SITCOMTN-128

Unrecognized Blends in ComCam ECDFS#

Abstract

Unrecognized blends are a class of blended objects that are mistakenly identified as a single object. These objects can cause a variety of issues for science and simple validation. We can identify such objects by using higher resolution imaging from a space based telescope that will not be affected by ground based seeing and then label detected objects as isolated, recognized blends, or unrecognized blends. We find that for \(i > 23\), 15% to 20% of objects are unrecognized blends.

Data#

The Extended Chandra Deep Field-South (ECDFS), or also known as GOODS-South, is an extension to the original Chandra Deep Field-South which was originally done in X-Ray but has since been observed across many bands. The Commissioning Camera (ComCam) was able to observe this patch of sky with over 1000 visits in total, 250 being in the \(i\)-band alone, similar to 10-year depth. This data was then processed several times through the Rubin pipelines enabling rapid improvement to the entire system. Unrecognized blends allows us to understand some of the inherent failure modes of object detection. We use the /repo/dp1 repo and LSSTComCam/runs/DRP/DP1/v29_0_0/DM-50260 collection for ComCam data along with HST CANDELS data.

The DP1 catalog includes a deblending algorithm which means with accurate detection it is able to parse isolated and recognized blends. Deblending produces children objects from a parent object, both of which are in the catalog and needs to be pruned in order to remove duplicates. We apply the general detect_isPrimary flag which removes the parent objects (if child object exist) from the catalog along with removing any sky objects and that the object is from the inner part of both a tract and a patch. We will use the terms “extended object” (defined by refExtendedness == 1) and “observed galaxy” interchangibly. We place two cuts on the HST catalog, that the F814 magnitude be greater than some tunable value which we call the space magnitude (\(m_s\)) and that FLAG == 0 which removes only 318 objects. Details on the HST FLAG parameter can be found here.

The overlap between the two catalogs can be seen in Fig. 1 and the magnitude distribution (\(i\) for ComCam and F814 for HST) in Fig. 2.

_images/hst_comcam_overlap.png

Fig. 1 Area of overlap between the two surveys.#

_images/hst_comcam_magdist.png

Fig. 2 Log scale histogram of i-magnitude distribution for ComCam and F814-magnitude for HST. The dashed lines are the completeness limits of 25.4 and 26.5 respectively.#

Matching#

Ground and space catalogs in hand, we can start to label objects in the ground catalog as isolated objects (pure), recognized blends, or unrecognized blends by matching between the two catalogs. The general idea will be to generate a list of candidate unrecognized blends and then prune that list for the problematic unrecognized blends. This includes removing pure and recognized blends, along with removing any unrecognized blends that are unlikely to be contaminated (a 23-mag blended with a 27 mag).

Seemingly the simplest way to match between the two catalogs would be to use pure spatial information, RA and DEC. Querying the ground and space catalogs within some search_radius (which we choose to be the same for both catalogs) and then comparing the counts which can be done quickly using a k-d tree datastructure like the one implemented in scipy as scipy.spatial.kdtree. This can work well for pure objects but can lead to inconsistent results when varying the search_radius parameter. The purely spatial matching will also be inconsistent in labelling recognized blends properly. However, it is a common matcher so the results are included below but elect to pursue a more involed ellipse matcher.

The ellipse matcher uses the position (RA, DEC) and shape parameters (A, B, \(\Theta\)) to model objects in both catalogs as ellipses and then require that there be overlap between the ground ellipse and space ellipse. If there are multiple space ellipses overlapping with the same ground ellipse, that object is an unrecognized blend. For DP1, the shape parameters come from shape_xx, shape_xy, and shape_yy that can be converted to A, B, and \(\Theta\) while the HST catalog includes these values as measured from Source Extractor. Note that a pixel-to-arcsecond factor must be used to make sure that the two catalogs have meaningfully consistent units when we make comparisons. The center of each object, measured by RA and DEC, with the above parameters, A, B, and \(\Theta\), can then be turned to the form of

\[Ax^2 + By^2 + Cxy + Dx + Ey + F = 0\]

which can be used in an analytic expression to determine if there is overlap with another ellipse. On average, the product \(\sqrt{A \times B} \approx\) the half-light radius so we scale both parameters by a candidate_boost_factor which we will set to 2 unless otherwise specified.

For each ground object, we query for objects within 5’’ of the original ground object in both the ground and space catalog and determine if there is any overlap in either catalog. We query the ground catalog to account for recognized blends. If there are more space objects (\(\hat{N_s}\)) than ground objects (\(\hat{N_g}\)), the object is an unrecognized blend. If there are equal amounts then the object is either pure (\(\hat{N_s} = \hat{N_g} = 1\))) or recognized blend (\(\hat{N_s} = \hat{N_g} > 1\)). In the case of missing space data or spurious detections (\(\hat{N_g} > \hat{N_s}\)), the object is ignored for subsequent analysis.

Once we have a set of candidate blends, we can apply magnitude cuts on these to isolate to the problematic unrecognized blends. For each candidate, we require that the set of truth objects pass 2 cuts:

  1. The truth objects should not be too dim in band X \(m_X < m_s\)

  2. The difference between a truth object and the brightest in the set in band X should be small \(\Delta_X < m_\Delta\)

The first cut can be understood as requiring completeness in the space catalog with the second restricting our search to blends that are likely to have an impact on measured properties such as flux and shape. For HST, we will focus on the F814 band. Once applying the cuts on the truth catalog we recount the number of objects in the sets and promote any surviving candidate unrecognized blends to candidate blends. In summary we have the following process:

  • For each ground detection

    1. Querying a radius \(r\) around the ground detection RA and DEC in the ground catalog gives \(\hat{N_g}\) ground objects.

    2. Querying a radius \(r\) around the ground detection RA and DEC in the space catalog gives \(\hat{N_s}\) space objects.

    3. Each of the \(\hat{N_g}\) objects are converted into ellipses and check for overlap with the ground detection leaving \(N_g\) objects.

    4. Each of the \(\hat{N_s}\) objects are converted into ellipses and check for overlap with the ground detection leaving \(N_s\) objects.

    5. If \(N_s > N_g\) we have a candidate unrecognized blend.

    6. If \(N_s \leq N_g\) we have a recognized blend or a spurious detection.

  • Promoting a candidate unrecognized blend requires the space objects to pass 2 cuts:

    • \(m_{F814} < m_s\).

    • \(\Delta_{F814} < m_\Delta\).

In total, we use two matching algorithms, ellipse and spatial to generate a list of candidate blends and then refine using the same magnitude requirements..

Unrecognized Blends#

Using the matching schemes detailed above we can label isolated objects (pure), recognized blends and unrecognized blends in the ground catalog. Any other object is left out of the catalog. Unless otherwise specified, we set candidate_boost_factor = 2, \(m_s = 26.5\), and \(m_\Delta = 2\). Due to setting \(m_\Delta = 2\), even though the ComCam \(i\)-mag distribution peaks at 25, we are only able to confidently label blends up to \(m_g = 24.5\). When relevant, the simpler KDTree method will also be presented showing results using search_radius = candidate_boost_factor.

Magnitude Dependence#

We expect that blending will increase at the higher magnitudes as dimmer objects are harder to uniformly detect and there are simply more galaxies. The fraction of unrecognized blends as a function of the observed i-mag is shown with a comparison between the two methods included. Restricting to only extended objects – observed galaxies – produces almost no change in the distribution of unrecognized blends.

_images/unrec_blend_imag.png

Fig. 3 Fraction of unrecognized blends as a function of observed i-mag. Ellipse matching results are shown in blue and pure spatial results using blend entropy in orange. The two show a similar bump at the faint end while there is not strict agreement.#

In comparison to the Roman-Rubin simulations by Troxel et al., we see find similar levels of blending when using purely spatial matching but not with the ellipse matching.

Shape Parameters#

Accurate shape measurements is necessary for weak lensing studies and it is expected that unrecognized blends will impact shear. The inverse question, if certain shapes will impact unrecognized blends is not as well studied. It is possible that there would be a bias due to the orientation of the pixel grid which we investigate below.

We look at the second moment, \(Q_{ij}\), of extended objects. We combine the second moments via

\[e_1 = \frac{Q_{xx} - Q_{yy}}{Q_{xx} + Q_{yy}} \;\;\; e_2 = \frac{2Q_{xy}}{Q_{xx} + Q_{yy}}\]
_images/unrec_blend_pol.png

Fig. 4 Fraction of unrecognized blend as a function of ellipse polarization on observed galaxies.#

Given that there is little to no difference among the shape parameters, this gives good confidence that the pixel grid is not impacting shape measurements and unrecognized blends in strange ways. The wing structure is not necessarily cause for concern but it is interesting that objects with larger polarization is correlated with to be unrecognized blends.

Local Density#

Finally, we know clusters and other dense fields (like the deep fields) are expected to be extremely blended which motivates looking into how local density affects unrecognized blend fraction.

To estimate the local density, \(\sum(r_i)\), we use Equation 7 from Darvish et al.

\[\sum(r_i) = \frac{\sum_{j=1}^k j}{\pi \sum_{j=1}^k d_{ij}^2}\]

Where \(d_{ij}\) is the distance between object \(i\) and \(j\) and \(k\) is the number of neighbors which we set to 5. We look at both the ground and space based catalog and calculate two independent densities.

The relationship of unrecognized blends and local density are shown below

_images/unrec_blend_density.png

Fig. 5 Fraction of unrecognized blend as a function of ComCam object density (blue) and HST object density (orange).#

As expected, the fraction of unrecognized blends monotonically increases with HST density; however, rather unexpectedly, we see that the blending rate decreases with the ground based ComCam density.

Note

What the heck is happening with the comcam density?! Something to do with the deblender doing well?

Conclusion#

We have outlined a matching scheme that allows for robustly classifying objects as isolated, recognized blends and unrecognized blends. Using the ellipse matching method, we investigate the occurance of unrecognized blends in the ComCam ECDFS data and how it varies with severalproperties like i-mag and local density. Comparing to simulations like the Roman-Rubin simulation, we find similar rates of unrecognized blends versus i-magnitude when using purely spatial matching but not ellipse matching. In total, unrecognized blends in ComCam is at the expected levels and not suffering from pipeline issues.