Measuring the Masses of Stars Binary Star Systems

1
Measuring the Masses ofStarsBinary Star Systems
2
How Can the Mass of a Star be Measured?

• Knowing the mass of a star is important to
  astronomers. Its the stars mass that controls
  all the other characteristics of the star its
  luminosity, temperature, color, size, even
  lifetime.
• BUTits not possible to directly measure the
  mass of a single, isolated star. So what can we
  do?

3
Binary Star Systems

• If something, like a planet or a 2nd star, is in
  orbit around the star whose mass we wish to
  knowwe can use Newtons form of Keplers 3rd Law
  to find the total mass of the system
• (MassStar A MassStar B) 4p2a3
• G p2
• (a is the distance between the stars in meters,
  and p is the period of revolution of the stars in
  seconds.)

4
Doesnt 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.

5
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.

6
Types of Binary Star Systems

• Optical Doubles the foolers
• Visual Binaries
• Spectroscopic Binaries
• Astrometric Binaries
• Eclipsing Binaries

7
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, theyre 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.

8
Alcor is81 LY away
Mizar is78 LY away.
Mizar and Alcor do not orbit each
other. http//jumk.de/astronomie/special-stars/miz
ar-alcor.shtml
9
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.

10
Albireo is the beak of Cygnus the
Swan. domeofthesky.com/clicks/images/albireo.gif
http//www.astro.princeton.edu/esirko/sky/pix/a
lbireo.jpg
11
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/proc
yon.gif
12
Sirius A is a class Astar about 25
times brighter than our sun, with a tiny white
dwarf companion, Sirius B.
http//www.space.com/images/sirius_a_b_photo_03071
5_03.jpg
13
Spectroscopic Binary Stars

• In a spectroscopic binary system, one of the two
  stars cant 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?

14
Its 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.

15
Its 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.

16
Watch it here

• http//csep10.phys.utk.edu/astr162/lect/binaries/s
  pectroscopic.html
• http//instruct1.cit.cornell.edu/courses/astro101/
  java/binary/binary.htm

17
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/dub
he1.gif http//www.carbonar.es/s33/Auriga/Capella
.jpg
18
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/pub
lic/AList/Gemini.jpg
19
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
20
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 stars wobble lets us know that something
  massive, but unseen, is in orbit with the primary
  star.

21
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.highp
oint.edu/atitus/ast121/Chapter_11/binary_stars/si
rius-orbit.jpg
22
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.

23
http//outreach.atnf.csiro.au/ education/senior/as
trophysics/ images/binvar/svcamweba.jpg
24
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.

25
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.
26
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.

27
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.
28
Algols Light Curve
29
Tomorrow

• youll have the opportunity to plot your own
  light curves for 2 different eclipsing binary
  star systems.