The uses of the black body radiation curves --- I illustrated Wien's law with
three examples: infrared radiation (infrared "cirrus") that comes from cool
dust, with a characteristic wavelength (to make the calculation simple) of 30
microns (30 x 10-4 cm); x-rays from a supernova remnant, at a
wavelength of 3 Angstroms (= 3 x 10-8 cm); and the black body
rdiation from the sky, at a wavelength of 1mm (= 10-1 cm). In all
cases, this is presumed to be the wavelength of the peak of the
spectrum. Then Wiens's law gives the corresponding temperature invovlved: for
the IR source, T(K) = 0.3cm/(30 x 10-4 cm) = 100 K; for the x-ray
source, T(K) = 0.3cm/(3 x 10-8 cm) = 107 K; for the
background radiation, T(K) = 0.3cm/0.1cm = 3K. In other words, the sky
"background" is very cold (nearly absolute zero), x-ray processes are
very hot (millions of degrees) and infrared processes are quite cold (colder
than we're used to, but not absolute zero). To first order, a high
temperature suggests a very energetic environment, so we already know that
x-rays can be expected to herald very violent places in the Universe.
The study of stars ---- is worth it: we have come to realise that it is in
the stars that the chemical elements of the Universe are made; in other
words, we really are made of star stuff. It also necessarily requires a
long chain of reasoning, starting from simple observations of what are
essentially points of light in the sky. I said that, although stars seem to
come in all sizes, masses, colors, "luminosities", their properties can really
be understood once you know their initial mass (how much material went into
the star when it was formed) and their initial chemical composition
("metallicity"), or what atoms of what elements went into the newly-formed
star. This is an amazing simplification, and we'll get into the story
gradually. The other simplification of what seems initially like a very
complicated picture is that the very complicated looking spectra of stars
really mask a very simple result, namely that hydrogen is the most abundant
element in the Universe, when we look at the UNiverse on the biggest possible
scale ("cosmically"). This is quite unlike the reult of looking at our local
environment on Earth, where hydrogen is by no means the most common element.
It's no accident that hydrogen is also the simplest atom.
Line Radiation --- Under the right conditions, a substance will
emit light at discrete frequencies (wavelengths, photon energies) that are
completely unique to the element in question, and also to its state of
ionization (how many electron(s) are left in the atom). We saw this in
class. We talk about
"emission lines" from the element and we know through nearly two hundred years
of work a lot about what lines are given off by what elements. The simplest
example is pure Hydrogen gas which shows series of absorption or emission
lines, some in visible light (the Balmer series), some in the UV (the Lyman
series), IR (the Brackett series) and so on. The longest wavelength line in
each series is labelled as alpha, then beta, gamma and so on. (So the Balmer
series is H_alpha, (6563 Angstroms), H_beta, and so on. The Lyman series is
L_alpha (1216 Angstroms), L_beta, and so on.) The lines get closer together
at shorter wavelengths and finally come to a limiting wavelength. Each
element or ion has its own unique series of lines. This light at discrete
wavelengths is coming from inside the atom, and directly tells you about the
arrangement of electrons in the atom or ion, in particular, their allowed
energies.
Energy levels --- The key point is that electrons cannot have arbitrary
energies in the atom, but are constrained to be in orbits with discrete
energies characteristic of the atom or ion. When an atom or ion interacts
with light, it does so by changing the orbit of an electron and since only
certain energy transitions are possible for any atom or ion, so only photons
with the corresponding energies (wavelengths, frequencies of light) can be
involved. We call a diagram of the possible electron energies arranged
vertically with the lowest at the bottom an energy level diagram. The lowest
possible energy is called the ground state of the atom or ion and the others
are called excited states. When an atom or ion absorbs light, an electron
moves from a lower to a higher state, and the opposite is true for emission of
light. The allowed energy levels get closer together (in energy) at the
higher levels and eventually come to a limiting energy, the ionization
potential of the atom or ion, which is the amount of energy needed to
ccmpletely remove an electron from it. The observed series of spectral lines
are now explained as transitions to a given energy level. For Hydrogen, the
Lyman series is all transitions to the ground state, the Balmer series is all
transitions to the first excited state, and so on.
Kirchhoff's Radiation Laws --- are about the radiation observed from elements
in a variety of situations, and how these are related. Black body radiation
is given off from a solid (such as a filament in a light bulb) or a dense gas,
emission lines are given off from a hot rarefied gas , such as in a tube (as
we saw in the class demo), or in a nebula. Athird situation, which we didn't
demonstrate in class, is the situation that gives rise to the Fraunhofer lines
in the solar spectrum: when you look at a source of continuous radiation, but
look through a rarefied gas of some element, then you see absorption
lines superimposed on the continuous spectrum, and, moreover, they are at
the same wavelengths as the hot gas itself would emit. These
absorption lines (places where light is missing) are very important in the
spectra of the Sun and stars.
Modern spectrum of the Sun --- showed very many such absorption lines,
including the Balmer lines of hydrogen, but also including lines of many
different atoms and stages of ionisation. All stars show this type of
complicated pattern, and it is from this kind of information that we try to
deduce the material makeup and conditions in the sun and stars. One first
deduction is that the interior of the Sun must be hotter than the regions in
its "atmosphere" (the outer layers of the Sun) where the absorption lines are
produced. But we already know that the "surface" of the Sun is pretty hot ---
about 6000 Kelvin --- so the interior must be even hotter. This is the first
step toward understanding that it might be hot enough in the very cores of
stars (and the Sun) to form heavy elements by nuclear fusion from the lighter
elements, like hydrogen and helium. Understanding the stars is understanding
where the chemical elements came from.
Absorption Lines in Stellar spectra --- A hot, low density gas can remove
light from a hotter black body source of continuum radiation if it is in front
of it. It will remove the light at precisely the same wavelengths as it would
emit. Photons from the continuum source can be absorbed by electrons in the
gas if they have the correct energies to kick electrons into higher energy
levels. Although those electrons do eventually jump back down to lower
levls, and so emit photons again, the net effect is to remove light from
certain discrete wavelengths, producing so-called "absorption lines" in an
otherwise continuous spectrum.
This is the circumstance in the light coming from the Sun or a star.
The cooler upper reaches of the atmosphere absorb light coming from the opaque
region below, to give the Fraunhofer lines in the Sun and characteristic lines
in other stars.
Spectral Classification of Stars --- is a shorthand method of
reducing the complexity of the various sorts of stars to manageable types. The
spectra of stars show an underlying continuum that is nearly a black body at
a given temperature, with superimposed lines of various species, usually in
absorption but sometimes in emission. The spectra were first classified by Annie
Cannon and others at the Harvard College Observatory in the early part of this
century. They were given the names A, B, C, ... in order of decreasing
strength of the hydrogen Balmer lines.
These were later rearranged into the sequence O,B,A,F,G,K,M when it was realised
that the various patterns of absorption lines were characteristic of a given
temperature of the absorbing region in the star, and that the O stars
were the hottest, then B, A etc. Although Hydrogen is the most
abundant element in the absorbing region (atmosphere) of most stars, it is
not always present in the absorption lines of the spectrum because the temperature
may not be correct to give rise to the Balmer lines, in the sense that, in order
to produce Balmer absorption lines (Balmer because stars were classified using
visible-light spectra), there have to be electrons in the first excited
level inside the hydrogen atoms and this will only be true for a limited range of
temperatures. When the temperature is high, atoms collide with each other very
energetically and the energy absorbed kicks the electron to high energy levels,
whereas if the temperature is too low, the electron will stay in the ground
level and so
not be available for Balmer absorption. The same is true for other atoms and ions
present in the stellar atmosphere.
Abundances --- There is no obvious correlation between the strength (depth
and width) of
the lines present in a star's spectrum and the amount of that element in the
stellar atmosphere because of this temperature effect, but the abundances of
the elements in a given star can be extracted from the spectrum with some work.
Hydrogen and Helium (in that order) are the most abundant elements in the
Sun and indeed cosmically, with C, N, O, Fe also being abundant.
The Cosmic Abundance Curve --- is a plot of the cosmic abundances of the
elements against the atomic mass (the number of protons plus neutrons in the
atom's nucleus). It shows the overall trend that the simplest atoms are the
most abundant and, with some exceptions, the abundance falls off smoothly
toward the more complicated atoms. These patterns strongly suggest two
things: one, that there is something to explain --- i.e. the abundances of
the elements aren't just random; and two, that the elements have been
assembled somehow, starting from the simplest, so that more complicated atoms
are rarer. Understanding the origin of the elements is one of the triumphs of
20th century science. We'll get back to this soon.