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Galaxy depth and completeness using Mangle Mask

- Diego Capozzi

Here I describe the results of a study aiming at identifying homogeneous depth regions using the information contained in the Mangle mask, using SVA1 data. These regions will be constructed in the molygon space, so they won't necessarily be constituted by contiguous molygons. In addition, relations between depths estimates measured with various types of magnitude (the one used for constructing the Mangle mask is a 2"-aperture magnitude, MAG_APER4) is explored so to be useful for data selection purposes, which can be different according to the science carried out. A first attempt to study these issues in detail has been carried out and described here: Some tests on depth with Mangle Mask. Here I implement the old tests with the selection cuts that have been discussed during the SVA1 telecons and in particular among Eli, Nacho and myself. These cuts also include the latest star/galaxy separation criteria described here: A Modest Proposal for Preliminary Star/Galaxy Separation.

Galaxy completeness cannot be studied at the moment, but I use the surface brightness information to identify what could possibly be the magnitude at which the survey is complete. However, without having a deeper reference for a standard 10=tilings field, at which completeness level this magnitude value corresponds to cannot be inferred.

I point out that the study described below is carried out only on the following fields: SPT (E & W); El Gordo; RXJ2248. As of today, there is no SVA1 data-based Mangle Mask for tew Bullet Cluster field. SN fields (as of now, a mangle mask is available only for SN_S) have been excluded on purpose, as my aim is to characterise a region with homogeneous depth for the standard 10-tilings Survey (from now on referred to as Wide Survey). In addition, I only considered tiles where the zero-point offsets are minimised according to Huan Lin's "galaxy-locus" criteria.

Finally, molygons with area>3 str and with i-band 2"-aperture mag=0 (the latter corresponding to regions that are masked by bright stars) have been excluded (see Some tests on depth with Mangle Mask for more details).

1. Studying galaxy depth via galaxy counts, using Mangle mask: comparing MAG_AUTO, MAG_DETMODEL & MAG_APER4 depths against molygon ones.

  • Data Selection
    • Galaxy selection step 1 (from SVA1_COADD_GRIZY table):
      1. Contained in SPT (E & W), El Gordo & RXJ2248 fields
      2. Contained in good tiles according to Huan Lin's "galaxy locus" zeropoint offsets criteria
      3. MAGERR_APER4_I<0.11
      4. -1<MAG_DETMODEL_G-MAG_DETMODEL_R<4
      5. -1<MAG_DETMODEL_I-MAG_DETMODEL_Z<4
      6. NITER_MODEL_GRIZ>0
      7. DEC>-61 (avoid LMC)
      8. FLAGS_I<4
      9. (((SPREAD_MODEL_I+(3*SPREADERR_MODEL_I))>0.003) and ((MAG_AUTO_I>12 and MAG_AUTO_I<18 and CLASS_STAR_I<0.3) or (MAG_AUTO_I>18 and MAG_AUTO_I<25))) and MAG_PSF<30
    • Molygon selection step 1 (from MOLYGON table):
      1. I-band molygons contained in SPT (E & W), El Gordo & RXJ2248 fields
      2. I-band molygons in tiles according to Huan Lin's "galaxy locus" zeropoint offsets criteria
      3. MAG_LIMIT (i-band)>0 (Avoiding regions masked by bright stars)
      4. AREA_STR<3 [Avoiding molygons with strangely large area (these are few outliers and reducing the cut to 1 or less won't change the extracted molygons)]
    • Galaxy selection step 2 (from COADD_OBJECTS_MOLYGON table):
      1. Contained in molygons selected in previous point (step necessary to extract information linking galaxies to the molygons they belong to)
    • Galaxy selection step 3:
      1. Selecting properties from SVA1_COADD_GRIZY of galaxies identified in step 1 which are contained in the identified molygons using the information obtained in "Galaxy selection step 2"
    • Molygon selection step 2:
      1. Checking the actual molygons used to identify the unique molygons ID values associated with the galaxy sample identified in "Galaxy selection step 3"
  • For the identified galaxy sample, values of magnitude (APER_MAG4 excluded, for which corrections are not available) and surface brightness have been corrected for zeropoint offset according to Huan Lin's tables.
  • The importance of what surface brightness measurement is used.
    In the previous study, the surface brightness measure that was used was model surface brightness [either effective (MU_EFF_MODEL) or that at the brightness peak (MU_MAX_MODEL)]. This measurement was always found to show a gausian-like distribution rather than the common steeply increasing distribution with a sharp drop at the faint end. This was proven to be independent on the depth inhomogeneity over the sky [see GEWG report (DES-doc-7617-v1) on SVA1 for details]. For this study I used MU_MAX, which is a model-independent measure of surface brightness. In the plot in Figure 1 below, I compare the distributions of MU_EFF_MODEL (whose shape is equivalent to the one of MU_MAX_MODEL) and MU_MAX for the galaxy catalogue identified above. One can see the great difference between the two distributions, and that the MU_MAX distribution is definitely closer to the expected distribution, despite its drop still lacking the expected sharpness.


Figure 1

This comparison indicates that there is something going on with model-based measures of surface brightness. I point out that DC6 data, despite lacking the sharp drop at the faint end, did not show as a gaussian-like shape of model-dependent surface brightness measures as for SVA1 data, as shown in Figure 2 below.


Figure2: Distribution of model-dependent surface brightness measure taken from DC6 data. See black full line.

  • I-band depth comparison. What has been done:
    • Binning molygons in mag_limit (2-arcsec aperture-magnitude depth associated with molygons as output of the Mangle masking process) bins of 0.2 mag.
    • In each bin, distributions of MAG_APER4, MU_MAX, MAG_AUTO and MAG_DETMODEL are analysed. Bin size used for all these distributions: 0.05 mag
    • For each distribution the depth is found as the peak in the number counts [if the peak is not unique, but more than 1 with the same value are seen, then the first peak (corresponding to the brightest magnituded) is taken]. The presence of more peaks should only happen with smaller galaxy samples, i.e. for the brighter molygon-depth bins. In general, the peak should be one and at magnitude fainter than this peak, galaxy number counts should decrease.
    • Galaxy depth is measured. In general, the process for defining galaxy depth for galaxies in molygons within a given mag_limit bin, works as follows:
      1. Find peak in the magnitude distribution. This peak is defined as the galaxy magnitude depth.
  • Approximate value for galaxy magnitude limit at which the sample is complete at an unknown completeness level is measured. In general, the process for defining this value for galaxies in molygons within a given mag_limit bin, works as follows:
    1. Find peak in the surface brigthness (in this case MU_MAX) distribution. NOTE: the shape of this distribution does not show the typical sharp drop after the peak. The situation is definitely better than when using MU_MAX_MODEL (see below for more details).
    2. Select galaxies with: reasonable lower limit<surface brightness values<surface brightness peak. In this study, reasonable lower limit=16.

Note that, as expected, the surface brightness strongly influences the galaxy completeness limit.

The following plots show the results obtained for molygons with 22.6<MAG_LIMIT<24.2.

PLOT CAPTION
upper left panel: 2-arcsec aperture-magnitude distribution for the identified galaxy sample within the selected molygons
upper centre panel: MU_MAX distributions for the identified galaxies in: a) all the molygons selected in the "Data Selection" section; b) molygons in the the MAG_LIMIT bin analysed
upper right panel: MAG_AUTO distributions for the identified galaxies in the molygons contained in the analysed MAG_LIMIT bin: with and without MU_MAX selection
lower left panel: MAG_DETMODEL distributions for the identified galaxies in the molygons contained in the analysed MAG_LIMIT bin: with and without MU_MAX selection
lower centre panel: MAG_APER4 distributions for the identified galaxies in the molygons contained in the analysed MAG_LIMIT bin: with and without MU_MAX selection
lower right panel: comparison between MAG_AUTO, MAG_DETMODEL & MAG_APER4 distribution for galaxies selected also in MU_MAX

22.6<MAG_LIMIT<22.8

Figure 3

22.8<MAG_LIMIT<23.0

Figure 4

23.0<MAG_LIMIT<23.2

Figure 5

23.2<MAG_LIMIT<23.4

Figure 6

23.4<MAG_LIMIT<23.6

Figure 7

23.6<MAG_LIMIT<23.8

Figure 8

23.8<MAG_LIMIT<24.0

Figure 9

24.0<MAG_LIMIT<24.2

Figure 10

Galaxy depth comparison:

The galaxy depths measured via number counts in each MAG_LIMIT bin are compared with those given as the output of the mangle masking process in Figure 11 (left panel). The same is done for galaxy completeness limits (i.e., magnitude values at which the sample is complete at an unknown completeness level, calculated using also surface brightness cuts) in the right panel of Figure 11. I point out that the "Reliable" region in Figure 11 plots represents MAG_LIMIT bins where the galaxy sample is large enough not to show multiple peaks in the magnitude distributions.

Note that, as expected, the galaxy completeness values are brighter (~0.5 mag brighter) than depth ones, a results that also shows how surface brightness cuts influences the completeness of a catalogue. Another result to note is that, differently form the results of the previous study, the number-counts derived depth follows very closely the one given by the Mangle mask (based on finding the 10-sigma cut a magnitude vs magnitude error plot). The main reason for this agreement (which should be anyway expected and is actually reassuring, given that two different methods for estimating depth are consistent with each other, as they should) is the use of magerr_aper4<0.11 in the catalogue selection. This is a natural consequence of the fact that the way the Mangle mask depth is calculated makes use of these mag_aper4 errors.


Figure 11: Case of MAGERR_APER4<0.11 used in sample selection. Left panel: Mangle Mask depth vs. number-counts depth; right panel: Mangle Mask depth vs. number-count completeness

The improved star/galaxy separation does not make a significant difference. In fact, when repeating the analysis using a catalogue selected as described in the Data Selection Section but using magerr_auto<0.11 instead of magerr_aper4<0.11, one gets the same results as in the old analysis, i.e. number-counts depth values for APER_MAG4 are significantly different than those given by the Mangle mask, as shown in the left panel of Figure 12 (the distribution plots for the magerr_auto<0.11 are shown in the Additional Plots Section). The improved star/galaxy separation has probably more effect for lower detection level (higher magnitude errors). [Eli, did you cut your sample to a 10-sigma level when doing your latest tests on star/galaxy separation?]


Figure 12: Case of MAGERR_AUTO<0.11 used in sample selection. Left panel: Mangle Mask depth vs. number-counts depth; right panel: Mangle Mask depth vs. number-count completeness

As expected, in all cases, the integrated-magnitude depth and completeness, as measured via MAG_DETMODEL or MAG_AUTO, are always ~0.5 mag shallower than the aperture-magnitude ones. It is also good news that MAG_DETMODEL and MAG_AUTO depths are always close to each other.

It is important to notice that one can use the Mangle mask depth only when selecting a galaxy sample similarly to what done for the Mangle mask process (e.g., using MAGERR_APER4). If for any scientific purposes the galaxy sample selection is carried out differently, the Mangle mask cannot be used or can only be used by applying corrections (e.g., magnitude scaling corrections), even when using the same magnitudes (e.g., MAG_APER4), as Figure 12 demonstrates. For instance, if for studying the galaxy luminosity function one wants to select a galaxy catalogue out to the 10-sigma level depth for MAG_AUTO (or MAG_DETMODEL), one cannot use mangle mask depth values only corrected for flux differences between aperture and integrated magnitude, to trace the 10-sigma level depth for MAG_AUTO (or MAG_DETMODEL). A correction taking also into account that the 10-sigma level for the integrated magnitude is different from the one corresponding to the aperture magnitude, is also needed. This fact is clear if one compares left panels of Figures 11 and 12. For instance, the sample selected as described in the Data Selection Section (so using MAGERR_APER4<0.11), contains about 2 millions more galaxies than the one selected in the same way but using the MAGERR_AUTO<0.11 criterion. This difference in galaxy selection causes the difference in depth and completeness values (see Figures 11 and 12).

We could model these magnitude differences so to calibrate them in the "Reliable" region identified in the plots in Figures 11 and 12. Transforming the 10-sigma mangle mask depth for MAG_APER4 to a 10-sigma MAG_AUTO or a MAG_DETMODEL depth, would mean applying an offset of ~1 mag [~0.5 mag due to the difference between aperture and integrated magnitudes and ~0.5 mag due to the difference in the 10-sigma detection level (so in the errors) for the mentioned magnitudes] towards brighter magnitudes. If one also needs a complete sample (at the moment this reference cannot be associated to a completeness level), then one should roughly apply an additional ~0.5 mag offset towards brighter magnitudes, making a total of 1.5 mag shallower than the the Mangle mask depth.

Additional plots (the MAGERR_AUTO<0.11 case)

22.6<MAG_LIMIT<22.8

Figure 13

22.8<MAG_LIMIT<23.0

Figure 14

23.0<MAG_LIMIT<23.2

Figure 15

23.2<MAG_LIMIT<23.4

Figure 16

23.4<MAG_LIMIT<23.6

Figure 17

23.6<MAG_LIMIT<23.8

Figure 18

23.8<MAG_LIMIT<24.0

Figure 19

24.0<MAG_LIMIT<24.2

Figure 20

Final Remarks

On average, molygons correctly tell us how the aperture magnitude depth varies over the surveyed area. However there are still suspicious molygons with too low a total exposure time for the depth value they are associated with. Below I report the tables obtained in the old analysis reporting the expected stellar magnitude in the i-band at several S/N levels (what we want to consider though is S/N~10 level) for two values of total exposure time. These are calculated by using the DECam Exposure Time Calculator for stellar photometry available on the CTIO DECam webpage. I have considered the case of best observing conditions, i.e. when the sky brightness is the lowest possible (so to speak, with new moon). This choice is to show that even in the best observing scenario, the depth reached in some molygons doesn't seem realisitic. One has to take into account that the Exposure Calculator is made for stellar photometry, so one should roughly subtract 0.5/1 mag from the stellar magnitude value it provides, to get a realistic value for galaxies.

Case of Total exposure time fixed at 540 s (i.e. 6 x pointings/90 s exposures)

Stellar i-band magnitude limit (mag) Galaxy i-band magnitude limit (mag) S/N
26 ~25/25.5 1.9
25.5 ~24.5/25 3.1
25 ~24/24.5 4.9
24.5 ~23.5/24 7.7
24 ~23/23.5 12.1
23.5 ~22.5/23 19.1
23 ~22/22.5 30.0

Table 1

Case of Total exposure time fixed at 450 s (i.e. 5 x pointings/90 s exposures)

Stellar i-band magnitude limit (mag) Galaxy i-band magnitude limit (mag) S/N
26 ~25/25.5 1.8
25.5 ~24.5/25 2.8
25 ~24/24.5 4.4
24.5 ~23.5/24 7.0
24 ~23/23.5 11.1
23.5 ~22.5/23 17.4
23 ~22/22.5 27.4

Table 2

I also show some plots (Figures 21, 22 and 23) summarizing the properties of the molygons identified in the Data Selection Section (MAGERR_APER4<0.11 case), which can be inspected having the results of Tables 1 and 2 in mind.


Figure 21


Figure 22


Figure 23

Next steps (to-do list)

  • Identify 3-4 different regions in the used footprint constituted by molygons with depth deeper than a minimum depth value and totalling, for each region, a reasonable area (at least ~100 sq. deg)
  • For each region, select galaxies out to the identified minimum depth value, so to homogenise depth over the identified region
  • Study Luminosity and Stellar Mass Functions (LF & MF) for the samples identified in the 3-4 identified regions
  • Study completeness as soon as this becomes possible and implement this into the study of LF and MF
  • Rescale MAG_DETMODEL values to i-band MAG_AUTO
  • Repeat all the analysis (including depth determination)