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Measuring the Masses of
Stars
Binary Star Systems
How Can the Mass of a Star be
Measured?
• Knowing the mass of a star is important to
astronomers. It’s the star’s mass that
controls all the other characteristics of the
star: it’s luminosity, temperature, color,
size, even lifetime.
• BUT…it’s not possible to directly measure
the mass of a single, isolated star. So
what can we do?
Binary Star Systems
• If something, like a planet or a 2nd star, is
in orbit around the star whose mass we
wish to know…we can use Newton’s form
of Kepler’s 3rd Law to find the total mass of
the system:
(MassStar A + MassStar B) = 4π2a3
G p2
(a is the distance between the stars in meters, and
p is the period of revolution of the stars in
seconds.)
Doesn’t sound too hard!
• The good thing is that 50% to 75% of all
stars are found in binary or multiple star
systems.
• If we can watch 2 stars orbit each other
and determine the period of revolution and
the distance between the stars, we can
calculate the total mass of the system and
maybe even the individual masses of the
two stars.
Extending to single stars
• Once we know the masses of many stars
in binary star systems, we can infer the
masses of single, isolated stars by
comparing them to similar stars with
known masses.
Types of Binary Star Systems
• Optical Doubles – the foolers
• Visual Binaries
• Spectroscopic Binaries
• Astrometric Binaries
• Eclipsing Binaries
Optical Doubles
• In a telescope, an optical double looks like
a binary star system, 2 stars that are in
orbit around a common center of mass.
• However, they’re really far apart from each
other. They just happen to be in the same
part of the sky.
• Mizar and Alcor are an optical double pair.
Alcor is
81 LY
away
Mizar is
78 LY
away.
Mizar and Alcor do not orbit each other.
http://jumk.de/astronomie/special-stars/mizar-alcor.shtml
Visual Binary Stars
• The 2 stars actually orbit a common center
of mass.
• Both stars are visible either to the naked
eye or through a telescope.
• We call the brighter star the primary, and
the fainter star the secondary.
Albireo is the beak of
Cygnus the Swan.
domeofthesky.com/clicks/images/albireo.gif
http://www.astro.princeton.edu/~esirko/sky/pix/albireo.jpg
Procyon, in the
winter triangle
is a class F
subgiant with
a white dwarf,
only 11 LY
away.
http://www.synapses.co.uk/astro/procyon.gif
http://www.glyphweb.com/esky/_images/illustrations/procyon.gif
Sirius A is a class A
star about 25 times
brighter than our
sun, with a tiny
white dwarf
companion, Sirius B.
http://www.space.com/images/sirius_a_b_photo_030715_03.jpg
Spectroscopic Binary Stars
• In a spectroscopic binary system, one of
the two stars can’t be seen in a telescope.
– The system may be too distant to resolve the
two stars.
– One of the stars may be too faint to see (a red
dwarf).
– The two stars may be very close to one
another.
• How do we even know 2 stars are there?
It’s all in the Doppler Shift
• If the orbits of the two stars are edge-on to
us, then one of the stars is moving
towards us, while the other star is moving
away.
• The light from the star moving towards us
is blueshifted, while the light from the star
moving away is redshifted.
It’s all in the Doppler Shift
• As we look in the spectrum of light from
the stars, over time we see each spectral
line split into two lines, then slowly come
back together.
• We can get the stars’ orbital period from
how long it takes the lines to split, come
back, split, and come back together again.
Watch it here…
http://csep10.phys.utk.edu/astr162/lect/binar
ies/spectroscopic.html
http://instruct1.cit.cornell.edu/courses/astro1
01/java/binary/binary.htm
Dubhe, in Ursa Major,
about 124 LY away, is
a spectroscopic binary
system, as is Capella
in Auriga, 40 LY away.
http://pioneer.utah.gov/utah_on_the_web/images/dubhe1.gif
http://www.carbonar.es/s33/Auriga/Capella.jpg
The “star” that we
call Castor, in
Gemini, is actually
3 pairs of stars.
Each pair is a
spectroscopic
binary pair.
Pairs A & B orbit each other every 400 years.
Pair C orbits A & B with a period of about
10,000 years. http://www.jb.man.ac.uk/public/AList/Gemini.jpg
Mizar in Ursa Major is also a spectroscopic
binary star. In fact, it was the first one ever
discovered, in 1889. Recent work has
been able to resolve the two stars.
http://paginas.terra.com.br/arte/astrophotography/double/Mizar_19-04-2004_hi.jpg
Astrometric Binary Stars
• An astrometric binary system is a
spectroscopic binary where we can
actually observe the primary star “wobble”
as it moves across the sky (proper
motion.)
• The star’s “wobble” lets us know that
something massive, but unseen, is in orbit
with the primary star.
Above is the proper motion
of Sirius A (orange) as it
moves across the sky.
At right are the
orbits of the two stars.
http://linus.highpoint.edu/~atitus/ast121/Chapter_11/binary_stars/sirius-path.jpg
http://linus.highpoint.edu/~atitus/ast121/Chapter_11/binary_stars/sirius-orbit.jpg
Eclipsing Binary Stars
• An eclipsing binary system is a special
type of spectroscopic binary, where the
orbit of the two stars is edge-on to our line
of sight.
• We periodically see one star pass in front
of or eclipse the other star. When this
happens the total amount of light that we
receive from the pair dims for a few hours.
http://outreach.atnf.csiro.au/
education/senior/astrophysics/
images/binvar/svcamweba.jpg
Special Information
• Eclipsing binaries give us some very
special information. If you plot the light
curve of the stars, the total amount of light
received over time, you can actually
measure the diameters of the two stars.
• The plot on the previous page was a light
curve.
Click here for an animation of
an eclipsing binary system.
Scroll down to the bottom of
the web page.
Click here for a good
illustration of a light curve.
Algol
• The first eclipsing binary system studied
was the “winking demon star” Algol, the
knee of Perseus.
• Algol has a period of 2.87 days and is
easily noticeable to the naked eye.
Algol
• The Algol system is about 96 LY away.
• The primary is a massive blue-white B8
star with 3.5 Msun and 100 Lsun.
• The secondary is an orange K2 subgiant
star with 0.8 Msun and 3 Lsun.
Click here for an animation of Algol.
Algol’s Light Curve
Tomorrow…
…you’ll have the opportunity to plot your
own light curves for 2 different eclipsing
binary star systems.