Stellar properties
Astronomy 100, Fall 2012
Stars are a basic unit of a galaxy
• The Milky Way galaxy
(ours) contains about
100 billion stars.
• The Milky Way is one of
billions of galaxies.
• The glowing “arms” of
the Milky Way are
illuminated partly by
the glow of numerous
stars.
Our Sun is a star, and a conveniently
close star to observe
Most photos of the Sun,
such as this one, are taken
using a filter; otherwise,
the light would be too
intense for the camera.
In this image, a hydrogenalpha filter was used,
which blocks all light but
the red light from glowing
hydrogen.
The features on the right
limb of the Sun are called
solar prominences.
Red
Orange
Yellow
Green
Blue
Indigo
Violet
R
O
Y
G
B
I
V
Isaac Newton in Opticks (1704)
demonstrated that sunlight
could be dispersed into various
colors by a prism, and then recombined by another prism to
yield sunlight again.
Herschel Thinks Outside the Box:
In 1800 William Herschel made a discovery when he tried to determine the temperature
of light.
• He noticed that a thermometer recorded
energy from the Sun`s spectrum even when
placed beyond the red end of the visible
rainbow.
•He called this emission Calorific Rays and it
was the first discovery that light had colors
invisible to the human eye.
•These rays are known today as Infrared
light.
Herschel’s work  color is associated with a temperature
Visible light is just a small part of the electromagnetic (EM)
spectrum
Fraunhofer’s Surprise
In 1813, Joseph von Fraunhofer, the owner of a glass manufacturing firm in Munich, made
an interesting discovery.
Using a precision dispersing prism, he discovered that the `solar blackbody` was
cut by thousands of dark bands.
Fraunhofer’s Surprise
Fraunhofer tried to test whether this effect was real.
1) He tested with different optics.
2) He tested by looking at different objects (moon and planets).
Bunsen and Kirchhoff`s solution:
Robert Bunsen (Univ. of Heidelberg) turned pyromania
into one of the great discoveries of modern physics.
Bunsen set fire to things in order to figure out their
elemental composition.
A colleague there, Gustav Kirchhoff,
suggested using a prism to break the
light apart. They quickly discovered
(1860) that burning substances
produced light in narrow bands with
unique patterns.
Iron
Blueprint to Composition:
Bunsen and Kirchhoff`s trick was the key to finding out the composition of anything
from the light it produced.
Many of the lines they found had the same wavelength as those of Fraunhofer`s dark
bands. They were seeing the composition of the Sun!
Kinds of Spectra:
Bunsen found that he could identify the signature of different elements in the
Fraunhofer spectrum of the Sun.
Why were Bunsen`s heated gas spectra composed of bright lines while Fraunhofer`s
exhibited a continuous spectrum with dark bands?
Bunsen`s fires were stimulating light emissions in the hot gas.
So what are Fraunhofer`s bands?
Absorption by (and re-emission from) a cooler gas!
Types of Spectra
Continuous: black body radiation
continuous
Absorption: requires a cool object
in front of a hot background
(ex: Fraunhofer) discrete
Emission: requires a hot object
with a cool background
(ex: Bunsen) discrete
Basic definitions:
• Element: a substance that cannot be broken
down by chemical means (defined by number
of protons)
• Atom: the smallest piece of matter that is still
an element
• Molecule: two or more atoms that are bound
together by chemical bonds
• Nucleus: the protons and neutrons bound
together at the center of an atom
Atoms and light
Why do elements have the `discrete` interactions that Bunsen saw?
Why do different elements (and molecules) have different interactions?
This has to do with the nature of atoms
and how they are put together.
A brief history of the atom
First discussion of the nature of matter (~400 BCE):
• Leucippus, a Greek philosopher, all matter consisted “tiny and
indivisible bodies called atoms”.
• The word atom comes from the Greek word `atomos` (not
divisible).
• Democritus, another Greek philosopher, these atoms were not all
alike, but had different shapes and sizes to make different matter.
• Opposed (Aristotle): The prevailing view that everything was made
up of four basic elements: earth, fire, air, and water, not atoms.
• Views such as Aristotle`s dominated science for many centuries,
until the Renaissance.
Dividing the ‘indivisible’:
The plum pudding model
• J. J. Thomson discovers cathode rays are
made of electrons (he called them
‘corpuscles’ – 1897). Electrons are
shown to have a negative charge
• Thomson proposes model of the atom
(1904):
– Atom has smaller components
– Negatively charged corpuscles/electrons
(plums)
– Positive ‘soup’ to balance negative charge
(pudding)
Discovering “nothing”
Meanwhile, Ernest Rutherford (Cambridge) discovers two new types of radiation
emitted by uranium (1899):
1. Alpha particles (): later found to be the helium nucleus
2. Beta particles (): later called the “electron” by Thomson
In 1909, Rutherford fires alpha particles at gold foil.
Expected only small angle scattering due to gold
atoms’ “plum pudding”.
Positive Nucleus
Saw mostly no scattering with occasional back
scattering
Matter is mostly empty space!!!!
Negative
electron
Rutherford’s atom
1. Mass is highly concentrated in the positivelycharged nucleus at the center of the atom.
2. Electrons (negatively charged) “orbit” the
nucleus.
3. Lots of empty space in-between
Positive
4. Similar to today’s atom
–
–
Number of protons determine
the element identity
Number of electrons determine
the chemical properties of the atom
Nucleus
Negative
electron
The nucleus is not uniform
Rutherford (1918): Discovers the proton. The proton is
about 2000 times as massive as the electron and has a
positive charge, exactly the same magnitude as the
electronic charge.
James Chadwick (1932): Discovers the neutron.
Neither positive nor negative, it has about the same
mass as a proton.
Nuclei are made up of protons and neutrons.
Atoms, elements, and isotopes
Atoms (below - periodic table (Mendeleev, Meyer, 1867))
– Nucleus
• Protons – number determines the element (atomic #)
• Neutrons – number determines the isotope (mass #)
– Electrons – number determines the chemical properties
Atoms, elements, and isotopes
Isotopes:
Atoms with the same number of protons but different numbers of neutrons are
called isotopes.
Isotopes have the same chemical properties, but different masses, different
emission spectra, and participate in different nuclear reactions.
hydrogen (1H)
deuterium (2H)
p+
p+
helium (4He)
tritium (3H)
e-
p+
n
n
n
n
p+
p+
n
e-
eA stable isotope
of hydrogen – 99.98%
natural abundance
eA stable isotope
of hydrogen – 0.02%
natural abundance
eRadioactive isotope
of hydrogen
New element; not an
isotope of H
Bohr atomic model
Energy States:
Niels Bohr (Copenhagen Univ.), based
on Rutherford’s work, suggested a
quantized structure of electronic
orbits in an atom (1913)
Bohr and Werner Heisenberg later
(1926) modify structure to account
for the wave properties of
electrons.
Electron distances and energies
are discrete values
p+
E1
E2
E3
e-
Atoms and light
Electrons exist in `orbits` (much like
planets in the solar system) that are
stable at specific separations from the
nucleus.
Energy States:
The distance from the nucleus
determines the energy of the
electron (lower E is closer).
p+
E1
eThe spacing of these energy levels
is not even.
E2
E3
E1E2 > E2E3 > E3E4
etc…
Atoms and light
So what does all of this have to do with Bunsen and
Franhofer lines?
Atoms and light
Energy States:
If you heat the atom up to high
enough temperatures, the electron
will jump to higher orbits (higher
energy state).
p+
E1
E2
E3
e-
How does `heating` do this?
Collisions
Atoms and light
Energy States:
If you heat the atom up to high
enough temperatures, the electron
will jump to higher orbits (higher
energy state).
p+
How does `heating` do this?
Collisions
E1
eE2
E3
Atoms and light
After a time, the electron falls back to the
lowest energy state.
Energy States:
A photon is given off.
p+
E1
E2
E3
e-
The energy of the photon is
exactly equal to the energy
difference between the two
energy states.
Atoms and light: absorption
Process of emission is fully reversible.
Energy States:
Electron can absorb a photon and
jump to a higher energy level.
p+
E1
E2
E3
e-
The energy of the photon must
be exactly equal to the energy
difference between the two
energy states.
Atoms and light: absorption
Process of emission is fully reversible.
Energy States:
Electron can absorb a photon and
jump to a higher energy level.
The energy of the photon must
be exactly equal to the energy
difference between the two
energy states.
p+
E1
eE2
E3
Conservation of energy
The energy difference between electron orbital states is exactly equal to the
energy of the photon emitted or absorbed.
E2 – E1 = h f
Where E1 and E2 are the energies associated with the electronic orbital
states, f is the frequency of light, and h is Planck’s constant = 6.62 × 10–34
J•s
hydrogen energy level diagram
Quantized energy
• Different frequencies are perceived as different
colors
• Atoms of different elements have different
allowable energy level transitions and thus emit
and absorb different discrete colors.
• Example: Each line in the spectrum of iron is
different energy level transition
Iron
Types of spectra
Continuous: black body radiation
continuous
Absorption: requires a cool object
in front of a hot background
(ex: Fraunhofer) discrete
Emission: requires a hot object
with a cool background
(ex: Bunsen) discrete
Ionization:
e-
Energy States:
What happens if a very energetic
photon interacts with an atom?
p+
e-
Such a photon can give enough
energy to the electron that it can
escape the atom.
The amount of energy necessary
to do this is called the binding
energy of the atom.
Ionization:
e-
Energy States:
p+
e-
e-
When an atom absorbs light (or
thermal) energy greater than the
binding energy, the electron
escapes.
The atom is left with a
positive charge and is called
an ion.
Together, ions and free electrons
are called plasma.
Plasma is found in stars, space, and
parts of our atmosphere.
What about molecules?
Electronic
Energy States:
e-
Molecules are atoms that are
connected by bonds (electrons). At
a basic level a molecule will
behave similarly to an atom.
ep+
p+
p+
Molecules also have
discrete electron energy
levels.
p+
-
Like atoms, electrons in
molecules can absorb a
photon and move to a
higher energy level
What about molecules?
e-
Electronic
Energy States:
A photon with enough energy
can free an electron by
overcoming the binding energy.
p+
p+
p+
This produces a
molecular ion.
p+
e-
Plasmas can also contain
molecular ions.
Photo-dissociation
Electronic
Energy States:
Or overcome the molecular binding energy and break the
molecule up (photo-dissociation).
e-
p+
e-
p+
p+
e-
e-
p+
Vibrational modes
Electronic Energy States:
With molecules there`s an additional
complexity.
In addition to electronic energy
levels, molecules have
vibrational energy levels.
ep+
p+
p+
t1
p+
t2
e-
t3
p+
p+
p+
p+
Rotational modes
Electronic Energy States:
Moreover, each vibrational state
has separate rotational energy
sub-levels.
e-
Mode 1:
p+
p+
p+
p+
(Out of page)
e-
Mode 2:
p+
p+
(in plane of page)
The spectra of molecules are more
complex than atomic spectra
The energies differences between electronic, vibrational, and
rotational levels are different.
Eelectronic ~ 103 Evibrational ~ 106 Erotational
Vibrational and rotational transitions are triggered by absorption or
emission of light at specific energies, just like transmissions in atoms.
This has two consequences:
1) Molecules have many more transitions than atoms.
2) Molecule rotational- vibrational transitions involve light with much less
energy than atomic electronic transitions.
Electron energy levels in molecules
Vibrational
Rotational
n=2
n=1
Eelectronic ~ 103 Evibrational ~ 106 Erotational
So the Sun’s composition was determined and
turned out to be relatively simple
Though the composition is relatively
uniform, the Sun is layered by density
Working outward, the
dense core (where fusion
takes place) goes from 0
to 0.25 Rsun, followed by
the radiative zone (0.25
to 0.7 Rsun), topped by
the convective zone (0.7
to 1 Rsun). The visible
surface of the sun is
called the photosphere,
and the “atmosphere” of
the Sun has two layers,
the relatively thin
chromosphere and the
thicker, but less dense,
corona.
Energy transfer = moving the energy of
fusion at the core to the Solar System
• As the names of the layers
imply, it is not the composition
of the sun that is interesting,
but the manner in which
energy is transmitted from
layer to layer.
• This difference in manner of
energy transfer will be a direct
result of the lessening density
of the Sun outwards; in fact,
the outer edge of the
convective zone (the
photosphere) is far less dense
than the Earth’s atmosphere!
Conduction is heat transfer by…
1.
2.
3.
4.
Direct contact
Material flow
Photons
Phase change
Convection is heat transfer by…
1.
2.
3.
4.
Direct contact
Material flow
Photons
Phase change
The second law of thermodynamics
governs energy (heat) transfer
Heat transfers from a hot body to a cooler body. The
transfer can never be stopped, only slowed down.
Evaporation
Convection: heat exchange due to
material flow
Conduction: heat exchange due to
direct contact
Radiation: heat exchange due to
photons (light)
Phase change: heat exchange due to
substance changing phase (for
example, evaporation or melting)
The solar interior
• Starting Point: We can’t actually get to the interior of the Sun.
We have to model it, based on observations.
• Model Basis: We do know (some!) solar physics and we have
some boundary conditions that help us.
1) The Sun’s COMPOSITION
2) The Sun’s MASS
3) The Sun’s TEMPERATURE
4) The Sun’s AGE
Summary of the solar interior
The Sun’s interior can be broken down into a few
regions based on how energy (heat) transfers
1) Where it is hot and dense enough for fusion
2) Where it is hot and dense enough to prevent electrons from
staying with atomic nuclei
3) Where it is not hot and not dense enough to permit
electrons to combine with atomic nuclei
These conditions then tell us:
1) how energy escapes from the Sun.
2) how material moves inside the Sun.
The standard model for the Sun’s properties
Lead
Water
Deepest
Ocean
Trench
The solar core
• Extends out to 0.25 Rsun
• Contains ~50% of the
Sun’s mass.
• Contains ~2% of the Sun’s
volume.
• Is bounded (loosely) by the
point where temperature and
density are too low to support
P-P fusion.
Structure of the solar core
Core Boundary
Core Boundary
The division between the radiative and convective zones
Radiative
convective
Radiative
convective
Energy transfer in the core and radiative zone
Radiative diffusion, modeled as a “random walk”
• Occurs in the core and in the radiative zone.
• Light scatters randomly off free
electrons and nuclei. This means a
photon can bounce back towards
the core, as well as go outwards.
• This is a SLOW process.
• A photon produced by fusion in
the core today will take 105 – 106
YEARS to exit the radiative zone!
The convective zone
• Extends from 0.7-1.0 Rsun
• Contains ~2% of the Sun’s mass.
• Contains ~66% of the Sun’s volume.
• Contains hot, neutral gases where
electrons and nuclei are together but not as
atoms. Thus, the energy transfer involves
absorbing enough photons to cause an
increase in material temperature, which
decreases its density, which moves the mass
towards the surface.
• The convective zone is bounded by the point
where light (photons) directly escapes from the
solar atmosphere (photosphere).
Energy/mass transport in the convective zone
Energy in the convection zone is transported as a property
of the matter.
Rising
Falling
• Hot gas expands and loses
density, and so rises from deep
in the zone, cooling as it does.
Rising
Falling
Falling
• At the top of the zone, the gas
becomes cooler than its
surroundings, compacts and
sinks back down.
• These rising and falling regions form adjacent convective cells.
Time and Size Scales in the Convective
Zone:
• These cells release solar energy to the photosphere in a
pattern similar to the surface of a boiling liquid. The lifetime of
any given cell is ~10 minutes.
• The cell structure exists on many different sizes within the
zone, with the largest regions measuring up to 105 km across.
The blue regions represent cooler,
and thus sinking, parts of the
convective cell. The red regions
represent warmer, and thus rising,
parts of the convective cell. Note the
rough equivalence in total area
between the two colors.
Time and size scales in the convective zone:
Granules are convection
cells about the size of
Texas (image shows 1%
of the solar surface,
121,000 km2 )
Each granule delivers, in 5
minutes, the equivalent
of 1000 yr of electricity
produced by the
Hoover Dam
How long does it take photons created
in the core to escape from the Sun?
1.
2.
3.
4.
5.
1 sec
1 day
1 year
100 years
105 years
So how applicable is what we know about
the Sun to other stars?
After all, even the nearby stars don’t resemble the Sun for the most part!
Stars come in different colors and groupings
47 Tucunae
The Pleiades are an example of an open cluster
47 Tucunae is an example of a globular cluster
It was from those differences (mostly
color) that stellar classification began
• Charles Edward Pickering
directed the Harvard
Observatory in the late 19th
century.
• Over his lifetime, he took glass
plate photographs of over
300,000 stars.
• He also began taking the spectra
of stars.
• Much of the equipment he used,
he had to invent as he went
along
The Draper Catalog of stellar spectra was
the data source for star classification
• Annie Jump Cannon was
hired in 1896 by Pickering
to find similarities and
differences in stellar
spectra.
• Cannon (1900) invented
the “OBAFGKM” system
of classification, based on
the relative strengths of
various hydrogen
emission lines.
• Earned 25 cents/hour for
this work, but was named
to a professorship at
Harvard in 1938.
Quick reminder of what spectral “lines” are
hot, multispecies
source
hot, few
species
source
cold, few
species
sample in
front of
continuous
source
The first mathematical relationship in stars
• Henrietta Leavitt was hired
by Pickering in 1893 to
study variable stars – stars
that vary in intensity over
time cyclically.
• Leavitt (1908) found that a
certain type of variable star,
the Cepheid variable,
followed a simple rule: the
more luminous the star, the
longer the cycle of
dimming/brightening (the
luminosity period).
• Edwin Hubble would use
this to determine the
universe’s expansion.
So what did these early astronomers
measure about stars?
• Luminosity (absolute
brightness)
• Color
• Distance
Through mathematical relationships, we
can infer other properties of stars
Wien’s Law allows the calculation of a
star’s surface temperature based on its
spectral maximum intensity
wavelength.
The radius (size) of a star can be calculated
from its temperature and luminosity
But the most important relationship was the
one between luminosity and temperature
• Ejnar Hertzsprung and
Henry Norris Russell, in
1911 and 1913,
independently discovered
this relationship and
plotted it (The H-R
diagram).
• Nearly all the stars in the
Milky Way fell onto the
Main Sequence: the cooler
the star’s surface, the less
luminous it is.