During
the last months, we have prepared the analysis of the Dec. 27, 2004
outburst of the SGR 1806-20. We summize in this page the main issues of
this anlysis and request for the unblinding of the data.
Introduction
Somehting written by Teresa..
Input files
Data
The burst under study happened at the beginning of file 127 of the run
9047, so we have removed from the analisys presented here the files 126
and 127.
On the other hand, we have also search for unstabilities in the PMTs rates. The main instabilies happended 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), 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-chere monitoring.
Since some of these OMs are not rejected by the unstability criteria
defined in [1], the files were removed from the analysis.
On the other hand, a sudden in the rates of OMs 86-195 and 428-460 was
observed for the files 157-163, so there were also removed.
Monte Carlo
This analysis is
almost independent on the Monte Carlo. The key point is the
estimation of the background off-time (and on-source) which comes only
from the data. The only point where we use the Monte Carlo is to
estimate which is the angular resolution of the experiment.
The Monte Carlo
sample has been produced from the CORSIKA sample of 1055 files
generated by Jessica Hodges and available at
/data/sim/AMANDA/combined/dcors/2003/mmc. We used these files as input
for AMASIM. The AMASIM configuration files [2] correspond to 2005 (since the set-up in Dec. 27 2004 was already the corresponding to 2005):
Calibration files
For the Sieglinde processing, we have also used the last version available at [2]:
The steering files for data and MC are the following:
Data: data-SGR.sl
MC: mc-SGR.sl
The cut in the azimuth angle is at 50 deg (instead of the usual value
of 70 deg) because the source is located at 70 deg. The margin of 20
degrees is enough to find the optimum cone as shown in the following.
Althought several reconstruction strategies have been used in the
steering file, the results presented here correspond to the Iterative
Likelihood (64 it.) previously fed by the output of the JAMS strategy.
Filtering
As
a previous step before applying an angular cut, many distributions were
studied to set a complementary cut in other variable. However, it was
seen that none of the studied variables could improve the results.
Basically, we only request the reconstructed track to be down-wards and
some minor cleaning of events for which topf encountered problems when
calculating some of its parameters (COG.Nom[0]>0,
COG_sigx[0]>0, COG_sigy[0]>0, Smooth_L.Nhit[0]>0). The
FlareChecker filtering is also applied with the cut:
InducB10Norm+Induc1119Norm + ShortMNorm < 10.
The only
variable which was found to be useful to improve the results (around
10%) is the number of 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
Several distributions can be compared between data and MC to check the robustness of the analysis.

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Reconstructed zenith angle
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Direct hits
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Reduced likelihood
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Total number of hits |

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Center of gravity
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Residual time
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Optimization of cuts for Model Discovery Potential
The aim of the analysis is to find a set of cut which minimizes the so-called Model Discovery Potential, defined as:
MDF = mu(bg,CI,SP) / nsig
where
mu is the number of signal events that are needed in order to produce
SP% of the time a fluctuation in the background which has a probability
lower than CI. SP is the statitstical power and CI is the confidence
interval.
Many variables related with the event were considered to define the
quality cuts. However, it was seen that the only powerful variable to
use is the angle around the the postion of the source. Since the event
is point-like source, with a very well defined timing, the background
can be effectively reduced.
There 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.

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Zenith dependence of background
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Phi dependence of background
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With the previous distributions, the total background rate at the position of the source can be calculated.
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 is 1.47, so we have psf
corresponding to the MC sample described above is re-weighed
accordingly. Since the statistics at high energies are low, the
fluctuations are large. In the plot below, the normalized rate of
signal vs the cone size is also shown.
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With this information we can calculate the dependence of the MDF on the cone size:
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 to the Poissoin discreteness.
Results
We have studied several factors that can modify the optimum size of the angular window.:
Number of events
From the defintion of the Model Discovery Factor, it is seen
that the number of events only scales the shape of the MDF vs optimum
cone size. Therefore, no change in the optimum bin size is expected
from this factor. 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 corresponing number of events
in our case would be a factor 2.5 larger.
Time window
The
time duration of the burst, according to Konus-Wind and RHESSI
experiments , is around 0.25 s. However, the appropriate time window
for this analysis could have to 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)
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MDF
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Optimum size (deg)
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Signal events
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Bkg events
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0.3
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1.37
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6.0
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3
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0.014
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1.0
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1.67
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6.6
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4
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0.059
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3.0
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2.03
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6.0
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5
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0.144
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5.0
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2.29
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4.8
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5
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0.151
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Our estimation of the propagation uncertainties shows that 3.0 s is a conservative value for the time window.

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Spectral index:
As
said before, several spectral indexes can be derived from the
observations. The harder the spectrum, the better is the angular
resolution. The effect of this is an improvement in the MDF factor,
since the signal is more concentrated around the source.
Spectral index
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Median
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MDF
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Optimum size (deg)
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Signal events
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Bkg events
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2.00
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3.38
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2.09
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6.0
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5
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0.144
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1.47
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3.34
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2.04
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6.0
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5
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0.144
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0.73
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3.27
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1.93
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6.0
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5
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0.144
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Quality cut: qual0, 5 events in a 3.0-sec window, C.I.=5 sigmas, Stat. Power=90%
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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.
Confidence interval and statistical power:
Once fixed the physical constraints of the anlysis, we can also study
the variation of the MDF and the optimum cone size at different
confidence intervals or statistical powers.
Confidence interval
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MDF
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Optimum size (deg)
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Signal events
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Bkg events
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3 sigma
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1.20
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8.0
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3
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0.264
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4 sigmas
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1.60
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7.0
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4
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0.199
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5 sigmas
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2.04
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6.0
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5
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0.144
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Statistical power
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MDF
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Optimum size (deg)
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Signal events
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Bkg events
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90%
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2.04
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6.0
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5
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0.144
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95%
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2.34
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6.0
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5
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0.144
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99%
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2.97
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6.0
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5
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0.144
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Juande D. Zornoza (
zornoza@icecube.wisc.edu)