Transcript Lecture4 - University of Waterloo

Matter and atomic structure
• Blackbody radiation
• Spectral lines
• States of matter
Review
• Resonances cause certain orbits to be either stable or unstable
 This gives rise to ring gaps, asteroid belt, etc.
 Can eject bodies from the solar system
• Tidal forces
 Control rotation of some moons and planets
 Can be a strong source of internal heating (e.g. Io)
 Make it difficult to form large bodies (e.g. moons) within the Roche
limit
• Radiation pressure and the solar wind can drive small particles out
of the solar system
Today’s lecture
• What is the solar system made of? What are the elements?
The wave nature of light
http://micro.magnet.fsu.edu/primer/java/polarizedlight/emwave/
Brief review:
 The wavelength of light (λ) is related to
frequency (n) by
c  n
 A photon’s energy is given by:
E  hn
Atmospheric transparency
The Earth’s atmosphere blocks most wavelengths of incident radiation very
effectively. It is only transparent to visual light (obviously) and radio
wavelengths.
Observations at other wavelengths have to be made from space.
Properties of blackbody radiation
1.
The wavelength at which radiation
emission from a blackbody peaks
decreases with increasing
temperature, as given by Wien’s
law:
max T  0.290 cm K
2. The total energy emitted (luminosity) by a blackbody with
area A increases with temperature (Stefan-Boltzmann
equation)
This defines the effective temperature of a star with
radius R and luminosity L
L  ATe4
 4R 2Te4
Examples
Although nothing in the Universe is a
perfect blackbody (they always absorb
certain wavelengths of light more
efficiently than others), we can get
some insight into the radiative
properties of most objects
The human body has a temperature of
37 C, or 310 K. Calculate the total
power radiated, and the rate of net
energy loss. At what wavelength is this
energy radiated?
max T  0.290 cm K
L  4R 2Te4
Examples
The sun has a luminosity L=3.826×1026
W and a radius R=6.96 ×108 m. What
is the effective temperature? At
what wavelength is most of the energy
radiated?
max T  0.290 cm K
L  4R 2Te4
Spectroscopy
•Although astronomy has been practiced for thousands of years, it
consisted mostly of observing and cataloguing the motions of stars.
•The use of spectroscopy to determine the properties of stars (c.a. 1814)
allowed astronomers to investigate the the stars scientifically.
The solar spectrum
Spectroscopy
In 1814, Joseph Fraunhofer catalogued
475 sharp, dark lines in the solar spectrum.
• Discovered but misinterpreted in
1804 by William Wollaston
• Spectrum was obtained by passing
sunlight through a prism
Spectral lines
The wavelength of one particular line in the solar spectrum (at 589
nm) was found to be identical to the wavelength emitted by sodium
(for example when salt is sprinkled on a flame).
Na D
Bunsen & Kirchoff designed a spectroscope and studied the
wavelengths of light emitted and absorbed by various elements
Atomic spectroscopy
Bunsen & Kirchoff found that each atom emits light in a unique
spectral fingerprint:
Neat java tool
The spectrum of a Helium
lamp obtained by grating
spectroscopy.
Kirchoff’s laws
1. A hot, dense gas or hot solid object produces a continuous spectrum
with no dark spectral lines (a blackbody)
2. A hot, diffuse gas produces bright spectral emission lines
3. A cool, diffuse gas in front of a source of a continuous spectrum
produces dark absorption lines in the continuous spectrum
Atomic absorption and emission
• The electrons of an atom occupy restricted regions around the
nucleus – called shells, or orbitals, or energy levels.
• Generally the electrons occupy the lowest possible orbital/energy
level but they will sometimes change to a higher level if they gain
enough energy from an incoming photon.
• The photon must have the right amount of energy to match the
energy difference between the electron’s first energy state and
the one it moves to.
E  hn 
2c

E  hn 
2c

• When this transition occurs, energy at the specific transition frequency is lost
from the radiation field –absorption has occurred.
• An excited electron will readily drop down to a lower energy level, emitting
radiation of a frequency/wavelength corresponding to the energy difference –
emission.
Spectral analysis
Thus the identification of absorption lines in stellar spectrum can
tell us about the chemical composition of stars
The presence of unidentifiable absorption
lines in the Sun’s spectrum led to the
prediction of a new element, Helium
(from Helios = Sun). Later this was
isolated on Earth and the prediction was
confirmed.
(However a similar, later prediction for a
new element called coronium was found
to be false. These lines are due to iron
but under conditions not found on Earth)
Example: the solar spectrum
What elements are present in the Sun?
Solar spectrum
Example: the solar spectrum
What elements are present in the Sun?
Balmer lines
Example: the solar spectrum
What elements are present in the Sun?
NaD
Example: the solar spectrum
What elements are present in the Sun?
Ca H+K
Example: the solar spectrum
So: the Sun is mostly calcium, iron and sodium?? No! Not quite that simple…
Solar spectrum
Molecules
• Like atoms and ions, molecules also emit or absorb light at specific
wavelengths, corresponding to different rotational and vibrational
states.
• The energy jumps in molecules are usually smaller than those in
atoms and therefore produce lower-energy photons. Thus, most
molecular bands lie in the infrared rather than in the visible or
ultraviolet.
This spectrum of molecular hydrogen (H2) shows that molecular
spectra consist of lines bunched into broad molecular bands.
Doppler shifts
Doppler shifts of the spectral lines yield the radial (i.e. toward the
observer) velocity of the star
obs  rest
1  vr / c
1  vr / c
obs  rest 
z

rest
rest
vr ( z  1) 2  1

2
c ( z  1)  1
 z if z  1
Doppler shifts: examples
1.
Typical stars in the solar neighbourhood have velocities ~25 km/s.
What is the size of their doppler shift?
Doppler shifts: examples
2.
Extragalactic objects (mostly galaxies and quasars) are strongly redshifted due to
the expansion of the Universe. The most distant object currently known is quasar
SDSS1148+5251, with z=6.42. Since z is not small, we have to use the full
expression:
Elemental abundances
• The chemical
compositions we find
for stars and gas
clouds are somewhat
surprising: ≥98% of
the mass is made up of
hydrogen and helium
alone!
• The elements which
are most abundant
around us, such as
carbon, nitrogen, iron
…, represent only 2%
(or less) of the matter
in the Universe.
• This abundance picture is true for our Sun but
not for most members of the SS. How can that
be? Why is our Earth so different in
composition from the Sun and other components
of the galaxy in which we exist?
States of Matter
• Matter can be in different states,
depending on how tightly bound the
atoms are.
• Changes in phase require the breaking
of a binding force
• For our purposes, we are mostly
concerned with gases, solids and (to a
lesser extent) liquids.
States of Matter
• Matter can coexist in different phases. At the triple
point, gas, solid and liquid coexist.
Phase diagram for water
States of Matter
• The phase diagram for different elements
tells us what phase they will be found in
under given conditions.
• Knowing the triple point and critical point
alone allow a rough estimate of the phase
diagram.
Phase diagram for water
Phase diagram for hydrogen
Gases
Ideal Gas Law: relates pressure, density and
temperature
kT
P  nkT 
mH
Where n is the number density and  is the mass
density of the gas.  is the mean molecular weight.
• Such an equation, relating pressure, density and
temperature, is known as an equation of state.
• The equation of state for solids and liquids is generally
much more complex and/or poorly known.
Solids
• Minerals are substances that occur naturally and include no
organic (animal or vegetable) compounds.
 The most commonly occurring minerals are made of the most
commonly occurring elements”
 In the inner SS these are dominantly O, Si, Mg, and Fe with lesser
amounts of things like Na, Al, Ca, and Ni.
 The minerals we find are vastly dominated by SiO4 – these are called
silicates.
• Rocks are solids made of more than one mineral and the mix of
minerals in rocks varies from one part of the SS to another and
well as within a given body.
• Ices are solids whose composition consists of the abundant
elements C,N,O in combination with H.
 These compounds (water, carbon dioxide, methane, ammonia etc.)
freeze at different temperatures; strictly speaking these are also
minerals but are referred to as ices because of their low
solidification temperatures.
 Most common in the outer SS beyond ~3AU from the Sun.
Silicates
• The main silicate families are olivines, pyroxenes and feldspars.
They are distinguished from each other by which elements are
present and how complex are their crystalline structures.
Olivine
• simplest silicate
• SiO4 + Fe and/or
Mg
• Most dense silicate
• High melting point
Pyroxene
• chains of SiO4 + Fe,
Mg, Al, Ca…
Feldspars
• SiO2 + K, Al, Na, Ca…
• Least dense silicate
• Low melting point
Rocks
• Igneous
 Formed directly from cooling
of molten magma
• Sedimentary
 Deposition or cementing of
small particles
• Metamorphic rocks
 Originally formed as igneous or
sedimentary, but changed to a
new form by high pressure,
high temperature or addition
of new chemicals
Ices
• solids that contain C,N,O – which are gaseous at T≥200K
• CNO overall more abundant than Fe,Mg,Ca,Al,Na…
 but Fe,Mg,…condense into grains at much higher T
• ices are more abundant in outer SS objects – i.e. satellites,
comets, some asteroids, Kuiper Belt…
• commonest ices: CH4 (methane), NH3 (ammonia), H2O (water)
• vapourous “at the least excuse”
• Core of Halley’s comet
shown outgassing as
Sun heats the ice
Next Lecture
The Sun and other stars
• Colours and luminosities: the Hertzsprung-Russel diagram
• Hydrostatic equilibrium
• The source of stellar luminosity
• Energy transport
• The lifetime of stars