Models of cosmic ray modulations in light of new data from AMS-02

Nicola Tomassetti
Models of cosmic ray modulation
in light of new data from AMS-02
with B. Bertucci, E. Fiadrini
Perugia University & INFN
Solar Energetic Particles, Solar Modulation and Space
Radiation: new opportunities in the AMS Era #3
23-26 April 2018 – Washington DC, USA

Galactic CR
Solar wind
Motivations
For Solar physicists
Aim: understanding CR transport in heliosphere.
Approach: physically motivated models of CR transport.
For GCR/DM physicists
Aim: unveiling the LIS’s of
particles and antiparticles
Approach: Minimal models
(parameters & CPU time)
For Space scientists
Aim: reliable and predictive
evaluations for space missions
Approach: Effective data-driven
models for forecasting.

Time dependent
INTERSTELLAR
Energy dependent Particle dependent
Space dependent
MODULATED
SSN
0
100
200
300 MONTHLY
SMOOTHED
Time (year)
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
NMrate(Hz)
80
90
100
110
OULU JUNG
NEWK KIEL
à Need of multichannel & time-resolved data
Basic phenomenology
à Connection with Sun’s magnetic activity
Tomassetti – SEP2018 - DC USA

Jan,01
2004
Dec,31
2005
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2008
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2016
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2017
SSN
0
50
100
150
200
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2004
Dec,31
2005
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2008
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2009
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2012
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2013
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(deg)a
0
20
40
60
80
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2004
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2005
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2009
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2013
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T)µPBF(
-100
0
100
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2005
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2012
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2013
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V(km/s)
300
400
500
600
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2005
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2009
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2013
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)-3
n(cm
0
5
10
ü Real time
ü In situ
Monthly number of sunspot [#]
Tilt-angle of the current sheet [deg]
Strength of the polar magnetic field [uT]
Solar wind plasma speed [km/s]
Solar wind plasma density [N/cm3]
• Sun’s properties and how they evolve with time
• Properties of the interplanetary plasma
Monthly
Smoothed
Model L
Model R
NORTH / SOUTH
WIND SPEED
DENSITY
Solar-activity observations
SIDC – Royal observatory of Belgium
WSO – Wilkox Solar Observatory -Stanford
WSO – Wilkox Solar Observatory -Stanford
NASA OMNIWeb spacecraft data (ISEE3, ACE)
NASA OMNIWeb spacecraft data (ISEE3, ACE)

ü NM ground data: good time-resolution. Unresolved in energy and particle.
ü CR data from space: energy-, particle-, and time- resolved.
Nuclei
Important source of radiation
To assess radiation dose
Cosmic ray data
Protons
Dominant in GCRs. Best data.
To probe GCR transport
Messengers for new physics
Precious source of information
Antiparticles

Observational milestones
1. Very first data from interstellar space
Voyager-1
Voyager 1
Voyager 2
Cummings et al. ApJ 831, 18, 2016
Eliosphere
Eliopause
Termination shock
GCRs
Interstellar space
Solar wind
Bow shock
1

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0
500
1000
1500
2000
)-1
sr-1
s-2
m-1
J(GeV
EPHIN/SOHO PAMELA
BESS-Polar I/II AMS-02
A<0 A>0[ 1-1.5 GeV ]
2. Time-resolved proton data
AMS-02, PAMELA, SOHO
PAMELA
Martucci et al. ApJ 854, L1, 2018
Monthly-resolved, 2006-2014
-> Munini talk
EPHIN / SOHO
Kuhl et al. Solar Phys. 291, 965, 2016
Yearly resolved, 1996 - 2015
AMS-02
Aguilar et al. in progress, 2018
Monthly resolved, 2011-2017
-> Consolandi talk
2 Observational milestones

AMS-02 data on proton,
helium, and p/He ratio
[2018, preliminary]
The ratio between
proton and helium
fluxes at the same
rigidity value is
not constant at
rigidity below ~3 GV
3. Long-term behavior of the p/He ratio
AMS-02

The decrease of the p/He ratio coincides with the flux recovery phase
AMS-02
3. Long-term behavior of the p/He ratio

PAMELA, e+/e-, Adriani et al. PRL 241105, 2016
AMS-02, electron and positron [2018, preliminary]
Gradual change of the e+/e- ratio after the solar polarity reversal.
Evidence for charge-sign dependent solar modulation.
10
4. Antimatter/matter ratios
AMS-02, PAMELA
4
• AMS-02
Observational milestones

Flux Diffusion Convection Particle drift Energy losses
@f
@t
= r · [K·rf] V · rf hvDi · rf +
1
3
(r · V)
@f
@ ln p
+ Q(r, p, t)
New insights on CR modulation models
Source
captures the whole phenomenology of CRs in the heliosphere
Parker spiralParker Solar Probe Parker Eugene
Parker equation

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SSN
1
10
2
10
3
10
Monthly SSN
Smoothed SSN
(t)S
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TiltAngle(deg)
0
20
40
60
80 Model-L
Model-R
Smoothed Model-R
(t)a
α( t )= ˆα( t − ΔT )
ˆα( t )
ˆs( t )
κ( t )= a⋅log10
( ˆs( t − ΔT ))+b
χ2
= χ2
( a,b,Δt )
Global fitting using CR data from space
Use “retarded” physics inputs
Tilt angle
Number of sunspots
Insights from CR protons: time lag
Connect model parameters to solar-activity data à
Flux Diffusion Convection Particle drift Energy losses
@f
@t
= r · [K·rf] V · rf hvDi · rf +
1
3
(r · V)
@f
@ ln p
+ Q(r, p, t)
Source
K-scaling
parameter
Tilt-angle
parameter
Parker eq.

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k(t
t1
)
<latexit
sha1_base64="+IsQy0aYDbQToXrWQCWgzOLTXcE=">AAACGXicbVDLSgMxFM34dnxVXboJloIuLDMiqLuiG5cKthU6ZchkbjU0kxmTO0IZ+h1u/BU3LlRc6sq/MX0stPVA4OSce0nOiTIpDHretzMzOze/sLi07K6srq1vlDa3GibNNYc6T2WqbyJmQAoFdRQo4SbTwJJIQjPqng/85gNoI1J1jb0M2gm7VaIjOEMrhSW/0giLIGF4p5OiKVTc77uV7h7u00DBPeUIrr0dBDFIZBRDfz8slb2qNwSdJv6YlMkYl2HpM4hTniegkEtmTMv3MmwXTKPgEvpukBvIGO+yW2hZqlgCpl0Mo/VpxSox7aTaHoV0qP7eKFhiTC+J7OQghJn0BuJ/XivHzkm7ECrLERQfPdTJJcWUDnqisdDAUfYsYVwL+1fK75hmthFtXFuCPxl5mtQPq6dV7+qoXDsbt7FEdsgu2SM+OSY1ckEuSZ1w8kieySt5c56cF+fd+RiNzjjjnW3yB87XD+acnxU=</latexit>
<latexit
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k(t
t2
)
<latexit
sha1_base64="IN9cRMacJBT62kO3jHcX8UK5gNs=">AAACKnicbVBNS8NAEN34bfyqevSyWArtwZIUQb2JXjwq2FZoSthsprp0s4m7E6GE/h8v/hUPelDx6g9xW3uw1QcLb96bYXZelElh0PM+nLn5hcWl5ZVVd219Y3OrtL3TMmmuOTR5KlN9EzEDUihookAJN5kGlkQS2lH/fOS3H0AbkaprHGTQTditEj3BGVopLJ1VWmERJAzvdFK0hYqHQ7fSr2KNBgruKUcYlwdBDBIZxdCvuVN1oxaWyl7dG4P+Jf6ElMkEl2HpJYhTniegkEtmTMf3MuwWTKPgEoZukBvIGO+zW+hYqlgCpluMbx3SilVi2ku1fQrpWP09UbDEmEES2c7RVWbWG4n/eZ0ce8fdQqgsR1D8Z1EvlxRTOgqOxkIDRzmwhHEt7F8pv2Oa2Yi0cW0I/uzJf0mzUT+pe1eH5dOzSRorZI/skyrxyRE5JRfkkjQJJ4/kmbyRd+fJeXU+nM+f1jlnMrNLpuB8fQNVMKTW</latexit>
<latexit
<latexit
k(t
t3
)
<latexit
sha1_base64="O20ag7NbASdBXZGg5NnT6wYg5mk=">AAACKnicbVBNS8NAEN34bfyqevSyWAr2YElUUG+iF48K9gOaEjabqS7dbOLuRCih/8eLf8WDHlS8+kPc1h5s9cHCm/dmmJ0XZVIY9LwPZ2Z2bn5hcWnZXVldW98obW41TJprDnWeylS3ImZACgV1FCihlWlgSSShGfUuhn7zAbQRqbrBfgadhN0q0RWcoZXC0nmlERZBwvBOJ0VTqHgwcCu9PazSQME95Qijcj+IQSKjGPpVd6I+rIalslfzRqB/iT8mZTLGVVh6CeKU5wko5JIZ0/a9DDsF0yi4hIEb5AYyxnvsFtqWKpaA6RSjWwe0YpWYdlNtn0I6Un9PFCwxpp9EtnN4lZn2huJ/XjvH7kmnECrLERT/WdTNJcWUDoOjsdDAUfYtYVwL+1fK75hmNiJtXBuCP33yX1I/qJ3WvOuj8tn5OI0lskN2yR7xyTE5I5fkitQJJ4/kmbyRd+fJeXU+nM+f1hlnPLNNJuB8fQNWtKTX</latexit>
<latexit
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k(t
t4)
<latexit
sha1_base64="ffU4kv6KYC13I41Lu8aus6YL7AY=">AAACKnicbVBNS8NAEN34bfyqevSyWArtwZJIQb2JXjwq2FZoSthsprp0s4m7E6GE/h8v/hUPelDx6g9xW3uw1QcLb96bYXZelElh0PM+nLn5hcWl5ZVVd219Y3OrtL3TMmmuOTR5KlN9EzEDUihookAJN5kGlkQS2lH/fOS3H0AbkaprHGTQTditEj3BGVopLJ1VWmERJAzvdFK0hYqHQ7fSr2KNBgruKUcYlwdBDBIZxdCvuVN1oxaWyl7dG4P+Jf6ElMkEl2HpJYhTniegkEtmTMf3MuwWTKPgEoZukBvIGO+zW+hYqlgCpluMbx3SilVi2ku1fQrpWP09UbDEmEES2c7RVWbWG4n/eZ0ce8fdQqgsR1D8Z1EvlxRTOgqOxkIDRzmwhHEt7F8pv2Oa2Yi0cW0I/uzJf0nzsH5S964a5dOzSRorZI/skyrxyRE5JRfkkjQJJ4/kmbyRd+fJeXU+nM+f1jlnMrNLpuB8fQNYOKTY</latexit>
<latexit
<latexit

Jan,01
2000
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2001
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2005
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2008
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2009
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2013
Jan,01
2016
Dec,31
2017
0
500
1000
1500
2000
)-1
sr-1
s-2
m-1
J(GeV
EPHIN/SOHO PAMELA
T = 8.1 monthsD
0ºTD
A<0 A>0[ 1-1.5 GeV ]
fit region prediction
ü Proton flux data reveal a 8.1 month time lag
forecast
ü Real-time solar data à ability to forecast 8 months in advance
ü Predictions on antiparticle/particle ratios (test for AMS)
NT, Orcinha, F. Barao, B. Bertucci ApJ 849, L32 (2017)

Jan,01
2000
Dec,31
2001
Jan,01
2004
Dec,31
2005
Jan,01
2008
Dec,31
2009
Jan,01
2012
Dec,31
2013
Jan,01
2016
Dec,31
2017
0
500
1000
1500
2000
)-1
sr-1
s-2
m-1
J(GeV
EPHIN/SOHO PAMELA
T = 8.1 monthsD
0ºTD
A<0 A>0[ 1-1.5 GeV ]
NT, Orcinha, F. Barao, B. Bertucci ApJ 849, L32 (2017)

-
m-1
J(R)[GV
0
200
400
600
Jan,01
2012
Dec,31
2012
Dec,31
2013
Dec,31
2014
Jan,01
2016
Dec,31
2016
p/Heratio
7
7.2
7.4
7.6
7.8
8
RbµModel K AMS-02
RµModel K
(c)
K(R) = (v/3)λ(R) parallel diffusion coefficient
λ(R) = universal “composition-blind” mean free path
K(R,t) = β x k0(t) x R
Insights from the p/He ratio: diffusion
NT+ (2018)
The p/He long-term behavior is a signature of universality of the CR mean free path λ(R)

ü The p/He time-dependence is predicted from a proton-driven model
ü The p/He structure is expected to disappear at relativistic rigidities
Jan,01
2012
Dec,31
2012
Dec,31
2013
Dec,31
2014
Jan,01
2016
Dec,31
2016
p/Heratio
5
5.5
6
6.5
7
7.5
8
8.5 AMS-02 Calculations (a)
rigidity [GV]
1 10
p/HeG
0.9
0.95
1
1.05
AMS-02
Calculations
(b)
1
[p/He]
2
[p/He]
=p/HeG
Insights from the p/He ratio: diffusion
NT+ (2018)
The p/He long-term behavior is a signature of universality of the CR mean free path λ(R)

Dynamics of the Heliospheric current sheet...
...Ballerina’s skirt shape
Insights from antimatter/matter ratios: drift

Small tilt
Flat current sheet
Large tilt
Wavy current sheet
?
GCR

e+ e-
A<0
A<0
A>0
e+/e- Cycle 24
e+
e-

A<0
A>0
e+/e-
A>0
A>0 e+ A>0 e-
Cycle 24
e+
e-

àCR proton-driven retuning using new AMS/PAMELA data
àSmooth transitrion across reversal.
àLIS, diffusion and drift parameters for GCR leptons.

va
-
/e+e 0.5
1
A<0 A>0[ 1-2.5 GeV ]
Jan,01
2000
Dec,31
2001
Jan,01
2004
Dec,31
2005
Jan,01
2008
Dec,31
2009
Jan,01
2012
Dec,31
2013
Jan,01
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Dec,31
2017
/pvariationp
0.5
1
1.5
2 BESS-TeV PAMELA
A<0 A>0[ 1-2.5 GeV ]

Golden age for cosmic ray measurements
• News from space: Voyager-1, SOHO, PAMELA, AMS
• Multi-channel data protons, He, Nuclei, antiparticles
New insights to CR physics
• Proton data -> evidence for a time-lag -> timescale of CR modulation
• P/He data -> test for low-energy diffusion of CRs in heliosphere
• Antimatter/matter -> test for charge-sign dependent effects
From multi-channel & long-term data to space physics
• Establishment of predictive model with forecast capabilities
• Improve risk assessment in manned exploration missions
Conclusions

Models of cosmic ray modulation
in light of new data from AMS-02
Nicola Tomassetti
with B. Bertucci, E. Fiadrini
Perugia University & INFN
Solar Energetic Particles, Solar Modulation and Space
Radiation: new opportunities in the AMS Era #3
23-26 April 2018 – Washington DC, USA

Models of cosmic ray modulations in light of new data from AMS-02

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