Caballero-Lopez, R A

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29th International Cosmic Ray Conference Pune (2005) 2, 8588The effect of cosmic ray energy changes in the heliosphere on K-capturesecondariesR.A. Caballero-Lopez  , H. Moraal , F.B. McDonaldand R.A. Mewaldt(a) Instituto de Geof·sica, UNAM, 04510, M·exico(b) School of Physics, North-West University, Potchefstroom 2520, South Africa(c) Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA(d) Space Radiation Laboratory, California Insitute of Technology, Pasadena, CA 91125, USAPresenter: R.A. Caballero-Lopez (rogelioc@geofisica.unam.mx), mex-caballero-lopez-RA-abs2-sh32-posterIn an accompanying paper we give a re-assessment of cosmic ray energy changes in the heliosphere to deter-mine the effects of acceleration at the solar wind termination shock and modulation in the heliosheath beyondthat. In this paper we show that these effects have important consequences for the interpretation of secondaryto primary ratios of cosmic rays at energies below 1 GeV, i.e. in the region where they are strongly modulated.1. IntroductionThe energy loss of cosmic rays in the radially expanding solar wind in the heliosphere is an integral part of thecosmic ray modulation, the other three processes being diffusion, convection and drift in the solar wind andthe heliospheric magnetic field (HMF). In an accompanying paper [1], henceforth called Paper 1, it is shownthat in a heliosphere surrounded by a solar wind termination shock and an extended heliosheath, the net energyloss is reduced, due to the fact that the shock accelerates particles, while in the heliosheath they are modulatedwithout energy loss.Spectral shapes determine cosmic ray properties, but at energies  1 GeV these spectra are modified dueto modulation. Energy losses play an important part in this modification. A good example is the ratio ofsecondary to primary cosmic rays which reflects the propagation, nuclear fragmentation and escape from thegalaxy. The effects of these processes on the spectra must be unfolded to determine the shape of the cosmicray spectra at the source. Such processes are best studied at low energies where the counting rates are high andgood statistical accuracy can be achieved. To exploit this low energy region, one must know how to accuratelydemodulate the spectra observed in the vicinity of Earth.A specific case is that of K-capture cosmic ray secondaries, as recently described by [2] and [3], using thehigh precision ACE observations. Cosmic ray nuclei attach electrons as they move through the galaxy. Typicalattachment times are 10y for 10 MeV and 10y for 10 GeV particles. For a radioactive isotope such as	Cr that decays by electron capture, this time is comparable with typical nuclear decay and escape lifetimes at 100 MeV, and therefore it has a reasonable chance to occur. At high energies, however, most of the	Crfragments or escapes before this can happen. After this attachment, the nucleus decays into	V with a mean-life of 27 days, and consequently the	V/	Cr ratio in interstellar space should be strongly energy dependent,being much higher at low energies. [2] and [3] have studied the energy dependence of this process as modifiedby cosmic ray modulation. They observed that the	V/	Cr ratio is less energy dependent at solar maximumconditions than at solar minimum. The authors interpret this as a signature of higher energy loss suffered bythese  = 2 particles at solar maximum conditions (  MeV/n), than at solar minimum (  200 MeV/n).They used the solution of the one-dimensional transport equation for their calculations. However, in Paper 1 itis shown that more complete solutions produce different amounts of energy loss, and here we explore how thismay affect the secondary to primary ratio.86 R.A. Caballero-Lopez et al.10-1100101102103100 101 102 103 104Ratio: 51 V / 51CrKinetic Energy (MeV/n)LISShock SolutionsNo-Shock SolutionsMin.-Max.-Min.+Max.+Min. -Min. +Max. +Max. -Force-Field SolutionsMin.   Max.Min. 1DMax. 1DMin.Max.0.00.10.20.30.40.50.60.7100 200 300 400 500Ratio: 51 V / 51CrKinetic Energy (MeV/n)LISMin.Max.Force-Field SolutionOne-Dimensional SolutionMin.Max.Figure 1. The  V/  Cr ratio. The thick line is the interstellar ratio, and the data points the observations at 1 AU from[2]. Calculated ratios at Earth are for the Force-Field approximation, and for no-shock and shock-heliosheath models of theheliosphere, for both drift states. Typical solar minimum and solar maximum values are shown. The right panel is a zoomedversion to show the observations better, together with the Force-Field, and a repeat of the one-dimensional calculations of[2] and [3].2. CalculationsWe calculate	V/	Cr ratios in a variety of models for cosmic ray modulation, ranging from a simple Force-Field solution of the transport equation to one that contains drift effects in a heliosphere with a wavy neutralsheet, a termination shock where acceleration occurs, and a heliosheath that provides additional modulation.We demonstrate the calculations with an LIS for	Cr of the form ﬁﬀﬃﬂ "!# %$'&)(+*, -/.0!1324# 54!6(	, 718# 5(+*,9:within GeV/n. (This spectrum was derived by [4] for He; the precise form is not important forour demonstration calculations.) According to [2], however, the secondary	Vr LIS is much steeper, and wefit the shape of that spectrum by multiplying the	Cr spectrum with 0.22+0.061/+0.007 ;*to represent theinterstellar	V/	Cr ratio given in their Figure 3. The results are shown in the left panel of Figure 1. Thesteep solid line is the fit to the Niebur et al. value of the	V/	Cr ratio in the LIS. The two solutions markedFF near the bottom are the modulated ratios for a Force-Field solution with Force-Field potentials of 400 and800 MV, to represent solar minimum and solar maximum conditions. The calculation is repeated for the one-K-capture isotopes ... 8710-310-210-1100101102100 101 102 103 104Intensity Part./(m2 .s.sr.MeV/nuc)Kinetic Energy (MeV/nuc)51Cr1 AULIS90 AUIntensity Part./(m2 .s.sr.MeV/nuc)Intensity Part./(m2 .s.sr.MeV/nuc)101 102 103 10410-310-210-1100101102  51V1 AULIS 90 AU  Figure 2. Spectra of  Cr and  V at 150 AU (input), at 90 AU (the termination shock) and at 1 AU (Earth), to demonstratethe very different acceleration and modulation effects on LIS inputs of different form.dimensional steady-state solution of the transport equation with the same parameters. In this case there is lessenergy loss, leading to a stronger energy dependence of the ratio. These two calculations are also shown in theright panel, which is a zoomed version, in the same format as Figures 8 and 9 of Niebur et al. This shows thatthe solid-line one-dimensional solutions are the same as theirs.Next, the calculation is repeated for the solution of the two-dimensional steady-state transport equation inthe qA < 0 and qA  0 drift states, once again for solar minimum and solar maximum conditions. The twosolar minimum solutions are for the same parameters as the two drift solutions in Figure 2b of Paper 1 -the parameters are given there. We point out that this model does not have a termination shock and that thesupersonic solar wind extends up to the modulation boundary at 150 AU. These ratios are significantly higherthan those for the Force-Field and one-dimensional solutions, reflecting even smaller energy losses, as foundin Paper 1. This result implies that to fit the observations, the propagation parameters and/or the interstellarinput spectra must be revised.Finally, the two drift calculations are repeated with the time-dependent shock-heliosheath model, i.e. thesupersonic solar wind extends only to 90 AU where there is a strong shock, with a heliosheath beyond that upto the boundary at 150 AU. Once again, the two solar minimum solutions are the same as those in Figure 2cof Paper 1. The effect of this shock on the ratio is dramatic, and it actually increases above the LIS value for< 10 MeV. This is due to very strong acceleration of the secondary	V spectrum by the termination shock(compression ratio = = 4), whereas it only has a moderate acceleration effect on the primary	Cr spectrum.These different acceleration effects on the two spectra are demonstrated in Figure 2. The left panel showsspectra of	Cr. The dashed line is the assumed LIS (>ﬀﬃﬂ?@!A# B$'&)(+*, -/.C!D1E28# 58!)(	, 71E8# 5)(+*,9:, whilethe other two are the spectra at 90 AU (at the shock) and at 1 AU. The same spectra are shown for	V in theright panel. There is a very large excess of	Fon the shock spectrum because of the acceleration. Because ofthe multiplication factor of 0.22 +0.061/+0.007 G*with the	Cr spectrum, this spectrum has a low energyform  ﬀIH6(+*, *J. According to the standard theory of shock acceleration a strong shock will acceleratesuch a soft spectrum to the formK7L,NMPORQ*TSVUMP	(OS.6(	for = = 4;)(	,for = = 2.5 at non-relativistic energies).This acceleration cuts off at a maximum energy determined by the shock radius. In the present model thisis at  100 MeV. At this point there is an extremely steep fall-off to the original LIS. The acceleration on88 R.A. Caballero-Lopez et al.	Cr is much less because there the low-energy limit of the LIS is  ﬀWH)(+7, *TJ. Such a hard spectrum is notsignificantly accelerated. This LIS is typical for primary cosmic ray species, and this is one of the reasons why[5] concluded that shock/heliosheath effects on galactic cosmic ray modulation are only moderate. The currentexample shows, however, that this statement is subject to the form of the LIS inputs.The case shown here is extreme because it has the strongest possible shock ( = = 4), and should not be regardedas realistic. A value of = = 2.5 may be more realistic. It is used, however, to demonstrate the extreme rangeof sensitivity of this	V/	Cr ratio to modulation and acceleration conditions. Even if the shock does notaccelerate galactic cosmic rays, the no-shock solutions show that this ratio is a sensitive diagnostic tool of themodulation/acceleration process.3. ConclusionsThe energy dependent	V/	Cr ratio turns out to be sensitive to modulation and acceleration conditions in theouter heliosphere. In particular, the amount of acceleration at the solar wind termination shock has an extremeinfluence on this ratio.In [5] we concluded the opposite, namely that observations at Earth are generally not sensitive to modulationand acceleration conditions in the distant heliosphere. It was found there that the modulation integral XYZ.F6[\']:, or equivalently the Force-Field potential ^ , which is related to X , is the most important parameterthat determines the amount of modulation and spectral shapes deep inside the heliosphere. This meant that thedistribution of the modulation/acceleration processes throughout the heliosphere was found not to be important,and that only the integral value matters. The current conclusion is different because of the difference in spectralshape of the secondary and primary species involved. This difference causes large differences in the amount ofacceleration and modulation of these species.The net result is that two-dimensional drift models, especially shock models, produce too little energy loss fora given amount of modulation to explain the K-capture ratios. This implies that more modulation may takeplace beyond the termination shock, and that interstellar spectra may be flatter below a few hundred MeV/nthan currently thought. We therefore conclude that K-capture secondary cosmic rays observed at 1 AU providean important diagnostic tool for modulation and acceleration studies of cosmic rays in the distant heliosphere,which needs to be investigated in greater detail.Acknowledgements. This work was supported by NSF Grant ATM 0107181 and the South African NationalResearch Foundation. RCL was supported by UNAM-DGAPA grant IN106105.References[1] R.A. Caballero-Lopez, H. Moraal and F.B. McDonald, 29th ICRC, Pune (2005), 1, 101.[2] S.M. Niebur et al., J. G. R., 108 (A10), 8033, doi:10.1029/2003JA009876, (2003).[3] R.A. Mewaldt et al., AIP Conf. Proc. 719, 127-132, (2004).[4] W.R. Webber and J.A. Lockwood, J. G. R., 106, 29323, (2001).[5] R.A. Caballero-Lopez et al., J.G.R., 109, A05105, doi:10.1029/2003JA010358, (2004).

The effect of cosmic ray energy changes in the heliosphere on K-capture secondaries

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