Application to the DIS field GROTH_00

We applied  EMphot to the very deep NUV image  in the GROTH field with Texp = 237ksec. The optical catalog and images for the priors are based on the CFHTLS deep survey  (T0005 release). We restricted the prior’s sample to sources with UAB<26.75.    


Image residuals :

After running EM, the distribution of the count rate residual (GALEX-EM image), shown in Fig 2a,  is very close to the expected Poisson distribution (slightly wider)  and does not show deviation in the wings.

The EM photometric software :

To minimize the  blending issues and obtain reliable flux for individual faint sources, we developed a bayesian  photometric code (EMphot) based on the knowledge of a predefined list of optical positions, under the realistic assumption that  the vast majority of GALEX sources are detected in optical images (sources bluer than flat  spectrum in fν  being rare).  EMphot  uses a list of optical prior positions and measures their UV fluxes on the GALEX  images by adjusting a GALEX PSF's model. The PSF's amplitude of each optical prior is obtained  via a global maximum likelihood estimation over regions with a typical size of 2x2arc min^2  and solved by using the expectation maximization (EM) iterative scheme.  The prior positions, local background level are known input ingredients. The  EMphot parametrization adopts a Poisson statistical law to allow also for low background counts, although this is not an issue for DIS fields which are close to a gaussian distribution.  An illustration of the EM  steps is shown in Figure 1.  The errors in the source’s fluxes are estimated from the residual images (GALEX-EM image)  to better account for systematics in the geometric centroid of the priors, extended galaxy profiles,  local background estimation. A description of the EM software is available in a recent poster for ADASS Conseil et al. (2009) and  references therein.




Figure 2b :  standard deviation estimation using a gaussian fit of the left side of pixel distribution of the original NUV image. 

 

Expected depth for the DIS fields  via simulations

To quantify the photometric accuracy in the DIS fields, we inject simulated PSF-like sources with different flux  intensity in the original images. The recovered fluxes of the simulated sources  vs the true flux are shown in Figures 7 for DIS fields with integration times spanning 18ksec to 250ksec.  The blue squares represent the median of the  difference between the input and recovered fluxes (b=<SIM - EM>), while the red circles show the sigma of the distribution. The grey shaded area shows the behavior of the Signal-to-Noise with a mean sky background level and an effective exposure time specific to each DIS field and for a source area of 49-68 sq. pixel. The vertical lines show the expected magnitudes at 5σ and 2σ.  The left figure uses the original low-resolution background map from the standard pipeline. The bias (b) observed  in the median suggests that the background level can be slightly overestimated,  introducing a systematic loss of flux, more pronounced for faint objects.  The right figure uses a higher resolution background map reconstructed after removing the expected EM flux of all the sources in the GALEX images.  The bias is significantly reduced  down to the 5σ magnitude limits. The photometric errors in the simulated sources  are in good agreement with the expected Poisson noise.

GALEX Deep Imaging Survey

UV-GALEX Format
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Purposes :  In the Deep Imaging Survey, the Galaxy Evolution Explorer  (GALEX) has obtained  imaging in Far-UV (~1500 Å) and Near-UV  (~2300 Å) channels with integration time spanning  10ksec to 250ksec with  a typical integration of 30ksec.  As data products, the standard GALEX pipeline (Morrissey et al. , 2007) provides, for every flux-calibrated image, a  catalog of  UV sources based on the detection and flux measurements with SExtractor software (Bertin & Arnouts, 1996).  However given the GALEX  PSF (FWHM~4.5 and 5.4 arcsec in FUV and NUV respectively), the source  confusion becomes a major issue in deep fields  (Xu et al., 2005; Hammer et al., 2010)  and  prevents an easy match with higher resolution images from optical surveys (with sub-arcsec seeing). 

GALEX image with shapes of optical priors overlay in red

EM simulated image with best UV flux estimated for the optical prior sources 

GALEX- EM  image residual

Figure 2a :  Distribution of the residual count rate (GALEX - EM image),  normalized by the expected Poisson noise (with σ derived in Fig 2b). The observed distribution is very similar to the ideal distribution (red dashed curve,  μ=0, σ=1).

Figure 2b :  Estimation of the background standard deviation in the NUV image (GROTH_00-nd-int.fits)  by using a gaussian fit of the left side of the count rate distribution.

Figure 3:  Comparison of the deblended EM magnitudes with the GALEX pipeline magnitudes (grey points). The black points show  isolated sources  with no neighbors within 7 arcsec.  The mean magnitude differences for the isolated sources are shown for the whole sample (large grey circles) and for the compact and extended optical sources (blue and red squares respectively). 

Left Fig:  EMphot  neglects the optical prior shape (Dirac function). Right Fig: EMphot uses the shape of the priors by replacing the Dirac function by the U band image of the prior.

Figure 4 :  Normalized distribution of the differences between EM and GALEX pipeline magnitudes in 4 magnitude bins.  The shade histogram is for all sources  while the blue and red histograms are for the compact and extended optical sources resp.   The dashed curves show a gaussian distribution with mean and  sigma reported in each caption. Left and Right Fig as for  Fig 3.

Figure 5:  Signal-to-Noise ratio versus EM magnitudes for the whole sample (black dots),  isolated  compact  (blue) and  isolated extended  (red) sources.  The grey lines show the expected SN for a mean sky background rate, a median effective exposure time and a source area of  49 &  68 sq. pixels.  Left and Right Fig as for  Fig 3.

Figure 1 :  Illustration of the EM method


The deblending and Prior shape assumptions  :

Figure 3 and 4 show the impact of the blending by comparing the EM magnitudes with the GALEX pipeline magnitudes.  For GALEX, we adopt a large aperture magnitude (34.5 arcsec, “mag_aper_7”). In Figure 3, the

magnitude difference is shown for the whole sample (grey dots)  while the heavy black dots  are sources without a neighbor within 7 arcsec in the CFHTLS prior catalog.  The isolated sources are those for which the GALEX pipelines ought to be the most reliable and they do show a good agreement with the EM photometry (mean and σ per mag bins are shown with large grey circles). We further analyzed the isolated sources in  two subclasses with compact and extended sources based on optical SExtractor classification (class-star>0.8  and class-star<0.2 resp.). For extended sources, EM photometry systematically underestimates their fluxes by neglecting the possible extended shapes of bright galaxies (Fig 3, left) . To improve it, we replaced the initial Dirac function of each prior by its 2D optical light distribution profile by extracting its stamp in the U band image  (Zamojski et al., 2007).  Fig 3 right panel, shows the improvement at bright magnitudes with respect to the initial EM method.  For isolated sources, EM and GALEX pipeline are in excellent agreement in the whole magnitude range (when including the extended profile for bright sources). The major impact of EM is then for all the blended sources  (grey dots) where the GALEX pipeline  overestimate their fluxes.  Figure 4 shows the normalized distributions of the magnitude differences for the whole galaxy sample (grey shaded histograms)  which show a long tail as well as a non-centered mode of the distribution. We also show the distribution for the isolated compact and extended sources.  When neglecting the extended shape of galaxies (Fig 4 left),  the compact and extended  distributions differ  at bright magnitudes but become comparable around NUV~23.   


EM photometric errors :   

The flux uncertainty for each object is estimated  directly from the residual image (GALEX-EM)  and weighted over  the object’s profile.  Figure 5 shows the Signal-to-Noise as a function of EM magnitude.  The expected Poisson estimates of the S/N is shown as grey line.  EM errors are consistent with  Poisson with a spread towards lower S/N  objects at a fixed flux due to  significative residuals.  Isolated  compact/extended sources are also  shown.  There is a large gain in S/N for extended sources at NUV<23  when EM uses the shape information which improves the residual image. This is not the case for bright stars where optical stamps are saturated degrading their residuals.   

Figure 7:  Errors in recovered fluxes of artificial sources added to original GALEX images as a function of true flux.

The systematic bias (<MagSIM-MagEM>) is shown as blue squares and standard deviation (σ) as  red circles.

The different panels refer to fields with different depth  (from 18 to 237ksec top to bottom).  In the Left side, we adopt the GALEX standard background map, while in the right side a higher resolution background is estimated after a first EM iteration and re-injected in a second pass.   


Number counts :  

In  Figure 6, we show the number count distribution (N(m)) as derived from the GALEX pipeline reference magnitude (based on mag_auto)  and the one derived using EM photometry including the shape of the prior and a  refined background map (see next section). GALEX pipeline N(m)  shows an excess of bright sources with respect to EM  due to blending and which is not observed when comparing  isolated sources.

GALEX pipeline  N(m) shows a severe incompleteness with a flattening around NUV~23.5. This incompleteness  is due to the confusion limit with a ~40 beam-per-source at NUV~24 (Xu et al., 2005).

This is 1.5-2 magnitude shallower than what would be expected based on the Signal-to-Noise

(5σ~25-5-26 for this deep field, see previous and next sections).  The EM method prevents this issue to happen by selecting the sources in high angular resolution optical images. The EM  N(m) shows a rise up to NUV~25.5 consistent with the expected S/N of this deep field (see next section). 

Figure 6:   Number counts N(m) derived with the GALEX pipeline magnitude (black solid line), EM photometry (solid blue line) and for EM sources with S/N>5 (blue dotted line).  The dashed lines show the GALEX and EM N(m) for isolated sources.