RecentresultsfromtheTibetASγexperiment

TakashiSAKOfortheTibetASγcollabora;on

TeVPA201526October

Contents1) TibetASγexperiment2) Sun’sShadow(10TeV)3) Cosmic-rayAnisotropy(∼10—1000TeV)

The Tibet ASγ Collaboration M. Amenomori1, X. J. Bi2, D. Chen3, T. L. Chen4, W. Y. Chen2, S. W. Cui5, Danzengluobu4, L. K. Ding2, C. F. Feng6, Zhaoyang Feng2, Z. Y. Feng7, Q. B. Gou2, Y. Q. Guo2, H. H. He2, Z. T. He5, K. Hibino8, N. Hotta9, Haibing Hu4, H. B. Hu2, J. Huang2, H. Y. Jia7, L. Jiang2, F. Kajino10, K. Kasahara11, Y. Katayose12, C. Kato13, K. Kawata14, M. Kozai13, Labaciren4, G. M. Le15, A. F. Li16,6,2, H. J. Li4, W. J. Li2,7, C. Liu2, J. S. Liu2, M. Y. Liu4, H. Lu2, X. R. Meng4, T. Miyazaki13, K. Mizutani11,17, K. Munakata13, T. Nakajima13, Y. Nakamura13, H. Nanjo1, M. Nishizawa18, T. Niwa13, M. Ohnishi14, I. Ohta19, S. Ozawa11, X. L. Qian6,2, X. B. Qu2, T. Saito20, T. Y. Saito21, M. Sakata10, T. K. Sako14, J. Shao2,6, M. Shibata12, A. Shiomi22, T. Shirai8, H. Sugimoto23, M. Takita14, Y. H. Tan2, N. Tateyama8, S. Torii11, H. Tsuchiya24, S. Udo8, H. Wang2, H. R. Wu2, L. Xue6, Y. Yamamoto10, K. Yamauchi12, Z. Yang2, S. Yasue25, A. F. Yuan4, T. Yuda14, L. M. Zhai2, H. M. Zhang2, J. L. Zhang2, X. Y. Zhang6, Y. Zhang2, Yi Zhang2, Ying Zhang2, Zhaxisangzhu4, X. X. Zhou7

1Department of Physics, Hirosaki University, Japan 2Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, China 3National Astronomical Observatories, Chinese Academy of Sciences, China 4Department of Mathematics and Physics, Tibet University, China 5Department of Physics, Hebei Normal University, China 6Department of Physics, Shandong University, China 7Institute of Modern Physics, SouthWest Jiaotong University, China 8Faculty of Engineering, Kanagawa University, Japan 9Faculty of Education, Utsunomiya University, Japan 10Department of Physics, Konan University, Japan 11Research Institute for Science and Engineering, Waseda University, Japan

12Faculty of Engineering, Yokohama National University, Japan 13Department of Physics, Shinshu University, Japan 14Institute for Cosmic Ray Research, University of Tokyo, Japan 15National Center for Space Weather, China Meteorological Administration, China 16School of Information Science and Engineering,

Shandong Agriculture University, China 17Saitama University, Japan 18National Institute of Informatics, Japan 19Sakushin Gakuin University, Japan 20Tokyo Metropolitan College of Industrial Technology, Japan 21Max-Planck-Institut fuer Physik, Deutschland 22College of Industrial Technology, Nihon University, Japan 23Shonan Institute of Technology, Japan 24Japan Atomic Energy Agency, Japan 25School of General Education, Shinshu University, Japan

TibetASγ Experiment

AtYangbajinginTibet,China(90.522° E,30.102° N,4,300ma.s.l.)

Scin;lla;onCounterArray:0.5m2x789counters Effec;vearea:∼ 37,000m2Energyregion:∼ TeV-100PeVF.O.V.:∼ 2srRela;ve;mingArrivaldirec+on�

ChargeAngularResolu;on∼0.4° @10TeV

EnergyResolu;on∼70%@10TeVPrimarycosmic-rayenergy

Contents1) TibetASγexperiment2) Sun’sShadow(10TeV)3) Cosmic-rayAnisotropy(∼10—1000TeV)

Sun’s shadow

Earth

TeV charged cosmic rays Larmor radius ~7.4AU (B=30µ G near Earth) ~0.16R☉ (B=300mG near the Sun) Capable of probing the structure of the heliospheric magnetic field

Shielding of cosmic rays by the Sun

Sun

Solar Surface: optical telescopes (Zeeman effect)

@1AU:satellites

Interpolation by models

7

Tibet-III Air Shower Array

p  Tibet (90.522oE, 30.102oN) 4300m a.s.l.

Solar cycle : 11-year period 23rd solar cycle starts from 1996à To keep the AS data consistency from 1996, we use the Tibet-II array configuration (221 detectors, 15m spacing)

p  Modal Energy 10 TeV

p  Angular Resolution 0.9°　　　　　　　　　　　　　　　　　　　　　　　

WestßàEast Northß

àSouth

Angularresolu+on

Op+caldisk

Sun’s shadow > 10TeV

Eclip;clongitude(deg.)

Eclip;cla;tud

e(deg.)

Map of deficit ratio (= deficit / B.G.(%))

4ox4o around the Sun’s optical position Angular resolution (∼0.9o)Optical disk radius (∼0.26o) ∼6% deficit ratio

Year 1996 (Solar min.)

20012002200320042005

1996　19971998 19992000

2006200720082009

Lowsta;s;cs

Solarmin.

Solarmin.

Solarmax.

Experimental data

>10 TeV

DeficitB.G.

(%)

19981997

obsGSE longitude (deg.)

2006

19991996 2000 2002

2005 20072003 2008 2009

2001

2004

0−2.0−5.0−6.0 −1.0−3.0−4.0East West

0

2 1 −1 −2GSE

latit

ude

(deg

.)

0D (%)

Sout

hN

orth

1

2

−1

−2

FIG. 1. Year-to-year variation of the observed Sun’s shadow between 1996 and 2009. Each panel

displays a two-dimensional contour map of the observed flux deficit (Dobs). The map in 2006 is

omitted because of insufficient statistics for drawing a map.

the modal energy of the Tibet-II array configuration are estimated to be 0.9◦ and 10 TeV,

respectively. For the analysis of the Sun’s shadow, the number of on-source events (Non)

is defined as the number of events arriving from the direction within a circle of 0.9◦ radius

centered at the given point on the celestial sphere. The number of background or off-source

events (⟨Noff⟩) is then calculated by averaging the number of events within each of the eight

off-source windows which are located at the same zenith angle as the on-source window

[12]. We then estimate the flux deficit relative to the number of background events as

Dobs = (Non −⟨Noff⟩)/⟨Noff⟩ at every 0.1◦ grid of Geocentric Solar Ecliptic (GSE) longitude

and latitude surrounding the optical center of the Sun.

Shown in Fig. 1 are yearly maps of Dobs in % from 1996 to 2009. We exclude the year of

2006 due to low statistics. Inspection of Fig. 1 shows that the Sun’s shadow is considerably

darker (with larger negative Dobs) around 1996 and 2008 when solar activity was close to

the minimum, while it becomes quite faint (with smaller negative Dobs) around 2000 when

the activity was high.

III. MC SIMULATION

We have carried out Monte Carlo (MC) simulations to interpret the observed solar cycle

variation of the Sun’s shadow. For the primary cosmic rays, we used the energy spectra and

chemical composition obtained mainly by direct observations [10, 13–15] in the energy range

4

Magnetic fields (MC)Geomag. -> Dipole modelIMF -> Parker Spiral Model including latitudinal dependence of solar windCoronal -> Source Surface models (PFSS / CSSS) derived from photospheric MF observation for each Sun rotation (∼27 days)

Maximum(Year 2000)

PFSS

Minimum(year 1996)PFSS

Pictures from K. Hakamada

0=×∇ B

1.  PFSS (Potential Field Source Surface) [widely used]

assumes electric currents are negligible in the corona

Source Surface models (MC)

2. CSSS (Current Sheet Source Surface)

includes large-scale horizontal currents14π(∇×B)×B−∇p− ρGM

r2r̂ = 0

⎥⎦

⎤⎢⎣

⎡

∂∂

Ψ∂−

∂∂

Ψ∂−= φ

φθ

φθη

µˆˆ

sin1)](1[1

22

0 rrr

rJ

φφθ

θθ

η ˆsin1ˆ1ˆ)(

∂

Ψ∂−

∂

Ψ∂−

∂

Ψ∂−=

rrr

rrB

Magnetostatic forcebalance equation

Ψ−∇=B0=⋅∇ B ∇2Ψ = 0

Laplace Equationà

Zhao & Hoeksema, JGR (1995)

Hakamada,SolarPhysics(1995)

Magnetograph (Zeeman Effect)Kitt Peak Vacuum Telescope (FeI 868.8, 630.1 and 630.2nm) Closed

Field

OpenField

ToParkerField

SourceSurface　B is calculated from measured photospheric magnetic fields using Maxwell equation. The source surface is definedas a boundary spherical surface where magnetic field lines become purely radial. Standard Rss=〜2.5R⊙

Density map of events hitting the SunMC takes into account CR composition & spectraDetector response & data analysis

Examples of MC Results

Soalr Minimumin 1996

Solar MaximumIn 2001

PFSS PFSS

20

Moo

n’s

shad

owD

efic

it (%

)Su

n’s

shad

owD

efic

it (%

)

CSSS Rss=10RCSSS Rss=2.5RPFSS Rss=2.5R

c

b

a

Suns

pot n

umbe

r

Year

−1−2−3−4−5−6

1996 1998 2000 2002 2004 2006 2008 2010

180

140

100

60

−5−4

−2−1

−3

−6

Sun’s Shadow : yearly variation >10TeV

14

From the MC simulations of the Sun’s shadow, wecalculate the central deficit (DMC) equivalent to Dobs byDMC ¼ "Nhit=Nall for each coronal field model where Nall

is the number of all initial shooting directions withinthe 0.9# circle centered at the Sun and Nhit is the numberof events hitting the Sun. The blue triangles, greensquares, and red circles show DMC assuming the PFSS(Rss ¼ 2:5RJ), the CSSS (Rss ¼ 2:5RJ), and the CSSS(Rss ¼ 10:0RJ) models, respectively. For quantitativecomparisons between observations and the MC expecta-tions in Fig. 3(b), we perform a !2 test as

!2 ¼X14

i¼1

ðDiobs "Di

MCÞ2ð"i

obsÞ2 þ ð"iMCÞ2 þ h"sysi2

; (1)

whereDiobs andD

iMC are the observed and predicted central

deficits for the ith year from 1996, while "iobs and "

iMC are

their respective (statistical) errors. The results of the !2 testare summarized in Table I. For the PFSS model, the !2

yields a very low likelihood of 4:9' 10"5 since the MCsimulations assuming the PFSS model yield too smallDMC

to explain the observed deficit shown in Fig. 3(b).The difference is particularly significant in 1996 and1997. On the other hand, the predictions assuming theCSSS model (green squares) are in good agreement withthe observations. Furthermore, we also find that the CSSSmodel with Rss ¼ 10:0RJ shown by red circles gives,overall, an even better agreement than the case with

Rss ¼ 2:5RJ . We note that the PFSS model assumingRss ( 2:5RJ was omitted from simulations, because thismagnetic field is dominated by the unrealistic closedfield lines.The model dependence of the predicted deficits in the

MC simulation can be interpreted in terms of the cosmic-ray trajectories in the different magnetic field models.Figure 4 shows sample trajectories in heliocentric Earthecliptic (HEE) coordinates of antiparticles hitting the Sunin CR1910 (Year 1996) in three cases we consider: (a) thePFSS (Rss ¼ 2:5RJ), (b) the CSSS (Rss ¼ 2:5RJ), and(c) the CSSS (Rss ¼ 10:0RJ) model. The same numberof antiparticles are ejected from Earth in each simulationwith the modal energy of 10 TeV similarly to analyzed AS

20M

oon’

s sh

adow

Def

icit

(%)

Sun

’s s

hado

wD

efic

it (%

)

CSSS Rss=10RCSSS Rss=2.5RPFSS Rss=2.5R

(c)

(b)

(a)

Sun

spot

num

ber

Year

−1−2−3−4−5−6

1996 1998 2000 2002 2004 2006 2008 2010

180

140

100

60

−4

−2−1

−3

−6−5

FIG. 3 (color online). Temporal variations of (a) the monthlymean sunspot number [24], (b) the deficit intensity due to theSun’s shadow, and (c) the deficit intensity due to the Moon’sshadow. The open squares in the panel (b) are the observedcentral deficit (Dobs). The blue triangles, green squares, and redcircles indicate the central deficits (DMC) by the MC simulationsassuming the PFSS (Rss ¼ 2:5RJ), the CSSS (Rss ¼ 2:5RJ ),

and the CSSS (Rss ¼ 10:0RJ) models, respectively. The dashed

lines in the panels (b) and (c) are the deficits expected from theapparent angular size of the Sun and the Moon.

TABLE I. Results on the !2 test for the consistency betweendata and MC models using the systematic error (only thestatistical error).

MC models !2=DOFa Probability

PFSS Rss ¼ 2:5RJ 44:5ð55:2Þ=14 4:9' 10"5ð7:9' 10"7ÞCSSS Rss ¼ 2:5RJ 21:1ð26:2Þ=14 0.099(0.024)

CSSS Rss ¼ 10RJ 8:3ð10:3Þ=14 0.87(0.74)

a!2 is defined in Eq. (1) and DOF means degrees of freedom.

(b)

x (Solar radii)

CSSS Rss=10R(c)6

z (S

olar

rad

ii)

4

1086420−2−6

−4

−2

0

2

4

6

x (Solar radii)x (Solar radii)

−2

2

0

−4

−6−2 0 2 4 6 8

1086420−2−6

−4

−2

0

4

2

6(a) PFSS Rss=2.5R

10

CSSS Rss=2.5R

z (S

olar

rad

ii)

FIG. 4 (color online). Simulated trajectories of antiparticlesejected toward the Sun from the Earth in CR1910 (year 1996)presented in HEE coordinates. Only trajectories of antiparticleshitting the Sun are plotted. The three panels refer to simulationsassuming (a) the PFSS (Rss ¼ 2:5RJ ), (b) the CSSS (Rss ¼2:5RJ ), and (c) the CSSS (Rss ¼ 10:0RJ ) model, respectively.

The inner solid and outer dashed circles indicate the size of thephotosphere and the SS, respectively.

PRL 111, 011101 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending5 JULY 2013

011101-4

DataMC

PFSS:unrealis;c(χ2/d.o.f. = 55.2/14)CSSS:OK(χ2/d.o.f. = 10.3/14)

Sun’sShadow:Summary● ObservedSun’sshadowfrom1996to2009 @10TeV(23rdcycleofsolaractivity)

●  FoundthatSun’sshadowissensi;vetosolarcoronalmagneticfieldstructures

●  FoundthattheCSSS(CurrentSheetSourceSurface)modelwellreproducestheyearlyvariationoftheSun’sshadow

Reference: M. Amenomori et al., Phys. Rev. Lett., 111, 011101 (5pp) (2013)

FirstsuccessfulaIempttoevaluatetheSun’scoronalMFmodelsusingtheSun’sshadow

Contents1) TibetASγexperiment2) Sun’sShadow(10TeV)3) Cosmic-rayAnisotropy(∼10—1000TeV)

RightAscension(°)

Large-scalesiderealanisotropymap(>7TeV)De

clina;

on(°)

Rela;veintensity

Sidereal

0360

+0.15%

-0.15%

Tail-InLoss-Cone

★heliotail

+80

-20

M.Amenomorietal.,Astrophys.SpaceSci.Trans.,6,49(2010)M.Zhangetal.,ApJ,790,5(2014)N.A.Schwadronetal.,Science,343,988(2014)X.B.Quetal.,ApJL,750,L1(2012)

Possiblemodels:

Global Anisotropy Model90° < 120° < 180°

Bi-directional flow (BDF) + Uni-directional flow (UDF)

~120°

GlobalAnisotropyModelBi-Directional Flow

(BDF)Uni-Directional Flow

(UDF)

a2//

α2

δ2 a1//a1⊥

(α1, δ1)

BDF reference axis(α2, δ2)

α :rightascensionδ :declina;on

χ 1,2:angulardistancefromtheaxis(α1, δ1) or(α2, δ2) BDF

UDF

(α1, δ1) ⊥ (α2, δ2)

+4σ

+0.15%

-0.15%

Intensitymap(data)

Galac+cplane

RightAscension(°)

Residualsignificancemap(data-model)

Galac+cplane

B:best-fitBDFreferenceaxis

+0.15%

-0.15%

-4σ

ModelFiingresults >7TeV

0

360

360

0

Declina+

on(°)

-20

+80

-20

+80Intensitymap(best-fitmodel)

-20

+80

B GF

Frischetal.,arXiv:1206.1273v1(2012)Grygorczuketal.,ApJL,727,L48(2011)F,G:localinterstellarmagne+cfieldorienta+onby:

B GFheliotail

heliotail

heliotail

Galac+cplane

Galac+cplane

L=RL/a1⊥ ∼ 2pc

Discussion:GlobalAnisotropy(1)

UDF(Bx∇n)

a1⊥ (%) a1//(%) a2// (%) α1(°) δ1(°) α2(°) δ2(°)

0.139±0.002 0.007±0.002 0.131±0.004 33.3±1.1 38.4±1.2 279.9±0.9 26.7±2.0

>7TeV

For7TeVcosmicrays,LarmorradiusRL∼ 0.002pc(in3µG)scameringm.f.p.λ//∼ 3pc(MoskalenkoV.etal,ApJ,534,825(2000))Bohmfactorλ//÷RL∼ 1500>>1∴ perpendiculardiffusionisnegligible.

(L:scaleofdensitygradient∇n)

a1//<<a1⊥ UDF⊥BDF,thus⊥LISMFa1⊥ ∼ a2//UDF∼BDFinamplitude

u BDF(Bi-Direc;onalFlow):cosmic-rayinflowalongthelocalinterstellarmagne;cfield(LISMF)

u UDF(Uni-Direc;onalFlow)

Diamagne;cdripcausedbythecosmic-raydensitygradientinLISMF

Localinterstellarspace(∼2pc)surroundingtheheliospherewouldberesponsibleforGlobalAnisotropy.

BDF

LISMF

LIC

Ø LISMFiscompressedintheregionbetweenLICandGcloud,causingmagne;c-mirroreffectthatgeneratesBDF.Ø Adiaba;cexpansionofLICmakesCRnumberdensitywithinLICsmallerthanoutside,crea;ngasteady∇n.Ø Diamagne;cdripbyCRdensitygradientinLISMFcreatesUDF.

Discussion:GlobalAnisotropy(2)LocalInterstellar

Cloud

Hypotheses

Lallement et al., Science, 307, 1447 (2005)Redfield & Linsky, ApJ, 534, 825 (2000)

15TeV

50TeV

100TeV

300TeV

1000TeV

Transi;onofthelarge-scalesiderealanisotropy (10TeV—1000TeV)

Above∼300TeV・GlobalAnistropyModelnolongerapplicable・Anisotropyorigina;nginspacefartherthan　afewparsecssurroundingheliosphere

M.Amenomorietal.,ICRC2015(id355)3600

EnergyDependenceofAmplitude&Phase(first-orderharmonicfiing)

thiswork

thiswork

100TeV1000TeV

100TeV1000TeV

Large-scalesiderealanisotropy:Summary

Inthelocalinterstellarspace(∼2pcfor7TeVcosmicrays)Combina;onofthebi-direc+onalinflowalongthelocalinterstellarmagne;cfieldandtheuni-direc+onalflowofthediamagne;cdripcausedbythecosmic-raydensitygradientinit.

Originofthegalac;ccosmic-rayanisotropy

M.Amenomorietal.,Astrophys.SpaceSci.Trans.,6,49–52,(2010)

Ourmodel

u Above∼300TeV—Modelinspacefartherthanafewparsecssurroundingheliospheremustbeconsidered

u TeVenergies