Preliminary SYNCH.  MC Results

The table below gives estimates of effective area based on a criteria of >3 photons in detector, all with energy>10KeV.  Effective areas are in m^2-sr
 
E(TeV) 
Aeff( 1x1 m2
Aeff(2x2 m2)
1
.068
0.6
2
.34
3.6
5
2.54
17.4
7
3.74
25.6
10
5.34
37.5
20
10.66
70.0
50
22.0
131.2

We now fit these effective area vs energy points to a quadratic in energy, and convolve these with the diffferential electon flux, based on our ApJ parameterization dn/dE = 227 E^-3.09.  The 2nd column is the number of events in a 100 day flight for a 1x1 m detector, the 3rd column is for the larger detector.
 
 
E(Tev) 
  N(100 days)
N(100 days) _large
1-2
62
670
2-5
112
832
5-10
45
319
10-20
22
152
20-50
12
76

Next, I've linked some postscript files, one for each of the energies above, and for the small and large detector configuration.  The plots in these files are, in order

1:  Distribution of the number of photons>10KeV in triggered events.  (no conversion efficiencies, etc)
2:  The distributions of photon energies, in KeV
3:  Event time duration in ns vs z direction cosine
4:  z direction cosine vs event time duration/event length
5:  distribution of average production height of photons, in cm
6:  distribution of x direction cosine
7:  distribution of y direction cosine
8:  distribution of z direction cosing
9:   x vs y direction cosines
10:  Primary energy, in GeV
 

 1tev_small.ps
 1tev_large.ps
 2tev_small.ps
 2tev_large.ps
 5tev_small.ps
 5tev_large.ps
 10tev_small.ps
 10tev_large.ps
 20tev_small.ps
 20tev_large.ps
 50tev_small.ps
 

Variation of Aeff with longitude for southern polar orbit.

The plot below show Aeff @ 2Tev, vs longitude for latitude 70S.  The variation in Aeff over and orbit is about a factor of two peak to peak.  It turns out (by accident) that Lynn Lake (the location I was running previously) is not too far from the average.  The variation of Aeff with longitude is a weak function of electron energy, with a smaller variation at higher energy.

Effect of Incomplete Energy Containment

Next, I add a model of energy conversion in the BGO, using a model from Chuck.  In the table below, I show
the 'loss' in effective area in percent as a function of energy bin, for a 2.54 cm thick detector.
 
 
Energy (TeV)
DAeff/Aeff  (%)
2
 4%
5
 11%
10
 20%
20
 20%
50
15%

 

Effective area of 'fixed volume' detector vs thickness

Next, I show the result of varying the detector thickness, keeping the total volume (weight) the same.  Here and in all
that follows, the MC includes the effect of incomplete energy containment in the detector.  The table below shows
the effective area @ 10 Tev vs thickness. The 2.54 cm thickness value can be compared with the 10TeV for the 1x1 m column in the first table on this page to see the consequences of incomplete containment on effective area at this energy and thickness.
 
 
Thickness (cm) 
Aeff (m2-sr)
0.25
 47
0.5
24.2 
1
11.7 
2
5.6 
2.54
4.3

 
 
 

Simulation of Power Law Electron Spectrum

Next, we investigate the relationship between the primary spectrum, and the spectrum of event-averaged photon energy.  In the plot below, I show the distribution of primary electron energies which generate events in a 1x1 m detector,  Black is for a differential spectrum for primaries vaying as  E-3 , red is E-3.5 , and green is E-4.

                                                                                           E (GeV)
 

Next, we plot the relationship between the primary energy and the event-averaged photon energy.  The vertical scale is event-averaged photon energy in keV, the horizontal axis is primary energy in GeV.


                                                                               Ee- (GeV)
 

Finally,we show the spectrum of event averaged photon energy, for the three primary power laws,  Black is for a differential spectrum for primaries vaying as  E-3 , red is E-3.5 , and green is E-4.  The horizontal axis has units of keV. As one goes to decreasing detector thickness, one sees a decreasing ability to measure the primary spectral shape.
 

2.54 cm thick detector

 

1 cm thick detector

 

0.5 cm thick detector