Properties of Stars
"There are countless suns and
countless earths all rotating
around their suns in exactly the
same way as the seven planets
of our system. We see only the
suns because they are the
largest bodies and are
luminous, but their planets
remain invisible to us because
they are smaller and nonluminous. The countless worlds
in the universe are no worse
and no less inhabited than our
Earth”
Giordano Bruno (1584)
in De L'infinito Universo E Mondi
Properties of Stars
•
•
•
•
•
Distance
Luminosity (intrinsic brightness)
Temperature (at the surface)
Radius
Mass
The Distances of Stars
Parallax is the apparent motion of a nearby object relative to a
distant object due to the changing position of the observer.
The Distances of Stars
As the Earth orbits the Sun, nearby stars appear to shift
relative to more distant stars. The size of this parallax
shift is larger for stars at smaller distances. Therefore, we
can use parallax to measure the distances of stars.
The Distances of Stars
The parallax shift of a star is measured as an angle in
units of arcseconds (abbreviated as ”) where
1”=1 degree/3600. The largest parallax angles (for the
nearest stars) are <1”. For perspective, the angular size of
the Moon as seen from the Earth is 1800” (0.5 degree).
Such tiny parallax shifts can be detected only with
telescopes, which is why Aristotle couldn’t see them.
The distance of a star can be computed from its parallax
angle with the following equation:
3.26
d(light years) 
p(")
The light year
Rather than kilometers, astronomers use a larger unit of
distance when referring to the distances to stars and
galaxies. One light year is the distance that light travels in
1 year, corresponding to 9.5 trillion km.
1 light sec
8 light min
5.5 light hours to Pluto
4 light years to nearest star
Distance to the nearest star to our solar system:
40 trillion km = 4 light years
The Luminosities of Stars
The luminosity of a star is the amount of light or energy that it
produces per second, like the number of watts produced by a light
bulb. But astronomers don’t use watts for the units of a star’s
luminosity. Instead, they refer to the luminosities of stars in terms
of the luminosity of the Sun, which is called a solar luminosity and
is abbreviated as L.
The Luminosities of Stars
If you measure the distance (d) to a star via parallax and the star’s
brightness as seen from the Earth (b), then you can compute the
star’s luminosity (L) from the inverse square law of light.
L
b = 2
d
The Temperatures of Stars: Colors
One way to estimate a
star’s temperature is by its
color. Red stars are cool,
blue stars are hot.
However, if there’s a lot of
dust in space between us
and a star, the light we
receive will appear red
because the blue photons
are scattered out of the
beam of light (like the Sun
at sunset).
The Temperatures of Stars:
Absorption Lines
In hydrogen, optical absorption lines begin in the n=2 level.
So some of the atoms must have electrons in n=2 for these
lines to be produced.
The Temperatures of Stars:
Absorption Lines
But at cold temperatures, the electron is in the ground state.
So optical absorption lines cannot appear.
The Temperatures of Stars:
Absorption Lines
And at hot temperatures, the electron is in high levels.
Again, no optical absorption lines are produced.
The Temperatures of Stars
Each element has a “favorite” temperature range in which it
produces absorption lines. By identifying which absorption lines
appear in the spectrum of a star, one can measure its temperature.
Astronomers assign a letter called a spectral type to a star based on
which absorption lines appear in its spectrum. Hence, a spectral type
is just another term for a star’s temperature.
Oh
Be
A
Fine
Girl
Kiss
Me.
Sun
The Radii of Stars
Only a few stars are large
enough and close enough that
telescopes can directly measure
their radii.
All other stars appear as unresolved
points of light. We must estimate
their sizes from T and L.
Like any blackbody source of
radiation, a star’s luminosity is
related to its temperature:
LT4
Luminosity is also proportional to a
star’s surface area, which is πR2:

L  R2
Combining those 2 relations:
L
,
or
R 2
LR T

2
4
T
So we can estimate R by measuring
L and T.
The Radii of Stars
Stars have a large
range of radii, from
0.01 R to 1000 R
http://www.youtube.com/watch?v=k7hsQA3wo3Q
The Masses of Stars
Using Kepler’s and Newton’s laws, the mass of a star can
be measured if it is orbiting with another star in a binary
system:
(M1 + M2) P2 = a3
where
 M1 and M2 are the stellar masses (in solar masses)
 P is the orbital period (in years)
 a is the semi-major axis of the orbit (in A.U.)
The Masses of Stars
The relative velocities of 2 stars in a binary system are
related to their relative masses. If 2 stars have different
masses, then the less massive one moves faster in its orbit.
The Masses of Stars
The velocities of the stars in a binary system can be measured from
the Doppler shifts of their absorption lines as they repeatedly move
towards and away from the observer during their obit.
The H-R Diagram
If a star’s luminosity and temperature are both measured, they can be
plotted versus each other. This is called the Hertzprung-Russel (H-R)
diagram. Stars appear in distinct locations on this diagram.
Red Giants and White Dwarfs
Some stars are very cool,
but also very bright.
Since cool objects don’t
emit much light, these
stars must be huge in
order to be that bright.
They are red giants.
Some stars are faint, but
very hot. For a hot star to
be faint, it must be very
small – they are white
dwarfs.
how size changes
with T and L
The Main Sequence
Most stars (including the
Sun) appear within the
middle band from high
temperatures and
luminosities to low
temperatures and
luminosities. This is called
the main sequence. Main
sequence stars are larger
(in diameter) than white
dwarfs but smaller than
giants.
Masses on the H-R diagram
1) All stars have masses
between 0.1 M and
100 M
2) Brighter stars on the
main sequence have
higher masses
3) All white dwarfs have
masses <1.4 M
4) There is no pattern to
the masses of red
giants.
3) All white dwarfs have
masses <1.4 M
4) There is no pattern to
the masses of red
giants.