Sodium D lines Credit: Bernard McCarty & Sarah Wilson

Planetary rotation

by M Coleman, H Coleman, S Binns and D Acreman

Introduction: The aim of the planetary rotation project was to measure the rotational periods of Saturn and Jupiter using the Doppler effect. By comparing the Doppler shift in the reflected solar spectrum at different points across the disk of the planet, the speed of rotation was be determined. The velocity of Saturn's rings enabled the mass os Saturn to be estimated.

Observations: Jupiter and Saturn were observed on 23/10/97 at the University of Birmingham observatory at Wast Hills. Exposure times of 2700 seconds for Saturn and 900 seconds for Jupiter were used. The observatory spectrometer was used to analyse the data by placing the spectrometer slit East-West across the disk of the planet. The resulting spectra were recorded on a CCD (Charge Coupled Device) and saved onto computer disks for later analysis. Before and after each exposure, a calib ration was made by recording the spectrum of a neon lamp with known emission lines. Flat fields were also taken by illuminating the CCD with uniform light from a tungsten lamp. The flat field enables the effect of different pixel sensitivity, on the CCD, to be accounted for.

Data analysis: The raw data was in the form of 2-dimensional spectra (see figures 1 and 2).

Figure 1: 2D Spectrum of Saturn in false colour.

Figure 2: 2D Spectrum of Jupiter in false colour.

These 2D spectra have wavelength increasing along the x-axis and position across the spectrometer slit varying along the y axis. The bright horizontal band of the planet can be seen in both spectra. The three dark absorption lines are the calcium triplet. The absoprtion lines will be tilted due to the Doppler effect and it is this tilt which enables the rotation speed to be measured. The astronomical data analysis package 'FIGARO' was used to analyse the data. The images were first processed by dividi ng by a flat field to remove the effects of pixel sensitivity. The 2D spectra were then collapsed along the x-axis to produce a surface brightness profile (see figure 3 and figure 4).

Figure 3: Surface brightness profile of Saturn

Figure 4: Surface brightness profile of Jupiter

Using the surface brightness profiles, the centre of each planet was found. The 2D spectra were then split up into 'bins'; each bin from a different point on the disk of the planet. Each bin had a Doppler shift relative to the central bin (which was taken to have a Doppler shift of zero). By performing a cross correlation it was possible to determine the Doppler shift (in pixels) of each bin. The spectrum of the neon lamp was used to calibrate the CCD in order to relate pixels to nanometres on the wav elength axis. The neon lamp was also used to remove the 'instrumental tilt'. Spectral lines will be tilted a certain amount by the instrument set up and this must be taken into account when calculating the Doppler shift.

The wavelength shift was converted to a velocity using the non-relativistic Doppler formula:

(The factor of 2 arises because the light is absorbed then remitted). A rotation curve (velocity vs. position) was then plotted for each planet. The gradient of the rotation curve gives the angular velocity of the planet (v=r) hence the rotational period could be determined. The mass of Saturn was determined by treating the rings as a Keplerian disk which has a speed given by

The speed of the rings (v) at a distance R from the centre of the planet was known enabling the mass of Saturn (M) to be found.

Results: The rotational period of Jupiter was measured to be (14.5+/-3.8) hours compared to the accepted value of 9.84 hours. The rotational period of Saturn was measured to be (10.3+/-1.9) hours compared to the accepted value of 10.2 hours. The mass of Saturn was estimated to be about 4x1026 kg; the accepted value is 5.69x10^26 kg.

Solar Rotation

by Bernard McCarty and Sarah Wilson

Introduction. During spring 1998 we endeavoured to determine the rotational velocity of the Sun at a point on its equator. Looking at the Sun from the Earth, an observer will see light that is slightly blue-shifted as the east limb moves towards the observer and conversely light from a point rotating away from us, on its west limb, shifted towards the red end of the spectrum. By measuring the small Doppler shift in the spectral lines in light seen from opposite limbs of the sun it is possible to make a determination of the rate of rotation of the Sun at its equator.

Spectral lines in the Sun's spectrum are displaced by an amount proportional to the speed of approach or recession of each limb. By comparison with the spectral line for a known element such as sodium, the Doppler shift of the light from each limb can be measured.

The relationship between the Doppler shift and the velocity of a point on either limb of the Sun is given by: dl / l = v/c

where c = velocity of light, v = velocity of a point on the Sun's equator, dl = the measured displacement of the wavelength of a spectral line in light coming from a limb of the Sun and l is the wavelength corresponding to a spectral line from a rest source in the laboratory.

Measurements. An image of the Sun was produced and a small perspex disc, with holes drilled to hold two fibre optic cables was aligned in the focal plane of the telescope so that the holes corresponded to the east and west limbs of the Sun's image. The fibre optic cables took light from each of the limbs on the Sun's image and were lined up with the slit of a spectrometer containing a grating of 1200 lines per mm and125mm wide. The diffracted image of the slit was received by a CCD ca mera and the resulting spectra were passed to an external PC for analysis. The calibration source was a Sodium lamp, from which the relative red and blue shifts were compared. A satisfactory image of the Sodium D lines at 588.995 nm and 589.5924 nm was obtained from a lamp at rest in the laboratory. See below

Image of Sodium D lines captured on CCD camera (reverse grey scale image).

Intensity plots of the spectra were taken and compared. The resulting offset due to the Doppler shift of the light from each limb allowed a calculation of the rotational velocity of the Sun to be made.

Results. Using the relation outlined in the introduction we calculated a value of 2.3 +/- 0.1 kms^-1 for the rotation of the Sun at its equator