1. Jeroen Stil Department of Physics & Astronomy University of Calgary Stacking of Radio Surveys

2. Stacking: piling up different sources Statistical properties of radio emission of a sample of faint sources below the detection limit of a survey. Special case: Polarization of most sources not directly detectable. Stil et al. (2014) showed sample median polarization can be recovered to the detection limit in Stokes I. Root-N improvement of noise up to N=10 5 demonstrated in NVSS. Requires a catalog of target positions from another survey. Special case: Stacking polarized intensity uses targets from the same radio survey. Stack continuum or radio spectral lines Information from stacking: Astrophysical modeling of trends/correlations revealed by stacking related subsamples. Example: Infrared-radio correlation for galaxies as a function of redshift.

3. Stacking Galaxies as a Function of Inclination 1.0 < R 25 < 1.4 1.4 < R 25 < 1.8 1.8 < R 25 < 2.5 R 25 > 2.5 Axial Ratio R 25 Flux Density (mJy) 74 MHz 325 MHz 1400 MHz 17,000 targets 14 10 2 4 Inclination-dependent selection effect in optical input catalog

4. Stacking AGN Polarization in NVSS Preliminary Spectral Index: Steep Intermediate Flat Differentiate the sample by observable parameters to reveal correlations that astrophysical models must reproduce. Beware of unintended selection effects that may also correlate with signal strength. Cannot be done with present deep fields Fractional polarization as a function of 1.4 GHz flux density Stil et al. (2014)

5. Requirements for Stacking Image cubes including “empty sky” (compromise on frequency resolution). Uniform angular resolution and sensitivity Flexible and efficient access to complete image archive. Computing resources with access to data (small footprint but enduring). Large input catalogs and advanced sample selection. Alignment with sub-pixel accuracy for Nyquist-sampled images

6. Technical Challenges Aperture-integration of intensity before stacking mitigates position errors, resolved target sources and discretization of data Seeding of artificial sources to understand systematics in the data Stacking offset positions In-situ noise statistics and coordinates of peak intensity in postage stamp Sample statistics other than mean or median Discretization of data values by design (NVSS) or by nature (X-ray photon statistics) Tiling of survey images (overlap, gridding, sorting of images) Copyright messages and missing data in the images Access to metadata (survey images and target catalog) Clustering of target sources Solutions

7. Future of Stacking Radio Surveys Integrate Stacking in the Archive? Increase in resolution and bandwidth boost survey data volume (EVLA, WSRT, ASKAP, MeerKAT, Square Kilometre Array). Solutions to limit the cost of data storage can create significant hurdles. Archives are not designed to retrieve millions of target sources and access thousands of survey images simultaneously. Use distributed science computing platforms such as CyberS KA.

8. Conclusions Stacking radio surveys provides astrophysical information for large samples that is otherwise inaccessible. Broad-band surveys create new opportunities for stacking. Current radio surveys can be downloaded and analyzed locally (NVSS, FIRST, WENSS, ATLAS). Stacking future surveys faces challenges in data transport and storage, unless science computing capability is integrated with the archive.