New Modeling of Galactic Proton Modulation During the Minimum of Solar Cycle 23/24

Abstract

During the recent prolonged solar minimum of cycle 23/24, the PAMELA detector measured 27-day averaged Galactic proton energy spectra over the energy range that is important for solar modulation. By comparing these spectra to computed spectra from a three-dimensional model that contains all of the important heliospheric modulation processes, the recent minimum can be studied in detail from a modulation perspective. This was done by setting up a realistic heliosphere in the model, and reproducing a representative selection of seven intermittent PAMELA spectra, separated by approximately six months, from 2006 July to 2009 December. Additionally, a new very local interstellar proton spectrum was constructed using measurements below 600 MeV from Voyager 1, taken beyond the heliopause, combined with PAMELA and AMS-02 measurements above 30 GeV at the Earth. As a result of the extreme minimum modulation conditions that governed the recent solar minimum, the highest ever Galactic cosmic ray spectrum at Earth was observed by PAMELA at the end of 2009. It was found that, apart from the self-consistent changes in the heliospheric current sheet and the heliospheric magnetic field over time, additional increases in the mean free paths during this period were required below~4 GV in order to reproduce the intensities observed by PAMELA.

Solar Modulation of the Local Interstellar Spectrum With Voyager 1, Ams-02, Pamela, and Bess

“…These results suggest that the solar modulation may affect GCRs below and above a few GVs in different ways; a similar conclusion is found also in (Vos & Potgieter 2015) by using a numerical model applied to the PAMELA monthly proton fluxes and in (Gieseler et al 2015) by comparing data from NMs, PAMELA and the EPHIN instrument on board the SOHO spacecraft. To account for this effect, we modify the force-field approximation by considering a rigidity-dependent solar modulation parameter:…”

Power requirements for cosmic ray propagation models involving diffusive reacceleration; estimates and implications for the damping of interstellar turbulence

“…However the situation has dramatically changed with the recent passage of the Voyager spacecraft into the local interstellar medium which allows us for the first time to have access to in situ measurements of the low-energy cosmic ray flux just outside the heliosphere (Potgieter 2014). A useful analytic fit to the local interstellar flux of protons, J LIS , has been given by Vos & Potgieter (2015) in the form j LIS = 2700.0 T 1.12 β 2 T + 0.67 1.67…”

“…3. The integral of (p/mc) 1−δ weighted by the local interstellar proton number spectrum from Vos & Potgieter (2015) as a function of δ -note that the dimensions are m −3 . The value for δ = 1 is just the cosmic ray number density.…”

Heliospheric modulation of cosmic rays during the neutron monitor era: Calibration using PAMELA data for 2006–2010

“…Here we revisit the reconstruction of the modulation potential along three main directions as follows: The earlier models were based upon previous generations of the NM yield functions [ Debrunner et al , ; Clem and Dorman , ; Matthiä et al , ] that were unable to reproduce the exact count rate of individual NMs and the shape of the latitudinal survey [ Caballero‐Lopez and Moraal , ]. By contrast, here we use the new‐generation NM yield function ( Mishev et al , ; see also erratum therein), which agrees, for the first time, with the actual measurements of the NM count rates and observational surveys [ Gil et al , ]. While the earlier models were based upon an estimate of the local interstellar spectrum (LIS) by Burger et al [] for earlier models such as [ Garcia‐Munoz et al , ], here we use a recent estimate of the LIS by Vos and Potgieter [] who revised the LIS by using precise measurements from AMS‐02 and PAMELA spaceborne detectors and considering also Voyager data beyond the heliospheric termination shock, not available until recently. Earlier models were based upon a calibration method using only two directly measured GCR spectra: MASS89 and AMS‐01. Here we use a newly available GCR spectra precisely measured by the PAMELA instrument [ Adriani et al , ] during 47 time intervals during 2006–2010. …”