Analysis of the Dec. 27, 2004 outburst
of SGR 1806-20

Unblinding Request

Juande Zornoza, Teresa Montaruli, David Boersma, Paolo Desiati, Jon Dumm
Universtiy of Wisconsin Madison


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):

ama.geo
ama.elec


Calibration files

For the Sieglinde processing, we have also used the last version available at  [2]:

Data:
    amacalib-data-2005.txt
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


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.



Reconstructed zenith angle
Direct hits



Reduced likelihood
Total number of hits



Center of gravity
Residual  time


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.


Zenith dependence of background
Phi dependence of background

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.








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)
MDF
Optimum size (deg)
Signal events
Bkg events
0.3
1.37
6.0
3
0.014
1.0
1.67
6.6
4
0.059
3.0
2.03
6.0
5
0.144
5.0
2.29
4.8
5
0.151

Our estimation of the propagation uncertainties shows that 3.0 s is a conservative value for the time window.






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
Median
MDF
Optimum size (deg)
Signal events
Bkg events
2.00
3.38
2.09
6.0
5
0.144
1.47
3.34
2.04
6.0
5
0.144
0.73
3.27
1.93
6.0
5
0.144
Quality cut: qual0,  5 events in a 3.0-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.

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
MDF
Optimum size (deg)
Signal events
Bkg events
3 sigma
1.20
8.0
3
0.264
4 sigmas
1.60
7.0
4
0.199
5 sigmas
2.04
6.0
5
0.144


Statistical power
MDF
Optimum size (deg)
Signal events
Bkg events
90%
2.04
6.0
5
0.144
95%
2.34
6.0
5
0.144
99%
2.97
6.0
5
0.144







Juande D. Zornoza (zornoza@icecube.wisc.edu)