Stars:
Their Properties
T. K. Prasad
http://www.cs.wright.edu/~tkprasad
(Adapted from a lecture by Daniel Wang of UMass)
Fundamental Problem and
Solution Approach
 No
direct access to star!
 Large
distance
 Nearest
stars: Sun (8 light minutes),
Proxima Centauri (4 light years), etc.
 High
 Will
temperature and radiations
melt/vaporize probes; interfere with
detector electronics even if we try to send
them closer!
Fundamental Problem and
Solution Approach
Only
Remote Access Feasible
 What
information can we glean using
remote observation?
 What information do we need to
understand star properties and
evolution?
STEM
Science
 E.g.,
Physics, Chemistry, Biology
Technology
 E.g.,
Vacuum tubes vs Transistors,
Nanotechnology, 3D-Printing, Virtual Reality
STEM
Engineering
E.g.,
Mechanical, Electrical, Computer,
Civil, Aeronautical, Materials, etc.
Mathematics
Geometry,
Trigonometry, Calculus,
Algebra, Probability and Statistics, etc.

What can we observe?
Apparent brightness (engineering + technology)
 Color (spectroscopy)
 Distance (telescopes + mathematics)


What do we need?
Luminosity (actual brightness) (total energy)
 Temperature (from Color)
 Composition (phy + chem)
 Size (…)








Apparent brightness + distance
=> Actual brightness
Nuclear physics will explain the real source of this
energy (e.g., Sun : Hydrogen fusion)
Ultimately Mass dictates the entire lifecycle of a star and
its volume (size)
Physics : Gravity, Optics, Velocity and its impact on
spectrum (Doppler’s effect), …
Tech : Materials to computers, …
Engineering : Right device …
Math for precision and accuracy + quantitative analysis
Stars
Twinkle, twinkle, little star,
How I wonder what you are.
Up above the world so high,
Like a diamond in the sky.
Are Stars similar to our Sun?
How far away are they?
Where did they come from?
What do they do?
Do they live forever?
Panorama view of the sky
The Four Basic Parameters of a Star
Luminosity
Size
Mass
Surface
Temperature
To infer these parameters, we need to
know the distance!
Luminosity and Apparent Brightness

Luminosity is the measure of energy radiated by
a star per second over all wavelengths. (Cf.
Visual Luminosity)



Luminosity depends both on temperature and surface area.
This cannot be determined by direct observation.
Apparent brightness is the amount of energy
coming from the star per square meter per
second, as measured on Earth. (cf. Flux)

This can be determined by direct observation.
(cont’d)


Luminosity is an intrinsic property of a star,
while apparent brightness depends on the
distance to the observer.
Luminosity is how bright a star really is, while
apparent brightness is how bright a star appears
to an observer.
Inverse Square Law
Distances by
Triangulation
We can measure
distances by
comparing the
position of objects
observed from two
ends of the
“baseline” of a
triangle.
Parallax
1.
2.
3.
4.
Hold your thumb up, steadily in front of you.
Move your head from side to side and note the
shift of your thumb with respect to background
objects—this angular shift is called parallax.
Now look at your thumb while keeping your head
steady but first closing one eye then the other.
Move your thumb closer to you—does it shift
more or less with respect to the background?
Stereovision



You use parallax constantly to estimate distances.
Close your eyes. Have a neighbor dangle a pen in
front of you, then open just one eye. Without
moving your head, bring your hand in from the side
and try to touch the pencil with just the tip of
another pen.
Your brain processes the information from each eye
and compares the angles to allow you to judge
distances.
The Geometry
of Parallax
p
We use the Earth’s
whole orbit as our
baseline.
DA
PB
1 (AU)
=
D (in Parsecs) =
P (in arcseconds) DB
PA
1 parsec (pc) = 3.26 ly. Other useful units: kpc and Mpc
Parallax Example
Parallax from a Different Planet
If we lived on Mars, orbiting 1.5 times farther
away from the Sun, the parallax would be
1.
the same as from Earth
2.
1.5 times smaller than from Earth
3.
1.5 times bigger than from Earth
Digression:
Proper Motion of
Stars (Very Slow)
100,000 yrs ago
Now
Surprising Fact:
It is easier to measure
radial velocity using
Doppler Effect than
transverse velocity!
100,000 yrs in future
Big Dipper
Stellar Parallax

Since ancient Greek times, astronomers expected
that if the Earth moved through space, we would
see the stars shifting due to parallax.


If the Copernican model is correct, parallax of stars was
a necessary consequence, but it was undetected until the
1830’s because of the huge distances of stars.
The nearest stars shift by only about 0.7 arcsec
1 / 0.7 = 1.4 parsec
This is about 4.3 light years
or about 27,000,000,000,000 miles !
Survey Question: Stellar Parallax
Suppose a star has a parallax of 0.01 arc
seconds. How many parsecs away is it?
distance (in parsecs) = 1 / parallax (in arcsec)
Answer: 100
Brightness, Distance, and
Luminosity
L=4D2 B
luminosity
distance
apparent brightness
There is a Big Range of Stellar
Luminosities Out there!
Star
Sun
Proxima Centauri
Rigel (Orion)
Deneb (Cygnus)
Luminosity (in
units of solar
luminosity)
1
0.0006
70,000
170,000
Apparent Brightness vs Luminosity
• Luminosity depends on Brightness & Distance
B
A
B
Earth
A
A appears brighter
b = L / 4πd2
How to measure the surface
temperature of a star?
Overall spectral shape (the peak of the
blackbody continuous spectrum) is related
to its temperature by
Wien’s Displacement Law:
T=
2.9 × 106 K
λmax (nm)
More accurately, spectroscopically
Wein’s Law
Peak frequency of radiation from a (star) blackbody
is proportional to its (surface) temperature
Spectral Types of Stars
Spectral types are defined by the:
•
•
existence of absorption lines belonging to
various elements, ions, & molecules in a star’s
spectrum
the relative strengths of these lines
However, spectral type is not determined by a
star’s composition.
•
all stars are made primarily of Hydrogen &
Helium
Reason for Spectral Types
Spectral type is determined by a star’s surface
temperature.
•
•
•
temperature dictates the
energy states of electrons in
atoms
temperature dictates the types
of ions or molecules which
exist
this, in turn, determines the
number and relative strengths
of absorption lines in the
star’s spectrum
Spectral Type Classification System
O B A F G K M (L T)
Oh Be A Fine Girl/Guy, Kiss Me!
50,000 K
3,000 K
Temperature
Other Mnemonics: e.g., Officially, Bill always felt
guilty kissing Monica Lewinsky tenderly
V Mag.
(m)
Bayer designation
Proper name
Distance
(ly)
Spectral class
(Sun)
0.000 016
G2 V
0
−26.74
1
−1.46
α CMa
Sirius
8.6
A1 V
2
−0.72
α Car
Canopus
310
F0 Ia
3
−0.04 var
α Boo
Arcturus
37
K1.5 III
4
−0.01
α Cen A (α1 Cen)
Rigil Kentaurus, Toliman
4.4
G2 V
5
0.03
α Lyr
Vega
25
A0 V
6
0.12
β Ori
Rigel
770
B8 Iab
7
0.34
α CMi
Procyon
11
F5 IV-V
8
0.42 var
α Ori
Betelgeuse
640
M2 Iab
9
0.50
α Eri
Achernar
140
B3 Vpe
10
0.60
β Cen
Hadar, Agena
530
B1 III
11
0.71
α1 Aur
Capella A
42
G8 III
12
0.77
α Aql
Altair
17
A7 V
13
0.85 var
α Tau
Aldebaran
65
K5 III
14
0.96
α2 Aur
Capella B
42
G1 III
15
1.04
α Vir
Spica
260
B1 III-IV, B2 V
Stellar Size

Stars are spherical so we characterize a star’s
size by its radius.
R
Stellar Radii vary in size
from ~1500 RSun for a
large Red Giant to
0.008 RSun for a White
Dwarf.
How do we determine the
radius of a star?
Angular Radius of Star
The angular radius of the Sun is about 103 arc
seconds. If another star like the Sun was 5
parsecs away (about 106 AU), what would its
angular radius be?




109 arc seconds
100 arc seconds
10-3 arc seconds
10-9 arc seconds
Temperature, Luminosity, and Size –
pulling them all together
A star’s luminosity, surface temperature, and size
are all related by the Stefan-Boltzmann Law:
Stefan-Boltzmann Law
L=4πR2 σT4
Luminosity
Stellar
radius
Surface
temperature
L=4πR2 σT4
Two stars have the same surface temperature, but
the radius of one is 10 times the radius of the other.
The larger star is
1) 10 times more luminous
2) 100 times more luminous
4) 1/10th as luminous
5) 1/100th as luminous
L=4πR2 σT4
L=4πD2 B
Suppose two stars are at equal distance and have the same
radius, but one has a temperature that is twice as great as the
other. The apparent brightness of the hotter star is ____ as
the other.
1) 1/2 as great
2) 1/4 as great
4) 4 times
5) 16 times as great
Measurements of Star Properties
Apparent brightness (B)
Distance
Luminosity
Temperature
Radius
Direct measurent
Parallax
Distance + apparent brightness
( L=4D2 B)
Spectral type (or color)
Luminosity + temperature
(L=4R2 T4)
Luminosity and temperature are the two
independent intrinsic parameters of stars.
Finding Star Properties
How do you weigh a star?
Mass is the single most important
property in how a star’s life and death
will proceed.
 The mass of a star can only be measured
directly by observing the effect of its
gravity on another object
 This is most easily done for two stars
which orbit one another --- a binary star!

Newton’s Version of Kepler’s Third Law
Star A Newton was able to derive Kepler’s
a
Third Law from his own Law of
Gravity. In its most general form:
P2 (mA + mB) = a3
The orbital period of two objects
(P) depends on the distance
Star B
between them (a) and the sum of
Each star in a binary
the masses of both objects (mA +
system moves in its own mB).
orbit around the system's So if P and a can be measured,
mA + mB can be estimated.
center of mass.
Orbits and Masses of Binaries
The primary importance of binaries
is that they allow us to measure
stellar parameters (especially mass).
We get the sum of the masses unless we see both
stars moving.
Visual Binaries
But for most binaries, one cannot separate the stars
even with most powerful telescopes. For them, we
need to use the spectroscopic information.
Sirius – the brightest
star in the sky.
Visual Binary Star Images
Mizar – in the handle of the
Big Dipper.
Albireo –
The “Cal” star
Spectroscopic Binaries
1
4
2
5
3
1. The total spread (size) of the
Doppler shift gives velocities about
center of mass  orbit sizes, a
2. The time to complete one repeating
pattern  period, P
Recall: Doppler Shift tells only if it is moving toward or away
•
•
Eclipsing Binaries
Binary orbiting edge-on to our line of sight.
The stars alternately eclipse each other changing
the apparent brightness.
From the eclipse
duration, and
orbital speed, we
can also find the
size of the star.
Thus one
typically can
tightly constrain
the star masses in
eclipsing binaries.
Eclipsing Binary :
Algol, The “Demon” Star
In Review

There are four principal characteristics
of a star:
 Luminosity
 Surface
Temperature
 Size
 Mass
How may we classify stars?
We can take a census of stars and see what’s
out there.
But first, let’s do some sociology in the classroom.
Star A has a parallax that is twice that of Star
B. What is the relationship between their
distances?

Star A is closer than Star B

Star B is closer than Star A

The stars are at the same distance

Not enough information is given
Stellar Classification
Discussion Question
Make a plot that shows the general
relationship between height and weight for
humans.
- now add to your plot the population of
basketball players who are very tall and
very thin.
- now add the population of obese
children
How can we classify stars
1) Collect information on
a large sample of stars.
2) Measure their
luminosities
(need the distance!)
3) Measure their surface
temperatures
(need their spectra)
Star clusters: Globular vs Open
The Hertzsprung-Russell Diagram
Around 1910, Ejnar Hertzsprung (Dane) and Henry Norris Russell
(American) had the idea of plotting the luminosity of a star against its
spectral type. For a star cluster, all the stars are at the same distance.
So, apparent brightness vs spectral type is basically the same as
luminosity vs temperature. They found that stars appeared only in
certain parts of the diagram.
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram
BRIGHT
HOT
COOL
FAINT
The Hertzsprung-Russell Diagram
The Main Sequence
 ~90% of all stars
are in the main
sequence (MS)
 ~90% of all MS
stars are cooler
spectral types than
the Sun (i.e., at the
lower MS)
 All MS stars fuse
H into He in their
cores.
The Hertzsprung-Russell Diagram
Mass-Luminosity
Relation:
 L  M3.5
 For example, if
the mass of a star
is doubled, its
luminosity
increases by a
factor 23.5 ~ 11.
The relation is for
main sequence
stars only!
Mass of MS Star
L  M3.5
The Hertzsprung-Russell Diagram
Red Giants
- Red Giant stars
are very large, cool
and quite bright.
e.g., Betelgeuse is
150,000 times more
luminous than the Sun
but is only 3,500K on
the surface. It’s
radius
is 1,000 times that of
the Sun.
The Hertzsprung-Russell Diagram
Supergiants
L=4πR2 σT4
Size of Star:
The Hertzsprung-Russell Diagram
White Dwarfs
- White Dwarfs
are hot, but since
they are so small,
they are not very
luminous.
Main Sequence
Lifetime


All M-S stars have temperatures sufficient to
fuse H into He in their cores.
Luminosity depends directly on mass:
more mass = more pressure from upper layers
 fusion rates must be high to maintain equilibrium



Lifetime  (Amt. of Fuel)/(Rate of Burning)
 M / L  M / M3.5  1 / M2.5
Higher mass stars have shorter lives!
The Hertzsprung-Russell Diagram
More mass,
more fuel,
very fast burning.
Shorter
Lifetime
of Star
Less mass,
less fuel,
slow, steady burning.
Think
SUV vs Honda Civic
Longer
Review Questions: The H-R Diagram
1.
2.
3.
4.
5.
6.
7.
8.
Where are most stars?
What is the common
characteristics of MS
stars?
What determines the
location of a star in
the MS?
Where do you find the
largest stars?
The smallest?
The most massive
one?
The coolest stars?
How do we know the age
of a star?
1. MS, 2. H He, 3. M, 4. upperright, 5. lowerleft, 6. upperleft, 7. lowerright, 8. normally we
Luminosity classes
Mass-Lifetime Relation (MS)
• High mass stars have more fuel
but they burn it much faster
fuel mass
• Lifetime = rate of consumption
M
M
tlife ~ L ~ M3.5 ~ M–2.5
O5 V (40Ms) :
G2 V (Sun) :
M5 V (0.2 Ms) :
1 Myr
10 Gyr
500 Gyr
• No star with M < 0.9Ms has yet died
(tUniverse = 13.7 Gyr)
e.g. for a 4 Msun star (e.g. Vega)
L = 43.5 = 128 Lsun
tlife = 4–2.5 = 0.03tsun = 300 Myr
1 Myr
30 Myr
40
300 Myr
18
1 Gyr
10
6
3
10 Gyr
1.7
60 Gyr
1.0
0.8
0.5
Radius of Stars
Aging of a cluster of stars



MS lasts until H is
exhausted in the core.
Clues to the next stage
are visible in older star
clusters.
The brightest stars are
gone, replaced by red
giants.
Why are clusters useful to
astronomers?
All stars in a cluster are at about same
distance from Earth.
 All stars in a cluster are of about the
same age.
 Clusters therefore are natural laboratory
in which mass, rather than age, of stars
is only significant variable.

The Hertzsprung-Russell Diagram
We can date a
cluster by
observing its
population of
stars.
The oldest clusters
known have been
measured to be
~13 billion years
old.
All these stars in the
cluster have burned
themselves out!
Anatomy of a Main Sequence Star
Hydrogen
fuel
Helium
“ash”
Hydrogen
burning core
shell
Up the red giant branch
As hydrogen in the core is being used up, it starts to contract,
raising temperature in the surrounding. Eventually, hydrogen
will burn only in a shell. There is less gravity from above to
balance this pressure. The Sun will then swell to enormous
size and luminosity, and its surface temperature will drop,  a
red giant.
Sun today
Sun in ~5 Gyr
Helium fusion at the center of a giant




While the exterior layers expand, the helium
core continues to contract, while growing in
mass, and eventually becomes hot enough (100
million Kelvin) for helium to begin to fuse into
carbon
Carbon ash is deposited in core and eventually a
helium-burning shell develops. This shell is
itself surrounded by a shell of hydrogen
undergoing nuclear fusion.
For a star with M< 1 Msun, the carbon core
never gets hot enough to ignite nuclear fusion.
In very massive stars, elements can be fused
into Fe.
The Sun will expand and cool again, becoming a red giant.
Earth will be engulfed and vaporized within the Sun. The
Sun’s core will consist mostly of carbon.
•Red Giants create most of the Carbon in the universe
(from which organic molecules—and life—are made)
How can two stars have the same temperature,
but vastly different luminosities?
•
The luminosity of a star depends on
2 things:
•
•
•
•
surface temperature
surface area (radius)
4
2
L=T 4R
The stars have different sizes!!
The largest stars are in the upper right
corner of the H-R Diagram.
Luminosity
4
2
L =  T 4  R . If Star A is twice as hot and
one fourth the radius of Star B, then it should
be…
(1) 1/4 as luminous as Star B
(2) just as luminous as Star B
(3) 16 times as luminous as Star B
(4) 64 times as luminous as Star B


Review: The Hertzprung-Russell (H-R)
Diagram
One of the most
important diagrams in
astronomy for star
classification
Spectral Types of Stars
OBAFGKM: O=hottest,
M=coolest.
 spectral type carries
almost same info as color
or temperature

H-R Diagram: main sequence




Most (about 90%) stars -- including the Sun -appear to lie on the main sequence (MS).
Mass determines location of star on MS:
L  M3.5 -- Luminosity depends very strongly
on mass.
The defining characteristic of a MS star is that
it is fusing H to He.
Other stars

Red Giants are bright because they're big, even
though cool.



Appear near the upper right section of the HR Diagram.
They have a bigger radius than the stars of the same
temperature which gives them a higher luminosity.
White Dwarf's are faint because they're tiny,
even though hot.


Appear in the lower left section of the HR Diagram.
They are extremely hot, yet appear very dim due to their
extremely small size.
Why are there no Main Sequence Mclass stars visible to the naked eye?
(1) they are very rare and all very far
away.
(2) they are so cool that they only emit in
the infrared.
(3) they are too dim to be seen even if
they are only a few light years away.
Star Census : Solar Neighborhood