1. Stellar Masses: Binary Stars

2. The HR Diagram Again

3. A Diagram for People
Q: What is happening here? A: People grow. They are born small, and then grow in height and mass as they age (with a fair bit of individual scatter).

4. Are the MS Stars Analogous? [MS = Main Sequence]
Here are two ‘obvious’ possibilities:
Stars start out raging hot (blue, bright) and cool off (get redder and fainter) as they use up their fuel, like a dying coal.
Stars start out cool, and get hotter and brighter as they use up fuel and contract under the influence of gravity.
Either one of these possibilities suggests that stars would move along the main sequence, from top left to bottom right or vice versa. (It still leaves unresolved the status of the white dwarfs and red giants.)

5. The Missing Evidence
To understand the astrophysics of the stars, we need new information:
their masses.
We do this by studying binary stars. They orbit one another because of their mutual gravitational influence.

6. Remember, Both Stars Move
The two stars in a binary system may be comparable in mass. Each one has a strong influence on the other, and they both move perceptibly. (It’s not like a tiny satellite going around the huge Earth.)
This complicates the mass determinations somewhat but does not make them impossible.

7. Beware ‘Optical Double’ Stars
There are some ‘optical doubles’ – two stars that appear to be close to one another, but only by chance. (One is in the foreground, one much farther away.)
This can be sorted out. As time passes, we realize that they are moving utterly independently, not orbiting one another, so not a true binary at all. Their motions give us no useful information.

8. Confirming a Binary Star’s Reality
We monitor the stars over time, to see if they are truly in mutual orbit.
But how would this show up? Answers:
Changing positions
Changing speeds
Changing brightnesses (through eclipses)

9. Several Classes of Binaries
Depending on how we detect and confirm them, there are several classes of binaries:
Visual binaries
Eclipsing binaries
Spectroscopic binaries
Astrometric binaries

10. We Want to Learn About Stars of All Kinds
There are two possible concerns:
Maybe only certain kinds of stars occur in binary pairs.
‘Selection effects’ may bias our results.

11. 1. Visual Binaries
Here, we actually see both stars: that is, two dots of light! We can watch them orbit each other.
Selection effect: the separate points of light will be easier to see if the stars are widely separated and if the binary is rather close to us. A good example: Sirius
(In a very remote binary system, the two points of light will be merged into one and we won’t be able to follow the orbits.)

12. One Consequential Problem
Widely-separated objects orbit more slowly than those close together, since they feel each other’s gravity less strongly. (In the Solar System, Mercury orbits the sun in 88 days; Neptune takes 165 years!)
Monitoring a typical visual
binary takes decades or even
centuries to see even one
complete orbit. Fortunately,
astronomers have been
doing this kind of work
for centuries.

13. Two Sobering Examples (Look at the Dates!)

14. Another Potential Complication: ‘Projection Effects’ (We may be looking from an angle, not seeing the ‘true orbit’)

15. 2. Eclipsing Binaries
To see an eclipse, we have to be close to the plane of the mutual orbit so that (from our point of view) one star occasionally passes in front of the other.
But (from ASTR 101) remember how rare the
transits of Venus are: once a century or so.
We would see more frequent transits if Venus
was much closer to the Sun.
There is a selection effect, therefore:
Seeing an eclipse is more likely if the two stars in the binary system are very close together.

16. The Implication
If the two stars are close together, we are more likely to see eclipses. But then:
the orbital periods will be quite short; and
the two dots of light will be hopelessly merged into one
On the other hand, they don’t need to be close to us. We can find very distant systems because they ‘wink’ at us!
So we look for a single dot of light which periodically goes dim and then recovers!
Many thousands are known.

17. Consider Algol (a 3-day period!)
The inferred behaviour.

18. Animations Visit http://astro.unl.edu/naap/ebs/animations/ebs.swf
to find interactive animations of eclipsing binaries. This animation works in Firefox.
Search the web for others kinds!

19. One Problem: Tidal Distortions
The stars in an eclipsing binary may be so close together that they distort each other’s shape, through tides, and (as we will learn) can even affect each other’s evolution.

20. Sometimes the Two Stars are Literally in Contact - and material can even move from one star to the other.
More on this later, when we learn about novae.

21. 3. Spectroscopic Binaries
We detect changing velocities, using the Doppler shift.
Take a spectrum of a single dot of light, and note and measure the positions of the absorption lines. Since there are two bright stars in the unresolved binary, there should be two sets of absorption lines, with different velocities. This is because at a given instant, one star is approaching, the other one receding.
Repeat this exercise later, and note that this lines have changed position in the spectrum because the velocities change as the stars move in their orbits!

22. As Demonstrated Here

23. Selection Effects
1. You have to be looking at the binary‘sideways on’ so that the stars alternately move towards and away from you.
2. The Doppler shifts are bigger and more noticeable for binary stars which are moving fast, and with large changes in velocity.
This favours finding massive stars in close binaries. Their close separation this means that we will not generally resolve the binary into two stars: we will see only a single dot of light.

24. ‘Single-Line’ Spectroscopic Binaries
Suppose one of the stars is very faint – a white
dwarf, a neutron star [to be described later], or
even a Black Hole, emitting no light!
Then we detect the light of only the other star.
We will see just one set of spectral lines, shifting
back and forth.
Remember this technique for later, when we search for black holes!

25. 4. Astrometric Binaries
We detect the existence of a binary because a star ‘wobbles’ in position as it moves across the sky.
Sirius is a good example:
Selection Effect: This is most easily detected for very nearby stars where the small ‘sideways’ deviations are noticeable. (Sirius is just 9 light years away.)

26. From Binaries, We Get Stellar Masses
Simply apply Newton’s laws! (It’s not guesswork!) How much mass must the stars contain to make each other move, under the influence of gravity, in the orbits they do?

27. Back to the HR Diagram - let’s put in those masses!
The interpretation follows in the next presentation!