In this section we present the road towards spatially resolved, panchromatic SED fitting. The data obtained from various sources and own Herschel observations are manipulated in order to make a consistent comparison over such a wide wavelength range (Appendix A.1). These manipulations bring with them a complex uncertainty propagation which is addressed in Appendix A.2.
The WISE and GALEX subsets had a non-zero average background value due to emission from unresolved sources. The Herschel images also come with a flat, non-zero background as a consequence of the data reduction process. The average background for the Spitzer and SDSS images was already zero, hence no background subtraction was performed for these frames.
While global background gradients were significant in the WISE frames, no clear gradients were identified in the GALEX or Herschel images. We therefore fit and subtract a second-order polynomial to the background in the WISE frames using standard ESO-MIDAS routines. In the other frames, we estimate the background as follows.
A set of regions was chosen far enough from visible emission from M 31 to avoid contamination by the galaxy, but close enough to make a reliable estimation of the background near the M 31. Inside these pre-defined regions, a number of aperture measurements was made. The number of measurements per region was set to be proportional to the number of pixels inside. For PACS and SPIRE, a total of 10 000 measurements were spread over 8 regions. In the GALEX fields, 20 000 measurements were divided over 23 regions. From the set of measured fluxes, a sigma clipped median was derived as a reliable estimate for the background flux. We used 3σ as a threshold and iterated until convergence. This median background value was consequently subtracted from the images.
Andromeda covers a large part of the sky for a single galaxy and lies close to the Galactic disk (with a Galactic latitude of ). It is consequently contaminated by the light of thousands of foreground stars, especially in the UV and optical part of the spectrum. At longer wavelengths, the infrared emission of background galaxies becomes the main source of contaminating sources. At Herschel wavelengths, however, most of the emission from non-M 31 point sources is negligible even at scales of the SPIRE 500 μm beam. As mentioned before, the extended emission of the Milky Way Galactic Cirrus is prominently visible here. This dust emission can fortunately be associated with HI emission. Using the velocity information of HI maps, the Galactic cirrus can partly be disentangled from the emission of M 31. Paper I goes into more detail about this technique.
We made use of SExtractor v2.8.6 (Bertin & Arnouts 1996) to list the location of all point sources above a certain threshold (5 times the background noise level). The program simultaneously produces background maps that can be tweaked to represent the diffuse emission from M 31. In this way, we could replace the non-M 31 point sources with the local M 31 background value obtained from these maps.
For each source an optimal radius was derived by comparing the pixel flux with the local background at increasing distance from the peak location. Once the pixel-to-background flux ratio dropped below 2, the radius was cut off at that distance. Based on this radius, a total flux was extracted in order to make colour evaluations. We constructed point source masks for the GALEX, SDSS, WISE, and Spitzer subsets based on different colour criteria.
The GALEX and SDSS point sources were evaluated based on their UV colour. This technique was applied by Gil de Paz et al. (2007) for over 1000 galaxies and proved successful. In practice, we mask all sources with (A.1)if they are detected at the 1σ level in their particular wavelength band. SExtractor identified 58 330 point sources in the UV fields, of which over 51 000 were masked in the FUV and NUV. Many point sources from the UV catalogue were not detected at optical bands, hence only 25 000 sources were masked in the SDSS bands. Around 7000 sources were identified as extragalactic. They were therefore assumed to belong to M 31 and were not masked.
As an example, Fig. A.1 shows the u-band image of M 31 before and after the mask was applied. The contamination of the image has been significantly reduced using the above technique.
Masking of point sources that do not belong to M 31: before and after view of the galaxy in the u band (top) and IRAC 3.6 μm band (bottom).
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The point sources in the WISE and the Spitzer IRAC and MIPS frames were masked analogously, based on their IRAC colours (see below). At these wavelengths, however, the non-M 31 point sources are a mix of foreground stars and background galaxies. Furthermore, some bright sources may be associated with Hii regions in M 31 and must not be masked. We designed a scheme based on the technique by Muñoz-Mateos et al. (2009b), which was successfully applied to the SINGS galaxies. Foreground stars have almost no PAH emission, while the diffuse ISM in galaxies shows a roughly constant F5.8/F8 ratio (Draine & Li 2007). Background galaxies are redshifted spirals or ellipticals and can consequently have a wide range in F5.8/F8. It is thus possible to construct a rough filter relying on the difference in MIR flux ratios. First, it was checked which point source extracted from the IRAC 3.6 μm had a non-detection at 8 μm. This criterion proved to be sufficient to select the foreground stars in the field. A second, colour-based, criterion disentangled the background galaxies from the Hii regions:
Figure A.2 shows the colour−colour diagram for these sources. The Hii regions follow a more or less horizontal track at the lower-left part of the plot. The colour criteria for filtering out these Hii regions were obtained empirically to ensure effective identification. Once identified, these star forming regions were consequently not masked. The resulting mask was applied to all IRAC and MIPS bands. Sources that were not detected at longer wavelengths were obviously not masked. Figure A.1 shows the IRAC 3.6 μm image of M 31 before and after the mask was applied. SExtractor identified 1933 sources in the IRAC bands and 536 in MIPS. From these catalogues, around 1800 sources were masked in IRAC and 230 in MIPS. All masked sources in IRAC were also masked in the WISE frames as both instruments cover roughly the same wavelength range. No additional masking was necessary for the WISE data.
Colour−colour plot of the IRAC selected bright sources. The sources inside the red rectangle are identified as Hii regions belonging to M 31. They were consequently not masked.
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As a way to check the reliability of our masks, we compared the masked regions with the locations of known Andromeda sources, i.e. Hii regions and planetary Nebula (Azimlu et al. 2011) and bright young clusters (Barmby et al. 2009). The overlap between our masked sources and actual M 31 sources proved negligible; 0.3%, 0.1%, 0.4%, 0.4%, and 1.5% of the identified sources were incorrectly masked in the GALEX, SDSS, WISE, IRAC, and MIPS bands, respectively. The handful of sources that were incorrectly masked were manually restored.
The masked images were all brought to the same resolution before extracting the separate pixel values. By doing this, information is lost because of the significantly lower resolutions of the end products. It is, however, a critical step to make a consistent comparison of the fluxes over this wide range of wavelengths. Our working resolution was limited by the SPIRE 500 μm point spread function, which is 36.0 arcseconds. As M 31 is the nearest spiral galaxy, this still corresponds to an unprecedented physical scale of 136.8 pc. Aniano et al. (2011) conducted an in-depth study on convolution kernels for most known telescope PSFs. Additionally they wrote an efficient IDL routine convolve_image.pro which makes use of their designed kernels and takes NaN values into account when convolving. The kernels for the GALEX, WISE, IRAC, MIPS, PACS, and SPIRE instruments were readily available to make the convolution. For the SDSS images, we used a Gaussian-to-SPIRE 500 kernel which assumes an initial FWHM of 4′′ for the SDSS images (see Sect. 2.2).
The SPIRE 500 μm beam is sampled with a pixel scale of 12′′ which means the PSF covers nine pixels which are not independent. The frame thus had to be rebinned to a pixel scale of 36′′ to make each pixel correspond to a statistically independent region in M 31. The convolved frames were consequently rescaled to match the pixel grid of the SPIRE 500 μm rebinned image. Our data cube covers the electromagnetic spectrum from UV to submm wavelengths. Figure A.3 gives an overview of all frames used for the fitting of a panchromatic SED to each pixel.
This series of steps results in sets of corresponding pixels which each represent a physical region of 136.8 × 608.1 pc along the major and minor axes (using an inclination of ). Off course, it must be noted that the third dimension, the direction along the line of sight, also contributes to the appearance of each pixel. Spiral galaxies are, however, known to have relatively thin disks compared to their lengths, so even along this axis, the resolution remains subgalactic. The attenuation effects of this larger dimension will, however, be treated during the modelling in terms of optical depth parameters (see Sect. 3.1).
Overview of the FUV to submm dataset at SPIRE 500 resolution, rotated from a position angle of .
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Each pixel comes with several sources of uncertainty, which will have to be estimated and combined to a total error. Uncertainty propagation based on initial errors can become complex and hazardous after masking, convolutions, rebinning, and rescaling. In their Appendix D.1, Aniano et al. (2012) opted to start the uncertainty estimation after all these steps in their resolved analysis for NGC 628 and NGC 6946. They postulate two sources of uncertainties: background variations and calibration errors. Additionally, we add a third source for the UV and optical subsets: the Poisson error. This term is negligible for infrared and submm observations because of the large number of incoming photons.
Variations of the background can give rise to errors in the flux measurements. To estimate the impact of this term, we select regions around M 31 where the background is dominant. A sigma clipping filter is used on the pixels inside each region. Different methods of sigma clipping were evaluated. They proved not to affect the resulting variance by much as the evaluated regions were chosen to be free of point sources. In the end, a low-level clipping was done (10σ and only two iterations) to filter out any non-background emission. The variance of the remaining pixels from all of the regions will be a good representation of the background variation error σbackground, following Equation D2 from Aniano et al. (2012), (A.4)where Nbg is the number of background pixels used and Iobs the observed background subtracted flux of the pixel with coordinates x and y. For each telescope, a different set of background regions was used. This was needed because the background and Galactic Cirrus features change in morphology and brightness along the electromagnetic spectrum.
Photon arrivals are considered a random event following a Poisson distribution; the variability of the counts scales with the square root of the number of photons. Infrared and submm observations deal with huge numbers of photons (all of which have low energy) and consequently have a negligible Poisson error compared to calibration uncertainties and background variations.
Optical and UV observations, however, do not collect as many photons and consequently their Poisson-like nature could start to play a more prominent role. In the cases of the GALEX and SDSS observations, the images were converted from flux to actual photon counts using the individual exposure time for each pixel and then converted to counts/Sr. This surface density unit was necessary to rebin and rescale the frames to the SPIRE 500 μm pixel grid without disrupting the exposure time information. We note that convolution did not take place here. The resulting images were converted back to counts using the new pixel scale and from here the Poisson errors could be computed for each individual pixel by taking the square root of the counts.
In higher signal-to-noise areas, the calibration of the instrumentation can become a dominant term. We therefore include a fixed percentage as calibration uncertainty for each filter (see Table A.1) in addition to the previous error terms.
Overview of the adopted relative calibration uncertainties for each pixel.
Overview of the obtained fluxes for the different regions of Andromeda.
© ESO, 2014