tokens: are compatible with there being no correlation of κ 500 with any of the parameters considered. Similarly, for each relationship, Spearman rank correlation tests do not allow us to reject the null hypothesis (of there being no correlation) to a likelihood of 0.01. We note, however, that the size of our sample is small compared to the scale of the uncertainties on κ 500 ; hence we in no way rule out that such correlations could exist, but not be detectable in our data. 7 COMPARISON TO PREVIOUS ESTIMATES As can be seen in Fig. 1 , our determined value of κ d is low compared to existing literature values (although the very commonly used values of Draine 2003 and Draine Li 2007 are within our bootstrapped uncertainty). Converting the James et al. value to a wavelength of 500 μm for comparison with our own, as per equation ( 1 ), translates it to κ 500 = 0.20 ± 0.06 m 2 kg −1 ; a factor of 3.92 larger than our value, despite the fact we employ the same fundamental technique; it is important to address the reasons for this. As discussed in Section 2 , our consideration of systematic effects, using ξ (i.e. the contribution of helium and metals to a galaxy's gas mass) and δ O (i.e. oxygen depletion in H ii regions) will account for a factor of 1.86 reduction in κ d relative to James et al. We also employ a slightly larger value of ε d (0.5 versus 0.456), leading to a further factor of 1.10 reduction in κ d . However, our use of a more modern, smaller value of (0.0134 versus 0.019) works in the opposite direction, diminishing the reduction in κ d by a factor of 0.71. In combination, these global effects correspond to a factor of 1.42 reduction in κ d relative to James et al.; additional effects must be at work to explain the full difference between our values. Fortunately, M 61 (NGC 4303) is present in both the James et al. sample and our own, allowing for a direct comparison of the reasons for the difference in values for a specific case. For M 61, we find that our result of κ 500 = 0.039 m 2 kg −1 (see Table 1 ) is a factor of 5.13 less than the κ 500 = 0.20 m 2 kg −1 value that James et al. found for their sample as a whole. James et al. did not work out values of κ d for individual sources, but do say that there is scatter of a factor of 2 around their sample-wide relation, hence we need to account for a factor of difference between our κ d for M 61, and the James et al. sample-wide value. In Appendix A , we work through each of the sources of difference in our values of κ d in the case of M 61, and find that a factor of 6.31 is to be expected, well within the predicted range – highlighting the dramatic influence of considering systematic effects and utilizing superior observations. During the Herschel science demonstration phase, Eales et al. ( 2010 ) applied a resolved variant of the James et al. method (where they pegged the dust mass surface density to the gas mass surface density, assuming a fixed Schmidt–Kennicutt law and a Milky Way
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Model I-Model O O B-CelestialObject I-CelestialObject