4. Instrument Performance and Expected Results
Modeling Procedure
The expected performance of the BEST instrument has been evaluated using a GEANTbased simulation of the generation, propagation, and detection of synchrotron photons
produced by UHE electrons in the Earth’s
magnetic field. The magnetic field model used
in this study is based on the International
Geomagnetic Reference Field (IGRF) for 2003.
Electrons are tracked from a starting altitude of
400 km down to a balloon altitude
corresponding to 5 g/cm 2 of vertical
atmospheric overburden. The synchrotron
photons generated by the electron are
propagated to balloon altitude, accounting for
losses due to absorption and scattering in the
atmosphere. The atmospheric model used in the
simulation is based on the 1976 U.S. Standard
Atmosphere. Figure 4.1 shows the location of
the primary electron and the surviving
synchrotron photons on a horizontal plane at
Figure 4-1 10TeV Electron and synchrotron photons at
balloon altidude.
balloon altitude for a 10 TeV electron at a
zenith angle of 45 degrees. In this
particular event, 95 synchrotron photons with energies greater than 10 keV were
generated at altitudes between 400 km and balloon altitude. The surviving photons in
this event lie on a ~ 120m long track in this horizontal plane, with the photon density
increasing near the electron transit point. The detection of these photons is simulated
through the use of a detailed model of the interaction of the photons in the BGO detector
and subsequent signal generation.
Effective Area vs Primary Energy
The detection of an UHE electron is based
on the observation of signals above
threshold in multiple isolated BGO cells,
all occurring with the proper relationship
in time. For a vertically incident electron,
all synchrotron photons will arrive at the
detector well within the 1 ns resolving
time of the BGO/PMT detector. In
general, the difference in propagation time
for two photons is given roughly by
l sec(z)/c, where l is the distance between
the observed locations of the two photons,
and z is the zenith angle of the electron.
The relationship between the measured
Figure 4-2 Effective area vs primary electron energy.
time and location of the signals in the BGO array therefore allows a crude measurement
of the zenith angle of the primary electron. Combined with the orientation of the line of
synchrotron-induced signals in the array, this provides a full three dimensional trajectory
for the electron.
An estimate of the rate of background trigger events due to random coincidences of
signals resulting from x-ray and charged particle backgrounds is presented below. The
results of this background study indicate that a minimum of four co-linear signals within
an effective 2 ns time window is needed to reduce the background rate to levels less than
1% that of the expected primary
events, assuming a 40 keV signal
threshold. The average detected
photon energy increases rapidly with
the energy of the primary electron,
allowing the offline signal threshold
to be scaled to the mean photon
energy of an event, reducing the
background rate at higher energy,
and allowing one in principle to
establish a looser requirement of
three co-linear signals at these
energies. However, in estimating the
effective area of the instrument, we
adopt the most conservative possible
Figure 4-3 Distribution of the number of detector photons, for
approach, and assume that a cluster
a 10 TeV primary.
of 4 or more co-linear in-time hits
constitutes an observation. Based on this observational criteria, the effective area of the
instrument can be obtained by determining the average area in which this criteria is met
in a horizontal plane at balloon altitude, for an ensemble of isotropic events. The
effective area is an increasing function of the primary energy, due to the increase in the
intensity of synchrotron radiation with primary energy, and the reduced probability for
loss of the photon in the atmosphere at
higher photon energies. Figure 4-2
shows the effective area of the BEST
instrument as a function of primary
energy averaged over a south-polar
orbit. Figure 4-3 shows the distribution
of observed cluster size for 20 TeV
electrons, illustrating that one could
roughly double the effective area at
this energy by reducing the minimum
cluster size to three. The signal events
result from primaries with a broad
zenith angle distribution, as shown in
Figure 4-4. Low zenith angle events
are suppressed due to the smaller
Figure 4-4 Zenith angle distribution of detected electrons.
‘footprint’ of the photon track at balloon altitude, and high zenith angle events are
suppressed due to scattering and absorption of the synchrotron radiation in the
atmosphere, and the smaller subtended area of the array at large zenith angle.
Sensitivity to Magnetic Field and Overburden Variations
The effective area of the instrument is dependent upon the magnetic field strength and
orientation, as this determines the size of the synchrotron ‘footprint’ at balloon altitude,
and on the overburden, which sets the probability for absorption of a photon in transit. It
is, therefore, important to understand
and compensate for these effects in
order to obtain a measurement of the
primary electron flux. Figure 4-5
shows the variation of effective area
for 10 TeV electrons with longitude
for a circumpolar orbit at latitude 70S.
As illustrated in this figure, a variation
in effective area (and hence event rate)
of roughly a factor of two is seen at
this energy. The accuracy of geomagnetic models is more than
sufficient to correct for this effect at
the level necessary to reduce this
potential systematic error in the flux to
Figure 4-5 Effective area vs longitude @ 70S latitude.
levels well below the statistical errors
inherent in this measurement. The
modest level of variation in effective
area is, in fact, beneficial, as the observed modulation of event rate with longitude will be
used to verify the level of background contamination in the final event sample, exploiting
the fact that the background event rates
would not be expected to vary with
longitude in this way.
During an LDB or ULDB balloon
flight, the atmospheric overburden can
be expected to vary substantially, in
particular due to day-night variations
in the balloon altitude. Figure 4-6
shows the dependence of the detector
effective area for 5 TeV electrons on
atmospheric overburden. Atmospheric
absorption of the synchrotron photons
decreases with photon energy, and
hence with the energy of the primary
electron, reducing the dependence of
the effective area on overburden at
higher energies. The BEST payload
Figure 4-6 Dependence of the effective area on overburden
for 5 TeV primaries.
will be instrumented with redundant sensors capable of 1% measurements of atmospheric
pressure, which will clearly allow this dependence to be corrected for at the required
level. One should note that this correction requires knowledge of x-ray attenuation
coefficients, and the chemical composition in the upper atmosphere, to an accuracy well
within the current state of the art in these areas.
Determination of the Primary Electron Spectrum
The basis for the primary electron energy measurement is the dependence of the average
synchrotron photon energy on the energy of the primary. In Figures 4-7 & 4-8 we show
Figure 4-7 Distribution of average
observed photon energy for 2 and 10 TeV
primary electrons.
Figure 4-8 Distribution of average
observed photon energy for 10 and 20 TeV
primary electrons.
the distribution of the average observed energy of the photons detected in a given event
for 2, 10, and 20 TeV primaries. As these figures illustrate, a measurement of the
average photon energy determines the
energy of the primary electron to within
roughly a factor of two. Simulations of the
response of the instrument to a primary
electron spectrum following a power law
with a range of spectral indices were
performed to determine the sensitivity of
in a 100 day flight of the BEST instrument
to the shape of the UHE electron
spectrum. A representative example is
shown in Figure 4-9, which compares the
distribution of event-averaged photon
energies observed assuming an E-3.1 input
spectrum, and the observed photon energy
Figure 4-9 Observed event-averaged photon energy for a
distribution with the same spectral index,
power
law electron spectrum (black), and for a power law
but assuming a cutoff in the primary flux
spectrum with a cuttoff @ 10 TeV (red).
at 10 TeV. In obtaining this result, we
assume that the response function of the detector is well known. The response function
depends upon well know properties of the upper atmosphere and geo-magnetic field, and
the response of the BGO cells as a function of photon energy. An important component
of our implementation plan is carrying out the laboratory and beam test measurements
needed to verify that our understanding of the instrument response function is sufficient
to allow a statistics-limited measurement of the UHE electron spectral shape.
Backgrounds
The rate of background events resulting from random coincidences of background x-ray
events in the detector is obtained using the measured x-ray flux at balloon altitude
reported in ( ). The veto system will
reduce the contribution of charged
particle backgrounds to a negligible
level, and they are not considered here.
A four-fold or greater coincidence of
signals within a 2 cell wide linear region,
and within a 2 ns effective time window,
constitutes a potential background to real
events. The expected number of such
background events in a 100 day flight is
shown in Figure 4-10 as a function of
energy threshold in keV. Comparing
Figure 4-10 with the distribution of
mean photon energies for given primary
energies, one sees that a trigger threshold
Figure 4-10 Number of 4-fold random coincidences in 100
of 40 keV provides essentially 100%
days vs the photon energy threshold.
efficiency for detecting photons from a 2
TeV primary, while providing a background to the final event sample of less than 1
event in a 100 day flight. Experience teaches us that estimates of low energy background
in balloon-borne experiments are subject to substantial errors, and our work plan includes
the flight on a conventional balloon of a small prototype, which will be used to validate
our background estimates through a direct measurement of neutral and charged particle
singles rates as a function of energy, as discussed in section 5.
Expected Number of Events
As emphasized earlier in this proposal, there is great uncertainty in the electron flux at the
extreme energies probed by this instrument. Not only can one expect that the electron
spectrum at these energies will reflect the detailed distribution of nearby sources, as
discussed in the science section, but there remains substantial uncertainty in the measured
flux at lower energies. Under the assumption that the electron spectrum measured by
this group previously using the HEAT instrument in the energy range 5-100 GeV can be
extrapolated into the multi-TeV range, and given the energy-dependent effective area
shown in Figure 4-2, we would observe roughly 250 electrons with energy greater than 2
TeV in a 100 day balloon flight. The distribution of these events with energy is shown in
Table 4-1.
Primary Electron Energy (TeV)
2-5
5-10
10-20
20-50
>50
# Electrons Seen in a 100 day ULDB Flight
116
56
31
21
20