Gamma-ray Large Area
Space Telescope
AGN light curves
simulation
G. Tosti,
Physics Dept. &INFN - Perugia
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
1
Blazar LC simulation – Introduction
Goal of this work was to provide a “realistic”(?) rappresentation
of the temporal and spectral variability of Blazars, to be included
in the DC2 sky simulation, in order to have a better
understanding of what may be the GLAST contribution to:
– Variability studies (single source, populations definition of
good Variability indexes, Source Classification based on
variability, etc.)
– Spectral analysis
– Emission models discrimination
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
2
BLAZARS
The standard Model
The Spectral Energy Distribution
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
3
Blazars LC simulation – MW observed “LC”
- AGN optical variability is often characterized by great outbursts spaced
out by long periods of lower emission. The distribution of flux values
is similar to a Poissonian.
- Radio variability presents frequent peaks and long period trends.
Flux values distribution is quasi-Gaussian.
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
4
Blazars LC simulation – MW observed “LC”
•The LC show flares with varying
amplitudes on a wide range of timescales
•Some high energy flares have no
counterparts at longer wavelengths,
•Possible interbands time-lags
Mkn 421 2002/2003
Blazejowski et al. (2005, astro-ph/0505325)
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
5
Blazars LC simulation – MW observed “LC”
3C 279
Wehrle et al. (1998)
3C 279
Hartman et al. (2001)
•the LC show flares with varying amplitudes on some range of timescales
•Possible interbands time-lags
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
6
Blazars LC – MW LCs Fourier Analysis
Fourier spectral analysis of LCs is an important tool because it allows the variance of a time
series to be separated into contributions associated with different time scales. It thus helps to
understand better the physical processes, which generate the variability recorded in a time
series.
Light curves of blazars appear to behave randomly at all the frequencies, from the radio to the
high energy rays. They are usually characterized by some kind of noise that produces a powerlaw PSD:
PSD( f )  f 
.......red noise
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
7
Blazars LC simulation – observed spectral evolution
There are indication of correlation between flux and spectral variations
X-ray
Optical
PKS 2155-204
Kataoka et al. (2000)
“Hysteresis loops” were observed.
Gino Tosti – INFN Perugia
GC 0109+224
Ciprini et al. (2003)
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
8
Blazars LC simulation – MW LC models
3C 279 – internal shock
Spada et al. (2002)
Blazar flares can be be related to
•internal shocks in the jet (e.g. Spada et al. 2001)
•ejection of relativistic plasma into the jet (e.g. Mastichiadis & Kirk 1997).
•magnetic reconnection events in a magnetically dominated jet (Lyutikov 2003)
•etc,.
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
9
Blazars LC simulation – Methods
How do we can reproduce the observed temporal-spectral
features?
•Time-dependant emission models (in progress...)
•Phenomenological models DC2 Simulation
•Temporal simulation
•Simple red noise model [AR(1)]
•Shot noise model
•Power Spectral Density (PSD) inversion
•Non linear models
•Spectral Simulation
•Hysteresis loops
•Other features...
A C++ Code was developed to perform the phenomenological simulation used in
the DC2 - Results from the different methods were discussed at the Blazar &
Other AGN LAT SG VRVS  Final Decision of the method for the DC2
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
10
Blazar LC simulation – Simple Red noise model
``Red noise'' is often used to refer to any linear stochastic process in which power
declines monotonically with increasing frequency. It can be represented by a AR(1)
process:
ut   (ut 1  u0 )  zt  u0
Where:
u0= mean
,=constants
zt=is a gaussian-distributed white-noise process
Arbitrary units on both the axes
3
2.5
=0.85
=0.2
u0=1
2
1.5
1
0.5
0
10
Gino Tosti – INFN Perugia
60
110
160
210
260
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
11
Blazars LC simulation – Shot noise model
The LC were obtained using the method described by Terrel & Olsen (1972).
The value of the flux in each time point is the superposition of a number of
pulses having a poissonian distribution. The input parameters are: pulse
rate, pulse lengths and pulse shape, variance. The pulse shape used here is
that adopted by Norris et al. (1996) to fit GRB LC. The amplitude of each
pulse was drawn from an exponential distribution.
Other pulse models are possible.
2.0
2.0
1.8
1.8
1.6
1.6
Normalized Flux
1.4
Rate = 10; t_rise=2, t_fall=2, std=0.3;
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
Rate = 1; t_rise=1, t_fall=5, std=0.5;
0.2
0.2
0.0
0
5
10
15
Tim e (days)
Gino Tosti – INFN Perugia
20
25
30
0.0
0
5
10
15
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
20
25
30
12
Blazars LC simulation – PSD inversion
We simulate light curves using the metod of Timmer & Konig (1995),
which is superior to the Done (1992) method (superposition of sine
waves with random phases) in that the power spectral amplitude is
drawn from a c2 distribution as should be the case for a noise process.
With this method it is posssible to generate LC starting from any PSD.
First we specify a PSD model to be used for LC generation.
We can use:
•Simple Power-Law
•Broken Power-Law
•Letho (1989, shot noise)
But .......Other forms are possible.
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
13
Blazars LC simulation – PSD inversion
These are example of LC obtained with a simple PL having  = 1.95
and an oversampling factor of 8 (to take into account that any
observed segment of LC includes components having much lower
frequencies - red-noise leakage).
1.8
Normalized counts
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
200000
400000
600000
1.6
800000 1000000 1200000 1400000
Time (s)
INPUT parameters:
•PSD(f) indexes
•Variance of the output LC
•Duration
•Sampling interval
•oversamplig
Gino Tosti – INFN Perugia
Normalized counts
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
200000
400000
600000
800000 1000000 1200000 1400000
Time (s)
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
14
Normalized flux
Blazars LC simulation – Non Linear LC
1.8
1.6
1.4
1.2
1.0
Original PSD Inverted LC
(gaussian distribution of the flux)
0.8
0.6
0.4
0.2
0.0
std =0.35
0
200000
400000
600000
800000 1000000 1200000 1400000
Time (s)
4.0
Non linearity is introduced by a
Exponential transformation of the
LC (Uttley et al. 2005)
Normalized Flux
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
200000
400000
600000
800000 1000000 1200000 1400000
Time (s)
Gino Tosti – INFN Perugia
THIS WAS THE
SELECTED METHOD
FOR the DC2
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
15
Blazars LC simulation – Spectral variation
The LC can be obtained using several energy distributions:
3
3
Power Law
1
Log(F) (a.u)
Log(F) (a.u)
Broken Power Law
2
2
0
-1
-2
1
0
-1
-2
-3
-3
-4
-4
-5
-5
1
2
3
4
5
1
Log(E) (a.u)
2
3
4
5
Log(E) (a.u)
0.5
Log(F) (a.u)
0
-0.5
-1
Log-parabola
-1.5
-2
-2.5
-3
1
2
3
4
5
Log(E) (a.u)
The rate of change of the ph index correlates with the fractional variation of the flux
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
16
Blazars LC simulation – Spectral variation
Normalized counts
Broken Power Law model
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0
5000
10000
15000
20000
25000
30000
35000
40000
Time (s)
1.5
Spectral index
1.7
1.9
2.1
2.3
2.5
2.7
2.9
3.1
0.4
0.5
0.6
0.7
0.8
Normalized counts
Simulation
Gino Tosti – INFN Perugia
0.9
1
PKS 2155-204
Kataoka et al. (2000)
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
17
LBL Blazar Light Curves
3c279
Parameters:
index_1;
the initial value is extracted from a Gaussian distribution having mean =2. and std=0.2
index_2;
the initial value is : index_2= index_1+rand(0.5,1.5)
Ebreak (MeV): rand (100-800)
The rate of change of the ph index correlates with the fractional variation of the flux.
A limit is imposed to the maximum value of the variation of the spectal index.
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
18
HBL Blazar Light Curves
Mkn 421
Less variable than lbl
Gino Tosti – INFN Perugia
DC2 Closeout Meeting - GSFC 31 May -2 June 2006
19