University (UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA,
LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory
(Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK);
and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been
supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES,
CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and
NASA (USA). HIPE is a joint development (are joint developments) by the
Herschel Science Ground Segment Consortium, consisting of ESA, the NASA
Herschel Science Center, and the HIFI, PACS and SPIRE consortia. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer, which is a joint project of the University of California, Los
Angeles, and the Jet Propulsion Laboratory/California Institute of Technology,
funded by the National Aeronautics and Space Administration. This research has
made use of the NASA/IPAC Extragalactic Database (NED) which is operated by
the Jet Propulsion Laboratory, California Institute of Technology, under
contract with the National Aeronautics and Space Administration.

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##  Appendix A Comparisons of H$\alpha$ and 24 $\mu$m emission

Table 9: Results of using different star formation tracers in comparison to infrared surface brightness ratios Galaxy | Weighted Correlation Coefficients
---|---
| log($I_{\nu}$(24 $\mu$)) | log($I_{\nu}$(160 $\mu$m)/$I_{\nu}$(250 $\mu$m)) | log($I_{\nu}$(250 $\mu$m)/$I_{\nu}$(350 $\mu$m))
| vs. log($I$(H$\alpha$)) | vs. log($I$(H$\alpha$) | vs. log($I$(H$\alpha$) | vs. log($I_{\nu}$(24 $\mu$)) | vs. log($I$(H$\alpha$) | vs. log($I$(H$\alpha$) | vs. log($I_{\nu}$(24 $\mu$))
| (uncorrected) | (uncorrected) | (corrected) |  | (uncorrected) | (corrected) |
NGC 628 | 0.86 | 0.73 | 0.82 | 0.83 | 0.57 | 0.72 | 0.76
NGC 925 | 0.92 | 0.81 | 0.82 | 0.84 | 0.86 | 0.88 | 0.91
NGC 2403 | 0.97 | 0.91 | 0.92 | 0.91 | 0.74 | 0.75 | 0.77
NGC 3031 | 0.93 | 0.40 | 0.47 | 0.55 | 0.29 | 0.36 | 0.48
NGC 3184 | 0.80 | 0.67 | 0.81 | 0.82 | 0.59 | 0.75 | 0.80
NGC 3621 | 0.94 | 0.84 | 0.87 | 0.90 | 0.87 | 0.89 | 0.90
NGC 3631 | 0.99 | 0.94 | 0.95 | 0.96 | 0.93 | 0.95 | 0.96
NGC 3938 | 0.95 | 0.92 | 0.96 | 0.97 | 0.84 | 0.88 | 0.90
NGC 3953 | 0.91 | 0.76 | 0.83 | 0.84 | 0.62 | 0.68 | 0.71
NGC 4254 | 0.98 | 0.89 | 0.88 | 0.87 | 0.68 | 0.69 | 0.70
NGC 4303 | 0.83 | 0.87 | 0.88 | 0.85 | 0.86 | 0.91 | 0.91
NGC 4321 | 1.00 | 0.97 | 0.97 | 0.97 | 0.85 | 0.85 | 0.85
NGC 4501 | 0.90 | 0.82 | 0.86 | 0.86 | 0.74 | 0.82 | 0.87
NGC 4535 | 0.89 | 0.85 | 0.91 | 0.92 | 0.85 | 0.87 | 0.87
NGC 4548 | 0.68 | -0.44 | 0.67 | 0.74 | 0.07 | 0.69 | 0.72
NGC 4579 | 0.99 | 0.97 | 0.96 | 0.94 | 0.84 | 0.83 | 0.83
NGC 4725 | 0.82 | 0.72 | 0.77 | 0.76 | 0.44 | 0.64 | 0.78
NGC 5055 | 0.97 | 0.97 | 0.98 | 0.98 | 0.92 | 0.93 | 0.92
NGC 5236 | 0.97 | 0.89 | 0.89 | 0.88 | 0.81 | 0.81 | 0.80
NGC 5364 | 0.87 | 0.47 | 0.46 | 0.41 | 0.71 | 0.75 | 0.79
NGC 5457 | 0.90 | 0.80 | 0.89 | 0.90 | 0.21 | 0.38 | 0.50
NGC 7793 | 0.80 | 0.78 | 0.84 | 0.91 | 0.62 | 0.69 | 0.80

Multiple authors (e.g. Calzetti et al., 2005, 2007; Prescott et al., 2007)
have found a good correspondence between H$\alpha$ and 24 $\mu$m emission from
compact sources within nearby galaxies. However, it is possible for diffuse
dust to produce 24 $\mu$m emission, and this diffuse emission will not
necessarily correspond to H$\alpha$ emission (Kennicutt et al., 2009).
Additionally, the ratio of H$\alpha$ to 24 $\mu$m emission may vary with
metallicity as well. To examine whether this could affect our analysis, we
compared uncorrected H$\alpha$ and 24 $\mu$m emission measured within the 24
arcsec binned data in our analysis, as we also compared the correlations of
the 160/250 and 250/350 $\mu$m ratios to the uncorrected H$\alpha$, corrected
H$\alpha$, and 24 $\mu$m emission. We selected data for 24 arcsec bins where
both the uncorrected H$\alpha$ and 24 $\mu$m emission were measured at the
$3\sigma$ level and where the data otherwise met the criteria for use in the
analysis in Section 5; the data meeting the criteria for analysis on the
250/350 $\mu$m ratio were also used for calculating correlation coefficients
for the relations between the uncorrected H$\alpha$ and 24 $\mu$m emission.
These selection criteria are necessary for directly comparing H$\alpha$ and 24
$\mu$m emission but may cause the resulting coefficients to differ slightly
($<$0.05) from the coefficients in Table 4 listed for the same relations.

The weighted correlation coefficients from this analysis are presented in
Table 9. First, we can see that while the uncorrected H$\alpha$ and 24 $\mu$m
data are often strongly correlated, the correlation coefficients do not always
equal 1, and some of the values drop to $<$0.80. Although the H$\alpha$ and 24
$\mu$m emission is clearly correlated, enough scatter exists that swapping one
for the other could potentially change the relations we see when comparing
these star formation tracers to the 160/250 and 250/350 $\mu$m surface
brightness ratios. Further analysis to understand these variations and, in
particular, to identify whether they are associated with other properties of
the ISM (such as the gas-to-dust ratio or metallicity), would be useful, but
this is beyond the scope of this paper.

In the comparison of the different star formation tracers to the infrared
surface brightness ratios, we generally found that the correlations with the
uncorrected H$\alpha$ emission were the weakest and the correlations with the
24 $\mu$m emission were strongest. The correlation coefficients for the
relations using the extinction-corrected H$\alpha$ emission usually fell
between the other two, which is expected given that the corrected H$\alpha$
emission is based on a combination of the uncorrected H$\alpha$ and 24 $\mu$m
emission. The coefficients for the relations with the corrected H$\alpha$
emission are sometimes higher than for the corresponding relations with the 24
$\mu$m emission, but with one exception (the relations for the 160/250 $\mu$m
ratio for NGC 5364, where all coefficients are $<$0.50), the difference never
exceeds 0.05.

For 15 of the 22 galaxies, the weighted correlation coefficients were $\geq
0.05$ higher for at least one (but usually two) of the relations between the
far-infrared ratios and the 24 $\mu$m surface brightness than for the
corresponding relations between the ratios and the uncorrected H$\alpha$
intensity. NGC 3031, 3953, 4548 and 4725 are all cases where we masked
emission in the centres of the H$\alpha$ image that we determined was
incompletely-subtracted continuum emission (based on the diffuse appearance of
the emission and the presence of artefacts similar to what was seen for
foreground stars). We did not remove any 24 $\mu$m emission from these
regions, which probably originates from dust heated in part or completely by
the evolved stellar population, particularly the bulge stars. If the emission
at 160-350 $\mu$m also originates from dust heated by the evolved stellar
population, then the 160/250 and 250/350 $\mu$m ratios may naturally correlate
with the 24 $\mu$m band very well within these central regions, and the
correlation coefficients for the overall relations between the far-infrared
ratios and 24 $\mu$m emission will be higher than the relations between the
ratios and the H$\alpha$ emission. We therefore should disregard the
“improved” relation found between the ratios and the 24 $\mu$m emission in
these four galaxies. Of the remaining 11 galaxies where a significantly
stronger correlation is found between either ratio and 24 $\mu$m emission, the
major question is whether changing the star formation tracer would alter our
interpretation of whether the far-infrared ratios were more strongly affected
by star forming regions or the evolved stellar population as presented in
Section 5. NGC 628, 925, 3184, 3938, 4303, 5364, and 7793 are the only
remaining cases where this could be an issue. In these six galaxies, we would
be more likely to infer that dust heating by star forming regions is less
significant when using the uncorrected H$\alpha$ emission or more significant
when using the 24 $\mu$m emission. This may still be caused in part by 24
$\mu$m emission from dust heated by the diffuse ISRF.

For most galaxies, though, the selection of the star formation tracer does not
affect the analysis in Section 5. Given these results, we will proceed with
using the extinction-corrected H$\alpha$ data as the primary star formation
tracer when comparing to the 3.6 $\mu$m emission. However, we will still use
the 24 $\mu$m data as a star formation tracer in the cases where H$\alpha$
data is not available, and we will also note any cases where the choice of
star formation tracer would affect the identification of the heating source.

##  Appendix B Tests on the removal of stellar emission from the 24 $\mu$m
band

To tests the effects of removing the stellar photospheric emission from the 24
$\mu$m band, we applied the correction

$\begin{split}I_{\nu}(24\mu\mbox{m (corrected)})=I_{\nu}(24\mu\mbox{m
(observed)})\\\ -0.032I_{\nu}(3.6\mu\mbox{m}),\end{split}$ (5)

from Helou et al. (2004). As we are primarily focused on how the logarithm of
the 24 $\mu$m emission relates to the logarithms of the 160/250 and 250/350
$\mu$m surface brightness ratios in our primary analysis, we will focus on how
the logarithm of the 24 $\mu$m changes when the correction is applied. We
selected data from the 24 arcsec bins within the optical discs of the galaxies
which met the criteia for the analysis on the 250/350 $\mu$m ratio in Section
5.

Table 10: Statistics from tests of subtracting stellar continuum from 24 $\mu$m data. Galaxy | Change in $I_{\nu}(24\mu\mbox{m})$ | Change in $\log(I_{\nu}(24\mu\mbox{m}))$
---|---|---
| Median | Max | Median | Max
NGC 628 | 0.8 % | 2.2 % | 0.1 % | 0.2 %
NGC 925 | 1.1 % | 3.9 % | 0.1 % | 0.3 %
NGC 2403 | 1.1 % | 5.0 % | 0.1 % | 0.4 %
NGC 3031 | 4.0 % | 22.0 % | 0.3 % | 2.3 %
NGC 3184 | 1.2 % | 2.2 % | 0.1 % | 0.2 %
NGC 3621 | 0.9 % | 2.3 % | 0.1 % | 0.2 %
NGC 3631 | 0.7 % | 1.4 % | 0.1 % | 0.1 %
NGC 3938 | 0.9 % | 2.1 % | 0.1 % | 0.2 %
NGC 3953 | 1.5 % | 6.3 % | 0.1 % | 0.6 %
NGC 4254 | 0.5 % | 1.2 % | 0.1 % | 0.1 %
NGC 4303 | 0.8 % | 2.5 % | 0.1 % | 0.2 %
NGC 4321 | 1.0 % | 3.0 % | 0.1 % | 0.2 %
NGC 4501 | 1.7 % | 4.5 % | 0.2 % | 0.4 %
NGC 4535 | 1.1 % | 1.9 % | 0.1 % | 0.2 %
NGC 4548 | 2.6 % | 8.1 % | 0.2 % | 0.8 %
NGC 4579 | 3.2 % | 7.2 % | 0.3 % | 0.6 %
NGC 4725 | 2.7 % | 13.4 % | 0.2 % | 1.2 %
NGC 4736 | 2.7 % | 4.9 % | 0.3 % | 0.4 %
NGC 5055 | 1.3 % | 2.7 % | 0.1 % | 0.2 %
NGC 5236 | 0.7 % | 2.5 % | 0.1 % | 0.2 %
NGC 5364 | 1.3 % | 3.8 % | 0.1 % | 0.3 %
NGC 5457 | 1.0 % | 3.6 % | 0.1 % | 0.3 %
NGC 6946 | 0.7 % | 2.6 % | 0.1 % | 0.2 %
NGC 7793 | 1.2 % | 3.7 % | 0.1 % | 0.3 %

Statistics on comparisons of the 24 $\mu$m data with and without the
correction are given in Table 10. The corrections have up to a 5% effect on
most of the 24 $\mu$m surface brightnesses. In a few situations, though, the
corrections are significantly stronger. The most notable cases are the centres
of NGC 3031 and 4725, where the 24 $\mu$m surface brighnesses change by up to
25%. However, our analysis is more strongly affected by the logarithms of the
24 $\mu$m surface brightnesses, and these values do not change significantly.
In the case of NGC 3031, the maximum change in the logarithm of the surface
brightness is 2.5%, in the case of NGC 4725, it is 1.2%, and for all other
galaxies, it is $<$1%. Moreover, the logarithms of the 24 $\mu$m surface
brightnesses with and without the corrections are very well correlated; the
weighted correlation coefficients for the relations is equivalent to 1.00 to
two decimal places.

Given these results, subtracting the stellar continuum emission from the 24
$\mu$m band is not critical for our analysis. In NGC 3031 and NGC 4725, where
the corrections have a significant effect, we already mention in Section 3.2
that the 24 $\mu$m emission includes stellar emission that could affect its
relation to the 160/250 and 250/350 $\mu$m ratios. In other galaxies, the
effects of stellar emission on the 24 $\mu$m is minor or even negligible. We
also have the issue that the 3.6 $\mu$m data may also include emission from
hot dust associated with star formation (Lu et al., 2003; Mentuch et al.,
2009, 2010), and while the analysis in Appendix C suggests that the effects of
this hot dust are minimal, it does complicate the stellar continuum
subtraction. We will therefore use the 24 $\mu$m data without applying the
correction given by Equation 5.

##  Appendix C Comparisons of 1.6 and 3.6 $\mu$m emission

As stated in Section 3.3, mid-infrared data from the 1.6-3.6 $\mu$m range will
generally trace starlight from the Rayleigh-Jeans side of the stellar SED.
However, shorter wavelengths will be more strongly affected by dust extinction
than longer wavelengths, while longer wavebands might include emission from
hot dust. Therefore, we may expect to see minor variations in the shape of the
1.6-3.6 $\mu$m SED that could potentially affect the relation between near-
infrared emission and the 160/250 or 250/350 $\mu$m ratios.

To investigate how the use of different near-infrared data may affect our
results, we examined the relations between the logarithms of the 1.6 and 3.6
$\mu$m surface brightnesses for all galaxies in our sample. We used data from
24 arcsec bins within the optical discs of the galaxies that met the criteria
for the analysis on the 250/350 $\mu$m surface brightness ratios in Section 5.

Table 11: Data from comparison of 1.6 and 3.6 $\mu$m emission. Galaxy | Mean Fractional Change in
---|---
| $\log(I_{\nu}(1.6\mu\mbox{m})/\log(I_{\nu}(3.6\mu\mbox{m})$
| over Full Range of $\log(I_{\nu}(3.6\mu\mbox{m}))$
NGC 628 | $-0.036\pm 0.003$
NGC 925 | $0.003\pm 0.019$
NGC 1097 | $0.001\pm 0.001$
NGC 2403 | $-0.039\pm 0.003$
NGC 3031 | $-0.033\pm 0.001$
NGC 3184 | $-0.035\pm 0.004$
NGC 3351 | $-0.025\pm 0.006$
NGC 3621 | $-0.014\pm 0.002$
NGC 3631 | $-0.009\pm 0.003$
NGC 3938 | $-0.043\pm 0.006$
NGC 3953 | $-0.036\pm 0.004$
NGC 4254 | $-0.029\pm 0.002$
NGC 4303 | $-0.026\pm 0.011$
NGC 4321 | $-0.015\pm 0.002$
NGC 4501 | $-0.031\pm 0.002$
NGC 4535 | $-0.040\pm 0.007$
NGC 4548 | $-0.020\pm 0.001$
NGC 4579 | $-0.014\pm 0.002$
NGC 4725 | $-0.010\pm 0.001$
NGC 4736 | $-0.033\pm 0.001$
NGC 5055 | $-0.021\pm 0.001$
NGC 5236 | $-0.005\pm 0.001$
NGC 5364 | $-0.044\pm 0.016$
NGC 5457 | $-0.026\pm 0.003$
NGC 6946 | $0.013\pm 0.002$
NGC 7793 | $-0.032\pm 0.003$
Figure 10: Example 1.6 and 3.6 $\mu$m images of NGC 925, with the color scale
adjusted to show the differences in the radial profiles of the observed 1.6
and 3.6 $\mu$m emission as well as low-level background artefacts in the 1.6
$\mu$m map. The PSFs of the data have been matched to the PSF of the 350
$\mu$m data, which has a FWHM of 25 arcsec. The cyan circles in each panel
show the size of the PSF.

We found a very strong correlation between the 1.6 and 3.6 $\mu$m surface
brightnesses. The weighted correlation coefficients for all of these relations
are $\sim 1.00$; the lowest value is 0.987 for NGC 5457 and 6946. This
indicates that swapping one waveband for the other in the analyses in Sections
5 and 6 should have a minimal impact on the results. Table 11 gives data
showing the mean fractional change in the
$\log(I_{\nu}(1.6\mu\mbox{m})/\log(I_{\nu}(3.6\mu\mbox{m})$ over the full
range of $\log(I_{\nu}(3.6\mu\mbox{m}))$, which was found by fitting a line to
the two quantities. The variations in the
$\log(1.6\mu\mbox{m})/\log(3.6\mu\mbox{m})$ ratio are typically $<$5%, which
suggests that we will not see any major differences related to near- infrared
colour variations if we use one of these wavebands instead of the other. It is
very likely that the systematic variations that we do see in the
$\log(1.6\mu\mbox{m})/\log(3.6\mu\mbox{m})$ ratio are caused by background
artefacts, usually in the 2MASS 1.6 $\mu$m image, where often spot alternating
dark and bright rectangular regions. Figure 10 shows NGC 925 as an example in
which the low surface brightness structure in the 1.6 $\mu$m image appears
much more asymmetrical than the background in the 3.6 $\mu$m image, probably
because the background was oversubtracted in a data frame covering the
southeast side of the galaxy.

Aside from these background artefacts, we detect only a small number of high
signal-to-noise sources where the $\log(1.6\mu\mbox{m})/\log(3.6\mu\mbox{m})$
ratios deviate significantly (more than 0.2) from the mean values found in
each galaxy. These are typically bright star forming regions, such as the
brightest star forming region in NGC 2403, one of the bright regions in NGC
5457, and a few of the regions in NGC 6946. Some of the galactic nuclei with
strong star formation activity, such as the nuclei of NGC 5236 and NGC 6946,
have ratios that are suppressed relative to the rest of the data from the
galaxies. In these situations, it is possible that we are either seeing
higher-than-average dust attenuation that is reddening the stellar emission,
or we are seeing significant hot dust emission in the 3.6 $\mu$m bands, as
suggested by Mentuch et al. (2009) and Mentuch et al. (2010).

Overall, though, we simply do not see many regions where the near-infrared
colours look significantly redder than average. This may be because we are
averaging over relatively large areas (areas that are $4\times$ larger than
what Mentuch et al. (2010) used). Reddening caused by extinction or hot dust
emission in extreme environments may be diluted by regions with more typical
colours. Given these results, we feel confident that the 3.6 $\mu$m data in
our analysis are generally unaffected by hot dust emission, although we do
acknowledge that we may encounter some problems with a few extreme cases.
Moreover, it is more advantageous to use the 3.6 $\mu$m images because of the
superior signal- to-noise and better background subtraction in the 3.6 $\mu$m
images. We therefore rely on the 3.6 $\mu$m band as a tracer of emission from
the evolved stellar population in our analysis.

##  Appendix D Tests of the removal of emission from star forming regions from
the 3.6 $\mu$m band

It would potentially be desirable to treat the 3.6 $\mu$m band as a tracer of
the intermediate and older stellar population by removing the contributing
emission from star forming regions. To derive such a correction, we used the
Starburst99 model version 6.0.3 (Leitherer et al., 1999)232323Accessed at
http://www.stsci.edu/science/starburst99/docs/default.htm . to model the
H$\alpha$ and 3.6 $\mu$m from stars formed either in an instantaneous burst of
star formation or in continuous star formation. We primarily used a Kroupa
initial mass function with $\Phi(M)\propto M^{2.3}$ for stars with masses
$>$0.5 M⊙ and $\Phi(M)\propto M^{1.3}$ for stars with masses $<$0.5 M⊙
(Kroupa, 2001). We performed simulations only for solar metallicities (which
should approximate the metallicities of the spiral galaxies in our sample) and
used all other default settings for the models. As Starburst99 does not
calculate flux densities in the IRAC bands, we derived these values by
following the instructions given in the Spitzer Data Analysis Cookbook
(Spitzer Science User Support and Instrument Teams and IRSA Science User
Support Team,
2012)242424http://irsa.ipac.caltech.edu/data/SPITZER/docs/dataanalysistools
/cookbook/.

Figure 11: Plot of the 3.6 $\mu$m to H$\alpha$ surface brightness ratio as a
function of time since the onset of star formation as determined using
Starburst99. The solid line represents the continuous star formation scenario,
while the dotted line represents the instantaneous burst scenario.

The 3.6 $\mu$m/H$\alpha$ ratios from the Starburst99 simulation are plotted in
Figure 11. In the first 3 Myr after an instantaneous burst of star formation
or after the onset of continuous star formation, the ratio of the 3.6 $\mu$m
flux density to H$\alpha$ flux stays at $(2.7\pm 0.2)\times 10^{8}$ Jy (erg
s-1 cm-2)-1 regardless of which star formation scenario is used. After 3 Myr,
photoionising stars evolve off of the main sequence, and the 3.6
$\mu$m/H$\alpha$ ratio changes notably, although how it changes depends on
which star formation scenario we use. In an instantaneous burst, the H$\alpha$
emission drops off significantly after 3 Myr, and the 3.6 $\mu$m/H$\alpha$
ratio increases exponentially to $\sim 8.5\times 10^{10}$ Jy (erg s-1 cm-2)-1.
However, it is unclear that we would detect H$\alpha$ emission from stellar
populations much older than 3 Myr, and if we did, then it would seem unlikely
that such stellar populations would produce a significant fraction of the
total H$\alpha$ emission. In the continuous star formation scenario, the ratio
rises upwards more gradually, increasing to $\sim 5.7\times 10^{8}$ Jy (erg
s-1 cm-2)-1 at 10 Myr. While the entire stellar population of a spiral galaxy
may be treated as undergoing continuous star formation, it may be more
appropriate to treat individual regions as instantaneous bursts of star
formation. We will therefore assume that the H$\alpha$ emission that we are
observing originates mainly from stars that formed in the past 3 Myr, in which
case, we will apply $2.7\times 10^{8}$ Jy (erg s-1 cm-2)-1 to the H$\alpha$
fluxes to estimate the 3.6 $\mu$m emission from stars that have formed in the
past 3 Myr.

We examined how the corrections affected the 3.6 $\mu$m surface brightness
itself as well as the logarithm of the 3.6 $\mu$m surface brightnesses in
galaxies for which we had H$\alpha$ data. The corrections were derived from
the extinction-corrected H$\alpha$ intensities calculated using Equation 1. We
used the same 24 arcsec binned data that were used for the analysis on the
250/350 $\mu$m surface brightness ratio in Section 5. The data are shown in
Table 12.

Table 12: Statistics from tests of subtracting emission from stars with ages $<$3 Myr from 3.6 $\mu$m emission. Galaxy | Change in $I_{\nu}(3.6\mu\mbox{m})$ | Change in $\log(I_{\nu}(3.6\mu\mbox{m}))$
---|---|---
| Median | Max | Median | Max
NGC 628 | 0.4 % | 1.3 % | 0.0 % | 0.1 %
NGC 925 | 0.9 % | 4.4 % | 0.1 % | 0.3 %
NGC 2403 | 0.7 % | 6.8 % | 0.1 % | 0.6 %
NGC 3031 | 0.2 % | 1.6 % | 0.0 % | 0.1 %
NGC 3184 | 0.5 % | 1.1 % | 0.0 % | 0.1 %
NGC 3621 | 0.7 % | 4.1 % | 0.1 % | 0.3 %
NGC 3631 | 0.9 % | 1.5 % | 0.1 % | 0.1 %
NGC 3938 | 0.5 % | 2.8 % | 0.0 % | 0.2 %
NGC 3953 | 0.2 % | 0.7 % | 0.0 % | 0.1 %
NGC 4254 | 0.9 % | 1.7 % | 0.1 % | 0.1 %
NGC 4303 | 0.6 % | 1.6 % | 0.1 % | 0.2 %
NGC 4321 | 0.5 % | 1.1 % | 0.0 % | 0.1 %
NGC 4501 | 0.3 % | 0.5 % | 0.0 % | 0.0 %
NGC 4535 | 0.6 % | 2.2 % | 0.1 % | 0.2 %
NGC 4548 | 0.1 % | 0.2 % | 0.0 % | 0.0 %
NGC 4579 | 0.2 % | 0.4 % | 0.0 % | 0.0 %
NGC 4725 | 0.2 % | 0.5 % | 0.0 % | 0.0 %
NGC 5055 | 0.3 % | 0.7 % | 0.0 % | 0.1 %
NGC 5236 | 0.5 % | 2.0 % | 0.0 % | 0.2 %
NGC 5364 | 0.4 % | 1.5 % | 0.0 % | 0.1 %
NGC 5457 | 0.4 % | 17.0 % | 0.0 % | 1.4 %
NGC 7793 | 0.8 % | 4.0 % | 0.1 % | 0.3 %

As can be seen by these tests, the correction generally has a very minor
impact on the 3.6 $\mu$m emission. In most cases, the correction is $<$2%,
indicating that $>$98% of the total 3.6 $\mu$m emission from all regions
within the optical discs comes from non-ionising intermediate-aged and evolved
stars. We did see some stronger changes in a few individual star forming
regions. In NGC 5471, which is a location containing a bright HII region in
the outer disc of NGC 5457, we estimate that 17% of the 3.6 $\mu$m emission
may originate from stars with ages $<$3 Myr. In a few other star forming
regions at the periphery of the disc of NGC 5457 and a couple of star forming
regions in NGC 925, 2403, 3621, 3938, 4535, and 7793, the correction changed
the 3.6 $\mu$m emission by 2-7%. However, these few “extreme” cases have a
$<$1% effect on the logarithm of the 3.6 $\mu$m emission, which we use in most
of our analysis. Moreover, the weighted correlation coefficients between the
logarithms of the uncorrected and corrected 3.6 $\mu$m surface brightnesses is
1.00 in all cases.

The relatively small effect of this adjustment to the 3.6 $\mu$m data
ultimately has no significant effect on our analysis. If we attempted to
account for stars older than 3 Myr, then the changes in the 3.6 $\mu$m
emission would be higher, but this would depend upon being able to determine
what the star formation history is for these regions. For reference, we
estimate using the physical dimensions of the 24 arcsec resolution elements in
Table 1 and assuming a rotational velocity of 200 km s-1 that stars may pass
through the resolution elements on periods ranging from 2 to 12 Myr. In some
cases, the correction for the 3.6 $\mu$m band that we are already using (which
assumes that the stellar populations are $<$3 Myr in age) is already
applicable. For older regions, we would need to guess the star formation
history of the regions. We also have the complicating issue that the star
formation tracers that we are using are imperfect for estimating this
correction. The H$\alpha$ emission without the extinction correction would
give a correction to the 3.6 $\mu$m band that is too low, while the H$\alpha$
emission combined with the 24 $\mu$m band may potentially be affected by 24
$\mu$m emission from diffuse dust heated by the ISRF (see Appendix A). These
issues along with the relatively minor benefit from removing the emission from
young stars from the 3.6 $\mu$m band leads us to the conclusion that we should
simply use the 3.6 $\mu$m surface brightnesses as observed for our analysis.

##  Appendix E Offsets between infrared surface brightness ratios and spiral
arms

Figure 12: The 350 $\mu$m images for NGC 5236 and 6946 with green lines
indicating locations where surface brightness profiles were measured across
the spiral arms. The cyan circles show the FWHM of the PSF. The profiles
themselves are shown in Figure 13.

Figure 13: Profiles of the surface brightnesses (shown as solid lines and
normalised so that the peaks equal 1) and surface brightness ratios (shown as
dotted lines and normalised so that the profiles range from 0 to 1) across
spiral arms in NGC 5236 and 6946. The locations of these profiles are shown in
Figure 12. Measurements were made at 1 arcsec intervals in 24 arcsec wide
regions in data where the PSF FWHM is 25 arcsec. The x-axes show the distance
from the peak in the 350 $\mu$m profile, with positive x-values showing
distance from the 350 $\mu$m peak on the downstream side of the arms. The
uncertainties for the normalised surface brightness profiles are
$<$$\sim$0.01, and the uncertainties for the normalised surface brightness
ratios are $\sim 0.10$. Table 13: Weighted correlation coefficients for
relations between 160/250 and 250/350 $\mu$m ratios and tracers of heating
sources in data with different bin sizes.

Galaxy | Bin Size | Weighted Correlation Coefficients
---|---|---
| (arcsec) | $\log(I_{\nu}(160\mu\mbox{m})/I_{\nu}(250\mu\mbox{m}))$ | $\log(I_{\nu}(250\mu\mbox{m})/I_{\nu}(350\mu\mbox{m}))$
|  | vs. $\log(I(\mbox{H}\alpha))^{a}$ | vs. $\log(I_{\nu}(3.6\mu\mbox{m}))$ | vs. $\log(I(\mbox{H}\alpha))^{a}$ | vs. $\log(I_{\nu}(3.6\mu\mbox{m}))$
NGC 3031 | 24 | 0.17 | 0.84 | 0.16 | 0.87
| 120 | -0.07 | 0.91 | 0.17 | 0.90
NGC 5457 | 24 | 0.89 | 0.57 | 0.40 | 0.89
| 120 | 0.92 | 0.57 | 0.53 | 0.94

a The H$\alpha$ data used here were corrected for extinction using 24 $\mu$m
data.

As stated in Section 4 we see small offsets between the star forming regions
and the colour temperatures in some of the images in Figure 1. This phenomenon
had been seen previously. Bendo et al. (2012a) and Foyle et al. (2012)
illustrated that regions with enhanced colour temperatures in the spiral arms
of M83 appeared offset from the star forming regions, and Mentuch Cooper et
al. (2012) had indicated that such an offset also appeared to be present in
M51 but did not illustrate this offset. To examine this further, we measured
the profiles of surface brightnesses across spiral arm segments in NGC 5236
and 6946, the two closest galaxies where we see this phenomenon. Figure 12
shows the locations where we measured the profiles in these galaxies, and
Figure 13 shows the profiles themselves.

These images illustrate similar structures in all three spiral arm segments.
The 350 $\mu$m data serve as a proxy for the dust mass, as the band lies in a
regime of the SED where it is relatively insensitive to the temperature
variations seen in these data. We will refer to the peak of the 350 $\mu$m
emission as the dust lane within these galaxies. The H$\alpha$ emission, which
traces gas photoionised by star forming regions, and the 24 $\mu$m emission,
which traces hot dust heated by the star forming regions, peak to one side of
the 350 $\mu$m emission, although the difference between the peaks is small
compared to the 25 arcsec resolution of the data. None the less, this would be
consistent with the classical depiction of spiral density waves in which gas
falls into the wave, gets compressed, and forms stars on the other side of the
wave (e.g. Roberts, 1969; Elmegreen, 1979). In the line segments we have
selected, material is flowing into the concave sides of the spiral density
waves, and new stars are found on the convex side. The asymmetric distribution
of dust and young stars around the star forming regions has a few potential
effects on dust heating in these locations.

First, we can see in the NGC 5236 data that the H$\alpha$ emission is offset
relative to the 24 $\mu$m emission, although this offset is small compared to
the 25 arcsec resolution of the data. This will occur in part because the star
forming regions closer to the dust lane are more obscured, leading to a change
in the H$\alpha$/24 $\mu$m ratio. The normalised H$\alpha$ emission is also
higher than the normalised 24 $\mu$m emission at locations downstream from the
spiral arms. Some fraction of this H$\alpha$ emission may originate from gas
in the diffuse ISM photoionised by photons escaping from star forming regions.
This enhancement in H$\alpha$ emission would be seen on only one side of the
star forming regions because the optical depth is much higher on the other
side of the regions, which means that photoionising photons can travel much
further away from the dust lane than towards it.

From the perspective of our analysis, the most interesting feature here is the
presence of the strongly enhanced 160/250 $\mu$m ratio on the opposite side of
the star forming regions from the dust lane, which can be offset by a distance
comparable to the 25 arcsec resolution of the data. The ratio is clearly not
tracing the temperature of dust heated locally by the star forming regions;
otherwise, the 160/250 $\mu$m ratio would peak at the same location as the
24/350 $\mu$m ratio. A similar offset in enhanced polycyclic aromatic
hydrocarbon (PAH) emission in the IRAC 8 $\mu$m band was found in M83 by Jones
et al. (2014, submitted). They even found that the 8/250 $\mu$m surface
brightness ratio (a measure of PAH excitation normalised by dust mass) was
correlated with the 160/250 $\mu$m ratio, suggesting that both the dust
emission at 160 $\mu$m and the PAH excitation were linked.

The peak in the 160/250 $\mu$m ratio may be offset for one of two reasons.
First, the 160 $\mu$m emission from these galaxies may primarily originate
from dust heated by photoionising light escaping the star forming regions into
the diffuse ISM. Because the light primarily propagates away from the dust
lanes, the peak in the 160/250 $\mu$m ratio appears offset. The physical
distance between the peak in the 160/250 $\mu$m ratios and the peak in the 350
$\mu$m emission is $\sim 0.5$ kpc. This distance is in the middle of the 0.1-1
kpc range of the mean free path of V-band photons in galaxies given by the
analysis from Xilouris et al. (1999) and Bianchi (2007), which implies that it
is from dust heated by diffuse light from star forming regions. The other
possibility is that emission in the 160 $\mu$m band is from dust in an
optically-thin environment heated locally by B and A stars that have emerged
from the dusty star forming regions 10-100 Myr ago. These stars would not
produce the photons needed to photoionise hydrogen but would produce
substantially high radiation fields that include large numbers of soft
ultraviolet photons that could warm up the large dust grains.

The 250/350 $\mu$m ratio presents relatively different results in the three
profiles. In profile A in NGC 5236, the ratio peaks on the side of the dust
lane opposite the side of the star forming region, and in NGC 6946, the peak
corresponds to the location of the peak in the 3.6 $\mu$m emission. This would
be consistent with the 250/350 $\mu$m ratio tracing the temperature of the
dust in the spiral arm that is shielded from the star forming regions and
heated by the radiation field from the evolved stellar population. In profile
B in NGC 5236, the 250/350 $\mu$m ratio peaks in two locations: one peak
corresponds to the location of the 24 $\mu$m peak, while the other appears
$\sim 15$ arcsec further downstream in a location where the 160/250 $\mu$m
ratio is also enhanced. This could indicate that the ratio in this location is
still sensitive to heating by either light diffusing from the star forming
regions or unobscured B and A stars. However, the structures in the 250/350
$\mu$m ratio map for NGC 5236 are relatively poorly defined overall and might
be affected by residual striping in the 350 $\mu$m data, so it is difficult to
interpret the significance of the 250/350 $\mu$m profiles for the galaxy.

As we stated earlier, NGC 5236 and 6946 are the two galaxies in our sample
where we see these structure most prominently. We do see some hints of similar
structures in the northern part of NGC 628, but the effect is not particularly
strong. Aside from these galaxies, though, we do not see any cases where we
can see significant offsets between the spiral arm structures traced by the 24
$\mu$m emission and the structures traced by the 160/250 and 250/350 $\mu$m
ratios. The structures appear on scales of $<$$\sim$0.5 kpc, so for galaxies
at $>$$\sim$5 Mpc, offsets between the surface brightness ratios and the star
forming regions may not be readily apparent within data at 25 arcsec
resolutions. The remaining galaxies within 5 Mpc may not exhibit these
structures for a large number of reasons. In NGC 3031, the 160/250 and 250/350
$\mu$m ratios appear more strongly influenced by the evolved stellar
population, so we would not expect to see this phenomenon at all. Meanwhile,
NGC 2403 and 7793 are both flocculent galaxies where, because these two
galaxies lack the large shock fronts created by the spiral density waves, star
formation is expected to occur in clouds that collapse because of local
graviational instabilities. Dust may be distributed symmetrically around star
forming regions in these galaxies, and simulations by Dobbs & Pringle (2010)
suggest that no stellar age gradients will be seen across the spiral segments.
In the scenario where the 160/250 or 250/350 $\mu$m ratios are enhanced by
light diffusing from star forming regions, the light would diffuse
symmetrically around star forming regions. In the scenario where the ratios
are enhanced by B and A stars, it may be possible that the B and A stars are
not located preferentially on one side of current star formation sites. In
either case, the 160/250 and 250/350 $\mu$m ratios will peak in the same
locations as the emission from the star forming regions themselves (if the
star forming regions influence the ratios).

We recommend treating these results cautiously. Although the offsets in the
peaks of the surface brightness ratio profiles are quite apparent, the offsets
among individual wave bands is relatively small compared to the 25 arcsec FWHM
of the PSF. Unidentified astrometry problems could produce some of the
patterns seen in these profiles, although we have checked the astrometry of
these data using foreground stars and background galaxies outside the optical
discs of the galaxies, and the structures in the profiles continue to appear
even when small adjustments are made to the astrometry of the data (or
adjustments are not applied). It is unlikely that the PSF-matching steps could
have introduced some structures. This step should match not only the FWHMs of
the PSFs but also the profiles of the PSFs, and the kernels from Aniano et al.
(2011) that we used are based on observational data and should contain
features related to the instrument and data processing. Even though these
kernels do not always work perfectly, the artefacts from this process that
appear around bright sources in the colour temperature maps usually look
symmetric, whereas the structures that we see in associated with the spiral
arms in the 160/250 $\mu$m maps are asymmetric. It is more likely that the
offset 160/250 $\mu$m features are intrinsic structures within the galaxies
rather than artefacts related to astrometry or PSF-matching issues.

##  Appendix F Tests of resolution effects on the data

Because the galaxies are located at distances that vary by a factor of 7 and
also because the same analytical methods have been applied to the same
galaxies using data at different resolutions, we tested the effects of
performing our analyses using data measured in different sized bins. For this
analysis, we selected NGC 3031 and 5457, the two galaxies with the largest
angular sizes in the sample. We rebinned the data for these galaxies into 120
arcsec bins. This is equivalent to shifting NGC 3031 from 3.6 to 18.0 Mpc and
to shifting NGC 5457 from 6.7 to 33.5 Mpc, which are equivalent to or larger
than the distances for the furthest galaxies in our sample. We then repeated
the analysis in Sections 5 and 6.

Table 13 shows the changes in the correlation coefficients in the relations
between the infrared surface brightness ratios and the tracers of different
dust heating sources. We generally see the correlation coefficients increase
up to 0.15 when we use the larger bin size except in the relation of the
160/250 $\mu$m ratio to H$\alpha$ emission, where the relation exhibited
uncorrelated scatter in both the 24 and 120 arcsec binned data. We also still
generally obtain the same results for these two galaxies that we did in
Section 5. Regardless of the bin size used, the 160/250 and 250/350 $\mu$m
ratios for NGC 3031 and the 250/350 $\mu$m ratios for NGC 5457 appear much
better correlated with the 3.6 $\mu$m surface brightness, while the 160/250
$\mu$m ratios for NGC 5457 still appear better correlated with the H$\alpha$
emission.

Table 13 shows the resulting $\eta$ after applying the decomposition analysis
in Section 6 to data with different bin sizes. Except for the $\eta$(250/350
$\mu$m) for NGC 5457, where the $I(\mbox{SFR})$ term was negligible, the
resulting $\eta$ all decrease. The decrease in $\eta$(160/250 $\mu$m) for NGC
3031 is relatively small compared to the uncertainties in the $\eta$ values
for the 120 arcsec bins. The $\eta$(250/350 $\mu$m) is 0.22, although this is
comparable to the uncertainty in the methodology following the analysis in
Appendix G (0.15) as well as the uncertainty of 0.17 in $\eta$(250/350 $\mu$m)
for the 120 arcsec binned data that was determined using the Monte Carlo
analysis. The $\eta$(160/250 $\mu$m) for NGC 5457 decreases by 0.16, which is
also approximately equivalent to the uncertainty of 0.15 in the methodology.
The change may have resulted from combining brighter emission from warmer dust
heated locally by star forming regions with fainter emission from cooler dust
heated by older stars. The dust emission observed in these coarser bins would
appear to be dominated more by dust heated by star forming regions, an issue
also highlighted by Galliano et al. (2011).

In summary, these tests represent the most severe tests of resolution effects
that could affect the data. The analysis of the correlation between surface
brightness ratios and dust heating sources in Section 5 should be robust
against resolution effects. The decomposition analysis in Section 6 is
somewhat affected by resolution effects, although the changes in the derived
$\eta$ values are generally consistent when taking into account both the 0.15
uncertainty in the methodology and the uncertainties from the Monte Carlo
analysis. These issues are noted in Section 6, but we will treat the $\eta$ as
though resolution has a minor affect on the data.

Table 15: Results from fitting Equation 2 to the 160/250 and 250/350 $\mu$m
surface brightness ratios.

Galaxy | Bin Size | $\eta$
---|---|---
| (arcsec) | 160/250 $\mu$m | 250/350 $\mu$m
NGC 3031 | 24 | $0.79\pm 0.02$ | $0.95\pm 0.03$
| 120 | $0.72\pm 0.11$ | $0.73\pm 0.17$
NGC 5457 | 24 | $0.37\pm 0.01$ | $1.00^{a}$
| 120 | $0.21\pm 0.05$ | $1.00^{a}$

a For these fits, $I(\mbox{SFR})$ in Equation 2 was found to be negligible
compared to $A_{1}I_{\nu}(3.6\mu\mbox{m})$. We therefore fit
$\ln(I_{\nu}(250\mu\mbox{m})/I_{\nu}(350\mu\mbox{m}))$ to
$\ln(I_{\nu}(3.6\mu\mbox{m}))$ using a linear function. The $\alpha$ listed
here is the slope, and $A_{2}$ is the constant.

##  Appendix G Tests of measuring $\eta$ using simulated data

Figure 14: Input and output data for tests in Appendix G showing the
effectiveness of using Equations 2 and 3 and the methodology in Section 6 to
measure the fraction of dust heated by different populatons of stars by
comparing the emission from the dust heating sources to the observed infrared
surface brightness ratios. All data are for a simulated face-on galaxy disc
where the emission is truncated at a diameter of 10 arcmmin and where the
resolution of the data is 25 arcsec. The top row shows the model surface
brightnesses for star forming and evolved stellar populatons (normalised for
one). The bottom two rows show, for scenario 5 in Table 16 (where the input
$\eta$(250 $\mu$m) is set to 0.50), the input $\eta$ and 160 and 250 $\mu$m,
the resulting input 160/250 and 250/350 $\mu$m colour temperature maps, the
best fitting output colour temperature maps, and the output $\eta$ maps for
the 160/250 and 250/350 $\mu$m ratios. The colour temperature maps are
computed using $\beta$=2. The output $\eta$(160/250 $\mu$m) should be compared
to the input $\eta$(160 $\mu$m), and the output $\eta$(250/350 $\mu$m) should
be compared to the input $\eta$(250 $\mu$m).

To test the effectiveness of using Equations 2 and 3 to derive the relative
fraction of variation in emission in a waveband that is related to heating by
a specific population of stars, we created simplified models of dust heating
within disc galaxies. The dust grains are treated as modified blackbodies
where $E\propto T^{6}$, which is appropriate for $\beta=2$. We assume that the
dust is at thermodynamic equilibrium with the local radiation field and that
the temperature depends upon heating from two stellar populations; this
effectively excludes stochastically heated dust as well as more complex
radiative transfer effects. The distribution of dust mass is treated as
arbitrary.

To represent the dust heated by the two different stellar populations, we
created two circular discs with diameters of 10 arcmin and pixel sizes of 1
arcsec. For the energy $E_{ES}$ from evolved stellar population (including
intermediate and older stars), we used a smooth exponential disc with a scale
length of 150 arcsec. For the energy $E_{SF}$ from the star forming regions,
we created a disc containing 150 randomly-placed unresolved sources scaled by
an exponential function with a scale length of 240 arcsec and five additional
randomly-placed sources that are set to 2 times the peak of the exponential
profile. This is a simplified representation of the star forming structures
that could be expected in a flocculent spiral galaxy, and the broader scale
length for the star forming regions compared to the evolved stellar
populations reflects how star forming regions are distributed more broadly in
spiral galaxies. We assume that the distribution of both stellar populations
and the dust perpendicular to the disc of the galaxy and the scale height of
the dust are similar and therefore do no additional computations for the
vertical propigation of light.

The $E$ functions were then rescaled to compute SEDs based on modified
blackbodies with $E\propto T^{6}$. The energy-weighted mean $T$ was set to 15
K for the evolved stellar population component and 25 K for the star forming
component, which is similar to the temperatures measured for the separate
thermal components in in Section 7.1. The data were then used to create maps
with 1 arcsec pixels of the intensities from these components at 160, 250, and
350 $\mu$m. The maps were convolved with a 25 arcsec Gaussian function, which
is similar to the PSF of the SPIRE 350 $\mu$m data. The maps were then
rebinned into 24 arcsec bins for the quantitative analysis.

We display data created for multiple scenarios where the $E$ values were
rescaled to create input $\eta$(250 $\mu$) ratios ranging from 0.1 to 0.9. We
then fit the 160/250 and 250/350 $\mu$m ratios using $E_{ES}$ and $E_{SF}$ in
Equation 2 and computed output $\eta$ values for these ratios using Equation
3, which we then compare to the input $\eta$ measured at the shorter
wavelength.

Table 16: Comparison of input and output $\eta$ results. Scenario | Input $\eta$ | Output $\eta$
---|---|---
Number | 160/250 $\mu$m | 250/350 $\mu$m | 160/250 $\mu$m | 250/350 $\mu$m
1 | 0.11 | 0.10 | 0.13 | 0.12
2 | 0.19 | 0.20 | 0.18 | 0.19
3 | 0.26 | 0.30 | 0.22 | 0.25
4 | 0.33 | 0.40 | 0.26 | 0.32
5 | 0.41 | 0.50 | 0.31 | 0.40
6 | 0.49 | 0.60 | 0.37 | 0.49
7 | 0.58 | 0.70 | 0.46 | 0.61
8 | 0.69 | 0.80 | 0.58 | 0.73
9 | 0.82 | 0.90 | 0.75 | 0.86

Mean input and output $\eta$ values from these tests are given in Table 16.
Figure 14 shows the model surface brightnesses for the star forming and
evolved stellar populatons, the input $\eta$ and 160 and 250 $\mu$m, the
resulting 160/250 and 250/350 $\mu$m colour temperature maps, and the output
$\eta$ maps for the 160/250 and 250/350 $\mu$m ratios for scenario 5 (where
the input $\eta$(250 $\mu$m) is set to 0.50).

The input and output maps agree within $\sim 1$ K in most locations, but the
brighter star forming regions tend to be $\sim 5$ K hotter in the output
images than in the input images. This illustrates the limitations of using
Equation 2 to relate an observed colour temperature to emission from multiple
dust heating sources, at least over large temperature ranges. The measured
$\eta$ in individual locations may be within 0.20 of the input value, but we
typically measure a global mean $\eta$ that is within 0.10 of the input value.
We get input and output $\eta$ values within 0.01 when $\eta~{}\hbox
to0.0pt{$<$\hss}{\lower 4.30554pt\hbox{$\sim$}}$0.20. On the other hand, the
difference between input and output $\eta$ values is 0.10-0.15 in situations
where $\eta$ is between 0.50 and 0.70. The output $\eta$ value is always lower
than the input $\eta$ value, which demonstrates that the methodology exhibits
a systematic bias that could potentially be corrected to improve the accuracy
of the measured $\eta$.

Given these results, we will use 0.15 as the uncertainties in the $\eta$
values from the analysis in Section 6 when rescaling global flux densities to
create SEDs for separate thermal components. However, we will point out that
the uncertainties could be higher in multiple circumstances. If the difference
between the dust temperatures is larger, then the assumptions behind Equation
2 no longer apply and the uncertainty in $\eta$ could increase. As mentioned
elsewhere in the text, the uncertainty in $\eta$ will be high if the star
forming regions and evolved stellar populations have similar distributions or
if the mean free path of light heating the dust is larger than the resolution
elements of our data.

Although we only show results for 160/250 and 250/350 $\mu$m ratios, we did
find that the results may still be reliable when creating surface brightness
ratios based on any two wavebands where the longer waveband samples emission
on the Rayleigh-Jeans side of the SED. However, the $\eta$ values could become
more uncertain if both wavebands sample emission from the peak or Wein side of
the dust SED. This should be taken into account when attempting to apply this
methodology to other datasets.

##  Appendix H Colour temperature images

This section includes the full versions of Figures 1 in Section 5 and 7 in
Section 6. These figures will appear only online in the final published
version of the paper.

Figure 15: H$\alpha$ (or 24 $\mu$m), 3.6 $\mu$m, 160/250 $\mu$m, and 250/350
$\mu$m images of all galaxies in the sample. All images are based on data
where the PSF has been matched to the PSF of the 350 $\mu$m image, which has a
FWHM of 25 arcsec. The 160/250 and 250/350 $\mu$m ratios are shown as colour
temperatures (based on modified blackbodies with $\lambda^{-2}$ emissivities)
so that the colours can be related to the SED shape, although the actual
temperatures may vary. Only data within approximately the optical disc of each
galaxy detected at the $5\sigma$ level in the H$\alpha$, 24 $\mu$m, or 3.6
$\mu$m maps or above the $3\sigma$ level in the colour temperature maps is
shown; other parts of the image are left blank.

Figure 15: Continued.

Figure 15: Continued.

Figure 15: Continued.

Figure 15: Continued.

Figure 15: Continued.

Figure 16: Examples of the results from using Equation 2 to fit the 160/250
and 250/350 $\mu$m surface brightness ratios as a function of both the
H$\alpha$ and 3.6 $\mu$m data. The first columns of images on the left show
the observed colour temperatures. The second column of images show the colour
temperatures produced by adding together the H$\alpha$ (or 24 $\mu$m) and 3.6
$\mu$m images using Equation 2 and the best fitting parameters from Table 5.
The third column shows the residuals from subtracting the fitted colour
temperature map from the observed colour temperature map. The fourth column
shows the fraction of dust heating by star forming regions predicted by the
parameters in Table 5 and Equation 3. The images are formatted in the same way
as the colour temperature images in Figure 1.

Figure 16: Continued.

Figure 16: Continued.

Figure 16: Continued.

Figure 16: Continued.

Figure 16: Continued.

Figure 16: Continued.

Figure 16: Continued.