate as function of temperature,
pressure, and current element abundances. Since these reactions, in
return, change the element abundances, the problem becomes
On the main sequence, time-dependent effects
are quite small, because the element abundances are still
close to their primordial values. However, once hydrogen starts to
get exhausted in the stellar core, things are changing. The stars
will change their inner structure, change their nuclear energy
production rates and start to evolve in the H-R diagram.
Consider a layer between r and r+dr with cross
section A and mass
density ρ. Write down force equilibrium (gravity, pressure from
above, pressure from below), and solve for pressure gradient. Use
definition of gravity g=GM(r)/r2. M(r) is the mass enclosed
within radius r.
Image credits: Borb (Wikipedia)
Image credits: Borb (Wikipedia)
In the Hertzsprung-Russel (H-R) diagram, one plots
stars with their luminosity Lstar
(theoretical models) on double
logarithmic axes, or - analogously - their absolute visual magnitude
versus spectral class (observations). The main
sequence roughly forms a diagonal line in this diagram: the
overwhelming majority of all stars (called "dwarfs") line up along
this line. However, there are also "giants" and "super-giants",
which can be found in the right upper corner above the main
sequence, as well as "sub-dwarfs" (denoted as white dwarfs in this
plot) below the main sequence.
The H-R diagram is first and foremost
a summary of observational findings, a tool by which stars can be
characterised. The theoretical insight, that stars actually move
along particular trajectories in the H-R diagram, is a quite recent
result of research carried out during about the last 60 years, an unequalled
triumph of modern science, where concerted efforts in the
development of stellar computer models, particle physics
(nuclear reaction rates), experimental physics (equation of state),
quantum mechanics (opacities) and observations have managed to solve
this puzzle in a convincing fashion, which nowadays fills standard
textbooks about stars.
Note that the diagram also shows the
stellar mass on the main sequence (pale magenta) and the main
sequence lifetime (green). Lines with constant Rstar are
also included. The sun is situated right in the centre
of this plot, a G2V star with Teff ~ 5800 K and
(obviously) Lstar = 1 Lsun.
Image Credits: ESO.
This figure shows some theoretical evolutionary
tracks for low mass stars. The main sequence is marked with "Zero
Age Main Sequence (ZAMS)", because strictly speaking, main sequence
stars do evolve already slightly during central hydrogen burning on
the main sequence. The plot marks the very last stages of low
mass star evolution in form of Early Asymptotic Giant Branch (Early
AGB) stars, Thermally Pulsing AGB stars and transition to Planetary
Nebula (PN) and White Dwarf (WD).
Credits: John Lattanzio
This sketch explains schematically the different
phases of the life of a 1 Msun
star. Once the core
becomes hydrogen-poor, hydrogen starts to burn in a radial shell
around the core, which causes the star to ascent along the red giant
branch. At its tip, helium ignites in the core (the "helium flash"),
causing the star to move temporarily leftward and downward along the
horizontal branch. Finally, even helium becomes exhausted in the
centre, and we find two shells with nuclear burning in the star,
which causes the star to leave the horizontal branch and ascent the
asymptotic giant branch. A helium burning shell above a degenerate
core, and a hydrogen burning shell above those layers.
shells first burn in a stable fashion (Early AGB) and later
in an time-dependent alternating way (thermally pulsing
AGB). Low mass stars (Mstar < 8 Msun) do not
reach high enough core temperatures to start burning carbon to
heavier elements. However, carbon may be dredged up to the
atmosphere, causing stars to become carbon-rich at the surface
(carbon stars). Once the AGB stars run out of helium and hydrogen
for shell burning, the stars end their lives by further core
contraction (producing a white dwarf in the centre) and ejection of
a planetary nebula.
Image credits: St Andrews University, AS1101.
Massive stars (Mstar > 8 Msun)
evolve on much shorter timescales. They start to burn He sooner, and
then further to C, Ne, O, Si and eventually to Fe in distinct
onion-like shells. As each major element is consumed, progressively
heavier elements ignite, temporarily halting collapse. Once the
nucleosynthesis process arrives at 56Fe, the continuation
of this process would rather consume energy then setting free energy.
Consequently, the burnt-out core can no longer withstand gravity and
collapses into a neutron star in the centre, or (for more massive
stars) into a black hole, whereas the envelope explodes in an
Image credits: St Andrews University, AS1101, and Wikipedia.
Interstellar clouds of gas and dust collapse to form stars by
gravitational instabilities. Once
their nuclear fuel is exhausted in the centre, they turn into red
giants which blow massive winds back into the interstellar medium,
partly containing processed elements and newly formed dust
grains. The further evolution of the stars branches into low-mass
and high-mass stars. Low-mass stars end their lives as planetary
nebulae, producing white dwarfs, whereas high-mass stars explode in
supernovae, partly producing neutron stars and black holes. All
these phenomena, that occur when stars die, enrich the interstellar
medium in heavy elements in characteristic ways.
products of stellar evolution (white dwarfs, neutron stars, black
holes) retire from the cosmic cycle of matter, but most of the mass
once confined in stars becomes available again for new star and
planet formation. In fact, the sun, its planets, and all living
organisms on Earth (including mankind) are made of elements that
have been processed already a couple of times in the interiors of
Today's statistics show that most of the mass returned to
the interstellar medium is provided by AGB star winds, but this may
have been different at earlier epochs, when the universe was younger,
denser, and less enriched in heavy elements. The current abundance of
heavy elements such as iron, which can only be assembled in the
cores of massive stars, bears witness that the matter that our world
is composed off was at least once part of a supernova explosion.
Image credits: Technische Universität Berlin (2004)
Low mass stars (< 8 Msun
) loose most of
their envelope mass during their final ascent along the Asymptotic
Giant Branch (AGB) in the H-R diagram in form of massive stellar
winds. These AGB stars are hence surrounded by large amounts of gas
and dust which can become optically thick in the visual, turning
these objects into pure infra-red (IR) objects, see the top figure
for an example, the extreme carbon star IRC+10216, which is expected
to end it's life soon by the ejection of a Planetary Nebula. Also
the sun is expected to turn into such a red giant, see lower left,
with a radius of about 2 astronomical units (AU), engulfing the
The massive mass loss of these AGB stars is thought to be
mainly caused by small solid particles (dust grains) forming in
their outer atmospheres, which absorb the stellar photons and hence
their momentum. Radiation pressure on dust can locally overcome
gravity, which leads to the generation of massive slow dust-driven
winds, which lifts off further stellar matter from the
For comparison, the sun looses about
10-14 Msun/year, i.e. 10 orders of magnitudes
less than IRC+10216. Download the movie of the lower right
model here. See also
Most objects shown here are planetary nebulae, but
this collection also includes other "stellar" sources such as
supernovae explosions and the Wolf-Rayet star eta Carinae.
Credits: HST archive.
High-mass stars generate fast massive stellar
winds which collide with the surrounding material from which the
central stars just have formed. At the interface between stellar wind and
interstellar medium, high-velocity shock waves occur which look like
bubbles in emission lines.
Credits: HST archive.
Credits: HST archive.
Find more amazing pictures from our universe at these
Picture of the Day
Hubble Space Telescope (HST)/ESA archive
. I do think that showing
pictures like these to pupils of various ages may have an important,
long-lasting effect on their enthusiasm for science and their
aspiration for understanding our world.
Image Credits: HST archive.
Find my answers to the blue
questions included in the
Peter Woitke, November 15th, 2015