R. Strickler, C. Bresloff, J. Graham (UC Berkeley)
The discovery of extra-solar planets has stimulated interest amongst undergraduates. The Doppler method for detecting exoplanets requires extraction of signals at the 1/1000 of a pixel level. To illustrate this technique, we used a newly built spectrometer to extract sub-pixel Doppler shifts in the solar photosphere.
We have used this spectrograph to measure the velocity gradient across the sun and hence infer the solar radius. The limb-to-limb Doppler shift is only 1.8 km/s. A spectral resolution > 100,000 would be required to manifest this motion. Achieving such high spectral resolution is unnecessary since even a small telescope can record high SNR (> 100) spectra. Within a few seconds it is possible to discern solar rotational Doppler shifts at resolutions as low as 10,000. We must also understand coordinate transformation to convert the Doppler signal along the observed diameter to the equatorial rotation speed assuming solid body rotation.
The spectrograph system includes an 8-inch Schmidt-Cassegrain stationary telescope; a 100-micron diameter multi-mode fiber; aspheric f-number reformatting optics; a collimating lens; a 110 mm, 80 grooves/mm, \thetablaze = 64.5 degree replica echelle grating; and an Apogee 1024 x 1024 thermo-electrically cooled CCD. The spectrometer optics are mounted on a 5-ft x 3-ft optical bench. Operating the spectrometer remotely using VNC and a wireless laptop, we pointed the telescope so that the fiber scanned across a diameter of the solar disk while the CCD took repeated exposures. Although we were "guinea pigs," using the spectrograph for the first time in a class, it worked remarkably well.
Combining measurement of the solar radius with observation of the rotation period from sunspots, the earth-sun distance can be deduced. In the future, students may measure the eccentricity of earth's orbit by measuring the sun's radial velocity over the course of a year.
This work was supported by the NSF through award DUE-0311536.
Bulletin of the American Astronomical Society, 37 #2
© 2005. The American Astronomical Soceity.