Day Lab - Step 2: Determine the Rotational Speed of the Sun

Now we can use measurements of doppler shift to measure the radial velocity of the Sun. Because the Sun is rotating, part of it is rotating toward us and part of it is rotating away, causing the light we receive to be shifted. If we can account for this shift, we can find the rotational speed of the Sun.

However, we do not know where the axis of the Sun lies, so we took 8 measurements around the circumference of the sun and chose the two that were the most different: the bottom left and top right.

So what exactly were we measuring? We took spectral measures of NaD (sodium) lines by carefully aligning a sodium lamp to find the sodium lines on a spectrum and then filtering in sunlight and taking data on those same spectral lines. Numerically, the data is not very exciting:

However, If we graph it, we can see the two sodium lines and to the left of them, Telluric absorption lines which come from water in the atmosphere.

Next we isolate the bottom left line and top right line as discussed above. Zooming in to each of the NaD lines allows us to find the shift between each line by using a best fit curve.

 

However, our measurements are never perfect (it is really hard not to bump the table where the experiment is taking place). We can correct for errors by looking at the Telluric lines (they should not be shifted as they come from Earth's atmosphere).

The offset between each line (in this case 1.089 pixels) tells us how much we need to shift each of the NaD lines. Taking the shift into account, we can use the corrected shift between each NaD line (about 3 pixels) to find the velocity of the sun. (Actually, excel does this for us by converting the data to angstroms and using to formula \( \frac{\delta v}{c} = \frac{\delta \lambda }{\lambda} \) where lambda is the wavelength of each NaD line). 

We get velocities of 1.473 km/s  and 1.411 km/s. Our average velocity is then:

\[\bar{v}= \frac{1.473 + 1.411}{2} = 1.442 \frac{km}{s} \times \frac{1 \times 10^5 cm}{1km} = 1.442 \times 10^5 \frac{cm}{s}\].

Thanks to my lab group: Richard, Daniel, Jonathan, Corey, and Sean and thanks to John and Allison for walking us through this process.