Download Chapter 10. Stellar Spectra

Chapter 10. Stellar Spectra
Please read the Wikipedia articles linked on the ”Links” section of the Homepage, as
well. They will give you additional important insights into this chapter and the next one on
stellar magnitudes and the HR diagram.
Most of the light in the Universe at optical wavelengths (i.e. wavelengths that can be
seen by the eye) comes from stars. Historically, the optical spectrum was most studied because it is what our eyes detect and because it passes easily through the Earth’s atmosphere.
By contrast, ultraviolet and infrared light is largely absorbed in the Earth’s atmosphere and
could not be studied until the advent of balloon astronomy and space astronomy. The spectrum of galaxies is largely just the sum of the spectra of the billions of stars that comprise it,
although sometimes there are other components such as the interstellar medium and active
black holes at the centers of galaxies. Therefore, understanding stellar spectra is key to most
areas of astronomy.
Our study of the Hydrogen spectrum showed that light passing through Hydrogen gas
atoms may excite internal energy levels of the atom causing the absorption of photons of a
particular energy (wavelength). This produces ”absorption” lines in the spectrum of stars
as the light from their hotter interiors passes through their cooler atmospheres (see lecture
slide on Kirchoff’s laws). The lines visible in any star’s spectrum depend on the chemical
composition of the atmosphere, but also on the temperature and pressure of the atmosphere.
Sometimes elements that are very abundant (e.g. Helium in the solar atmosphere) are not
evident in the spectrum because the temperature and/or pressure of the gas is not right for
the excitation of the atom to levels needed to absorb optical light. On the other hand, we
sometimes see strong lines due to atoms of very low abundance (e.g. Lithium) because the
internal energy levels of that atom happen to be conducive to absorbing optical photons of the
proper energy given the temperature and pressure of the solar atmosphere. Understanding
the differences in the appearance of stellar spectra that arise because of temperature, pressure
and composition differences in their atmospheres is decades of fun!
1.
Spectral Classification
Early studies of stellar spectra, done approximately 100 years ago, immediately revealed
a variety of different ”types” of spectra. Note that these observations were, of necessity, done
in the optical part of the spectrum. Hence, the dominant feature was the Balmer lines of
Hydrogen (since H is the most abundant element and since transitions from the n=2 level
to high levels – Balmer transitions – have energies that put them in the optical part of the
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spectrum). Stars showing the strongest Balmer lines were called ”A” stars. Those with
weaker lines were labeled ”B”, ”F”, ”G”, etc. using various letters of the alphabet. Our
modern classification scheme retains many of these letter classes, although not all of them,
and adds a number, or ”subclass” that divides each spectral class into about 10 subclasses.
These are just finer gradations of the classification scheme.
It was discovered in the 1920’s that the dominant parameter that made one spectral
class different from another was ....... temperature. The classes were then re-organized into
a temperature sequence, which is the basis of the modern classification. It runs like this
(where I have not shown all the subclasses)
O3, O4, ...O9, B0, B1, ...B9, A0....A9, F0...F9, G0...G9, K0....K9, M0...M9, L, T
Not all numbers are used and sometimes a decimal is added for even finer division (e.g.
a B1.5 star is between a B1 and a B2 star). The L and T stars are extremely cool recent
additions to the scheme. These ”stars” are probably actually ”brown dwarfs” since their core
temperatures are unlikely to be high enough for the nuclear fusion of Hydrogen to Helium.
One pneumonic device for remembering the odd order of the letters (not including L and T)
is: Oh Be A Fine Guy (or Girl) Kiss Me.
Since stellar spectra depend not only on the temperature of the stellar atmosphere but
also on its pressure, there is a second parameter that is needed to classify them. This is called
the ”Luminosity Class” and is designated by a Roman Numeral in the modern classification
scheme. The names associated with luminosity class are as follows: I – supergiant; II - bright
giant; III - giant; IV - subgiant; V - dwarf. A full classification consists of the spectral class,
spectral subclass and luminosity class. An example is the Sun, whose classification is G2V.
2.
Understanding the Temperature Sequence
A basic understanding of the behavior of the Hydrogen lines with stellar temperature
(and, note that this is the surface temperature of the star, not its interior temperature, which
can be millions of degrees) is as follows. Hydrogen lines in the optical part of the spectrum
come from the Balmer lines, which are transitions from the first excited state (n=2) to higher
levels. Their strength depends on the abundance of HI (neutral Hydrogen) in the n=2 (first
excited state). This is a maximum at a temperature of around 10,000 K, characteristic of
A stars. A stars therefore have the strongest H lines (this is, in fact, why they were called
A stars). Hotter stars (O and B stars) have weaker H lines because more of the Hydrogen
is excited to higher levels and/or ionized (creating HII). Recall that at higher temperatures,
all atoms and electrons are moving more rapidly (have higher kinetic energy) so that when
–3–
they collide with one another they can excite the other atoms to higher energy states and/or
ionize them.
For stars of lower temperature than A (i.e. the FGK and M stars) the Hydrogen is
mostly still in the ground state. There is not enough kinetic energy around, in general, or
photons of high enough energy to excite the atoms to n - 2. Hence, although there is a lot
of HI, there is not a very strong set of Balmer lines, because there are not a lot of HI atoms
in the n=2 state to absorb photons of the right energy.
Similar things apply to the other atoms but they have much different energy level
diagrams. For example, the optically visible lines in Helium also arise from excited states,
but the energy needed to excite those states is much higher than the energy needed to get
HI to the n=2 level. Hence, Helium is often hard to see in stars. Only the hottest stars
(O and B stars) show lines of Helium, even though it is the second most abundant atom
in the atmospheres of almost all stars. Note that Helium also has two ionization states. In
its neutral state (HeI) it has 2 electrons. It can lose one of those, in which case it becomes
HeII, or singly ionized Helium. We see lines of HeI in B stars, which are hotter than A stars,
but not as hot as O stars. We see lines of HeII in O stars. These are the distinguishing
characteristics of these classes of stars and, once the lines can be identified, this helps us
understand how to sort the spectral classes in terms of temperature.
Some lines of some “metals” (for astronomers, the term metals is used for everything
other than Hydrogen or Helium – no one ever said we were good chemists!), such as Sodium
(Na) there are lines visible in the optical region of the spectrum that arise from the ground
state of the neutral atom (NaI). Hence, it turns out that the NaI line (or lines) can be
extremely strong in stars of the right temperature (e.g. the Sun), even though sodium is
way less abundant that, say, helium. Similarly, some metals, such as calcium have optical
transitions from the ground state of one of the ionized stages of the atom, in this case CaII
(the singly ionized Ca atom). Hence, we see strong lines in the Sun due to singly ionized
Ca, although, again, it is not nearly as abundant as helium or many other atoms.
In this way, the interpretation of stellar spectral types (the term “spectral type” is used
to indicate spectral class plus luminosity class) in terms of surface temperature and surface
pressure (or radius, as we shall see) has been developed. It turns out that most stars have
about the same chemical composition in the stellar atmospheres (surfaces). By mass, they
are about 73% Hydrogen and 25% Helium and 2% metals. Some stars tend to be more metal
poor – i.e. down to only a fraction of a percent of metals, but none are much richer in metals
and all have about the same proportion of H and He. What makes one star’s spectrum
different from another star’s spectrum is primarily temperature and pressure (radius). Of
course, these remarks apply to “normal” stars – the vast majority. Naturally, there are
–4–
some odd balls that go against the trend, but these are covered later (or not at all in this
introductory course!)
3.
Relationship between Spectral Type and Luminosity of a Star
One of the great advantages of the two-dimensional (spectral class plus luminosity class)
aspect of the spectral classification scheme is that it is sufficient to specify the luminosity of
a star. To understand the reason, we recall that the spectrum of a star is approximately the
same as the spectrum of a black body (i.e. the Planck law) at the same temperature. The
Stefan-Boltzmann law for black bodies comes from integrating the flux at all wavelengths
and tells how the total flux (represented here by F) varies with temperature (T), namely
F = σT 4 .
Recall that σ is the Stefan-Boltzmann constant.
The flux is the energy per unit time per unit area (e.g. joules/sec/m2 or watts/m2 ).
The luminosity of a star is its total power output (i.e. its wattage if it were a light bulb) and
is measured in Watts (in the mks system). To go from flux (F) to luminosity (L) we need
to multiply by the area of the star, which for a sphere of radius R is 4πR2 . Combining with
the Stefan-Boltzmann equation, we have the fundamental equation for the luminosity of a
star, that depends on its surface temperature and size, namely
L = 4πR2 σTe4
Note that we have written the temperature here as “effective temperature” (Te ). This
recognizes that it is not really appropriate to assign a single temperature to the atmosphere
of a star – many different layers, at different temperatures, contribute to the visible light that
we see. Therefore, we refer to the effective temperature of the atmosphere as the temperature
of a Black Body that would have the equivalent flux (watts per square meter) as the star
does. Note also that we assume when we write the equation above that the star is spherically
symmetric and radiates exactly the same amount of flux in all directions. This is generally
true for most normal stars.
We see then, that the spectral type of a star should be well correlated with its luminosity, since the spectral type has two parameters, T and pressure, and L depends on two
parameters, T and R. Since pressure depends on R (a large star has a lower surface gravity
and therefore a lower pressure), there is essentially a one-to-one correspondence between L
and spectral type. Astronomers slip back and forth between radius and luminosity all the
time, even in the way we name the luminosity classes:
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I - supergiant
II - bright giant (mixed terminology!)
III - giant
IV - sub-giant
V - dwarf
As an example, the Sun is a G2V star and has a certain luminosity (wattage). All other
G2V stars have the same luminosity (to within our ability to determine it!) All B2V stars,
also have the same luminosity and that is much larger than the luminosity of a G2V star.
All BI stars (i.e. B supergiants) have much larger luminosity than all B2V stars, etc. etc.