The object SS433 is named because of its entry number in a catalog compiled by Sanduleak and Stephenson. This catalog picked out stars with strong emission lines. As it happens, SS433 is particularly weird for other reasons as well. These emissions lines seem to come from hydrogen jets shooting out from the object, most likely a neutron star orbiting a "normal" star. In this exercise, you will use emission line data to sketch the orientation of these jets, and to determine some information about their direction.

SS433 is unremarkable in the optical (R band) until you look at the spectrum, where the three spectra shown were taken on successive nights. There is a clear H-alpha emission line at 656.6nm. However, there are also two "satellite" peaks in each spectrum. One is blue shifted down to about 600nm, and the other is red shifted up to near 750nm. Furthermore, the amount of the red and blue shift changes each night!

The accepted model of SS433 is a binary star system, where the compact object draws matter from the normal companion, and spews jets out along its axis of rotation. The jets have in fact been imaged using the Very Long Baseline Array (VLBA) of radio telescopes. One jet gives one of the doppler shifted lines, and the other jet gives the other shift. As the axis of rotation, and therefore the jets, precess about some direction, the amount of doppler shift chantes.

The doppler shift Z, that is the difference in observed and laboratory wavelengths, divided by the laboratory wavelength, has been followed for over twenty years. The precession period is 162 days. The amount of doppler shift is plotted as a function of day for one jet and for the other. (Also plotted is the deviation from the sinusoidal fit for the 162 day period.) You will use this data to answer the questions below.

You will need to review some Special Relativity to do this problem. In particular, you need to use the "full" doppler shift formula, including time dilation effects. See Chapter Seven of your textbook, in particular Section 7.4.

Now work through and hand in your answers to the following problems. Everyone please hand in your own work, but you are welcome to collaborate to figure all this out.

1. Explain why the doppler shift curves do not cross at Z=0. At what Z do they cross? Make a sketch of the orientation of the "jets" (relative to an observer on Earth) when the curves cross.
2. Use the answer above to calculate the speed of the jets. You can leave the answer in terms of v/c.
3. Explain why one doppler curve reaches a minimum when the other reaches a maximum, and vice versa. Make a sketch of the jet orientation when the maximum doppler shift is observed.
4. What is the smallest angle the jet axis makes with respect to the Earth observer?
5. What is the largest angle the jet axis makes with respect to the Earth observer?
6. Draw a sketch to show how the minimum and maximum angles are related to the tilt angle and precession angle of the jet axis. Calculate the tilt and precession angles.