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Metodi statistici per lo studio delle direzioni d’arrivo di muoni in MACRO

Metodi statistici per lo studio delle direzioni d’arrivo di muoni in MACRO. Monica Brigida Università di Bari & INFN Via Amendola 173 – BARI. Introduzione. Ombra della Luna: binned likelihood. Metodi per la ricerca di segnale da sorgenti continue (SKY MAP).

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Metodi statistici per lo studio delle direzioni d’arrivo di muoni in MACRO

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  1. Metodi statistici per lo studio delle direzioni d’arrivo di muoni in MACRO Monica Brigida Università di Bari & INFN Via Amendola 173 – BARI

  2. Introduzione • Ombra della Luna: binned likelihood. • Metodi per la ricerca di segnale da sorgenti continue (SKY MAP). • Metodi per la ricerca di segnale da sorgenti di natura sporadica. Perugia 18-19 Marzo 2002

  3. Moon shadowing effect • Moon (and Sun) produce a dip in the Cosmic Ray flux • This dip can be found if detector has a good angular capability (the source diameter is 0.5°) Perugia 18-19 Marzo 2002

  4. Moon shadowing effect THE EFFECT WAS PROPOSED BY CLARK(Phys. Rev. D 1957) THE SIGNAL PRODUCED IS VERY SMALL AND IS AN EVENT DEFICIT CAN BE DETECTED ONLY BY DETECTORS WITH AN ANGULAR RESOLUTIONLESS THAN 1° SINCE WE EXPECT A SMALL EFFECT RESPECT TO THE BACKGROUND WE HAVE CAREFUL ANALYZED EVENTS TO EXTRACT THE SIGNAL Perugia 18-19 Marzo 2002

  5. RAW MAP OBSERVED Perugia 18-19 Marzo 2002

  6. HOW TO EXTRACT SOURCE SIGNAL? • TO EXTRACT SOURCE SIGNAL TAKING INTO ACCOUNT DETECTOR RESPONSE FUNCTION THERE ARE SEVERAL METHODS: THIS ONE TAKES ORIGIN FROM COS-B ANALYSIS(Pollock A.M.T. et al., Astron. Astrophys. 94, 116 (1981)) THE MOON SHADOWING EFFECT ANALYSIS USED IS A MODIFIED VERSION OF THE COS-B METHOD Perugia 18-19 Marzo 2002

  7. A PRIORI KNOWLEDGE OF THE DETECTOR: POINT SPREAD FUNCTION (PSF) • KNOWLEDGE ORA MODEL FOR THE BACKGROUND • FILLING OF A GRID CENTERED ON THE SOURCE (2-D HISTOGRAM) CONTAINING EVENTARRIVAL DIRECTIONS • FILLING OF A SIMILAR GRID OF SIMULATED EVENTS FORBACKGROUND • IN EVERY BIN OF THEBACKGROUND GRID A TRIAL SOURCE IS ADDED,AT THE BIN CENTER, WHOSE SIGNAL IS SPREAD ACCORDING TO THE PSF ON ALL THE OTHER BINS OF THE GRID PRODUCING A MAP • A COMPARISON OF THIS NEW MAP WITH THE REAL ONE PRODUCED ALIKELIHOOD ESTIMATION FOR THE SOURCE IN THIS BIN • THEN REPEAT FOR ALL OTHER BINS Perugia 18-19 Marzo 2002

  8. THE FOLLOWING EXAMPLE IS WHAT WE HAVE USED FOR THE LIKELIHOOD CALCULATION (POISSONIAN PROCESSES) i, j actual bin coordinate, is, js trail source position Nk observed events Nbck background events NOTE THAT THE BACKGROUND COULD BE FLAT OR BE THE RESULT OF A BACKGROUND MODEL CALCULATION LIKE THE DIFFUSE COMPONENT FOR GAMMA RAYS Perugia 18-19 Marzo 2002

  9. FOR EACH BIN WE MAXIMIZE THE LIKELIHOOD FUNCTION (VARYING THE INTENSITY OF THE TRAIL SOURCE) THIS IS EQUIVALENT TO COMPARE THE HYPOTHESIS WITH A NULL HYPOTHESIS (NO SIGNAL) THIS FUNCTION SHOULD FOLLOW A DISTRIBUTION WHEN NO SOURCE IS PRESENT Other details onM. Ambrosio et al., Phys. Rev. D 59, 012003 (1999) Perugia 18-19 Marzo 2002

  10. RESULTS TEST OF IPOTHESIS: WE USE FAKE MOONS (DISPLACED IN R.A.) TO TEST THE METHOD AND STUDYING THE λ DISTRIBUTION FOR ALL BINS OF ALL FAKE MOON GRIDS Perugia 18-19 Marzo 2002

  11. 6 s effect !! MOON Χ2 MAP Perugia 18-19 Marzo 2002

  12. Moon intensity map Perugia 18-19 Marzo 2002

  13. Conclusions Easy and fast method It is possible to include specific models for background (i.e. A diffuse background) Tuning:BIN SIZE CHOICE EVOLUTION:unbinned likelihood methods: more powerful but CPU-consuming Perugia 18-19 Marzo 2002

  14. Analisi dei dati e del fondo • 49 x 106 eventi selezionati dopo i tagli. • 73000 h di tempo vivo di osservazione. • Simulazione del fondo: ipotesi di distribuzione isotropa del flusso di raggi cosmici. • Eventi di fondo generati accoppiando le direzioni di arrivo di ciascun muone con 25 tempi di arrivo estratti casualmente dal medesimo run. Perugia 18-19 Marzo 2002

  15. Ricerca di sorgenti stazionarie Perugia 18-19 Marzo 2002

  16. Ricerca di eccessi da sorgenti localizzate su scala giornaliera • Integrazione degli eccessi del segnale di muoni rispetto al fondo. • Calcolo della probabilità poissoniana: Perugia 18-19 Marzo 2002

  17. Emissioni sporadiche: MKN421 e MKN501 (secondo metodo) Perugia 18-19 Marzo 2002

  18. Quale probabilità ? 19% di compatibilità con fluttuazioni del fondo Numero medio di eventi attesi in D giorni Perugia 18-19 Marzo 2002

  19. Applicazione a tutto il cielo Pendenza: 1 Perugia 18-19 Marzo 2002

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