Observations of Large Scale Sidereal Anisotropy in 1 and 11 TeV Cosmic Rays from the MINOS Experiment

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1 Observatios of Large Scale Sidereal Aisotropy i 1 ad 11 ev Cosmic Rays from the MINOS Experimet Jeffrey de Jog Oxford Uiversity For the MINOS Collaboratio August 12 th, d ICRC Beijig, Chia

2 Presetatio Outlie Itroductio to the MINOS detectors Cosmic Rays i MINOS the data sample Sidereal Aisotropy & Seasoal Variatios Maths & Measuremets Summary 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 2

he MINOS Detectors (Mai Ijector Neutrio Oscillatio

Oscillatio experimet he two detectors, located i

54 cm Fe Detectors are steel-scitillatig samplig

are positio vertically o We have o acceptace to vertical

o Allows for 3D track recostructio good poitig Average

3 esla (orroidal) o Ca distiguish charge sig of muo

3 he MINOS Detectors (Mai Ijector Neutrio Oscillatio Search) MINOS Is a two detector log base lie Neutrio Oscillatio experimet he two detectors, located i Fermilab, IL ad Souda MN, are fuctioally idetical cm Fe Detectors are steel-scitillatig samplig calorimeters Iterleaved steel-scitillator plaes Plaes are positio vertically o We have o acceptace to vertical muos Scitillatig strips are orthogoal i eighbourig plaes o Allows for 3D track recostructio good poitig Average <B>~ 1.3 esla (orroidal) o Ca distiguish charge sig of muo Extruded PS scit. 4.1 x 1 cm 2 WLS fiber U V plaes +/ Clear Fiber cables Multi-aode PM 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 3

98 ko 5.4 ko Vertical Depth 95 m 730 m Overburde 225mwe 2070 mwe Cosmic rigger Rate 27.5Hz 0.

4 he MINOS Detectors MINOS Is a two detector cosmic ray experimet! Near Detector Far Detector Near Detector Far Detector Dimesios 3.8x4.8x15 m 3 8x8x30 m 3 Mass 0.98 ko 5.4 ko Vertical Depth 95 m 730 m Overburde 225mwe 2070 mwe Cosmic rigger Rate 27.5Hz 0.5 Hz Locatio FNAL, IL Souda, MN I Operatio from March 2005 From August /08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 4

5 Sidereal Aisotropy Expect arrival directio of ~ev cosmic ray primaries to be isotropic. hey origiate i our galaxy Have curvature radii of 1000s of AU i the ~0.1 Galactic Magetic Field (GM) No-uiformities i the GMF serve as scatterig cetres, radomizig their directio 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 5

Sidereal Aisotropy Expect arrival directio of ~ev cosmic ray primaries to be isotropic. hey origiate i our galaxy Have curvature radii of 1000s of AU i the ~0.

6 Sidereal Aisotropy Expect arrival directio of ~ev cosmic ray primaries to be isotropic. hey origiate i our galaxy Have curvature radii of 1000s of AU i the ~0.1 Galactic Magetic Field (GM) No-uiformities i the GMF serve as scatterig bodies, radomizig their directio Several experimets (SuperK, Milagro, IceCube, Argo-YBJ, ibet ASg ) have observed large scale aisotropies i the ev eergy regime. Ca be caused by local magetic fields or cosmic ray sources ARGO-YBJ ICRC 2009 <Ep>~1.1 ev 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 6

7 he MINOS Data Set o measure the sidereal aisotropy of cosmic rays we select a sample of muos which should poit i the directio of the origial primary. Select well recostructed straight muo tracks; Straight tracks have 1. Well recostructed directios i the detector 2. High eergy while traversig the overburde mitigatig multiple scatterig 3. Large surface eergy miimizes bedig i the geomagetic field ad esures the muo poits i the directio of the origial primary Far Detector Near Detector otal Live ime (years) Number of Selected Evets 67.7x x10 9 Mea Surface Eergy(GeV) Mea Primary Eergy (ev) /08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 7

8 Whe usig muos to map out the cosmic ray sky oe eeds to take ito accout the variatio i muo rate due to chages i the atmospheric coditios! R Spurious Aisotropies R A 2Bcos 2 t f cos 2 Nt f C cos 2 N t f Seasoal effect Diural variatio Atmospheric effects Sidereal variatio Atmospheric muos are produced from the decays of secodary mesos (/K) that are produced i the primary cosmic ray shower. Icreasig the atmospheric temperature, decreases desity icreasig the probability of meso decay 3 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 8

9 Whe usig muos to map out the cosmic ray sky oe eeds to take ito accout the variatio i muo rate due to chages i the atmospheric coditios! R Spurious Aisotropies R A 2Bcos 2 t f cos 2 Nt f C cos 2 N t f Seasoal effect Diural variatio Atmospheric effects Sidereal variatio Atmospheric muos are produced from the decays of secodary mesos (/K) that are produced i the primary cosmic ray shower. Icreasig the atmospheric temperature, decreases desity icreasig the probability of meso decay Iterferece betwee yearly ad daily variatios ca create spurious sidereal sigals Ca estimate the magitude by lookig at variatio i ati-sidereal time OR Measure of the temperature variatio above the detector ad correct for it. We take this approach (which essetially sets A=B=0!) 3 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 9

10 Seasoal Variatios here is a strog correlatio betwee the temperature() of the atmosphere ad the muo flux (R m ) measured udergroud. ( X ) eff dx( X ) 0 eff R R m m 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 10

11 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 11 Seasoal Variatios here is a strog correlatio betwee the temperature() of the atmosphere ad the muo flux (R m ) measured udergroud. 0 eff eff ) ( ) ( m m R R X X dx Defie a effective temperature that accouts for the productio poit of muo K N K N W W X W W X X 0 0 eff Where, W,K are the pio weights pertaiig to the ad K cotributio to the overall variatio i muo itesity.

12 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 12 Seasoal Variatios here is a strog correlatio betwee the temperature() of the atmosphere ad the muo flux (R m ) measured udergroud. 0 eff eff ) ( ) ( m m R R X X dx Defie a effective temperature that accouts for the productio poit of muo K N K N W W X W W X X 0 0 eff Where, W,K are the pio weights pertaiig to the ad K cotributio to the overall variatio i muo itesity.

13 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 13 Seasoal Variatios here is a strog correlatio betwee the temperature() of the atmosphere ad the muo flux (R m ) measured udergroud. 0 eff eff ) ( ) ( m m R R X X dx Defie a effective temperature that accouts for the productio poit of muo K N K N W W X W W X X 0 0 eff Where, W,K are the pio weights pertaiig to the ad K cotributio to the overall variatio i muo itesity.

14 Near Detector Seasoal Data he ECMWF collaboratio determies the temperature at 37 pressure levels above our detector at 0000, 0600, 1200 ad 1800 hours every day. Each data poit represets oe six hour period (±0.5K) 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 14

15 Near Detector Seasoal Data he ECMWF collaboratio determies the temperature at 37 pressure levels above our detector at 0000, 0600, 1200 ad 1800 hours every day. Each data poit represets oe six hour period (±0.5K) he muo rate is calculated by evaluatig the uptime i each 6 hour period ad muo coutig. No differece i rate whe detector B- field is flipped(grey vs black) Vertical error bars are statisical 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 15

16 Near Detector Seasoal Data (ND)=0.421±0.004(stat.) ±0.046(syst.) 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 16

17 Far Detector Seasoal Data (FD)=0.886±0.009(stat.) Cosistet with previous PRD publicatio 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 17

18 Measurig Sidereal Aisotropy As the earth rotates, the detector y-axis traces out 360º of right ascesio Create 2D maps of muos, i ra ad dec, at each detector ra scale evet cout to mitigate seasoal variatio Detector RA=(0-1) Detector RA=(90-91) Detector RA=( ) he empty arcs betwee 0 ad 50 are due to zero acceptace for vertical muos. 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 18

Detector RA=(0-1) Detector RA=(90-91) +.

19 Measurig Sidereal Aisotropy As the earth rotates, the detector y-axis traces out 360º of right ascesio Create 2D maps of muos, i ra ad dec, at each detector ra scale evet cout to mitigate seasoal variatio Calculate livetime for each detector ra (scale to average) Detector RA=(0-1) Detector RA=(90-91) & he lifetime i each detector right-ascesio bi varies by ±1%, ot correctig for this would create spurious aisotropies of equivalet magitude i a similar directio. 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 19

Measurig Sidereal Aisotropy As the earth rotates, the detector y-axis traces out 360º of right ascesio Create 2D maps of muos, i ra ad dec, at each detector ra scale evet cout to mitigate seasoal

20 Measurig Sidereal Aisotropy As the earth rotates, the detector y-axis traces out 360º of right ascesio Create 2D maps of muos, i ra ad dec, at each detector ra scale evet cout to mitigate seasoal variatio Calculate livetime for each detector ra (scale to average) he data is expected to be flat i right ascesio, the shape of the decliatio distributio is due to detector acceptace ad muo flux 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 20

21 Quatifyig Aisotropy- Far Detector he level of aisotropy is usually quatified by fittig the projectio oto right ascesio() to a secod order harmoic A 2 A i 1 A1 cos =(8.2±1.7)x f A cos 180 f f 1 =(8.9±12.1) Ca look for large scale aisotropy by searchig for the bi width ad locatio that gives largest sigificace 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 21

22 Quatifyig Aisotropy- Far Detector he level of aisotropy is usually quatified by fittig the projectio oto right ascesio() to a secod order harmoic A 1 f A cos f i 2 A cos A deficit of SD is observed betwee 150º ad 245º Chace probability ~0.0012% A excess of 3.3 SD is observed betwee 275º ad 375º Chace probability ~1.8% Where: SD Observed Expected Expected 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 22

23 Quatifyig Aisotropy- Near Detector he level of aisotropy is usually quatified by fittig the projectio oto right ascesio() to a secod order harmoic A 1 =(3.8±0.5)x A i 1 A1 cos 180 f1 A2 cos 180 f2 f 1 =(27.2±7.2) A deficit of SD is observed betwee 155 ad 225 Where: Observed Expected Chace probability << SD Expected A excess of 7.8 SD is observed betwee 50 ad 140 Chace probability <<0.0001% 12/08/ /03/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 23

24 Aisotropy at the Near Detector he ear detector data sample cotais ~1E9 evets ad allows for a ivestigatio of the aisotropy i two dimesios. his is the Near Detector sky-map whe a 5 smoothig fuctio has bee applied. Each etry represets the total evets i a 10 x10 bi cetred o that poit 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 24

25 Aisotropy at the Near Detector he ear detector data sample cotais ~1E9 evets ad allows for a ivestigatio of the two-dimesioal aisotropy. he level of aisotropy i the Near Detector, where the aisotropy is defied as Observed Aisotropy Expected ad is calculated separately for each decliatio bi 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 25

26 Aisotropy at the Near Detector he ear detector data sample cotais ~1E9 evets ad allows for a ivestigatio of the two-dimesioal aisotropy. he Sigal Stregth of the Near Detector aisotropy i Stadard Deviatios(SD). SD Observed Expected Expected Locatio of excess ad deficit are i similar locatios as idetified by ARGO-YBJ 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 26

27 Summary We have preseted a 1-Dimesioal sky map usig 67.7x10 6 evets collected at the far detector, with a mea primary eergy of ~ 11 ev he level of aisotropy is observed to be of order 0.1% he amplitude ad phase of the first harmoic are : A 1 =(8.2±1.7)x10-4, f 1 =(8.9 ±12.1) We have preseted a 2-Dimesioal sky map usig 0.989x10 9 evets collected at the ear detector with a mea primary eergy of ~1 ev Large regios of excess ad deficits observed are cosistet with ARGO-YBJ We have measured the seasoal variatio of the atmospheric muo flux at the ear ad far detectors (ear)=0.421±0.004(stat.)±0.046(syst.) (far)= 0.886±0.009(stat.); 2009 PRD result 0.873±0.0095(stat.) 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 27

28 Backup Slides 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 28

Cosmic Ray Muos Atmospheric muos are produced from the decays of secodary mesos (/K) that are produced i the primary cosmic ray shower he differetial muo spectrum(gaisser) dn de μ 2.7 pios 0.

29 Cosmic Ray Muos Atmospheric muos are produced from the decays of secodary mesos (/K) that are produced i the primary cosmic ray shower he differetial muo spectrum(gaisser) dn de μ 2.7 pios 0.14Eμ,0 1 = 2 cm s srgev 1.1 Eμ,0cos GeV θ kaos Eμ,0cos GeV θ he probability a high eergy meso decays Pdecay (decay) cem 0, M EM (iteract) Does this make sese? m M cos( ) Costat Icreasig the atmospheric temperature, icreases the probability of decay. Amout of atmosphere does ot chage Icreasig temperature decreases desity Decreased desity meas less material traversed ad cosequetly it s less likely to iteract. 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 29

30 SSystematic Ucertaities Near Detector echique Forward/Backward Parameters of Effective emperature Formula X Weightig r k/ Ecos e e K g Systematic Error /08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 30

31 Seasoal S Variatios vs heory 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 31

32 Aisotropy Algebra 1/ Cout the umber of muos at a particular (ra, dec) ( i,d j ) for a give detector sidereal bi k Nm m m, d 1, d N i Nbis, d, d i j k j 2/ Sum over all the detector sidereal bis i j k m1 R( m k1 i j k K R ) Correctio for atmospheric effects (ie the seasoal variatio) Expected to be small evet by evet correctio Correctio for detector livetime ca be large effect bi by bi correctio 3/ Determie level of aisotropy : A, d i j N i, d j Nd j Nd j Average over all ra i a give decliatio bi (ca also do a sigma sigificace) 4/ Quatify the level of aisotropy A A cos f i 2 A 1 f cos For cosmic rays betwee 1-10 ev: A1~6x10-4, f 1 = /08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 32

33 Near Detector Life ime 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 33

34 Aisotropy i the Far Detector 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 34

35 wo-d Aisotropy Stregths Super-K Aisotropy Locatios MINOS (SD) (alpha,dec) Radius Super K Far Near (75,-5) /-0.020% (205,54) /-0.014% Argo-YBJ Aisotropy Locatios MINOS (SD) (alpha,dec) Radius Argo-YBJ Far Near (65,-10) (120,25) (200,20) 30?? /08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 35

36 ARGO-YBJ Sky Map A 1 =(3.9±0.2)x10-4 f 1 =(60.3±2.7)º A 1 =(6.9±0.3)x10-4 f 1 =(39.3±2.4)º A 1 =(9.3±0.3)x10-4 f 1 =(34.1±2.0)º 0.7 ev 1.5eV 3.9eV Aisotropy results from ARGO-YBJ, 65x10 9 evets 12/08/2011 J.K. de Jog - Sidereal Aisotropy i MINOS 36

Lecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting

Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would