Day Lab Part 2: Rotational Speed of the Sun

The doppler shift allows us to measure radial velocity. We will make several spectral measures of the NaD lines (at 5889 and 5896 Angstroms) from the East limb of the Sun and then the West limb of the Sun. Then with the CCD (and attached microscope lens) we take careful measurements of the Doppler shifts of these two lines relative to that of a Telluric absorption line, which arised from H20 in the Earth's atmosphere. Because we do not know the orientation of the solar equator, we will take 8 measurements around the edge in pairs (left, right; top, bottom; top, right; bottom, left; top, left; bottom right).

To begin, we used several mirrors to focus the light into the spectrophotometer. This device breaks up the light into its component wavelengths, which allows us to see each of their corresponding intensities using a CCD. Below is the layout of the experiment setup:

To generate a sort of coordinate system of the sun, we took measurements at 8 different locations. Once we collected the measurements for each location, we entered the data into an excel spreadsheet for analysis. Below is the Normalized plot of spectral lines:

Normalized Plot of Spectral Lines

We can notice from the plot that there are two distinct spikes in the lines. These depict the sodium absorption lines, where we expect to see the doppler shift. Since we wanted to find the lines that were on opposite sides of the sun, we looked at the minimum values, and chose the lines with the greatest separation. From our plots, we found these to be the top and bottom data sets.

We then plotted these values, and fit a curves to each dataset. These are shown below:

Rather than simply taking the difference, however, we also needed to take into account any shift that should not be attributed to the doppler effect. To do this, we also considered the Telluric absorption lines that should remain the same in both graphs. Below is the plot of the Telluric absorption lines. 

We found the telluric shift to have an offset of 0.9288 pixels, which we factored into the calculation for final rotational velocity. Overall, we found a shift of approximately 3 pixels per dataset, which resulted in a final rotational velocity of: 1.36 km/s