Galaxy Completeness Estimate with SN Field Coadds

Background Info

I (Diego) have used Eli's new coadds of part of the SN fields to estimate galaxy completeness as a function of surface brightness (mu max, i.e. the surface brightness of the brightest pixel of a galaxy) and total magnitude. Eli obtained two kinds of coadds, the first being approximately as deep as the standard 10 tilings DES survey (hereafter referred to as Wide survey) and the second being as deep as the standard SN fields (hereafter referred to as Deep survey). The latter is used as reference for the analysis carried out. The idea behind this analysis is to sky cross-match objects classified as galaxies from the Wide and Deep surveys, determine the distribution of the matched galaxies in the total magnitude vs. mu_max plane, compare the obtained map with that of the entire Deep survey by taking their ratios (Wide/Deep) and so obtain a completeness map in the same plane. What we are interested into is the completeness as a function of mu_max and total magnitude in the photometric system of the Wide survey, which in our case should be the same as the one of the Deep one. The sky cross-matching is performed using a radius of 0.5". This can be changed, with the obvious consequence of increasing or decreasing the derived completeness with increasing or decreasing the matching radius. However this effect shouldn't modify the results significantly, if the astrometry is consistent between the Wide and Deep coadds. The analysis described below is carried out for the i-band only!

The punch line is that there are differences between the values of surface brightness and total magnitudes measured in the two surveys for the same galaxies. In particular, the Wide survey surface brightness values tend to be brighter than the Deep survey ones, the bluer is the colour measured in the Deep survey. The dependence on colour is quite puzzling. Maybe it is due to depth and/or seeing variations over the surveyed sky. These differences cause the Wide survey catalogue to be over-complete with respect to the Deep survey one, something which is obviously impossible. I tried to re-calibrate the Deep survey catalogue, in order to correct for these differences and then re-calculate the Wide survey completeness in its photometric system. This produced better results and significantly reduced the surface brightness-total magnitude regions of over-completeness.

Checking which is the culprit of the problems identified above (sky variations of seeing and/or depth) by using systematic and depth maps. Click the following link for new tests on these issues:Completeness as fcn of seeing and depth

1. Sample Selection

Note that MAG_TOTAL here refers to the total magnitude for which completeness is studied. It can either be MAG_AUTO or MAG_MODEL, on which I have focused the study so far.

  • Cuts on sample performed on both Wide and Deep survey catalogues, to match those applied on SVA1 Gold 1.0.2:
  • Because the analysis is carried out in the i band, and because of the need of a calibration (see Section 5), the following additional very coarse cuts have been applied in order to select reliable objects in both the Wide and the Deep catalogues:
    • MAG_TOTAL_I≠99
    • MU_MAX_I≠99
    • -10<MAG_TOTAL_R-MAG_TOTAL_I<10
    • -10<MU_MAX_R-MU_MAX_I<10

2. Wide Survey depth

In order to perform the analysis as correctly as possible, I have determined the galaxy total magnitude depth at 10-sigma level for the Wide survey. This was done by determining the galaxy number-counts faint-end drop on galaxies with MAGERR_TOTAL_I<0.11. I have done this for MAG_AUTO and MAG_MODEL, obtaining in both cases depth_i=~23. This is somewhat unexpected given that when doing the same study or using Eli's depth maps on the SVA1 Gold 1.0.2 catalogue, one obtains different depth values or, equivalently, different areas characterized by the same galaxy depth for different magnitude types (see Is something going wrong with errors on MAG_AUTO?). For SVA1 Gold this was due to the error distributions for different magnitude types being different, concluding in particular that the use of errors on MAG_AUTO for estimating galaxy depth is questionable as it would result in a significant loss of objects compared to MAG_MODEL and MAG_APER4. However, this situation is not reproduced in the new Wide survey SN coadds, as the same depth is found for both MAG_AUTO and MAG_MODEL.

The estimate of galaxy depth for the Wide survey was carried out in order to additionally cut the Wide survey catalogue by selecting galaxies brighter than the estimated 10-sigma lever depth. The reason behind this additional selection is to increase the reliability of the sky cross-matching process. In fact, when carrying out such a process, one should make sure to cut the deeper catalogue (in this case the Deep survey one) at a total magnitude value fainter than the depth of the shallower catalogue (in this case the Wide survey one) but still close to to it, in order to avoid mismatch of galaxies in the Wide survey catalogue with extremely fainter galaxies in the Deep one, which could have not been detected in the former. Formally, the Deep catalogue should be cut at the same magnitude depth as the Wide survey one, but since the magnitude estimates between the two survays might not perfectly coincide, one should allow some tolerance. The tolerance I have used here is 0.5 mag.

As a consequence, the following additional cuts have been applied on the Wide and the Deep survey catalogues:

  • Wide survey catalogue
    • MAG_TOTAL_I<23
  • Deep survey catalogue
    • MAG_TOTAL_I<23.5

3. Completeness estimate in the Deep Survey photometric system



4. Completeness estimate in the Wide Survey photometric system



5. Photometric calibration

As one can notice by looking at the plots obtained in the Wide survey photometric system, something is odd as according to them the Wide survey is over-complete at the faint end when looking at the completeness map projection on the surface brightness variable. In addition, the Wide survey looks also over-complete in the surface-brightness vs. total-magnitude plane, in particular in the regions of relatively high surface brightness (at all total magnitude values by a factor out to ~30!). In particular, note the different shape of the mu_max completeness functions obtained in the Wide and the Deep surveys photometric systems. This is obviously wrong an it must be due to astrometric mismatch or to photometric offsets between the measured magnitude and mu_max values in the two surveys, or a combination of both. Under the assumption of a correct astrometry, I tried to re-calibrate the Deep survey photometry in order to transform it into the Wide photometric system. The approach used is statistical and is carried out using only the galaxies satisfying the 0.5" sky cross-match process. After the calibration is determined, it is then applied on magnitude and surface brightness values of the galaxies selected in the Deep survey as described in Sections 1 and 2.

For both total magnitude and surface brightness, I assumed a linear relation between the differences between Wide and the Deep surveys values and galaxy colours as calculated in the Deep survey considering the closest bluewards filter (r) to the one used for the completeness calculation (i band):

  • Delta_mag_i=m_wide_i-m_deep_i=A+B*(m_deep_r-m_deep_i)
  • Delta_mu_i=mu_wide_i-mu_deep_i=A+B*(mu_deep_r-mu_deep_i)

I fitted such linear relationships to the data. In order to have an as reliable as possible calibration, I focused on galaxies selected according to the following criteria:

  • Wide_mag_i≠99
  • Deep_mag_i≠99
  • -2<Wide_mag_r-Wide_mag_i<2
  • -2<Deep_mag_r-Deep_mag_i<2
  • -2<Wide_mu_r-Wide_mu_i<2
  • -2<Deep_mu_r-Deep_mu_i<2

Calibration for MAG_AUTO

Calibration for MAG_MODEL

6. Results: completeness in the Wide photometric system after calibration