1 Giuseppe Romeo Voronoi based Source Detection

2 Voronoi cell The Voronoi tessellation is constructed as follows: for each data point  i (also called node), let D i be the area consisting of all locations in the space which are closer to  i than to any other point of N. This definition is applicable to Voronoi tessellations in any metric space. The area D i is the Voronoi cell.

3 Spherical Tessellation Spherical Voronoi tessellation is achieved by first performing a Delaunay triangulation, which is so defined: for a set P of points in the R 2, the triangulation DT(P) of P is such that no point in P is inside the circumcircle of any triangle in DT(P)

4 Spherical Tessellation Tessellation of random point on a sphere

5 Computational load For n data points,  Non optimized code, time spent for tessellation goes as O(n 2 log n)  Using optimized code, with “divide and conquer” algorithm, the time spent goes as O(n log n)!

6 Source Finding, assumptions  Each Voronoi cell contains only one event (photon)  The cell area distribution follows a Poisson statistics: Where with and

7 Area Distribution, No Sources randomly generated data points, no sources included

8 DC2 data  The whole sky was subdivided in 9 regions  galactic coordinates where used instead of RA & DEC. This allowed the region with the galactic plane not to drive the whole sky for the threshold area identification used for the Voronoi cut.

9 Area Distribution, with Sources Data from DC2, with 0 =< L =< 120, and 20 =< B =< 90 ( data points):

10 Voronoi Source Detection, the method 1. Remove any photon whose Voronoi cell area is larger than +3*  (This usually removes any photon that is at the boundary of the region under consideration) 2. Find the “Threshold” cell area  t, and remove any photon whose cell area is larger than  t. 3. From  t find a binning size to bin data in L. 4. Find local maxima in L, and B which give the location of a potential source and their errors.

11 DC2 data

12 DC2 data

13 DC2 data

14 DC2 data

15 Results  The Voronoi based sources detection finds 2550 potential sources. Other methods must be used to remove the large number of false positive (more to come)  Comparing with DC2 source catalog, 341 sources were identified (~91%)  ~10 hours were needed to process all data/all sky

16 PSF study Goal: Goal: check source detection method by comparing the predicted PSF with the distribution of counts. Description of the method Description of the method: _For each detected source calculate the distribution of counts (background subtracted). _Compare the distribution of counts with the predicted PSF in the position of the source. _Calculate cumulative predicted PSF and the cumulative distribution of counts.

17 PSF study (cont.) Predicted PSF: Obtain the predicted PSF using gtpsf. This generates a fits file with the differential PSF for different energy bins. Generate “one” PSF weighted by the number of counts in each energy bin. Calculate the cumulative distribution.

18 PSF study (cont.) Distribution of counts: _ Bin the data (radial distribution). _ Calculate the differential distribution of counts. _ Calculate the cumulative distribution of counts.

19 PSF-study (examples) RA =  DEC= 

20 PSF-study (examples-cont.) RA =  DEC= 

21 PSF-study (examples-cont.) RA =  DEC= 