Spectropolarimetry

The first step in the data reduction, like for most of the data presented in this thesis, was to subtract the bias frames. Several bias frames were median averaged, with theiraf taskzerocombine, and then the task ccdprocwas used to subtract the bias frames from the science data. Then, the flatfielding was performed, using the iraf taskimarithto divide the science images by the flatfield frames. The next step was to extract the flux counts from the CCD images. The CCD of FORS2 is divided into

strips, as illustrated in Figure 3.8, with adjacent strips contained fluxes for ordinary and extraordinary beams.

Figure 3.8: An image of earthshine data on the FORS2 CCD.

A dedicated FORTRAN script was then used to carry out the remainder of the data reduction, namely: wavelength calibration, defining of apertures around the individual strips, summing of fluxes, and spectrum extraction.

FORS2 has a polarimetric module that allows the use of the beam-swapping tech- nique, which is fully described in Bagnulo et al. [2009], with the key concepts and equations given here. The beam-swapping technique minimises the errors that can be introduced through instrumental polarisation, with any value of instrumental polarisation less than 0.1% [Cikota et al., 2017], which is less than the size of the error due to photon noise. The flux combinations to calculate the Stokes parameters were carried out in MATLAB. After the fluxes of the ordinary and extraordinary beams were extracted and written to ASCII files, the beam-swapping technique was applied to calculate the Stokes parameters:

PX = 1 2N N X j=1 2 4 fk f? fk_+f? ! ↵j fk f? fk_+f? ! ↵j+ ↵ 3 5 (3.1)

angles,f?is the flux in the perpendicular beam,fk is the flux in the parallel beam, ↵is the retarder angle with respect to its zero point in degrees, and ↵is 45 . The sum is over all pairs of retarder angles which the observations have been obtained over; in our case, N = 4, since 8 di↵erent retarder waveplate angles were used for measuring each Stokes parameter (thus 16 angles in total: 0 - 337 in steps of 22.5 ). The uncertainties are calculated as in Bagnulo et al. [2009]. The error on PX is

given by

PX =

1

2pN F, (3.2)

whereN is the number of pairs of exposures, and F is the flux accumulated in both ordinary and extraordinary beams from all exposures. The error on the position angle, , is given by = 1 2 PL PL , (3.3) with PL = PX. 3.3.3.2 FoReRo2

As for the FORS2 data reduction, the beam swapping technique was used, thus any instrumental polarisation is negligible. An image of the CCD of Uranus spectropo- larimetry is shown in Figure 3.9. The data reduction for the FoReRo2 spectropo- larimetry was carried out iniraf, with the flux combinations to calculate the Stokes parameters carried out in MATLAB. The science frames were bias subtracted, and then collapsed into 1D spectra with a wavelength calibration then performed using arc-lamp spectra taken just after the observations. The fluxes of the ordinary and extraordinary beams were then extracted, and the beam-swapping technique was applied to calculate the Stokes parameters.

Observations were taken at either four or eight individual retarder waveplate angles. The reduced Stokes parameters were calculated with Eqn. 3.3.3.1. The spectrum of a solar analogue was also obtained. The solar analogue was used to derive the reflectance spectrum of the objects: since the light reflected by the planet or moon is from the Sun, the spectral energy distribution will be mostly composed of that of the Sun’s, so this must be divided out in order to extract the true reflectance spectrum. As is shown in the following chapters, the solar analogue is not entirely an exact match of the Sun’s spectrum, therefore some features or remnants of the solar flux

Figure 3.9: Left: spectrum of Uranus as shown on the CCD of FoReRo2, both ordinary and extraordinary beams.

remain in the reflectance spectra of the object. Polarised standard stars were also observed in order to characterise the instrumental position angle o↵set, and these are shown in Table 3.1 along with the solar analogue star. The position angle of polarisation that is obtained from the data is one that is an instrumental angle,

✓inst, and in order to obtain the real value the following calculation is performed:

=✓inst+✓cat (3.4)

✓actual= ✓inst (3.5)

with✓catthe catalogue values of✓, taken from Schmidt et al. [1992]. This calculation

was performed for all spectropolarimetry datasets that had a polarised standard star taken along with the data.

An unpolarised standard star was also observed by Galin Borisov in April 2017, de- tails of which are given in Table 3.1 and the result of which is shown in Figure 3.10. The non-zero value of linear polarisation increasing with wavelength is most likely due to the slit [Keller, 2002], since the instrumental polarisation for imaging po- larimetry measurements has been found to be virtually zero. This is the subject of an ongoing investigation at the time of writing.

500 550 600 650 700 750 800 850 Wavelength (nm) 0 0.5 1 1.5 2 P L (%)

Figure 3.10: PL of an unpolarised standard star taken with FoReRo2.

Table 3.1: Standard stars observed with FoReRo2.

Object Type Date UT Exp. Time (s) Filter/Grism

HD1835 Solar analogue 19/09/2014 21:38 1 GrismW

HD204827 Polarised 06/11/2015 18:02 60 GrismW HD161056 Polarised 10/07/2016 23:13 60 GrismW HD161056 Polarised 11/07/2016 23:12 12 IF642 HD161056 Polarised 11/07/2016 23:28 10 IF620 HD161056 Polarised 11/07/2016 23:49 18 IF590 HD154892 Unpolarised 25/04/2017 22:40 60 GrismW

3.3.3.3 ISIS

The blue and red arms were e↵ectively treated as separate instruments in the data

reduction process, since di↵erent bias frames were required, as well as di↵erent

wavelength calibration images from arc-lamps. Additionally, the positions of the ordinary and extraordinary beams on the CCD are swapped between the red and

blue arms (the di↵erence between ordinary and extraordinary beams was determined

by measuring the Stokes parameters of a standard star, and comparing against known values).

The data reduction procedure for both arms involved the same steps. The first step was to subtract the bias. This was done in the standard way, with several bias

frames median averaged, with theiraftaskzerocombine, and then the taskccdproc

was used to subtract the bias frames from the science data. Depending on the dataset, either a one dimensional or a two dimensional wavelength calibration was carried out. The 1D calibration is the standard method for reducing observations of point sources, such as stars or most asteroids. In the case of this thesis, the only point sources observed were the ice giant planets (depending on the resolution of the instrument), Titan, and standard stars.

The 1D reduction method firstly involves collapsing the spectra for each retarder

angle in theiraf ask apall. This task takes the average of a certain number of lines,

and then adds these together, producing a 1D spectrum. This was done interactively for one image, and then the rest of the images are collapsed using the first image as a reference, using the same aperture sizes and polynomial fit. The next step was to combine the images taken for each individual retarder angle, to increase the signal-to-noise ratio. So for example, if ten exposures were taken for each retarder position, then the ten images would be combined to form one master image, with

a higher pixel intensity value for the science data. The iraf task speccombine was

used for this, which added the 1D images together.

Spectra of arc-lamp emissions were also taken several times on the night of observing. This is in order to fit a wavelength scale to the CCD images. Arc-lamp spectra were taken either before or just after the observations, so that all of the instrumental setup and observing conditions were preserved. As with the science images, the arc images were collapsed and combined in the same way, so that one master arc-lamp image was produced. Each arc-lamp spectrum only pertained to a single observation. Theiraf taskidentify was used to identify the emission lines of the lamp recorded by the CCD. This was done separately for each aperture, since the line positions

could be slightly di↵erent for each part of the CCD. Once a good fit was performed between the data and the known lines, the wavelength identification was written to the database. After this, the calibration was applied to the science images using the taskdispcor. It is in this task where rebinning was also carried out. After this, the task wspectext was used to convert the images to text files, with a list of the intensity value per pixel.

Since most of the data presented in this thesis are of extended objects, such as Jupiter and Saturn, the images recorded on the CCD are quite di↵erent to those from stars, thus cannot be treated in the same way when attempting to extract the scientific content. Figure 3.11 shows on the CCD the line spread function of the raw spectrum of a standard star, along with the size of the apertures. Figure 3.12 show the corresponding images for Saturn. It is clear that the apertures are larger for Saturn, and also the figure shows that they are extended, and clearly not similar to those from a point source. Collapsing the spectrum of an extended object could potentially lead to a less accurate wavelength calibration, thus a 2D data reduction method was attempted for some of the observations of extended objects presented in this work.

Figure 3.11: Left: spectrum of a polarised standard star as shown on the red CCD of ISIS, both ordinary and extraordinary beams. Right: both beams shown in iraf, for definition of apertures for 1D spectrum extraction.

The 2D reduction method produced the same end result, with some di↵erent in- termediate steps. The first di↵erence is that neither the science images nor the arc-lamp images are collapsed into 1D spectra before wavelength calibration. The CCD image is first mapped in wavelength, and then the distortion is corrected for. Theiraf taskidentify was used firstly to define arc-lamp emission lines for a section of the 2D image, then reidentify was used to do this for sections across the entire

Figure 3.12: Left: spectrum of Saturn as shown on the red CCD of ISIS, both

ordinary and extraordinary beams. Right: both beams shown iniraf, for definition

of apertures for 1D spectrum extraction. Note that the apertures are much wider than those in Figure 3.11.

image. The taskfitcoord was then used to fit a 2D function to the arc-lamp images,

withtransform finally applied to fit the 2D calibration to the science images.

Unfortunately, the 2D reduction method often failed. The reason for this is still unclear. However, this was not a significant issue, because the 1D reduction method provided very similar results to the 2D method, for the objects that the 2D reduction method proved to be successful. Figure 3.13 shows the reduced linear polarisation spectrum of Saturn data taken on the 03/02/2015, with the red arm of ISIS. The results of both the 2D reduction and the 1D reduction are shown. For clarity, error bars are included for the 2D reduction, but not the 1D, and it can be seen that the results are virtually the same, with any variations contained entirely within the error bars.

Whether a 1D or 2D reduction was used, the final output files containing the flux values in the ordinary and extraordinary beams for each wavelength were combined with the beam-swapping technique (see Eqn. 3.3.3.1).

The use of the beam-swapping technique ensured a minimisation of instrumental polarisation. To demonstrate this, two unpolarised standard stars were observed by Stefano Bagnulo with ISIS in spectropolarimetric mode in January 2015. The observing log of these stars is shown in Table 3.2. Polarised standard stars were

also observed at each epoch to characterise the instrumental position angle o↵set,

and these are also shown in Table 3.2, along with solar analogues that were used to divide out the solar spectrum and obtain the reflectance of the objects. The correction for the position angle of polarisation was carried out as in Section 3.3.3.2.

500 550 600 650 700 750 800 850 900 950 Wavelength (nm) -0.2 0 0.2 0.4 0.6 0.8 1 P L (%) 2D reduction 1D reduction

Figure 3.13: Comparison of the 2D and 1D reduction methods for Saturn data. Figures 3.14 and 3.15 show the degree of linear polarisation of two unpolarised standard stars as a function of wavelength, observed with ISIS. The figures show that the instrumental polarisation is zero within the error bars.

400 450 500 550 600 650 700 750 800 850 900 950 Wavelength (nm) -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 PL (%)

Figure 3.14: Polarisation as a function of wavelength in both blue and red arms of ISIS for unpolarised standard star HD103095.

400 450 500 550 600 650 700 750 800 850 900 950 Wavelength (nm) -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 PL (%)

Figure 3.15: Polarisation as a function of wavelength in both blue and red arms of ISIS for unpolarised standard star HD125184.

Table 3.2: Solar analogues along with polarised and unpolarised standard stars observed over the three epochs of ISIS observations.

Object Type Date UT Exp. Time (s) Grism

HD25443 Polarised 11/03/2014 20:30 30 R300B HD25443 Polarised 11/03/2014 21:03 10 R158R HD159222 Solar analogue 12/03/2014 07:04 10 R158R HD159222 Solar analogue 12/03/2014 07:05 20 R300B HD204827 Polarised 05/01/2015 19:24 10 R158R HD204827 Polarised 05/01/2015 19:31 60 R300B HD28099 Solar analogue 06/01/2015 01:12 20 R158R HD28099 Solar analogue 06/01/2015 01:16 30 R300B HD103095 Unpolarised 07/01/2015 06:10 5 R158R HD103095 Unpolarised 07/01/2015 06:13 10 R300B HD125184 Unpolarised 07/01/2015 06:20 5 R158R HD125184 Unpolarised 07/01/2015 06:24 20 R300B HD28099 Solar analogue 02/02/2015 23:09 60 R158R HD28099 Solar analogue 02/02/2015 23:13 180 R600B HD154445 Polarised 04/02/2015 06:30 2 R158R HD154445 Polarised 04/02/2015 06:35 20 R600B