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Stars!
A star is a big ball of gas, with fusion
going on at its center, held together by
gravity!
There are variations
between stars, but
by and large they’re
really pretty simple
things.
Massive
Star
Sun-like
Star
Low-mass
Star
What is the most important
thing about a star?
MASS!
The mass of a normal star almost completely
determines its LUMINOSITY and
TEMPERATURE!
 Note: “normal” star means a star that’s fusing Hydrogen
into Helium in its center (we say “hydrogen burning”).
HOW and WHY is that so?
The mass of a star determines
the pressure in its core:
The more mass the
star has, the higher the
central pressure!
The core supports
the weight of the
whole star!
The core pressure determines the rate of fusion…
MASS
PRESSURE &
TEMPERATURE
…which in turn determines
the star’s
RATE OF
FUSION
luminosity!
Usually, what we know is how
bright the star looks to us here
on Earth…
We call this its
Apparent Magnitude
The Magnitude Scale
 Magnitudes are a way of
assigning a number to a star
so we know how bright it is
Rigel and Betelgeuse,
stars in Orion with
apparent magnitudes
0.9 and 0.3
The historical magnitude scale…
 Greeks ordered the
stars in the sky
from brightest to
faintest…
 …so brighter stars
have smaller
magnitudes.
Magnitude
Description
1st
The 20 brightest
stars
2nd
stars less bright
than the 20
brightest
3rd
and so on...
4th
getting dimmer
each time
5th
and more in each
group, until
6th
the dimmest stars
(depending on your
eyesight)
Later, astronomers accepted and
quantified this system.
 Modern measurements showed it
was actually a logarithmic scale
Every one magnitude corresponds to a
factor of 2.51 change in brightness
because (2.51)5 = 2.51 x 2.51 x 2.51 x 2.51 x 2.51 = 100
(99.626)
5 magnitudes change is 100 change in brightness
Brighter = Smaller magnitudes
Fainter = Bigger magnitudes
 Magnitudes can even be
negative for really bright stuff!
Object
Apparent Magnitude
The Sun
-26.8
Full Moon
-12.6
Venus (at brightest)
-4.4
Sirius (brightest star)
-1.5
Faintest naked eye stars
6 to 7
Faintest star visible from
Earth telescopes
~25
log scale, no kidding?
b1  b2  2.512 
b – apparent brightness
m – apparent magnitude
 m1  m2 
b1
log   m1  m2  log  2.512 
b2
b1
1
m1  m2 
 log
b2
log  2.512 
The last thing to introduce is the
question of mass
That question can be translating into
question: What are binary stars ????????
star
A large ball of gas that creates
and emits its own radiation.
Binary Stars
two balls – not necessarily gas,
not necessarily emitting radiation
>60% of Stars are in
Binary Systems
Contains two (or sometimes more)
stars which orbit around their
common center of mass.
Importance - only when a star is in a
binary system that we have the
possibility of deriving its true mass.
The period – watching the system for many years. The more unequal
the masses are, the
The distance between the two stars - if we know
the distance to the system and their separation in more it shifts toward
the more massive
the sky.
star.
→ the masses can be derived.
T2 
4 d
G  M1  M 2 
2
3
The masses of many single stars can then be determined by extrapolations made
from the observation of binaries.
Visual Binaries
The ideal case:
Both stars can be
seen directly, and
their separation and
relative motion can
be followed directly.
Visual Binary
Stars
the most common case:
Spectroscopic Binaries
Usually, binary separation d
can not be measured directly
because the stars are too
close to each other.
information from: Doppler Shifts for Binary Stars
Idealized binary star system: two stars have equal masses
and are in circular orbits and each star has a single spectral
line at the same frequency when the stars are at rest.
The approaching star produces
blue shifted lines; the receding
star produces red shifted lines
in the spectrum.
have patience
Doppler shift → Measurement
of radial velocities
→ Estimate of separation d
→ Estimate of masses
Spectroscopic
Binary Star
Eclipsing Binaries
There is the rare case when the system is turned so that we see it
directly edge-on. This is called an eclipsing binary system. In the
case of an eclipsing binary, we see each star pass directly in front
of the other one. In these cases, the masses can be directly
determined for the stars.
Eclipsing
Binary Star
Algol known colloquially as the Demon Star, is a bright star in
the constellation Perseus. It is one of the best known eclipsing
binaries, the first such star to be discovered.
Peculiar “double-dip” light curve
NASA
X-ray Binaries
A special class of binary stars is the X-ray binaries, so-called
because they emit X-rays. X-ray binaries are made up of a
normal star and a collapsed star (a white dwarf, neutron star,
or black hole). These pairs of stars produce X-rays if the
stars are close enough together that material is pulled off the
normal star by the gravity of the dense, collapsed star. The
X-rays come from the area around the collapsed star where
the material that is falling toward it is heated to very high
temperatures (over a million degrees!).
An eclipsing binary, with an
indication of the variation in
intensity.
An animation of an eclipsing binary
system undergoing mass transfer.
What is the defining characteristic of an
eclipsing binary system?
That at some point in its orbit one star eclipses the other along our
line of sight.
How many eclipses occur during a complete orbital cycle?
(Two for this system) Add that most systems have two eclipses but
not all systems.
When does the large dip in the light curve occur?
(When the hot blue star is eclipsed.)