Transcript High Energy Gamma Ray Group

High Energy Gamma Ray Group

Observing Galactic Center & Dark Matter Search
MAGIC Team
Ryoma Murata (UT B3)
Hiroki Sukeno (UT B3)
Tomohiro Inada (Kobe Univ. B3)
Fermi Team
Yuta Sato (TUS B4)
Taketo Mimura (Waseda Univ. B3)
Masahiko Yamada (UT B3)
Introduction
 Target: Galactic Center (Our Galaxy)
 Objective: Activities of Galactic Center
 Gas blob(4MEarth) is approaching the
black hole-> Flare in the near future?
 Dark Matter Search at 133GeV
 cf. C. Weniger 2012
 Data: MAGIC and Fermi analysis
How to Measure (1): MAGIC
Image of Magic Telescope and Signals acquired
How to Measure (2) : MAGIC
How to Measure (3) : MAGIC
Gamma rays vs. Hadron(Proton)
Hadronic components are 1000 times larger than Gamma rays
Low Energy Gamma rays -> difficult to distinguish with Hadron
Centered
Scattered
High Energy Gamma Rays
Hadron (Proton…)
How to Measure: Fermi
Tracker
Analyzing direction
Calorimeter
Measuring energy
Difference between MAGIC and Fermi
EF(>E) (TeV/cm2s)
Sensitivity of Fermi and MAGIC
E(GeV)
Theta Square Plot (High Energy) : MAGIC
θ2
[deg2 ]
Theta Square Plot (High Energy) : MAGIC
Skymap (E > 1 TeV) : MAGIC
Galactic Plane
Galactic Polar
Skymap : Fermi
00
4. 0
2FGL J1731.9-2703c
2.0
2FGL J1739.6-2726
00
Galactic Plane
00
3. 0
2FGL J1728.0-2737c
2. 0
2FGL J1733.4-2812c
0
1.0
Galactic Polar
00
0
1.0
2FGL J1747.3-2825c
00
2FGL J1746.6-2851c
00
0. 0
2FGL J1745.6-2858
0. 0
2FGL J1754.1-2930
00
2FGL J1733.2-2913c
0
35
2FGL J1747.1-3000
9.0
0
-2.
2FGL J1759.4-2954
00
- 1.
2FGL J1738.9-2908
00
2FGL J1748.6-2913
00
2FGL J1731.8-3004
0
-3.
00
2FGL J1745.5-3028c
2FGL J1743.9-3039c
8
35
0.2
2FGL J1740.4-3054c
00
0
0
. 00
0
-4.
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Light Curve : MAGIC
Integral Flux [cm-2 s-1]
500GeV
1TeV
2TeV
Consistent with constant
3/9/2013
MJD(Date)
7/7/2013
Light Curve : MAGIC
 Light Curve combined with new plots
3/9/2013
3/7/2014
30
25
20
15
10
-9
´10
Time Development of Integrated flux
c2 / ndf
9.24.97362 / 89
0.267
0.003426
Prob
p0 1.4223e-08
71e-09
08e-08 ± 1.2198e-09
56300 56320 56340 56360 56380 56400 56420 56440 56460 56480
MJD
8/2/2013
1/1/2013
5
0
Integrated flux : 3-300 GeV [cm-2 s-1]
Light Curve : Fermi
By integrating dN/dE from 3 to 300 GeV
Integrated flux 3 < E > 300 GeV [cm-2 s -1]
Latest Data from Fermi
Integrated flux @ 3 < E < 300 GeV [cm -2 s -1]
30
25
20
15
10
5
0
-9
´10
Time Development of Integrated flux
56300 56350 56400 56450 56500 56550 56600 56650 56700
MJD
Spectrum : Fermi
E^2 dN/dE (TeV/cm^2/s)
10^{-10}
10^{-11}
10^{-12}
1
Seems good,
but bending slightly
Spectrum
10
E (GeV)
dN/dE ~ E-3.00(6)
reduced chi-squared: 1.60
(dof : 6)
E^{-1}
100
Fermi cannot detect higher energy. Is this bending real?
Spectrum: MAGIC & Fermi
Spectrum Fitting : MAGIC & Fermi
MAGIC
Fermi
reduced chi-squared: 7.12
reduced chi-squared: 1.08
Single power law fitting is bad,
but chi-squared has improved significantly assuming two components
By F-test the significance of the two-component model exceeds 5σ
Spectrum Comparison
MAGIC & Fermi Spectrum
Other Known Result
DM Search at 133GeV from Fermi
 Counting ALL events within 3° from Galactic Center
 Assuming Power Low background + Gaussian Peak
 Peak width is 11% of Energy (red)
 Free peak width (blue)
 old data (43 months) & old+new data (56 months)
 C. Weniger claimed that there existed a peak
at 133 GeV in old data
 Local significance (130-140 GeV) from Li&Ma
DM Search from Old Fermi Data
43 months
70
60
50
40
30
20
10
0
70
60
50
40
30
20
10
0
Fit1
p4
p3
p3
p2
p1
p0
3.589 ± 0.871
134 ±± 1.245
135.5
2.388
9.246
3.168 ± 3.078
1.514
-2.988
-3.039 ± 0.1898
0.2054
4.558e+06 ± 4.682e+06
3.552e+06
5.588e+06
33.83 / 30
p0
-2.874 ± 0.1767
2.906e+06 ± 2.128e+06
40 60 80 100 120 140 160 180 200
E (GeV)
p1
40 60 80 100 120 140 Prob
160 180 200 0.2876
E (GeV)
c / ndf
2
Peak at 135.5 ± 2.4 GeV
Local significance: 3.6σ
Co
Count
DM Search from Old + New Fermi Data
56 months
Fit1
40 60 80 100 120 140
p1
p0
9.405±± 1.663
3.085
2.793
-3.06±± 0.1486
0.1382
-3.077
9.719e+06±± 6.311e+06
5.521e+06
1.04e+07
0.07092
0.2445
p2
133.9±± 2.492
1.393
136.5
Prob
p3
3.649 ± 0.7955
42.58 / 30
p4
2
c / ndf
7.092e+06 ± 3.81e+06
180 200 0.06382
E (GeV)
p0
-2.98 ± 0.1298
160
Prob
p1
40 60 80 100 120 140 160 180 200
E (GeV)
Consistent with 136.5 GeV Dark Matter, but the significance has decreased
100
80
60
40
20
0
100
80
60
40
20
0
Peak at 136.5 ± 2.5 GeV
Local significance : 3.3σ
Coun
Count
Conclusion
 We have found two components in the spectrum
 Related to X-ray super Flare 300 years ago?
 Molecule blob Gamma ray
has not reached yet?
 CTA is needed
for the future research


Wider covering range
More statistics
EF(>E) (TeV/cm2s)
 Decrease in the significance of Dark Matter at 133GeV
E(GeV)
Conclusion
 We have found two components in the spectrum
 Decrease in the significance of Dark Matter at
133GeV
 CTA is needed for the future research
Appendix A. Maximum Likelihood Method
 Assuming Poisson Distribution
k -l
pk =
le
k!
 Estimate the total likelihood of the pattern
L = P pki
i
 Maximize via parameters of the distribution
 Or minimize log-likelihood
-ln L
Appendix A. Model Fitting
 For Fermi, we use Maximum Likelihood Method to
determine a fitting model
 Minimum Chi-squared Method is bad due to few
stats
 Result: Point-Like Source Model is better than
Circle-Like Source Model (radius 0.4°) for G.C.
 Ln (Lgood/Lbad )=32
 For MAGIC, we use < 0.2° (the best fit)
Appendix B.
Minimum Chi-squared Method

c =å
2
Minimize chi-squared via parameters of f(x)
( y - f ( x ))
i
i
s
i
2
i
2
σi: expected statistical error

Chi-squared obeys chi-squared distribution χ2(dof) assuming
the statistical error is Gaussian

Chi-squared / dof should be 1



When more than 1, the fitting function is bad
When less than 1, it is suspected to be a fabrication
dof=N-(# of fitting parameters)

Because parameters are not independent of data
Appendix C. F-test
 Compare two fittings (Which is better?)
 F should obey F-distribution assuming the improvement
of fitting is only from the increase in fitting parameters


(null-hypothesis)
Obeys F(Δdof,dofgood)
F=
æ c2 - c2
ö
bad
good
çç
÷÷
è dofbad - dofgood ø
2
c good
dofgood
 When the possibility is lower than expected,
improvement of fitting is NOT from the decrease in dof,
BUT from “dark matter”.
Appendix C. F-distribution
 F-distribution is defined by the quotient of two
independent chi-squared distribution
c12 ( d1 ) / d1
F ( d1, d2 ) = 2
c 2 ( d2 ) / d 2
 F should obey F-distribution assuming the null-
assumption
 When F is in the tale of the distribution, the null
assumption is dismissed (indication of dark matter)
Appendix D. Li&Ma
 Assuming Poisson Distribution
 Compare whole count and background
 Complicated formula from likelihood method
 α is assumed to be 1/2
 From Li & Ma 1983
Theta Square Plot (Middle Energy) :
MAGIC
Theta Square Plot (Low Energy) : MAGIC
How to Measure: MAGIC
 Calibration (auto) electronic signal ->photo
electrons
 Image Cleaning (auto)
 Data Selection (auto)
 Unite Data from Telescopes
 Gamma/Hadron separation
etc…
How to Measure (2) : MAGIC
1. Clean up Signals
2. Parameterize (ellipse shape fitting)
→automatically done
3. Data Selection eg.) Cloud, Moon, Cars…
Skymap from MAGIC E>500GeV
Skymap from MAGIC E>2TeV
Spectrum Fitting :Fermi & MAGIC
Hadronness-Energy distribution: MAGIC
Left: Monte-Carlo simulation for Gamma rays
Right: Background distribution
(Hadron >> Gamma → Background ≒ Hadron)
-> at higher Energy, separation goes well !!
Monte-Carlo simulation for Gamma rays
Background distribution