Current Sheet Tilt Research Articles

Relationship between Cosmic rays’ Modulation and Solar Wind Parameters in Solar Cycle 24 and Ascending Phase of Cycle 25

The solar cycle 24 behaviour of several heliospheric parameters and activity indices is contrasted with the persistent changes in cosmic rays throughout time. Previous to this, a series of was used for the geomagnetic indices Ap, Kp, and aa, solar flare group counts, cosmic ray strengths during solar cycles 22, 23, and 24, and sunspot counts. We found the interrelationships between solarheliospheric factors such the interplanetary magnetic field, cosmic-ray modulation, the present solar cycle, which is marked by several rare and powerful solar occurrences, and the heliospheric current sheet tilt, using this model. We show that these parameters may be used together to replicate most of the modulation potential fluctuations that occur throughout this cycle. Observed variations in cosmic ray fluxes every eleven years are mostly due to variations in solar activity, which also occur every eleven years. In addition to this, every about eleven years, the heliosphere and solar polar regions experience a reversal of the orientations of their magnetic fields. Also, this adds features to the acknowledged ~11-cycle and causes an extra 22-year solar magnetic cycle to exist. Looking at the correlations, time delays, and temporal patterns of cosmic-ray intensity versus various parameters from 1996 to 2022, the cycle's distinctive traits are discovered to be strange. Intervals for correlational analysis and obtained hysteresis curves from cycle pro are also included.

Measurements of anomalous cosmic rays from the WIND spacecraft over 1994–2021

ABSTRACT Observations provide direct evidence for a sustained decline in solar activity since the 1980s, with the minimum between solar cycles 24 and 25 (P24/25) reaching its deepest trough in the past hundred years. In response to the reduced solar modulation, low-energy (<GeV) galactic cosmic rays (GCRs) at 1 au attain historical new highs in P24/25, while anomalous cosmic rays (ACRs) show very inconsistent variations with GCRs. To better understand the long-term ACR variations, we revisit the 6.0–13.4 MeV nuc−1 oxygen measurements from the WIND/LEMT instrument over 1994–2021, with particular interests to the recent three solar minima: P22/23 (solar magnetic polarity A > 0), P23/24 (A < 0), and P24/25 (A > 0). We find that the peak ACR intensities in P24/25 are ∼20 per cent lower than those in P22/23 but ∼48 per cent above those in P23/24. Additionally, for a specified heliospheric current sheet (HCS) tilt angle, the GCR intensities in P24/25 are inferred to be significantly higher than those in P22/23 (both are in A > 0 cycles), whereas the ACR intensities in P24/25 are close to those in P22/23. These results indicate that large variability in ACRs exists not only between opposite-polarity cycles, but also between different cycles of the same polarity, and ACRs may be more sensitive to varying HCS compared to GCRs. We speculate that variations in the ACR source intensity may be a key to understanding the ACR–GCR discrepancies. This is the first time for such a long-term study being possible with the same instrument.

Constraining the charge-, time-, and rigidity-dependence of cosmic-ray solar modulation with AMS-02 observations during Solar Cycle 24

Our basic theoretical understanding of the sources of cosmic rays and their propagation through the interstellar medium is hindered by the Sun, that through the solar wind affects the observed cosmic-ray spectra. This effect is known as solar modulation. Recently released cosmic-ray observations from the Alpha Magnetic Spectrometer (AMS-02) and publicly available measurements of the solar wind properties from the Advanced Composition Explorer and the Wilcox observatory allow us to test the analytical modeling of the time-, charge- and rigidity-dependence of solar modulation. We rely on associating measurements on the local heliospheric magnetic field and the heliospheric current sheet's tilt angle, to model the time-dependence and amplitude of cosmic-ray solar modulation. We find evidence for the solar modulation's charge- and rigidity-dependence during the era of solar cycle 24. Our analytic prescription to model solar modulation can explain well the large-scale time-evolution of positively charged cosmic-ray fluxes in the range of rigidities from 1 to 10 GV. We also find that cosmic-ray electron fluxes measured during the first years of cycle 24 are less trivial to explain, due to the complex and rapidly evolving structure of the Heliosphere's magnetic field that they experienced as they propagated inwards.

Solar Modulation of Galactic Cosmic-Ray Protons Based on a Modified Force-field Approach

Abstract In this work, a modified force-field approach is established to investigate the long-term solar modulation of galactic cosmic-ray (GCR) protons. In this approach, the solar modulation potential ϕ is assumed to be energy dependent. As ϕ also depends on the local interstellar spectrum (LIS), a new proton LIS model is first presented based on data from Voyager 1 and 2, PAMELA, and AMS-02. Then, a double power-law expression is proposed to model ϕ as a function of proton energy. By fitting to the selected GCR measurements, the solar cycle variation characteristics of parameters in the expression of ϕ are obtained, and these parameters are reconstructed using the sunspot number, the heliospheric current sheet tilt angle, and the polarity of heliospheric magnetic field. Finally, a new analytical predictive model for GCR protons is established. It is shown that the 11 and 22 yr cyclic variations of GCRs are reproduced, and the computed proton intensities are in good agreement with GCR measurements at various energies since 1954.

The Effects of Solar Wind Structure on Nanodust Dynamics in the Inner Heliosphere

AbstractSeveral interplanetary spacecraft have inferred the presence of nanometer‐sized dust grains in the inner heliosphere accelerated to near‐solar wind velocities based on observations by radio wave antennas. These “nanodust” grains exhibit unique behavior in interplanetary space as they are strongly affected by both the solar gravitational force and the electromagnetic Lorentz force from the convecting interplanetary magnetic field. Here, we study the dynamics of nanodust grains in the inner heliosphere via a combination of background electromagnetic fields from the coupled Wang‐Sheeley‐Arge/Enlil heliospheric model and a nanodust grain charging and dynamics model. The model results predict strong time variability in the nanodust velocity and flux distributions at 1 au within a single Carrington rotation (CR) driven by a combination of nanodust grain size, heliospheric current sheet tilt, and varying heliospheric plasma parameters. In contrast, the general character of nanodust dynamics does not drastically change from one CR to the next. Despite including observationally driven heliospheric plasma conditions, the modeled nanodust impact rates do not agree with in situ observations by the STEREO A and B WAVES instruments, especially with regard to CR‐to‐CR variability. We interpret this data‐model disagreement as evidence that additional time variability must be present in the production rate of nanodust grains in the inner heliosphere. We discuss possibilities for this time variability, including non‐steady‐state collisional cascades, variability in nanodust trapping regions, and the impulsive disruption of inner solar system comets and/or asteroids.

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

Abstract We develop a numerical model to study the time-dependent modulation of galactic cosmic rays in the inner heliosphere. In the model, a time-delayed modified Parker heliospheric magnetic field (HMF) and a new diffusion coefficient model, NLGCE-F, from Qin & Zhang, are adopted. In addition, the latitudinal dependence of magnetic turbulence magnitude is assumed to be from the observations of Ulysses, and the radial dependence is assumed to be , where we choose an expression of S as a function of the heliospheric current sheet tilt angle. We show that the analytical expression used to describe the spatial variation of HMF turbulence magnitude agrees well with the Ulysses, Voyager 1, and Voyager 2 observations. By numerically calculating the modulation code, we get the proton energy spectra as a function of time during the recent solar minimum, it is shown that the modulation results are consistent with the Payload for Antimatter-Matter Exploration and Light-nuclei Astrophysics measurements.

Coronal and heliospheric magnetic flux circulation and its relation to open solar flux evolution.

Solar cycle 24 is notable for three features that can be found in previous cycles but which have been unusually prominent: (1) sunspot activity was considerably greater in the northern/southern hemisphere during the rising/declining phase; (2) accumulation of open solar flux (OSF) during the rising phase was modest, but rapid in the early declining phase; (3) the heliospheric current sheet (HCS) tilt showed large fluctuations. We show that these features had a major influence on the progression of the cycle. All flux emergence causes a rise then a fall in OSF, but only OSF with foot points in opposing hemispheres progresses the solar cycle via the evolution of the polar fields. Emergence in one hemisphere, or symmetric emergence without some form of foot point exchange across the heliographic equator, causes poleward migrating fields of both polarities in one or both (respectively) hemispheres which temporarily enhance OSF but do not advance the polar field cycle. The heliospheric field observed near Mercury and Earth reflects the asymmetries in emergence. Using magnetograms, we find evidence that the poleward magnetic flux transport (of both polarities) is modulated by the HCS tilt, revealing an effect on OSF loss rate. The declining phase rise in OSF was caused by strong emergence in the southern hemisphere with an anomalously low HCS tilt. This implies the recent fall in the southern polar field will be sustained and that the peak OSF has limited implications for the polar field at the next sunspot minimum and hence for the amplitude of cycle 25.

LONG-TERM TRENDS IN THE SOLAR WIND PROTON MEASUREMENTS

ABSTRACT We examine the long-term time evolution (1965–2015) of the relationships between solar wind proton temperature (T p) and speed (V p) and between the proton density (n p) and speed using OMNI solar wind observations taken near Earth. We find a long-term decrease in the proton temperature–speed (T p–V p) slope that lasted from 1972 to 2010, but has been trending upward since 2010. Since the solar wind proton density–speed (n p–V p) relationship is not linear like the T p–V p relationship, we perform power-law fits for n p–V p. The exponent (steepness in the n p–V p relationship) is correlated with the solar cycle. This exponent has a stronger correlation with current sheet tilt angle than with sunspot number because the sunspot number maxima vary considerably from cycle to cycle and the tilt angle maxima do not. To understand this finding, we examined the average n p for different speed ranges, and found that for the slow wind n p is highly correlated with the sunspot number, with a lag of approximately four years. The fast wind n p variation was less, but in phase with the cycle. This phase difference may contribute to the n p–V p exponent correlation with the solar cycle. These long-term trends are important since empirical formulas based on fits to T p and V p data are commonly used to identify interplanetary coronal mass ejections, but these formulas do not include any time dependence. Changes in the solar wind density over a solar cycle will create corresponding changes in the near-Earth space environment and the overall extent of the heliosphere.

Study of Cosmic-Ray Modulation During the Recent Unusual Minimum and Mini-Maximum of Solar Cycle 24

After a prolonged and deep solar minimum at the end of Cycle 23, the current Solar Cycle 24 is one of the lowest cycles. These two periods of deep minimum and mini maximum are separated by a period of increasing solar activity. We study the cosmic-ray intensity variation in relation with the solar activity, heliospheric plasma and field parameters, including the heliospheric current sheet, during these three periods (phases) of different activity level and nature: (a) a deep minimum, (b) an increasing activity period and (c) a mini maximum. We use neutron monitor data from stations located around the globe to study the rigidity dependence on modulation during the two extremes, i.e., minimum and maximum. We also study the time lag between the cosmic-ray intensity and various solar and interplanetary parameters separately during the three activity phases. We also analyze the role of various parameters, including the current sheet tilt, in modulating the cosmic-ray intensity during the three different phases. Their relative importance and the implications of our results are also discussed.

The Solar Polar Field in the Cosmic-Ray Intensity Modulation

In this work the modulation of galactic cosmic-ray intensity based on solar and heliospheric indices for the solar cycle 23 (1996-2008), is studied. In previous works a number of different indices such as the sunspot number, the CME-index, the interplanetary magnetic field and the heliospheric current sheet tilt were selected to be the most appropriate ones in order to describe the cosmic ray intensity of 10 GV observed by the network of neutron monitors. The new approach is an extension of this study to the influence of the solar magnetic field parameters, such as the mean magnetic field and the polar magnetic field, on the cosmic ray (CR) modulations. Using the wavelet analysis method a major periodicity of about 20-21 years was confirmed in the solar magnetic field data, indicating the existence of the solar magnetic cycle in CR variations. The best empirical relation of the cosmic ray modulation taking into account the sunspot number, the CME-index, the mean solar magnetic field and the solar polar field was improved significantly: a relative root mean square deviation (RMSD) between the observed and the calculated cosmic ray intensity values is found to be 8.7% instead to the previous one of about 10%.

The heliospheric Hale cycle over the last 300 years and its implications for a “lost” late 18th century solar cycle

A Hale cycle, one complete magnetic cycle of the Sun, spans two complete Schwabe cycles (also referred to as sunspot and, more generally, solar cycles). The approximately 22-year Hale cycle is seen in magnetic polarities of both sunspots and polar fields, as well as in the intensity of galactic cosmic rays reaching Earth, with odd- and even-numbered solar cycles displaying qualitatively different waveforms. Correct numbering of solar cycles also underpins empirical cycle-to-cycle relations which are used as first-order tests of stellar dynamo models. There has been much debate about whether the unusually long solar cycle 4 (SC4), spanning 1784–1799, was actually two shorter solar cycles combined as a result of poor data coverage in the original Wolf sunspot number record. Indeed, the group sunspot number does show a small increase around 1794–1799 and there is evidence of an increase in the mean latitude of sunspots at this time, suggesting the existence of a cycle “4b”. In this study, we use cosmogenic radionuclide data and associated reconstructions of the heliospheric magnetic field (HMF) to show that the Hale cycle has persisted over the last 300 years and that data prior to 1800 are more consistent with cycle 4 being a single long cycle (the “no SC4b” scenario). We also investigate the effect of cycle 4b on the HMF using an open solar flux (OSF) continuity model, in which the OSF source term is related to sunspot number and the OSF loss term is determined by the heliospheric current sheet tilt, assumed to be a simple function of solar cycle phase. The results are surprising; Without SC4b, the HMF shows two distinct peaks in the 1784–1799 interval, while the addition of SC4b removes the secondary peak, as the OSF loss term acts in opposition to the later rise in sunspot number. The timing and magnitude of the main SC4 HMF peak is also significantly changed by the addition of SC4b. These results are compared with the cosmogenic isotope reconstructions of HMF and historical aurora records. These data marginally favour the existence of SC4b (the “SC4b” scenario), though the result is less certain than that based on the persistence of the Hale cycle. Thus while the current uncertainties in the observations preclude any definitive conclusions, the data favour the “no SC4b” scenario. Future improvements to cosmogenic isotope reconstructions of the HMF, through either improved modelling or additional ice cores from well-separated geographic locations, may enable questions of the existence of SC4b and the phase of Hale cycle prior to the Maunder minimum to be settled conclusively.

Galactic Cosmic Ray Modulation and the Last Solar Minimum

In this work the galactic cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the years 1996 – 2010 covering solar cycle 23 and the solar minimum between cycles 23 and 24 is studied. A new perspective of this contribution is that cosmic ray data with a rigidity of 10 GV at the top of the atmosphere obtained from many ground-based neutron monitors were used. The proposed empirical relation gave much better results than those in previous works concerning the hysteresis effect. The proposed models obtained from a combination of solar activity indices and heliospheric parameters give a standard deviation < 10 % for all the cases. The correlation coefficient between the cosmic ray variations of 10 GV and the sunspot number reached a value of r=−0.89 with a time lag of 13.6±0.4 months. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 7.15 % for all of solar cycle 23; it also works very well during the different phases of the cycle. Moreover, the use of the cosmic ray intensity of 10 GV during the long minimum period between cycles 23 and 24 is of special interest and is discussed in terms of cosmic ray intensity modulation.

The orientation and current density of the magnetotail current sheet: A statistical study of the effect of geomagnetic conditions

We examine the orientation and current density of the current sheet during current sheet crossings from Cluster's 2001–2007 tail seasons. The curlometer technique is used to estimate the current density and is combined with Minimum Variance Analysis (MVA) to calculate the direction of the current sheet normal. The SYM‐H and AE indices at the time of each crossing are employed to assess how the tilt angle (the angle the normal makes with the Z axis in the GSM YZ plane) and current density depend on geomagnetic conditions. Our results indicate a larger current sheet tilt in the YZ plane during intervals of stronger and/or more prolonged substorm activity, as indicated by the AE index. There is also evidence that when the ring current is enhanced during magnetic storms, the current sheet is less tilted even though the AE index is also disturbed. In addition larger current densities are seen during times of both magnetic storms and substorms, compared to crossings during only substorms and a quiet ring current. We conclude that increased substorm activity disrupts the current sheet structure resulting in greater motion of the current sheet (as found by Davey et al. (2012)) and a greater local tilt to the current sheet. We propose that the increased open flux in the tail during magnetic storms stabilizes the current sheet such that the tilt angle of the current sheet is reduced. The increased amount of open flux during magnetic storms also results in larger current densities within the current sheet.

Cyclic loss of open solar flux since 1868: The link to heliospheric current sheet tilt and implications for the Maunder Minimum

Open solar flux (OSF) variations can be described by the imbalance between source and loss terms. We use spacecraft and geomagnetic observations of OSF from 1868 to present and assume the OSF source, S, varies with the observed sunspot number, R. Computing the required fractional OSF loss, χ, reveals a clear solar cycle variation, in approximate phase with R. While peak R varies significantly from cycle to cycle, χ is surprisingly constant in both amplitude and waveform. Comparisons of χ with measures of heliospheric current sheet (HCS) orientation reveal a strong correlation. The cyclic nature of χ is exploited to reconstruct OSF back to the start of sunspot records in 1610. This agrees well with the available spacecraft, geomagnetic, and cosmogenic isotope observations. Assuming S is proportional to R yields near‐zero OSF throughout the Maunder Minimum. However, χ becomes negative during periods of low R, particularly the most recent solar minimum, meaning OSF production is underestimated. This is related to continued coronal mass ejection (CME) activity, and therefore OSF production, throughout solar minimum, despite R falling to zero. Correcting S for this produces a better match to the recent solar minimum OSF observations. It also results in a cycling, nonzero OSF during the Maunder Minimum, in agreement with cosmogenic isotope observations. These results suggest that during the Maunder Minimum, HCS tilt cycled as over recent solar cycles, and the CME rate was roughly constant at the levels measured during the most recent two solar minima.

Modelling heliospheric current sheet drift in stochastic cosmic ray transport models

Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of α=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.

Long-Term Cosmic Ray Variability and the CME-Index

The cosmic ray modulation in relation to solar activity indices and heliospheric parameters during the period January 1996–October 2011, covering the solar cycle 23 and the ascending phase of solar cycle 24, is studied. The new perspective of this contribution is that the CME-index, obtained from only the CMEs with angular width greater than 30 degrees, gives much better results than in previous works. The proposed model for the calculation of the modulated cosmic ray intensity obtained from the combination of solar indices and heliospheric parameters gives a very satisfactory value of the standard deviation. The best reproduction of the cosmic ray intensity is obtained by taking into account solar and interplanetary indices such as sunspot number, interplanetary magnetic field, CME-index, and heliospheric current sheet tilt. The standard deviation between the observed and calculated values is about 6.63% for the solar cycle 23 and 4.13% for the ascending part of solar cycle 24.

Anomalous and Galactic Cosmic Rays at 1 AU During the Cycle 23/24 Solar Minimum

Anomalous cosmic ray (ACR) intensities at 1 AU at solar minimum generally track galactic cosmic ray (GCR) intensities such as those measured by neutron monitors, albeit with differences between solar polarity cycles. The unusual cycle 23/24 solar minimum was long-lasting with very low sunspot numbers and significantly reduced interplanetary magnetic field strength and solar wind dynamic pressure and turbulence, but also featured a heliospheric current sheet tilt that remained high for an extended period. Peak ACR intensities did not recover to the maximum values reached during the last two A>0 solar minima and just barely reached the last A<0 levels. However, GCR intensities in 2009 (neutron monitor rates and also at ∼200 MeV/nucleon) were the highest recorded during the last 50 years, indicating their intensities were not as heavily modulated during their transport from the outer heliosphere. This unexpected difference in the behavior of ACRs and GCRs remains unexplained, but suggests that either the ACR source intensity may have weakened since the last A<0 epoch, or perhaps that ACR intensities at 1 AU in the ecliptic may be more sensitive than GCRs to the higher tilt angle. This seems plausible if the ACR source intensity is greater at low latitudes during A<0 cycles, while the GCR distribution at the heliospheric boundary is more uniform in latitude. Shortly after an abrupt increase in the current sheet tilt angle in late 2009, both ACR and GCR intensities showed dramatic decreases, marking the end of solar minimum modulation conditions for this cycle.

Time-dependent cosmic ray modulation

Time-dependent cosmic ray modulation is calculated over multiple solar cycles using our well established two-dimensional time-dependent modulation model. Results are compared to Voyager 1, Ulysses and IMP cosmic ray observations to establish compatibility. A time-dependence in the diffusion and drift coefficients, implicitly contained in recent expressions derived by Teufel and Schlickeiser (2002), Shalchi et al. (2004), Minnie et al. (2007), Engelbrecht (2008), is incorporated into the cosmic ray modulation model. This results in calculations which are compatible with spacecraft observations on a global scale over consecutive solar cycles. This approach compares well to the successful compound approach of Ferreira and Potgieter (2004). For both these approaches the magnetic field magnitude, variance of the field and current sheet tilt angle values observed at Earth are transported time-dependently into the outer heliosphere. However, when results are compared to observations for extreme solar maximum, the computed step-like modulation is not as pronounced as observed. This indicates that some additional merging of these structures into more pronounced modulation barriers along the way is needed.

About the role of the Sun magnetic field characteristics in the long-term galactic cosmic rays modulation

The solar magnetic field characteristics, along with the current sheet tilt and the index taking into account X-ray flare properties, have been considered as modulating parameters in the model description of long-period cosmic rays (CR) variations in the 21st-23rd solar activity (SA) cycles. The features of behavior of the proposed indices in SA cycles are analyzed. The role of each index (and their combinations) in the CR modulation is revealed and the contribution to CR modulation at their cyclic changes is determined. The features of SA change and CR modulation during the 23rd cycle up to the end 2007 are discussed.

Heliospheric current sheet and GCR modulation in 1976–2007

The correlation between the GCR intensity and the tilt of the heliospheric current sheet (HCS) during three solar cycles is considered. The correlation coefficients for the periods of decreasing and increasing intensity have been calculated, and the time lag of the GCR variations delay relative to changes in the HCS tilt has been determined. It has been shown that the correlation coefficients are independent of the heliospheric magnetic field (HMF) direction. The possible diffusive mechanism, by which the current sheet tilt is related to the GCR intensity, is briefly discussed.