Muons from the Dec. 27,
2004 burst
of SGR 1806-20
Unblinding Request for AMANDA-II data
Juande Zornoza, Teresa Montaruli, David Boersma, Paolo Desiati, Jon Dumm
University of Wisconsin - Madison
During the last months, we have prepared the
analysis of the
- Introduction
- Stability checks on data
- Calibration files and other input files for
data processing with Sieglinde SLART
- Filtering cuts
- Comparison
between data and MC
- Optimization of cuts for Model Discovery
Potential
- Results
- Unblinding request
Introduction
The useful information about this burst are collected here.
Stability Checks on Data
The burst under study
happened at the beginning of file 127 of the run 9049, so we have removed from
the analysis presented here the files 126 and 127.
We have determined the badOM list
according to the criteria described in Jon's page.
Analyzing PMTs rates (see also this) we
have found that the main instabilities happened in files 40-60 and in files
155-163.
In the first case, a large increase in the dark noise rate was measured in
several PMTs. The rate in OM=428
was particularly large (a factor 6 compared to the average rate
of the run), although not unique (OM=210, OM=219, OM=228, OM=272,
OM=288, OM=294, OM=296). This increase in the rate was also in coincidence
with a peak in the flare fraction measured by the on-line
flare-checking monitoring.
On the other hand, a sudden decrease in the rates of OMs 86-195 and 428-460 was
observed for the files 155-163, so these files were also removed from the
analysis.
Another check for instabilities is done at the analysis level using the flare
checker variables and the file Flare_calib_2005_online_date20050208.dat, specifically prepared for this run (see below and many thanks to A. Pohl).
We have also estimated the dead time of the run (16.9%) according to the pages (here or here). The decrease in the effective time of observation due to the dead time is taken into account in this analysis.
Monte Carlo
This analysis is almost independent from the
The atmospheric muon Monte Carlo sample has been
produced using a CORSIKA sample of 1055 files generated
by Jessica Hodges and available at /data/sim/AMANDA/combined/dcors/2003/mmc (equivalent to ~19 hours). We
used these files as input for AMASIM. The AMASIM configuration files [2] correspond to 2005 (since the set-up in
Calibration
files and other Input files for data processing with Sieglinde
SLART
For the analysis we used Sieglinde SLART. For the Sieglinde processing, we have
used the files also collected in the AMANDA Calibration File page by M.
Walter [2]. The amacalib files also include the X-talk cuts. For the MC the values have been specifically produced.
Data:
amacalib-data-2005.txt
(laser T0)
MC:
amacalib-mc-2005.txt
Common:
badOMs_all-run9049.dat
hitcleaning_totcuts_2005.list
Flare_calib_2005_online_date20050208.dat
The steering
files for data and MC are the following:
Data: data-SGR.sl
MC: mc-SGR.sl
We cut events with JAMS-reconstructed zenith angle larger than 50 deg (instead of the usual value of 70 deg) because the
source is located at theta=70 deg. The margin of 20 degrees is enough to find the
optimum cone as shown in below.
Although several reconstruction strategies have been used in the steering file
and their results analyzed, we have chosen to present the results corresponding
to the Iterative Likelihood (64 iterations) fed by the output of the JAMS
strategy.
Filtering cuts
Before applying an angular cut, we studied the dependence of the angular
resolution (the angle between the true muon and the
reconstructed one) on many variables (eg. # direct hits, reduced likelihood, cogx, cogy, cogz,
smoothness...)
We realized that the discovery potential is not enhanced cutting severely
to achieve an extremely good angular resolution. As a matter of fact, it is more convenient to use very
basic cuts allow to keep a larger fraction of the
signal, since this produce a better MDF (Model Discovery Factor).
Basically we only request the reconstructed track to be downwards and
some minor cleaning of events for which topf
encountered problems when calculating some of its parameters (COG.Nom>0,
COG_sigx>0, COG_sigy>0,
Smooth_L.Nhit>0). The FlareChecker
filtering is also applied using the cut: InducB10Norm+Induc1119Norm+ShortMNorm<10. We call this set of cuts "qual0".
The only variable which
was found to be useful to improve the results (MDF 10% better) is the number of
direct hits. However, some discrepancies in the comparison between MC and data
for this variable were observed (see below) so it was not used for the sake of
robustness.
Comparison between data and MC
We show some distributions for data and MC (with "qual0" cuts) to understand the level
of agreement between them. Though the MC is not used for estimating the
background (but the data off-source), it will be used to estimate the
sensitivity and the upper limits if we do not find any signal.
Also it is important that the MC reasonably reproduces the data
because we optimize the angular cut based on the information of the angular
resolution from the MC.
|
|
|
|
Reconstructed zenith angle |
Direct hits |
|
|
|
|
Reduced likelihood |
Total number of hits |
|
|
|
|
Center of gravity |
Residual time |
We
notice that at this stage it is not possible to have a perfect agreement in the
time residual and in the Ndirect distributions at the
same time. This is a problem that occurs in more than one
analysis (see some of the Zeuthen analysis plots;
Jessica Hodges observes a similar trend in the data/MC Ndirect
distribution in the diffuse flux analysis). We did many investigations,
but
still we cannot improve the agreement in the direct hit distribution.
The agreement in the residual time distribution improves with stringent
cuts (see plot).
Nonetheless
this analysis is not much affected by this discrepancy that can be accounted
for as a systematic error.
Optimization of
cuts for Model Discovery Potential
The aim of the analysis is to find a set of cuts which minimizes
the so-called Model Discovery Potential, defined as:
MDF = mu(bg,CI,SP) / nsig
where mu is the
number of signal events needed to produce SP% of the times a number of events equivalent to a fluctuation of the
background that corresponds to the confidence interval CI. SP is the statistical
power and CI is the confidence interval and nsig is the number of signal events.
Moreover, the other relevant variable to reduce the background is the
angular window around the source. We also assume that the muon
produced in the shower induced by a high energy gamma from the source is collinear
with the parent (no kinematic
angle) while we spread
the signal according to the angular resolution. We have also used
several spectral indeces in order to test the stability of the results
against a change in the spectrum.
The first step is to estimate the background, which is done with the on-source,
off-time data. The level of background depends on the zenith and azimuth angle.
 Zenith dependence of background |
|
Using the above distributions, the total background rate at the position of the
source at the time of the burst can be calculated:
Background rate versus the size of the search cone, calculated
from the on-source, off-time data.
The next step is to determine the signal angular distribution, which
depends on
the spectral index. To build this point-spread function we have assumed
that
the spectral index of the differential spectrum in energy is 2.7 (like atmospheric muons), so
we have evaluated
the PSF corresponding to the MC sample. On
the other hand, we only use events with multiplicity equal to one to
simulate more realistically the signal. In the plot below, the
normalized rate of signal vs
the cone size is also shown.
|
|
|
|
Spectral index: 1.47, Quality cut: qual0 |
|
A direct comparison between the normalizated distribution of signal and background can be seen here.
With this information we can
calculate the dependence of the MDF on the cone size:
Model Discovery Factor (black) and Model Rejection factor as a function
of the cone size (Spectral index: 2.7, Quality cut: qual0, 5 events,
time window: 1.5 s, C.I.=5 sigmas,
Stat. Power=90%)
In the figure above, the Model Rejection Factor is also shown. It is defined
as:
MRF = mulim(bg,CL) / nsig
where mulim is
the Feldman Cousin limit for the level of background bg
at a confidence level CL.
It can be seen that, whereas the MRF depends smoothly on the bin size, the MDF
shows jumps due to the Poisson discreteness. This is because for a
detection discrete numbers of signal events are needed, while for the
MRF only the estimated background is used.
Results
Model Discovery Factor
We
have studied several factors that can modify the optimum size
of the angular window. In the tables where the results for different
values of these factors are compared, our reference set of values (Spectral index: 2.7, Quality cut:
qual0, 5 events, time window: 1.5 s, C.I.=5 sigmas,
Stat. Power=90%) is marked with an asterisk.
Number of events
The MDF decreases with increasing signal events, which for a given
time window only depends on the angular window. The time window is assumed after
a study of the variations of the MDF and MRF with the constrain that the gamma observations and their
uncertainty has to be larger than 1 s.
A reasonable value of the
time window is 1.5 s.
Notice that the expected number of events depends on the spectral
index assumed for the source. There is also an additional ambiguity from the
maximum photon energy which is assumed. For instance, using the values
observed the Beppo-SAX, Halzen
el al. [3] calculated that the total number of muons
detected by AMANDA would be between 0.8-6. Indeed, this calculation assumed a
set of quality cuts stronger than what is used in this analysis. The corresponding
number of events in our case would be a factor 2.5 larger.
Dependence of the MDF of the mean number of expected signal events.
(Spectral index: 2.7, Quality cut:
qual0, 5 events in 1.5 s, C.I.=5 sigmas,
Stat. Power=90%)
Time window
The time duration of the burst,
according to Konus - Wind and RHESSI experiments (see Introduction), is
around 0.3-0.5 s. However, the appropriate time window for this analysis should
be larger in order to take into account the uncertainties in the propagation
times up to the AMANDA-II detector. We have studied, furthermore, several
cases:
|
Time window (s) |
MDF |
Optimum size (deg) |
# observed events |
Bkg events |
|
0.4 |
1.78 |
5.8 |
3 |
0.01 |
|
1.0 |
2.00 |
7.4 |
5 |
0.06 |
| 1.5* |
2.18 |
6.0 |
4 |
0.06 |
|
3.0 |
2.46 |
6.6 |
5 |
0.15 |
|
5.0 |
2.76 |
7.0 |
6 |
0.27 |
| Spectral index: 2.7, Quality cut: qual0, 5 events, C.I.=5 sigmas, Stat. Power=90% | ||||
Our estimation of the propagation uncertainties shows that 1.5 s is
a conservative value for the time window.
|
Model discovery factor dependence on the size of the time window where the signal events are expected |
|
|
|
|
Spectral
index:
As
said before,
several spectral indeces can be derived from the observations. It
is important to check the effect of a change in the spectrum on the
results.
|
Spectral index |
Median |
MDF |
Optimum size (deg) |
# observed events |
Bkg
events |
| 2.7* |
3.48 |
2.18 |
6.0 |
4 |
0.06 |
| 2.0 |
3.40 |
2.15 |
6.0 |
4 |
0.06 |
|
1.47 |
3.37 |
2.12 |
6.0 |
4 |
0.06 |
| 0.73 |
3.14 |
2.07 |
6.0 |
4 |
0.06 |
|
Quality cut:
qual0, 5 events in a 1.5-sec window, C.I.=5 sigmas,
Stat. Power=90% |
|||||
It
is seen that the optimum bin size is the same in all cases. Indeed, the
position of the local minima is not expected to change for a given
level of
background. The position of the absolute minimum could change if the
change in
the signal distribution is large enough, but this is not the case. The
dependence on the spectral index, therefore, is small (as expected from the almost flat dependence of the angular resolution on the energy of the primary) and does not
affect the choice of the optimum cone size. On the other hand, the
change in the norm which would be associated with this will be
more significant.
Confidence interval and
statistical power:
Once we fixed the time window of the analysis, we can also study the variation
of the MDF and the optimum cone size at different confidence intervals or
statistical powers.
|
Confidence interval |
MDF |
Optimum size (deg) |
# observed events |
Bkg
events |
|
3 sigmas |
1.20 |
6.6 |
2 |
0.07 |
|
4 sigmas |
1.65 |
6.6 |
3 | 0.07 |
|
5 sigmas* |
2.18 | 6.0 |
4 | 0.06 |
| Spectral index: 2.7, Quality cut: qual0, 5 events in a 1.5-sec window, Stat. Power=90% | ||||
|
Statistical power |
MDF |
Optimum size (deg) |
# observed events |
Bkg
events |
|
90%* |
2.18 |
6.0 |
4 |
0.06 |
|
95% |
2.53 |
6.0 |
4 |
0.06 |
|
99% |
3.22 |
9.2 |
5 |
0.15 |
| Spectral index: 2.7, Quality cut:
qual0, 5 events in a 1.5-sec window, C.I.=5 sigmas |
||||
Model Rejection Factor
Similarly to the case of the MDF, we can study the effect of several relevant variables in the analysis:
|
Time window (s) |
MRF |
Optimum size (deg) |
Bkg events |
|
0.4 |
0.654 |
15.8 |
0.131 |
|
1.0 |
0.690 |
13.0 |
0.213 |
| 1.5* |
0.708 |
12.2 |
0.277 |
|
3.0 |
0.756 |
9.8 |
0.341 |
| Spectral index: 2.7, Quality cut: qual0, 5 events, C.I.=5 sigmas, Stat. Power=90% | |||
|
Spectral index |
Median |
MRF |
Optimum size (deg) |
Bkg
events |
|
2.70 | 3.48 | 0.708 | 12.2 | 0.277 |
|
2.00 |
3.40 |
0.703 |
11.6 |
0.248 |
|
1.47 |
3.37 |
0.699 |
11.6 |
0.248 |
|
0.73 |
3.14 |
0.684 |
12.8 |
0.309 |
|
Quality cut:
qual0, 5 events in a 1.5-sec window, C.I.=5 sigmas,
Stat. Power=90% |
||||
Unblinding request
After this analysis we ask for unblinding of the data where the signal is located, using the following parameters for discovery potential:
| Bin size |
6.0 deg |
| Time window |
1.5 s |
This would optimize the discovery potential for a confidence interval of 5 sigmas and with a statitical power of 90%.
Juande D. Zornoza (zornoza@icecube.wisc.edu)
Teresa Montaruli (tmontaruli@icecube.wisc.edu)