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A Physical difference between Short and Long GRBs L.G. Balázs, Z. Bagoly, I. Horváth ,

A Physical difference between Short and Long GRBs L.G. Balázs, Z. Bagoly, I. Horváth , A. Mészáros, and P. Mészáros. Structure of this talk. Basic properties of GRBs Analysis of the durations Analysis of the fluences Correlation between fluence and duration Conclusions.

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A Physical difference between Short and Long GRBs L.G. Balázs, Z. Bagoly, I. Horváth ,

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  1. A Physical difference between Short and Long GRBs L.G. Balázs, Z. Bagoly, I. Horváth , A. Mészáros, and P. Mészáros GRB meeting, PSU 2004

  2. Structure of this talk Basic properties of GRBs Analysis of the durations Analysis of the fluences Correlation between fluence and duration Conclusions GRB meeting, PSU 2004

  3. Basic properties of GRBs Sample: Current BATSE Gamma ray Burst Catalog Measured quantities: • Fluences: F1 [25,50]keV, F2 [50,100]keV, F3 [100,300]keV, F4 [>300] keV, Ftot=F1+F2+F3+F4 • Durations: T90[5%;95%], T50[25%;75%] • Peak fluxes: on 64 ms, 256 ms, 1024 ms time resolution Principal Component Analysis (PCA) Two physically important quantities: • T90, T50, F1, F2, F3, F4 • P64, P256, P1024 F  Tm GRB meeting, PSU 2004

  4. 1. -0.6 - -0.4 5 1 0 2. -0.4 - -0.2 113 5 0 3. -0.2 - 0.0 385 44 1 4. 0.0 -0.2 434 104 4 5. 0.2 - 0.4 365 126 8 6. 0.4 - 0.6 254 79 3 7. 0.6 - 0.8 166 47 2 8. 0.8 - 1.0 95 34 0 9. 1.0 - 1.2 74 22 0 10. 1.2 - 1.4 39 6 0 11. 1.4 - 1.6 19 5 0 12. 1.6 - 1.8 15 2 0 13. 1.8 - 2.0 6 1 0 14. 2.0 < 2 0 0 Basic properties of GRBs Strip P64 Tot. No. T90< 2s T90< 64 ms GRB meeting, PSU 2004

  5. Analysis of the durations Distribution of logT90: Superposition of two Gaussians Consequence: distribution is intrinsic Proof: Cramer theorem logT90 = logt90+logf(z) If logT90 is Gaussian then logt90 and logf(z) are as well intrinsic GRB meeting, PSU 2004

  6. -.50 -.57 -.87 .55 .60 7 -.30 -.65 -1.01 .53 .57 43 -.10 -.40 -.77 .49 .51 103 .10 -.35 -.74 .35 .32 105 .30 -.33 -.75 .39 .41 75 .50 -.27 -.69 .35 .36 54 .70 -.29 -.72 .36 .34 25 .90 -.35 -.76 .39 .36 22 1.10 -.18 -.72 .44 .39 7 1.30 -.74 -1.21 .31 .43 5 >1.40 -.72 -.90 .00 .00 1 Analysis of the durations (short) log P256 log T90 log T50 logT90 logT50 N GRB meeting, PSU 2004

  7. -.50 1.24 .85 .48 .47 49 -.30 1.42 1.00 .47 .50 230 -.10 1.48 1.08 .49 .53 309 .10 1.46 1.02 .51 .57 272 .30 1.51 1.01 .52 .61 194 .50 1.43 .94 .51 .59 161 .70 1.45 .96 .48 .56 104 .90 1.42 .83 .54 .62 56 1.10 1.41 .83 .50 .49 44 1.30 1.44 .88 .50 .53 34 >1.40 1.21 .68 .41 .50 29 Analysis of the durations (long) log P256 log T90 log T50 logT90 logT50 N GRB meeting, PSU 2004

  8. Analysis of the fluences The observed total fluence can be written in the form: In case of short burst log Ftot is Gaussian Cramer theorem is applicable For long GRBs by direct measurements of z >50% of Ftot is intrinsic GRB meeting, PSU 2004

  9. Correlation between fluence and duration • Effect of the detection threshold • Intrinsic relationship between fluence and duration • ML estimation via EM algorithm • Possible sources of bias GRB meeting, PSU 2004

  10. Effect of the detection threshold According to the Law of full Probability The kernel represent intrinsic relationship G(p) is strongly influenced by the threshold GRB meeting, PSU 2004

  11. Intrinsic relationship between fluence and duration From PCA two important quantities: Duration and peak flux  is a noise term fixing p - power law relationship between Ftot and T90 GRB meeting, PSU 2004

  12. ML estimation via EM algorithm Fitting function: superposition of two 2D Gaussians GRB meeting, PSU 2004

  13. 4. .293 -.199 -6.58 .549 .502 .593 434 0.86 5. .418 -.275 -6.48 .575 .503 .591 365 0.80 6. .321 -.365 -6.24 .486 .497 .515 254 1.04 7. .332 -.188 -5.92 .510 .420 .342 166 0.58 8. .358 -.325 -5.91 .440 .347 .279 95 0.46 ML estimation via EM algorithm (short) Strip freq. axayx y  Nm Etot = t900.81 GRB meeting, PSU 2004

  14. 4. .707 1.56 -5.48 .400 .434 .586 434 1.15 5. .582 1.61 -5.23 .445 .463 .599 365 1.07 6. .679 1.41 -5.21 .538 .613 .753 254 1.19 7. .668 1.46 -4.89 .448 .459 .610 166 1.04 8. .642 1.39 -4.77 .541 .531 .656 95 .97 ML estimation via EM algorithm (long) Strip freq. axayx y  Nm Etot = t901.11 GRB meeting, PSU 2004

  15. ML estimation via EM algorithm 4. 5. 8. 6. 7. GRB meeting, PSU 2004

  16. Possible sources of bias • Effect of the threshold • True vs. observed fluence • Bias from the spectral response • Bias from the finite time resolution GRB meeting, PSU 2004

  17. Effect of the threshold Direct effect on the form of G(p): Three time scales (64 ms, 256ms. 1025 ms) No sharp cut. Indirect effect: on T90 and Ftot Influence on P(logT90, logFtot) mainly through G(p) GRB meeting, PSU 2004

  18. True vs. observed fluence Observed light curve: „iceberg” effect in duration and fluence Possible effect on the shape of P(Ftot,T90): Long GRBs: no gradual changes in the shape Short GRBs: gradual changes GRB meeting, PSU 2004

  19. Bias from the spectral response Short GRBs are harder - apparent positive correlation with duration assuming no intrinsic correlation The spectral bias is more serious at faint GRBs Short GRBs gradual decrease of slope Long GRBs no significant change in Strips 4.-8. GRB meeting, PSU 2004

  20. 1. 0 1 0 0 1 2. 3 0 1 1 5 3. 19 10 7 8 44 4. 57 15 14 18 104 5. 53 28 14 31 126 6. 17 16 17 29 79 7. 4 3 4 36 47 8. 2 4 4 24 34 9. 0 0 3 19 22 10. 1 0 1 4 6 11. 0 0 0 5 5 12. 0 0 0 2 2 13. 0 0 0 1 1 Bias from the spectral response (short) Strip S/N N 0 1 2 >3 GRB meeting, PSU 2004

  21. 1. 2 1 0 1 4 2. 71 19 7 11 108 3. 193 58 37 53 341 4. 135 65 42 88 330 5. 72 33 40 94 239 6. 33 23 16 103 175 7. 12 9 10 88 119 8. 1 2 7 51 61 9. 1 1 1 49 52 10. 0 0 0 33 33 11. 0 0 0 14 14 12. 0 0 0 13 13 13. 0 0 0 5 5 14. 0 0 0 2 2 Bias from the spectral response (long) Strip S/N N 0 1 2 >3 GRB meeting, PSU 2004

  22. Bias from the finite time resolution If T90 < 64 ms no correlation with Ftot Peak flux is computed from the same bin as Ftot As T90 increases – increasing no of 64 ms bins We compared the variances and covariances within and between bins Results of Multivariate Analysis of variance (MANOVA) : 1st bin differs at 99.5% sig. level GRB meeting, PSU 2004

  23. 1. -7.024 .504 .353 .191 .762 17 2. -6.628 .510 .381 .244 .633 33 3. -6.675 .512 .369 .237 .633 37 4. -6.486 .540 .409 .262 .579 36 5. -6.548 .442 .369 .246 .712 26 6. -6.580 .563 .348 .237 .611 16 7. -6.449 .382 .419 .227 .224 31 8. -6.331 .475 .427 .280 .686 20 9. -6.453 .451 .334 .238 .678 16 10. -6.429 .382 .368 .225 .562 16 Bias from the finite time resolution log Ftot log P64 Bin mean st.dev. mean st.dev. Corr. N GRB meeting, PSU 2004

  24. Conclusions • there is a power law relation betweenthe fluence and duration • this relation is significantly different for the two groups • values of exponents were obtained, 0.81 (short) and 1.11 (long) • difference is significant on the 4.7level. The result is completely model independent based on Cramer theorem and Law of full Probability GRB meeting, PSU 2004

  25. The End GRB meeting, PSU 2004

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