Eclipsing Binaries

If the binary stars are eclipsing, then it is guaranteed that we are in the orbital plane. This means that the maximum radial velocity on the velocity plot gives us the orbital velocity. Now we have “a” and we have “P”. We can get rid of one of the “M”s because we know how they are related.

Example (M 1 + M 2 )P 2 = (4π 2 /G)a 3 If v 2 = 3v 1 then M 1 = 3M 2 then we can write: (3M 2 + M 2 )P 2 = (4π 2 /G)a 3 (4M 2 ) = (4π 2 /G)(a 3 /P 2 ) Once we find M 2 we know that M 1 is three times the mass

Masses of Stars Many such measurements show us that mass increases on the Main Sequence as the temperature and luminosity increase. As theory predicts. Furthermore, Mass does not correlate with luminosity for giant, evolved stars. Giants might have a large mass, or they might have a small mass, but still they are very luminous. Also the mass of a white dwarf is not correlated to its luminosity. Something different is happening for these guys.

Well established relation on Main-Sequence L * /L sun = (M * /M sun ) 4 Example: If a star has M * = 5M sun then (M * /M sun ) = 5 But 5 4 = 625. So L * /L sun = 625. The star has 5 times the fuel but is burning it 625 times as fast. Lifetime = 80 million years.

Spectral Typing of Stars Spectral typing involves comparison of the absorption lines in stars in order to determine temperature and the amount of various elements in a star. In particular, it is comparing the strength (how dark) of the line.

Different stars have different absorption line strengths

Early Spectral typing In the 1900s, scientists didn’t know why stars had different line strengths. Not knowing the physical reason, they just classified them from A to O. A-stars had the strongest hydrogen lines. O-stars the weakest. Later they found many classifications were actually the same spectral type. Finally they realized that the strength of the hydrogen line correlated to the stars color, or temperature. The spectral type order was changed to go from the hottest stars to the coolest. O,B,A,F,G,K,M They were later subdivided, A0, A1, A2, … A9 ; with A0 the hottest Cooler stars where added, L, T.

Different stars have different absorption line strengths

Plot of Intensity versus wavelength (λ)

How strong a line appears depends primarily on TWO PARAMETERS The surface temperature Example: If an element is ionized then it can not form an absorption line. The amount of a particular element present in the star. Example: If there is no Iron in a star, how strong will the absorption line for Iron appear to be?

If there is no Iron in a star, how strong will the absorption line for Iron appear to be? 1. Very Weak 2. Strong 3. Can’t say, it depends on the star’s temperature 4. Non-existent

No shortage of hydrogen in normal stars. But, Balmer lines are transistion between levels n=2 and n=3,4,5,6,etc.

In order to have the hydrogen Balmer lines appear, Hydrogen has to be in the first excited state. (n = 2) Which stars are the most likely to not have enough energy to maintain the hydrogen electrons at the first excited state?

1. Cool stars (M-type) 2. Warm stars (G-type) 3. Hot stars (A-type) 4. Hottest stars (O-type)

If a star is very hot, the electrons will be freed from the hydrogen atom. (Ionized) Once they are free, they act like particles and emit a continuous spectrum. If the star is hot enough that hydrogen is ionized all the way to the surface, then there will be no hydrogen Balmer lines.

Here is how line strength depends of temperature

Remember, the line strength depends primarily on two parameters. (1) Surface Temperature and (2) Number of absorbers. If we want learn about the number of absorbers for a given element (say, calcium, iron, gold, etc) then we need to know the temperature of the star. If we know the temperature we can account for its effect and… The line strength will only depend on the Number of Absorbers.

Why doesn’t the spectrum of HD line up with the model spectrum? 1. The model spectrum is wrong 2. The star is very far away 3. It is caused by the doppler effect 4. I f’ed up and plotted the spectrum wrong

Spectral typing Summary Spectral typing can be used to find the surface temperature of a star. (Along with color and Wien’s Law) Spectral typing can also be used to find out how much of a given element is in a star. HD has much less of all the elements, other than Hydrogen and Helium, than the Sun. In fact, it has about 0.03 the value of the Sun for all 90 elements. That is 3% the amount in the Sun. The most deficient star known has about 0.001% the Sun. There are also stars with up to 3 times the amount in the Sun.