PH507
Astrophysics
Professor Michael Smith
1
WEEK 6 (18).
TEST: Tuesday 9:05 Week 19.
TEST TOPICS INCLUDE:
Extrasolar planet detection
Spectral types
Parallax, cosmic ladder
Opacity
Magnitudes and luminosity
ASSIGNMENT 4: deadline Week 18
SPECTRAL LINES
RADIATION PROCESSES
HR DIAGRAMS
STELLAR EVOLUTION
Stellar Atmospheres – The Sun
Formation of solar absorption lines. Photons with energies well away from
any atomic transition can escape from relatively deep in the photosphere,
but those with energies close to a transition are more likely to be reabsorbed
before escaping, so the ones we see on Earth tend to come from higher,
cooler levels in the solar atmosphere. The inset shows a close-up tracing of
two of the thousands of solar absorption lines, those produced by calcium
at about 395 nm.
PH507
Astrophysics
Professor Michael Smith
2
Apparent paradox: how can the solar limb appear darkened when the
temperature rises rapidly through the chromosphere? Answering this question
requires an understanding of the concepts of opacity and optical depth. Simply
put, the chromosphere is almost optically transparent relative to the
photosphere. Hence, the Sun appears to end sharply at its photospheric surface
- within the outer 300 km of its 700,000 km radius.
Our line of sight penetrates the solar atmosphere only to the depth from which
radiation can escape unhindered (where the optical depth is small). Interior
to this point, solar radiation is constantly absorbed and re-emitted (and so
scattered) by atoms and ions.
Spectral line formation
• Lines form higher in atmosphere than continuum. For optical lines this
corresponds to lower temperature than continuum and therefore lower
intensity (absorption lines, where S < I).
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Astrophysics
Professor Michael Smith
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small
6500
~2/3 low in
atmosphere
T (K)
high
~2/3 high in
atmosphere
4500
F

0
200
400 km
Height above photosphere
Spectral line strength & profile
Spectral lines are never perfectly monochromatic. Quantum
mechanical considerations govern minimum line width, and
many other processes cause line broadening.
Shape of absorption line — line profile.
Natural broadening — consequence of uncertainty principle.
Doppler broadening — consequence of velocity distribution.
Pressure broadening — perturbation of energy levels by ions.
• For abundance calculations we want to know the total line
strength. Total line strength is characterised by EQUIVALENT
WIDTH.
� Equivalent width: measure strength of lines.
� Rectangle with same area as line, i.e. same amount of
absorption.
� EW is width in °A across rectangle. The equivalent width is thus
measured in wavelength unit (in angstroms for example).
� Need EW to determine number of absorbing atoms
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Astrophysics
Professor Michael Smith
4
A Maxwellian velocity distribution: the line shape is Gaussian.
Full Width at Half Maximum (FWHM) is the width measured at half level
between the continuum and the peak of the line. The FWHM is expressed
either in wavelength unit or in speed unit. The width in km/sec is given by
c *FWHM /wavelength,
with c the speed of the light = 3.105 km/s). Example, suppose that the
FWHM is of 2A at 6563A, the equivalent resolved velocity is about 90
km/s.
Notice that the FWHM measured has to be corrected for instrumental
width: target profile is convolved with instrumental profile.
Stellar composition
Derived from spectral line strengths in stellar atmospheres.
Spectroscopy shows that hydrogen makes up about 94% of the
solar material, helium makes up about 6% of the Sun, and all the
other elements make up just 0.13% (with oxygen, carbon, and
nitrogen the three most abundant ``metals''---they make up
0.11%).
In astronomy, any atom heavier than helium is called a ``metal''
atom. The Sun also has traces of neon, sodium, magnesium,
aluminum, silicon, phosphorus, sulfur, potassium, and iron.
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Astrophysics
Professor Michael Smith
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The percentages quoted here are by the relative number of atoms.
If you use the percentage by mass, you find that hydrogen makes
up 78.5% of the Sun's mass, helium 19.7%, oxygen 0.86%,
carbon 0.4%, iron 0.14%, and the other elements are 0.54%.
Published data on stellar composition show that carbon in the sun is
substantially more abundant than in other stars. A carbon abundance of
225 carbon atoms per 10 hydrogen atoms is representative of galactic
stars, whereas published values for the sun range from 350 to 470
carbon atoms per 10 hydrogen atoms. Other elements are also present in
enhanced quantities in the solar system, consistent with suggestions that
a supernova event was closely associated with the formation of the
solar system.
Spectral line structure
• NATURAL WIDTH: Due to uncertainty principle, E=h/t,
applied to lifetime of excited state. For "normal" lines the atom is
excited (by a photon or collision) to an excited state which has a
short lifetime t ~ 10-8 s. The upper energy level therefore has
uncertain energy E and the resultant spectral line (absorption or
emission) has an uncertain energy (wavelength). The line has a
Lorentz profile,  ~ 10-5 nm for visible light.
• COLLISIONAL/PRESSURE BROADENING:
Outer energy levels of atoms affected by presence of neighbouring
charged particles (ions and electrons). Random effects lead to
line broadening since the energy of upper energy level changes
relative to the unexcited state energy level. This is the basis of the
Luminosity classification for A,B stars. Gaussian profile.  ~
0.02 - 2 nm.
• DOPPLER BROADENING:
Due to motions in gas producing the line. Doppler shift occurs
for each each photon emitted (or absorbed) since the gas
producing the line is moving relative to the observer (or gas
producing the photon).
Thermal Doppler broadening due to motions of individual atoms
in the gas. ~0.01 - 0.02 nm for Balmer lines in the Sun. Gaussian
profile.
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Astrophysics
Professor Michael Smith
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Bulk motions of gas in convection cells. Gaussian profile.
• ROTATION:
If there is no limb darkening, then lines have hemispherical
profile due to combination of radiation from surface elements
with different radial velocities. Effect depends on rotation rate,
size of star and angle of polar tilt.
In general, V sin i is derived from the profile.
_
V -1
(km s )
200
Receding
+V
A
F

C
B
A
C
B
Approaching
-V
100

o
0
O B A F G K
• ATMOSPHERIC OUTFLOW:
Many different types.
Star with expanding gas shell (result of outburst) gives P-CYGNI PROFILE.
Continuum (+ absorption lines) from star, emission or absorption lines from
shell:
F
Expanding
gas
shell

D
C
Star
D
B
D
A
o

Observer
B
C
A
C
B
Radiation from star, A, passes through cooler cloud giving absorption line
due to shell material which is blue shifted relative to star. Elsewhere,
emission lines are seen.
Be STARS: Very rapid rotators with material lost from the equator:
Radiation from star, A, passes through cooler cloud giving absorption line.
Overall line structure is hemispherical rotation line (B,D). Emission lines
seen due to shell material (C,E).
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Astrophysics
Professor Michael Smith
C
F
Rotating
gas
shell
7
E
Star
B
A
o
D

Observer
C
B
A
D
E
Forbidden lines
• Only certain transitions are generally seen for two reasons:
1) Outer energy levels are far from the nucleus so in dense gases,
levels are distorted or destroyed by interactions.
2) Selection rules for change of quantum numbers restrict possible
transitions.
• In fact forbidden transitions are not actually forbidden. However,
the probability of a forbidden transition is very low, so an
allowed transition will generally occur.
The lifetimes in an excited state for which there are no allowed
downward transitions are ~10-3 - 109 seconds (ie very low
transition probability). These are called METASTABLE STATES.
• De-excitation from a metastable state can be by:
1) Collisional excitation, or absorption of another photon to
higher energy state allowing another downward transition to the
equilibrium state,
2) FORBIDDEN TRANSITION producing a FORBIDDEN LINE.
Usually denoted with [], e.g. [OII 731.99].
• Forbidden lines are usually much fainter than those from allowed
transitions due to low probability.
• In interstellar nebulae excited by UV from nearby hot stars, some
elements' excited states have no allowed downward transitions to
the ground state. In the absence of frequent collisions (due to low
density) or high photon flux, a forbidden transition is the only
way to the ground state.
• These lines were not understood for a long while. A new element
Nebulium was invented to account for them.
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Astrophysics
Professor Michael Smith
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Radiation Mechanisms
1. 21 cm: radio, spectral line.
Hydrogen gas is observed in a variety of states: in ionized, neutral
atomic, and molecular forms.
The ionized hydrogen emits light in the visible band as the
electrons recombine with the protons.
Neutral atomichydrogen emits light in the radio band of the
electromagnetic spectrum.
Molecular hydrogen emits in the infrared.
Most of the hydrogen in space (far from hot O and B-type stars) is
in the ground state. The electron moving around the proton can
have a spin in the same direction as the proton's spin (i.e.,
parallel) or spin in the direct opposite direction as the proton's
spin (i.e., anti-parallel). The energy state of an electron
spinning anti-parallel is slightly lower than the energy state of a
parallel-spin electron.
Remember that the atom always wants to be in the lowest energy
state possible, so the electron will eventually flip to the antiparallel spin direction if it was somehow knocked to the parallel
spin direction. The energy difference is very small, so a hydrogen
atom can wait on average a few million years before it undergoes
this transition.
The two levels of the hydrogen 1s ground state, slightly split by
the interaction between the electron spin and the nuclear spin.
The splitting is known as hyperfine structure.
Even though this is a RARE transition, the large amount of
hydrogen gas means that enough hydrogen atoms are emitting the
21-cm line radiation at any one given time to be easily detected
with radio telescopes. Our galaxy, the Milky Way, has about 3
billion solar masses of H I gas with about 70% of it further out in
the Galaxy than the Sun. Most of the H I gas is in disk component
of our galaxy and is located within 720 light years from the
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Astrophysics
Professor Michael Smith
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midplane of the disk.
What's very nice is that 21-cm line radiation (1420 MHz) is not
blocked by dust! The 21-cm line radiation provides the best way
to map the structure of the Galaxy.
See:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html
NGC5055 This is illustrated in the picture: it shows the stars (yellow) in the
galaxy NGC 5055, while the blue shows the distribution of the neutral gas.
2. Thermal free-free or Bremsstrahlung emission
(continuous, from radio to X-rays)
Another form of thermal emission comes from gas which has been
ionized. Atoms in the gas become ionized when their electrons
become stripped or dislodged. This results in charged particles
moving around in an ionized gas or "plasma", which is a fourth state
of matter, after solid, liquid, and gas.
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Astrophysics
Professor Michael Smith
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As this happens, the electrons are accelerated by the charged
particles, and the gas cloud emits radiation continuously. This type
of radiation is called "free-free" emission or "bremsstrahlung".
2. Synchrotron radiation (continuum)
Non-thermal emission does not have the characteristic signature
curve of blackbody radiation. In fact, it is quite the opposite, with
emission increasing at longer wavelengths.The most common form
of non-thermal emission found in astrophysics is called synchrotron
emission. Basically, synchrotron emission arises by the acceleration
of charged particles within a magnetic field. Most commonly, the
charged particles are electrons. Compared to protons, electrons
have relatively little mass and are easier to accelerate and can
therefore more easily respond to magnetic fields.
As the energetic electrons encounter a magnetic field, they
spiral around it rather than move across it. Since the spiral is
continuously changing the direction of the electron, it is in effect
accelerating, and emitting radiation. The frequency of the emission
is directly related to how fast the electron is traveling. This can be
related to the initial velocity of the electron, or it can be due to the
strength of the magnetic field. A stronger field creates a tighter
spiral and therefore greater acceleration.
For this emission to be strong enough to have any astronomical
value, the electrons must be traveling at nearly the speed of
light when they encounter a magnetic field; these are known as
"ultrarelativistic" electrons”. (Lower-speed interactions do
happen, and are called cyclotron emission, but they are of
considerably lower power, and are virtually non-detectable
astronomically).
As the electron travels around the magnetic field, it gives up energy
as it emits photons. The longer it is in the magnetic field, the more
energy it loses. As a result, the electron makes a wider spiral
around the magnetic field, and emits EM radiation at a longer
wavelength. To maintain synchrotron radiation, a continual supply
of relativistic electrons is necessary. Typically, these are
supplied by very powerful energy sources such as supernova
remnants, quasars, or other forms of active galactic nuclei (AGN).
It is important to note that, unlike thermal emission, synchrotron
emission is polarized. As the emitting electron is viewed side-on in
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Astrophysics
Professor Michael Smith
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its spiral motion, it appears to move back-and-forth in straight lines.
Its synchrotron emission has its waves aligned in more or less the
same plane. At visible wavelengths this phenomenon can be viewed
with polarized lenses (as in certain sunglasses, and in modern 3-D
movie systems).
The radiation typically includes radio, infrared, optical, ultraviolet, x-rays.
The Crab: recombination (red) and synchrotron (blue), VLT image
3. Inverse Compton radiation (X-rays)
Inverse Compton scattering is important in astrophysics. In X-ray
astronomy, the accretion disk surrounding a black hole is believed to
produce a thermal spectrum. The lower energy photons produced from
this spectrum are scattered to higher energies by relativistic
electrons in the surrounding corona. This is believed to cause the
power law component in the X-ray spectra (0.2-10 keV) of accreting black
holes.
The effect is also observed when photons from the Cosmic microwave
background move through the hot gas surrounding a galaxy cluster. The
CMB photons are scattered to higher energies by the electrons in this gas,
resulting in the Sunyaev-Zel'dovich effect.
The Inverse Compton process boosts up synchrotron photons by
means of scattering against the high energy electrons. Since the
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Astrophysics
Professor Michael Smith
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electrons that scatter against the synchrotron photons belong to
the same seed of the electrons that have produced the synchrotron
photons, this process is also called ``Self Synchrotron
Compton'' or SSC
4. Masers: line emission
Another form of non-thermal emission comes from masers. A
maser, which stands for "microwave amplification by stimulated
emission of radiation", is similar to a laser (which amplifies
radiation at or near visible wavelengths). Masers are usually
associated with molecules, and in space masers occur naturally in
molecular clouds and in the envelopes of old stars. Maser action
amplifies otherwise faint emission lines at a specific frequency. In
some cases the luminosity from a given source in a single maser
line can equal the entire energy output of the Sun from its whole
spectrum.
Masers require that a group of molecules be pumped to an
energized state, like compressed springs ready to uncoil. When the
energized molecules are exposed to a small amount of radiation at
just the right frequency, they uncoil, dropping to a lower energy level
and emit a radio photon. The process entices other nearby
molecules to do the same, and an avalanche of emission ensues,
resulting in the bright, monochromatic maser line. Masers rely on an
external energy source, such as a nearby, hot star, to pump the
molecules back into their excited state, and then the whole process
starts again.
The first masers to be discovered came from the hydroxl radical
(OH), silicon oxide (SiO), and water (H2O). Other masers have been
discovered from molecules such as methanol (CH3OH), ammonia
(NH3), and formaldehyde (H2CO).
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Astrophysics
Professor Michael Smith
13
For instance, the UBV system has about 100 standard stars measured to about ±
0.01 magnitude. Then if we can calibrate the flux of just one of these stars, we
have calibrated the system. The calibration is usually given for zero magnitude
at each filter; all fluxes are then derived from this base level. The star usually
chosen as the calibration star is Vega.
Colour index in the BV system. Blackbody curves for 20,000 K and 3000 K, along with
their intensities at B and V wavelengths. Note that B - V is negative for the hotter star,
positive for the cooler one.
Nearby objects………
PH507
Astrophysics
Professor Michael Smith
Sun
Proxima CentauriAlpha Cen C
Rigil Kentaurus Alpha Cen A
Alpha Centauri B
Barnard's Star
Wolf 359
Lalande 21185
Sirius A
Alpha CMa A
Sirius B
Luyten 726-8A
Luyten 726-8B
UV Cet
Ross 154
distance ly
mV
0.00001
-26.8
4.3
11.0
4.3
-0.1
4.3
1.5
5.9
9.5
7.6
13.5
8.1
7.5
8.6
-1.5
8.6
7.2
8.9
12.5
8.9
13.0
9.4
10.6
14
MV
4.75
15.5
4.3
5.8
3.2
16.8
10.4
1.4
11.5
15.3
15.8
13.3
http://en.wikipedia.org/wiki/List_of_nearest_stars
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Astrophysics
Professor Michael Smith
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Astrophysics
Professor Michael Smith
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Astrophysics
Professor Michael Smith
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STARS
The Hertzsprung-Russell Diagram
In 1911, Ejnar Hertzsprung plotted the first such two-dimensional diagram
(absolute magnitude versus spectral type) for observed stars, followed
(independently) in 1913 by Henry Norris Russell.
PH507
Astrophysics
Professor Michael Smith
18
The simple HR diagram represents one of the great observational syntheses in
astrophysics. Note that any two of luminosity, magnitude, temperature, and
radius could be used, but visual magnitude and temperature are universally
obtained quantities.
An original idea was that a star was born hot (early type)and cooled (late type).
It’s a particular colour-magnitude diagram.
PH507
Astrophysics
Professor Michael Smith
19
Important stars: no obvious pattern…Sirius B, Betelgeus in opposite corners:
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Astrophysics
Professor Michael Smith
20
Nearby stars: main-sequence appears. Most stars are less luminous and
cooler than the Sun (alpha Centauri, nearest to us and a triple system, is
similar).
Note the hot small stars: the white dwarfs.
PH507
Astrophysics
Professor Michael Smith
21
Most stars have properties within the shaded region known as the main
sequence. The points plotted here are for stars lying within about 5 pc of the
Sun. The diagonal lines correspond to constant stellar radius, so that
stellar size can be represented on the same diagram as luminosity and
temperature.
The first H-R diagrams considered stars in the solar neighbourhood and plotted
absolute visual magnitude, M, versus spectral type, which is equivalent to luminosity versus spectral type or luminosity versus temperature. Note (a) the welldefined main sequence (class V) with ever-increasing numbers of stars toward
later spectral types and an absence of spectral classes earlier than A1 (Sirius),
(b) the absence of giants and supergiants (class III and I), and (c) the few white
dwarfs at the lower left.
The brightest stars:
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Astrophysics
Professor Michael Smith
22
An H-R diagram for the 100 brightest stars in the sky. Such a plot is biased in
favour of the most luminous stars--which appear toward the upper rightbecause we can see them more easily than we can the faintest stars. These
are the GIANTS and SUPERGIANTS
In contrast, the H-R diagram for the brightest stars includes a significant
number of giants and supergiants as well as several early-type main-sequence
stars. Here we have made a selection that emphasises very luminous stars at
distances far from the Sun. Note that the H-R diagram of the nearest stars is
most representative of those throughout the Galaxy: the most common stars
are low-luminosity spectral type M.
The most prominent feature of the H-R diagram is the Main
Sequence:

Strong correlation between Luminosity and Temperature.

Hotter stars are Brighter than cooler stars along the M-S.

About 85% of nearby stars, including the Sun, are on the M-S.
All other stars differ in size:
Giants & Supergiants:

Very large radius, but same masses as M-S stars
White Dwarfs:

Very compact stars: ~Rearth but with ~0.6 Msun!
Example: Betelgeuse: M2 Iab (supergiant)
PH507
Astrophysics
o
Professor Michael Smith
L ~ 40,000 Lsun, T ~ 3,500 K
Sun: G2 V (main-sequence)
o
T ~ 5,000 K
Stellar luminosity classes:

Ia : Brightest Supergiants

Ib : Less luminous supergiants

II : Bright giants

III : Giants

IV : Subgiants

V : Main-sequence stars
Luminosity Classes
23
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Astrophysics
Professor Michael Smith
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Stellar luminosity classes in the H-R diagram. Note that a star's
location could be specified by its spectral type and luminosity class
instead of by its temperature and luminosity. Giants possess cool
low-density photospheres, hence absorption lines identify them (e.g.
narrower lines). After spectral classification, their distance can be
estimated according to their luminosity class. This is their
spectroscopic parallax.
Magnitude versus Colour
Because stellar colours and spectral types are roughly correlated,
we may construct a plot of absolute magnitude versus colour called a colour-magnitude diagram. The relative ease and
convenience with which colour indices (such as B - V) may be
determined for vast numbers of stars dictates the popularity of
colour-magnitude plots. The resulting diagrams are very similar to
the magnitude-spectral type H-R diagrams considered above.
The Mass-Luminosity Relationship
Just as the determination of the period and size of the Earth’s orbit
(by Kepler’s third law) leads to the Sun’s mass, so also have we
deduced binary stellar masses. Because it is necessary to know
the distance to the binary system in order to establish these
masses, we need only observe the radiant flux of each star to find
its luminosity.
When the observed masses and luminosities for stars in binary
systems are plotted, we obtain the correlation called the massluminosity relationship.
PH507
Astrophysics
Professor Michael Smith
25
In 1924, Arthur S. Eddington calculated that the mass and
luminosity of normal stars like the Sun are related by
L  M 

 
L  M  

His first crude theoretical models indicated that α ≈ 3. On a log-log
plot, this gives a straight line with a slope of 3. Main sequence
stars do seem to conform to this relationship, although the
f
low mass. From a sample of 126 well-studied binary systems, we
find that the break in slope below this value is 2.26; above it, 3.99.
Or :
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Astrophysics
Professor Michael Smith
26
Rate of burning hydrogen depends on a star's central temperature
Central temperature depends on a star's mass
Therefore, it is not surprising that a star's luminosity depends on
its mass.
n,
value of exponent n
3.9
3.0
2.7
Mass range M
M<7M
7M
< M < 25 M
25 M < M
Lifetime Mass/Luminosity Mass-3
 S
Suunn ccaann bbee ppoow
weerreedd ffoorr 55 bbiilllliioonn yyeeaarrss bbyy
ccoonnvveerrttiinngg 55%
% ooff iittss hhyyddrrooggeenn ttoo hheelliiuum
m..
 A
A ssttaarr 1100 ttiim
meess aass m
maassssiivvee aass tthhee S
Suunn hhaass 1100 ttiim
meess
m
moorree hhyyddrrooggeenn ttoo ppoow
weerr nnuucclleeaarr ffuussiioonn
 B
Buutt iitt iiss 1100000000 ttiim
meess aass bbrriigghhtt
 T
Thheerreeffoorree iitt sshhoouulldd uussee uupp iittss ffuueell 11000000 ttiim
meess m
moorree
qquuiicckkllyy
 Massive stars are very short-lived
If we use the mass-luminosity relation for stars of
0.4MSun and greater,
or
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Astrophysics
Professor Michael Smith
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so a star with 10x the mass of the Sun will have a main
sequence lifetime of only 10 million yrs!
So we know that O stars, the most massive stars, have
main sequence lifetimes of only a million years so the fact
that we see some O stars now means that star formation is
still occurring in the Milky Way.
See:
http://www.shef.ac.uk/physics/teaching/phy111/
The more massive stars burn their fuel very rapidly, leading to
short lifetimes………..
Stellar (Main Sequence) Properties With Mass
Mass
Temp
40
35,000 K
MSun
17
21,000
7
13,500
2
8,100
1
5,800
0.2
2,600
Radius
18 RSun
Luminosity
tMS
320,000 LSun 106 yrs
8
4
2
1
0.32
13,000
630
20
1
0.0079
107
8x107
2x109
1010
5x1011
In order of spectral class….………..
Spectral
Class
Mass
(Msun)
L
(Lsun)
Temp.
(K)
Radius
(Rsun)
O5
40
400,000
40,000
13
B0
15
13,000
28,000
4.9
A0
3.5
80
10,000
3.0
F0
1.7
6.4
7,500
1.5
G0
1.1
1.4
6,000
1.1
K0
.08
.46
5,000
0.9
M0
0.5
0.08
3,500
0.8
habitable zone
350-600 AU
1-2
0.1-0.2
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Astrophysics
Professor Michael Smith
28
Some stars have still not left the main sequence………
M*/Msun
60
30
10
3
1.5
1
0.1
time (years)
3 million
11 million
32 million
370 million
3 billion
10 billion
1000's billions
Spectral type
O3
O7
B4
A5
F5
G2 (Sun)
M7
tthhee lliiffeettiim
meess ooff ssttaarrss w
wiitthh m
maassss << 00..99 M
Mssuunn aarree
lloonnggeerr tthhaann 1155 bbiilllliioonn yyeeaarrss ((tthhee aaggee ooff tthhee uunniivveerrssee))

Note that the M-L law does not apply to highly evolved stars, such
as red giants (with extended atmospheres) and white dwarfs (with
degenerate matter.
The ranges. While most
stellar masses lie in the narrow range from 0.085Msun
100Msun ,
stellar luminosities cover the vast span 10-4 ≤ L/L ≤ 106.
to
A useful relationship to give a rule of thumb estimate of a stars
surface temperature is;
0.5
 M 
T  5870  
M* 
Stellar Density
Mean Stellar Density: Mean Density = Mass / Volume
Main Sequence: quite small range of mean densities:
 Sun (G2v): ~1.6
g/cc

O5v Star:
~0.005 g/cc

M0v Star:
~5
g/cc
Giants: Low-density stars: ~10-7 g/cc (e.g., K5III)
Supergiants: Very low-density: ~10-9 g/cc (e.g., M2I)
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Astrophysics
Professor Michael Smith
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White Dwarfs: High-density stars: ~105 g/cc
For reference, at sea level on Earth, water has a density of
1 g/cc, and air has a density of ~0.001 g/cc.
Stellar Evolution:
In this section, we explain the HR tracks qualitatively in terms of:
1. The energy source…..chemical, gravitational and nuclear
reactions. We exclude chemical energy (e.g. forest fires) for
stars. Gravity (if contracting) can operate for short periods.
2. Transport from the source to the surface…..conduction,
convection or radiation. We exclude conduction as ineffective.
3. Radiative transfer through the photosphere, as discussed
above. Hydrogen ions can provide the opacity in stars like the
Sun.
The internal structure of stars will be quantified in later lectures.
end of Hydrogen burning:
The
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Astrophysics
Professor Michael Smith
30

During main sequence lifetime hydrogen burning is confined to
the core. Hydrogen burning converts hydrogen into helium
in the core.

Eventually the core hydrogen is exhausted . Energy is then
derived from a hydrogen shell

With no energy production in the core, it contracts to maintain
thermal hydrostatic equilibrium. The collapse of the core will
cause it to heat up.

The hydrogen burning shell dumps further helium onto the
core. Hydrogen burning moves outward.

The core collapses, releasing energy and the star’s envelope
expands and cools – a subgiant branch phase

Over a million years, the core of a Sun sized star decreases to
about 1/10 original size.

The core temperature rises from 15 to about 100 million K.

The core is composed of helium ‘ash’.

The outer layers of the star become heated by their
proximity to the energy source. The inert hydrogen outside
the shell hinders the movement of the photons.

The energy is then transported by convection. (low
temperature, high opacity, high temperature gradient, just
what you need for convection)

Processed material from the core mixes for the first time with
the envelope - and photosphere. We call this the first dredgeup which should be visible as a increase in N at the expense
of C and O.

The outer layers are not so tightly bound by gravity and will
expand enormously forming a red giant
Why Helium won’t burn yet
 Hydrogen, a single proton, has a single electrostatic charge

Helium has two.

Helium nuclei must have a much higher kinetic energy (speed)
to get close enough to bind
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Astrophysics
Professor Michael Smith
31
Helium burning begins
 When the central temperature reaches 100 million K, helium
burning starts.

Two helium nuclei fuse to form an isotope of beryllium.

Beryllium is very unstable. If it is hit by another helium they
fuse into a stable isotope of carbon.

This is known as the triple alpha process.

A high energy gamma ray is released by each reaction
A Star’s Safety-valve
 Gravity tries to compress a star

When a perfect gas is compressed its density and
temperature increase.

If a gas heats up its pressure increases.

The pressure tries to expand the star.

If a reaction starts to run away, the temperature rises and the
star expands.

This drops the temperature and the reaction is slowed.
Perfect and degenerate
 In a low-mass red giant (< 3 Msol), the core must undergo
considerable compression to drive the temperature high
enough to start helium burning.

No two identical particles may occupy the same quantum
state.

The electrons obey the Pauli exclusion principle (Wolfgang
Pauli, 1925) and will not be compressed any further.

The gas is said to be degenerate and is supported by
degenerate-electron pressure.

In the highly compressed core, free electrons are so crowded
together that quantum effects must be considered.
Helium flash:
 When the temperature in the core reaches that required for
helium fusion, energy begins to be released.
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Astrophysics
Professor Michael Smith
32

Because the star is supported by electron degenerate
pressure, it does not expand.

(Remember degeneracy is a quantum effect and not
influenced by temperature in the same way.)

Without its safety valve the temperature soars and the fusion
process runs away.

This runaway takes only a few seconds and is called a Helium
Flash

It releases a vast quantity of energy which drives the
temperature so high that the gas behaves in an ideal way
again: the degeneracy is ‘lifted’.

The Helium Flash is not observable, since the photons
produced in the explosion are trapped in the Hydrogen layers.
Low mass stars:
 After the helium flash, substantial carbon and oxygen ‘ash’ is
dumped at the core.

The core contracts until electron degeneracy again
supports the star.

The temperature reached is enough to start shell helium
burning around the core

Helium shell burning, like the hydrogen shell before it, heats
the outer layers of the star and it expands again to form a red
supergiant.
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Astrophysics
Professor Michael Smith
33
Low mass planetary nebulae
 The helium shell is much thinner than the hydrogen one and is
unable to swell the star to relieve the temperature build up.

The process runs away until the helium layer is thick enough
to expand the star thus cooling it.

These helium flashes raise the luminosity from 100 to 100,000
times that of the Sun.

The flashes can also re-start the hydrogen burning.

Can be so energetic that the outer layers of the star are
blown clean off. The escape velocity from the surface of a
star is vesc = (2GM/R)1/2 .

The expanding shell of ejected gasses is ionized by ultraviolet
light from the hot core left behind. The White Dwarf core has
a surface temperature over 100,000 K. Wein's law for a hot
body with this temperature gives a peak wavelength of 2.9 x
10-8m, corresponding to ultraviolet light.

When the electrons recombine with the surrounding ions, they
often enter an excited state and then jump down to the ground
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Astrophysics
Professor Michael Smith
34
state emitting visible photons. This process is known as
fluorescence.
HST images of
Planetary Nebulae
Henize 1357
The Helix
NGC 6543
MyCn18
Planetary nebulae

Last for around 50,000 years after which it has dispersed and
faded from view.

Accounts for 15% of matter returned to the Inter-Stellar
Medium (ISM) by stars.

The planetary nebula takes ~ 60% of the star with it leaving
only the core.
White dwarfs

< 4 Msol, never produce temperature high enough to ignite
carbon and oxygen.

During this phase, the star moves to the left on the H-R
diagram.

The track will sometimes loop corresponding to thermal
pulses.
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Astrophysics
Professor Michael Smith
35

As the ejected nebula fades and the core cools, the stars
track turns sharply downward.

The core becomes more and more compressed as the
temperature drops.

Most of the matter becomes degenerate again and the
contraction halts.

The star is now called a white dwarf - about the same size as
the Earth.

Its density is typically 109 kg/m3.

One teaspoon weighs as much as an elephant (5.5 tons)

Remember that electron degeneracy is a quantum effect. This
means that the more massive a white dwarf, the smaller it
becomes.
The end of the road
 The Chandrasekhar mass (1.4 Msun) is the largest mass that
a white dwarf can possibly have.

Highly ionized atoms floating in a sea of degenerate electrons.

As the star cools, the random motions of the particles slow
and the electric forces between ions line them up in a
crystalline lattice.

From this point on the star is ‘solid’

the electrons, though degenerate, may move around the
lattice.

The core is similar to copper or silver.

As it cools further it evolves into a cold dark diamond sphere
of carbon and oxygen, about the size of the Earth.
Higher Mass Stars: How far can it go?
 For an element to serve as fuel energy must be given off when
its nuclei collide and fuse.

This energy comes from packing together more tightly the
neutrons and protons in the ash nuclei than in the fuel nuclei.
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Astrophysics
Professor Michael Smith
36

Once iron is reached with 56 protons and neutrons, no further
energy can be extracted by the addition of more.

Iron does not burn.

The fuel layers burn outward dumping more and more iron
onto the core which is supported by degeneracy pressure
alone.

Eventually this fails, catastrophically and violently.