On The Nature of High Energy Correlations Daniel Kocevski Kavli Institute for Particle Astrophysics and Cosmology SLAC - Stanford University
High Energy Correlations Epk vs. Eiso Amati et al. 2002 νf ν peak (Epk) is related to the total isotropic equivalent radiated energy (Eiso) Seen in data from several spacecraft, including Fermi Has been used to determine z and hence Eiso by proxy Interesting GRB Physics? GRB Cosmology? Epk,src ~ Eiso 0.5 Amati 2009
Contentious History Nakar & Piran 2005 Band & Preece 2005 Amati 2007 Cabrera et al. 2007 Butler, Kocevski, Bloom 2007 Ghirlanda et al. 2008 Nava et al. 2008 Butler, Kocevski, Bloom 2009
Malmquist Type Correlations 1056 1055 30σ 20σ 10σ 5σ Eiso (erg cmï ) 1054 1053 1052 1051 1050 1027 Daniel Kocevski - NASA Goddard, Oct 29th 2010 1028 Luminosity Distance 1029
Missing Bursts?? Why don t we see high fluence bursts with low Epk?
Simulate The Entire Process Assume source frame properties ϕ(l), Δtsrc, Epk distributions Populate GRBs at various redshifts Assume ρ(z) ~ SFR Simulate a detector response Sensitivity, energy window Calculate observed quantities Epk, Eiso, Δtobs
Spectral Evolution 1000.00 ergs cm-2 s-1 High z GRBs are fainter, redshifted, and evolve slower 10000.00 i F i (photons kev cm s ) How does the time integrated spectrum of GRBs depend on redshift? 100.00 10.00 1.00 0.10 How does this effect T90 and Eiso? 0.01 1 10 100 Energy (kev) 1000 10000 10 100 Energy (kev) 1000 10000 100.000 z=4 10.000 ergs cm s i F i (photons kev-2 cm 2-1 s 1) What is the net effect on the time integrated Epk and estimated Eiso? z=1 1.000 0.100 0.010 0.001 1
Step 1: Simulate the GRB Assume a spectral shape Use Batse α, β, Epk distributions Assume some spectral evolution νfν Consistent with relativistic curvature Epk ~ t -1 ; Flux ~ Epk 2 Assume a luminosity function Flux Broken power law (Butler et al. 2010) Assume source frame T90 distribution Energy Time
Step 2: Distribute the GRBs Assign a comoving rate density Assume ρ(z) ~ Modified SFR Assume CDM Cosmology This gives a GRB rate Peaks at z ~ 2 Matches the observed distribution Rare GRBs are most probable at z ~ 2
Step 3: Simulate the detector Run simulated time-integrated spectrum through a detector response function BATSE Data Response Matrix Gives us the sensitivity vs. energy Produce counts light curves Assume background noise level Determine if spacecraft would have triggered on GRB If so, find duration using Bayesian Block algorithm
1.2 10 4 1.0 10 4 8.0 10 3 z = 1 T90 = 35 Eiso = 4.21e+53 3500 3000 z = 2 T90 = 32 Eiso = 4.10e+53 Counts 6.0 10 3 Counts 2500 4.0 10 3 2000 2.0 10 3 0 0 100 200 300 400 Time (sec) 1500 0 100 200 300 400 Time (sec) 2600 2300 2400 z = 3 T90 = 31 Eiso = 3.88e+53 2200 z = 4 T90 = 24 Eiso = 3.37e+53 2100 Counts 2200 Counts 2000 2000 1900 1800 0 100 200 300 400 Time (sec) 1800 0 100 200 300 400 Time (sec)
T90 vs. Redshift 10000 Swift 1000 Simulated 1000 100 Duration (sec) 100 10 Duration (sec) 10 158 LGRBs 1 0 2 4 6 Redshift 344 LGRBs 1 0 2 4 6 Redshift No evidence for time dilation in GRB durations vs. redshift Similar to problems of measuring galaxy size vs distance
1060 1056 1059 1054 Eiso (ergs) Luminosity (photons cmï2) Simulation Demographics 1058 1052 1057 1050 1056 1 1048 0.01 1+z 0.10 1.00 10.00 z Assuming ϕ(l), Δtsrc, and a trigger criteria (5σ) we can reproduce the observed luminosity and Eiso distribution as a function of redshift Dim bursts are only seen at low redshift, bright (rare) bursts occur at high redshift
Results We can plot Epk-Eiso for all simulated GRBs (regardless of whether they triggered the detector)
Results: Luminosity Intrinsic luminosity increases from left to right
Results: Burst Duration Higher Epk and Eiso GRBs appear longer
Results: Trigger Significance Amati 2002 Very distinct pattern of trigger significance that matches the shape of the Epk-Eiso correlation
Results: Redshift Distribution High Eiso GRBs only occur at high redshift Low Epk, High Eiso GRBs are redshifted out of the bandpass
Simulated Epk-Eiso Relation Low Observed Flux Swift Pre-Swift Low Observed Epk Detector thresholds convolved with probability of seeing bright (rare) GRBs can reproduce the observed relation
Conclusions The Epk-Eiso correlation appears to be due to a combination of complex threshold effects and a population cutoff Very simple FRED model demonstrates the effects How do the Epk-Eiso correlations seen within individual pulses fit into this picture? How do X-ray flares fit into this picture? Nice example (and warning): It s not enough to understand just your detector thresholds Must also consider how objects are distributed in space
Results We can plot Epk-Eiso for all simulated GRBs (regardless of whether they triggered the detector) Daniel Kocevski - NASA Goddard, Oct 29th 2010
Results: Luminosity Intrinsic luminosity increases from left to right Daniel Kocevski - NASA Goddard, Oct 29th 2010
Results: Burst Duration Higher Epk and Eiso GRBs appear longer Daniel Kocevski - NASA Goddard, Oct 29th 2010
Results: Trigger Significance Very distinct pattern of trigger significance that matches the shape of the Epk-Eiso correlation Daniel Kocevski - NASA Goddard, Oct 29th 2010
Results: Redshift Distribution High Eiso GRBs only occur at high redshift Low Epk, High Eiso GRBs are redshifted out of the bandpass Daniel Kocevski - NASA Goddard, Oct 29th 2010
Simulated Epk-Eiso Relation Low Observed Flux Low Observed Epk Detector thresholds convolved with probability of seeing bright (rare) GRBs can reproduce the observed relation Daniel Kocevski - NASA Goddard, Oct 29th 2010
Conclusions The Epk-Eiso correlation appears to be due to a combination of complex threshold effects and a population cutoff Very simple FRED model demonstrates the effects How do the Epk-Eiso correlations seen within individual pulses fit into this picture? How do X-ray flares fit into this picture? Nice example (and warning): It s not enough to understand just your detector thresholds Must also consider how objects are distributed in space Daniel Kocevski - NASA Goddard, Oct 29th 2010