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The IRAC Dark Field, ELAIS-N1 and the ADF-S number counts have been plotted with the NEP Deep AKARI number counts of Murata et al. (2014a), the AKARI 15 µm number counts of Abell 2218 from Hopwood et al. (2010), the Spitzer/IRAC 3.6, 4.5, 5.8 and 8.0 µm number counts of Fazio et al. (2004), the Spitzer/IRS number counts at 16 µm of Teplitz et al. (2011), and the models of Pearson (2005) and Cai et al. (2013). The 3, 4, 7 and 11 µm ADF-S number counts are inconsistent with those of the ELAIS- N1 and the IRAC Dark Field. They are also inconsistent with the published NEP num- ber counts. This offset is too large to have been caused by an incorrect survey area. The survey area in the ADF-S images was calculated using the same method as for the ELAIS-N1 and IRAC Dark Field, both of which do not show this rise in bright end number counts. This difference is thought to be due to an incorrect stellar subtrac- tion. Section 3.7.2 describes the two different methods used to remove the stars in the ADF-S. Figure 3.11 shows the large difference in the bright end slope by using the two different stellar subtraction methods. As there are not many sources in the bright end flux bins, a change of one or two will make quite a significant difference. As the survey area of the ELAIS-N1 and IRAC Dark Field is _{. 10% the survey area of ADF-S, one} would expect the ADF-S to have over 10 times the number of stars as the ELAIS-N1 and IRAC Dark Field.

The ADF-S number counts also suffer from a possible incorrect completeness, be- cause the faintest flux number count has a much smaller value than the number count values. An incorrect completeness could be due to the fact that a Gaussian point spread function (PSF) was used to test for incompleteness. An analytical PSF created using AKARI data may give a better completeness correction.

The 3 µm ADF-S number counts are shown in Figure 3.19, and have been plotted with the published NEP and IRAC 3.6 µm counts and the model of Pearson (2005). The possible error due to incorrect stellar subtraction has been discussed above. The NEP

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Figure 3.19: The 3 microns number counts. Comparison of the ADF-S number counts with AKARI NEP survey number counts (Murata et al., 2014a), Spitzer/IRAC number counts (Fazio et al., 2004) and Pearson model (Pearson, 2005). The ADF-S number counts are shown as red diamonds, the AKARI NEP number counts are shown as orange open triangles, the Spitzer/IRAC number counts are shown as cyan open circles. The Pearson model is shown as a solid black line, the grey line is the contribution of normal type galaxies and the magenta line is the contribution of elliptical type galaxies.

number counts seem to be showing a rise at fainter fluxes, which is inconsistent with galaxy evolution models. The Pearson model does not seem to fit the counts of the ADF-S, AKARI NEP or the IRAC 3.6 µm number counts.

The 4 µm has been observed by ELAIS-N1, IRAC Dark Field and ADF-S. These counts have been plotted in Figure 3.20 with the AKARI NEP counts, the IRAC 4.5 µm counts and the Pearson model. The 4 µm number counts figure is a good example of what was hoped to be achieved with the AKARI data, by using deep and shallow field data. The ELAIS-N1 and IRAC Dark Field both have a small survey area (∼ 10 arcmins by ∼ 10 arcmins), but are both deep fields, thus probing the fainter flux number counts. The ADF-S is a wide, but shallow field, and hence probes the brighter end of the counts. As can be seen in Figure 3.20, the ADF-S does indeed constrain the

brighter fluxes, and the two deep fields, ELAIS-N1 and IRAC Dark Field constrain the fainter number counts. The ELAIS-N1, IRAC Dark Field and the IRAC 4.5 µm number counts are all similar at fainter fluxes. They all have fewer fainter flux counts than predicted by the Pearson model. This seems to imply that one (or several) of the galaxy models making up the Pearson model are over predicted. Most likely the model has over predicted the number of star forming galaxies. Over all fluxes, the IRAC Dark Field, ADF-S and the IRAC 4.5 µm counts are in good agreement. The Pearson model does not fit them very well. Surprisingly all counts seem to show a peak at ∼ 0.1 mJy, the galaxy evolution models do not predict a peak in the 4 µm counts.

Figure 3.21 shows the AKARI ADF-S 7 µm number counts plotted with the AKARI NEP counts, the IRAC 8 µm, the Pearson model and SISSA model. The ADF-S counts seem to be in better agreement with the IRAC 8 µm counts than the NEP counts. The SISSA models appear to fit the ADF-S counts better than the Pearson models, but as discussed above, the ADF-S count may not have a correct stellar subtraction. The counts may, in fact, be lower.

The 11 µm number counts are shown in Figure 3.22. ELAIS-N1, IRAC Dark Field and the ADF-S all have observations at 11 µm. These counts are plotted with the AKARI NEP counts, the Pearson model and the SISSA model. The IRAC Dark Field and the NEP counts appear to be in agreement. The Pearson model fits the IRAC Dark Field better at fainter fluxes, whereas the SISSA model appears to fit the brighter counts better. The variation in the ELAIS-N1 counts could be due to a remnant of Earthshine light. The removal of the Earthshine light was discussed in Section 2.4.3.9. Due to the angle of the telescope between the Earth, the ELAIS-N1 images are the most affected by the Earthshine light, and out of the four filters observed in the ELAIS-N1, S11 contained the most amount of Earthshine light. The sudden drop in ELAIS-N1 counts at fainter fluxes could be due to an incorrect completeness correction. As discussed above for the ADF-S, using a non-Gaussian PSF for completeness may improve the completeness correction. The ADF-S counts are greater than the other surveys, this could be due to an incorrect stellar subtraction, as discussed above.

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Figure 3.20: The 4 microns number counts. Comparison of the AKARI IRAC Dark Field, ELAIS-N1 and ADF-S number counts with AKARI NEP survey number counts (Murata et al., 2014a), Spitzer/IRAC number counts (Fazio et al., 2004) and Pearson model (Pearson, 2005). The IRAC Dark Field number counts are shown as blue circles, ELAIS-N1 number counts are shown as green squares, the ADF-S number counts are shown as red diamonds, the AKARI NEP number counts are shown as open orange triangles and the Spitzer/IRAC number counts are shown as open cyan circles. The SISSA model is shown as a dashed line. The Pearson model is shown as a solid line, the grey line is the contribution of normal type galaxies, the magenta line is the contri- bution of elliptical type galaxies, the red line is the contribution of star forming galax- ies, the cyan line is the contribution of LIRGs and the green line is the contribution of AGN.

Figure 3.21: The 7 microns number counts. Comparison of the AKARI ADF-S number counts with AKARI NEP survey number counts (Murata et al., 2014a), Spitzer/IRAC number counts (Fazio et al., 2004), Pearson model (Pearson, 2005) and SISSA model (Cai et al., 2013). The ADF-S number counts are shown as red diamonds, the AKARI NEP number counts are shown as open orange triangles and the Spitzer/IRAC number counts are shown as open cyan circles. The SISSA model is shown as a dashed line. The Pearson model is shown as a solid line, the grey line is the contribution of normal type galaxies, the magenta line is the contribution of elliptical type galaxies, the red line is the contribution of star forming galaxies, the cyan line is the contribution of LIRGs, the blue line is the contribution of ULIRGs and the green line is the contribution of AGN.

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Figure 3.22: The 11 microns number counts. Comparison of the AKARI IRAC Dark Field, ELAIS-N1 and ADF-S number counts with AKARI NEP survey number counts (Murata et al., 2014a), Pearson model (Pearson, 2005) and SISSA model (Cai et al., 2013). The IRAC Dark Field number counts are shown as blue circles, ELAIS-N1 number counts are shown as green squares, the ADF-S number counts are shown as red diamonds and the AKARI NEP number counts are shown as open orange trian- gles. The SISSA model is shown as a dashed line. The Pearson model is shown as a solid line, the grey line is the contribution of normal type galaxies, the magenta line is the contribution of elliptical type galaxies, the red line is the contribution of star forming galaxies, the cyan line is the contribution of LIRGs and the green line is the contribution of AGN.

AKARI is the only satellite to have an 11 µm channel. The other extensive work on the AKARI S11 number counts is of NEP observations by Murata et al. (2014a), which are shown as orange triangles in Figure 3.22. As can be seen in Figure 3.22, the IRAC Dark Field and the ELAIS-N1 number counts go down to fainter fluxes, hence are deeper than those of Murata et al. (2014a). The ELAIS-N1 number counts tail off at fainter fluxes possibly due to the raw frames containing Earthshine light. As dis- cussed above, the ELAIS-N1 frames were badly effected by Earthshine light, because they were observed late Phase 2. The 11 µm IRAC Dark Field number counts do not show a drop off at fainter fluxes. The IRAC Dark Field pointings were early and mid Phase 2, hence not badly affected by Earthshine light, and thus more reliable. Figure 3.22 shows that the S11 number counts are deeper than those of Murata et al. (2014a). Thus the AKARI IRAC Dark Field 11 µm image created in the work of this thesis, shown in Figure 3.1.b, is likely to be the deepest 11 µm image.

ELAIS-N1, the IRAC Dark Field and the ADF-S were also all observed at 15 µm. These number counts are shown in Figure 3.23. Also plotted are the AKARI NEP counts, the AKARI 15 µm number counts of Hopwood et al. (2010), the Spitzer/IRS 16 µm number counts of Teplitz et al. (2011), the Pearson model and the SISSA model. Like the 4 µm, the 15 µm number count figure, this is another good example of what was hoped to be achieved with the deep and shallow AKARI surveys. There is a probable incorrect completeness correction for the faintest flux bin of ELAIS-N1 and ADF-S. Due to the fact that less Galactic stars are observable at 15 µm, the wavelength will require less stars to be removed from galaxy catalogues. As can be seen in Fig- ure 3.23, the ADF-S counts seem to be in much better agreement with the ELAIS-N1 and the IRAC Dark Field than at the shorter wavelengths. Both the number counts of Hopwood et al. (2010) and Teplitz et al. (2011) go deeper than the AKARI number counts of this thesis. The number counts of Hopwood et al. (2010) appear to match the AKARI IRAC Dark Field number counts better than those of Teplitz et al. (2011). The Pearson model and the SISSA model are fairly similar at this wavelength, thus it is inconclusive which model fits the number counts of this thesis better. The Pearson

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model does not fit the Teplitz et al. (2011) numbers, but the model does fit the num- ber counts of Hopwood et al. (2010); although the final bin of the number counts of Hopwood et al. (2010) show an increase in number from that predicted by the Pearson model. According to the Pearson model, the faint end number counts are dominated by star forming galaxies.

The 18 µm number counts are shown in Figure 3.24. The figure shows the ELAIS- N1 and IRAC Dark Field number counts, plotted with them are the AKARI NEP num- ber counts and the Pearson model. The 18 µm data for ELAIS-N1 and the IRAC Dark Field do not look as reliable as that for the other filters, they appear more inconsistent and have larger errors on average. The 18 µm IRAC Dark Field is only 5 pointings deep, see Table 3.1. The 18 µm ELAIS-N1 survey was deeper by two pointings, see Table 3.8, but as the data were observed towards the end of Phase 2, the frames were badly affected by Earthshine light. The number counts show that possibly the Earth- shine light has not been completely removed.

If two deep field number counts do not exactly match, this does not mean that one of the counts is necessarily wrong. There is an uncertainty in the number of galaxies in a given volume density, caused by large-scale density fluctuations. This is known as cosmic variance (Somerville et al., 2004). The percentage of cosmic variance is greater for deep, narrow fields. Figure 3.25 shows the cosmic variance predictions of Moster et al. (2011), assuming a stellar mass range of log(m/MJ) ∼ 10.25. Using the results

for the GOODS field (10 x 16 arcminutes) for ELAIS-N1 and the IRAC Dark Field, and the EGS (10 x 70 arcminutes) for ADF-S, the figures show that for galaxies at a redshift of z = 1, the ELAIS-N1 and the IRAC Dark Field have a cosmic variance of ∼ 14% and the ADF-S has a cosmic variance of ∼ 9%. Cosmic variance could account for small differences in the ELAIS-N1 and the IRAC Dark Field number counts.

Figure 3.23: The 15 microns number counts. Comparison of the AKARI IRAC Dark Field, ELAIS-N1 and ADF-S number counts with AKARI NEP survey number counts (Murata et al., 2014a), the AKARI Abell 2218 number counts (Hopwood et al., 2010), Spitzer/IRS number counts (Teplitz et al., 2011), Pearson model (Pearson, 2005) and SISSA model (Cai et al., 2013). The IRAC Dark Field number counts are shown as blue circles, ELAIS-N1 number counts are shown as green squares, the ADF-S number counts are shown as red diamonds, the AKARI NEP number counts are shown as open orange triangles, the AKARI Abell 2218 number counts are shown as open purple diamonds and the Spitzer/IRS number counts are shown as open cyan circles. The SISSA model is shown as a dashed line. The Pearson model is shown as a solid line, the grey line is the contribution of normal type galaxies, the red line is the contribution of star forming galaxies, the cyan line is the contribution of LIRGs, the blue line is the contribution of ULIRGs and the green line is the contribution of AGN.

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Figure 3.24: The 18 microns number counts. Comparison of the AKARI IRAC Dark Field and ELAIS-N1 number counts with AKARI NEP survey number counts (Murata et al., 2014a) and Pearson model (Pearson, 2005). The IRAC Dark Field number counts are shown as blue circles, ELAIS-N1 number counts are shown as green squares and the AKARI NEP number counts are shown as open orange triangles. The Pearson model is shown as a solid line, the grey line is the contribution of normal type galaxies, the red line is the contribution of star forming galaxies, the cyan line is the contribution of LIRGs and the green line is the contribution of AGN.

Figure 3.25: The Cosmic Variance fraction from Moster et al. (2011) for the Ultra Deep Field (UDF) (3.3 x 3.3 arcminutes) shown as a black line, Great Observatories Origins Deep Survey (GOODS) (10 x 16 arcminutes) field shown as a dotted line, the Galaxy Evolution from Morphology and SEDs survey (GEMS) (28 x 28 arcminutes) shown as a dashed line, the Extended Groth Strip (EGS) (10 x 70 arcminutes) shown as a dot-dashed line and the Cosmic Evolution Survey (COSMOS) (84 x 84 arcminutes) shown as a dot-dot-dashed line.