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Stellar Structure
Section 1: Basic Ideas about Stars
Lecture 1 – Observed properties of stars
Relationships between observed properties
Outline of the life history of a star
Introduction
A star is:
a “vast mass of gas”
self-gravitating
supported by internal pressure
self-luminous
Some questions:
source of pressure?
energy source?
do they stay hotter than surroundings?
how long do they live?
Real and ideal stars
Ideal stars are:
• isolated
• Spherical
Real stars may be:
• Embedded in gas and/or dust
• In a double or multiple star system
• Connected to surrounding gas by
magnetic field lines
• Rotating rapidly
Factors affecting observational
properties of stars
Observed appearance depends on:
• Distance (and any gas/dust in the way)
• Initial mass
• Initial chemical composition
• Current age
How do we measure observed properties?
Distance measurement
Direct: trigonometric parallax
Distant
stars
Earth (January)
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Nearby
1 AU
d
Sun
p
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star
Earth (July)
p = ‘parallax’  0.76 arcsec
d = 1 parsec (pc) when p = 1 arcsec
d(in pc) = 1/p(in arcsec)
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Light output
Deduce luminosity L (total power output) from
flux density F (Wm-2) measured on Earth and
distance d (when known): L = 4πd2F.
Spectrum gives surface temperature (from
overall shape of continuum – best fit to a black
body) and chemical composition (from relative
strengths of absorption lines).
Mass and Radius
Mass:
• Directly, only from double star systems
• Indirectly, from surface gravity (from spectrum) and radius
Radius:
• Interferometry
• Eclipse timings
• Black body approximation: L = 4π Rs2 Ts4, if L, Ts known.
Can also define the effective temperature Teff of a star by:
L  4π Rs2 Teff4
Typical observed values
0.1 M < M < 50 M
10-4 L < L < 106 L
10-2 R < R < 103 R
2000 K < T < 105 K
Stellar magnitudes
Hipparchus (~150 BC):
6 magnitude classes (1 brightest, 6 just visible)
Norman Pogson (~1850): defined apparent magnitude m by
m = constant – 2.5 log10F ,
choosing constant to make scale consistent with Hipparchus.
Absolute magnitude M is defined as the apparent magnitude a star
would have at 10 pc. If D = distance of star:
M = m – 5 log10(D/10pc).
[We can hence also define the distance modulus m-M by:
m - M = 5 log10(D/10pc).]
Relationships:
Hertzsprung-Russell diagram (HRD)
Relation between absolute magnitude and surface temperature
(Handout 1):
• Dominated by main sequence (MS) band (90% of all stars)
• Giants & supergiants (plus a few white dwarfs): ~10%
• L  R2 – so most luminous stars are also the largest
Either:
• 90% of all stars are MS stars for all their lives
Or
• All stars spend 90% of their lives on the MS 

Relationships:
Mass-luminosity relation (MS stars)
• Strong correlation between mass and luminosity (Handout 2)
• Main-sequence stars only
• Calibrated from binary systems
• Slope steepest near Sun (L  M4)
• Less well-determined for low-mass stars (hard to observe) …
• … and high-mass stars (rare)
Indirect ways of finding stellar
properties
• Spectrum: absorption line strengths depend on
Chemical composition
Temperature
Luminosity
• Chemical composition similar for many stars …
• … so Teff, L can be deduced
• Variability:
• some pulsating variables show period-luminosity relation
• Measure P  L  M; plus measure m  distance
Star clusters
Gravitationally bound groups of stars, moving together
Globular clusters:
• compact, roughly spherical, 105-106 stars;
• in spherical halo around centre of Galaxy
Galactic (or open) clusters:
• open, irregular, 102-103 stars;
• concentrated in plane of Galaxy
Small compared to distance  all stars at ~same distance
 Apparent magnitude/temperature plot gives the shape of the
HR diagram
Globular cluster HR diagrams
(Handout 3)
All globular cluster HR diagrams are similar:
• short main sequence
• prominent giant branch
• significant horizontal branch (containing RR Lyrae variables)
Find distances by comparing apparent magnitudes of
• main sequence stars
• red supergiant stars
• RR Lyrae variable stars
with those of similar nearby stars of known absolute magnitudes
Galactic cluster HR diagrams
(Handout 3)
Much more variety, but all diagrams show
• Dominant main sequence, of varying length
• Some giant stars, in variable numbers
If all main sequences are the same (i.e. have the same absolute
magnitude at a given temperature), then can create a composite
HR diagram (Handout 3) – plausible if all stars formed at same
time out of same gas cloud  same age and composition
Then find distances to all, if know distance of one, by this “mainsequence fitting” procedure
Mean MS is narrow – suggests it is defined by a single parameter
– the mass increases from faint cool stars to hot bright ones
Life history of stars:
Birth
Interstellar cloud of dust and cool gas:
• Perturbed by external event: self-gravity starts contraction
• If spinning, contraction leads to faster spin
• High angular momentum material left behind in disc
• Disc may form planets, and may also eject jets
• Central blob radiates  initial isothermal collapse
• When blob opaque, radiation trapped and temperature rises
• Thermal pressure slows collapse
• “Proto-star” – hot interior, cool exterior
• Contraction releases just enough energy to balance radiation
Life history of stars:
Energy sources
Gravitational energy, from contraction – if sole energy source for
Sun (Kelvin, Helmholtz, 19th century), then timescale ~ E/L where
E = gravitational energy of star, L = luminosity:
tKH = GM2/LR ~ 3107 yr for Sun.
But geology requires much longer timescale – only nuclear fuel
provides this; nuclear binding energy releases up to ~1% of rest
mass energy: EN ~ 0.01Mc2, so
tN ~ 0.01Mc2/L ~ 1.5 1011 yr for Sun.
Over-estimate, because not all mass of Sun is hot enough to be
transformed. Strong mass dependence, because L  M4 – so, for
50 M, tN ~ 108 yr – massive stars were born recently.
Life history of stars:
Life and death
• Proto-star contracts until centre hot enough for hydrogen to
fuse to helium
• Nuclear energy source enough to balance radiation, and
contraction ceases (no more need for gravitational energy)
• Very little change for a nuclear timescale – i.e. until nuclear fuel
exhausted
• Series of phases of alternating contraction (releasing
gravitational energy until centre hot enough) and further nuclear
reactions (helium to carbon, etc, possibly up to iron)
• After all possible nuclear fuels exhausted, star contracts to a
dead compact object: white dwarf, neutron star or black hole.