July 17, 2017 ICRC2017 Charge-sign dependence in the solar modulation during the solar cycle 23 Shoko Miyake (NIT, Ibaraki Col., Japan.) Shohei Yanagita (Ibaraki Univ., Japan) Good afternoon. In this study, We tried to develop a model for the solar modulation that reproduce a charge-sign dependence observed by BESS and PAMELA.

July 17, 2017 ICRC2017 Introduction Charge-sign dependence in the solar modulation is caused by the drift motion of GCRs. We developed the model for the solar modulation of GCRs on the basis of the drift model. Our results of the charge-sign dependence in the solar modulation are compared with the energy spectra of the GCR protons and antiprotons observed by BESS and PAMELA during the solar cycle 23. As you know, the solar modulation has a charge-sign dependence caused by the drift motion of the galactic cosmic rays. In this study we have developed the numerical model for the solar modulation on the basis of the drift model to study quantitatively the charge-sign dependence. In the last solar cycle, the long term observations of multiple GCRs have been performed by BESS and PAMELA. These observations entirely cover the solar minimum, the solar maximum, and the solar magnetic polarity reversal. So, these observations provide a crucial test of a charge-sign dependence of the solar modulation. We calculated the solar modulation of protons and antiprotons during the last solar cycle and compared our results with these observations. BESS PAMELA

Outline Introduction Overview of our model Results Summary July 17, 2017 ICRC2017 Outline Introduction Overview of our model Results Energy spectrum of GCR protons and antiprotons Antiproton/proton ratio Summary This is outline. Next, I talk about overview of our model for the solar modulation.

Overview of our Model 3D numerical simulation of the solar modulation July 17, 2017 ICRC2017 Overview of our Model 3D numerical simulation of the solar modulation based on the stochastic differential equation (SDE) adopting fully anisotropic diffusion process considering variations of Vsw, B1AU, and tilt angle of HCS Stochastic Differential Equation (Yamada, Yanagita and Yoshida 1998) (Zhang 1999) We performed a full 3D numerical simulation of the solar modulation. This model is based on the stochastic differential equation equivalent to the Parker’s transport equation. We considered the diffusion, convection, drift motion, and the adiabatic energy losses. The drift velocity along the heliospheric current sheet are calculated by using approximate function proposed by Burger and Potgieter. position of pseudo particle Wiener process given by a Gaussian distribution HCS drift velocity: approximate function (Burger and Potgieter, 1989)

Overview of our Model 3D numerical simulation of the solar modulation July 17, 2017 ICRC2017 Overview of our Model 3D numerical simulation of the solar modulation based on the stochastic differential equation (SDE) adopting fully anisotropic diffusion process considering variations of Vsw, B1AU, and tilt angle of HCS Diffusion Coefficient This is the diffusion coefficient considered in this calculation. It is fully anisotropic and the parameters are iteratively searched so that our results are largely consistent with the observations. We found that, to reproduce the observations, the diffusion coefficient in the polar angle direction has to change with the polar angle so that has large values at the heliospheric polar region. Necessity of this consideration is consistent with the findings by the studies of latitudinal gradient of GCRs observed by Ulysses. But the detailed function is different with our model.

Overview of our Model 3D numerical simulation of the solar modulation July 17, 2017 ICRC2017 Overview of our Model 3D numerical simulation of the solar modulation based on the stochastic differential equation (SDE) adopting fully anisotropic diffusion process considering variations of Vsw, B1AU, and tilt angle of HCS Heliospheric Model Isotropic solar wind speed Standard Parker spiral HMF Radial dependent tilt angle of the heliospheric current sheet (HCS) And we also considered the variations of the solar wind speed, the magnitude of the heliospheric magnetic fields, and the tilt angle of the heliospheric current sheet. As the simple model, we assumed an isotropic solar wind speed and the standard Parker spiral HMF. On the other hand, we precisely reproduce the structure of the heliospheric current sheet. This is because the drift motion along the current sheet strongly affect the charge-sign dependence of the solar modulation. The tilt angle of the current sheet changes with not only the time but also the radial distance from the Sun

Outline Introduction Overview of our model Results Summary July 17, 2017 ICRC2017 Outline Introduction Overview of our model Results Energy spectrum of GCR protons and antiprotons Antiproton/proton ratio Summary BESS97〜BESS Polar II PAMELA Now, I'll show our results. We made a calculation and a comparison with the observations of the energy spectra of protons and antiprotons from 1997 in which the solar minimum at a positive magnetic polarity to the 2009 in which the solar minimum at a negative magnetic polarity. Year Solar Min. (A>0:Positive) Solar Max. Solar Min. (A<0:Netative)

Energy Spectrum of GCR Protons and Antiprotons July 17, 2017 ICRC2017 Energy Spectrum of GCR Protons and Antiprotons These are our results of the energy spectra of protons and antiprotons and the observations corresponding each result. We can find that our results are largely consistent with the observations by BESS and PAMELA except for a few observations.

Energy Spectrum of GCR Protons and Antiprotons July 17, 2017 ICRC2017 Energy Spectrum of GCR Protons and Antiprotons Solar Min. A>0:Positive Solar Max. 1997 (BESS97) 1998 (BESS98) 1999 (BESS99) 2000 (BESS00) These are the energy spectra of protons and antiprotons in a each year in which a positive magnetic polarity from the solar minimum to the solar maximum. We succeeded to reproduce the most of the energy spectra.

Energy Spectrum of GCR Protons and Antiprotons July 17, 2017 ICRC2017 Energy Spectrum of GCR Protons and Antiprotons Solar Min. A>0:Positive Solar Max. 1997 (BESS97) 1998 (BESS98) 1999 (BESS99) 2000 (BESS00) Solar maximum But there are some discrepancies with the observations; the spectrum of protons in 2000, and the spectra of antiprotons in 1998 and 1999. The year 2000 was in the solar maximum and we assumed that the magnetic polarity reversal occurred just before the time in which the observation by BESS was performed. So it is reasonable that our model considering simple and standard magnetic field is hard to reproduce the observations in such a special phase. As for the discrepancies in the transition period for the qA negative charge-sign phase, it seems that we need a further verification. Transition period for qA<0

Energy Spectrum of GCR Protons and Antiprotons July 17, 2017 ICRC2017 Energy Spectrum of GCR Protons and Antiprotons Solar Max. A<0:Negative Solar Min. 2002 (BESS02) 2004 (BESS-Polar I) 2007 (BESS-Polar II) 2006~ (PAMELA) Next, these are the energy spectra in these years, in which the negative magnetic polarity from the solar maximum to the solar minimum.

Energy Spectrum of GCR Protons and Antiprotons July 17, 2017 ICRC2017 Energy Spectrum of GCR Protons and Antiprotons Solar Max. A<0:Negative Solar Min. 2002 (BESS02) 2004 (BESS-Polar I) 2007 (BESS-Polar II) 2006~ (PAMELA) Transition period for qA<0 We can see large discrepancy with the observations of protons in 2004. 2004 is also in the transition period for a qA negative charge-sign phase. So we conclude that our model fails to reproduce the energy spectrum at the transition period for the qA negative charge-sign phase. This implies that there is any physical reason that is not considered in our model.

Antiproton/proton ratio July 17, 2017 ICRC2017 Antiproton/proton ratio These are our results of the antiproton/proton ratios and those time profiles from 1995 to 2010. We can find that our results reproduce the quick increase of the ratio in 2000 in which the magnetic polarity reversal occurred. This is caused by the charge-sign dependence of the solar modulation.

July 17, 2017 ICRC2017 Possible reasons for the discrepancy of the flux at the transition period for qA<0 (Negative) Solar wind speed (Vsw) HMF strength (B1AU) Tilt angle of HCS (α) Finally let’s discuss the possible reasons for the discrepancy of the flux at the transition period for the qA negative charge-sign phase. In our calculation, we considered the variations of the solar wind speed, the HMF strength, and the tilt angle of the current sheet. These energy spectra show the effects of these three parameters on the solar modulation. We can find that the largest change of flux in the qA negative charge-sign phase shown by this blue area is caused by the variations of the tilt angle of the current sheet. So, we think that the discrepancy of the flux at the transition period for the qA negative charge-sign phase could be related with the current sheet.

July 17, 2017 ICRC2017 Possible reasons for the discrepancy of the flux at the transition period for qA<0 (Negative) CS in the heliosheath Latitudinal dependence of Vsw (Florinski, AdSpR, 2011) (McComas, GRL, 2008) Although the consideration is insufficient, we have two ideas for the possible reasons now. One is the current sheet in the heliospheath. As Florinski discussed, the current sheet in the heliosheath may play a important role of the modulation in the heliosheath. If it is true, there could be a change of the energy spectrum at the termination shock where we set the local interstellar spectrum. As another possible reason, we suspect the effect of the latitudinal dependence of the solar wind speed on the structure of the heliospheric current sheet. Ulysses observed the strong latitudinal dependence of the solar wind speed at the solar minimum. There is a possibility that these latitudinal dependence would be still remain in the middle phase of the solar cycle. If it is true and the current sheet flare out into the region where the high speed solar wind exist, there could be a change of the structure of the HCS. These are just ideas. To clarify these possible reasons, we should need further verifications. There could be any change of the energy spectrum at TS… There could be any change of the structure of the HCS…

Summary We developed the model of the solar modulation July 17, 2017 ICRC2017 Summary We developed the model of the solar modulation based on the SDE adopting anisotropic diffusion process considering variations of Vsw, B1AU, and tilt angle of HCS Necessity of consideration of the latitudinal dependence of the diffusion coefficient in the polar angle direction is consistent with the findings by the studies of latitudinal gradient of GCRs observed by Ulysses. The energy spectra of GCR protons and antiprotons observed by BESS and PAMELA are largely reproduced except for the discrepancy at the transition phase for qA<0. The discrepancy of the flux at the transition phase could be caused by the complex physics of the HCS that cannot explain by the standard Parker-spiral HMF. Further verification should be necessary to clarify the possible reasons of the discrepancy of the flux at the transition phase. This is the summary and I’ll skip to say. Thank you very much.

July 17, 2017 ICRC2017 Backup

AMS-02 Measurement of GCR protons: May 2011 ~ Nov. 2013 July 17, 2017 ICRC2017 AMS-02 (Aguilar et al., PRL, 2015; Aguilar et al., PRL, 2016) Measurement of GCR protons: May 2011 ~ Nov. 2013 Measurement of GCR antiprotons: May 2011 ~ May 2015 AMSがtime profileをもうすぐ出すから、それを使ってour modelをさらに検証したい。 ただし今はpositive magnetic fieldなので、protonのtime profile がでても検証できない。 electron、もしくはantiprotonのようなnegative charged particle のデータが必要であり、CALETのデータを使った検証も有効だと思っている。 また現在、MHDシミュレーションによる精密な太陽圏環境とSDEのカップリングによる研究も進めている。 この研究はHCSを精密に再現するモデルであることが大きな特徴であって、MHDシミュレーションが実現した段階でHCSの構造の変化が起きるのかどうかを知ることができるし、そこでの太陽変調を計算することで定量的な検証を行うことができる。

Antiproton/proton ratio July 17, 2017 ICRC2017 Antiproton/proton ratio 1997 (BESS97) 1998 (BESS98) 1999 (BESS99) 2000 (BESS00) 2002 (BESS02) 2004 (BESS-Polar I) 2007 (BESS-Polar II) 2006~ (PAMELA) These are antiproton/proton ratio corresponding each observation. As I already told, our calculation failed to reproduce the energy spectrum at the transition period for the negative charge-sign phase. We can see the discrepancy between our result and the observation at 2004, too. But it seems that the discrepancies at 1998 and 1999 are small. This is because of the discrepancies of the flux of antiprotons are smaller than that of protons.

July 17, 2017 ICRC2017 Possible reasons for the large diffusion coefficient of polar angle direction at the heliospheric polar region Fisk-type HMF caused by the differential rotation of the Sun Large magnitude of the randomly-oriented transverse magnetic fields (Fisk, ApJ, 1999) (Jokipii and Kota, GRL, 1989) どうして磁場のべき指数にtheta依存性を入れたのか、対策 This may suggest the Fisk-type HMF caused by the differential rotation of the Sun [25, 26], in which the structure of the magnetic field is different with that of the Parker-Spiral HMF at the polar region. As other possible reason of the large diffusion coefficient of the polar angle direction, one could expect the magnetic field near the pole that is dominated by the randomly-oriented transverse magnetic fields with magnitude much larger than that of the Parker-Spiral HMF

Latitudinal gradient of GCR protons observed by Ulysses spacecraft July 17, 2017 ICRC2017 Latitudinal gradient of GCR protons observed by Ulysses spacecraft (Burger and Potgieter, JGR, 2000)

Local Interstellar Spectrum July 17, 2017 ICRC2017 Local Interstellar Spectrum LIS at the termination shock where r=100AU is assumed to be constant. The LIS of GCR protons Jp has a similar energy dependence with a LIS that is in agreement with the flux of GCR protons measured by Voyager 1 in the outer heliosphere, though we modified it so that the flux of the high energy protons consists with the data measured by BESS-TeV. The LIS of GCR antiproton Jpbar that has the same power-law index at high energy region is assumed.

Drift Motion of the GCRs July 17, 2017 ICRC2017 Drift Motion of the GCRs Charge sign dependence is caused by the drift motion qA>0 (Positive;+) qA<0 (Negative;-) 1 GeV proton flux Positive(+) Flat Before moving to the next topic, I'd like to talk about the effect of the drift motion of the GCRs. The GCRs drift along the magnetic field by following the curvature-gradient drift motion. So the drift motions affect the trajectories of the GCRs in the heliosphere. These two panels show the trajectories of the charged particles in the heliosphere. If the combination of the particle charge q and the polarity of the magnetic field A is Positive, the particle propagate along the polar region from the heliospheric boundary and go away along the the heliospheric current sheet that exist around the equatorial plane. So, in the positive polarity, the particles can reach near the earth without being affected by the structure of the current sheet. However, in the case of the Negative polarity, the particles are strongly affected by the structure of the current sheet, because the drift motion turn into the opposite direction. At the solar minimum, the current sheet exist around the equatorial plane. But at the solar maximum, the current sheet trails almost throughout the heliosphere. So, the GCR flux at the negative polarity changes drastically during the solar cycle. These features causes the charge sign dependences of the solar modulation, and we obtained the results of predictions that has the charge sign dependence. For the discussions, please keep in your mind the two points of charge sign dependence. One is, at the solar minimum, the flux at the positive polarity is smaller than that at the negative polarity. The second is, the variations of the flux at the positive polarity has a flat profile, but sharp profile at the negative polarity. Sharp Negative(-) Flux(+) < Flux(-) at solar min. Flat Profile (+); Sharp Profile (-)