SERENDIPITY OBSERVATIONS OF FAR INFRARED CIRRUS EMISSION IN THE SPITZER INFRARED NEARBY GALAXIES SURVEY: ANALYSIS OF FAR-INFRARED CORRELATIONS^*

The observations at 160 μm were reduced using the GeRT software⁶ on the raw MIPS observations. Standard parameters were used for the reduction, but data where flashes of the internal source led to a significant number of saturated pixels were removed. The removed data are most often positioned on the bright center of the galaxy. Other saturated pixels removed from processing were due to cosmic ray hits. These saturated flashes when not removed can bias the sensitivity of the diffuse extended emission. This step in the reduction may not be appropriate for the photometry of the galaxy, but significantly reduces latents (stripes) in the outer regions we are interested in. Each region targeted was observed twice. Discrepant fluxes at the same position between the two observations are removed, and the data are combined into a mosaic for each region.

The MIPS 160 μm maps and IRIS 60 μm are convolved to the IRIS 100 μm resolution assuming Gaussian beams with FWHM of 40, 43, and 37'' for IRIS 60, 100 μm, and MIPS 160 μm observations, respectively.

For each MIPS strip, the galaxy and other point sources are detected in the 25, 60 and 100 μm maps using the method described in Miville-Deschênes et al. (2002). These point sources at the IRIS resolution (but with the MIPS sampling) are then smoothed by a Gaussian kernel with a full width half maximum of 3 × 3 pixels (at the MIPS original pixel size) to encompass possible extended emission from these galaxies. The smoothed point sources are then masked in all the maps. All maps are then projected on the IRIS grid to avoid oversampling. The observation targeting the galaxy Holmberg IX was removed from the sample since the emission in the whole strip is dominated by the galaxy and its interaction features with nearby galaxies. We chose to remove the observation containing the galaxy NGC3034 (M82), which was hampered by saturation effects in the whole central region of the galaxy, affecting the observation globally. The observations containing the galaxies NGC1266, NGC2915, and M81 Dwarf B were also removed, because the width of the region observed was too narrow to be convolved meaningfully to the IRIS resolution. We ended up with 70 fields of view⁷ at a resolution of 43 observed at 60, 100, and 160 μm. Due to uncertainties in the zodiacal light subtraction at 60 μm that can dominate the flux at the low surface brightnesses we sample, we limited the sample at 60 μm to the nine observations at high-ecliptic latitude (|β|>15°).

A constant brightness of 0.78 MJy sr⁻¹ is removed from the IRIS 100 μm maps to account for the cosmic infrared background (Lagache et al. 2000), i.e., the emission from the distant unresolved galaxies (called hereafter CIB). The exact level of CIB emission has not yet been established at 60 μm, and the MIPS observations can have offsets in the calibration of the brightness that are not physical. To overcome the uncertainties (physical or instrumental) on the zero levels in the different maps, we hereafter perform the analysis of the data through the use of correlations (see Section 3.1).

The errors on the surface brightness are taken to be 0.03 and 0.06 MJy sr⁻¹ at 60 and 100 μm, respectively (Miville-Deschênes & Lagache 2005). At 160 μm, we take a quadratic combination of a constant sensitivity limit⁸ of 0.12 MJy sr⁻¹ and a 2% uncertainty on the brightness (due to the uncertainty on the calibration factor from instrumental units to surface brightness (Stansberry et al. 2007)).

In low surface brightness regions, the variations of the infrared emission in the observations can come from cirrus emission, fluctuations in the cosmic infrared background or from noise. Since we want to study the variations of cirrus emission only, we want to select observations in the SINGS sample that are dominated by the dust emission variations.

The different contributions (cosmic infrared background, cirrus emission) to the infrared emission have different power spectra that can help to disentangle them. In particular, the cirrus power spectrum normalization depends on the mean surface brightness, while the contribution from background galaxies does not. This dependence can be translated into a relationship between the mean brightness and the standard deviation square, σ²_cirrus, in a region and depends on the size of the region (Miville-Deschênes et al. 2007). For each of the observed field of view, we computed the standard deviation at 100 μm and the mean brightness at 100 μm (minus the average CIB contribution at this wavelength) and then plot the σ² – 〈B〉 relationship observed at 100 μm in our sample. To model σ_cirrus, we use the relationship derived by Miville-Deschênes et al. (2007) below 10 MJy sr⁻¹, for a maximum scale length of 50' (the dotted line in Figure 2). We observe that our observations are consistent with the model, with a large scatter as in the original relationship. This dispersion is likely enhanced due to the fact that our fields of view are elongated and the size of the region mapped varies between fields. The contribution from the CIB fluctuations can be described by two terms: a Poisson noise that represents the galaxies distributed homogeneously with respect to the resolution and a component with correlated spatial variations corresponding to the clustering of galaxies on large scales. The contribution from the clustering of infrared galaxies is predicted by using the Lagache et al. (2003) model for galaxy evolution, with a bias parameter from Lagache et al. (2007). The contribution from the Poisson noise to the σ² observed at 100 μm is taken to be that measured by Miville-Deschênes et al. (2002), since we used the same point source detection method. However, compared to their study, we removed point sources applying the detection scheme at all wavelength (25, 60, and 100 μm). This enables us to mask faint galaxies at 100 μm more efficiently, and the Poisson noise in our measurements could be lower than their measurement. Because we want to select the fields with the least contribution from other sources (CIB) than cirrus to the observed variations, this choice is therefore conservative.

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Combining all contributions (represented in Figure 2) to the observed variations, we determine that a cut at 2.5 MJy sr⁻¹ corresponds to σ_cirrus/σ_CIB = 1.5 (so that the total infrared fluctuations $\sigma _{\rm tot}=\sqrt{\sigma _{\rm cirrus}^2+\sigma _{\rm CIB}^2}$ are less than 20% larger than from cirrus fluctuations alone). The regions with a mean 100 μm brightness above this threshold will therefore be dominated by variations of cirrus emission. In each field, we computed the mean brightness at 100 μm as well as the standard deviation at 60, 100, and 160 μm (see Table 1). By keeping only the fields above the 2.5 MJy sr⁻¹ cut, the subsample we will study in this paper is composed of 15 fields with 100 and 160 μm brightnesses, among which nine can be studied as well at 60 μm (|β|>15°, see Section 2.1).

Stellar reddenings obtained from the analysis of the Sloan Digital Sky Survey data enable us to put an upper limit of 1.2 mag on the extinction in these fields.⁹ This confirms that the variations in the infrared cirrus emission studied in each region come from diffuse clouds according to the van Dishoeck & Black (1988) classification.

In each field of the selected sample, we plot the point-to-point correlation between the brightnesses observed at 100 and 160 μm (represented in Figures 3 and 4) and apply a linear fit taking into account the errors at both wavelengths. This enables us to obtain for each field a slope corresponding to the ratio B₁₆₀/B₁₀₀ unbiased by variations of the zero point level (residuals from the zodiacal light subtraction, absolute value of the CIB). The correlation coefficient and the slope derived in each region are summarized in Table 2.

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Large-scale observations of high-galactic latitude emission of cirrus with COBE were well characterized by a modified blackbody with a dust temperature of 17.5 K and an emissivity index proportional to ν² (Boulanger et al. 1996). Using this law, we estimate the large-scale 160/100 color for cirrus to be of B₁₆₀/B₁₀₀ = 2.0 (taking into account color corrections). This ratio is represented in the correlation plots (Figures 3 and 4) to guide the eye. While some correlations between B₁₀₀ and B₁₆₀ are in agreement with the B₁₆₀/B₁₀₀ = 2.0 obtained on large scales, clear deviations are also seen (four fields out of 15 have a slope discrepant at a 5σ–6σ level with respect to the value of 2.0. The most extreme case is the field of NGC2976, with a fitted slope on the B₁₆₀ versus B₁₀₀ correlation that is 10σ away from the 2.0 standard value).

In Figure 5, we compare the obtained ratios B₁₆₀/B₁₀₀ to the mean surface brightness at 100 μm in each field (black points). We observe a large dispersion in the 160/100 colors that cannot be explained by the error on the data or the fitting process. At 100 and 160 μm, the interstellar emission is dominated by the emission from big dust grains at thermal equilibrium with the radiation field (Désert et al. 1990), and the B₁₆₀/B₁₀₀ ratio is therefore related to that characteristic dust temperature. Taking a standard emissivity of dust per hydrogen atom in H i from Boulanger et al. (1996) and an emissivity index of 2, the 160/100 color variations, we are probing, can therefore be related for illustrative purposes to temperatures between 15.7 and 18.9 K for column densities ranging from N_H = 3 × 10²⁰ to 2 × 10²¹ cm⁻². We note that these variations are consistent on average with the large-scale estimate (the blue solid line), confirming that the fields used in this study are sampling the cirrus emission observed on large scale.

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For a given grain size and composition, this characteristic temperature depends on the local radiation field strength and spectrum which depends on the presence and distance of nearby heating sources and on the extinction. In the framework of this model, the presence of large variations in the 160/100 μm ratio observed in our sample would suggest the presence of large variations in the heating of grains at small scales (variations by a factor of 3 of the intensity of the incident radiation field). This can be surprising, since at low-FIR surface brightness and at high latitude the interstellar radiation field might be expected to be homogeneous. We looked at the FIR color temperature maps derived from DIRBE observations by Lagache et al. (1998) and Schlegel et al. (1998). The regions we are studying appear to be reasonably representative of the high-latitude cirrus given the small number statistics. For the sightlines covered by our sample, the FIR color variations seen in the DIRBE data are compatible with the variations that we observe. Our study is indeed more sensitive than previous observations and therefore we are able to probe color variations smaller than the uncertainties in the previous studies.

The shape of the optical spectrum heating the grains could also affect the FIR colors: the radiation field could become gradually harder with position off the galactic plane (Mattila 1980). Using the cirrus model from Efstathiou & Rowan-Robinson (2003) with different stellar populations heating the clouds, we checked that changes in the shape of the optical radiation field is unlikely to affect the 160/100 and 60/100 colors of cirrus by more than 20%.

The dust equilibrium temperature depends however also on the structure of the grains. Grain aggregates for example cool more efficiently. The temperature variations observed in the diffuse medium could therefore be either due to variations of the intensity of the interstellar radiation field or to changes in the grain structure.

We compared our findings with different studies of FIR emission from the literature: the quiescent high-galactic latitude clouds from del Burgo et al. (2003), the large sample from archival ISOPHOT data by Kiss et al. (2006), the two regions in a high-latitude cirrus MCLD 123.5+24.9 observed by Bernard et al. (1999), and the quiescent filament in the Taurus molecular complex from Stepnik et al. (2003). Because other observations were obtained with different instruments, we have to interpolate the brightnesses at various FIR wavelengths to estimates at 100 and 160 μm. To do so, we took the dust temperatures determined in each study with a brightness at 100 or 200 μm and used a modified blackbody law with a spectral index. The power index is either taken from the study itself (if it was computed) or is fixed to a standard value of 2. For each region, we also compute the mean 100 μm brightness as observed by IRIS and subtract a mean CIB contribution as for our observations. Despite large scatter, we observe a trend between 〈B₁₀₀〉 and the 160/100 color that is consistent with the idea that denser regions are colder. However, the effect of selection biases of these studies remains unclear. The comparison of our results with that from the literature (Figure 5) shows that previous studies in the FIR have been targeting higher B₁₆₀/B₁₀₀ and 〈B₁₀₀〉, i.e., denser and colder clouds. Due to our better sensitivity, our observations fill the gap at low B₁₀₀ and low B₁₆₀/B₁₀₀.

For the first time, we observe interstellar dust emission at low-surface brightness in an unbiased way (in the observing strategy) with a high sensitivity. These observations show that former studies on dust properties at FIR wavelength at small scale have been biased toward colder and denser clouds. Our study shows that the 160/100 brightness ratios of high galactic cirrus clouds at small scales are consistent on average with the observations on large scales. However, these 160/100 colors show a wide dispersion that could arise from variations in the heating of the clouds or from change of the dust grain structure. In order to investigate further the origin of the 160/100 variations, we extend the comparison to the 60 μm data.

To investigate the origin of the 160/100 color variations observed in the diffuse cirrus, we compare the 160 and 100 μm data to the 60 μm emission. The sample for this part of the study is however reduced to fields with an ecliptic latitude above 15° in order to avoid artifacts due to the uncertainties in the zodiacal light subtraction in the IRIS data. For each field, we determine a 60/100 color by using the same correlation technique as above. The correlations in each region are shown in Figure 6, and the obtained B₆₀/B₁₀₀ are summarized in Table 2.

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Figure 7 presents the B₆₀/B₁₀₀ ratio obtained in each field with respect to the B₁₆₀/B₁₀₀ ratio. Here again, large variations are observed in the 60/100 colors that cannot be explained by the uncertainties in the data or in the analysis. As for the 160/100 colors, the 60/100 brightness ratios are consistent on average with the "reference values" (the pink cross and the blue star in the figure) obtained for high-latitude emission on large scales (Boulanger & Perault 1988; Boulanger et al. 1996; Arendt et al. 1998). Furthermore, there is a trend of decreasing B₆₀/B₁₀₀ with increasing B₁₆₀/B₁₀₀.

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To try to interpret this trend, we used two models of the dust grain emission at different interstellar radiation fields: the Draine & Li (2007) model for the Milky Way¹⁰ and the "DUSTEM" model (updated model based on Désert et al. (1990)). The models take into account the shape of the IRAS and MIPS/Spitzer filters, the color corrections. For both models, the abundances of different grain types are kept constant. The tracks obtained are compared to the data in Figure 7. The comparison shows that, if the variations of colors are due to variations in heating of the grains, this would imply large changes in the interstellar radiation field at high-galactic latitude (from U ≈ 0.3 to 1). Furthermore, the trend observed between the 60/100 and 160/100 colors is not well reproduced with the current models by changing the interstellar radiation field alone. In that respect, the Draine & Li (2007) model is however closer to the observed trend than the DUSTEM model (only three fields are more than 3σ deviant from the expected curve), but for B₁₆₀/B₁₀₀ < 2.1 all observations show systematically higher B₆₀/B₁₀₀ than predicted by both models, while for B₁₆₀/B₁₀₀ > 2.1 all data points have systematically lower B₆₀/B₁₀₀ values than expected from both models.

Current dust models might be missing an additional dust grain type. Such an addition might reproduce all color variations while changing the interstellar radiation field alone. Another way to interpret the observed trend is that the variations in the dust emission spectrum reflect spatial changes in the grain properties—composition, structure or size distribution.

The equilibrium temperatures of dust grains is expected to decrease for increasing grain sizes and small grains (⩽0.01 μm) undergo temperature excursions following single-photon heating that enhances the 60 μm emission. Thus, regions with fewer small grains may have lower 60/100 ratios. The observed trend between the 60/100 and 160/100 infrared colors could be reproduced by changing the dust grains size distribution or composition. For example, enhancing the amount of small grains in regions with higher interstellar radiation field (i.e., higher temperatures) and reducing it at low equilibrium temperatures could reproduce the observed variations.

In the same way, regions with enhanced populations of large grains may have increased 160/100 ratios. In that case, reproducing the observations could be obtained with only modest variations in the starlight heating rate and shifts in the grain size distribution (fewer small grains and increased sizes for the larger grains at low temperatures, more small grains and smaller sizes for the big grains at higher dust temperatures).

The 60/100 colors, we observe, therefore suggest changes of the dust properties (dust size distribution and/or composition) from one region to the other. These changes are related to variations in the 160/100 brightness ratio. Whether the 160/100 color variations require a change of the starlight intensity heating the clouds or result from the change of dust properties alone is unclear. The interpretation of the color variations and of the trend between the 160/100 and 60/100 colors is discussed further in the following section.

Because the MIPS observations were taken to observe nearby galaxies, it is legitimate to ask whether the infrared emission that we observe could be associated with these targets. In particular, H i observations have shown that gaseous disks can extend much farther than the optical diameters. Dust grains could be present in these outer parts of the galaxies and bias our measurements.

To avoid this extended emission from the galaxies, we were careful in masking regions larger than the detected emission (see Section 2.1). Some of the galaxies in the observations used in this study have been observed in H i observations through The H i Nearby Galaxies Survey (THINGS; Walter et al. 2005). We checked that the H i diameters reported for these galaxies are smaller than the region masked for our study. We are therefore confident that the variations observed in the infrared emission between fields do not come from the targeted galaxies, but rather from diffuse cirrus emission.

A possibility to interpret the variations of FIR colors at high-galactic latitude is that we are sampling clouds in different physical conditions and/or composition (different heating of the clouds, different dust size distribution,...). The color changes would then be due to mixing along the sightline of these different components.

An unbiased survey of H₂ absorption in high-galactic latitude clouds by FUSE (Gillmon et al. 2006) has been interpreted as showing that some clouds have been compressed. The dynamical history leading to this compression may involve shock waves or strong turbulence, which could also lead to changes in the grain size distribution by shattering in grain–grain collisions, possibly explaining the regions of higher than average 60/100 and lower than average 160/100 colors.

One tantalizing possibility, in terms of mixing, is the presence of Intermediate or high velocity clouds (IVCs and HVCs) along the sightline. These cloud falling onto our galaxy could have very different dust properties (e.g., Miville-Deschênes et al. 2005) and would bias the measured infrared emission from more local cirrus clouds. We checked for the presence of intermediate-velocity clouds in the LAB H i survey spectra (Kalberla et al. 2005) in the direction of the fields in our sample. For about half of the sample, there is a intermediate-velocity component seen in H i in the sightline. Two sightlines also have a high-velocity component. However, no conclusive trend between the fraction of the H i in the IVCs and/or HVCs and the infrared colors could be seen. This may be due to the lack of resolution of the H i observations (∼06), to the difficulty to disentangle IVCs and the Milky Way in some regions or to the small size of our sample.

The grain size distribution is the result of processes such as sputtering, shattering, and coagulation, and sightline-to-sightline variations in the wavelength dependence of optical and ultraviolet extinction toward stars have already demonstrated regional variations in the grain properties. Whether the observed variations in emission can be fully explained by variations in the size distribution alone, or whether other properties (e.g., composition or porosity) are also involved is uncertain.

In denser clouds, variations of infrared colors (Stepnik et al. 2003; Kiss et al. 2006) have been interpreted with a grain coagulation scenario, combining changes of the size distribution with changes of the dust emissivity properties. The trend observed between the 60/100 and 160/100 colors would be consistent with this idea. In this scenario, most of the 160/100 color variations would then be due to the change of emissivity of dust grains (due to changes of their structure), while the 60/100 colors would change with the incorporation or release of small grains in large dust aggregates. We could be witnessing variations of dust properties due to variations in turbulent motions in the diffuse interstellar medium. Alternatively, dust grains in the diffuse medium could retain for some time the aggregate structure they had previously acquired in denser regions. So we could be seeing a sequence of regions corresponding to increasing time since their release from high density environments.

Such changes in the dust size distribution and structure of grains would imply related variations of the UV–optical extinction curves at high-galactic latitude. An extinction and reddening study of stars at high-galactic latitude behind translucent clouds (Larson & Whittet 2005) shows variations in the extinction curves obtained with respect to the average curve for the diffuse interstellar medium. In particular, 48% of their sightlines have R_V < 2.8, much lower that the diffuse ISM average of 3.05. Such values are indicative of enhanced abundances of small grains, and these regions could have a higher that average 60/100 color. To test if the high 60/100 colors and low R_V values are connected, we computed the 60/100 colors from IRIS data in a similar fashion to this study for a ∼1° × 1° region around each sightline of the Larson & Whittet (2005) sample. We do not observe any correlation however between the R_V and 60/100 color, nor between A_V and the 60/100 color. Unfortunately, no longer wavelength observations exist for these regions, and it would be important to determine the 160/100 colors in these regions as well and study their dependency with extinction properties. This result is however a concern for the coagulation scenario as an interpretation of the 60/100 color variations we observe.

Interpreting the trend observed between the 60/100 and 160/100 colors with a change of dust optical properties and dust size distribution remains hypothetical without further observations. In particular, H i observations of these diffuse sightlines, with a high resolution (at least similar to the IRIS one), will be needed to determine the emissivity of dust per hydrogen atom and test if variations are observed and correlated with the infrared colors.

It is presently not possible to interpret further the FIR color variations in terms of physical condition changes, grain size distribution, grain properties, etc. A larger number of observations of high-latitude cirrus could help us to probe the spatial variations. H i studies of these regions at high resolution would also be crucial to probe possible variations of dust grain emissivities, or to check whether the velocity structure of the cirrus correlates with the 60/100/160 colors. Finally, extinction curves on sightlines where cirrus emission properties have been determined would be most useful to see whether extinction properties would correlate with the FIR colors.