1. Computation of centroid locations in photon and electron maps Marco Prato Pure and Applied Mathematics Department University of Modena and Reggio Emilia, Italy CNR – INFM LAMIA, Genova, Italy IX RHESSI Workshop Genova, September 2 nd 2009 www.dima.unige.it/~piana/mida/group.html

2. Flare location Measures of a source location: - location of peak intensity - peak of a best-fit Gaussian form - first normalized moment (centroid) Centroid of the X-ray emission Centroid of the electron distribution in the source

3. Centroid vs peak Centroid advantages: - no need of an instrument with high spatial resolution (as required to find the location of peak intensity) - no imposition of simmetry constraints (as assumed by best- fit Gaussian forms) Centroid restrictions: - ‘physically’ (but not ‘mathematically’) meaningful only for simple extended sources

4. Centroid from visibilities Question: is it possible to infer the (X-ray and/or electron) centroid straightly from the (corresponding) visibilities? Answer: in principle, yes Way 1: apply the hsi_vis_fwdfit routine with a selected shape Disadvantages: - simmetry imposed - the use of different detectors (with different resolutions) leads to a weighted average of different centroids locations What are electron visibilities? (see M Prato, Thu 3, Session 2, WG 1)

5. Centroid from visibilities Question: is it possible to infer the (X-ray and/or electron) centroid straightly from the (corresponding) visibilities? Answer: in principle, yes Way 2: use some math X-ray visibilities Derivative Centroid Disadvantages: - inferring is a complicated and instable problem

6. Centroid from images What we can do is to build a (X-ray or electron) image from the (corresponding) visibilities and calculate the centroid by direct integration Visibilities Image Centroid

7. Feb 20 2002, 11:06:00-11:06:40 UT 14-18 keV22-26 keV30-34 keV38-42 keV X-rays Images produced with uv_smooth (see A M Massone, Thu 3, Session 1, WG 1) 46-50 keV54-58 keV62-66 keV70-74 keV Electrons Both footpoint sources show considerable variation of centroid position with energy (the electron centroids have been displaced 3 arcsec to the right)

8. Conclusions Centroid calculation as standard-bearer for flaring location Locations of the observable radiation from flares may not be a good indicator of the locations where the acceleration of the particles takes place Centroid calculation from uv_smooth + integration Future work: infer the centroid coordinates directly from the visibilities