10
−3 10
−2 10
Figure 4.61: Left: selected proton events with the MIP trigger in the period (01/01/2016-30/04/2018) as a function of energy. Right: migration matrix for the selected MIP sample.
reconstructed events distribution provides a complete proton flux measurement at least until 10 TeV and the result compared to the standard HET measurement is shown in Fig. 4.62. The proton flux measured with the MIP sample is up to 5% higher than that measured with the HET sample until 5 TeV. Above the difference is reduced with respect to the standard HET proton flux. This difference can be due to the modeling of the interaction cross-section (see current inelastic cross-section measurements compared to different models used in various MC simulations in [97]), however it is not clear in which specific part it is due only on that.
4.7 Results
The previous steps allowed us to give a preliminary proton flux measured by DAMPE based on 1.59006 ·107 selected proton candidates that are shown in Fig. 4.63 and Fig. 4.64. Tab. 4.6 shows a summary of the observed events in two bins per decade.
The flux is measured from 50 GeV to 100 TeV and it is shown in Fig. 4.65. Tab. 4.7 The measured proton fluxes are presented in Tab. 4.7 as a function of the energy. In
CHAPTER 4. MEASUREMENT OF THE PROTON FLUX
Energy (GeV)
102 103 104 105
)-1 sr-2 m-1 s1.7 (GeV2.7 E×Flux 8000
10000 12000 14000
16000 DAMPE
DAMPE MIPT analysis
Figure 4.62: Central points of the proton flux multiplied by E2.7 measured by DAMPE with the MIP sample (empty circles) compared to the standard HET sample (filled circles).
BGO Energy [GeV]
102 103 104 105
)1.7 Number of Entries (GeV×2.7E
109
1010
1011
raw data events in 32 bin/dec raw data events in 2 bin/dec
Figure 4.63: Selected proton candidates as a function of the reconstructed energy multiplied by E2.7in 32 bin per decade (red) and in 2 bin per decade (blue).
these figure, the points are placed along the y axis with an energy calculated for a flux E−2.7 following [95]. Tab. 4.6 and Tab. 4.7 also contain a representative value of the energy in the bin interval for a flux E−2.7. The error breakdown is shown in Fig. 4.66.
The systematic error related to the preselection cuts will be added in the next iteration of the analysis.
The proton flux measurement performed in this thesis was compared with the pre-vious results in Fig. 4.67. The DAMPE data confirms the spectral hardening at ∼300 GeV observed by ATIC02 [41], CREAM [48], PAMELA [44] and AMS-02 [40], and
re-138
BGO Energy [GeV]
1 10 102 103 104 105 106
Number of Entries
102
103
104
105
106
107
Figure 4.64: Selected proton candidates as function of the reconstructed energy, with the helium background subtraction.
Energy [GeV] Emin [GeV] Emax [GeV] Events
24.9 20 31.6 (8.033±0.003)·106
54.2 31.6 100 (6.739±0.003)·106
171 100 316 (9.68±0.01)·105
542 316 1000 (1.354±0.003)·105
1714 1000 3162 (2.10±0.01)·104
5419 3162 10000 (3.16±0.06)·103
17135 10000 31623 (3.63±0.19)·102
54186 31623 100000 (29±5)
Table 4.6: Number of proton candidates reconstructed in the various energy ranges.
veals a spectral softening above ∼ 10 TeV that is much more clear now in the current measurements scenario. This “early knee” in the spectrum could be explained by the three component model in the acceleration of cosmic rays described in [99] (used already by CREAM in [48]) and [100]. As explained in [99], this feature in the spectrum after 10 TeV could depict the maximum energy of one type of particle accelerator source.
Only after an other type of source starts in contributing with particle acceleration. This softening should be rigidity dependent and be visible in all other nuclear species as well, like for the hardening [62], but only looking at the flux of other nuclei species above 10 TeV will give a clearer picture.
CHAPTER 4. MEASUREMENT OF THE PROTON FLUX
Energy (GeV)
102 103 104 105
)-1 sr-2 m-1 s1.7 (GeV2.7 E×Flux
6000 8000 10000 12000 14000 16000 18000
DAMPE, this work
Figure 4.65: Proton flux multiplied by E2.7 measured by DAMPE. The systematic error band is also drawn.
Energy [GeV] Emin [GeV] Emax[GeV] φ±σstat±σsys 49.8 39.8 63.1 (283±0.09+21−17)·10−3 78.9 63.1 100 (80.8±0.04+5.6−4.9)·10−3
125 100 159 (23.2±0.01+1.6−1.4)·10−3 198 159 251 (66.4±0.04+4.4−4.1)·10−4
314 251 398 (19.0±0.03±1.2)·10−4
498 398 631 (54.8±0.08+3.5−3.3)·10−5 789 631 1000 (16.05±0.04+1.00−0.98)·10−5 1251 1000 1585 (4.69±0.02+0.29−0.28)·10−5 1983 1585 2512 (14.09±0.06+0.86−0.87)·10−6 3142 2512 3981 (4.36±0.03+0.27−0.26)·10−6 4981 3981 6310 (1.30±0.01±0.08)·10−6 7895 6310 10000 (3.81±0.06±0.24)·10−7 12512 10000 15849 (1.10±0.02±0.72)·10−7 19830 15849 25119 (2.99±0.08±0.18)·10−8 31429 25119 39811 (0.73±0.03±0.06)·10−8 49812 39811 63096 (0.19±0.01±0.02)·10−8 78946 63096 100000 (0.49±0.05±0.06)·10−9 Table 4.7: Results for the proton fluxes according to Eq. 4.1 in units of [GeV s m2sr]−1.
140
Energy [GeV]
102 103 104 105
Error [%]
2 4 6 8 10 12 14 16 18
Statistical Trigger (HET) Charge slection Track selection PSD smear MC until 251 TeV
Figure 4.66: Error breakdown for the proton flux measurement. The error on the background subtraction is included in the statistical error calculation.
Energy (GeV)
102 103 104 105
)-1 sr-2 m-1 s1.7 (GeV2.7 E×Flux
4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000
ATIC02 (2009) PAMELA (2011) AMS-02 (2015) CREAM III (2017) NUCLEON (IC) (2018) NUCLEON (KLEM) (2018) DAMPE, this work
Figure 4.67: Proton flux multiplied by E2.7 measured by DAMPE compared with various experimens: ATIC02 [41], PAMELA [44] corrected according to the note on page 4 in [98], AMS02 [40], CREAM III [48] and NUCLEON [67].
CHAPTER 4. MEASUREMENT OF THE PROTON FLUX
142
The discovery of cosmic rays is quite recent compared to other kinds of physics, as shown in the introduction in chapter 1. Our understanding of the mechanisms that de-scribe the acceleration of cosmic rays and their origin is also relatively new (sections 1.1 and 1.2.2). The rather young age of this field of research makes it deeply interesting, but also extremely challenging. Many detectors on the ground (section 1.3), on bal-loons (introduction of chaper 2) and in space (section 2.1) already made a lot of efforts to improve cosmic-ray measurements, and several are currently continuing them. The DAMPE detector is designed to pursue this task, as described in section 2.2.
Only the best components were chosen during the construction of the DAMPE Sili-con Tungsten tracKer (STK), starting from selecting the tungsten plates (section 3.1.1) and measuring the planarity of the trays, evaluating also the effects of thermal cycles on them (section 3.1.2). All the silicon ladders were tested after the production and individually characterized, so that a final selection could be made to choose the best samples. Several distributions were recorded and evaluated to summarize their linearity and thickness (Fig. 3.14 and Fig. 3.15).
The signals of the read-out chips of the silicon ladders were calibrated with an analy-sis based on ground (section 3.2.3) and orbit data (section 3.2.5). We monitored the calibrated gain of the chips, at scheduled time intervals, by studying on-orbit data (Fig. 3.34). A charge-loss correction of the tracker response was performed on-ground (section 3.2.4) and on-orbit (section 3.2.6). Using on-orbit data, this calibration im-proved the preliminary tracker charge resolution for protons and helium by 13% and 21%, respectively (Fig. 3.39).
We performed an analysis based on 30 months of data from DAMPE, dedicated to calculate precisely the proton flux, and described in every detail in chapter 4. MC events were studied, simulated with several physics lists (summarized in section 4.3.1).
A systematic comparison between data and MC using all the studied distributions for protons allowed to select the list that matched most closely the data (Fig. 4.14, Fig. 4.34 and Fig. 4.27). We estimated the systematic uncertainties of all the cuts applied on the data by comparing the cut efficiencies between data and MC for various subdetec-tors, as detailed in section 4.4. The electron (section 4.3.7) and helium (section 4.3.8)
Conclusions and outlooks
contaminations were studied and taken into account in the final measurement. The sys-tematic error study was completed by estimating the MC related uncertainties, reported in section 4.5.1. The unfolded flux was obtained iteratively, as explained in section 4.5.2, and the method employed was cross-checked by injecting a known input spectrum (sec-tion 4.5.4). The proton flux measured with this analysis, allowed to improve the current knowledge of the energy dependence of the proton spectrum, which is the key element in understanding the origin, propagation and acceleration of cosmic rays in the Universe.
Looking at the flux of other nuclei species above 10 TeV will help to understand if this softening is rigidity dependent or if it is only visible in protons. Future space mis-sions, like HERD [101], plan to contribute to the cosmic-ray flux measurements, reaching energies up to 1 PeV.
144
Appendix A
Metrology of the STK
A.1 The tungsten plates
The ID number position with respect to the tray are shown in the left panel of Fig. A.1, the plates chosen for the three trays of STK are shown in the right panel of Fig. A.1 and in Fig. A.2. As completeness the information on the measurements regarding the
Figure A.1: Left: position of the tungsten plates in the STK tray. Right: ID of the plates used for the first STK tray containing W.
selected plates are reported in Tab. A.1, A.2, A.3, A.4, A.5 and A.6 respectively to the first, second and third layer with W in STK. For the first tray the 16 plates chosen fulfill all the requirements in Tab. 3.1. Among the other 32 plates, 6 do not fulfill completely the requirements. It was decided to place those plates at the edge of the trays.
APPENDIX A. METROLOGY OF THE STK
Figure A.2: ID of the plates used for the second (left) and third (right) STK tray containing W.
Plate ID tray Dx1(mm) Dx2(mm) Dy1(mm) Dy2(mm)
3 1 188.030 188.022 188.034 188.034
8 1 188.008 187.988 188.027 188.027
12 1 188.027 188.020 187.996 187.996
13 1 187.979 187.999 188.026 188.026
17 1 188.030 188.025 188.006 188.006
20 1 188.049 188.029 188.054 188.054
21 1 188.014 188.003 188.040 188.040
23 1 188.036 188.033 188.022 188.022
24 1 187.992 187.994 188 188
25 1 188.021 188.036 188.026 188.026
26 1 188.028 188.016 188.001 188.001
31 1 188.027 188.044 188.033 188.033
34 1 188.046 188.038 188.050 188.050
36 1 188.050 188.044 188.046 188.046
38 1 188.042 188.057 188.047 188.047
46 1 187.992 187.999 188.048 188.048
Table A.1: Sides information for the selected W plates for the first tray.
146
Plate ID tray area (mm2) thickness (mm)
3 1 35355,5 1.04
8 1 35348,5 1.03
12 1 35348 1.02
13 1 35346.6 1.03
17 1 35351.6 1.01
20 1 35360.2 1.03
21 1 35353.6 1.
23 1 35353.7 1.03
24 1 35346.3 0.99
25 1 35354.1 0.98
26 1 35349.1 1.02
31 1 35356.3 1.
34 1 35360.7 1.
36 1 35363 1.02
38 1 35362.8 1.02
46 1 35351.2 1.
Table A.2: Area and thickness information of W plates for the first tray.
Plate ID tray Dx1(mm) Dx2(mm) Dy1(mm) Dy2(mm)
2 2 188.014 188.024 188.017 187.988
5 2 188.022 188.026 188.028 188.042
6 2 188.013 187.996 188.031 188.027
10 2 188.044 188.031 188.011 188.016
29 2 188.050 188.026 188.021 188.015
33 2 188.040 188.052 188.048 188.055
35 2 188.056 188.056 188.036 188.05
42 2 188.047 188.046 188.060 188.053
44 2 188.008 188.011 188.027 188.043
47 2 188.052 188.044 188.045 188.056
48 2 188.036 188.047 188.049 188.052
49 2 188.047 188.056 188.050 188.053
54 2 188.048 188.041 188.023 188.026
14 2 188.036 188.034 187.997 188.006
16 2 188.040 188.051 188.056 188.045
30 2 188.045 188.053 188.063 188.053
Table A.3: Sides information for W plates of the second tray.
APPENDIX A. METROLOGY OF THE STK
Plate ID tray area (mm2) thickness (mm) Weight (g)
2 2 35348. 1.0 689.07
5 2 35355.1 1.01 699.09
6 2 35350.3 1.0 688.09
10 2 35353.6 1.03 691.87
29 2 35354.5 1.02 702.63
33 2 35362.3 1.0 693.81
35 2 35362.6 1. 683.45
42 2 35363.4 1.01 680.81
44 2 35352.4 1.02 700.37
47 2 35362.5 1. 687.78
48 2 35361.3 1. 686.35
49 2 35363.4 1. 695.7
54 2 35357. 1.02 699.46
14 2 35380.9 1.01 698.4
16 2 35350.9 0.99 684.68
30 2 35362. 1.02 699.26
Table A.4: Area, thickness and weight information for W plates of the second tray.
Plate ID tray Dx1(mm) Dx2(mm) Dy1(mm) Dy2(mm)
56 3 188.025 188.017 187.994 188.003
57 3 188.035 188.035 187.992 187.998
58 3 188.000 187.998 187.953 188.030
59 3 188.009 188.026 188.014 188.035
63 3 188.024 188.045 188.041 188.070
64 3 188.044 188.016 188.079 188.083
68 3 188.031 188.046 188.081 188.076
70 3 188.051 188.085 188.058 188.026
71 3 188.024 188.045 188.077 188.087
72 3 188.042 188.023 188.085 188.080
73 3 188.020 188.038 188.078 188.081
79 3 188.049 188.022 188.080 188.091
81 3 188.046 188.021 188.064 188.082
19 3 188.003 188.016 188.03 188.033
27 3 188.042 188.038 187.999 188.017
28 3 188.026 188.031 187.994 188.006
Table A.5: Sides information for W plates of the third tray.
148
Plate ID tray area (mm2) thickness (mm) Weight (g)
56 3 35347.7 1.02 702.88
57 3 35349.6 1.0 682.94
58 3 35342.2 1.0 687.61
59 3 35351.9 1.0 702.17
63 3 35360.9 1.04 691.47
64 3 35364.9 1.0 697.42
68 3 35366. 1.02 697.91
70 3 35364.7 1.03 698.56
71 3 35365.9 1.01 688.01
72 3 35365.6 1. 693.55
73 3 35364.4 1. 691.04
79 3 35366.8 1.0 689.08
81 3 35364. 1.0 688.01
19 3 35351.7 1.01 688.01
27 3 35353. 1. 691.94
28 3 35349.4 1.01 688.57
Table A.6: Area, thickness and weight information for W plates of the third tray.