Using temporal distributions of transient events to characterize cosmological source populations AIGO Conference 22-24 February 2010 Eric Howell University of Western Australia
Plan Brief overview cosmological transients Explain how a population of transient events evolves with observation time Show how the temporal distribution can be modeled using a brightness- observation time relation (a simple power law invariant to the luminosity distribution) Use Swift GRB data to demonstrate how the relation can be used to constrain rate densities of transient source populations Apply the relation to BATSE GRB data as a probe of selection bias
The temporal distribution of Cosmological transients Transient events Cataclysmic astrophysical events with peak emission durations much shorter than the observation time. Examples Supernovae (GW and EM) GW - milliseconds GRBs (gamma ray bursts) (seconds-minutes) CCOs - Coalescing compact objects NS (neutron stars) and/or BH (black hole) systems (GW and EM)- (secs-mins) Radio transients (e.g. Lorimer Pulse) (ms - wks)
Highly energetic beamed emissions observable out to cosmological distances Gamma Ray Bursts Long GRBs Durations 2 secs Supernovae Median z ~ 2.5 (sub-luminous GRBs) Short GRBs Durations < 2 secs NS/NS BH/NS Median z ~ 0.25 Instrumental Satellites BATSE launched 1991 recorded >2000 GRBs - 9 years operation Number-Intensity distribution brightness distribution not -3/2 power law for Euclidean distribution Number Swift 2004 recorded > 470 GRBs >140 redshifts - GRB 090423 z ~ 8.2 (12.8 Gly) Peak Flux
Temporal distributions of cosmological transients
A population of cosmological transients obeys an observation time dependence The temporal evolution of brightness in Swift Peak Flux data Waiting time between brightest events increases with T obs RARE EVENTS FREQUENT EVENTS Swift long GRB ( > 2 sec) Peak Flux time series to August 09 This temporal dependence can be exploited to constrain global properties of a transient population
FREQUENT EVENTS RARE EVENTS Temporal Evolution of an Astrophysical GW Background Spectrum CC-SN 1kHZ damped sinusoid - 10ms (~T1 DFM) Rapid bandwidth growth - dependent on rate and space distribution of events Stationary Spectra 20 mins
The Probability Event Horizon (PEH) Using Poisson statistics and knowledge of the event rate we can define a PEH * The min z (T obs ) for at least 1 event to occur at a 95% confidence level High z PEH Curve Low z PEH data Single free parameter - local rate density r0 ~ yr -1 Mpc-3 * PEH - see D.M.Coward & R.R.Burman, Mon. Not. R. Astron. Soc.,, 361, 362, (2005)
Application of the PEH filter to simulated BBH triggers (Advanced LIGO) A PEH filter 1) Only small amount of data used 2) What if the first event is bright Howell et al.(2007), Mon. Not. R. Astron. Soc., 377, 719
How can you enhance the PEH filter output? Image provided by the Max Planck Institute for Gravitational Physics/Zuse Institute Berlin
For time scales short in comparison with the age of the Universe we can invoke: An enhanced PEH A) Time reversal invariance The distribution of independent events is invariant wrt temporal direction B) The temporal cosmological principle There is nothing special about the time we switch on our detector We can therefore treat the data as a closed loop Howell et al.(2007), Astrophys.. J. Letters, 666, L65
FMTR From Max + Time reversal 1. Brightness Flux time Time series 2. Apply PEH filter from maximum in 2 directions 3. Brightness Flux PEH filter output time
What about non standard candle sources? Image provided by the Max Planck Institute for Gravitational Physics/Zuse Institute Berlin
Brightness distribution (Euclidean) - convolution of radial distribution and luminosity function. Integrating over radial distance r gives the log N log P relation: Log P Log T relation N(>P) α r 0 T obs P -3/2 Φ(L)L -3/2 dl Rate Peak Luminosity dens flux function 1) Use PEH condition: N(>P) α R(r) T obs = ln(1 - ε) =r 0 (4/3)π r 3 ε - probability Brightness Observation time log P log T relation: 2) P(T obs )α [r0 Φ(L)L 3/2 dl] 2/3 T obs 2/3 Solve numerically for a cosmological population Howell et al.(2007), Astrophys.. J. Letters, 666, L65
Non standard candle sources Application To Swift GRB data (5-95)% CI The PEH Filter has extracted the geometrical signature of the GRB population Howell et al.(2007), Astrophys.. J. Letters, 666, L65
Log P log T Predictive tool 2007 Howell et al.(2007), ApJ Letters, 666, L65
Estimating GRB rate density using Log P Log T Least squares fit using Log P - log T as a non-linear regression model Source rate evolution and luminosity function are assumed 0.08 r0~0.10 ± 0.06 Guetta, 2007
Application to BATSE GRB data (50-300) kev BATSE triggered on photon counts within different energy ranges e.g. (50-300)keV, (>100)keV, (20-100)keV (50-300)keV Peak Flux (> 100)keV Intrinsic Or Bias? Peak Flux
Peak energy distribution BATSE distribution of peak energies Maximum around 250 kev Most around (100 400)keV Low energy cutoff explained by X-ray rich events seen by BEPPO-SAX/HETE High energy cutoff suggestions BATSE was less sensitive to harder bursts with peak energies > 500 kev a) a harder burst with same luminosity as a softer burst emits fewer photons b) as burst become harder - more photons outside (50-300) kev range
The log P-log T relation can provide estimates of the rate densities of transient cosmological events. Summary The time dependence allows the relation to be used as a predictive tool. Using only the brightest events can result in loss of resolution. However, it can be useful for incomplete/contaminated data sets The log P-log T method can potentially be used as a probe of selection bias.