In Section 6.3 we presented a new method to estimate the ISP in the data of SN 1993J. It differs from previous methods employed by Trammell et al. (1993) and Tran et al. (1997) in a number of ways. Firstly, the historical analyses used the assumption that Hα emission was completely depolarised. This idea stems from the fact that the emission component of P Cygni profiles are the result of light being scattered into the observers line of sight by resonant scattering, which is a depolarising process. However, the superposition of an He i λ6678 absorption component and its associated polarisation can render the assumption of complete depolarisation in this region of the spectrum invalid. To derive their ISP,
Trammell et al. (1993) and Tran et al. (1997) used the data on April 20 (+26 days) and justified their assumption by saying that no helium component could be seen. However, the flat top profile of Hα on April 20 (see Figure 6.4) suggests that some He i λ6678 is present, putting the assumption of complete depolarisation into question.
In order to compute our ISP, we assumed that the data at our latest epoch was represen- tative of the ISP. This is valid if the electron density in the ejecta has decreased sufficiently such that intrinsic supernova polarisation is negligible. This assumption, however, is not completely exact, as line polarisation features remain somewhat visible at +48 days. Con- sequently, some latent SN continuum polarisation may have biased our ISP estimate.
Another difference between our ISP and previous estimates is the wavelength depen- dence. In Trammell et al. (1993), a Serkowski type law was used, whereas in Tran et al.
(1997) negligible wavelength dependence was assumed. In the former case, this poses the question of the validity of the Serkowski law (Serkowski, 1973) to account for the dust properties in other galaxies and in the vicinity of SNe. We now know of a number of cases where the form of the ISP in the line of sight to the SN have been shown to be significantly different from that of the Milky Way (e.g.Patat et al. 2015, Chapter 4), and therefore this assumption should be used with care. Using the approximation of a constant ISP can be sufficient if the wavelength dependency is very shallow and consequently negligible given the noise levels.
The ISP Stokes parameters we derive in Section 6.3 do not make use of the Serkowski assumption, and are expressed as linear functions of wavelength (see Eqs 6.1 and 6.2). This also results in a wavelength dependence in the P.A. of the ISP. This can be caused by the superposition in the line of sight of dust clouds with different particle sizes and orientations, or by the superposition of ISP and some latent intrinsic SN polarisation, as
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mentioned above (Coyne & Gehrels, 1966).
Despite the caveats associated with our assumptions, the ISP estimates we derived result in ISP removed data (see Figure 6.4) which show a behaviour that is consistent with expectations. As mentioned in Section 6.3, the blue region of the spectrum between 4600 and ∼5500˚A is mostly depolarised, apart from some peaks of line polarisation. This is consistent with the expected depolarisation in that part of the spectrum caused by line blanketing (Howell et al., 2001). Moreover, Hα emission is associated with polarisation that is close to zero, apart from peaks associated with the absorption component of He i λ6678. Finally, our new ISP solves the issue of the high level of polarisation (∼0.7 percent) observed near 6600˚A in the Tran et al.(1997) data on April 30, which was highlighted by
Chornock et al. (2011) and which they suggested could be solved if different ISP values were to be used.
As a result we are confident that the method described in Section 6.3 was successful in estimating the ISP present in the SN 1993J data. Nevertheless, this method should be applied with care and with full consideration of the caveats mentioned above, particularly when fitting data that show residual intrinsic SN polarisation.
An alternative way to estimate the ISP is to make use of the assumption that the blue part of the spectrum is completely depolarised due to line blanketing (Howell et al.,2001), and simply average the Stokes parameters in this range. To test this method we applied it to April 20, 26, 30 and May 11. A weighted average of the Stokes parameters was performed; the errors on the weighted mean were also calculated, and propagated through to the degree of polarisation and polarisation angle. The degree of polarisation was also debiased. The wavelength ranges used and resulting ISP values are given in Table 6.3 alongside the literature ISP values and equivalent 5200˚A ISP values obtained from Eqs 6.1 and 6.2, for comparison purposes. Note that the range used for the average on April 20 is different from the other epochs because no data is available between 5300˚A and 5500˚A.
On the whole, the estimates in Stokes parameters, degree of polarisation and polari- sation angle using this method vary from epoch to epoch. This is inconsistent with the behaviour of the ISP, which is constant on short timescales, and shows that the results were biased by intrinsic polarisation. It is interesting to note that the values obtained from May 11 (+48 days) are very close to the ISP values we derived at 5200˚A. This can be understood as the result of a decreasing amount of intrinsic polarisation at later dates due to the decreasing electron density, causing the observed polarisation to be dominated by ISP.
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Table 6.3: Comparison of ISP values obtained using different methods. Date Wavelength q u p P.A.
Assuming depolarisation in the blue
April 20 4500-5300˚A 0.58±0.03 0.19±0.03 0.61±0.03 9◦±5◦
April 26 4800-5500˚A 0.61±0.05 0.65±0.04 0.89±0.04 23◦±1◦
April 30 4800-5500˚A 0.42±0.03 0.53±0.03 0.68±0.02 26◦±1◦
May 11 4800-5500˚A 0.28±0.04 0.45±0.04 0.53±0.04 29◦±1◦
sigma clipping method
May 14 5200˚A 0.30±0.15 0.60±0.15 0.63±0.15 32◦±3◦
Tran et al.
April 20 6390-6890 0.60 -0.19 0.63 171◦ Trammell et al.
April 20 Hα emission 0.55 -0.95 1.1±0.1 150◦±0.1◦
through line blanketing is a real effect, this region of the spectrum does sometime show significant line polarisation, as can be clearly seen in SN 1993J at +30 days, or in SN 2008aq at +27 days (see Chapter 3). Consequently, although keeping in mind the expected effects of line blanketing makes for a good sanity check, it is difficult in practice to use it to find reliable ISP values.