4.2 H.E.S.S. Data Analysis
4.2.3 Driftscan
Figure 4.21 shows events recorded in driftscan observations of the galactic center region.
Driftscan runs are scheduled at a constant zenith and azimuth angle array pointing. The celestial pointing at the beginning of a run is chosen such that the galactic center region
’drifts through’ the field of view after approximately half of the 68 min observation time.
The observed region is divided into many pixels, i.e. bins, each of which is much smaller than the H.E.S.S. I angular resolution. Each run is divided in time into one signal region enclosing the galactic center and one background region. Two arguments that lead to the exposure ratio are given below. The first argument is rather complicated but useful in order to become familiar with the driftscan analysis.
The division of a driftscan run into two halves can be realized with a method that is indicated in fig. 4.22. The upper panel of fig. 4.22 shows black rectangles indicating a segment of 2◦ in right ascension (half of the used H.E.S.S. I field of view radius) and 4◦in declination (full used H.E.S.S. I field of view). Indicated in blue is half of a used H.E.S.S.
I field of view drifting (indicated by black arrows) through the black segments. Consider first the process that is labeled with A in the upper panel of fig. 4.22. Here, half of the H.E.S.S. I field of view drifts out of a black segment. The situation is equivalent to the first 2◦ in right ascension observed in the driftscan. In the last two degrees in right ascension observed in the driftscan, the same process occurs time reversed (see fig. 4.22 label C). The first and last 2◦ in right ascension of a 68 min runtime driftscan
14In practice the ’SetPoissonBkgGaussEff(non,noff,eff,1/α, σ(eff))’ routine of the TRolke ROOT pack-age described in Rolke et al. [2005] is used. eff = 1 is the assumed event collection efficiency with a Gaussian error ofσ(eff) = 0.02. This is in practice equivalent to a 2% Gaussian error on the exposure ratioα.
4.2 H.E.S.S. Data Analysis
DM Mass (TeV)
1 10
/s)3 v> (cmσ<
10-25
10-24
10-23
10-22
10-21
Einasto+Tasitsiomi Einasto+Bergstrom NFW+Tasitsiomi NFW+Bergstrom
Annihilation
Figure 4.19: 95% CL upper limit on the velocity averaged WIMP annihilation cross section as infered from the analysis of the On/Off dataset. The color code for the different upper limit lines corresponding to different models for the dark matter density parametrization in the Milky Way and the γ-ray spectrum resulting from the annihilation of WIMPs is given in the lower right box.
The spread between the different lines indicates the order of magnitude of the model dependence of the upper limits.
Figure 4.20: Significance skymap for the considered driftscan dataset of∼9.5 h livetime (9 observation runs with 68 min observation time) in galactic coordinates.
The ring background subtraction method has been used to create the map which is correlated with a radius of 0.1◦. The galactic center source is clearly visible.
4.2 H.E.S.S. Data Analysis
Figure 4.21: H.E.S.S. I events (colorscale) for the driftscan observation of the Milky Way dark matter halo in galactic coordinates. The data is recorded with a constant zenith and azimuth pointing of the array. The galactic center region ’drifts’ through the field of view after approximately half of the ob-servation time. Each run is subsequently divided into two parts, the signal region enclosing the galactic center region in the upper panel and the back-ground region in the lower panel. Known γ-ray sources and the galactic plane (|b|<0.3◦) are excluded. Excluded regions are treated with a special method (see text) to guarantee the same total instrumental acceptance in the signal and background region.
Figure 4.22: Exposure ratio calculation for the driftscan. The upper panel shows two elementary drift processes (labeled by 1 and 2) as well as the corresponding time reversed process. The integrated acceptance corresponding to the pro-cesses is 1 and 2 respectively (see text). The lower panel shows in color the driftscan field of view for a 68 min observation. The blue, orange and red regions correspond to the process labeled by A,B and C in the upper panel respectively.
4.2 H.E.S.S. Data Analysis observation are colored in blue in the lower panel of fig. 4.22. The integrated acceptance of each of the processes is 1. The second and next to last 2◦ in right ascension are colored in orange in the lower panel of fig. 4.22. Here, the process labeled with B in the upper panel of fig. 4.22 occurs. Half of the H.E.S.S. I field of view moves out of the black segment and at the same time the other half of the H.E.S.S. I field of view moves in. The integrated acceptance for each of the processes - one process being again the time reverse of the other - is 2. The last half of the field of view moves eventually out of the black segment. This is equivalent to the process labeled with A in fig. 4.22 and thus the total acceptance of process B in fig. 4.22 is 1+ 2 2. Finally, all other segments of 2◦ in right ascension are colored in red in the lower panel of fig. 4.22. The process here is the same as for the orange labeled segment but additionally the first half of the H.E.S.S. field of view moves into the segments and the total acceptance of every red colored segment of 2◦in right ascension is thus 2( 1+ 2). Assuming that the signal region in the vicinity of the galactic center is completely in the acceptance region colored in red in the lower panel of fig. 4.22, the total acceptance in units of the acceptances of the processes labeled in the upper panel of fig. 4.22 for the signal region is
AON = 2( 1+ 2)∆L 2
where ∆Lis the length of the signal region in right ascension in degrees. Then, the total acceptance for the background region in the same units is given by
AOFF = L−4◦−∆L
2 2 ( 1+ 2) + 2 12◦
2 + 2 ( 1+ 2 2) 2◦
2 = (L−∆L)( 1+ 2) whereLis the total interval covered in right ascension by array pointings, i.e. the range colored by orange and red in the lower panel of fig. 4.22. Eventually, the ratio of the signal region to the background region acceptance is for a runlengthLand signal region size ∆L given by
α= AON
AOFF = ∆L
L−∆L . (4.37)
For instance, if α = 1 is requested for a 68 min runtime driftscan observation, the re-sulting signal region pointing range in right ascension is with 34 min the same as for the background region. However, the background region has a larger total field of view than the background region - a result of the total acceptance of the first and last four degrees covered in the field of view being smaller than for the rest of the field of view.
A simpler argument that leads to eq. 4.37 is to state that due to the constant horizon system pointing position, the exposure ratio has to be the ratio of the observation time TRun spent in the signal (TRunON = ∆L) and background region (TRunOFF =L−∆L).
Equation 4.37 holds if the assumption of constant instrumental acceptance is exactly fulfilled during the runtime. It is in practice to be expected that differences in the night sky background lead to trigger rate differences which in turn lead to differences for the livetime in the signal and background region. Additionally, atmospheric changes are expected which lead to acceptance differences between the signal and the background
region. This leads in practice to deviations from eq. 4.37 for the exposure ratio and to the necessity for respective corrections.
The method described above (eq. 4.29) to infer statements on the velocity averaged WIMP annihilation cross section, hσvi, is not directly applicable to the driftscan data because it is more complicated to say what f.i. the field of view, ∆ΩONi , of the signal region in a driftscan analysis or the livetime of the signal region observation is. A pre-cise and general treatment of this problem is given in appendix E and involves a time dependent field of view direction in celestial coordinates. The problem is that in general the astrophysical factor is obviously changing with observation time. An approximate treatment that translates the situation into a case that is described with eq. 4.21 is pos-sible by dividing the signal region resulting from the full driftscan observation into many small regions. The average astrophysical factor in the signal and background region is calculated and the difference JiON −JiOFF, which is necessary to evaluate eq. 4.29, is obtained. The livetime of the signal region observation, which is also necessary to eval-uate eq. 4.29, is in that case, however, not the full livetime but smaller. In practice, the effective signal region livetime is approximated by the mean length in right ascension that a small solid angle in the signal region stays in the field of view of the instrument15. The overall picture of the approach is to use that the observation of a drifting region of which only a small part can be seen in every point of time is equivalent to the ob-servation of the whole region for a reduced time. This reduced time is the average time a small element of the full region stays in the field of view corrected for dead time effects.
Dataset and Data Quality
A dataset of 11 driftscan observation runs, each with ∼ 68 min length is investigated in this section. Figures 18 and 19 in appendix C show the array trigger rate and the temperature of one radiometer as a function of runtime for each considered run. In two cases, the radiometer temperature variation during the run is very large, i.e. larger than ∼ 1◦ and the runs are discarded in the following. Additionally, in three of the nine remaining runs, almost one complete telescope was not operational (see fig. 20 in appendix C). These runs are also discarded in the following, however, they have been used to generate the skymap in fig. 4.20. The significance map is generated for a driftscan dataset of∼9.5h livetime with the ring background algorithm and an integration radius of 0.1◦. The map shows that no previously unknown γ-ray source is detected in the considered driftscan dataset within the regions below and above the galactic plane that have not been systematically observed before. The livetime of the dataset considered here is so small that only the galactic center source is detected as aγ-ray source with a local background algorithm and thus the exclusion of the galactic plane (|b| <0.3◦) is sufficient for the further analysis. All exclusion regions are within the region colored in red in fig. 4.22. Excluded pixels within the red region in fig. 4.22 are shifted mutually in right ascension between signal and background region at constant declination. This special treatment guarantees that the shifting of the exclusion regions does not imbalance
15The mean is calculated involving only pixels that are not excluded from the analysis.
4.2 H.E.S.S. Data Analysis
Figure 4.23: Number of broken pixels in all four cameras as a function of observation time for one analyzed driftscan observation run (run number 58862). For similar figures that belong to the other considered observation runs, see fig.
21 in appendix C.
the instrumental acceptance of signal and background region as the acceptance is by construction constant for constant declinations within the red region in fig. 4.22. To minimize the expected γ-ray flux from WIMP annihilation in the background region, every pixel excluded in the signal region is shifted along right ascension and constant declination as close as possible to the edge of the background region. Similarly, every pixel excluded in the background region is shifted as close as possible to the edge of the signal region to maximize the expectedγ-ray flux from WIMP annihilation in the signal region.
Out of the six remaining runs, three runs have an unusually large number of broken pixels in the four cameras (see fig. 21 in appendix C for details). Typically, 400-600 pixels are broken in these runs which is∼10% of the total number of pixels in the four cameras and compares to the typical number of 100-200 or ∼ 2−5% broken pixel in typical observation runs. The respective runs are also discarded from the analysis. For the remaining three runs, the number of broken pixels is significantly increasing after
∼40 min of observation time (see fig. 4.23 and fig. 21 in appendix C). For a driftscan analysis as described above, this means in practice that the number of broken pixels in the background region is systematically larger (by typically ∼ 10 pixels on average) than in the signal region. This stands in contrast to the situation in the On/Off analysis where the number of broken pixels in the background and signal region are not equal but no systematic preference for one region to have more or less broken pixels exists.
The reason for the increase in the number of broken pixels is very probably that the region in the south of the galactic center, that is in the field of view when the number of broken pixels is increasing in the driftscan observation runs, has a larger density of stars than other regions of the sky.
The systematic increase of the number of broken pixels with time in the background region will eventually lead to a systematic difference of theγ-ray event acceptance in the signal and the background region. Based on the very small number of three observation runs that are finally analyzed it is, however, very difficult to quantify or correct for the increasing number of broken pixels in the background region. In the following, the dataset of three driftscan observation runs is analyzed under the assumption of a 5%
systematic error on each of the runwise exposure ratios. A motivation for the numerical value of the systematic error on the exposure ratio is derived based on the experience from the analysis of the On/Off dataset that is discussed above. There, it has been found that:
• Atmospheric changes and differences in the number of broken pixels lead to a typical change ofσ(R)/R= 2% on the preslected event rate. This can be corrected for.
• The systematic cut efficiency difference between the ON and OFF observation data from preselected to selected events isσ()/= 3%. This can not easily be corrected for.
In the following, no correction for the 2% change in the preselected event rate is applied for simplicity in the driftscan data analysis. The total systematic error on the exposure ratio for every observation run is estimated to be
σ(αi) =√
The estimation of the systematic error on the exposure ratio is similar to the estimation of the systematic error on the exposure ratio for the On/Off analysis (see eq. 4.35).
This is justified because the time difference between the signal and background region observation (.30 min) as well as the order of magnitude of the difference in the number of broken pixel (10−20, see fig. 4.23) is similar for the driftscan as well as for the On/Off analysis. However, due to the expected systematic bias in the number of broken pixels between the signal and the background region observation, the systematic error on the exposure ratio is not assumed to become smaller when multiple driftscan observation runs are considered. In other words, it is not assumed that systematic differences in the γ-ray event acceptance average out when multiple driftscan runs are analyzed and the systematic error on the exposure ratio is thus decreasing with 1/√
K where K is the number of analyzed driftscan observation runs. The fact that the systematic error on the exposure ratio is not decreasing will eventually limit the sensitivity of the driftscan method.
Data Analysis and Results
Table 4.3 summarizes the results of the individual analyses of the three driftscan obser-vation runs that pass the data quality criteria discussed above. No significant excess is observed. The average observation time a pixel in the signal region is observed is 859.5