利用不同背景估计方法对 Mrk421 的观测

查敏，张建立，陈松战(ARGO-YBJ)

2010.04.18

高能物理分会

2

content

工作背景的介绍方法的简介结果和讨论

Introduction: Mrk421 single flare: 10ICrab

ARGO has seen a 4σ effect• 2008/05/02

• 2010/02/18

Whipple

--continued

4

Multi-wave-length Observation of Flares of Mrk421

Method (D.E. Alexandreas NIMA (1993))

Optimize bin size method Non & Nbg estimation + the formula to

estimate statistical significance Background estimation

• Isotropic background from charged cosmic ray;

• Event rate is constant except when changes in the detector configuration are made

• A strong function of zenith angle;

• Event rate may change with experimental conditions

• Detector threshold / dead time

• External changes (e.g. local atmospheric pressure)

• Time-swapping method

• Direct integral method;

• Equi-zenith method

5

)(cos)cos(

7.5

d

dR dtddtRNb )cos(),,(

)(),(),,( tTAtR

Data information

6

•数据 11-13 June 2008 ； •nHit on carpet > 100;•400

时间交换法 (time-swapping) Assumption: A(h,,t) = A(h,,t0)(t), where (t0)

= 1 Effective acceptance map in local coordinate

is tabulated within certain time period (Tw) Artificial background events are created with

the randomly combination of above map and arriving time within this time period;

advantage

• Keep most properties of background parameters

• Time-shuffling length （ Tw ） ?

• Swapping times （ Nsw ） ?

• Possible correction?• 6.4% 180 minutes;

• 6.4% *180./T;

limitation

• Conservative result

• Not applicable to the investigation of high declination sky.

7

8Tw

Sig

nific

ance

()

3h + 10 + 3.8

直接积分法（ Direct Integral ）

E(ha, ): the acceptance distribution in Local Equatorial Coordinates (LEC) for certain period;

R(t): event rate of the detector; (ha,ra,t) is 1 if events falls within this special bin or 0 othersize; limitation

• Time integration period?/ conservative result / Not applicable for the source near the North/South pole;

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dtdtrahatRhaEraN ),,()(),(],[exp

10

4h + 4.4 24h + 4.6

等天顶角法（ Equi-Zenith Method ） Minimize the detecting factors from

detector and environmental variation

• See Source/background at the same time;

• Free from zenith dependence;

• Free from acceptance/ efficiency changes;

• Free from Pressure and tempreture; Limitation:

• Giving up small zenith angle data due to number of off-source windows

• non-uniformity distribution for the azimuth angle

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方位角的不一致性

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•Zenith angle dependence and < 2% •geomagnetic field;•other unknown factrors?

地磁场使带电次级粒子发生偏转，拉宽次级粒子的横向分布，使得芯区粒子密度降低，从而降低了原初簇射的触发率。

地磁场因子

13

)cossinsincos(coscos

cos

sin

1

2

HH

g

Ivanz, CPTL(1998), Zhouyuan (HEP&NP)

1-2%

equi-declination normalization The correction happen within a day; Repeat above measurement 35 times; 35 dummy on-source windows on the orbit has the same

Declination band with the on-source window.

The corrected background is obtained

The uncertainty of signal

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35

1

'

35

1

'

35/

35/j

j

BGj

j

jONj

N

N

BGBG NN *

BGNNS

*

0637.1

15

10 off windows + 5.2

Summary & discussion

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Equi-Zenith Time-swapping Direct Integral

sigma 5.2 3.7 4.4

--continued Differences

• difference from parameters: 0.3-0.4

• From method itself: 0.8 ;

• For a fixed point source “seeing” in 2 ways

(s1-s2)=(1 + 2)1/2 =0.447 (here 1= 2=0.1)

• Here (s1-s2)=0.8, thus not just statistical fluctuations

• Data quality

• Different method may have different dependence on data.

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Direct integral .vs. equi-zenith

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2008 1 year Crab from SongZhan + JianLI

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The optimal smooth angle

58.1

1

)(

1)(

max

2

2

2

2

2

2

N

eca

N

NS

N

eN

N

bkg

s

bkg

S

Non-point source

>1.58σ

~ 1.58σ+Rsource

Point source

Angular resolution of proton

Φ70=1.58σ Nhit>20: 2.90 deg Nhit>60: 1.60 deg Nhit>100: 1.14 deg Nhit>500: 0.56 deg Nhit>1000:0.48 deg

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Equi-Zenith Angle method

Without considering the effect from non-uniform azimuth angle distribution, the number of background events can be estimated as

Azimuth correction:Repeat the above measurement 35 times. Assigned as

This 35 dummy on-source windows on the orbit has the same Decl. with the on-source window.

The azimuth correction factor η is given by

Using error spread law, the statistical error of the excess events in a on-source window is

The number of background are estimated using 10 off-source windows which are at the same zenith angle as the on-source direction in the azimuthal direction.

Detailed information refer to

Finally, the corrected estimation of the number of background events is obtained as