ASTR 400/700:
Stellar Astrophysics
Stephen Kane
Absorption lines in the Sun’s spectrum
(Fraunhofer lines)
The hydrogen atom
The Formation of
Spectral Lines
Chapter 8.1
Pioneers of Stellar Classification
• Edward Pickering,
Annie Jump
Cannon and the
“calculators” at
Harvard laid the
foundation of
modern stellar
classification.
The spectra of stars reveal their chemical
compositions as well as surface temperatures
• Stars are classified into
spectral types
– divisions of the spectral
classes
• O, B, A, F, G, K, and M
– Subclasses
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The original letter
classifications originated
from the late 1800s and
early 1900s
Lines in a star’s spectrum correspond to a spectral type
that reveals its temperature:
(Hottest)
O B A F G K M
(Coolest)
•The spectral class of a star is directly related to its
surface temperature
– O stars are the hottest
– M stars are the coolest
Spectral Lines
• Balmer lines are associated
with electronic transitions in
Hydrogen atom’s first excited
state n=2. Balmer lines reach
their maximum “intensity” in
the spectra of A0 stars with
T=9250 K
• Neutral Helium lines are
strongest for B2 stars with
T=22,000K
• Singly ionized calcium are most
intense for K0 stars with
T=5250 K
• Another fine astronomical
convention: METAL is any
element heavier than
helium!!!!!!
Understanding Spectral Lines
Need to understand…
• The atom
• Statistical Mechanics
First excited state occupancy for hydrogen
atom from Boltzmann Equation
Atomic Transitions
Boltzmann Energy Distribution
Saha Ionization Equation
Maxwell-Boltzmann Velocity Distribution
The root-mean-squared is the square root
of the average value of v2
vrms = < v2 >
The Boltzmann Equation
The probability distribution of a system
occupying a given energy state may be
described by the Boltzmann Factor…
The Saha Equation
• Ionization levels depend on:
– Temperature
– Density/Pressure
– Ionization Energy from
given level
– Degeneracy of levels
–
Number of Excited Hydrogen Atoms
• Convolution of Boltzmann and
Saha Equations
• Maximum occurs at 9900K due
to lack of un-ionized atoms
above this temperature
A star’s full classification includes spectral
type (line identities) and luminosity class (line
shapes, related to the size of the star):
I
II
III
IV
V
— supergiant
— bright giant
— giant
— subgiant
— main sequence
Examples: Sun — G2 V
Sirius — A1 V
Proxima Centauri — M5.5 V
Betelgeuse — M2 I
Luminosity Class Implies Size
• Consider the Sun and Capella
The Sun
G2V M=5
Capella
G2III M=0
Luminosity Class Implies Size
• Equal sized pieces of each star are equally
bright
• Capella is 100X brighter (5 magnitudes)
• Capella must have 100X as much area
• Surface area ∝ radius2
• Capella must be 10X larger than Sun.
By carefully examining a star’s spectral lines, astronomers
can determine whether that star is a main-sequence star,
giant, supergiant, or white dwarf
Luminosity Classes
The width of the absorption lines in a star’s spectrum
indicates its density. The thinner the line the less
the density.
Supergiants & Giants are the least dense.
In general the less dense a star is the more luminous it
will be (because it has more surface area).
Luminosity and the thickness of the absorption lines
are combined to group stars into Lumniosity
Classes.
Luminosity Classes are combined with spectral class
to describe Stars. The Sun is Class V so …
The Sun is a “G2 V” star.